螺杆转子刀具设计 数学模型
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: \8 _5 f9 k! ?$ ]- |% O8 U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
% D& ^4 l' ^, [# X求当x=-1.361时 y=?
! R4 G8 C" M$ P8 w2 J>> syms x y/ J, n! D9 O; H G: L6 l
>> 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
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5 b ]6 r, A: l! D* x. L(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)$ c# P' ^9 ]) J$ Y! G
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f =3 h8 M( D4 r- A2 H- X; o: v
1 V4 Z- b$ P7 ]
(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)$ z' ] R1 N0 ?2 K1 C( u8 V& f
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*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/343597383685 i: V5 w# }$ Y/ B
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>> subs(f, x, -1.361): z; C" [4 q( z3 s2 I" s. u
1 [. L! C, `6 A( ?ans =" O8 b0 {9 j9 ?5 X9 d5 i6 s$ N
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(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin
+ J& L0 w( k q6 q6 b5 ]- Z1 g# {( G- V* r, e
(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -
9 X2 k. j9 V2 P) a/ k$ k
0 g8 K: O; i7 ~2 l/ @; u(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368! w- Q9 i+ ]0 C( \" m* I. y
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2 o# U- K; K* f1 q7 b* F9 k9 h>> a=0; b=1;
; M @1 j( s. {# c9 w5 \3 x- M* w4 t$ leps1=1e-8;eps2=1e-8;
5 }) e x0 y+ z9 o* g; A, w5 V N=300;
2 R6 j/ q3 m6 g2 s" p* y+ nf=@ (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); ! N* P3 d- g& T* w6 a1 W
Hfun=@Bisection;$ W7 G7 o& M& @- q
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);. Y' ~5 ~! m! f; I) @' g6 ^
$ c) S% H- \6 n; x6 S0 Y) m. b运行结果) \: V- h y. u" V# I6 k8 T
k ,a ,b ,x, f, R: Y8 i# a& T. R: ?
1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
! J0 B* G9 ~$ `5 o0 Z$ ?5 O 2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
; t& H9 }$ v: b! T* N 3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
9 S9 O8 |1 r3 |. J, U/ A 4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,4 R; _9 C7 [: g, U# w5 V6 m
5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,! R1 ?; P$ u0 T. c
6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,. [' w9 f1 H# `) b- Y) j
7, 0.109375000, 0.125000000, 0.117187500,430.092693351,, _! ~, c! }: {1 S( m
8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,' p9 \8 k. [& H+ @
9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
# W0 w; F& `2 A! \, z 10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
$ s' O D3 n' d+ j) e( N 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
7 Q& u9 ^( T1 i; e; J8 F 12, 0.117675781, 0.118164063, 0.117919922,5.969190901, B& V% A- l+ L5 I5 E
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,- L* V, O5 } }! ], e/ Z1 P
14, 0.117919922, 0.118041992, 0.117980957,-29.420780403, Q0 M8 O. A2 g
15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
$ \7 U: ^2 D; O6 N* C' n7 m' V5 z5 T' k 16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,& e: ~" h7 T! x
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
7 s8 z, T# e$ N$ t) }1 {$ A# m 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,8 S/ ~: O( g9 U7 f+ n4 v0 ^. _
19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
7 C, n$ H! L* z. \$ e( f+ g 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
( h% ]/ t0 @4 A1 l5 Z 21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
% V7 ?) U8 P M) q5 d# N9 v 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,# j; ^- z U# D9 L; g
23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,# {1 _- p' w8 W/ a
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
) e9 X; n2 m8 D) {4 \+ S 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,# a5 L& d, k/ D+ e
26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,* m# k) y1 T! Z9 P
27, 0.117930204, 0.117930219, 0.117930211,0.003680972,# d5 V5 z J6 M
>> 6 M* _4 T( y6 ~2 p, Z5 ^
+ j9 Y! k6 {) U6 [- v" p8 S结论 当x=-1.361时 y=0.117930219
# U+ r/ {" m( H9 o" M+ i按此方法 可依次 得出150对x与y的值
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发表于 2015-6-4 11:00:10
