Machinery's Handbook, 31st Edition
364 DISC SPRING EXAMPLES 15) Fatigue life of selected disc springs, Equation (21): N = 10 [10.10734911 – 0.00537616 (1149 – 0.5 3 815)] = 10 10.10734911 – 3.98642264 = 10 6.12092647 N = 1,321,000 cycles. Thus, the calculated actual fatigue life exceeds required minimum number of cycles by 31 percent. In conclusion, the six 80-41-4 disc springs arranged in series stacking, satisfy the requirements and will provide a 32 percent longer fatigue life than required by the design criteria. Example 2: A company wishes to use Group 3 disc springs with contact surfaces on cou plings to absorb bumping impacts between railway cars. Given: h = 4.2 mm, cone height of unloaded spring n = 22, number of springs in series stacking S i = 33.9 mm, initial deflection of the pack S a = 36.0 mm, additional deflection of the pack Find the fatigue life in cycles and determine if the selected springs are suitable for the application. The calculations are performed in the following sequence: 1) Determine the minimum s min and maximum s max deflections of a single disc spring: . . . . s n S S s n S 22 339 36 318 22 339 154 mm mm max min i a i = + = + = = = = ^ h ^ h 2) Use Equations (16) and (17) to calculate tensile stresses σ 2 and σ 3 at s min and s max deflections: σ 2 min = 674 N/mm 2 , σ 2 max = 1513 N/mm 2 , σ 3 min = 707 N/mm 2 , σ 3 max = 1379 N/mm 2 3) Determine critical stress points: σ 2 max − 0.5 σ 2 min = 1513 − 0.5 3 674 = 1176 N/mm 2 σ 3 max − 0.5 σ 3 min = 1379 − 0.5 3 707 = 1025.5 N/mm 2 Because ( σ 2 max − 0.5 σ 2 min ) > ( σ 3 max − 0.5 σ 3 min ), then tensile stresses at point 2 are used to calculate fatigue life. The selected disc springs at the above-mentioned minimum and maximum deflection values will not sustain any number of cycles. It is imperative to check the selected disc springs for dimensional ratios: Outside-to-inside diameters ratio, 200/102 = 1.96; within recommended range. Cone height-to-thickness ratio is 4.2/13.1 = 0.3; out of range, the minimum ratio is 0.4. Outside diameter-to-thickness ratio is 200/13.1 = 15; out of range, the minimum ratio is 18. Thus, only one of the dimensional ratios satisfies the requirements for the best disc spring performance. D = 200 mm, disc spring outside diameter d = 102 mm, disc spring inside diameter t = 14 mm, spring standard thickness t ′ = 13.1 mm, spring reduced thickness 4) Fatigue life N is calculated using Equation (22): N = 10 [13.23985664 − (0.01084192 3 1176)] = 10 0.49 = 3 cycles
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