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FIGURE 6.11 Wire cross section before and after coiling. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.25
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The spring rate for a rectangular-wire spring is k= P K 2Gbt 3 = Na D3 f (6.15)
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Since the wire is loaded in torsion, it makes no difference whether the wire is wound on the flat or on edge. See Fig. 6.12. Stress is calculated by S= K E PD K 1bt 2 or S= K F PD K 1bt 2 (6.16)
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Values for K 1 and K 2 are found in Fig. 6.13, and those for K E and K F are found in Figs. 6.15 and 6.14, respectively. When a round wire cannot be used because the solid height exceeds the specification, the approximate equivalent rectangular dimensions are found from t= where d = round-wire diameter. 6.4.7 Variable-Diameter Springs Conical, hourglass, and barrel-shaped springs, shown in Fig. 6.16, are used in applications requiring a low solid height and an increased lateral stability or resistance to surging. Conical springs can be designed so that each coil nests wholly or partly within an adjacent coil. Solid height can be as low as one wire diameter. The rate for conical springs usually increases with deflection (see Fig. 6.17) because the number of active coils decreases progressively as the spring approaches solid. By varying the pitch, conical springs can be designed to have a uniform rate. The rate for conical springs is calculated by considering the spring as many springs in series. The rate for 2d 1 + b/t (6.17)
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FIGURE 6.12 Rectangular-wire compression spring wound on flat or edge. (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 6.26
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
FIGURE 6.13 Constants for rectangular wire in torsion. (Associated Spring, Barnes Group Inc.)
FIGURE 6.14 Stress correction factors for rectangular-wire compression springs wound on flat. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.27
SPRINGS
FIGURE 6.15 Stress correction factors for rectangular-wire compression springs wound on edge. (Associated Spring, Barnes Group Inc.)
each turn or fraction of a turn is calculated by using the standard rate equation. The rate for a complete spring is then determined, given that the spring rate follows the series relationship in Eq. (6.3). To calculate the highest stress at a given load, the mean diameter of the largest active coil at load is used. The solid height of a uniformly tapered, but not telescoping, spring with squared and ground ends made from round wire can be estimated from LS = Na d 2 u 2 + 2d (6.18)
where u = OD of large end minus OD of small end, divided by 2Na. Barrel- and hourglass-shaped springs are calculated as two conical springs in series.
6.4.8 Commercial Tolerances Standard commercial tolerances are presented in Tables 6.8, 6.9, and 6.10 for free length, coil diameter, and load tolerances, respectively. These tolerances represent the best tradeoffs between manufacturing costs and performance.
FIGURE 6.16 Various compression-spring body shapes. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.28
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
FIGURE 6.17 Typical load-deflection curve for variablediameter springs (solid line). (Associated Spring, Barnes Group Inc.)
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