Machinery's Handbook, 31st Edition
2366
CAMS AND CAM DESIGN
B
Acceleration
Velocity
V
h
A
T
Acceleration
Fig. 5. Cam Displacement, Velocity, and Acceleration Curves for Parabolic Motion The most important advantage of this curve is that for a given angle of rotation and rise it produces the smallest possible acceleration. However, because of the sudden changes in acceleration at the beginning, middle, and end of the stroke, shocks are produced. If the follower system were perfectly rigid with no backlash or flexibility, this would be of little significance. But such systems are mechanically impossible to build and a certain amount of impact is caused at each of these changeover points.
B
Acceleration Velocity
V
h
A
T
Fig. 6. Cam Displacement, Velocity, and Acceleration Curves for Simple Harmonic Motion 3. Simple Harmonic Motion: (Fig. 6 ) (3a) } (3b) 0 ≤ t ≤ T (3c) Smoothness in velocity and acceleration during the stroke is the advantage inherent in this curve. However, the instantaneous changes in acceleration at the beginning and end of the stroke tend to cause vibration, noise, and wear. As can be seen from Fig. 6, the maxi mum acceleration values occur at the ends of the stroke. Thus, if inertia loads are to be overcome by the follower, the resulting forces cause stresses in the members. These forces are in many cases much larger than the externally applied loads. cos cos y h T t y h 2 1 = − : 180 2 1 = − ; 180 or ° ° β φ a c k m D E sin sin T T t v 180 180 or ° ° π β πω β φ = v h 2 = a c k m h 2 · · cos cos T T t a h = 180 2 180 or 2 2 2 ° ° π β πω β φ = a h 2 · a a c k k m ·
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