螺杆转子刀具设计（2） matlab 解法

shouce

螺杆转子刀具设计 数学模型
  o1 b5 ^4 ^! C2 G/ g
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& l6 x) {, g. t! v0 q- U求当x=-1.361时  y=?  
2 C4 X+ ?' r7 |- O>> syms x y
>> 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( \- v0 n7 R! s$ b(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
4 \" x& ]" ^! ?7 v( f
f =
* L- Q1 D" g+ F3 [! B3 M, j" 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)

2 c: D+ O- R7 T2 H) W; q# v. ?*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368
; H" w" R2 M6 [
>>  subs(f, x, -1.361)

. }. d) D9 G: d) R+ v# I# Wans =

, |. G5 A% r7 t: H' I$ P(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin

0 p! \! v% q) j& i2 S( ?* k! W(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -

  c7 s0 |8 e; y% I: Y0 a$ E(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368
& p' U, b& r  t
' N; g6 l# p& S2 ~! i* J
2 F" ~8 q2 A$ J, n# t' G5 A>>  a=0; b=1;
- a% P% `! o" ^eps1=1e-8;eps2=1e-8;
+ b& _9 f( v% s N=300;
# V* G( W/ _& B) L9 g$ A/ jf=@ (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);
4 ?7 ?* ?2 d0 W( |$ VHfun=@Bisection;
* S! t* f, K  ~0 d0 |" h[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);

运行结果
k ,a ,b ,x, f
8 Q' D$ t$ z& H  1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
+ B! F! Y5 m9 {6 H/ ~+ h4 z  2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
: N+ H. L7 O) f9 r  3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
) K7 ?( d" r- [5 ^" B5 q! }; }  4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
  5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
% x& q/ b2 H2 a! h4 }: o  6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
. U: x) }! H- u4 Q  7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
6 ^- b  [0 n4 R* g& T- t/ p6 r  8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,
  9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
9 q" Z- c9 y6 q! V$ k7 r 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
5 r# a$ y5 U8 v* z 12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
4 c9 s0 u1 `  }5 e- l6 W 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
, `1 x/ E! V( a6 |# H 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
( a3 U0 w$ r* I5 w 19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
5 r- y1 D+ f# v2 y: {8 y/ F 20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
; w/ F# P3 d3 x1 `; `$ o 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
% x4 C8 S9 T7 a! C) m% W, q 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
: H( [) o2 X: `; J" ~0 L! y$ Z 27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
>>

结论 当x=-1.361时  y=0.117930219
; S; m1 n7 W* W( v* d' p按此方法   可依次  得出150对x与y的值

单车居士

西交大学生？？问邢老师

明月山河

你这个是代数方程？

cosxuan

算法？

shouce

cosxuan 发表于 2015-6-4 19:45
' w; u/ l: R; \: x( J算法？

+ n. a8 {5 B- r1 C; ^3 g二分法        
) v6 x( W6 B* P/ n还有一个程序
% Bisection.m
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
9 Z+ O- J0 k- rfprintf('k ,a ,b ,x, f\n')
for k=1:N
0 t: ?. n# X9 ~, h    x=(a+b)/2;
    f_value=f(x);
    fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
5 n/ A0 ]5 x- J& k' W4 \      ,k ,a ,b ,x, f_value)
, ^, U$ c% r# ~. Y3 j; c: f    if abs(f_value)< eps1||0.5*(b-a)<eps2
    return
& [  K* F2 M' I    else
        if f(x)*f(a)<0
& \1 E+ S% x0 j3 v' e          b=x;
  n  k* I; C: K1 @        else
          a=x;
        end
        if k== N
/ @! v6 K+ A4 A; p          warning ('算法超出最大迭代数!')   
5 K: s$ I4 N& N3 `8 ]7 L        end
    end
' b7 j, e0 O( R+ w

shouce

单车居士 发表于 2015-6-4 12:41
西交大学生？？问邢老师

这点问题   自己就可以解决
( x  K  X! h# d4 u& Q

shouce

明月山河 发表于 2015-6-4 19:12
4 W. Y0 }" G1 D& y8 f$ ^) K3 ^你这个是代数方程？

是的呀      不过matlab写出来的方程  括号很多  不好看   
1 s' ~  }/ B1 T) x1 H

shouce

明月山河 发表于 2015-6-4 19:12
你这个是代数方程？

是超越方程      


[chāo yuè fāng chéng
# n9 W& l* s$ B1 O8 G. X