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In Chap 12 mathematical models of the differential equations were employed to establish the performance of cam-follower systems Modeling techniques were utilized to investigate the vibratory response of the follower in the time domain In this chapter much of the dynamic study is done as an input of time transients to the cam-follower system Also, Wiederrich (2001) has contributed in the development of this chapter In the beginning, we will be operating in the frequency domain The dynamic response of a cam-follower system has the following three considerations: The driving motion produced by the cam, called the base excitation Note that other external disturbing forces may also act on the follower at the same time The mass, elasticity, and damping of the system between the base excitation and the follower end point The behavior of the follower caused by the excitation, which is called the response The studies presented in this chapter all use the single degree-of-freedom (DOF) model As stated in Chap 12, one DOF is suf ciently accurate to model most cam-follower systems This DOF, the fundamental mode of the system, usually represents the great majority of the dynamic deformation of the system In systems in which one DOF is not clearly dominant, the error in a one-DOF model may be too great When this occurs, either a multi-DOF system must be used or the system structurally redesigned to mitigate the adverse effect of the other signi cant modes Otherwise, the improvement by use of multiDOF does not justify the additional analytical and modeling complexity or the additional data required Multi-DOF system responses are occasionally referred to but will not be treated in this chapter The response of a typical dynamic system consists of both steady state and transient responses For cam-follower systems it is the transient response that is pertinent Steady state vibration is usually not a concern since the cam angular velocity is low in comparison to the natural frequency of the system Therefore, vibrations excited by the acceleration periods are not signi cantly reduced or reinforced by succeeding cam cycles For ease of analysis and simplicity to compare the different cam curve responses we usually assume that vibration damps out during the dwell period and does not carry over to the next cycle The designer will consider The primary response produced during the application of the base excitation or stroke The residual response that remains at the start of the dwell after the removal of the excitation Figure 131 (Hrones, 1948 and Mitchell, 1950) shows the primary and residual responses of a relatively low speed cam-follower system Note that the vibrations occur at the natural frequency of the system Vibrations take place during the stroke and the dwell periods, with their peak magnitudes in uenced by the sudden application, reversal, or removal of the excitation The acceleration discontinuity in the harmonic cam pro les leads to the high vibrations shown As speed is increased, the cycloidal cam vibrations will increase rapidly as the signi cant excitational frequencies approach the natural frequency of the system At suf ciently high speeds the cycloidal system vibrations will approach those of harmonic pro les As Sec 134 will illustrate, we cannot generally assume that pro les with acceleration discontinuities will always perform less well than those without such discontinuities in high-speed systems Sometimes the optimal solution will have signi cant discontinuities in acceleration.

using System;

This line indicates that the program is using the System namespace In C#, a namespace defines a declarative region Although we will examine namespaces in detail later in this book, a brief description is useful now Through the use of namespaces, it is possible to keep one set of names separate from another In essence, names declared in one namespace will not conflict with names declared in a different namespace The namespace used by the program is System, which is the namespace reserved for items associated with the NET Framework class library, which is the library used by C# The using keyword simply states that the program is using the names in the given namespace The next line of code in the program is shown here:

5 + 14 3

Nominal (Theoretical) curve:

class Example {

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This line uses the keyword class to declare that a new class is being defined As mentioned, the class is C# s basic unit of encapsulation Example is the name of the class The class definition begins with the opening curly brace ({) and ends with the closing curly brace (}) The elements between the two braces are members of the class For the moment, don t worry too much about the details of a class except to note that in C#, most program activity occurs within one The next line in the program is the single-line comment, shown here:

Actual curve:

// A C# program begins with a call to Main()

5 74 14 = 3 3

2:

Tolerance:

An Overview of C#

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