Mathcad Professional 14.0 <description/> <author>delete</author> <company/> <keywords/> <revisedBy>delete</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>B9659800-A3D2-4AB6-B999-CBCA60D8DED7</documentID> <versionID>2C2DECDA-E3A4-48FD-AC78-7704B8F637DE</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#00f"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="14" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="bold" font-style="italic" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 3"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="16.8" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="11.4" margin-right="0" text-indent="-11.4" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="86.4" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.2" page-height="841.8"> <margins left="56.66457" right="70.86614" top="56.66457" bottom="56.66457"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="120"/> <miscellaneous> <handbook handbook-region-tag-ub="1502" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1360" left="6" top="4.8" width="414" height="28.8" align-x="6" align-y="18" 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"> <p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">Example 3.8</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="11"> <b> <inlineAttr line-through="false"> <c val="#800000">Designing an interference fit (press-fit, shrink-fit, expansion-fit).</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="1361" left="6" top="36" width="361.8" height="4.2" align-x="6" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="360.6" display-height="3"/> </picture> <rendering item-idref="3"/> </region> <region region-id="1363" left="6" top="45" width="442.2" height="11.4" align-x="6" align-y="54" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="40.2"> <b>Problem: <tab/>Calculate the mounting force, transmission torque and stresses.</b> </p> </text> </region> <region region-id="1366" left="6" top="63" width="37.2" height="10.8" align-x="22.8" align-y="72" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Notation:</p> </text> </region> <region region-id="1367" left="54" top="58.2" width="59.4" height="17.4" align-x="78" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">GPa</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>9</ml:real> </ml:apply> <ml:id xml:space="preserve">Pa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="1368" left="138" top="58.2" width="61.2" height="17.4" align-x="163.8" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">MPa</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>6</ml:real> </ml:apply> <ml:id xml:space="preserve">Pa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="1061" left="6" top="81" width="24" height="10.8" align-x="16.2" align-y="90" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Input :</p> </text> </region> <region region-id="1062" left="42" top="81" width="53.4" height="12.6" align-x="52.8" align-y="90" 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">r</ml:id> <ml:apply> <ml:mult/> <ml:real>11.5</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="1063" left="102" top="81" width="32.4" height="12.6" align-x="114.6" align-y="90" 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">d</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="1064" left="150" top="81" width="48" height="14.4" align-x="162.6" align-y="90" 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="i">r</ml:id> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="1065" left="204" top="81" width="50.4" height="14.4" align-x="219" align-y="90" 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="o">r</ml:id> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1066" left="270" top="81" width="50.4" height="12.6" align-x="282" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">δ</ml:id> <ml:apply> <ml:mult/> <ml:real>0.001</ml:real> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1078" left="336" top="81" width="26.4" height="12.6" align-x="348.6" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1067" left="42" top="105" width="57" height="14.4" align-x="56.4" align-y="114" 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="i">E</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">GPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1068" left="114" top="105" width="59.4" height="14.4" align-x="130.8" align-y="114" 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="o">E</ml:id> <ml:apply> <ml:mult/> <ml:real>210</ml:real> <ml:id xml:space="preserve">GPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="1069" left="186" top="105" width="35.4" height="14.4" align-x="201" align-y="114" 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="i">ν</ml:id> <ml:real>0.3</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1073" left="240" top="105" width="37.8" height="14.4" align-x="257.4" align-y="114" 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="o">ν</ml:id> <ml:real>0.3</ml:real> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1076" left="294" top="105" width="38.4" height="12.6" align-x="307.2" align-y="114" 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">μ</ml:id> <ml:real>0.15</ml:real> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1482" left="0" top="126" width="4806.6" align-x="0" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1080.6"> <confidentialArea item-idref="21"/> <rendering item-idref="22"/> </region> <region region-id="1433" left="6" top="147" width="86.4" height="10.8" align-x="31.8" align-y="156" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Transmission torque:</p> </text> </region> <region region-id="1434" left="114" top="147" width="61.8" height="12.6" align-x="126.6" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve">μ</ml:id> </ml:apply> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1435" left="186" top="142.2" width="78" height="17.4" align-x="197.4" align-y="156" 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">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3277.3060649102226</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="1436" left="276" top="140.4" width="37.2" height="27" align-x="288.6" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="1437" left="330" top="147" width="64.8" height="12.6" align-x="341.4" align-y="156" 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">T</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>37.689019746467558</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="1483" left="6" top="183" width="109.2" height="14.4" align-x="55.8" align-y="192" 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:apply> <ml:id xml:space="preserve" subscript="r">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-17.768675191807525</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="1484" left="216" top="183" width="103.2" height="14.4" align-x="265.2" align-y="192" 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:apply> <ml:id xml:space="preserve" 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