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FIGURE 6.28 Compressive stress constants for Belleville washers. (Associated Spring, Barnes Group Inc.)
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TABLE 6.19 Elastic Constants of Common Spring Materials
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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 6.29 Tensile stress constants for Belleville washers. (Associated Spring, Barnes Group Inc.)
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Sc = ST1 = ST2 =
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Ef f C1 h + C2 t (1 2 )Ma2 2 Ef f C1 h C2 t (1 2 )Ma2 2 Ef f T1 h + T2 t (1 2 )a2 2
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(6.41) (6.42) (6.43)
The design approach recommended here depends on first determining the loads and stresses at flat position, as shown in Fig. 6.30. Intermediate loads are determined from the curves in Fig. 6.31. Figure 6.30 gives the values graphically for compressive stresses Sc at flat position. The stress at intermediate stages is approximately proportional to the deflection. For critical applications involving close tolerances or unusual proportions, stresses should be checked by using the equation before the design is finalized. The stress level for static applications is evaluated in accordance with Eq. (6.41). This equation has been used most commonly for appraising the design of a Belleville spring because it gives the highest numerical value. It gives the compressive stress at the point shown in Fig. 6.27.
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SPRINGS
6.46 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.
FIGURE 6.30 Loads and compressive stresses Sc for Belleville washers with various outside diameters and h/t ratios. (Associated Spring, Barnes Group Inc.)
SPRINGS 6.47
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FIGURE 6.31 Load-deflection characteristics for Belleville washers. If a washer is supported and loaded at its edges so that it is deflected beyond the flat position, then the greatest possible deflection can be utilized. Since the load-deflection curve beyond the horizontal position is symmetric with the first part of the curve, this chart has been labeled at the right and top to be read upside down for deflection beyond horizontal. Dotted lines extending beyond the chart indicate continuation of curves beyond flat. (Associated Spring, Barnes Group Inc.)
A Belleville spring washer should be designed so that it can be compressed flat by accidental overloading, without setting. This can be accomplished either by using a stress so low that the spring will not set or by forming the spring higher than the design height and removing set by compressing flat or beyond flat (see Table 6.21). The table values should be reduced if the washers are plated or used at elevated temperatures. For fatigue applications it is necessary to consider the tensile stresses at the points marked ST1 and ST2 in Fig. 6.27. The higher value of the two can occur at either
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SPRINGS 6.48
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the ID or the OD, depending on the proportions of the spring. Therefore, it is necessary to compute both values. Fatigue life depends on the stress range as well as the maximum stress value. Figure 6.32 predicts the endurance limits based on either ST1 or ST2, whichever is higher. Fatigue life is adversely affected by surface imperfections and edge fractures and can be improved by shot peening. Since the deflection in a single Belleville washer is relatively small, it is often necessary to combine a number of washers. Such a combination is called a stack. The deflection of a series stack (Fig. 6.33) is equal to the number of washers times the deflection of one washer, and the load of the stack is equal to that of one washer. The load of a parallel stack is equal to the load of one washer times the number of washers, and the deflection of the stack is that of one washer.
FIGURE 6.32 Modified Goodman diagram for Belleville washers; for carbon and alloy steels at 47 to 49 Rc with set removed, but not shot-peened. (Associated Spring, Barnes Group Inc.)
FIGURE 6.33 Stacks of Belleville washers. (Associated Spring, Barnes Group Inc.)
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