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<ml:real>100</ml:real> <ml:id xml:space="preserve">Δ°F</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="52" left="18" top="255" width="177.6" height="10.8" align-x="27" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 1 Inner Body Poisson Radial Displacement </text> </region> <region region-id="53" left="36" top="286.8" width="301.2" height="39" align-x="78.6" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Poisson">U</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="axial">Force</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="axial">Force</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">E</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="54" left="378" top="297" width="59.4" height="16.2" align-x="419.4" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Poisson">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="60" left="12" top="345" width="135" height="10.8" align-x="31.2" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 2 Differential Thermal Expansion </text> </region> <region region-id="59" left="42" top="375" width="75.6" height="16.2" align-x="86.4" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="interface">D</ml:id> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="57" left="42" top="388.8" width="261.6" height="30.6" align-x="82.8" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="thermal">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="ambient">Temp</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="shaft">Kthermal</ml:id> <ml:id xml:space="preserve" subscript="hub">Kthermal</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="interface">D</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="58" left="378" top="399" width="69.6" height="16.2" align-x="417.6" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="thermal">U</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="62" left="18" top="435" width="209.4" height="10.8" align-x="28.2" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 3 Outer Body Radial Displacement due to Rotation </text> </region> <region region-id="85" left="42" top="456" width="393" height="39" align-x="88.8" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="86" left="462" top="466.2" width="122.4" height="21" align-x="507.6" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.3613975945876831E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="34"/> </region> <region region-id="66" left="18" top="519" width="206.4" height="10.8" align-x="18" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 4 Inner Body Radial Displacement due to Rotation </text> </region> <region region-id="89" left="48" top="546" width="439.2" height="39" align-x="99" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="shaft">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve" subscript="shaft">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="91" left="510" top="556.2" width="126.6" height="21" align-x="559.8" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.932769006781808E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="101" left="18" top="585" width="83.4" height="10.8" align-x="33.6" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 5 Interface Pressure </text> </region> <region region-id="95" left="36" top="609" width="152.4" height="16.2" align-x="85.8" align-y="618" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="total">Uradial</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="96" left="252" top="604.2" width="125.4" height="21" align-x="300.6" align-y="618" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="total">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.5546744952658642E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="109" left="30" top="651" width="99" height="10.8" align-x="50.4" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Diametrical Interference </text> </region> <region region-id="105" left="42" top="675" width="105.6" height="16.2" align-x="57.6" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:apply> <ml:minus/> <ml:parens> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> </ml:parens> <ml:parens> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="106" left="312" top="675" width="56.4" height="12.6" align-x="326.4" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.010160000000000377</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="107" left="396" top="670.2" width="67.2" height="17.4" align-x="410.4" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00040000000000001487</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="102" left="42" top="716.4" width="336" height="58.2" align-x="54.6" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Δ</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:id xml:space="preserve" subscript="shaft">E</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="103" left="420" top="728.4" width="60" height="31.8" align-x="431.4" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>49.200200095906695</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="104" left="504" top="728.4" width="81" height="31.8" align-x="515.4" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7135.88571778393</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="119" left="12" top="801" width="314.4" height="10.8" align-x="19.2" align-y="810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 6 Hub Radial Displacement of the inner surface casued by Internal Pressure </text> </region> <region region-id="112" left="60" top="822" width="201.6" height="43.8" align-x="104.4" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uinner</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="113" left="318" top="832.2" width="120" height="21" align-x="361.2" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uinner</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0039634358734713208</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="118" left="12" top="879" width="198" height="10.8" align-x="19.2" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 7 Hub Radial Stess caused by internal Pressure </text> </region> <region region-id="116" left="66" top="912" width="203.4" height="43.8" align-x="126.6" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="157" left="300" top="920.4" width="113.4" height="31.8" align-x="359.4" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-49.200200095906695</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="154" left="444" top="920.4" width="134.4" height="31.8" align-x="503.4" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-7135.88571778393</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="49"/> </region> <region region-id="121" left="18" top="969" width="192" height="10.8" align-x="19.8" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 8 Circumferential stress caused by axial Force </text> </region> <region region-id="125" left="42" top="996" width="205.8" height="43.8" align-x="105" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="160" left="306" top="1004.4" width="124.8" height="31.8" align-x="367.8" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>114.31450001318575</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="51"/> </region> <region region-id="158" left="474" top="1004.4" width="131.4" height="31.8" align-x="535.8" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>16579.916471672434</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="128" left="18" top="1053" width="163.8" height="10.8" align-x="19.8" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 9 Hub axial stress caused by axial force </text> </region> <region region-id="129" left="42" top="1066.8" width="129" height="39" align-x="73.8" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve" subscript="axial">Force</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="131" left="234" top="1070.4" width="60" height="31.8" align-x="264.6" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="136" left="18" top="1119" width="160.8" height="10.8" align-x="22.2" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 10 Hub Shear stress caused by Torque </text> </region> <region region-id="137" left="54" top="1144.8" width="126.6" height="39" align-x="80.4" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>16</ml:real> <ml:id xml:space="preserve">Torque</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="138" left="246" top="1148.4" width="76.2" height="31.8" align-x="271.2" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>16.153458839458008</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="140" left="384" top="1148.4" width="78.6" height="31.8" align-x="409.2" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.11137417814324802</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="57"/> </region> <region region-id="134" left="12" top="1203" width="186" height="10.8" align-x="16.2" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 11 Hub circumferential stress at inner surface </text> </region> <region region-id="141" left="48" top="1218" width="342" height="39" align-x="118.8" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:real>8</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> 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item-idref="29"/> </region> <region region-id="60" left="12" top="345" width="135" height="10.8" align-x="31.2" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 2 Differential Thermal Expansion </text> </region> <region region-id="59" left="42" top="375" width="75.6" height="16.2" align-x="86.4" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="interface">D</ml:id> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="57" left="42" top="388.8" width="261.6" height="30.6" align-x="82.8" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="thermal">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="ambient">Temp</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="shaft">Kthermal</ml:id> <ml:id xml:space="preserve" subscript="hub">Kthermal</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="interface">D</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="58" left="378" top="399" width="69.6" height="16.2" align-x="417.6" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="thermal">U</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="62" left="18" top="435" width="209.4" height="10.8" align-x="28.2" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 3 Outer Body Radial Displacement due to Rotation </text> </region> <region region-id="85" left="42" top="456" width="393" height="39" align-x="88.8" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="86" left="462" top="466.2" width="122.4" height="21" align-x="507.6" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.3613975945876831E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="34"/> </region> <region region-id="66" left="18" top="519" width="206.4" height="10.8" align-x="18" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 4 Inner Body Radial Displacement due to Rotation </text> </region> <region region-id="89" left="48" top="546" width="439.2" height="39" align-x="99" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="shaft">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve" subscript="shaft">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="91" left="510" top="556.2" width="126.6" height="21" align-x="559.8" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.932769006781808E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="101" left="18" top="585" width="83.4" height="10.8" align-x="33.6" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 5 Interface Pressure </text> </region> <region region-id="95" left="36" top="609" width="152.4" height="16.2" align-x="85.8" align-y="618" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="total">Uradial</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="hub">Uradial</ml:id> <ml:id xml:space="preserve" subscript="shaft">Uradial</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="96" left="252" top="604.2" width="125.4" height="21" align-x="300.6" align-y="618" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="total">Uradial</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.5546744952658642E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="109" left="30" top="651" width="99" height="10.8" align-x="50.4" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Diametrical Interference </text> </region> <region region-id="105" left="42" top="675" width="105.6" height="16.2" align-x="57.6" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:apply> <ml:minus/> <ml:parens> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> </ml:parens> <ml:parens> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="106" left="312" top="675" width="56.4" height="12.6" align-x="326.4" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.010160000000000377</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="107" left="396" top="670.2" width="67.2" height="17.4" align-x="410.4" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00040000000000001487</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="102" left="42" top="716.4" width="336" height="58.2" align-x="54.6" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Δ</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:id xml:space="preserve" subscript="shaft">E</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="shaft">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="shaft">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="103" left="420" top="728.4" width="60" height="31.8" align-x="431.4" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>49.200200095906695</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="104" left="504" top="728.4" width="81" height="31.8" align-x="515.4" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7135.88571778393</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="119" left="12" top="801" width="314.4" height="10.8" align-x="19.2" align-y="810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 6 Hub Radial Displacement of the inner surface casued by Internal Pressure </text> </region> <region region-id="112" left="60" top="822" width="201.6" height="43.8" align-x="104.4" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uinner</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="hub">E</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="113" left="318" top="832.2" width="120" height="21" align-x="361.2" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">Uinner</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0039634358734713208</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="118" left="12" top="879" width="198" height="10.8" align-x="19.2" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 7 Hub Radial Stess caused by internal Pressure </text> </region> <region region-id="116" left="66" top="912" width="203.4" height="43.8" align-x="126.6" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="157" left="300" top="920.4" width="113.4" height="31.8" align-x="359.4" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-49.200200095906695</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="154" left="444" top="920.4" width="134.4" height="31.8" align-x="503.4" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-7135.88571778393</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="49"/> </region> <region region-id="121" left="18" top="969" width="192" height="10.8" align-x="19.8" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 8 Circumferential stress caused by axial Force </text> </region> <region region-id="125" left="42" top="996" width="205.8" height="43.8" align-x="105" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="160" left="306" top="1004.4" width="124.8" height="31.8" align-x="367.8" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>114.31450001318575</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="51"/> </region> <region region-id="158" left="474" top="1004.4" width="131.4" height="31.8" align-x="535.8" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>16579.916471672434</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="128" left="18" top="1053" width="163.8" height="10.8" align-x="19.8" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 9 Hub axial stress caused by axial force </text> </region> <region region-id="129" left="42" top="1066.8" width="129" height="39" align-x="73.8" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve" subscript="axial">Force</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="131" left="234" top="1070.4" width="60" height="31.8" align-x="264.6" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="136" left="18" top="1119" width="160.8" height="10.8" align-x="22.2" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 10 Hub Shear stress caused by Torque </text> </region> <region region-id="137" left="54" top="1144.8" width="126.6" height="39" align-x="80.4" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>16</ml:real> <ml:id xml:space="preserve">Torque</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="138" left="246" top="1148.4" width="76.2" height="31.8" align-x="271.2" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>16.153458839458008</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="140" left="384" top="1148.4" width="78.6" height="31.8" align-x="409.2" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.11137417814324802</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="57"/> </region> <region region-id="134" left="12" top="1203" width="186" height="10.8" align-x="16.2" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 11 Hub circumferential stress at inner surface </text> </region> <region region-id="141" left="48" top="1218" width="342" height="39" align-x="118.8" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="hub">ρ</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:real>8</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">OD</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="hub">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">ID</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="147" left="426" top="1226.4" width="115.8" height="31.8" align-x="495.6" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.0222347297224794</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="59"/> </region> <region region-id="145" left="600" top="1226.4" width="153" height="31.8" align-x="669.6" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0070480603580840538</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter" power-numerator="-2"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="149" left="24" top="1305" width="180.6" height="10.8" align-x="28.2" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> 12 Von Mises at the inner surface of the hub </text> </region> <region region-id="150" left="48" top="1330.2" width="631.8" height="37.2" align-x="111.6" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σVonMises</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="hub">σθPressure</ml:id> <ml:id xml:space="preserve" subscript="hub">σθCentrifugal</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="hub">σrPressure</ml:id> <ml:id xml:space="preserve" subscript="hub">σZ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="hub">τ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="151" left="48" top="1376.4" width="132" height="31.8" align-x="110.4" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="hub">σVonMises</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> 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