螺杆转子刀具设计 数学模型$ P' `; k& \1 L# w+ h8 E. B7 V
C3 h# n5 p! t$ @, d( M$ j
解如下方程:1679999.7*sin(x)-1679997.5*cos(y)*sin(x)-1499997.5*sin(y)*cos(x)-75000*sin(x)^3-179999.4000005*y*cos(y)*cos(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)=0 N! k2 }/ V7 b# b! x( D: E" ]& ?
求当x=-1.361时 y=? ( K/ K/ H0 V9 @8 a# b8 a, R
>> syms x y# p- y3 p. z- q0 [6 K" h
>> f=1679999.7*sin(x)-1679997.5*cos(y)*sin(x)-1499997.5*sin(y)*cos(x)-75000*sin(x)^3-179999.4000005*y*cos(y)*cos
* I L# d8 y" K0 m7 d' \& M3 r' J% [' E! n' o% e3 y
(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
$ J* [% y8 W1 J/ ]' }* O0 o% v/ Z3 A7 H( r
f =; G- ?% t$ ?( w7 s1 h5 i4 Z
" s8 \! D; U/ a5 c1 D1 P
(7215543768789811*sin(x))/4294967296 - (2999995*cos(x)*sin(y))/2 - (3359995*cos(y)*sin(x))/2 - 75000*sin(x)^3 + 75000*cos(x)*cos(y)
& {) s5 M, p) S0 ?6 a5 ?
1 t- j0 `5 @1 k* G% s*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368
c# I0 k& S+ ]$ |( `
0 [) A+ M* N2 H>> subs(f, x, -1.361)
9 g, _# p; f* L2 X( Y
3 d$ e5 y b4 }* Z# Rans =9 o# o" r O) W( w# x
, G% y/ y: M* o! N. i
(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin) [2 R( B' H% T; G: E! v2 r3 W9 X+ d
7 E. t- Y) q3 w2 f, S(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -
+ s% ^/ C+ F8 {7 \; d r" t
- @+ v( g& a7 Y/ ^(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368, d% I+ w. f- Y0 G ?
, o5 `) [8 E V/ x) |9 R
% [2 H7 C6 D8 T# C>> a=0; b=1;4 Y H$ S k- b( M1 \5 k
eps1=1e-8;eps2=1e-8;
1 P9 Q. E( ^2 [( v* }3 n( A2 { N=300;3 i! G- d2 ?# b( ?2 l a6 S/ \
f=@ (x) ((3359995*sin(1361/1000)*cos(x))/2 - (2999995*cos(1361/1000)*sin(x))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin(1361/1000)^3- 75000*cos(1361/1000)*sin(1361/1000)*cos(x) - (6184732290414159*x*cos(1361/1000)*cos(x))/34359738368 -(6184732290414159*x*sin(1361/1000)*sin(x))/34359738368); ; {/ k# V* s( B: g! }1 ?
Hfun=@Bisection;
2 s8 Y/ m! E% T1 M% G6 D- V4 M[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
. m; d! F4 o+ D0 e0 r/ f
: ~5 V" {/ a5 n运行结果- n- L6 X7 @/ v7 z
k ,a ,b ,x, f# R* g0 n x* D8 ? [
1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
- A, h8 N! I4 U4 H3 K' m) ] _5 j 2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711," g5 v( I+ h K9 R3 t
3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,' S" U u l& _
4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,, x% O6 y0 r$ d8 G) L& x
5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,6 `. G; m! c+ I9 b! W1 h
6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
* Y( v# G/ y/ d8 f/ f _1 u1 @ 7, 0.109375000, 0.125000000, 0.117187500,430.092693351,: m1 r- Q. w- M. \
8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,. w" H1 P. K# W
9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,. O$ S: U' l; z# G) I, c/ x
10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,9 L7 \: k/ X5 ^; B, V. F
11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
4 Y1 f3 E8 h, g 12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
* H, ~+ a- V. U 13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,4 F5 n! |, R3 E0 t0 U5 [" I9 k
14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
6 A' {3 U! r! ` 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
! k1 t( @5 P/ v( R$ G- j 16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,/ A8 f- H. Y) B
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
/ E8 c. T' ^& C L/ p 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,! W6 D- n. o7 J q
19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
3 U; B0 j" I# I; q9 [ 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,; B+ U) f- b Q0 ?# u( l* f
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
, `. ?5 R- s* D8 L ]2 a) } 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,( i$ }9 P) ~6 m; M
23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,8 @( R+ K0 U' E
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,3 T* K3 t: b; ], |+ ]
25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
2 r/ j# d% v! b( A/ l- k. ` 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,7 F# s: q5 P) [$ v( c* _9 M
27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
/ M: |4 `! N: G5 F>> # X) t6 `: V8 s+ }$ l' [' a
, B( K9 S% \% W7 v结论 当x=-1.361时 y=0.117930219
1 Z+ B! e0 K2 k按此方法 可依次 得出150对x与y的值
* K9 x3 K; f, B* V |