Applying Constraints According to the principle of minimizing unnecessary constraints under design conditions, the following constraints are listed: 1 Stiffness conditions According to the required range of spring stiffness kminFkFkmax (where K=Gd48D32n), the constraint g1 is obtained. (x)=kmin−Gx418x32x3F0(3)g2(x)=Gx418x32x3-kmaxF0 (4) where G is the shear modulus of the spring material.

2 The limit range dminFdFdmax of the spring wire diameter d, the constraint condition g3(x)=dmin-x1F0(5)g4(x)=x2-dmaxF0(6)<3>Wang Ruiping. Spatial distribution law and evaluation method of reservoirs in bedrock buried hills.

3 According to the limitation range of the spring installation space to D2, the constraint condition g5(x)=D2min-x2F0(7)g6(x)=x2-D2maxF0(8)

4 According to the specified range nminFnFnmax for the number of working circles of the spring, g7(x)=nmin-x3F0(9)g8(x)=x3-nmaxF0(10)5 according to the range of the winding ratio (spring index) c=D2d is g9 (x)=4-x2x1F0(11)g10(x)=x2x1-9F0(12)6 According to the requirement that the spring does not touch the circle under the maximum working load: H0-DmaxEHb.

Where: H0) free height of the spring, when the number of support turns n2=2 and both ends are flattened, H0=nt+1.5d; t) pitch, tU(0.28-0.5)D2, can be taken as t=0.4D2; Dmax The deformation of the spring under the maximum working load Fmax, Dmax=8FmaxD32nGd4Hb) The spring tightness height, when the number of support turns n2=2 and the two ends are flattened, the constraint condition of Hb=(n+1.5)d: g11(x) =8Fmaxx32x3Gx41+x1x3-0.4x2x3F0(13)7 According to the strength condition of the spring: Smax=K8FmaxD2Pd3F|S| where: Smax) the maximum torsional stress generated inside the steel wire section under the action of the maximum working load Fmax or in the pressed state ; K) curvature coefficient: K = 4C-14C-4 + 0.615 CU1.66 (dD2) 0.16; | S |) allowable stress g12 = 1.66 (dD2) 0.16@8FmaxD2Pd3-570F0 (14)

According to the stability condition of the spring: b=H0D2=nt+1.5dD2=0.5n+1.5(dD2)Fbg13(x)=1.5x1x2+0.5x3-bF0(15) where: bc) critical height to diameter ratio, according to the spring The support method is different: bc=5.3 when fixed at both ends; bc=3.7 when one end is fixed; bc=2.69 when both ends can be rotated according to the above constraints: g1(x)=270-9857x41x32x3F0( 16) g2(x)=9857x41x32x3-600F0(17)g3(x)=2.0-x1F0(18)g4(x)=x1-6.0F0(19)g6(x)=x2-40F0(20)g5(x )=10-x2F0(21)g7(x)=2-x3F0(22)g8(x)=x3-8F0(23)g9(x)=4-x2x1F0(24)g10(x)=x2x1-9F0( 25) g11=0.09x32x3x41+x1x3-0.4x2x3F0(26)g12(x)=3804.43(x1x2)0.16x2x13-570F0(27)g13(x)=1.5x1x2+0.5x3-3.7F0(28)

Using MATLAB optimization toolbox to optimize the solution Using the MATLAB7.0 software optimization toolbox Fmincon function to solve the established mathematical model, first of all to establish two function files, one is the function file of the objective function, named fmin-cony. m; the second is the constraint function file, named fminconydy.m.

Finally, the initial value x0=<3.5,19,5>, the lower bound constraint of the given variable, and the optimization process is called to solve <3>: the result: x1=4.6246mm; x2=18.4983mm; x3=2.0000mm; =1.952@103mm3.

Conclusion 1 After the optimized design method, the diameter of the spring is increased in the original installation space, so that the strength and rigidity of the spring are improved and the maximum load can be withstood. And its volume is reduced by 32% compared with the original; o using MATLAB optimization toolbox to solve, the statement is simple, no need to understand a lot of complex computer language. Moreover, the optimization process parameters can be controlled in time during the solution process, and the method is very simple.

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