In the fatigue strength condition τmaxσb≤0.45, σb is the tensile strength limit of the spring wire, which is related to the material quality and the wire diameter d, and takes σb=1520MPa. The stability condition of the spring is for the compression spring, in order to avoid the occurrence of instability, the spring The slenderness ratio shall not exceed its allowable value, ie H0D≤3.7.

Conditions where resonance does not occur For a spring subjected to a variable load, the condition in which resonance does not occur is: fnfr>10(3) where fn is the spring self-vibration frequency, fn=3.56×105×dnD2; fr is the spring operating frequency , fr = ω2π, ω is the maximum speed of the shaft. Substituting type (3): fr-0.356×105×dnD2≤0 spring non-coupling constraint to ensure that the spring does not occur under the maximum load, the height of the spring under the maximum load is required to be greater than the crush height. That is, (n+2)D≤H0-fmax.

Other structural constraints, the winding ratio C=Dd, 4≤C≤7. According to the product size specification of the spring steel wire, the limit range of the spring wire diameter d is 3≤d≤8; the range of the spring working circle n is 4≤ n ≤ 8; the spring installation space has a limit on the medium diameter D, then there is 30 ≤ D ≤ 40.

Using the MATLAB optimization toolbox for spring optimization design spring optimization design example According to the mathematical model formula (2), the spring optimization design of the spring is performed by using the fmincon function of the MATLAB optimization toolbox. The format of the fmincon function is: fmincon(@objfun,x0,<>,<>,<>,<>,<>,<>,@confun,options).

Where objfun is the name of the m function describing the objective function; x0 is the initial value of the design variable; confun is the name of the m function describing the constraint; options is the optimization option, generally options=optimset("LargeScale.","off" ). The calculation results and analysis of the optimized spring design results can be seen from the optimized design, the quality of the valve spring is reduced by 39.3% compared with the traditional design.

End a. A set of unreasonable spring parameters not only causes difficulties in manufacturing, but also does not provide good spring performance. Optimizing the design with optimization methods not only saves material, reduces costs, but also gives the best value. b. Using MATLAB optimization toolbox to optimize the spring design, you can directly use the objective function and constraints to establish an optimization program, saving design time and improving design accuracy. c. The MATLAB optimization toolbox can be applied not only to the optimized design of springs, but also to the optimization design of various mechanical parts.

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