Machinery's Handbook, 31st Edition
2380
CAMS AND CAM DESIGN
2 3 ⁄ 2
180 πβ
h
°
. 091
2
R
h
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E
h
c
m
^
+
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min
(13d)
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h
min
°
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πβ
( ρ min occurs near φ = 0.75 β ) Example: Given h = 1 inch (m), R min = 2.9 inch (m), and β = 60 ° . Find ρ min for parabolic motion, simple harmonic motion, and cycloidal motion. Solution: ρ min = 2.02 inch (m) for parabolic motion, from Equation (10) ρ min = 1.8 inch (m) for simple harmonic motion, from Equation (10) ρ min = 1.6 inch (m) for cycloidal motion, from Equation (13d) The value of ρ min on any cam may also be obtained by measurement on the layout of the cam using a compass. Cam Forces, Contact Stresses, and Materials.— After a cam and follower configuration has been determined, the forces acting on the cam may be calculated or otherwise de- termined. Next, the stresses at the cam surface are calculated and suitable materials to withstand the stress are selected. If the calculated maximum stress is too great, it will be necessary to change the cam design. Such changes may include: 1) increasing the cam size to decrease pressure angle and increase the radius of curvature; 2) changing to an offset or swinging follower to reduce the pressure angle; 3) reducing the cam rotation speed to reduce inertia forces; 4) increas- ing the cam rise angle, β , during which the rise, h , occurs; 5) increasing the thickness of the cam, provided that deflections of the follower are small enough to maintain uniform loading across the width of the cam; and 6) using a more suitable cam curve or modifying the cam curve at critical points. Although parabolic motion seems to be the best with respect to minimizing the calculated maximum acceleration and, therefore, also the maximum acceleration forces, nevertheless, in the case of high speed cams, cycloidal motion yields the lower maximum acceleration forces. Thus, it can be shown that owing to the sudden change in acceleration (called jerk or pulse ) in the case of parabolic motion, the actual forces acting on the cam are doubled and sometimes even tripled at high speed, whereas with cycloidal motion, owing to the gradually changing acceleration, the actual dynamic forces are only slightly higher than the theoretical. Therefore, the calculated force due to acceleration should be multiplied by at least a factor of 2 for parabolic and 1.05 for cycloidal motion to provide an allowance for the load-increasing effects of elasticity and backlash. The main factors influencing cam forces are: 1) displacement and cam speed (forces due to acceleration); 2) dynamic forces due to backlash and flexibility; 3) linkage dimensions which affect weight and weight distribution; 4) pressure angle and friction forces; and 5) spring forces. The main factors influencing stresses in cams are: 1) radius of curvature for cam and roller; and 2) materials. Acceleration Forces: The formula for the force acting on a translating body given an acceleration a is: (14) In this formula, g = 386 inches/second squared, a = acceleration of W in inches/second squared; R = resultant of all the external forces (except friction) acting on the weight W . For cam analysis purposes, W , in pounds, consists of the weight of the follower, a portion R g Wa Wa 386 = =
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