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a rod, can minimize the buckling but can result in additional friction which will affect loads, especially when the Lf /D ratio is high. Buckling conditions are shown in Figs. 6.8 and 6.9 for springs loaded axially and with squared and ground ends. Buckling occurs at points above and to the right of the curves. Curve A is for the springs with one end on a fixed, flat surface and the other end free to tip. Curve B is for springs with both ends on fixed, flat surfaces. The tendency to buckle is clearly less for curve B springs.
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6.4.3 Choice of Operating Stress The choice of operating stress depends on whether the application is static or cyclic. For static applications, yield strength or stress-relaxation resistance of the material limits the load-carrying ability of the springs. The required cycles are few, if any, and the velocity of the end coils is so low as to preclude surging or impact conditions. The maximum allowable torsional stresses for static applications are shown in Table 6.6 as percentages of tensile strengths for common spring materials. To calculate the stress before set removal, use the K w1 correction factor. If the calculated stress is greater than the indicated percentage of the tensile strength, then the spring will take a permanent set when deflected to solid. The amount of set is a function of the amount by which the calculated stress exceeds the tabular percentage.
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FIGURE 6.8 Critical buckling curves. (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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FIGURE 6.9 End conditions used to determine critical buckling. (Associated Spring, Barnes Group Inc.)
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It is common practice, in static applications, to increase the load-carrying capability of a spring by making it longer than the desired free length and then compressing it to solid. The spring sets to its final desired length. This procedure is called removing set. It induces favorable residual stresses which allow for significantly higher stresses than in springs not having the set removed. The loss of the length should be at least 10 percent to be effective (see Fig. 6.10). Note that set removal causes stresses to be more uniformly distributed about the cross section. Therefore, stress after set removal is calculated by using the K w 2 correction factor. If the stress calculated by using the K w 2 correction factor exceeds the percentage of tensile strength shown in Table 6.6, the spring cannot be made. It is then necessary either to lower the design stress or to select a higherstrength material. For cyclic applications, the load-carrying ability of the spring is limited by the fatigue strength of the material. To select the optimum stress level, spring costs must be balanced against reliability. The designer should know the operating environ-
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TABLE 6.6 Maximum Allowable Torsional Stresses for Helical Compression Springs in Static Applications
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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FIGURE 6.10 Spring load-carrying ability versus amount of set removed. (Associated Spring, Barnes Group Inc.)
ment, desired life, stress range, frequency of operation, speed of operation, and permissible levels of stress relaxation in order to make a cost-reliability decision. Fatigue life can be severely reduced by pits, seams, or tool marks on the wire surface where stress is at a maximum. Shot peening improves fatigue life, in part, by minimizing the harmful effects of surface defects. It does not remove them. Additionally, shot peening imparts favorable compression stresses to the surface of the spring wire. Maximum allowable stresses for fatigue applications should be calculated by using the K w1 stress correction factor. Table 6.7 shows the estimated fatigue life for common spring materials. Note the significant increase in fatigue strength from shot peening.
TABLE 6.7 Maximum Allowable Torsional Stress for Round-Wire Helical Compression Springs in Cyclic Applications
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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