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6.10.4 Design Equations M= Ebt 3D3 1 1 + 13 Dn D3 1 1 + Dn D3
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(6.58) (6.59) (6.60)
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L = N(D3 + Nt) + 10D3 Rc = Rn 4+ 4R3 Rn R3 + + Rn R3 Rn
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(6.61)
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Design Suggestions. Let b = 100 t where Dn Rn D2 D3 R3 N Rc = = = = = = = Dn = 250 t D3 =2 Dn D3 = 1.6 D2
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6.11 TORSION BARS
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Torsion bars used as springs are usually straight bars of spring material to which a twisting couple is applied. The stressing mode is torsional. This type of spring is very efficient in its use of material to store energy. The major disadvantage with the torsion bar is that unfavorable stress concentrations occur at the point where the ends are fastened. Although both round and rectangular bar sections are used, the round section is used more often.
6.11.1 Design Equations: Round Sections = S= where = rotation angle in degrees S = shear stress L = active length 584ML d 4G 16M d 3
(6.62) (6.63)
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SPRINGS 6.63
SPRINGS
6.11.2 Design Equations: Rectangular Sections = S= 57.3ML K 1bt 3G M K 2 bt2 (6.64) (6.65)
where factors K 1 and K 2 are taken from Table 6.26. The assumptions used in deriving these equations are (1) the bar is straight, (2) the bar is solid, and (3) loading is in pure torsion. Torsion-bar springs are often preset in the direction in which they are loaded by twisting the bar beyond the torsional elastic limit. Care must be taken in the use of a preset bar: It must be loaded in the same direction in which it was preset; otherwise, excessive set will occur.
6.12 POWER SPRINGS
Power springs, also known as clock, motor, or flat coil springs, are made of flat strip material which is wound on an arbor and confined in a case. Power springs store and release rotational energy through either the arbor or the case in which they are retained. They are unique among spring types in that they are almost always stored in a case or housing while unloaded. Figure 6.49 shows typical retainers, a case, and various ends.
6.12.1 Design Considerations Power springs are stressed in bending, and stress is related to torque by S= 6M bt2 (6.66)
Load-deflection curves for power springs are difficult to predict. As a spring is wound up, material is wound onto the arbor. This material is drawn from that which
TABLE 6.26 Factors for Computing Rectangular Bars in Torsion
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SPRINGS 6.64
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
FIGURE 6.49 Typical power spring retainers and ends. (Associated Spring, Barnes Group Inc.)
was at rest against the case.Thus, the length of active material is constantly changing, which makes it difficult to develop a workable expression for the spring rate. For these reasons, ratios, tables, and graphical presentations are used to develop the design criteria. The ratio of arbor diameter to thickness Da /t is sometimes called the life factor. If it is too small, fatigue life will suffer. The life factor is usually maintained from 15 to 25. The ratio of active strip length to thickness L/t determines the flatness of the spring-gradient (torque-revolution) curve. The curve is flatter when L is longer. The usual range of the L/t ratio is from 5000 to 10 000. The ratio of the inside diameter of cup (case or housing) to thickness Dc /t is the turns factor. This determines the motion capability of the spring or indicates how much space is available between the arbor and the material lying against the inside of the case.
6.12.2 Design Procedure In order to design a power spring that will deliver a given torque and number of turns, first determine its maximum torque in the fully wound condition. If a spring is required to deliver a minimum torque of 0.5 N m for 10 revolutions (r) of windup and 10 r equals 80 percent unwound from solid, then from Fig. 6.50 we see that the torque at that point is 50 percent of the fully wound. Thus the fully wound torque is 1.0 N m. Table 6.27 shows that a strip of steel 0.58 mm thick and 10 mm wide will provide 1.0 N m of torque at the fully wound position per 10 mm of strip width. Figure 6.51 shows that the average maximum solid stress for 0.58-mm-thick stock is about 1820 MPa. At the hardness normally supplied in steel strip for power springs, this is about 95 percent of tensile strength. In Fig. 6.52, 10 turns relate to a length-to-thickness L/t ratio of 4300. With t = 0.58, L equals 2494 mm. Similarly, 4300 L/t relates to a Dc /t ratio of 107. Then Dc = 62.06 mm. If
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