A crankshaft system model for structural dynamic analysis of internal combustion engines

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<ul><li><p> !" #!$%#</p><p>&amp; % ' ( ) * !* %% +,</p><p> ! " # </p><p> $ %</p><p> " &amp; </p><p>' "" () * " </p><p> " +) % )" $</p><p> % , * -" (</p><p>." / ( " )</p><p>+ 0 1 2 </p><p>-. -3 ! 4 ! ! 0 &amp; </p><p>! - </p><p>2 " )</p><p> "(&amp;</p><p> $ " &amp; )</p><p> &amp; ' </p><p> ( " </p><p> " </p><p> * </p><p>"&amp; (&amp; ( ))</p><p> 5"$ " )</p><p> * " $</p><p>1" </p><p> " " </p><p>( " " % </p><p>" &amp; )</p><p>$ " " )</p><p> " "</p><p>% +)</p><p> " " )</p><p> +) "" (</p><p> ". +) </p><p>6 &amp; &amp; </p><p>C40/89: </p><p>" " ( </p><p> " /89 </p><p> ( " * </p><p>! '&amp; &amp; " </p><p> " 0. </p><p> " " </p><p> " </p><p> ;3&lt; /89 " ;=3&gt; )?&gt;#)?! .B C)&gt; )?&gt;#) ?&gt;</p><p>/! $D C40 :</p><p> =)@??A AE ) </p><p> 0 1 2 66B 1 = )@?? C40 : ? )=</p></li><li><p>"3 % "</p><p>"" " ( </p><p> )</p><p>" "3 %</p><p> "3 " </p><p> " ( % " </p><p> F </p><p> ' + )</p><p> &amp; G </p><p>&amp; </p><p>* ( " )</p><p>! &amp; </p><p>% " </p><p> 3 " </p><p> + " "</p><p> ;&amp; 3@</p></li><li><p> ' ' </p><p>(&amp; " &amp; </p><p> %</p><p> H )</p><p> ( NN,, )</p><p> % ' </p><p> &amp; " </p><p>" ( " </p><p>% </p><p>" , * </p><p>+) G H </p><p> % </p><p> H )</p><p> % </p><p>" H ( </p><p> % </p><p> " ( </p><p> ( " H</p><p>( O ' </p><p> &amp; </p><p> " % .)</p><p> &amp; </p><p>"</p><p>% </p><p>% " )</p><p> " +)</p><p> () ( ")</p><p> $ " 6&amp; )</p><p> +) </p><p> 0 </p><p> C40J( : ")</p><p> 0 </p><p> )" $ </p><p>1*&amp; </p><p> " ( </p><p> $ " </p><p> )" $ </p><p>% </p><p>" ." F&amp; "" </p><p> " + " </p><p> "" 6 *</p><p> * &amp; </p><p>" "" + </p><p> G&amp; ( )</p><p> "" "" </p><p> * C40" )</p><p>: G )</p><p>&amp; M </p><p> ". )</p><p>H . 6 (&amp; "</p><p>$ </p><p> )</p><p> 6 )</p><p> $ </p><p>&amp; </p><p> ". ;I3@</p></li><li><p>% . ) $ ( </p><p> % &amp; . ( ")</p><p> C40 % : % $" $ . .( " " </p><p>F 0* C40:&amp; " (B</p><p>=</p><p>"" 0* C40=: 0* C40: )</p><p> ( B</p><p> #</p><p>(</p><p> % </p><p>% </p><p>% </p><p> @</p><p> %</p><p> @</p><p> % @</p><p> % %</p><p> % @</p><p>1 ." % </p><p>% &gt;</p><p>(</p><p> &gt;</p><p> &gt;</p><p> " )" $</p><p> ;I</p></li><li><p>&amp;1$1 , 8 ''' </p><p>% " 0* C40=: " ( $ G &amp; </p><p> " ( )</p><p>% " % ?( " )</p><p> " </p><p> " &amp; </p><p> ) " </p><p> ( ( + )</p><p> 4 " 0* C40?:&amp; )</p><p> " % (</p><p> % % &amp; </p><p> + " 0* C40 : C40 :&amp; </p><p>" " "" "</p><p> ( $ . ; &lt; % &amp; ( )</p><p>&amp; 0* C40#:&amp; </p><p>6 . ""</p><p> "" </p><p>&amp; $ </p><p> $</p><p> &amp; =3 $ )</p><p> )</p><p> " </p><p> " )</p><p> "</p><p> ( &amp; </p><p> "". = 3 %</p><p> " ")</p><p> % ")</p><p> " ( </p><p> " ( </p><p> + </p><p>"</p><p>% () </p><p> + $ C40% : </p><p> " "" " 1-1-A</p><p>/1%//1%/ ;&gt;&lt; 44 2%012%01 ;? ?&amp; I 1 </p><p> R )$ " </p><p> % </p><p> R )$ " 1" R )$ 1" I I</p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 I</p></li><li><p> ' ( </p><p> . M)</p><p> 6&amp; 1-1-A/1%//1%/ </p><p>' % ( " 44</p><p>2%012%01&amp; 1-1-A/1%//1%/ " $</p><p> % ( )</p><p> 6 "&amp; 44 2%012%01 "</p><p> " "</p><p> " &amp; </p><p> ' &amp; </p><p> *&amp; % " </p><p>" ' 1-1-A/1%//1%/ " </p><p> " M</p><p>&amp;1&amp;1 =8 </p><p>% ")</p><p> ( </p><p>% </p><p> " )</p><p> " % "</p><p> ( </p><p> % "" </p><p>" % </p><p> "" </p><p>1 " )</p><p> &amp; )</p><p> "" G </p><p>" +) &amp; </p><p> * &amp; ( + &amp; </p><p> . )</p><p> % </p><p> ( NNO</p><p>,, % </p><p>&amp;11 ,'' </p><p> " " </p><p> " % " . 0* C40#: </p><p>( ( </p><p>( "+ " ( " (</p><p>* * 6 </p><p>( ;I &lt; ;</p></li><li><p>% &amp; "</p><p> " &amp; " </p><p> 1 ' ."&amp; </p><p> * )</p><p> + 9(&amp; </p><p>M " 1&amp;</p><p>' 1 </p><p> + &amp; </p><p> 3</p><p>&amp; ' ( </p><p>% "" </p><p> 6 ( </p><p>" ' </p><p> % ')</p><p> " $</p><p> 6 "&amp; </p><p>$ ' ( ' </p><p>% "" )</p><p> ' ) " )</p><p> ' 6 </p><p>&amp; 6</p><p> )</p><p> &amp; ( H </p><p>9(&amp; +</p><p>J " % </p><p> ( </p><p> ) </p><p> 8# + ( * </p><p>" </p><p>% H </p><p> J. ( </p><p>' C40G I: 6 &amp;</p><p> " </p><p>C40 " " </p><p>) : " </p><p> J. $</p><p>" C40G I: % " </p><p> ' </p><p>&amp; </p><p> 6 ' </p><p>&amp; " ' #&amp; I #C40G I: % ' </p><p> '</p><p>( " ) </p><p>( ' *)</p><p> ' </p><p> " </p><p> &amp; )</p><p> " ' (&amp; </p><p>&amp; " )</p><p> %&amp; </p><p> ( </p><p>' </p><p> ( )</p><p> G " M&amp; </p><p> " " </p><p> ( '</p><p> " % </p><p> * ' " (</p><p> " </p><p>J. % )</p><p>" ' ( $ "</p><p> % "</p><p>' ' )</p><p>) # ( </p><p>% "" )+</p><p> " % )</p><p>+ " </p><p>* ( /31</p><p>* * "</p><p>" ;I</p></li><li><p>% " " " " ( </p><p>( )+ ("+ " % )+ " </p><p> * C40I:</p><p>H 0* C40: %</p><p> ( ( " )</p><p> ( </p><p> + C40 G : G &amp; </p><p> 0* C40I: )+</p><p>" </p><p>% </p><p> % " 9 1</p><p> )</p><p> ( " " .</p><p> ;I</p></li><li><p> ;I#&lt; M </p><p> H </p><p> " &amp; ( " </p><p>=</p><p>( 1) 0* C40=: 0* C40I:&amp; </p><p>+ " </p><p>( ( *</p><p>I </p><p>I </p><p> # </p><p>#</p><p>I </p><p>I </p><p>I </p><p>I </p><p> # </p><p>#</p><p>F 0* C40#: C40#: ( +)</p><p> % ( C40 : </p><p> $ )+ </p><p> )</p><p>( </p><p>%1$1 (= 8'</p><p>% R ( </p><p> &amp; (&amp; 0*</p><p>C40#: C40#: 0* C40#: " </p><p> " 0* C40#: " " " 1* * )+ 6 " ( ( </p><p>0* C40#: C40#:&amp; "I </p><p>I </p><p># </p><p> @</p><p>I </p><p>I </p><p> I </p><p>I </p><p>#</p><p>@</p><p> " </p><p>$ " "+ </p><p> 0* C40:</p><p>%1&amp;1 : 8 !A ' </p><p>' </p><p>% $ () )+</p><p> )</p><p> ;I@&amp;I&gt;</p></li><li><p> I </p><p> I</p><p> #</p><p> I </p><p> I </p><p> I</p><p>/ J . </p><p> " " ( )</p><p> ( </p><p> &amp; </p><p>"( + I 1) C400* C40 : </p><p>C40 :: " &amp;</p><p> &amp; )</p><p> + *$ +</p><p> % </p><p>J . &amp; &amp; % )</p><p> " " )</p><p> ;I&gt;&lt; </p><p> S ;</p></li><li><p> %&amp; % C40" %: " </p><p> "&amp; </p><p> C40G :&amp; </p><p> &amp; NN,, </p><p>&amp; " % ( </p><p>' C40" : </p><p> &amp; )</p><p>" &amp; " % " </p><p> "</p><p> " &amp; " </p><p> % )</p><p> + </p><p> " + C40 :</p><p> C40J(: % ' +</p><p> $ % NN)</p><p>,, &amp; </p><p> &amp; ' % </p><p> "+ ( </p><p>+. </p><p>F " 0* C40I:&amp; 0* C40: </p><p>(</p><p> %</p><p>C40 </p><p>%</p><p>C40 </p><p>%</p><p> ?</p><p>% + ' </p><p> " </p><p> ! </p><p> % % I </p><p> 0* C40&gt;: C40&gt;:</p><p> I</p><p> &amp;</p><p> I</p><p>- 0* C40:&amp; C40I: C40I: </p><p> II</p><p>1 NN,, ) &amp; (* $ 9(&amp; +. &amp; </p><p> 0*</p><p>C40#: 4 &amp; $ </p><p> $ </p><p>1 0* C40II: 0* C40?: B</p><p> %</p><p>C40 </p><p>%</p><p>C40 </p><p>%</p><p> I</p><p>(</p><p> I</p><p>6 &amp; 9( &amp; </p><p> " * 0*</p><p>C40I:&amp; ( "" *)</p><p> 0* C40I: C40I: ." </p><p>F 0* C40I: + </p><p>" &amp; </p><p> "" J( </p><p> ) G )</p><p> "" &amp;</p><p>" " "" ' G</p><p> ""&amp; "</p><p> " ")</p><p>" * </p><p>0* C40I: C40I: </p><p> " </p><p> + /()</p><p> ;I&lt; ( /(3" )</p><p> "&amp; " </p><p> 0* C40I: C40I: "&amp;</p><p> ( " B</p><p>1" B 1" B - </p><p> 9L45 &amp; 1" </p><p>1" IB - ")</p><p> 0* C40I: C40I:&amp; </p><p>1" B - "</p><p> 0* C40I:1" =B - </p><p> 0* C40:&amp; 1" </p><p>1" #B 6 ' ( 9L45 &amp; " " " 1" 5(&amp; "</p><p> . "</p><p>% 0* C40I: C40I: )</p><p> " 3</p><p> % " </p><p> ( (</p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 ?</p></li><li><p> C40 :</p><p>% " )</p><p>* " "</p><p>, ! </p><p>31"1 8 ! A! </p><p>6 ." </p><p> "" &amp; </p><p>+) ) C402=: ( ")</p><p> +) </p><p>-/K1L ( " ")</p><p> "" % " 2= </p><p> ()")</p><p> C40O5%: " </p><p>( ( </p><p>G = # ( " )</p><p> 2= &amp; " </p><p>NN(,, % " </p><p> "</p><p> ' </p><p>" / </p><p>" "))" " C40</p><p> "))":&amp; " % </p><p> ( ( -/K1L</p><p> " ."</p><p> # " = ( -/K)</p><p>1L, " S )</p><p> % ' ( </p><p>G&amp; </p><p> , "</p><p>( , </p><p> "</p><p>% </p><p> " ( </p><p>' " %</p><p> "" ( )</p><p>* )</p><p>" % </p><p> ' </p><p>G = )&amp; +) </p><p>G # 1 )&amp; +) </p><p>G @ )&amp; +) </p><p>( , </p><p>G &gt; 1 )&amp; +) </p><p>( , </p><p> 011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3</p></li><li><p>G ? % +) "33J." 8# </p><p>G 4 </p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 </p></li><li><p>&amp; ' ( </p><p> ( ."</p><p>% " ( </p><p> ( , </p><p> " % </p><p>( ' * </p><p> % ' ( </p><p> ,</p><p> * )</p><p> """ % ' </p><p>" ' , </p><p> + " ( )</p><p>" " ( A- </p><p>6 </p><p> , &amp; )</p><p>, ( " C40 : )</p><p> &amp; ' , "</p><p>G&amp; " ( , )</p><p> ( " ( )</p><p> " G @ </p><p>&gt; ( " </p><p> 2= &amp; " %</p><p> ( . / " </p><p> " )</p><p>, " </p><p>31$1 8 # C40% 8# &amp; ( G ?&amp; </p><p> " "" )</p><p> " " </p><p> 3 F )</p><p> " J." </p><p>% +) #&gt; </p><p> &gt;?# C40#&amp;&gt;&gt;# : % </p><p>( " = " %( $ (</p><p> + </p><p>F </p><p>" 3)</p><p> 3" ( </p><p> " </p><p>% ' )</p><p> "" ( </p><p>G % $ ( </p><p> $ "</p><p> + " </p><p> ' &amp; /A</p><p> $ " (&amp; .</p><p>G 0' ' </p><p> 011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3</p></li><li><p> .</p><p> $ "</p><p>1 ' . </p><p>$ </p><p> H ( </p><p>&amp; "</p><p>G ' ' </p><p> % &amp; J. </p><p>" &amp; /A</p><p> ' J. ( ")</p><p> % ' </p><p> # &amp; =&amp; /A</p><p> (</p><p> + ( "</p><p> ' ( </p><p> % ' </p><p> &amp; ( </p><p> % " </p><p>' </p><p> " </p><p>C40 :</p><p>% J ' </p><p> $</p><p> ( G </p><p> % " C40</p><p> : ' &amp; /A</p><p> G &amp; ' )</p><p> ( = &amp; = &amp; /A</p><p> " C40: </p><p> C40 ": </p><p> &amp; " % </p><p>( &amp; /A</p><p> ( " </p><p> ( +&amp; </p><p> ' . </p><p> "". I / .</p><p>$ "". </p><p>/</p><p>G I ( ' </p><p> % </p><p> + </p><p> "( </p><p> ' &amp; /A</p><p> % ")</p><p> $ </p><p>9(&amp; </p><p>% </p><p> &amp; ( </p><p> * " )</p><p> G &amp; </p><p>G 0' ' </p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 I</p></li><li><p> " ( )</p><p>" &amp; </p><p> '</p><p>G I 0' </p><p>G 0' </p><p> 011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3</p></li><li><p>G = - H " </p><p>G # - + </p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 =</p></li><li><p>% ' </p><p> ( G </p><p>= </p><p> ' &amp; /A</p><p> ( </p><p> +&amp; </p><p> . </p><p> . $ G =</p><p>( </p><p> % ' (</p><p> ( 4 </p><p> &amp; </p><p> 1 J </p><p> &amp; </p><p>( ( " )</p><p> G&amp; G # ( + )</p><p> % + </p><p> = ." + ( % " G</p><p> &amp; + </p><p> ( = </p><p>(</p><p>% ( ." 4</p><p>% F 1 4)</p><p>"</p><p> R ( 4 </p><p>" ." " </p><p> "" G&amp; ' "$</p><p> $ -/K1L ( R</p><p> "" 9 ( .)</p><p>" )</p><p> " </p><p>" -/K1L " ( </p><p>;&lt; 9 &amp; %" &amp; $ - )</p><p> " 3 ( I)4 "" 10 "" </p><p>? &gt;@&amp; ??</p><p>;&lt; 9 &amp; / - 3</p><p> + *</p><p>10 6-0 ?&gt;?!?</p><p>;I&lt; K &amp; K &amp; % K&amp; /( 0</p><p>4 " </p><p> B M $</p><p>/1%/ " F 0 1</p><p>" ?&gt;&gt;!#C40:</p><p>;&lt; )</p><p>3J( 8# 0 10</p><p>6 ??= / 8</p><p>-&amp; &amp; 10 "" ?=@#&amp; ??=</p><p>;=&lt; K$ %&amp; 9 L&amp; 9( L&amp; K K</p><p> 10 "" &gt;I I#&amp;</p><p>?&gt;I</p><p>;#&lt; 6 1&amp; T %&amp; 5$( K&amp; 6$( K 6" </p><p> * ( J( </p><p>J. 10 "" </p><p>? I?&amp; ?? </p><p>;@&lt; 5 K&amp; / ( </p><p> 10 "" </p><p>@? I#=&amp; ?@?</p><p>;&gt;&lt; 4H T </p><p> * 6B 9 &amp; K &amp; </p><p>0 &amp; .&amp; /(</p><p>LB ! ?&gt; " I3#</p><p>;?&lt; O O 4 </p><p>1 %&amp; - T&amp; ?&gt;</p><p>; &lt; K 9&amp; 6( &amp; 1 % 4 </p><p>" 6 0&amp;</p><p>" -I A ?&amp; ?? " =3#</p><p>;&lt; / 4&amp; 1 19 -" " </p><p> 3 10 ?&gt;?!40)&gt;)BI@?3&gt;=</p><p>;&lt; 21&amp; &amp; 1 &amp; G </p><p>J. ( J. </p><p>1-1-A/1%//1%/ 441441 ??= 1- O T,</p><p>-&amp; ??=</p><p>;I&lt; 6%&amp; 2( F J(</p><p> 6 0&amp; " </p><p>-I&gt;A #&amp; ?&gt;?</p><p>;&lt; 2( F&amp; 9 K </p><p> " = -6-</p><p>-&amp; &amp; ?&gt;I</p><p>;=&lt; 5 9&amp; 1 &amp; L %&amp; 1$ &amp; 1</p><p>K ' . "" </p><p> ) </p><p> 6B "" </p><p> 10 O &amp; 4&amp; %U&amp;</p><p>?? </p><p>;#&lt; %&amp; 5 9 ' .</p><p>"" ) </p><p> B "" </p><p>+ 10 O &amp; 4&amp;</p><p>%U&amp; ?? </p><p>;@&lt; 5 9&amp; % 6J 3"</p><p> )</p><p> 10 6 </p><p>??I / 8 - 10 "" </p><p>?II I&amp; ??I " I?3I&gt;</p><p>;&gt;&lt; 1 - - " )</p><p> 4 %&amp; - T&amp; ?@</p><p>;?&lt; F G 4 H B )</p><p> "" % 10&amp;</p><p> 2 % ?@!?IC40:</p><p>; &lt; H" 1&amp; -$ G20G20B (</p><p>" </p><p> 66B ." 10 </p><p>1)?? 0 %&amp; 10 "" ? &gt;&gt;&amp; ??</p><p>" =@3#=</p><p>;&lt; R K&amp; H" 1 ( </p><p> R 10 1)</p><p>?? 0 %&amp; 10 "" ? &gt;?&amp; ??</p><p>" #@3@=</p><p> # 011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3</p></li><li><p>;&lt; 6 &amp; 9 L&amp; K$ % </p><p> H +</p><p>10 "" &gt; @@&amp; ?&gt;</p><p>;I&lt; M </p><p> ( $ 1 8</p><p> !I&gt;C40I:B?=3=@</p><p>;&lt; O 02&amp; L O&amp; 4 4 </p><p> "" $ 0* 0</p><p>1 4 ?&gt;! B&gt;I3</p><p>;=&lt; &amp; - 2&amp; - &amp; R 4 "")</p><p> $ </p><p> -" 1 ?&gt;=!B#3@</p><p>;#&lt; O 02&amp; F 0 T " $ </p><p> 1 0 ?&gt;#!C40&gt;:B</p><p>?3=</p><p>;@&lt; 2 &amp; O 02 R " $</p><p> 0</p><p>-" ?&gt;@!BI ?3&gt;</p><p>;&gt;&lt; R &amp; &amp; 1-1-AA/1%//1%/B )</p><p> % / 3 1( -"&amp; ?&gt;I</p><p>;?&lt; &amp; &amp; 1-1-AA/1%//1%/B T, %</p><p>/)1( -"&amp; ??</p><p>;I &lt; F K&amp; O 02 / + </p><p> 0( -' /B )9! ?@#</p><p>;I&lt; 5&amp; 1 F % )</p><p> /( LB R()9! ?#</p><p>;I&lt; F( 40 % " </p><p> H % 10&amp;</p><p> % ?&gt;#! &gt;B#&gt;3I&gt;</p><p>;II&lt; H" 1&amp; R K </p><p> 1%20 % %</p><p>?? !IIC40I:BIII3</p><p>;I&lt; 1$ &amp; %&amp; &amp; (</p><p>/( LB 9"! ?&gt; </p><p>;I=&lt; - % "" /( LB</p><p>O! ?##</p><p>;I#&lt; K &amp; 2 O - M </p><p> H &amp; "" 10</p><p>" &gt;=)%)@ 10A120 2 -)</p><p>&amp; &amp; R&amp; 5 ?&gt;=</p><p>;I@&lt; R K 4 H B +)</p><p> % 10&amp; % 1 G</p><p>?&gt;B?3I?</p><p>;I&gt;&lt; &amp; R G) </p><p> 1/0 % ?&gt;=!</p><p>?IB=3=?</p><p>;I?&lt; F %&amp; 2 OK&amp; K 9 </p><p> " 6B 1&amp; /&amp;</p><p> -" </p><p>&amp; =&amp; 10A4 1 </p><p> 0&amp; /( L&amp; ?&gt;I " I@3#I</p><p>; &lt; K / G 4")</p><p> 0&amp; % T </p><p>&amp; ?&gt;=</p><p>;&lt; K 9&amp; R&amp; %)</p><p> H 10 % ?&gt;@!</p><p> ?C40:</p><p>;&lt; M + </p><p> % % !C40I:B</p><p>I=3=&gt;</p><p>;I&lt; /( / " </p><p> 1 -</p><p>0&amp; ?=?</p><p>011 ' 2 ' ,'' 3* C40$ "5 $ *6$ $3 @</p></li></ul>

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