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设一对中心距为110的齿轮 齿数比为6：5 则大齿轮的参数方程为：x=60*(cos(t)+t*sin(t)) y=60*(sin(t)-t*cos(t)) 根据啮合原理 利用matlab编程
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>> x=60*(cos(t)+t*sin(t))2 H& R$ O) c* V) `8 A0 `
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9 z6 ~! ` |. `( J, Ux =
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~# k; M$ q# x; H60*cos(t) + 60*t*sin(t)! a" e8 H( F% n+ Q9 C: A( a0 ]- V
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>> y=60*(sin(t)-t*cos(t))* K& S; E, F+ ~. B
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60*sin(t) - 60*t*cos(t)8 d7 }: t" b/ X9 \2 @& Q$ H
( ?) _1 A' v6 D' _( e. _9 J>> x1=-x*cos(11/6*q)-y*sin(11/6*q)+110*cos(q)9 [- o5 h4 D+ R$ h' _$ M I
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x1 =% u, w- Q! A" I) D, G" ~. X
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# {/ V, C+ c m. }110*cos(q) - cos((11*q)/6)*(60*cos(t) + 60*t*sin(t)) - sin((11*q)/6)*(60*sin(t) - 60*t*cos(t))% r4 `" c4 Y! G$ |/ B) U$ g) X( H
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; a9 u6 |* i; l/ {+ n7 K* Z- L>> y1=-x*sin(11/6*q)+y*cos(11/6*q)+110*sin(q)- G3 q* t" b0 A( q1 s7 Z
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y1 =! M# {+ h( H5 s0 b% Q' T6 ^) d
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110*sin(q) + cos((11*q)/6)*(60*sin(t) - 60*t*cos(t)) - sin((11*q)/6)*(60*cos(t) + 60*t*sin(t))
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3 |. \3 c c" F) e8 _2 i>> diff(x1,t)! h. a/ N: O2 V2 K: w. C5 X
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ans =# E9 ~0 V5 K7 l! H% f |) _) d
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- 60*t*cos((11*q)/6)*cos(t) - 60*t*sin((11*q)/6)*sin(t)" v9 m# E+ O* ?: k6 f7 P: Z- l3 a2 v+ j& G' }) {
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>> diff(y1,t)+ N! `! Q( i3 @% n9 o- D7 ?+ j G8 }! \! o
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. ]; i% M" d+ N* H- t6 u60*t*cos((11*q)/6)*sin(t) - 60*t*sin((11*q)/6)*cos(t): ~7 j8 B# U+ w+ i3 q9 ~ ]3 v# v* r
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& {9 y8 l* ?- Q6 X) F5 F>> diff(x1,q)3 m$ q' {! }: S# g5 S' O$ k
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" [" a! B1 \9 N1 x# v: p4 a( Ians =$ W7 o4 ^' @. m* u/ [& R
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(11*sin((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6 - (11*cos((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6 - 110*sin(q)+ z3 V0 _& w6 O3 X
% u! g5 `, Q7 T8 g- }>> diff(y1,q)3 J5 s6 T9 l" G$ S! f! T; j9 e' S8 z) L5 ^# |) d7 L: g
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ans =
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9 d( w R6 v7 L! s9 m& B110*cos(q) - (11*cos((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6 - (11*sin((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6
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# _& `: v4 g1 k4 j7 x# e' C>> f1=sym('(110*cos(q) - (11*cos((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6 - (11*sin((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6)*(- 60*t*cos((11*q)/6)*cos(t) - 60*t*sin((11*q)/6)*sin(t))-((11*sin((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6 - (11*cos((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6 - 110*sin(q))*(60*t*cos((11*q)/6)*sin(t) - 60*t*sin((11*q)/6)*cos(t))')
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, U) F Z5 z5 M4 r# _f1 =
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) `( a z2 t. P. V& t(60*t*cos((11*q)/6)*cos(t) + 60*t*sin((11*q)/6)*sin(t))*((11*cos((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6 - 110*cos(q) + (11*sin((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6) + (60*t*cos((11*q)/6)*sin(t) - 60*t*sin((11*q)/6)*cos(t))*(110*sin(q) + (11*cos((11*q)/6)*(60*sin(t) - 60*t*cos(t)))/6 - (11*sin((11*q)/6)*(60*cos(t) + 60*t*sin(t)))/6)4 R4 r9 [4 x ]& {9 G- ]: E; t- P
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, C, @/ u. }5 h6 I! _* C3 K4 y>> simplify(f1)) [ m8 o C& N b2 a/ @
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( t6 c" Y4 ~" C/ J% H" L8 kans =4 i' A% H% c% V; u# N# ~4 ?
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% ]. s3 k3 L k) S-6600*t*(cos((5*q)/6 - t) - 1)
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-6600*t*(cos((5*q)/6 - t) - 1)=0 解得q=6/5*t 代入 x1=-x*cos(11/6*q)-y*sin(11/6*q)+110*cos(q) * q1 K: y3 z1 G3 m4 N- }% z2 A+ J
; S: L3 p3 W% m; O y1=-x*sin(11/6*q)+y*cos(11/6*q)+110*sin(q) & t: J, }3 Q1 P9 P" _
化简后得X1=50*(cos(1.2*t)+1.2*t*sin(1.2*t)) y=50*(sin(1.2*t)-1.2*t*cos(1.2*t))
# i8 M. d* w* C& N/ ]从方程上可以看出小齿轮的方程仍为渐开线8 c! B5 ?3 p- C7 e. H9 e% c1 V6 {
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发表于 2015-5-15 21:37:12
