螺杆转子刀具设计 数学模型4 @" {7 C; s- k: ^; y( q
' y9 m% C# y1 c6 w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
, t: f8 A7 @" d5 Z' m" z1 V求当x=-1.361时 y=? + K7 v8 c+ S& F
>> syms x y% i# o% Q5 f& E1 i
>> 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- S+ W% V2 ~6 Q+ B' w% R7 i7 u: R" d
5 ?' M. c2 U0 @& C(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
, p3 G0 _# I4 F0 I* X2 o* u* {5 I" V) _2 \! c! T1 x
f =
9 i! O( k! n; ?% k& v) ]2 K. `! X* w5 N
(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)
* S) G0 c, W+ O, L1 J( V$ U
. t5 I; h+ X) m" R! f2 S% W0 [*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/343597383686 L5 @& d5 m' p( f K1 f
( F$ }0 v8 p' ~: f1 c1 |7 m$ y% ]+ s>> subs(f, x, -1.361)
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7 X6 ~/ g$ G/ u) B7 f1 k8 E tans =9 O, H. O3 [: P* I& T7 _, h/ r2 d
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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* F* s3 T" K& C9 B
, g) P+ \% w7 ?& O; \(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -
' H. _, o) H0 M7 x2 o
. n6 W& M- S8 B0 A5 ^. B: y(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368) E6 ?' P8 f/ {- T' {
6 A& i/ t- L W! F
0 Z! A. Y8 L4 a7 O, u* Z>> a=0; b=1;
T8 \. y/ `( l0 T& n5 h* aeps1=1e-8;eps2=1e-8;
0 p( E; l7 i- Y v" j3 b N=300;
* N$ S1 M" b) ]0 g% {& mf=@ (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); : j6 V/ l$ l# G, X
Hfun=@Bisection;
0 x+ G2 |: Z- y" N[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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运行结果8 o8 P. V1 m* o( ]
k ,a ,b ,x, f
1 b$ p [3 Q) V' j1 j) k3 g( Q& R 1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,7 c* X! b1 A1 x$ f D m3 t
2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,! J. Z1 k( Y: ]: L4 L# l
3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,( K! _5 s8 J# m0 y% Y
4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
]% _% _, B) K. X8 G 5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
* {. t' R" j) d$ O$ U 6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,) m4 l" G/ Y$ e, c& \ i# Y% y( f
7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
) W8 C; m5 }2 z# z7 w 8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,) x w- O! J' @
9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
; ~* W3 J& O q2 }$ E 10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
) y% K6 R6 \6 A& Q 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,# w* O2 J6 R# u2 j |8 ]
12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
L q% }, g1 ?. E: P' j3 {- \ 13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,8 ~4 h* _8 G2 {) G. H) m
14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
5 K( s: X* ?) l5 ~) i/ f 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,+ n; I% [! c# Z. S
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,2 @- b' W( j/ O; `3 a' x: ]. Y
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
) B! z$ U3 J. k! b2 z* V, J! h 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
9 W8 `$ y9 |0 z- Y" a 19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
( C1 c6 L* A2 w& P0 { 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,; G; i: B5 p- @0 L% S% i/ z7 Z9 |; X
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,, c+ A; }% Z/ J+ g/ v
22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
/ ~' i4 L u- _$ }: W0 l, ? 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
7 ]3 {8 o8 \9 I9 O+ C# o 24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
0 N+ J ?3 O6 |6 `+ D1 H+ M 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
, Q$ |8 f) M- I: d; Q4 E 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
# I5 Y2 b; m% U4 T6 F 27, 0.117930204, 0.117930219, 0.117930211,0.003680972,4 q: w2 Y- O/ F2 S* g
>> 7 X* x# E z6 U" H$ J/ _% ?
" ?$ n, |' A# @& ~% n结论 当x=-1.361时 y=0.117930219
# ~" A, g. a' K Y1 y8 l按此方法 可依次 得出150对x与y的值0 n; y! h: w& G% O
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