螺杆转子刀具设计 数学模型
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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 y2 H; G3 G8 p& M. \5 t3 k
>> 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- c' T# s, K' K& q: Q) k5 h; i
: S( \- v0 n7 R! s$ b(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x)
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f =
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(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 M- w$ ^: H) j6 r
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
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>> subs(f, x, -1.361)- C; f9 n! l4 k
. }. d) D9 G: d) R+ v# I# Wans =& y3 w; n$ v# V0 X; f( v
, |. 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. _+ s5 c9 z s6 H8 A' d j @0 U
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 - / \! }8 l# W1 ^! [8 j4 g$ S
c7 s0 |8 e; y% I: Y0 a$ E(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368
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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);* m( }- c! T0 {" F
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运行结果/ O h! V- Q/ q, c1 N
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,) _. [9 U0 c @
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,% _% I4 A. t' C- s) C* l
9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,+ q5 S- W4 [. h& U( y1 b2 q
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, 0.117919922,5.969190901,8 |) {# O5 C6 v
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,$ A! {0 ~; J5 T/ H
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,+ g9 S9 H" Q/ o6 ~
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532,6 C2 e- h, E; h4 x3 Q* a# i; Z
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,& a" G: W. q! h6 B7 f
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,& m* a, f6 L* J: p& t
22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
; w/ F# P3 d3 x1 `; `$ o 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,3 j4 i- j8 ^3 h O- \) X6 @- @9 V
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
% x4 C8 S9 T7 a! C) m% W, q 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,6 U" u! o9 L+ d8 e7 i7 B- G2 M. f
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,: t$ n9 T7 i/ L, j; q
>> ( I+ k" p" m0 N( @) j5 i8 B Q1 M
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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. \8 ^5 F* _2 }
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