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Spring ends most commonly used are shown in Fig. 6.24, although the possible variations are unlimited. In considering spring mounting, it must be recognized that for each turn of windup, the overall length L of the spring body will increase as L1 = d(Na + 1 + ) where = deflection in revolutions. Also note that the body coil diameter will be reduced to D= DINa Na + (6.31) (6.30)

where DI = initial mean coil diameter. Experience indicates that the diameter of the arbor over which the spring operates should be approximately 90 percent of the smallest inside diameter to which the spring is reduced under maximum load. Too large an arbor will interfere with deflection, while too small an arbor will provide too little support. Both conditions lead to unexpectedly early failure. Coil diameter tolerances are given in Table 6.17.

6.6.1 Spring Rate The spring rate, or moment per turn, is given by k= Ed 4 M = 10.8DNa (6.32)

FIGURE 6.24 Common helical torsion-spring end configurations. (Associated Spring, Barnes Group Inc.)

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Each of those defines allows me to turn on specific debugging code without having to remember the four places in the code where I need to enable the debugging functionality. Hooray! For example, turning on ENABLE_CELL_POSITION_VISUAL_DEBUG allows me to output the positions of all my sprites every frame for animation debugging.

RJ-45

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.

The number of coils is equal to the number of body coils plus a contribution from the ends. The effect is more pronounced when the ends are long. The number of equivalent coils in the ends is Ne = L1 + L2 3 D (6.33)

where L1 and L2 = lengths of ends, and so Na = Nb + Ne , where Nb = number of body coils. The load should be specified at a fixed angular relationship of the spring ends rather than at a specific angular deflection from free or load positions. Helical torsion springs are stressed in bending. Rectangular sections are more efficient than round sections, but round sections are normally used because there is usually a premium cost for rectangular wire.

6.6.2 Stresses Stress in round-wire torsion springs is given by S= 32K BM d 3 (6.34)

1 2 3 4

Figure 4-4 shows the output. Note that I m using the SC_LOG macro that was mentioned earlier for the output.

where KB = a stress correction factor. Stress is higher on the inner surface of the coil. A useful approximation of this factor is KB = 4C 1 4C 4 (6.35)

6.6.3 Rectangular-Wire Torsion Springs When rectangular wire is formed into coils, it approaches a keystone according to the relation bI = b C + 0.5 C (6.36)

where bI = axial dimension b after keystoning. The radial dimension is always t. The rate equation is k= Ebt3 M = 6.6DNa (6.37)

18 17 16

Stress in rectangular-wire torsion springs is given by S= 6K BM bt2 (6.38)

Crash!

where KBID = 4C/(4C 3) and b = axial dimension of rectangular cross section. Maximum recommended stresses are given in Table 6.15 for static applications and in Table 6.16 for 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.

Because (m 1) Fu = F 2 m = exp w 180 (14.19)

5 6 7 8 9

No matter how hard you might try to write bug-free code, sooner or later you ll run into problems. Whether you experience a problem while running your app locally or one of your beta testers has a crash, you need to know how to track it down and fix it.

w becomes greater, until the belt slips on the pulley with the smaller arc of contact when w = . When Ff = F2, there are no usable forces; that is, F 2 = F 1 = Fu = 0. In this case, no torque can be transmitted. If belt velocity v is increased further, the belt runs off the pulley. The maximum force in the belt sides is given by Fmax = F1 = F 2 + Fu + Ff (14.20)

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