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

1 \) `; O# v) F6 `4 N$ ?# 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
/ }/ `! {+ p1 c) }* y3 W% q  J5 G2 i1 ]求当x=-1.361时  y=?  
7 M& U$ q6 A" S3 X; x! P9 d& i>> 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

$ ~' V/ `. _* w" M+ |5 A(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
# x: D& N) G& ^, o3 ?
f =

: _5 d* X+ U& h6 Q(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)
( U) Q! F" V& l0 N. {
*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368

>>  subs(f, x, -1.361)

ans =

$ B: b9 l: e# P2 D' B( T" h: h  R(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin
9 [* a/ ?/ i: g+ w
$ |* H  C' |/ ^1 ^* {6 ?6 J) n2 r3 u(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 -
( x- Q! n6 p# M! ?' X3 a" c
(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368

8 B% H# f# O" L6 l( M, \- `& ]
>>  a=0; b=1;
; |+ P. {/ l' Y- f, Z; f- x, ueps1=1e-8;eps2=1e-8;
N=300;
) g/ g  v$ E0 F! ]3 Wf=@ (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);
: S& |( B# J5 {5 c( K, A4 mHfun=@Bisection;
- G: ?' p1 m) @6 b* B5 h2 D6 v[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
3 R3 g0 H! ]  U8 |+ `
运行结果
2 n" ]# C9 }. `+ p) _/ D! Vk ,a ,b ,x, f
  1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,
  2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
  Z* ^2 c( Z1 N+ |; x5 R  3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,
# ], s5 X. {' J5 N4 j; K  4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
0 J# F6 y, `( F% k& e  5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
! H, x% f% n2 J, n7 l  6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,
  7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
8 \$ u0 D( v* p0 O  8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,
8 u3 c, \& F5 `  I4 S& {  9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
6 |! n2 e/ D+ v$ h6 ] 10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,
" P! j, s3 U7 N/ ? 11, 0.117187500, 0.118164063, 0.117675781,147.457778641,
12, 0.117675781, 0.118164063, 0.117919922,5.969190901,
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
3 n+ [# H9 w; _3 z0 K; G  C 14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,
9 ^$ C* v" \( r7 q5 ]/ ?5 X 15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,
5 f5 H3 D! `% X& J2 W2 N( A 18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
. \) _& w) ]% b) v 19, 0.117927551, 0.117931366, 0.117929459,0.439977849,
20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
( Z; r) n) {4 X2 y+ A* E0 { 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
2 h% G$ ]+ y8 P' o2 X6 ~, e% e 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,
27, 0.117930204, 0.117930219, 0.117930211,0.003680972,
  Q8 K5 W* k) l6 c) l( b, L1 @0 b>>

6 h9 U$ R0 ?5 x! S: o结论 当x=-1.361时  y=0.117930219
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
; V9 @' S4 Z% ]9 T算法？

' ]6 q7 T+ K3 W- D7 |4 c9 p二分法        
还有一个程序
% Bisection.m
( m( `8 ]$ E* F* Xfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
4 b  f5 X: S& l% F: t* @5 ufprintf('k ,a ,b ,x, f\n')
5 W+ s% }8 W: d) ?) F8 c4 ]for k=1:N
+ U' |8 k8 ^4 ~" h    x=(a+b)/2;
    f_value=f(x);
    fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
( H5 Y: p6 H9 v" J. ?      ,k ,a ,b ,x, f_value)
    if abs(f_value)< eps1||0.5*(b-a)<eps2
    return
$ ~* \. ~; J  |    else
  q8 U% K- v% F1 `        if f(x)*f(a)<0
          b=x;
( l0 v$ t/ B+ c, |' w/ W        else
          a=x;
3 o5 J3 C- H+ z. b% q8 g. E        end
        if k== N
8 r1 }- k2 \' ]& H9 x0 P          warning ('算法超出最大迭代数!')   
4 o" |" c! C) E' z0 t1 w  k        end
    end

shouce

单车居士 发表于 2015-6-4 12:41
2 I9 c; F* H; \, g西交大学生？？问邢老师

+ Q- l3 z0 h) B4 O+ L& ^这点问题   自己就可以解决
& f4 k# O& B, L) g( g( w* E7 \

shouce

明月山河 发表于 2015-6-4 19:12
+ X9 G" E# j- Y( J$ Z$ F8 O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   

$ s( g+ c6 x9 l8 N. [, M

shouce

明月山河 发表于 2015-6-4 19:12
$ x! e/ n& L  [7 }2 R, Y你这个是代数方程？

$ O$ C' A  o  S是超越方程      
3 X$ H/ K' t% o) l/ q1 E
, }! X" h4 M' H$ _
, n( O( n: J  n2 I* B* e[chāo yuè fāng chéng