螺杆转子刀具设计 数学模型& i) [- H- V/ K0 O0 R! }9 O. D
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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
& {1 D0 @3 ^5 f0 M求当x=-1.361时 y=? ' B! `: L: O9 o8 D& Y( B5 e$ p
>> syms x y
! @4 D, ]2 q8 i/ w7 ^6 R" y2 j>> 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/ b. B* |0 Y5 V
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(x)+179999.4000005*y*sin(y)*sin(x)+75000*cos(y)*cos(x)*sin(x); `6 I+ H8 y2 r8 Z/ }
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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)+ D V4 [3 b( t8 k7 k
# x# K0 x& ^8 O5 L*sin(x) - (6184732290414159*y*cos(x)*cos(y))/34359738368 + (6184732290414159*y*sin(x)*sin(y))/34359738368+ ~5 X0 \( O/ X
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>> subs(f, x, -1.361)
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+ p0 X ?# S' C3 b$ L% Eans =/ f6 X1 \, @: G! u$ I6 j' q, u
9 d R0 K/ g& P(3359995*sin(1361/1000)*cos(y))/2 - (2999995*cos(1361/1000)*sin(y))/2 - (7215543768789811*sin(1361/1000))/4294967296 + 75000*sin) \6 `: |0 U7 U5 m: Z
) f: y5 T$ }: I: }! p, M(1361/1000)^3 - 75000*cos(1361/1000)*sin(1361/1000)*cos(y) - (6184732290414159*y*cos(1361/1000)*cos(y))/34359738368 - + \" H" f2 J/ J. a, h
5 v' C y# e$ q1 z: C& n. ~# V(6184732290414159*y*sin(1361/1000)*sin(y))/34359738368
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>> a=0; b=1;
7 L4 o8 E2 O$ F8 Q5 reps1=1e-8;eps2=1e-8;
! p+ }" V' t4 H N=300;& Q- P5 N9 F, ^* y
f=@ (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); ?1 ]! Y4 i1 F/ z" l
Hfun=@Bisection;
* N5 a) O3 @# c3 j[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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0 v. P" B8 H- C( H! H( c运行结果5 O' T/ l0 L9 P
k ,a ,b ,x, f
2 }+ E, c0 \, n 1, 0.000000000, 1.000000000, 0.500000000,-352805.622314164,4 P3 S9 u% R1 S
2, 0.000000000, 0.500000000, 0.250000000,-92968.331400711,
& g- H$ k. H8 \" Z 3, 0.000000000, 0.250000000, 0.125000000,-4146.780462183,# T: B1 |9 W& W7 Y8 ~& W0 P! c
4, 0.000000000, 0.125000000, 0.062500000,29178.936016433,
" c6 I4 O3 a. J5 { 5, 0.062500000, 0.125000000, 0.093750000,13458.364371693,
* }' Z ^8 p) a: k# ]8 { 6, 0.093750000, 0.125000000, 0.109375000,4890.124291139,3 Z' X$ A6 C6 q* K, ]
7, 0.109375000, 0.125000000, 0.117187500,430.092693351,
4 c: b- T2 V/ {' J& l+ I R 8, 0.117187500, 0.125000000, 0.121093750,-1843.759437944,
# _$ f, A( b6 ~; a. k" C" g5 q 9, 0.117187500, 0.121093750, 0.119140625,-703.184646645,
3 ^# Z* H! O' i7 L 10, 0.117187500, 0.119140625, 0.118164063,-135.633470273,+ g, d9 V9 G5 ]0 T: Y& D) K
11, 0.117187500, 0.118164063, 0.117675781,147.457778641,, p# X8 {/ w2 Q( r9 y6 ] M
12, 0.117675781, 0.118164063, 0.117919922,5.969190901,) O: u( _) J# Y! o9 F# A- H
13, 0.117919922, 0.118164063, 0.118041992,-64.817881139,
& \; d; s& e: V8 @4 R 14, 0.117919922, 0.118041992, 0.117980957,-29.420780403,3 v, F# }; M$ _! W
15, 0.117919922, 0.117980957, 0.117950439,-11.724903562,7 L! A: G0 o+ N$ l4 b
16, 0.117919922, 0.117950439, 0.117935181,-2.877633532, q3 Z2 Z1 ~) ]5 ] f) s4 A
17, 0.117919922, 0.117935181, 0.117927551,1.545834384,+ J' |% ?+ R, C* C
18, 0.117927551, 0.117935181, 0.117931366,-0.665885649,
& m, p2 Y1 ?, Y 19, 0.117927551, 0.117931366, 0.117929459,0.439977849,! C4 j {7 {( v, P# c# L" c
20, 0.117929459, 0.117931366, 0.117930412,-0.112953030,: A) i# X B) z
21, 0.117929459, 0.117930412, 0.117929935,0.163512627,
- v2 M4 d& L0 T( W+ w: @ t 22, 0.117929935, 0.117930412, 0.117930174,0.025279853,
" ^: w( l) G7 \) g5 _, E 23, 0.117930174, 0.117930412, 0.117930293,-0.043836575,6 v0 M& P7 O$ h5 c3 k: G1 [
24, 0.117930174, 0.117930293, 0.117930233,-0.009278357,
8 V) X- Q- X$ v' B* e5 C 25, 0.117930174, 0.117930233, 0.117930204,0.008000749,
' l! G- Y( r- f0 t 26, 0.117930204, 0.117930233, 0.117930219,-0.000638804,7 ]3 a- y4 D" i" `! T! _4 d6 h
27, 0.117930204, 0.117930219, 0.117930211,0.003680972,: Q; R' `" c) V: g1 {
>>
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结论 当x=-1.361时 y=0.117930219
: ~6 [- ~" m7 _6 {3 v% H! }% h按此方法 可依次 得出150对x与y的值! [: Q- P& Y( f7 y+ M% K5 i% f
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