Machinery's Handbook, 31st Edition
DISC SPRING EXAMPLES 361 Example: A dynamically loaded stack, which utilizes disc springs in Group 2 , must have the fatigue life of 5 3 10 5 cycles. The maximum allowable tensile stress at Points 2 or 3 is 1250 N/mm 2 . Find the minimum tensile stress value to sustain N = 5 3 10 5 cycles. Solution: Substitution of σ max = 1250 and N = 5 3 10 5 in Equation (24) gives: . . . . . . log 1250 05 000537616 10 10734911 5 10 000537616 10 10734911 5 69897 820 min 5 # − σ = − = − = ^ h from which . / , N 05 1250 820 860 mm 124 700 psi min 2 σ = − = ^ h Recommended Dimensional Characteristics of Disc Springs.— Dimensions of disc springs play a very important role in their performance. It is imperative to check selected disc springs for dimensional ratios, that should fall within the following ranges: 1) Diameters ratio, δ = D ∕ d = 1.7 to 2.5. 2) Cone height-to-thickness ratio, h ∕ t = 0.4 to 1.3. 3) Outside diameter-to-thickness ratio, D ∕ t = 18 to 40. Small values of δ correspond with small values of the other two ratios. The h ∕ t ratio deter mines the shape of force-deflection characteristic graphs, that may be nearly linear or strongly curved. If h ∕ t = 0.4 the graph is almost linear during deflection of a disc spring up to its flat position. If h ∕ t = 1.6 the graph is strongly curved and its maximum point is at 75 percent deflection. Disc spring deflection from 75 to 100 percent slightly reduces spring force. Within the h ∕ t = 0.4 − 1.3 range, disc spring forces increase with the increase in deflection and reach maximum values at 100 percent deflection. In a stack of disc springs with a ratio h ∕ t > 1.3 deflection of individual springs may be unequal, and only one disc spring should be used if possible. Example Applications of Disc Springs Example 1, Disc Springs in Group 2 (no contact surfaces): A mechanical device that works under dynamic loads must sustain a minimum of 1,000,000 cycles. The applied load varies from its minimum to maximum value every 30 seconds. The maximum load is approximately 20,000N (4,500 lbf). A 40-mm diameter guide rod is a receptacle for the disc springs. The rod is located inside a hollow cylinder. Deflection of the disc springs under minimum load should not exceed 5.5 mm (0.217 inch) including a 20 percent preload deflection. Under maximum load, the deflection is limited to 8 mm (0.315 inch) maximum. Available space for the disc spring stack inside the cylinder is 35 to 40 mm (1.38 to 1.57 inch) in length and 80 to 85 mm (3.15 to 3.54 inch) in diameter. Select the disc spring catalog item, determine the number of springs in the stack, the spring forces, the stresses at minimum and maximum deflection, and actual disc spring fatigue life. Solution: 1) Disc spring standard inside diameter is 41 mm (1.61 inch) to fit the guide rod. The outside standard diameter is 80 mm (3.15 in) to fit the cylinder inside diameter. Disc springs with such diameters are available in various thickness: 2.25, 3.0, 4.0, and 5.0 mm (0.089, 0.118, 0.157, and 0.197 inch). The 2.25- and 3.0-mm thick springs do not fit the applied loads since the maximum force values for disc springs with such thickness are 7,200N and 13,400N (1,600 lbf and 3,000 lbf) respectively. A 5.0-mm thick disc spring should not be used because its D ∕ t ratio, 80 ∕ 5 = 16, is less than 18 and is considered as unfavor able. Disc spring selection is narrowed to an 80-41-4 catalog item. 2) Checking 80 - 41 - 4 disc spring for dimensional ratios: δ = D ∕ d = 80 ∕ 41 = 1.95 h ∕ t = 2 . 2 ∕ 4 = 0.55 D ∕ t = 80 ∕ 4 = 20 Because the dimensional ratios are favorable, the 80-41-4 disc springs are selected.
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