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6.10 CONSTANT-FORCE SPRINGS
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A constant-force spring is a roll of prestressed material which exerts a nearly constant restraining force to resist uncoiling. Its unique characteristic is force independent of deflection. The force required to produce a unit deflection is the same for
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TABLE 6.24 Maximum Design Stresses for Cantilever and Simple Beam Springs in Static Applications
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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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SPRINGS 6.59
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SPRINGS
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TABLE 6.25 Maximum Design Stresses for Carbon-Steel Cantilever and Simple Beam Springs in Cyclic Applications
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each increment of coil because the radius of curvature of each increment is the same as any other. Although these springs are not constant-load or constant-torque springs in the precise meaning of those terms, they produce a more nearly constant load over a greater deflection than any other spring design covered here. See Fig. 6.45. Constant-force springs are made of both type 301 stainless steel and ultra-high-strength high-carbon steels, with many of the applications using stainless steel because of its inherent resistance to corrosion. One of the most severe limitations on the use of constant-force springs is their relatively short operating life. The most efficient use of material will produce a life of about 3000 cycles. Although life of hundreds of thousands of cycles is possible,
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FIGURE 6.45 Load-deflection curves for various spring configurations. (Associated Spring, Barnes Group Inc.)
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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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SPRINGS 6.60
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
most applications fall into the range of 3000 to 30 000 cycles. Figure 6.46 shows the relationship between stress and fatigue life. These curves are derived from experimentally obtained data. Some applications involving constant-force and constant-torque springs are simple extension springs, window sash counterbalances, camera motors, toys, machine carriage returns, constant-pressure electric-motor brush springs, space vehicle applications, and retraction devices.
6.10.1 Extension Type This type of spring is a spiral spring made of strip material wound on the flat with an inherent curvature such that, in repose, each coil wraps tightly on its inner neighbor. In use the strip is extended with the free end loaded and the inner end supported on a drum or arbor. Very long deflections are possible, but the strip becomes unstable in long deflections and must be guided or supported to avoid kinking or snarling on the return stroke. The rated load is not reached until after an initial deflection of 1.25 times the drum diameter, as shown in Fig. 6.47. Idler pulleys can be used but should be no smaller in diameter than the natural diameter of the coils and should never be used in a direction to cause backbending against the strip curvature.
6.10.2 Design Equations P= Ebt 3 6.5D 2 n Ebt 3 2 1 6.5D1 Dn D1 for N 10
(6.55)
for N > 10
(6.56)
FIGURE 6.46 Maximum bending stress versus number of stress cycles for constant-force springs. These curves are based on no. 1 round-edge strip. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.61
SPRINGS
FIGURE 6.47 Typical constant-force extension spring (extension form). (Associated Spring, Barnes Group Inc.)
If unknown, let b/t = 100/1, D2 = 1.2 Dn, S= and L = 1.57N(D1 + D2 ) where N D1 D2 Dn E = = = = = number of turns outside coil diameter drum (arbor) diameter natural diameter modulus of elasticity or L f + 5D2 Et Dn (6.57)
6.10.3 Spring Motor Type When a constant-force spring is mounted on two drums of different diameters and the spring is backbent onto the larger diameter, the result is a constant-force spring motor. The strip is in repose on the smaller (storage) drum and is backbent onto the larger (output) drum. Torque is taken from the output drum shaft as shown in Fig. 6.48. Note here that constant torque does not mean constant speed. Constant torque implies uniform acceleration, and the mechanism so driven will continue to speed up unless restrained by a governor mechanism. Load tolerances are normally held within 10 percent.
FIGURE 6.48 Typical constant-torque motor spring. (Associated Spring, Barnes Group Inc.)
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