Machinery's Handbook, 31st Edition
2382 CAMS AND CAM DESIGN these friction forces. The effect of the friction forces and the pressure angle are taken into account in the formula, (19a) where μ = coefficient of friction in bushing; l 1 , l 2 , and d are as shown in Fig. 21; and P = the sum of all the forces acting down against the upward motion of the follower (acceleration force + spring force + follower weight + external force) (19b) Cam Torque: The follower pressing against the cam causes resisting torques during the rise period and assisting torques during the return period. The maximum value of the resisting torque determines the cam drive requirements. Instantaneous torque values may be calculated from (20) in which T o = instantaneous torque in pound-inches. Example of Force Analysis: A radial translating follower system is shown in Fig. 21a. The follower is moved with cycloidal motion over a distance of 1 in. and an angle of lift β = 100 ° . Cam speed N = 900 rpm. The weight of the follower mass, W f , is 2 pounds. Both the spring weight W s and the external weight W e are negligible. The follower stem diameter is 0.75 in., l 1 = 1.5 in., l 2 = 4 in., coefficient of friction μ = 0.05, external force F e = 10 lbs, and the pressure angle is not to exceed 30 ° . (a) What is the smallest radius R min to the pitch curve? From Formula (9b) the rise angle φ p to where the maximum pressure angle α max exists is: [ ( )] tan α max 180 ° β arccot 360 ° β φ p = = 180 ° 100 ° [ ( )] tan 30 ° arccot 360 ° 100 ° × = 44.94 ° = 45° From Formula (9c) the radius, R α max , at which the angle of rise is φ p is: cos sin µ α F l l l d P 2 n 2 1 2 + − ^ h µ α = − P W a yK # = ^ W F f e 386 preload s + + + + h cos sin T N vF R y F min 30 o n n π α α = = + ^ h
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2 D The same results could have been obtained graphically. If this R min is too small, i.e., if the cam bore and hub require a larger cam, then R min can be increased, in which case the maximum pressure angle will be less than 30 ° . ° π = − − (b) If the return spring K s is specified to provide a preload of 36 lbs when the follower is at R min , what is the spring constant required to hold the follower on the cam throughout the cycle?
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