Disc Spring Forces and Stresses Machinery's Handbook, 31st Edition
356
From Fig. 8,
D D a b 2 2 a = − + ^ h
(5) where a = t sin α and b = r cos α . Substitution of a and b values into Equation (5) gives: (6) The cone angle α is found from: (7) Substituting α from Equation (7) and r t 6 = into Equation (6) gives: (8) Finally, (9) Substituting D a from Equation (9) for D in Equation (4) yields Equation (10), that pro vides better accuracy for calculating disc spring forces. (10) The constant K 1 depends on disc spring outside diameter D , inside diameter d , and their ratio δ = D ∕ d : (11) Table 2 compares the spring force of a series of disc springs deflected by 75 percent of their cone height, i.e., s = 0.75 h , as determined from manufacturers catalogs calculated in accordance with Equation (4), calculated forces by use of Equation (10), and measured forces. Table 2. Comparison Between Calculated and Measured Disc Spring Forces 1 1 2 1 δ sin cos D D t r 2 2 a α α = − + ^ h tan atan D d h 2 2 − D d h 2 D d h 2 − a k α α = = − = sin atan : cos atan : D D t 2 2 a = − D d h 2 D d h 2 − 6 1 − + a a k k D D & 0 sin atan : cos atan : D D t 2 a = − D d h 2 D d h 2 − 6 1 − + a a k k D D & 0 F K D 1 · E s h s h s t t − − + ^ j h · · 1 4 2 a 2 2 3 µ = − ^ ` h 8 B · · ln K 1 2 π δ δ δ − + − − δ = a a k k
Schnorr Handbook for Disc Springs
Christian Bauer Disc Spring Handbook
Key Bellevilles Disc Spring Catalog
Disc Spring Catalog Item 50 – 22.4 – 2.5 S = 1.05 mm 60 – 30.5 – 2.5 S = 1.35 mm 60 – 30.5 – 3 S = 1.275 mm 70 – 35.5 – 3 S = 1.575 mm 70 – 35.5 – 3.5 S = 1.35 mm
Spring Force Calculated by Equation (10)
Measured Disc Spring Force
8510 N 1913 lbf 8340 N 1875 lbf 13200 N 2967 lbf 12300 N 2765 lbf
8510 N 1913 lbf 8342 N 1875 lbf 13270 N 2983 lbf 12320 N 2770 lbf 16180 N 3637 lbf
8616 N 1937 lbf 8465 N 1903 lbf 13416 N 3016 lbf 12397 N 2787 lbf
9020 N 2028 lbf 8794 N 1977 lbf 14052 N 3159 lbf 12971 N 2916 lbf 17170 N 3860 lbf
9563 N 2150 lbf 8896 N 2000 lbf 13985 N 3144 lbf 13287 N 2987 lbf 17304 N 3890 lbf
Comparison made at 75 percent deflection, in newtons (N) and pounds (lbf)
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