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is no force reversal at the operating speed For spring-loaded open-track cam systems to be fully effective in eliminating backlash the spring must be applied not just to the follower but also at a point in the output transmission that affects all signi cant clearances In summation, the complete action of the roller follower as it rides on the cam is unknown as it rolls, slides, and impacts the cam surface during its cycle of operation 12353 Spring Surge For open-track cam-follower systems, the force loading compression spring has the basic function of keeping the cam and follower in contact At high speeds, a phenomenon occurs that may seriously reduce the effective force of the spring, allowing the follower to leave the cam, even though considerable surplus spring force was provided This is called spring surge It is a torsional wave transmitted through the wire up and down the spring at the natural frequency of the spring It has been found to be a state of resonance at the natural frequency of the spring with the cam high-amplitude harmonics Preventing spring surge is simple In general, the lower the harmonic number, the higher are the vibratory amplitudes Therefore, the natural frequency of the spring should be high enough so that if resonance occurs it will be with higher harmonic numbers and vibratory amplitudes will be kept to a minimum The harmonic number should be 11 or higher However, a ratio as low as 9 may be used with good follower dynamics and a smooth acceleration curve In modeling the system, it is common practice to consider that the weight of the spring substituted should be one-third the total spring weight The phenomenon of jump exists for high-speed springs as well as the linkages For further discussion of the subject of spring surge, see Jehle and Spiller (1929).

1241 Introduction to Elastic Camshaft The power input of almost all mechanisms and machinery is transmitted torsionally from an electric motor to the output where it performs its function In this book, the output is a cam-follower system Also, every torsional motion has a rotating mass or ywheel that is generally located near the cam and support bearing The ywheel provides stability to the system and, depending on its size, aims to control uctuations in speed as energy surges through the system In this section, torsionally elastic camshafts are discussed with a selection of diverse kinds of compliant shafts and followers We will explore the dynamic phenomena of the total machine performance The model system takes into account cam shaft compliance and leads to a set of nonlinear equations owing to the fact that the driving cam function is no longer a known function For more on torsionally compliant cam-follower systems, see Koster (1975a and b)

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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,

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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