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The Influence of Main Design Parameters on the Overall Cost of a Gearbox

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Title: The Influence of Main Design Parameters on the Overall Cost of a Gearbox
Authors: Ngoc-Pi Vu, Dinh-Ngoc Nguyen, Anh-Tung Luu, Ngoc-Giang Tran, Thi-Hong Tran, Van-Cuong Nguyen, Thanh-Danh Bui, Hong-Linh Nguyen
Source: Applied Sciences, Vol 10, Iss 7, p 2365 (2020)
Publisher Information: MDPI AG, 2020.
Publication Year: 2020
Collection: LCC:Technology
LCC:Engineering (General). Civil engineering (General)
LCC:Biology (General)
LCC:Physics
LCC:Chemistry
Subject Terms: gearbox, gear ratio, optimum gearbox design, three-stage helical gearbox, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999
More Details: This study is aimed at determining optimum partial gear ratios to minimize the cost of a three-stage helical gearbox. In this work, eleven input parameters were investigated to find their influence on the optimum gear ratios of the second and the third stages ( u 2 and u 3 ). To reach the goal, a simulation experiment was designed and implemented by a cost optimization program. The results revealed that in addition to the input parameters, their interactions also have important effects in which the total ratio gearbox ratio ( u t ) and the cost of shaft ( C s ) have the most impact on u 2 and u 3 responses, respectively. Moreover, the proposed models of the two responses are highly consistent to the experimental results. The proposed regression equations can be applied to solve optimization cost problems.
Document Type: article
File Description: electronic resource
Language: English
ISSN: 10072365
2076-3417
Relation: https://www.mdpi.com/2076-3417/10/7/2365; https://doaj.org/toc/2076-3417
DOI: 10.3390/app10072365
Access URL: https://doaj.org/article/1840f0484a244d72b21a540d952c0651
Accession Number: edsdoj.1840f0484a244d72b21a540d952c0651
Database: Directory of Open Access Journals
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  Value: <anid>AN0142923975;[fdtu]01apr.20;2020Apr29.01:42;v2.2.500</anid> <title id="AN0142923975-1">The Influence of Main Design Parameters on the Overall Cost of a Gearbox </title> <p>This study is aimed at determining optimum partial gear ratios to minimize the cost of a three-stage helical gearbox. In this work, eleven input parameters were investigated to find their influence on the optimum gear ratios of the second and the third stages ( u 2 and u 3 ). To reach the goal, a simulation experiment was designed and implemented by a cost optimization program. The results revealed that in addition to the input parameters, their interactions also have important effects in which the total ratio gearbox ratio ( u t ) and the cost of shaft ( C s ) have the most impact on u 2 and u 3 responses, respectively. Moreover, the proposed models of the two responses are highly consistent to the experimental results. The proposed regression equations can be applied to solve optimization cost problems.</p> <p>Keywords: gearbox; gear ratio; optimum gearbox design; three-stage helical gearbox</p> <hd id="AN0142923975-2">1. Introduction</hd> <p>In gearbox optimization design, determining optimum gear ratios has been a greatly important task. It can be explained by the fact that the size, the mass, and therefore, the cost of a gearbox is significantly affected by the gear ratios. To illustrate, Figure 1 shows the relation between the gear mass and the gear ratio of the second stage <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> [[<reflink idref="bib1" id="ref1">1</reflink>]]. It can be seen from the figure that with the optimum value of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn></mrow></semantics></math> </ephtml> ), the mass of gears is merely about 178 (kg) whereas it reaches about 275 (kg) when <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub><mo>=</mo><mn>6</mn></mrow></semantics></math> </ephtml> . Therefore, there has been various research work dealing with optimizing gear ratios so far [[<reflink idref="bib1" id="ref2">1</reflink>]]. The methodology of gear ratio optimization can basically be divided into three groups, e.g., graph method, practical method, and model method. The oldest method is the graph method [[<reflink idref="bib2" id="ref3">2</reflink>], [<reflink idref="bib12" id="ref4">12</reflink>]], whereby the gear ratios are found based on the graph of the relationship between the component ratios and the total gearbox ratio. Figure 2 is an example of this method in which the gear ratios of the first and the second stages <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> of a three-stage helical gearbox are determined graphically. The practical method is introduced in [[<reflink idref="bib13" id="ref5">13</reflink>]], in which the optimum gears are determined based on the actual data from gearbox companies. For example, the mass of a two-stage helical gearbox is minimum when the ratio of the center distances of the second to the first stage is 1.4–1.6 [[<reflink idref="bib13" id="ref6">13</reflink>]]. From that comment, the optimum gear ratios are given. The most common method is the model method [[<reflink idref="bib3" id="ref7">3</reflink>], [<reflink idref="bib14" id="ref8">14</reflink>]]. In this method, models for calculating optimum gear ratios are determined by solving optimum problems with different target functions such as minimal gearbox length [[<reflink idref="bib3" id="ref9">3</reflink>], [<reflink idref="bib15" id="ref10">15</reflink>]], minimal mass of gears [[<reflink idref="bib4" id="ref11">4</reflink>]] or minimal gearbox cross section [[<reflink idref="bib4" id="ref12">4</reflink>], [<reflink idref="bib14" id="ref13">14</reflink>], [<reflink idref="bib16" id="ref14">16</reflink>]].</p> <p>In literature these studies have investigated various levels of gear stages such as two-stage gearboxes [[<reflink idref="bib17" id="ref15">17</reflink>]], three-stage gearbox [[<reflink idref="bib4" id="ref16">4</reflink>], [<reflink idref="bib14" id="ref17">14</reflink>]], and four-stage gearboxes [[<reflink idref="bib19" id="ref18">19</reflink>]]. Also, the determination of optimum gear ratios of bevel gearbox was carried in [[<reflink idref="bib20" id="ref19">20</reflink>]]. Recently, the optimum partial gear ratios have been found for mechanical driven systems using a gearbox and a chain drive [[<reflink idref="bib5" id="ref20">5</reflink>], [<reflink idref="bib9" id="ref21">9</reflink>], [<reflink idref="bib23" id="ref22">23</reflink>]] or a V-belt drive [[<reflink idref="bib22" id="ref23">22</reflink>], [<reflink idref="bib24" id="ref24">24</reflink>]].</p> <p>As previously mentioned, the optimal gear ratios directly impact the cost of the gearbox. However, up to now, there has been no research on calculating the optimal gear ratios with cost objective function. For this reason, this article presents a study on cost optimization in terms of finding the optimum gear ratio of three-stage Helical Gearboxes. The objective functions selected were the optimum gear ratios for second and third stage gears. Eleven input parameters were taken to investigate each parameter's influence and their interaction on the objective functions. A simulation experiment was planned using computer program to carry out the above issue.</p> <hd id="AN0142923975-3">2. Optimization Problem</hd> <p></p> <hd id="AN0142923975-4">2.1. Cost Analysis of Three-Stage Helical Gearbox</hd> <p>In practice, the cost of a gearbox depends on many cost elements, including the cost of the casing, shafts and gears, and bearings. However, due to the complicated cost calculation, the cost of bearings has not been considered in this study. As a result, the cost of a three-stage helical gearbox, namely <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>b</mi></mrow></msub></mrow></semantics></math> </ephtml> , can be calculated as the Equation (<reflink idref="bib1" id="ref25">1</reflink>):</p> <p>(<reflink idref="bib1" id="ref26">1</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>b</mi></mrow></msub><mo>=</mo><msub><mi>C</mi><mi>g</mi></msub><mo>+</mo><msub><mi>C</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>+</mo><msub><mi>C</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> indicate the cost of gears, the cost of gearbox housing and the cost of shafts respectively.</p> <p>Theoretically, the cost of a gear (the price of a gear) includes material costs, machining costs, heat treatment costs, labor costs including management and overhead costs, etc. The gear cost also depends on the gear shape and the gear size. The above component costs help to calculate the cost of a gear. In addition, in practice, the gear cost is usually calculated by unit price per kilogram and it varies by company policy and periodically. Therefore, in this study, the gear cost is investigated as a variable and calculated by the Equation (<reflink idref="bib2" id="ref27">2</reflink>):</p> <p>(<reflink idref="bib2" id="ref28">2</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>g</mi></msub><mo>=</mo><msub><mi>c</mi><mrow><mi>g</mi><mo>.</mo><mi>m</mi></mrow></msub><mo>·</mo><msub><mi>m</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml></p> <p>in which, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mrow><mi>g</mi><mo>.</mo><mi>m</mi></mrow></msub></mrow></semantics></math> </ephtml> is the cost per a kilogram of gears (USD/kg), and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml> is representative for the mass of all gears in the gearbox (kg).</p> <p>The cost of gearbox housing can be determined by Equation (<reflink idref="bib3" id="ref29">3</reflink>):</p> <p>(<reflink idref="bib3" id="ref30">3</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>=</mo><msub><mi>c</mi><mrow><mi>g</mi><mi>h</mi><mo>.</mo><mi>m</mi></mrow></msub><mo>·</mo><msub><mi>m</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml></p> <p>in this situation, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mrow><mi>g</mi><mi>h</mi><mo>.</mo><mi>m</mi></mrow></msub></mrow></semantics></math> </ephtml> is the cost per a kilogram of gearbox housing (USD/kg), and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> is the mass of the gearbox housing (kg).</p> <p>Finally, the cost of shafts is determined by Equation (<reflink idref="bib4" id="ref31">4</reflink>):</p> <p>(<reflink idref="bib4" id="ref32">4</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub><mo>=</mo><msub><mi>c</mi><mrow><mi>s</mi><mo>.</mo><mi>m</mi></mrow></msub><mo>·</mo><msub><mi>m</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mrow><mi>s</mi><mo>.</mo><mi>m</mi></mrow></msub></mrow></semantics></math> </ephtml> is the cost per a kilogram of shaft (USD/kg), and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> is the mass of all shafts in the gearbox (kg).</p> <p>Based on previously mentioned equations, it can be drawn that in order to get the cost of the gearbox ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>b</mi></mrow></msub></mrow></semantics></math> </ephtml> ) two factors should be identified. The first is the cost per a kilogram of gears, gearbox housing, and shafts which are varied according to the market. The second is the mass of gears, the gearbox housing, and shafts corresponding to <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> . However, it is noticed that the first factor is beyond the scope of this study, because it depends on the price of commercial markets. Then the later will be obtained by the detailed calculations in the next part of this study.</p> <hd id="AN0142923975-5">2.2. The Determination of Gearbox Housing Mass</hd> <p>The mass of gearbox housing ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> ) can be simply calculated by using Equation (<reflink idref="bib5" id="ref33">5</reflink>):</p> <p>(<reflink idref="bib5" id="ref34">5</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>·</mo><msub><mi>V</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml></p> <p>where, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ρ</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> is the weight density of gearbox housing materials referred in Table 1; <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub></mrow></semantics></math> </ephtml> is the volume of the gearbox housing (m<sups>3</sups>).</p> <p>Figure 3 presents the schematic relations of the gearbox housing dimensions. It is realized that the shape of gearbox housing is constructed by various component rectangulars. Hence, the volume of the gearbox housing can be determined by Equation (<reflink idref="bib6" id="ref35">6</reflink>).</p> <p>(<reflink idref="bib6" id="ref36">6</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>·</mo><msub><mi>V</mi><mi>b</mi></msub><mo>+</mo><mn>2</mn><mo>·</mo><msub><mi>V</mi><mrow><mi>A</mi><mn>1</mn></mrow></msub><mo>+</mo><mn>2</mn><mo>·</mo><msub><mi>V</mi><mrow><mi>A</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>b</mi></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>A</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>A</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> are the volumes of bottom housing, side A1, and side A2 (kg), respectively.</p> <p>(<reflink idref="bib7" id="ref37">7</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>b</mi></msub><mo>=</mo><mi>L</mi><mo>·</mo><msub><mi>B</mi><mn>1</mn></msub><mo>·</mo><mn>1.5</mn><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib8" id="ref38">8</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>A</mi><mn>1</mn></mrow></msub><mo>=</mo><mi>L</mi><mo>·</mo><mi>H</mi><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib9" id="ref39">9</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>b</mi></msub><mo>=</mo><msub><mi>B</mi><mn>2</mn></msub><mo>·</mo><mi>H</mi><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub><mo>=</mo><mrow><mo>(</mo><mrow><msub><mi>B</mi><mn>1</mn></msub><mo>−</mo><mn>2</mn><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow><mo>)</mo></mrow><mo>·</mo><mi>H</mi><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>Substituting (<reflink idref="bib7" id="ref40">7</reflink>), (<reflink idref="bib8" id="ref41">8</reflink>), and (<reflink idref="bib9" id="ref42">9</reflink>) into (<reflink idref="bib6" id="ref43">6</reflink>) gets:</p> <p>(<reflink idref="bib10" id="ref44">10</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><mo>=</mo><mn>3</mn><mo>·</mo><mi>L</mi><mo>·</mo><msub><mi>B</mi><mn>1</mn></msub><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub><mo>+</mo><mn>2</mn><mo>·</mo><mi>L</mi><mo>·</mo><mi>H</mi><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub><mo>+</mo><mn>2</mn><mo>·</mo><mrow><mo>(</mo><mrow><msub><mi>B</mi><mn>1</mn></msub><mo>−</mo><mn>2</mn><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow><mo>)</mo></mrow><mo>·</mo><mi>H</mi><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>In which, <emph>L</emph>, <emph>H</emph>, <emph>B</emph><subs>1</subs>, and <emph>S<subs>G</subs></emph> can be determined by [[<reflink idref="bib26" id="ref45">26</reflink>]]:</p> <p>(<reflink idref="bib11" id="ref46">11</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mo>=</mo><mo stretchy="false">(</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>11</mn></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>21</mn></mrow></msub><mo>/</mo><mn>2</mn><mo>+</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>12</mn></mrow></msub><mo>/</mo><mn>2</mn><mo>+</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>22</mn></mrow></msub><mo>/</mo><mn>2</mn><mo>+</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>13</mn></mrow></msub><mo>/</mo><mn>2</mn><mo>+</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>22</mn></mrow></msub><mo>/</mo><mn>2</mn><mo>+</mo><mn>22.5</mn><mo stretchy="false">)</mo><mo>/</mo><mn>0.975</mn></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib12" id="ref47">12</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi><mo>=</mo><msub><mi>d</mi><mrow><mi>w</mi><mn>23</mn></mrow></msub><mo>+</mo><mn>6.5</mn><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib13" id="ref48">13</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mn>1</mn></msub><mo>=</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub><mo>+</mo><mn>6</mn><mo>·</mo><msub><mi>S</mi><mi>G</mi></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib14" id="ref49">14</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>G</mi></msub><mo>=</mo><mn>0.005</mn><mo>·</mo><mi>L</mi><mo>+</mo><mn>4.5</mn></mrow></semantics></math> </ephtml></p> <hd id="AN0142923975-6">2.3. Gear Mass Calculations</hd> <p>The studied gearbox includes three stages, consequently the total mass of gears can be summed up as follow:</p> <p>(<reflink idref="bib15" id="ref50">15</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>g</mi></msub><mo>=</mo><msub><mi>m</mi><mrow><mi>g</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow><mi>g</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow><mi>g</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml></p> <p>where, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> represent the gear mass of the first, the second, and the third stages (kg) in which the first one can be determined by the following equations:</p> <p>(<reflink idref="bib16" id="ref51">16</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>g</mi></msub><mo>·</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>1</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>11</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>1</mn></mrow></msub></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>2</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>21</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>1</mn></mrow></msub></mrow><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ρ</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml> is the weight density of gear material (kg/m<sups>3</sups>), cf. Table 1; <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> are the volume coefficients of the drive gear and the driven gear of the first stage, respectively. In practice, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> can be orderly selected by the values of 1 and 0.6; <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> is the width of the gears calculated by: <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>1</mn></mrow></msub><mo>·</mo><msub><mi>a</mi><mrow><mi>w</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> (mm).</p> <p>Similarly, we have:</p> <p>(<reflink idref="bib17" id="ref52">17</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>g</mi></msub><mo>·</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>1</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>12</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>2</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>22</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub></mrow><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml></p> <p>and</p> <p>(<reflink idref="bib18" id="ref53">18</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>g</mi><mn>3</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>g</mi></msub><mo>·</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>1</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>13</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><mi>π</mi><mo>·</mo><msub><mi>e</mi><mrow><mn>2</mn></mrow></msub><mo>·</mo><msubsup><mi>d</mi><mrow><mi>w</mi><mn>23</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>b</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub></mrow><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> are the gear widths which can be determined in order by (mm); <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>2</mn></mrow></msub><mo>·</mo><msub><mi>a</mi><mrow><mi>w</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>b</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub><mo>=</mo><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>3</mn></mrow></msub><mo>·</mo><msub><mi>a</mi><mrow><mi>w</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> .</p> <hd id="AN0142923975-7">2.4. Shaft Mass Calculation</hd> <p>It is known that a three stage gearbox contains four shafts constructing three stages. For this reason, the mass of the gearbox shafts can be determined by:</p> <p>(<reflink idref="bib19" id="ref54">19</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>s</mi></msub><mo>=</mo><msub><mi>m</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub></mrow></semantics></math> </ephtml></p> <p>In which,</p> <p>(<reflink idref="bib20" id="ref55">20</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>s</mi></msub><mo>·</mo><mi>π</mi><mo>·</mo><msubsup><mi>d</mi><mrow><mi>s</mi><mn>1</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>l</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>/</mo><mn>4</mn></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib21" id="ref56">21</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>s</mi></msub><mo>·</mo><mi>π</mi><mo>·</mo><msubsup><mi>d</mi><mrow><mi>s</mi><mn>2</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>l</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>/</mo><mn>4</mn></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib22" id="ref57">22</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>s</mi></msub><mo>·</mo><mi>π</mi><mo>·</mo><msubsup><mi>d</mi><mrow><mi>s</mi><mn>3</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>l</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub><mo>/</mo><mn>4</mn></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib23" id="ref58">23</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mi>s</mi></msub><mo>·</mo><mi>π</mi><mo>·</mo><msubsup><mi>d</mi><mrow><mi>s</mi><mn>4</mn></mrow><mn>2</mn></msubsup><mo>·</mo><msub><mi>l</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub><mo>/</mo><mn>4</mn></mrow></semantics></math> </ephtml></p> <p> <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub></mrow></semantics></math> </ephtml> are the mass of shafts 1, 2, 3, and 4 of the gearbox (kg) respectively; <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ρ</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> is the weight density of shaft material (cf. Table 1); <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub></mrow></semantics></math> </ephtml> are orderly the length of shaft 1, 2 , 3, and 4 of the gearbox established by (cf. Figure 1):</p> <p>(<reflink idref="bib24" id="ref59">24</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>B</mi><mn>1</mn></msub><mo>+</mo><mn>1.2</mn><mo>·</mo><msub><mi>d</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib25" id="ref60">25</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>l</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>B</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib26" id="ref61">26</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub><mo>=</mo><msub><mi>B</mi><mn>1</mn></msub><mo>+</mo><mn>1.2</mn><mo>·</mo><msub><mi>d</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub></mrow></semantics></math> </ephtml></p> <p>In the above equations [[<reflink idref="bib12" id="ref62">12</reflink>]]:</p> <p>(<reflink idref="bib27" id="ref63">27</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><msub><mi>T</mi><mrow><mn>11</mn></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><mn>0.2</mn><mo>·</mo><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib28" id="ref64">28</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><msub><mi>T</mi><mrow><mn>12</mn></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><mn>0.2</mn><mo>·</mo><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib29" id="ref65">29</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>s</mi><mn>3</mn></mrow></msub><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><msub><mi>T</mi><mrow><mn>13</mn></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><mn>0.2</mn><mo>·</mo><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib30" id="ref66">30</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>s</mi><mn>4</mn></mrow></msub><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><msub><mi>T</mi><mrow><mn>14</mn></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><mn>0.2</mn><mo>·</mo><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></semantics></math> </ephtml></p> <p>where <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow></semantics></math> </ephtml> is the allowable shear stress. In this study, its value is chosen as <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo>[</mo><mi>τ</mi><mo>]</mo></mrow></mrow></semantics></math> </ephtml> = 17 MPa.</p> <hd id="AN0142923975-8">2.5. Determination of the Centre Distances of the Gear Stages</hd> <p>In addition to the module of gears, center distance is also an important factor for designing as well as optimizing gearbox. According to [[<reflink idref="bib12" id="ref67">12</reflink>]], the center distance of the i stage of the gearbox can be calculated by equation (<reflink idref="bib31" id="ref68">31</reflink>):</p> <p>(<reflink idref="bib31" id="ref69">31</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mrow><mi>w</mi><mi>i</mi></mrow></msub><mo>=</mo><msub><mi>k</mi><mi>a</mi></msub><mo>·</mo><mrow><mo>(</mo><mrow><msub><mi>u</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>·</mo><mroot><mrow><msub><mi>T</mi><mrow><mn>1</mn><mi>i</mi></mrow></msub><mo>·</mo><msub><mi>k</mi><mrow><mi>H</mi><mi>β</mi></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><msup><mrow><mrow><mo>[</mo><mrow><msub><mi>σ</mi><mrow><mi>H</mi><mi>i</mi></mrow></msub></mrow><mo>]</mo></mrow></mrow><mn>2</mn></msup><mo>·</mo><msub><mi>u</mi><mi>i</mi></msub><mo>·</mo><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>1</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><mn>3</mn></mroot></mrow></semantics></math> </ephtml></p> <p>where:</p> <p></p> <ulist> <item> – <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>H</mi><mi>β</mi></mrow></msub></mrow></semantics></math> </ephtml> is the contacting load ratio for pitting resistance selected by 1.1 [[<reflink idref="bib12" id="ref70">12</reflink>]];</item> <p></p> <item> – <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo>[</mo><mrow><msub><mi>σ</mi><mrow><mi>H</mi><mi>i</mi></mrow></msub></mrow><mo>]</mo></mrow></mrow></semantics></math> </ephtml> is the allowable contact stress of the i stage (MPa);</item> <p></p> <item> – <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mi>a</mi></msub></mrow></semantics></math> </ephtml> is the material coefficient; As the gear material is steel, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mi>a</mi></msub></mrow></semantics></math> </ephtml> = 43;</item> <p></p> <item> – <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>1</mn></mrow></msub></mrow></semantics></math> </ephtml> is the coefficient of wheel face width of the i stage;</item> <p></p> <item> – <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mrow><mn>1</mn><mi>i</mi></mrow></msub></mrow></semantics></math> </ephtml> is the torque on the drive shaft of the i stage (Nmm) determined by: (<reflink idref="bib32" id="ref71">32</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mrow><mn>1</mn><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>T</mi><mi>r</mi></msub></mrow><mrow><msubsup><mo>∏</mo><mrow><mi>j</mi><mo>=</mo><mi>i</mi></mrow><mn>3</mn></msubsup><mo stretchy="false">(</mo><msub><mi>u</mi><mi>i</mi></msub><mo>·</mo><msubsup><mi>η</mi><mrow><mi>h</mi><mi>g</mi></mrow><mrow><mn>4</mn><mo>−</mo><mi>i</mi></mrow></msubsup><mo>·</mo><msubsup><mi>η</mi><mrow><mi>b</mi><mi>e</mi></mrow><mrow><mn>5</mn><mo>−</mo><mi>i</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></mfrac></mrow></semantics></math> </ephtml></item> </ulist> <p>According to [[<reflink idref="bib12" id="ref72">12</reflink>]], the pinion and the gear pitch diameters of the i stage can be calculated by the value of the center distance as the following equations:</p> <p>(<reflink idref="bib33" id="ref73">33</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>w</mi><mn>1</mn><mi>i</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>·</mo><msub><mi>a</mi><mrow><mi>w</mi><mi>i</mi></mrow></msub><mo>/</mo><mrow><mo>(</mo><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml></p> <p>(<reflink idref="bib34" id="ref74">34</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mrow><mi>w</mi><mn>2</mn><mi>i</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>·</mo><msub><mi>a</mi><mrow><mi>w</mi><mi>i</mi></mrow></msub><mo>·</mo><msub><mi>u</mi><mi>i</mi></msub><mo>/</mo><mrow><mo>(</mo><mrow><msub><mi>u</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml></p> <hd id="AN0142923975-9">2.6. Optimization Problem</hd> <p>Based on previously mentioned analyses, it can be emphasized that in order to reduce the cost of gearbox, minimizing the objective function ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>b</mi></mrow></msub></mrow></semantics></math> </ephtml> ) or <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>g</mi><mi>b</mi></mrow></msub></mrow></semantics></math> </ephtml> should satisfy the following constraints:</p> <p>(<reflink idref="bib35" id="ref75">35</reflink>) <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mn>1</mn><mo>≤</mo><msub><mi>u</mi><mn>1</mn></msub><mo>≤</mo><mn>9</mn></mrow><mspace linebreak="newline" /><mrow><mn>1</mn><mo>≤</mo><msub><mi>u</mi><mn>2</mn></msub><mo>≤</mo><mn>9</mn></mrow><mspace linebreak="newline" /><mrow><mn>1</mn><mo>≤</mo><msub><mi>u</mi><mn>3</mn></msub><mo>≤</mo><mn>9</mn></mrow></mrow></semantics></math> </ephtml></p> <p>It can be clarified that to solve the optimizing solution, it is essential to optimize the values of partial gear ratios of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml> , <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> , and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> . On the other hand, we have the relation between transmission ratios and partial ratios, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>·</mo><msub><mi>u</mi><mn>2</mn></msub><mo>·</mo><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> . Hence, in this study, instead of optimizing all three mentioned partial ratios, the optimization of only two partial ratios ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> ) are considered. The partial ratio can be determined by equation: <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><msub><mi>u</mi><mi>t</mi></msub><mo>/</mo><mrow><mo>(</mo><mrow><msub><mi>u</mi><mn>2</mn></msub><mo>·</mo><msub><mi>u</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml> .</p> <hd id="AN0142923975-10">3. Experimental Work</hd> <p>To investigate the influences of factors on objective functions of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> , simulation experiments, namely screening experiments, are carried out. Eleven factors (or input parameters) listed in Table 2 are selected for the exploration. Low and high values are considered to test each input factor. As the experiment in this work is a simulation experiment, it is not necessary to reduce the number of experiments required to be performed like real experiments. Therefore, it is desired to perform full factorial design of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mrow><mn>11</mn></mrow></msup></mrow></semantics></math> </ephtml> instead of the Taguchi method as the usual practice. Nevertheless, the expecting function is not available in Minitab@19, therefore the model of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mrow><mn>11</mn><mo>−</mo><mn>4</mn></mrow></msup></mrow></semantics></math> </ephtml> and 1/16 fraction is purposely adopted. Consequently, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mrow><mn>11</mn><mo>−</mo><mn>4</mn></mrow></msup><mo>=</mo><mn>128</mn></mrow></semantics></math> </ephtml> tests for the simulation experiment are utilized. This method is also the way for the largest number of experiments. Moreover, the use of a screening design is aimed at eliminating influential parameters. This is the simplest method to determine the effects of parameters as well as their interactions on the target function. On the other hand, it is possible to provide mathematical models that the Taguchi method cannot.</p> <p>The demonstration of the input parameters and the responses can be seen in Table 2, where the factors are orderly assigned as factors A, B, etc. The output responses are presented in Table 3.</p> <hd id="AN0142923975-11">4. Results and Discussions</hd> <p></p> <hd id="AN0142923975-12">4.1. The Influence of Input Parameters and Their Interactions</hd> <p>The evolution of the optimum gear ratio of the second step ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> ) as functions of each input parameter is presented in Figure 4. It is observed that <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> increases when Total gearbox ratio <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>u</mi><mi>t</mi></msub><mo stretchy="false">)</mo><mo>,</mo></mrow></semantics></math> </ephtml> Allowable contact stress of stage 2 ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> ), and Cost of shafts ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> ) increase also. Nevertheless, for this tendency it is realized that Total gearbox ratio <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>u</mi><mi>t</mi></msub></mrow></semantics></math> </ephtml> ) has greater influence than that of other factors. Conversely, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> decreases with the growth of Allowable contact stress of stage 1 and 3 ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><msub><mi>S</mi><mn>1</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><msub><mi>S</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> ), and Output torque ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mrow><mi>o</mi><mi>u</mi><mi>t</mi></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math> </ephtml> . Moreover, it is shown that Coefficients of wheel face width of stage 1, 2, and 3 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>1</mn></mrow></msub><mo>,</mo><mo /><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>2</mn></mrow></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>X</mi><mrow><mi>b</mi><mi>a</mi><mn>3</mn></mrow></msub></mrow></semantics></math> </ephtml> ) do not have influence on <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> . Regarding to the case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> (c.f. Figure 4b), the experimental results reveal that Cost of gears <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo>(</mo><mrow><msub><mi>C</mi><mi>g</mi></msub></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml> and Cost of shafts ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> ) have a significant effect on the value of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> . It means that <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> develops when Cost of shafts rises or Cost of gears declines. Furthermore, the first five input parameters mentioned in Table 2 do not have impact on the evolution of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> . It is noticed that the influence investigation of the input factors on response as previously mentioned do not take their interactions into account. This will be considered in the next part of the current study.</p> <p>Figure 5a displays the interactions between the input parameters on the response of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> . It is observed that the interactions between <emph>u<subs>t</subs></emph> and some input parameters such as AE (<emph>u<subs>t</subs>*AS</emph><subs>1</subs>), AF (<emph>u<subs>t</subs>*AS</emph><subs>2</subs>), AG (<emph>u<subs>t</subs>*AS</emph><subs>3</subs>), AK (<emph>u<subs>t</subs>*C<subs>g</subs></emph>), and AL (<emph>u<subs>t</subs>*C<subs>s</subs></emph>) in both values of 30 and 100 has the most significant influence on the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response, while the stable tendency is observed for the interactions between <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>t</mi></msub></mrow></semantics></math> </ephtml> and remaining input parameters, e.g., AB (<emph>u<subs>t</subs>*X</emph><subs><emph>ba</emph>1</subs>), AC (<emph>u<subs>t</subs>*X</emph><subs><emph>ba</emph>2</subs>), AD (<emph>u<subs>t</subs>*X</emph><subs><emph>ba</emph>3</subs>), AH (<emph>u<subs>t</subs>*T<subs>out</subs></emph>), and AJ (<emph>u<subs>t</subs>*C<subs>gh</subs></emph>). Similarly, we can realize the interactions which have significant influence on the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response but are lesser than the ones of <emph>u<subs>t</subs></emph> like BF (<emph>X</emph><subs><emph>ba</emph>1</subs><emph>*A</emph><subs><emph>S</emph>2</subs>), BE (<emph>X</emph><subs><emph>ba</emph>1</subs><emph>*A</emph><subs><emph>S</emph>1</subs>), CL (<emph>X</emph><subs><emph>ba</emph>2</subs><emph>*C<subs>s</subs></emph>), CK (<emph>X</emph><subs><emph>ba</emph>2</subs>*<emph>C<subs>g</subs></emph>), CF (<emph>X</emph><subs><emph>ba</emph>2</subs><emph>*AS</emph><subs>2</subs>), FH (<emph>AS</emph><subs>2</subs>*<emph>T<subs>out</subs></emph>), FG (<emph>AS</emph><subs>2</subs>*<emph>AS</emph><subs>3</subs>), FL (<emph>AS</emph><subs>2</subs><emph>*C<subs>s</subs></emph>), FK (<emph>AS</emph><subs>2</subs><emph>*C<subs>g</subs></emph>), FL (<emph>AS</emph><subs>2</subs><emph>*C<subs>s</subs></emph>), FJ (<emph>AS</emph><subs>2</subs><emph>*C<subs>gh</subs></emph>), HK (<emph>T<subs>out</subs>*C<subs>g</subs></emph>), GL (<emph>AS</emph><subs>3</subs><emph>*C<subs>s</subs></emph>), GJ (<emph>AS</emph><subs>3</subs><emph>*C<subs>gh</subs></emph>), and GH (<emph>AS</emph><subs>3</subs><emph>*T<subs>out</subs></emph>). Referring to the case of the response <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> (cf. Figure 5b), it is visualized that the interactions JK (<emph>C<subs>gh</subs>*C<subs>g</subs></emph>), JL (<emph>C<subs>gh</subs>*C<subs>s</subs></emph>), GK (<emph>AS</emph><subs>3</subs><emph>*C<subs>g</subs></emph>), GL (<emph>AS</emph><subs>3</subs><emph>*C<subs>s</subs></emph>), FK(<emph>AS</emph><subs>2</subs><emph>*C<subs>g</subs></emph>), FL(<emph>AS</emph><subs>2</subs><emph>*C<subs>s</subs></emph>), KL (<emph>C<subs>g</subs>*C<subs>s</subs></emph>), BH (<emph>X</emph><subs><emph>ba</emph>1</subs><emph>*T<subs>out</subs></emph>), BL (<emph>X</emph><subs><emph>ba</emph>1</subs><emph>*C<subs>s</subs></emph>), DG (<emph>X</emph><subs><emph>ba</emph>3</subs><emph>*AS</emph><subs>3</subs>), EG (<emph>AS</emph><subs>1</subs><emph>*AS</emph><subs>3</subs>), and EK (<emph>AS</emph><subs>1</subs><emph>*C<subs>g</subs></emph>) have significant influences on the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response.</p> <p>Figure 6 presents the Normal Plot of the standardized effects in which the relationship between the responses ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> ) and the input parameters as well as their interactions are exposed. Based on the results presented in the figure, it is seen that <emph>u<subs>t</subs></emph> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> have the greatest influence on the response <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> as previously documented. Furthermore, it is realized that, in addition to single input parameters as early presented (<emph>u<subs>t</subs></emph>, <emph>AS</emph><subs>2</subs>, <emph>C<subs>s</subs></emph>, <emph>C<subs>g</subs></emph>, <emph>AS</emph><subs>1</subs>, and <emph>AS</emph><subs>3</subs>) the interactions of some input parameters also have both positive and negative impacts on the response of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> . For instance, the increase in the interactions of AK, EL, AJ, AF, BH, HK, and GK leads to the augment of the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response. Conversely, the decrease in the interactions of AL, KL, EK, AE, JL, and AG causes the reduction of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response. Considering the case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> , the results anew reveal that Cost of gears ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>g</mi></msub></mrow></semantics></math> </ephtml> ) and Cost of shafts ( <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub></mrow></semantics></math> </ephtml> ) have dominant impact on the value of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> as mentioned above. Besides, the interactions between the input parameters also have influence in both positive and negative trends. For example, the response of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> is positively influenced by the interactions of JK, EK, and BL, while being negatively affected by those of KL, GK, EG, and BH. Based on the results shown in the Normal Plot of the Standardized Effects, the parameters or interactions with insignificant influence can be eliminated, while those with strong impact are remained. The testing process can go further and in more detailse with the remained parameters. In these situations, the remained parameters are listed in Table 4 and Table 5 in the case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> , respectively.</p> <hd id="AN0142923975-13">4.2. Proposed Regression Model of the Response</hd> <p>In order to achieve equations of the response <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> , a regression process with two interaction factors is carried out using Minitab@19. The significance of this regression is α = 0.05. The estimated effects and the coefficients for <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response are exhibited in Table 4 where the factors with no influence on them are eliminated. It is noticed that if the effect of each input parameter or interaction has <emph>p</emph>-value higher than the significance of α, it does not strongly impact the response. For example, the factor of <emph>X</emph><subs><emph>ba</emph>1</subs> has <emph>p</emph>-value of 0.111 superior to α = 0.05, which means that <emph>X</emph><subs><emph>ba</emph>1</subs> is not significant to the response <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> . The regression equation of the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response is described by following model (Regression Equation in Uncoded Units):</p> <p> <emph>u</emph> <subs>2</subs> = 4.241 + 0.01830 <emph>u<subs>t</subs></emph> − 1.106 <emph>X</emph><subs><emph>ba</emph>1</subs> + 0.190 <emph>X</emph><subs><emph>ba</emph>2</subs> + 1.925 <emph>X</emph><subs><emph>ba</emph>3</subs> − 0.00601 <emph>AS</emph><subs>1</subs> + 0.004379 <emph>AS</emph><subs>2</subs> − 0.00686 <emph>AS</emph><subs>3</subs> − 0.000058 <emph>T<subs>out</subs></emph> + 0.00397 <emph>C<subs>gh</subs></emph> + 0.1013 <emph>C<subs>g</subs></emph> + 0.1261 <emph>C<subs>s</subs></emph> − 0.000036 <emph>u<subs>t</subs>*AS</emph><subs>1</subs> + 0.000030 <emph>u<subs>t</subs>*AS</emph><subs>2</subs> − 0.000014 <emph>u<subs>t</subs>*AS</emph><subs>3</subs> + 0.000405 <emph>u<subs>t</subs>*C<subs>gh</subs></emph> + 0.000587 <emph>u<subs>t</subs>*C<subs>g</subs></emph> − 0.001144 <emph>u<subs>t</subs>*C<subs>s</subs></emph>+ 0.000131 <emph>X</emph><subs><emph>ba</emph>1</subs><emph>*T<subs>out</subs></emph> − 0.327 <emph>X</emph><subs><emph>ba</emph>2</subs><emph>*C<subs>s</subs></emph> − 0.2243 <emph>X</emph><subs><emph>ba</emph>3</subs><emph>*C<subs>g</subs></emph> + 0.000012 <emph>AS</emph><subs>1</subs><emph>*AS</emph><subs>3</subs> − 0.000404 <emph>AS</emph><subs>1</subs><emph>*C<subs>g</subs></emph> + 0.000670 <emph>AS</emph><subs>1</subs><emph>*C<subs>s</subs></emph> + 0.000101 <emph>AS</emph><subs>2</subs><emph>*C<subs>g</subs></emph> − 0.000218 <emph>AS</emph><subs>2</subs><emph>*C<subs>s</subs></emph>+ 0.000105 <emph>AS</emph><subs>3</subs><emph>*C<subs>g</subs></emph> + 0.000001 <emph>T<subs>out</subs>*C<subs>g</subs></emph> − 0.00676 <emph>C<subs>gh</subs>*C<subs>s</subs></emph> − 0.007003 <emph>C<subs>g</subs>*C<subs>s</subs></emph> (<reflink idref="bib36" id="ref76">36</reflink>)</p> <p>It can be said that the experimental data are greatly consistent with the proposed model when the minimum value of R-square is approximately 98% (all of them are more than 98%).</p> <p>In the case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response, the results obtained from regression process show the difference from those of <emph>u</emph><subs>2</subs> response. Indeed, <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>t</mi></msub></mrow></semantics></math> </ephtml> and <emph>X</emph><subs><emph>ba</emph>2</subs> have no influence on the response, moreover, only eight interactions between input parameters have impact on it (cf. Table 5). It is observed that the factors of B, D, E, and H have <emph>p</emph>-value of 0.078, 0.184, 0.146, and 0.052 respectively, larger than significance α (0.05). Hence, these parameters have little influence on the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response. However, the interactions of BH, BL, DG, EG, and EK have <emph>p</emph>-value inferior to α. For this reason, they strongly influence the response of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> . The regression equation of this response can be presented as following model (Regression Equation in Uncoded Units):</p> <p> <emph>u</emph> <subs>3</subs> = −16.99 + 0.19 <emph>X</emph><subs><emph>ba</emph>1</subs> + 29.9 <emph>X</emph><subs><emph>ba</emph>3</subs> + 0.01838 <emph>AS</emph><subs>1</subs> − 0.005652 <emph>AS</emph><subs>2</subs> + 0.0599 <emph>AS</emph><subs>3</subs> + 0.000197 <emph>T<subs>out</subs></emph> − 0.1537 <emph>C<subs>gh</subs></emph> − 0.079 <emph>C<subs>g</subs></emph> + 0.072 <emph>C<subs>s</subs></emph> − 0.000575 <emph>X</emph><subs><emph>ba</emph>1</subs><emph>*T<subs>out</subs></emph> + 1.404 <emph>X</emph><subs><emph>ba</emph>1</subs><emph>*C<subs>s</subs></emph> − 0.0737 <emph>X</emph><subs><emph>ba</emph>3</subs><emph>*AS</emph><subs>3</subs> − 0.000053 <emph>AS</emph><subs>1</subs><emph>*AS</emph><subs>3</subs> + 0.000524 <emph>AS</emph><subs>1</subs><emph>*C<subs>g</subs></emph>− 0.000528 <emph>AS</emph><subs>3</subs><emph>*C<subs>g</subs></emph> + 0.01440 <emph>C<subs>gh</subs>*C<subs>g</subs></emph> − 0.03934 <emph>C<subs>g</subs>*C<subs>s</subs></emph> (<reflink idref="bib37" id="ref77">37</reflink>)</p> <p>The results in Table 5 also report that the experimental data are highly consistent with the proposed model when the minimum value of R-square approximately 92.02% (all of them are more than 92.02%). However, this is less reliable when compared to that of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response.</p> <p>Based on previous analysis, it can be said that the proposed models of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> can be utilized to get the optimum gear ratio of the second and third stages. As a consequence, the optimum gear ratio of the first stage can be obtained by <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><msub><mi>u</mi><mi>t</mi></msub><mo>/</mo><mrow><mo>(</mo><mrow><msub><mi>u</mi><mn>2</mn></msub><mo>·</mo><msub><mi>u</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml> .</p> <hd id="AN0142923975-14">4.3. Analysis of Variance—ANOVA</hd> <p>In order to quantitatively conclude the impact of each parameters and their interactions on the responses, Analysis of Variance is necessary. Table 5 reveals the Analysis of Variance in case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response. It is observed that F-values of some parameters of A, F, K, E, L, G, AK, AL, EK, AE, KL, H, EL, AF, AJ, and JL exhibit the F-value higher than 50, and it can be concluded that these parameters have static significance. The R-square value in this case is high when the lowest R-square approaches <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>92</mn><mo>%</mo></mrow></semantics></math> </ephtml> . In a similar way, we can also identify the high F-value of parameters in case of the <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response, such as K, L, G, KL, F, and J. the lowest value of R-square reaches 92%.</p> <hd id="AN0142923975-15">4.4. Validation of Proposed Model</hd> <p>The estimation of errors resulting from the difference between experiments and model of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> is qualitatively described in Figure 7. From the Normal Probability Plot, it is observed that the contribution of errors is similar to normal distribution. The Versus fits graph discloses that the relation between residual and fitted value of model is random. Moreover, the Versus Order also exhibits the random relationship between residual and order of data point. The identical tendency is also noted when comparing experiments and proposed model in case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response. The observed phenomena given by the graphs one more time show the reliability of the proposed model which is highly fitted for the experiments.</p> <p>Another way to validate the approximation of data is probability plot exhibited in Figure 8. The Anderson–Darling test in Minitab@19 which is a statistical test to validate the data set come from a specific distribution, e.g., the normal distribution or not. In this way, the data set is representative by blue points. There are three straight lines in the plot where the middle line presents the probability of normal distribution, while two lines in the left and the right refer to limiting boundary with significance of 95%. It is observed that all data set for both case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> are sited inside two limiting line when the <emph>p</emph>-value of 0.289 and 0.097 are greater than α value of 0.05. This indicates that the data set follows the distribution.</p> <hd id="AN0142923975-16">5. Conclusions</hd> <p>The influence of main design parameters on the optimum partial gear ratios for three-stage helical gearboxes was conducted. The optimum partial gear ratios are derived from the results of optimization problem for getting minimum gearbox cost. This is the first result appearing in scientific publications. To solve the optimum problem, a computer program was built, while a plan of simulation experiments was designed and carried out. The influences of eleven input parameters and their interactions on the output response of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> were investigated. The input parameters include total gearbox ratio, coefficient of wheel face width of stage 1, coefficient of wheel face width of stage 2, coefficient of wheel face width of stage 3, allowable contact stress of stage 1, allowable contact stress of stage 2, allowable contact stress of stage 3, output torque, cost of gearbox housing, cost of gears, and cost of shafts. The following conclusion can be made:</p> <p></p> <ulist> <item> ✓ The influence of input parameters and their interactions on <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response is different from those of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> response. The ANOVA results showed that the parameters of A, F, K, E, L, G, AK, AL, EK, AE, KL, H, EL, AF, AJ, and JL have significant influence on <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> response (R-square value approaching 98%), while the corresponding to be the parameters of K, L, G, KL, F, and J in case of <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> (R-square of 92%).</item> <p></p> <item> ✓ The parameters having insignificant influence were eliminated, inversely, the others that had strong influence would be considered for deeper experiments.</item> <p></p> <item> ✓ The proposed models of both <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math> </ephtml> and <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mn>3</mn></msub></mrow></semantics></math> </ephtml> responses are highly consistent to experimental data. The reliability of the models is validated. It can be said that the proposed models can be applied to optimize the costs of gearbox.</item> </ulist> <hd id="AN0142923975-17">Figures and Tables</hd> <p>Graph: Figure 1 Gear mass versus second stage gear ratio [[<reflink idref="bib1" id="ref78">1</reflink>]].</p> <p>Graph: Figure 2 Partial gear ratios versus total gearbox ratio.</p> <p>Graph: Figure 3 Schema for determination of gearbox mass.</p> <p>Graph: Figure 4 Main effects plot for (a) u2 and (b) u3.</p> <p>Graph: Figure 5 The interactions between input parameters on the response of u2 (a) and u3 (b).</p> <p>Graph: applsci-10-02365-g005b.tif</p> <p>Graph: Figure 6 The evolution of response as a function of input parameters and their interactions (a) u2 and (b) u3</p> <p>Graph: applsci-10-02365-g006b.tif</p> <p>Graph: Figure 7 Graphs estimating errors between experiments and model of u2.</p> <p>Graph: Figure 8 Probability plot of the validity of proposed model for the response of u2 and u3.</p> <p>Table 1 Weight density of used materials.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><msub><mi mathvariant="bold-italic">ρ</mi><mi mathvariant="bold-italic">g</mi><mi mathvariant="bold-italic">h</mi></msub></semantics></math></p> (kg/m<sup>3</sup>)</th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><msub><mi mathvariant="bold-italic">ρ</mi><mi mathvariant="bold-italic">g</mi></msub></semantics></math></p> (kg/m<sup>3</sup>)</th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><msub><mi mathvariant="bold-italic">ρ</mi><mi mathvariant="bold-italic">s</mi></msub></semantics></math></p> (kg/m<sup>3</sup>)</th></tr></thead><tbody><tr><td align="center" valign="middle" style="border-bottom:solid thin">7.2</td><td align="center" valign="middle" style="border-bottom:solid thin">7.82</td><td align="center" valign="middle" style="border-bottom:solid thin">7.85</td></tr></tbody></table> </ephtml> </p> <p>Table 2 Input parameters.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">Real Factor</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Minitab<sup>®</sup>19</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Name</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Unit</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Low</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">High</th></tr></thead><tbody><tr><td valign="middle" align="left">Total gearbox ratio</td><td align="center" valign="middle">A</td><td align="center" valign="middle"><italic>u<sub>t</sub></italic></td><td align="center" valign="middle">-</td><td align="center" valign="middle">10</td><td align="center" valign="middle">100</td></tr><tr><td valign="middle" align="left">Coefficient of wheel face width of stage 1</td><td align="center" valign="middle">B</td><td align="center" valign="middle"><italic>X</italic><sub><italic>ba</italic>1</sub></td><td align="center" valign="middle">-</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.35</td></tr><tr><td valign="middle" align="left">Coefficient of wheel face width of stage 2</td><td align="center" valign="middle">C</td><td align="center" valign="middle"><italic>X</italic><sub><italic>ba</italic>2</sub></td><td align="center" valign="middle">-</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.38</td></tr><tr><td valign="middle" align="left">Coefficient of wheel face width of stage 3</td><td align="center" valign="middle">D</td><td align="center" valign="middle"><italic>X</italic><sub><italic>ba</italic>3</sub></td><td align="center" valign="middle">-</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.4</td></tr><tr><td valign="middle" align="left">Allowable contact stress of stage 1</td><td align="center" valign="middle">E</td><td align="center" valign="middle"><p>AS1</p></td><td align="center" valign="middle">MPa</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td></tr><tr><td valign="middle" align="left">Allowable contact stress of stage 2</td><td align="center" valign="middle">F</td><td align="center" valign="middle"><p>AS2</p></td><td align="center" valign="middle">MPa</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td></tr><tr><td valign="middle" align="left">Allowable contact stress of stage 3</td><td align="center" valign="middle">G</td><td align="center" valign="middle"><p>AS3</p></td><td align="center" valign="middle">MPa</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td></tr><tr><td valign="middle" align="left">Output torque</td><td align="center" valign="middle">H</td><td align="center" valign="middle"><p>Tout</p></td><td align="center" valign="middle">Nm</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">10000</td></tr><tr><td valign="middle" align="left">Cost of gearbox housing</td><td align="center" valign="middle">I</td><td align="center" valign="middle"><p>Cgh</p></td><td align="center" valign="middle">USD/kg</td><td align="center" valign="middle">1</td><td align="center" valign="middle">5</td></tr><tr><td valign="middle" align="left">Cost of gears</td><td align="center" valign="middle">J</td><td align="center" valign="middle"><p>Cg</p></td><td align="center" valign="middle">USD/kg</td><td align="center" valign="middle">2</td><td align="center" valign="middle">9</td></tr><tr><td valign="middle" style="border-bottom:solid thin" align="left">Cost of shafts</td><td align="center" valign="middle" style="border-bottom:solid thin">K</td><td align="center" valign="middle" style="border-bottom:solid thin"><p>Cs</p></td><td align="center" valign="middle" style="border-bottom:solid thin">USD/kg</td><td align="center" valign="middle" style="border-bottom:solid thin">1.5</td><td align="center" valign="middle" style="border-bottom:solid thin">5</td></tr></tbody></table> </ephtml> </p> <p>Table 3 Experimental plans and output responses.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">Run Order</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Center Pt</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Blocks</th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>u<sub>t</sub></italic></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>X</italic><sub><italic>ba</italic>1</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>X</italic><sub><italic>ba</italic>2</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>X</italic><sub><italic>ba</italic>3</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>AS</italic><sub>1</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>AS</italic><sub>2</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>AS</italic><sub>3</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>T<sub>out</sub></italic></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>C<sub>gh</sub></italic></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>C<sub>g</sub></italic></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>C<sub>s</sub></italic></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>u</italic><sub>2</sub></th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>u</italic><sub>3</sub></th></tr></thead><tbody><tr><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.02</td><td align="center" valign="middle">3.64</td></tr><tr><td align="center" valign="middle">2</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.08</td><td align="center" valign="middle">4.24</td></tr><tr><td align="center" valign="middle">3</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">3.73</td></tr><tr><td align="center" valign="middle">4</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.63</td><td align="center" valign="middle">3.58</td></tr><tr><td align="center" valign="middle">5</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">5.22</td><td align="center" valign="middle">2.59</td></tr><tr><td align="center" valign="middle">6</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.03</td><td align="center" valign="middle">3.28</td></tr><tr><td align="center" valign="middle">...<break />(Appendix A)</td><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /><td align="center" valign="middle" /></tr><tr><td align="center" valign="middle">127</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">5.83</td></tr><tr><td align="center" valign="middle" style="border-bottom:solid thin">128</td><td align="center" valign="middle" style="border-bottom:solid thin">1</td><td align="center" valign="middle" style="border-bottom:solid thin">1</td><td align="center" valign="middle" style="border-bottom:solid thin">100</td><td align="center" valign="middle" style="border-bottom:solid thin">0.3</td><td align="center" valign="middle" style="border-bottom:solid thin">0.38</td><td align="center" valign="middle" style="border-bottom:solid thin">0.36</td><td align="center" valign="middle" style="border-bottom:solid thin">420</td><td align="center" valign="middle" style="border-bottom:solid thin">350</td><td align="center" valign="middle" style="border-bottom:solid thin">350</td><td align="center" valign="middle" style="border-bottom:solid thin">10000</td><td align="center" valign="middle" style="border-bottom:solid thin">5</td><td align="center" valign="middle" style="border-bottom:solid thin">9</td><td align="center" valign="middle" style="border-bottom:solid thin">5</td><td align="center" valign="middle" style="border-bottom:solid thin">4.02</td><td align="center" valign="middle" style="border-bottom:solid thin">3.55</td></tr></tbody></table> </ephtml> </p> <hd id="AN0142923975-18">Table 4</hd> <p>Estimated Effects and Coefficients for <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>u</mi><mn>2</mn></msub></semantics></math> </ephtml> .</p> <p>Table 4a Coded Coefficients.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">Term</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Effect</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Coef</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">SE Coef</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">T-Value</th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>p</italic>-Value</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">VIF</th></tr></thead><tbody><tr><td align="center" valign="middle">Constant</td><td align="center" valign="middle" /><td align="center" valign="middle">4.03383</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">674.32</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle" /></tr><tr><td align="center" valign="middle">ut</td><td align="center" valign="middle">0.80109</td><td align="center" valign="middle">0.40055</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">66.96</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba1</td><td align="center" valign="middle">−0.01922</td><td align="center" valign="middle">−0.00961</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−1.61</td><td align="center" valign="middle">0.111</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba2</td><td align="center" valign="middle">−0.04359</td><td align="center" valign="middle">−0.02180</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−3.64</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba3</td><td align="center" valign="middle">0.02766</td><td align="center" valign="middle">0.01383</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.31</td><td align="center" valign="middle">0.023</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1</td><td align="center" valign="middle">−0.25172</td><td align="center" valign="middle">−0.12586</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−21.04</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS2</td><td align="center" valign="middle">0.43266</td><td align="center" valign="middle">0.21633</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">36.16</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS3</td><td align="center" valign="middle">−0.16828</td><td align="center" valign="middle">−0.08414</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−14.07</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Tout</td><td align="center" valign="middle">−0.08484</td><td align="center" valign="middle">−0.04242</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−7.09</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cgh</td><td align="center" valign="middle">0.03328</td><td align="center" valign="middle">0.01664</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.78</td><td align="center" valign="middle">0.006</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cg</td><td align="center" valign="middle">−0.27141</td><td align="center" valign="middle">−0.13570</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−22.68</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cs</td><td align="center" valign="middle">0.17766</td><td align="center" valign="middle">0.08883</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">14.85</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*AS1</td><td align="center" valign="middle">−0.08766</td><td align="center" valign="middle">−0.04383</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−7.33</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*AS2</td><td align="center" valign="middle">0.07359</td><td align="center" valign="middle">0.03680</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">6.15</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*AS3</td><td align="center" valign="middle">−0.03422</td><td align="center" valign="middle">−0.01711</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−2.86</td><td align="center" valign="middle">0.005</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*Cgh</td><td align="center" valign="middle">0.05672</td><td align="center" valign="middle">0.02836</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">4.74</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*Cg</td><td align="center" valign="middle">0.14391</td><td align="center" valign="middle">0.07195</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">12.03</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">ut*Cs</td><td align="center" valign="middle">−0.14016</td><td align="center" valign="middle">−0.07008</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−11.71</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba1*Tout</td><td align="center" valign="middle">0.02953</td><td align="center" valign="middle">0.01477</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.47</td><td align="center" valign="middle">0.015</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba2*Cs</td><td align="center" valign="middle">−0.02859</td><td align="center" valign="middle">−0.01430</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−2.39</td><td align="center" valign="middle">0.019</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba3*Cg</td><td align="center" valign="middle">−0.03141</td><td align="center" valign="middle">−0.01570</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−2.63</td><td align="center" valign="middle">0.010</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1*AS3</td><td align="center" valign="middle">0.03047</td><td align="center" valign="middle">0.01523</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.55</td><td align="center" valign="middle">0.012</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1*Cg</td><td align="center" valign="middle">−0.09891</td><td align="center" valign="middle">−0.04945</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−8.27</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1*Cs</td><td align="center" valign="middle">0.08203</td><td align="center" valign="middle">0.04102</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">6.86</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS2*Cg</td><td align="center" valign="middle">0.02484</td><td align="center" valign="middle">0.01242</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.08</td><td align="center" valign="middle">0.040</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS2*Cs</td><td align="center" valign="middle">−0.02672</td><td align="center" valign="middle">−0.01336</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−2.23</td><td align="center" valign="middle">0.028</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS3*Cg</td><td align="center" valign="middle">0.02578</td><td align="center" valign="middle">0.01289</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.15</td><td align="center" valign="middle">0.034</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Tout*Cg</td><td align="center" valign="middle">0.03234</td><td align="center" valign="middle">0.01617</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">2.70</td><td align="center" valign="middle">0.008</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cgh*Cs</td><td align="center" valign="middle">−0.04734</td><td align="center" valign="middle">−0.02367</td><td align="center" valign="middle">0.00598</td><td align="center" valign="middle">−3.96</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle" style="border-bottom:solid thin">Cg*Cs</td><td align="center" valign="middle" style="border-bottom:solid thin">−0.08578</td><td align="center" valign="middle" style="border-bottom:solid thin">−0.04289</td><td align="center" valign="middle" style="border-bottom:solid thin">0.00598</td><td align="center" valign="middle" style="border-bottom:solid thin">−7.17</td><td align="center" valign="middle" style="border-bottom:solid thin">0.000</td><td align="center" valign="middle" style="border-bottom:solid thin">1.00</td></tr></tbody></table> </ephtml> </p> <p>Table 4b Model Summary.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">S</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq(adj)</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq(pred)</th></tr></thead><tbody><tr><td align="center" valign="middle" style="border-bottom:solid thin">0.0676794</td><td align="center" valign="middle" style="border-bottom:solid thin">98.77%</td><td align="center" valign="middle" style="border-bottom:solid thin">98.41%</td><td align="center" valign="middle" style="border-bottom:solid thin">97.90%</td></tr></tbody></table> </ephtml> </p> <hd id="AN0142923975-19">Table 5</hd> <p>Estimated effects and coefficients for <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>u</mi><mn>3</mn></msub></semantics></math> </ephtml> .</p> <p>Table 5a Coded Coefficients.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">Term</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Effect</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">Coef</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">SE Coef</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">T-Value</th><th align="center" style="border-top:solid thin;border-bottom:solid thin"><italic>p</italic>-Value</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">VIF</th></tr></thead><tbody><tr><td align="center" valign="middle">Constant</td><td align="center" valign="middle" /><td align="center" valign="middle">4.2002</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">187.27</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle" /></tr><tr><td align="center" valign="middle">Xba1</td><td align="center" valign="middle">0.0797</td><td align="center" valign="middle">0.0398</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">1.78</td><td align="center" valign="middle">0.078</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba3</td><td align="center" valign="middle">0.0600</td><td align="center" valign="middle">0.0300</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">1.34</td><td align="center" valign="middle">0.184</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1</td><td align="center" valign="middle">0.0656</td><td align="center" valign="middle">0.0328</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">1.46</td><td align="center" valign="middle">0.146</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS2</td><td align="center" valign="middle">−0.3956</td><td align="center" valign="middle">−0.1978</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−8.82</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS3</td><td align="center" valign="middle">0.6103</td><td align="center" valign="middle">0.3052</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">13.61</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Tout</td><td align="center" valign="middle">0.0881</td><td align="center" valign="middle">0.0441</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">1.96</td><td align="center" valign="middle">0.052</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cgh</td><td align="center" valign="middle">−0.2981</td><td align="center" valign="middle">−0.1491</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−6.65</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cg</td><td align="center" valign="middle">−1.1550</td><td align="center" valign="middle">−0.5775</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−25.75</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cs</td><td align="center" valign="middle">1.0922</td><td align="center" valign="middle">0.5461</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">24.35</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba1*Tout</td><td align="center" valign="middle">−0.1294</td><td align="center" valign="middle">−0.0647</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−2.88</td><td align="center" valign="middle">0.005</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba1*Cs</td><td align="center" valign="middle">0.1228</td><td align="center" valign="middle">0.0614</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">2.74</td><td align="center" valign="middle">0.007</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Xba3*AS3</td><td align="center" valign="middle">−0.1031</td><td align="center" valign="middle">−0.0516</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−2.30</td><td align="center" valign="middle">0.023</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1*AS3</td><td align="center" valign="middle">−0.1294</td><td align="center" valign="middle">−0.0647</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−2.88</td><td align="center" valign="middle">0.005</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS1*Cg</td><td align="center" valign="middle">0.1284</td><td align="center" valign="middle">0.0642</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">2.86</td><td align="center" valign="middle">0.005</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">AS3*Cg</td><td align="center" valign="middle">−0.1294</td><td align="center" valign="middle">−0.0647</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">−2.88</td><td align="center" valign="middle">0.005</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle">Cgh*Cg</td><td align="center" valign="middle">0.2016</td><td align="center" valign="middle">0.1008</td><td align="center" valign="middle">0.0224</td><td align="center" valign="middle">4.49</td><td align="center" valign="middle">0.000</td><td align="center" valign="middle">1.00</td></tr><tr><td align="center" valign="middle" style="border-bottom:solid thin">Cg*Cs</td><td align="center" valign="middle" style="border-bottom:solid thin">−0.4819</td><td align="center" valign="middle" style="border-bottom:solid thin">−0.2409</td><td align="center" valign="middle" style="border-bottom:solid thin">0.0224</td><td align="center" valign="middle" style="border-bottom:solid thin">−10.74</td><td align="center" valign="middle" style="border-bottom:solid thin">0.000</td><td align="center" valign="middle" style="border-bottom:solid thin">1.00</td></tr></tbody></table> </ephtml> </p> <p>Table 5b Model Summary.</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-top:solid thin;border-bottom:solid thin">S</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq(adj)</th><th align="center" style="border-top:solid thin;border-bottom:solid thin">R-sq(pred)</th></tr></thead><tbody><tr><td align="center" valign="middle" style="border-bottom:solid thin">0.253752</td><td align="center" valign="middle" style="border-bottom:solid thin">94.10%</td><td align="center" valign="middle" style="border-bottom:solid thin">93.19%</td><td align="center" valign="middle" style="border-bottom:solid thin">92.02%</td></tr></tbody></table> </ephtml> </p> <hd id="AN0142923975-20">Author Contributions</hd> <p>All authors discussed the original idea. V.-C.N., A.-T.L., N.-G.T., and N.-P.V. conducted the optimization problem. On the other hand, D.-N.N. wrote this manuscript with support from T.-D.B., T.-D.B., T.-H.T., H.-L.N., and N.-P.V. In addition, A.-T.L., N.-G.T., and N.-P.V. carried out the figures and experimental analysis. All authors provided critical feedback and helped shape the research, analysis, and manuscript. Finally, N.-P.V. supervised this work and revised the article. All authors have read and agreed to the published version of the manuscript.</p> <hd id="AN0142923975-21">Funding</hd> <p>This research received no external funding.</p> <hd id="AN0142923975-22">Conflicts of Interest</hd> <p>The authors state no conflict of interest.</p> <hd id="AN0142923975-23">Acknowledgments</hd> <p>The authors gratefully acknowledge Thai Nguyen University of Technology for supporting this work.</p> <hd id="AN0142923975-24">Appendix A</hd> <p></p> <p> <ephtml> <table><tbody><tr><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold>Run Order</bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold>CenterPt</bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold>Blocks</bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>u<sub>t</sub></italic></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>X</italic><sub><italic>ba</italic>1</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>X</italic><sub><italic>ba</italic>2</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>X</italic><sub><italic>ba</italic>3</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>AS</italic><sub>1</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>AS</italic><sub>2</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>AS</italic><sub>3</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>T<sub>out</sub></italic></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>C<sub>gh</sub></italic></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>C<sub>g</sub></italic></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>C<sub>s</sub></italic></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>u</italic><sub>2</sub></bold></td><td align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin"><bold><italic>u</italic><sub>3</sub></bold></td></tr><tr><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.02</td><td align="center" valign="middle">3.64</td></tr><tr><td align="center" valign="middle">2</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.08</td><td align="center" valign="middle">4.24</td></tr><tr><td align="center" valign="middle">3</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">3.73</td></tr><tr><td align="center" valign="middle">4</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.63</td><td align="center" valign="middle">3.58</td></tr><tr><td align="center" valign="middle">5</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">5.22</td><td align="center" valign="middle">2.59</td></tr><tr><td align="center" valign="middle">6</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.03</td><td align="center" valign="middle">3.28</td></tr><tr><td align="center" valign="middle">7</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.62</td><td align="center" valign="middle">5.14</td></tr><tr><td align="center" valign="middle">8</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">5.07</td><td align="center" valign="middle">3.25</td></tr><tr><td align="center" valign="middle">9</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.26</td><td align="center" valign="middle">4.63</td></tr><tr><td align="center" valign="middle">10</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.93</td><td align="center" valign="middle">4.75</td></tr><tr><td align="center" valign="middle">11</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.45</td><td align="center" valign="middle">3.58</td></tr><tr><td align="center" valign="middle">12</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.36</td><td align="center" valign="middle">4.3</td></tr><tr><td align="center" valign="middle">13</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.3</td><td align="center" valign="middle">3.37</td></tr><tr><td align="center" valign="middle">14</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.36</td><td align="center" valign="middle">3.07</td></tr><tr><td align="center" valign="middle">15</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.44</td><td align="center" valign="middle">3.67</td></tr><tr><td align="center" valign="middle">16</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.35</td><td align="center" valign="middle">4.69</td></tr><tr><td align="center" valign="middle">17</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.72</td><td align="center" valign="middle">6.16</td></tr><tr><td align="center" valign="middle">18</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">6.28</td></tr><tr><td align="center" valign="middle">19</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">2.97</td><td align="center" valign="middle">3.79</td></tr><tr><td align="center" valign="middle">20</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.26</td><td align="center" valign="middle">6.04</td></tr><tr><td align="center" valign="middle">21</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.95</td><td align="center" valign="middle">2.89</td></tr><tr><td align="center" valign="middle">22</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.41</td><td align="center" valign="middle">3.91</td></tr><tr><td align="center" valign="middle">23</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.72</td><td align="center" valign="middle">4.15</td></tr><tr><td align="center" valign="middle">24</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.51</td><td align="center" valign="middle">4.63</td></tr><tr><td align="center" valign="middle">25</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.18</td><td align="center" valign="middle">3.67</td></tr><tr><td align="center" valign="middle">26</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.63</td><td align="center" valign="middle">6.43</td></tr><tr><td align="center" valign="middle">27</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.44</td><td align="center" valign="middle">3.13</td></tr><tr><td align="center" valign="middle">28</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.09</td><td align="center" valign="middle">3.16</td></tr><tr><td align="center" valign="middle">29</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.38</td><td align="center" valign="middle">5.65</td></tr><tr><td align="center" valign="middle">30</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.41</td><td align="center" valign="middle">4.15</td></tr><tr><td align="center" valign="middle">31</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.81</td><td align="center" valign="middle">4.06</td></tr><tr><td align="center" valign="middle">32</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.77</td><td align="center" valign="middle">4.99</td></tr><tr><td align="center" valign="middle">33</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.72</td><td align="center" valign="middle">2.83</td></tr><tr><td align="center" valign="middle">34</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.77</td><td align="center" valign="middle">3.97</td></tr><tr><td align="center" valign="middle">35</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.44</td><td align="center" valign="middle">4.3</td></tr><tr><td align="center" valign="middle">36</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.51</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">37</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.81</td><td align="center" valign="middle">6.22</td></tr><tr><td align="center" valign="middle">38</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.86</td><td align="center" valign="middle">5.53</td></tr><tr><td align="center" valign="middle">39</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.9</td><td align="center" valign="middle">5.5</td></tr><tr><td align="center" valign="middle">40</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.23</td><td align="center" valign="middle">3.76</td></tr><tr><td align="center" valign="middle">41</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.62</td><td align="center" valign="middle">4.51</td></tr><tr><td align="center" valign="middle">42</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.26</td><td align="center" valign="middle">3.52</td></tr><tr><td align="center" valign="middle">43</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.84</td><td align="center" valign="middle">5.65</td></tr><tr><td align="center" valign="middle">44</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.71</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">45</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.93</td><td align="center" valign="middle">3.46</td></tr><tr><td align="center" valign="middle">46</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.42</td><td align="center" valign="middle">4.12</td></tr><tr><td align="center" valign="middle">47</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.68</td><td align="center" valign="middle">4.51</td></tr><tr><td align="center" valign="middle">48</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.32</td><td align="center" valign="middle">7.03</td></tr><tr><td align="center" valign="middle">49</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.5</td><td align="center" valign="middle">2.92</td></tr><tr><td align="center" valign="middle">50</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.66</td><td align="center" valign="middle">3.76</td></tr><tr><td align="center" valign="middle">51</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.14</td><td align="center" valign="middle">5.86</td></tr><tr><td align="center" valign="middle">52</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.05</td><td align="center" valign="middle">6.16</td></tr><tr><td align="center" valign="middle">53</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.24</td><td align="center" valign="middle">4.63</td></tr><tr><td align="center" valign="middle">54</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.26</td><td align="center" valign="middle">4.15</td></tr><tr><td align="center" valign="middle">55</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.69</td><td align="center" valign="middle">4.45</td></tr><tr><td align="center" valign="middle">56</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.2</td><td align="center" valign="middle">4.81</td></tr><tr><td align="center" valign="middle">57</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.3</td><td align="center" valign="middle">4.87</td></tr><tr><td align="center" valign="middle">58</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.45</td><td align="center" valign="middle">3.58</td></tr><tr><td align="center" valign="middle">59</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.81</td><td align="center" valign="middle">3.52</td></tr><tr><td align="center" valign="middle">60</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.32</td><td align="center" valign="middle">4.54</td></tr><tr><td align="center" valign="middle">61</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.93</td><td align="center" valign="middle">3.43</td></tr><tr><td align="center" valign="middle">62</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.32</td><td align="center" valign="middle">4.15</td></tr><tr><td align="center" valign="middle">63</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.62</td><td align="center" valign="middle">3.28</td></tr><tr><td align="center" valign="middle">64</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.78</td><td align="center" valign="middle">4.48</td></tr><tr><td align="center" valign="middle">65</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.2</td><td align="center" valign="middle">6.34</td></tr><tr><td align="center" valign="middle">66</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.96</td><td align="center" valign="middle">3.85</td></tr><tr><td align="center" valign="middle">67</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.93</td><td align="center" valign="middle">4.18</td></tr><tr><td align="center" valign="middle">68</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.29</td><td align="center" valign="middle">5.86</td></tr><tr><td align="center" valign="middle">69</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.74</td><td align="center" valign="middle">5.59</td></tr><tr><td align="center" valign="middle">70</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.27</td><td align="center" valign="middle">3.91</td></tr><tr><td align="center" valign="middle">71</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.8</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">72</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.77</td><td align="center" valign="middle">3.4</td></tr><tr><td align="center" valign="middle">73</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.2</td><td align="center" valign="middle">4.15</td></tr><tr><td align="center" valign="middle">74</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.93</td><td align="center" valign="middle">3.34</td></tr><tr><td align="center" valign="middle">75</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.69</td><td align="center" valign="middle">3.61</td></tr><tr><td align="center" valign="middle">76</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">5.1</td><td align="center" valign="middle">3.1</td></tr><tr><td align="center" valign="middle">77</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.47</td><td align="center" valign="middle">3.19</td></tr><tr><td align="center" valign="middle">78</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.23</td><td align="center" valign="middle">4.87</td></tr><tr><td align="center" valign="middle">79</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.26</td><td align="center" valign="middle">5.86</td></tr><tr><td align="center" valign="middle">80</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.57</td><td align="center" valign="middle">3.4</td></tr><tr><td align="center" valign="middle">81</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.81</td><td align="center" valign="middle">3.7</td></tr><tr><td align="center" valign="middle">82</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.18</td><td align="center" valign="middle">4.57</td></tr><tr><td align="center" valign="middle">83</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.54</td><td align="center" valign="middle">4.03</td></tr><tr><td align="center" valign="middle">84</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.54</td><td align="center" valign="middle">4.36</td></tr><tr><td align="center" valign="middle">85</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.47</td><td align="center" valign="middle">6.31</td></tr><tr><td align="center" valign="middle">86</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.17</td><td align="center" valign="middle">4.24</td></tr><tr><td align="center" valign="middle">87</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.62</td><td align="center" valign="middle">3.22</td></tr><tr><td align="center" valign="middle">88</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.29</td><td align="center" valign="middle">3.97</td></tr><tr><td align="center" valign="middle">89</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.29</td><td align="center" valign="middle">3.55</td></tr><tr><td align="center" valign="middle">90</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.77</td><td align="center" valign="middle">3.43</td></tr><tr><td align="center" valign="middle">91</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.69</td><td align="center" valign="middle">3.97</td></tr><tr><td align="center" valign="middle">92</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.51</td><td align="center" valign="middle">3.73</td></tr><tr><td align="center" valign="middle">93</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.18</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">94</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.66</td><td align="center" valign="middle">3.52</td></tr><tr><td align="center" valign="middle">95</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.05</td><td align="center" valign="middle">5.47</td></tr><tr><td align="center" valign="middle">96</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.38</td><td align="center" valign="middle">3.67</td></tr><tr><td align="center" valign="middle">97</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.75</td><td align="center" valign="middle">3.7</td></tr><tr><td align="center" valign="middle">98</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.36</td><td align="center" valign="middle">3.31</td></tr><tr><td align="center" valign="middle">99</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.45</td><td align="center" valign="middle">3.85</td></tr><tr><td align="center" valign="middle">100</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">6.22</td></tr><tr><td align="center" valign="middle">101</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.99</td><td align="center" valign="middle">4.24</td></tr><tr><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.08</td><td align="center" valign="middle">4.09</td></tr><tr><td align="center" valign="middle">103</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.36</td><td align="center" valign="middle">4.93</td></tr><tr><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.3</td><td align="center" valign="middle">3.1</td></tr><tr><td align="center" valign="middle">105</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.33</td><td align="center" valign="middle">4.69</td></tr><tr><td align="center" valign="middle">106</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.72</td><td align="center" valign="middle">2.83</td></tr><tr><td align="center" valign="middle">107</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.6</td><td align="center" valign="middle">3.91</td></tr><tr><td align="center" valign="middle">108</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.74</td><td align="center" valign="middle">4.96</td></tr><tr><td align="center" valign="middle">109</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.32</td><td align="center" valign="middle">3.97</td></tr><tr><td align="center" valign="middle">110</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.38</td><td align="center" valign="middle">3.67</td></tr><tr><td align="center" valign="middle">111</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.39</td><td align="center" valign="middle">2.89</td></tr><tr><td align="center" valign="middle">112</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.84</td><td align="center" valign="middle">3.67</td></tr><tr><td align="center" valign="middle">113</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.81</td><td align="center" valign="middle">4.21</td></tr><tr><td align="center" valign="middle">114</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.47</td><td align="center" valign="middle">2.92</td></tr><tr><td align="center" valign="middle">115</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">2.94</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">116</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">5.13</td><td align="center" valign="middle">4.93</td></tr><tr><td align="center" valign="middle">117</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">3.36</td><td align="center" valign="middle">3.88</td></tr><tr><td align="center" valign="middle">118</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.44</td><td align="center" valign="middle">5.23</td></tr><tr><td align="center" valign="middle">119</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.62</td><td align="center" valign="middle">4.48</td></tr><tr><td align="center" valign="middle">120</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">5</td><td align="center" valign="middle">5.01</td><td align="center" valign="middle">3.04</td></tr><tr><td align="center" valign="middle">121</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.17</td><td align="center" valign="middle">3.82</td></tr><tr><td align="center" valign="middle">122</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">4.17</td><td align="center" valign="middle">4.72</td></tr><tr><td align="center" valign="middle">123</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">5.19</td><td align="center" valign="middle">2.59</td></tr><tr><td align="center" valign="middle">124</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">350</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.66</td><td align="center" valign="middle">3.04</td></tr><tr><td align="center" valign="middle">125</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">100</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.36</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">5</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.65</td><td align="center" valign="middle">4.78</td></tr><tr><td align="center" valign="middle">126</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.35</td><td align="center" valign="middle">0.33</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">350</td><td align="center" valign="middle">1000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">9</td><td align="center" valign="middle">1.5</td><td align="center" valign="middle">3.42</td><td align="center" valign="middle">2.98</td></tr><tr><td align="center" valign="middle">127</td><td align="center" valign="middle">1</td><td align="center" valign="middle">1</td><td align="center" valign="middle">30</td><td align="center" valign="middle">0.3</td><td align="center" valign="middle">0.38</td><td align="center" valign="middle">0.4</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">420</td><td align="center" valign="middle">10000</td><td align="center" valign="middle">1</td><td align="center" valign="middle">2</td><td align="center" valign="middle">5</td><td align="center" valign="middle">4.11</td><td align="center" valign="middle">5.83</td></tr><tr><td align="center" valign="middle" style="border-bottom:solid thin">128</td><td align="center" valign="middle" style="border-bottom:solid thin">1</td><td align="center" valign="middle" style="border-bottom:solid thin">1</td><td align="center" valign="middle" style="border-bottom:solid thin">100</td><td align="center" valign="middle" style="border-bottom:solid thin">0.3</td><td align="center" valign="middle" style="border-bottom:solid thin">0.38</td><td align="center" valign="middle" style="border-bottom:solid thin">0.36</td><td align="center" valign="middle" style="border-bottom:solid thin">420</td><td align="center" valign="middle" style="border-bottom:solid thin">350</td><td align="center" valign="middle" style="border-bottom:solid thin">350</td><td align="center" valign="middle" style="border-bottom:solid thin">10000</td><td align="center" valign="middle" style="border-bottom:solid thin">5</td><td align="center" valign="middle" style="border-bottom:solid thin">9</td><td align="center" valign="middle" style="border-bottom:solid thin">5</td><td align="center" valign="middle" style="border-bottom:solid thin">4.02</td><td align="center" valign="middle" style="border-bottom:solid thin">3.55</td></tr></tbody></table> </ephtml> </p> <ref id="AN0142923975-25"> <title> References </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> Hong T.T., Cuong N.V., Ky L.H., Tuan N.K., Pi V.N. 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Konstruktion. 1992; 44: 229-236</bibtext> </blist> </ref> <aug> <p>By Ngoc-Pi Vu; Dinh-Ngoc Nguyen; Anh-Tung Luu; Ngoc-Giang Tran; Thi-Hong Tran; Van-Cuong Nguyen; Thanh-Danh Bui and Hong-Linh Nguyen</p> <p>Reported by Author; Author; Author; Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib12" firstref="ref4"></nolink> <nolink nlid="nl2" bibid="bib13" firstref="ref5"></nolink> <nolink nlid="nl3" bibid="bib14" firstref="ref8"></nolink> <nolink nlid="nl4" bibid="bib15" firstref="ref10"></nolink> <nolink nlid="nl5" bibid="bib16" firstref="ref14"></nolink> <nolink nlid="nl6" bibid="bib17" firstref="ref15"></nolink> <nolink nlid="nl7" bibid="bib19" firstref="ref18"></nolink> <nolink nlid="nl8" bibid="bib20" firstref="ref19"></nolink> <nolink nlid="nl9" bibid="bib23" firstref="ref22"></nolink> <nolink nlid="nl10" bibid="bib22" firstref="ref23"></nolink> <nolink nlid="nl11" bibid="bib24" firstref="ref24"></nolink> <nolink nlid="nl12" bibid="bib10" firstref="ref44"></nolink> <nolink nlid="nl13" bibid="bib26" firstref="ref45"></nolink> <nolink nlid="nl14" bibid="bib11" firstref="ref46"></nolink> <nolink nlid="nl15" bibid="bib18" firstref="ref53"></nolink> <nolink nlid="nl16" bibid="bib21" firstref="ref56"></nolink> <nolink nlid="nl17" bibid="bib25" firstref="ref60"></nolink> <nolink nlid="nl18" bibid="bib27" firstref="ref63"></nolink> <nolink nlid="nl19" bibid="bib28" firstref="ref64"></nolink> <nolink nlid="nl20" bibid="bib29" firstref="ref65"></nolink> <nolink nlid="nl21" bibid="bib30" firstref="ref66"></nolink> <nolink nlid="nl22" bibid="bib31" firstref="ref68"></nolink> <nolink nlid="nl23" bibid="bib32" firstref="ref71"></nolink> <nolink nlid="nl24" bibid="bib33" firstref="ref73"></nolink> <nolink nlid="nl25" bibid="bib34" firstref="ref74"></nolink> <nolink nlid="nl26" bibid="bib35" firstref="ref75"></nolink> <nolink nlid="nl27" bibid="bib36" firstref="ref76"></nolink> <nolink nlid="nl28" bibid="bib37" firstref="ref77"></nolink>
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  Data: The Influence of Main Design Parameters on the Overall Cost of a Gearbox
– Name: Author
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  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Ngoc-Pi+Vu%22">Ngoc-Pi Vu</searchLink><br /><searchLink fieldCode="AR" term="%22Dinh-Ngoc+Nguyen%22">Dinh-Ngoc Nguyen</searchLink><br /><searchLink fieldCode="AR" term="%22Anh-Tung+Luu%22">Anh-Tung Luu</searchLink><br /><searchLink fieldCode="AR" term="%22Ngoc-Giang+Tran%22">Ngoc-Giang Tran</searchLink><br /><searchLink fieldCode="AR" term="%22Thi-Hong+Tran%22">Thi-Hong Tran</searchLink><br /><searchLink fieldCode="AR" term="%22Van-Cuong+Nguyen%22">Van-Cuong Nguyen</searchLink><br /><searchLink fieldCode="AR" term="%22Thanh-Danh+Bui%22">Thanh-Danh Bui</searchLink><br /><searchLink fieldCode="AR" term="%22Hong-Linh+Nguyen%22">Hong-Linh Nguyen</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: Applied Sciences, Vol 10, Iss 7, p 2365 (2020)
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: MDPI AG, 2020.
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2020
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  Label: Collection
  Group: HoldingsInfo
  Data: LCC:Technology<br />LCC:Engineering (General). Civil engineering (General)<br />LCC:Biology (General)<br />LCC:Physics<br />LCC:Chemistry
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22gearbox%22">gearbox</searchLink><br /><searchLink fieldCode="DE" term="%22gear+ratio%22">gear ratio</searchLink><br /><searchLink fieldCode="DE" term="%22optimum+gearbox+design%22">optimum gearbox design</searchLink><br /><searchLink fieldCode="DE" term="%22three-stage+helical+gearbox%22">three-stage helical gearbox</searchLink><br /><searchLink fieldCode="DE" term="%22Technology%22">Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+%28General%29%2E+Civil+engineering+%28General%29%22">Engineering (General). Civil engineering (General)</searchLink><br /><searchLink fieldCode="DE" term="%22TA1-2040%22">TA1-2040</searchLink><br /><searchLink fieldCode="DE" term="%22Biology+%28General%29%22">Biology (General)</searchLink><br /><searchLink fieldCode="DE" term="%22QH301-705%2E5%22">QH301-705.5</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22QC1-999%22">QC1-999</searchLink><br /><searchLink fieldCode="DE" term="%22Chemistry%22">Chemistry</searchLink><br /><searchLink fieldCode="DE" term="%22QD1-999%22">QD1-999</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This study is aimed at determining optimum partial gear ratios to minimize the cost of a three-stage helical gearbox. In this work, eleven input parameters were investigated to find their influence on the optimum gear ratios of the second and the third stages ( u 2 and u 3 ). To reach the goal, a simulation experiment was designed and implemented by a cost optimization program. The results revealed that in addition to the input parameters, their interactions also have important effects in which the total ratio gearbox ratio ( u t ) and the cost of shaft ( C s ) have the most impact on u 2 and u 3 responses, respectively. Moreover, the proposed models of the two responses are highly consistent to the experimental results. The proposed regression equations can be applied to solve optimization cost problems.
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  Data: English
– Name: ISSN
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  Data: 10072365<br />2076-3417
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  Data: https://www.mdpi.com/2076-3417/10/7/2365; https://doaj.org/toc/2076-3417
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.3390/app10072365
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  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.3390/app10072365
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 1
        StartPage: 2365
    Subjects:
      – SubjectFull: gearbox
        Type: general
      – SubjectFull: gear ratio
        Type: general
      – SubjectFull: optimum gearbox design
        Type: general
      – SubjectFull: three-stage helical gearbox
        Type: general
      – SubjectFull: Technology
        Type: general
      – SubjectFull: Engineering (General). Civil engineering (General)
        Type: general
      – SubjectFull: TA1-2040
        Type: general
      – SubjectFull: Biology (General)
        Type: general
      – SubjectFull: QH301-705.5
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      – SubjectFull: Physics
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      – SubjectFull: Chemistry
        Type: general
      – SubjectFull: QD1-999
        Type: general
    Titles:
      – TitleFull: The Influence of Main Design Parameters on the Overall Cost of a Gearbox
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Ngoc-Pi Vu
      – PersonEntity:
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            NameFull: Dinh-Ngoc Nguyen
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            NameFull: Anh-Tung Luu
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            NameFull: Ngoc-Giang Tran
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            NameFull: Thi-Hong Tran
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            NameFull: Van-Cuong Nguyen
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            NameFull: Thanh-Danh Bui
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            NameFull: Hong-Linh Nguyen
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            – D: 01
              M: 03
              Type: published
              Y: 2020
          Identifiers:
            – Type: issn-print
              Value: 10072365
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            – TitleFull: Applied Sciences
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