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produced by a milling cutter taking too large a feed in the continuous generation of a cam See Harris (1991) for the effect of waviness on vibration and noise Another kind of error is the misalignment of assembled parts Misalignment of parts is a fault that should not be tolerated The parts should be tted properly for machine running conditions The sources of misalignment include inaccurate machining or large tolerances in the mounting surfaces Misalignment produces a reduced fatigue life in camfollower contacting surfaces In the roller follower there are two types of misalignment: (1) the cam follower axis is not parallel to the plane of rolling, eg, the axis is lifted on one end This condition will shift the contact area to one end of the outer ring (2) Also, the cam-follower axis is not perpendicular to the direction of motion; in other words, the axis is skewed Misalignment can be accommodated by using crowned followers Straight rollers produce an elliptical contact stress surface, and crowned runners produce a circular stress surface Also, a large radius crown should be used 1045 Probabilistic Model of Cam Pro le The stochastic nature of the cam pro le used by Kim and Newcombe (1982) is presented in this section Also, the designer is referred to Chap 12, which shows the combined effects of the cam follower dynamics and the probabilistic model of the cam pro le In Fig 107, we see that the desired location of the cutter is within a tolerance band in both the x and the y directions Thus, the resulting pro le shape will have a random waviness, and surfaces produced by milling, turning, grinding, and honing have an almost gaussian, or normal, distribution For the cam pro le, a normally distributed random value with a given mean and a standard deviation is generated from a sequence of uniform random numbers To obtain a smooth acceptable shape, the random points that lie within a selected tolerance band are connected by a cubic spline curve, Fig 108 Kim and Newcombe (1982) applied a spline curve on displacement values from the two-dimensional tolerance of the cam pro le and the roughness of the roller surface, assuming both obey the gaussian distribution, Fig 109 The resulting continuous spline function was differentiated to obtain the theoretical characteristic acceleration, pressure angle, and radius of curvature of the cam pro le so that the dynamic simulation may be investigated, Fig 109
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Cutter or grinder
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Tolerance in Y direction Desired profile
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FIGURE 107 Tolerance band for setting cutter
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Tolerance lines in Y direction Actual machine setting point
FIGURE 108
Cam pro le waviness produced by tolerance band in setting cutter
Normal distribution curve One-dimensional tolerance line
Chosen points
Theoretical displacement curve Dq Actual displacement curve
FIGURE 109 Combined effects of cam and follower tolerance on follower displacement curve
1046 Manufacturing Discussion Note that pro le accuracy does not wholly lie in orthodoxy to or deviation from the theoretical pro le Also important are the increment deviation and its proportion to the theoretical change in increment displacement For example, an error of 0001 in at the beginning of a stroke, where the increment change in displacement is small, is of more concern that the same error at the middle of the stroke where the increment change is much larger Also, the effect of a gradual error occurring over a long period is less important than the same total error in a much shorter period Furthermore, the location of error deviation is a critical factor only if it affects the performance of the nal machine The error in dwell period may be more important than any other part of the cam action Roughness is the lack of surface smoothness Smoothness can be increased (roughness decreased) by pressure grinding of the cam surface Roughness in the cam pro le always produces high-frequency and low-amplitude vibrations The only practical way to improve this outcome requires the expense of more accurate fabrication and checking (preferably dynamic characteristics) of surface smoothness Reduced roughness on surface-ground
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