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FIGURE 6.3 Tensile strength versus hardness of quenched and tempered spring steel. (Associated Spring, Barnes Group Inc.)
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Spring Index. Spring index C is the ratio of the mean diameter to the wire diameter (or to the radial dimension if the wire is rectangular). The preferred range of index is 5 to 9, but ranges as low as 3 and as high as 15 are commercially feasible. The very low indices are hard to produce and require special setup techniques. High indices are difficult to control and can lead to spring tangling. Free Length. Free length Lf is the overall length measured parallel to the axis when the spring is in a free, or unloaded, state. If loads are not given, the free length should be specified. If they are given, then free length should be a reference dimension which can be varied to meet the load requirements.
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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 6.4 Edges available on steel strip. (Associated Spring, Barnes Group Inc.)
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Types of Ends. Four basic types of ends are used: closed (squared) ends, closed (squared) ends ground, plain ends, and plain ends ground. Figure 6.6 illustrates the various end conditions. Closed and ground springs are normally supplied with a ground bearing surface of 270 to 330 . Number of Coils. The number of coils is defined by either the total number of coils Nt or the number of active coils Na. The difference between Nt and Na equals the number of inactive coils, which are those end coils that do not deflect during service. Solid Height. The solid height Ls is the length of the spring when it is loaded with enough force to close all the coils. For ground springs, Ls = Nt d. For unground springs, Ls = (Nt + 1)d. Direction of the Helix. Springs can be made with the helix direction either right or left hand. Figure 6.7 illustrates how to define the direction. Springs that are nested one inside the other should have opposite helix directions. If a spring is to be assembled onto a screw thread, the direction of the helix must be opposite to that of the thread. Spring Rate. Spring rate k is the change in load per unit deflection. It is expressed as k= where G = shear modulus. Gd 4 P = f 8D3Na (6.2)
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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 6.4 Formability of Annealed Spring Steels
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SPRINGS
TABLE 6.5 Typical Properties of Spring-Tempered Alloy Strip
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SPRINGS 6.18
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FIGURE 6.5 Dimensional terminology for helical compression springs. (Associated Spring, Barnes Group Inc.)
FIGURE 6.6 Types of ends for helical compression springs. (Associated Spring, Barnes Group Inc.)
FIGURE 6.7 Direction of coiling of helical compression springs. (Associated Spring, Barnes Group Inc.)
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SPRINGS 6.19
SPRINGS
The rate equation is accurate for a deflection range between 15 and 85 percent of the maximum available deflection. When compression springs are loaded in parallel, the combined rate of all the springs is the sum of the individual rates. When the springs are loaded in series, the combined rate is k= 1 1/k1 + 1/k2 + 1/k3 + + 1/kn (6.3)
This relationship can be used to design a spring with variable diameters. The design method is to divide the spring into many small increments and calculate the rate for each increment. The rate for the whole spring is calculated as in Eq. (6.3). Stress. Torsional stress S is expressed as S= 8K w PD d 3 (6.4)
Under elastic conditions, torsional stress is not uniform around the wire s cross section because of the coil curvature and direct shear loading. The highest stress occurs at the surface in the inside diameter of the spring, and it is computed by using the stress factor K w. In most cases, the correction factor is expressed as K w1 = 4C 1 0.615 + C 4C 4 (6.5)
The stress-concentration factor K w1 becomes K w 2 after a spring has been set out because stresses become more uniformly distributed after subjecting the cross section to plastic flow during set-out: K w2 = 1 + 0.5 C (6.6)
The appropriate stress correction factor is discussed in Sec. 6.4.3. Loads. If deflection is known, the load is found by multiplying deflection by the spring rate. When the stress is either known or assumed, loads can be obtained from the stress equation. Loads should be specified at a test height so that the spring manufacturer can control variations by adjustments of the free length. The load-deflection curve is not usually linear at the start of deflection from free position or when the load is very close to solid height. It is advisable to specify loads at test heights between 15 and 85 percent of the load-deflection range. Loads can be conveniently classified as static, cyclic, and dynamic. In static loading, the spring will operate between specified loads only a few times. In other instances, the spring may remain under load for a long time. In cyclic applications, the spring may typically be required to cycle between load points from 104 to more than 109 times. During dynamic loading, the rate of load application is high and causes a surge wave in the spring which usually induces stresses higher than calculated from the standard stress equation. Buckling. Compression springs with a free length more than 4 times the mean coil diameter may buckle when compressed. Guiding the spring, either in a tube or over
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