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MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
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TABLE 6.15 Maximum Recommended Bending Stresses for Helical Torsion Springs in Static Applications
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TABLE 6.16 Maximum Recommended Bending Stresses (KB Corrected) for Helical Torsion Springs in Cyclic Applications
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6.6.4 Tolerances The tolerances for coil diameter and end position are given in Tables 6.17 and 6.18, respectively. Use them as guides.
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6.7 BELLEVILLE SPRING WASHER
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Belleville washers, also known as coned-disk springs, take their name from their inventor, Julian F. Belleville. They are essentially circular disks formed to a conical shape, as shown in Fig. 6.25. When load is applied, the disk tends to flatten. This elastic deformation constitutes the spring action.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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TABLE 6.17 Commercial Tolerances for Torsion-Spring Coil Diameters
TABLE 6.18 End-Position Tolerances (for D/d Ratios up to and Including 16)
Belleville springs are used in two broad types of applications. First, they are used to provide very high loads with small deflections, as in stripper springs for punchpress dies, recoil mechanisms, and pressure-relief valves. Second, they are used for their special nonlinear load-deflection curves, particularly those with a constantload portion. In loading a packing seal or a live center for a lathe, or in injection molding machines, Belleville washers can maintain a constant force throughout dimensional changes in the mechanical system resulting from wear, relaxation, or thermal change. The two types of performance depend on the ratio of height to thickness. Typical load-deflection curves for various height-thickness ratios are shown in Fig. 6.26. Note that the curve for a small h/t ratio is nearly a straight line.At h/t = 1.41 the curve shows a nearly constant load for approximately the last 50 percent of deflection
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FIGURE 6.25 Belleville washer. (Associated Spring, Barnes Group Inc.)
before the flat position. Above h/t = 1.41 the load decreases after reaching a peak. When h/t is 2.83 or more, the load will go negative at some point beyond flat and will require some force to be restored to its free position. In other words, the washer will turn inside out. The design equations given here are complex and may present a difficult challenge to the occasional designer. Use of charts and the equation transpositions presented here have proved helpful. Note that these equations are taken from the mathematical analysis by Almen and Laszlo [6.5]. The symbols used here are those originally used by the authors and may not necessarily agree with those used elsewhere in the text.
FIGURE 6.26 Load-deflection curves for Belleville washers with various h/t ratios. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.43
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6.7.1 Nomenclature a C1 C2 E f h ID M OD P Pf R Sc ST1 ST2 t T1 T2 OD/2, mm (in) Compressive stress constant (see formula and Fig. 6.28) Compressive stress constant (see formula and Fig. 6.28) Modulus of elasticity (see Table 6.19), MPa (psi) Deflection, mm (in) Inside height, mm (in) Inside diameter, mm (in) Constant Outside diameter, mm (in) Load, N (lb) Load at flat position, N (lb) OD/ID Compressive stress (Fig. 6.27), MPa (psi) Tensile stress (Fig. 6.27), MPa (psi) Tensile stress (Fig. 6.27), MPa (psi) Thickness, mm (in) Tensile stress constant (see formula and Fig. 6.29) Tensile stress constant (see formula and Fig. 6.29) Poisson s ratio (Table 6.19)
6.7.2 Basic Equations P= PF = Ef f (h f ) h t + t3 (1 2 )Ma2 2 Eht 3 (1 2 )Ma2
(6.39) (6.40)
FIGURE 6.27 Highest-stressed regions in Belleville washers. (Associated Spring, Barnes Group Inc.)
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