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1242 Single-Degree-of-Freedom Torsional System In high-speed camera studies of cam-driven systems, Rothbart (1961) observed a phenomenon that was termed shaft windup This phenomenon arose under the conditions of a high inertia load, a large pressure angle, and a exible drive shaft Although the power input end of the shaft rotates at a constant speed, the speed of the cam itself uctuates as it twists due to the time-varying torque During this period, the follower is at rst reluctant to move and later moves slower than intended Beyond the instant of maximum torque,

Solution: Make a change of variable Let U = x 2 so that du = 2xdx This transforms the integral Replace xdx by du/2 and x 2 wt U ih

Since /6 1 = , 2 12 the angle subtends an arc of the unit circle corresponding to 1/12 of the full circumference Since /6 > 0, the angle represents a counterclockwise rotation It is illustrated in Figure 128 The degree measure of this angle is 180 = 30 6

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the energy stored in the shaft is released and drives the cam at an increasing speed, thus causing the follower mass to catch up with the forcing cam action and then to overshoot it In this section (Szakallas and Savage, 1980), we will present the dynamic investigation of two basic types of models: The open-track cam-follower system uses a spring-loaded follower to constrain the follower to the cam The spring force is transmitted to the cam at all times in which the torque on the cam drive has the same frequency as the rotation of the cam The closed-track cam-follower system uses rollers constrained in cam grooves or, as in the conjugate design, dual rollers on two cams It is seen that the closed-track system subjected to an inertia load will have signi cant compliances to yield twice the frequency of the cam speed This phenomenon affects both the torsion and exure in the shaft 12421 Open-Track Cam System Figure 1210 depicts the schematic open-track cam-follower system in which the cam rotation qc differs from the camshaft input rotation qi because of shaft elasticity Where a = ratio of maximum return spring force to the maximum nominal follower inertia force Fh = contact force in the circumferential direction between the cam surface and the follower, lb (N) Fn = nominal cam force, lb (N) Fs = follower return spring force, lb (N)

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In this book we always use radian measure for angles (The reason is that it makes the formulas of calculus turn out to be simpler) Thus, for example, if we refer to ''the angle 2 /3'' then it should be understood that this is an angle in radian measure See Figure 129 Likewise, if we refer to the angle 3 it is also understood to be radian measure We sketch this last angle by noting that 3 is approximately 477 of a full rotation 2 ---refer to Figure 130

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