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6.9 FLAT SPRINGS
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6.9.1 Introduction The classification flat springs applies to a wide range of springs made from sheet, strip, or plate material. Exceptions to this classification are power springs and washers. Flat springs may contain bends and forms. Thus the classification refers to the raw material and not to the spring itself. Flat springs can perform functions beyond normal spring functions. A flat spring may conduct electricity, act as a latch, or hold a part in position. In some flat springs, only a portion of the part may have a spring function. Most flat springs are custom designs, and the tooling is often a major cost consideration. Flat springs can be cantilever or simple elliptical beams or combinations of both. These two elementary forms are discussed in this secFIGURE 6.39 Slotted washers. (Associated tion. For a description of the methods Spring, Barnes Group Inc.) used to compute complex flat-spring designs, see [6.6]. Load specification in flat springs is closely connected with the dimensioning of the form of the spring. From the equations it can be seen that the deflection and load vary in proportion to the third power of the material thickness. The important factors in load control are first, the material thickness and second, the deflection. Where close load control is required, the material may have to be selected to restricted thickness tolerance, and/or the free shape may be trued.
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6.9.2 Cantilever Springs The basic type of cantilever is a rectangular spring as shown in Fig. 6.40. The maximum bending stress occurs at the clamping point, and the stress is not uniform through the section. This stress is
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FIGURE 6.40 Rectangular cantilever spring. (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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S= The load is given by P=
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6PL bt2 fEbt 3 4L3
(6.49)
(6.50)
These equations are satisfactory when the ratio of deflection to length f/L is less than 0.3. For larger deflections, use the method described in Fig. 6.41. In cantilever springs with a trapezoidal or triangular configuration (Fig. 6.42), the stress is uniform throughout and is S= The corresponding load is 6PL bot2 (6.51)
FIGURE 6.41 Calculating large deflection in cantilever beams [6.7]. To utilize this figure for any load P, first calculate the quantity 12PL3/Ebt3. Using this value, from the curves find f/L and xo/L, where xo is the moment arm of the load P. Deflection then equals L multiplied by f/L. The maximum stress is reduced in the ratio xo/L. (Associated Spring, Barnes Group Inc.)
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.
SPRINGS 6.57
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FIGURE 6.42 Trapezoidal cantilever spring. (Associated Spring, Barnes Group Inc.)
fEbot 3 4L3K
(6.52)
where K = constant based on the ratio b/bo (Fig. 6.43). These equations are valid for f/L ratios of less than 0.3. 6.9.3 Simple Beams or Elliptical Springs Simple beams are usually rectangular and are formed into an arc as in Fig. 6.44. If holes are introduced for clamping purposes, stress will increase at the hole and at the clamping point owing to stress concentration.
FIGURE 6.43 Correction factor for trapezoidal beam-load equation. (Associated Spring, Barnes Group Inc.)
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.
SPRINGS 6.58
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FIGURE 6.44 Simple beam spring. (Associated Spring, Barnes Group Inc.)
When ends are free to move laterally, the equation for load is P= and stress is given by S= 1.5PL bt2 (6.54) 4fEbt 3 L3 (6.53)
These equations apply when the ratio f/L is less than 0.15. Stress Considerations. The maximum design stresses for cantilevers and simple beams are given in Table 6.24 for static applications and in Table 6.25 for cyclic applications. These recommendations do not apply when holes, sharp corners, notches, or abrupt changes in cross section are incorporated in the design, and should be used for guidance only.
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