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In cam-follower systems, follower vibrations are always induced At low speeds, they are rarely a factor for concern, but at high speeds, they can become great enough to signi cantly degrade system performance At very high speeds the vibration may be suf cient to destroy the system or at least stop it from functioning Vibrations arise from many sources: 1 Vibrations due to the shape of the follower acceleration curve (the main source addressed in this chapter) 2 Vibrations resulting from separation of the cam and the follower With positive-drive cams with backlash, impact of the roller on the cam is produced as the contact force changes direction This is called cross-over shock With spring-loaded followers separation is due to the jump condition that occurs when the preload force is insuf cient to maintain a positive contact force 3 Vibrations due to surface irregularities caused by de ciencies in cam and/or follower manufacturing
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4 Vibrations due to variations in the external load For example, a cam-driven punch indexing mechanism has its load applied suddenly as the punch starts into the workpiece This quick-load application cannot be eliminated, and, therefore, the ultimate design must account for it 5 Miscellaneous sources One of these sources is camshaft unbalance In this case, intelligent practical design of the cam structure and the body to reduce the offset mass and maximize camshaft stiffness and support will keep this vibration to a minimum Vibration may be transmitted to the cam surface from the driving mechanism through the frame from such sources as electrical motors, gears, and chains Vibrations may be transmitted from an external source through the foundation of a machine base or the body structure of a vehicle to the cam-follower system For example, the vibration source could be terrain interaction on a ground vehicle or aerodynamic loads on an airplane To reduce vibrations in a cam-follower system, all members from the driver to the follower end should be as rigid as possible The follower should also be as light as possible Damping devices are rarely practical as a means of reducing vibrations in cam mechanisms 1381 Design Guidelines and Rules of Thumb Some generally accepted guidelines in designing cam curves for moderate to high-speed operation are: 1 The maximum acceleration values should be kept as low as possible 2 A continuous jerk function should be maintained, with the peak value preferably not exceeding the maximum for an equivalent cycloidal curve 3 Modi ed sine, modi ed trapezoidal, and cycloidal cam curves are reasonable choices in most cases, usually giving lower peak forces, vibratory amplitudes, noise, stresses, and, in general, smoother performance than other basic curves Other cam curves have the same characteristics that make cycloidal curves good Like cycloidal curves, they provide continuity of all derivatives throughout the lift and their lowest order of discontinuity at each end of the lift curve is at the jerk level or higher Their peak acceleration is comparable to a cycloidal s and they do not possess unnecessary relative maxima or minima in the jerk characteristic Other curves such as polynomials, for example, are also good choices Most methods for the design of high-speed cam pro les that do not involve a formal optimization procedure rely strongly on rules of thumb such as those above When a formal design optimization procedure, such as one of those discussed in this chapter, will not be performed, these guidelines are generally good ones to use The resulting design is likely to be much better than a design obtained without use of any guidelines or formal design procedure, and will be obtained with minimal effort However, if an optimization procedure is employed, such as one of those given in this chapter, it will provide a better design than use of these guidelines will The optimal solution for a high-speed system will often violate guideline 2 to a signi cant degree; there is a high likelihood of discontinuities in the acceleration, equivalent to in nite jerk, at the ends of the cam curve This is particularly true when the objective of the optimization is to reduce the dynamic forces on the cam and follower while still maintaining low vibration characteristics over a wide range of operating speeds Guideline 2 applies most accurately to low-speed systems (where the cam lift duration is very long relative to the system
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