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发布日期:2021年11月29日
Compression Spring Example

An as-wound helical compression spring, made of music wire, has a wire size of 0.080in, an outside coil diameter of 10/16 in, a free length of 4in, 22 active coils, and both endssquared and ground. The spring is unpeened. This spring is to be assembled with apreload of 8 lbf and will operate with a maximum load of 22 lbf during use.

(a) Estimate the factor of safety guarding against fatigue failure using a torsionalGerber fatigue failure criterion with Zimmerli data.

(b) Repeat part (a) using the Sines torsional fatigue criterion (steady stress componenthas no effect), with Zimmerli data.

(c) Repeat using a torsional Goodman failure criterion with Zimmerli data.

(d) Estimate the critical frequency of the spring.

Solution of Compression Spring Design Problem:

Step 1 : Write down input parameters.

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INPUT PROPERTIES SUMMARY
Parameter Value
Wire diameter d 0.080 inch
Spring outer diameter OD 0.625 inch
Spring free length (height) Lf 4 inch
Number of active Na 22 ---
End types for compression spring Both ends squared and ground
Maximum cyclic force Fmax 22 lbf
Minimum cyclic force (preload) Fmin 8 lbf
Material Music wire (unpeened)
Density ρ 0.283 lb/in3

Step 2 :Visitcompression spring design for fatigue loading and solve the problem. Results generated by the calculator are as follows.

 RESULTS
Parameter Value
Wahl factor Kw1.22 ---
Shear stress amplitude
τa23.14 ksi
Midrange shear stress
τm49.58
Ultimate tensile strength of material Sut289.35
Shearing ultimate strength Ssu193.86
Endurance limit ( according to Gerber) Se38.01
Endurance limit (according to Goodman) Se48.79
Strength amplitude component ( according to Gerber) Ssa32.96
Strength amplitude component ( according to Sines) Ssa34.95
Strength amplitude component ( according to Goodman)年轻的小痍子2中文云播在线观看 年轻的小痍子2中文云 ,神马午夜dy888电影院BD高清在线观看全集免费完整版20190930 雪梨 Ssa31.7
Factor of safety (Acc. to Gerber)+ fosgerber 年轻的小痍子2中文云播在线观看 年轻的小痍子2中文云 ,神马午夜dy888电影院BD高清在线观看全集免费完整版20190930 雪梨 1.42 ---
Factor of safety (Acc. to Sines)+ fossines1.51
Factor of safety (Acc.to Goodman)+ fosgoodman1.37
Material ASTM No.A228

Step 3 : For the calculation of critical working frequency of the spring, spring rate shall be calculated. Visit rate based compression spring design calculator and calculate spring rate (k).  Results generated by the calculator are as follows.

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 RESULTS
Parameter Value
Number of active coils Na22 ---
Number of total coils Nt24
Spring index C*6.81
Spring rate k 16.89 lbf/inch
Wire diameter d0.08 inch
Spring outer diameter OD0.625
Spring mean diameter D0.545
Spring inner diameter ID0.465
Outer diameter at solid length ODat solid***0.63
Spring free length (height) Lf4
Spring solid height Ls1.92
Maximum deflection (Lf to Ls) Δx2.08
Pitch at free length p**0.17

Step 4 : Visit critical frequency of compression springs  and solve the problem. Results generated by the calculator are as follows.

 RESULTS
Parameter Value
Natural frequency of spring f+174.428 Hz
Mass of the active coils  m0.054 lb
Spring index C*6.812 ---
OD Spring outer diameter0.625 inch
D Spring mean diameter0.545
ID Spring inner diameter0.465

Conclusion:

The natural frequency of the spring is calculated as 174.4 Hz. According to Ref-1, the cyclic loading frequency shall be minimally 13 times smaller than natural frequency. Based on this information, maximum cyclic loading frequency is calculated as 174.4/13= 13.4 Hz. If the loading frequency is lower than 13.4 Hz,  the effect of resonance is negligible and fos values given in Step-2 can be used.

If a spring cannot be designed to have a natural frequency more than 13 times operating frequency, or if thespring is to serve as a vibration damping device, it must utilize one of several methods of energy absorption.

Reference: