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since a model is not a real representation of the performing machine There is no real model, only approximate representations of values Since vibration is generally an undesirable side effect, it seldom controls the primary design of the cam-follower machine system Such systems are designed rst to ful ll their main function and are then analyzed from a vibration viewpoint possibly for equipment damage or malfunction, noise, or human discomfort or annoyance The most severe effects of vibration generally occur at resonance; therefore, one usually is concerned rst with determination of the resonance frequencies of the preliminary design Damping is usually neglected in the pertinent calculations for all but the simplest systems If resonance frequencies are found to lie within the intended range of driving frequencies, one should attempt a redesign of the cam and follower system to shift the resonances out of the driving frequency range Added stiffness with little addition of mass results in shifting of the resonances to higher frequencies Added mass with little addition of stiffness results in lowering of the resonance frequencies Damping generally has little effect on the resonance frequencies Excitation reduction of vibration may take the form of running a machine at reduced power, isolating the resonating system from the source of excitation, or shielding the system from exciting inputs Also, increased damping may be obtained by addition of energy-dissipating devices or structures For example, one might use metals with high internal damping for the primary structure or attach coatings or sandwich media with large energy-dissipation capacities to a primary structure of common materials In addition to the basic vibrations that result from compliant systems as discussed in this chapter, vibrations may occur in the cam follower for the following reasons: As a result of separation of the cam and follower with backlash With closed-track cams impact of the roller on the cam is produced and is called crossover shock With opentrack cams vibrations are due to the jump condition of the follower leaving the cam surface Because of surface imperfections or irregularities These can affect the performance of the machine depending on the loads or speeds Due to the rate and phase of application of 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 design by necessity must include it Note that sometimes the application of load during the minus acceleration period tends to reduce or even eliminate the reversal of forces acting on the cam surface Due to cam or linkage unbalance These may be fabricated with blowholes or nonhomogenous contaminants Due to installation of improper and worn parts and misalignment Due to support structures (frame) being either too light in weight or elastic These vibrations may occur at high speed and may be of signi cant magnitude to affect the design action Incidentally, the author has observed a textile machine that performed properly and used an elastic frame to its advantage In other words, the machine only worked utilizing the compliancy of the frame Vibrations transmitted to the cam from a relatively external power source These may arise from electrical motor, gearing, or other machinery action as part of the whole system Due to moving parts of complex linkages affecting the vibration mounts and substructures of the machine.

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As a result of the machine systems being old Generally the older the machine is, the more vibrations, noise, and lack of smoothness of operation occur As result of periodic change in power input voltage of the electrical motor or prime mover This has occurred in the performance of a high-speed textile machine in which the function had transient energy malfunction Due to the inclusion of belts and chains in the torsional drive This may produce large backlash and high compliancy in the system, seriously reducing the effective performance Note that in cases where the vibrating system cannot be modi ed satisfactorily, one may avoid resonance effects by not operating the machine at excitation frequencies at which resonances are excited This may be accomplished by speed controls on a machine or by prescribing limitations on use of the system, eg, red lines on engine tachometers to show operating speeds to be avoided

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1231 Single-Degree-of-Freedom System Modeling, as discussed in Chap 11, transforms the system into a set of tenable mathematical equations that describe the system in suf cient detail for the accuracy required Various tools of analysis are at the disposal of the designer-analyst and range in complexity from classical linear analysis for single-degree-of-freedom systems to complex multipledegree-of-freedom nonlinear computer programs In this section we present a single-degree-of-freedom system (DOF) with a rigid camshaft The cam mechanism consists of a camshaft, cam, follower train including one or more connecting links, and springs terminating in a load mass or force For lumped systems, linkages and springs are divided into two or more ideal mass points interconnected with weightless springs and dampers Springs The spring force generally follows the law

A more accurate approximation could be attained with a finer approximation:

n =1

This little exercise is sufficiently easy so that you do not have to use precious memory space remembering it, just work it out as needed The total length of an arc is the integral between the appropriate limits of this differential statement

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where terms under the S sign are nonlinear Dampers Damping takes the general form C( x ) = Cx x r -1 0 C( x ) is Coulomb damping For r = 1 C( x ) is viscous damping 2 C( x ) is quadratic damping Stiction is accounted for as the breakaway force, , in one element i sliding along another element j Fst = 0 for xi x j for xi x j = at breakaway

10 j=1

Damping value ranges from 4 to 8 percent in most cam-and-follower systems; it is the transient response of the follower that is of basic concern Steady-state vibration in most systems rarely occurs, because in practice the angular velocity of the camshaft is low in comparison with the natural frequency of the follower system We assume that the vibration damps out during the dwell period and does not carry over to the next motion cycle The model is the one-degree-of-freedom system, which lumps the follower train and mass load into a single equivalent mass with equivalent springs and dampers connected to the closed-track cam, as shown in Fig 121 Let m = mass, lb b = damping coef cient, lb/in/sec k = spring rate, lb/in x = follower displacement, in x = follower velocity, in/sec = follower acceleration, in/sec2 x y = cam displacement, in y = cam velocity, in/sec = cam acceleration, in/sec2 y Utilizing Newton s second law, we see that mx + b( x - y) + k ( x - y) = 0 The vibration form of Eq (121) is m( x - y) + b( x - y) + k ( x - y) = - my (122) (121)

FIGURE 121 Single-degree-of-freedom system (closed-track cam)

e ( j 01) 01

Substituting z = x - y yields mz + bz + kz = - my (123)

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HiQPdf Support and Sales Frequently Asked Questions
You can use the HiQPdf library in Windows Azure Cloud Services and Virtual Machines but not in Azure App Service which is a restricted sandbox.

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