Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN 2383 The follower tends to leave the cam at the point of maximum negative acceleration. Fig. 7 shows this to be at φ = 3 ∕ 4 β = 75 ° . From Formula (4c), / sin sin sec a h 2 360 100 2 1 6 900 100 360 75 18,300 in 2 2 2 2 2 # # # # ° ° ° ° β π ω β φ π = = =− ° c ^ ^ a m h h k From Formulas (14) and (15), R Wa W W W a 386 386 3 1 386 2 0 0 18,300 95lbs (upward) + + − = ^ h h f s e = = + + = a ^ k Using Formula (16) to determine the spring force F s to hold the follower on the cam, F R W F F s f e f = − − − as stated on page 2380 , the value of R in the above formula should be multiplied by 1.05 for cycloidal motion to provide a factor of safety for dynamic pulses. Thus, . . F R W F F 105 105 95 2 10 0 88lbs (downward) s f e f # = − − − = − − − = The spring constant from Formula (17) is: K y F y 88 36 preload s a s a = − = − and, from Formula (4a), y a is: . sin sin y h 2 1 360 1 100 75 2 1 100 360 75 0 909 in a # # ° ° ° ° ° ° β φ π β φ π = − = − = c a m k ; : E D so that K s = (88 − 36)/0.909 = 57 lb/in. (c) At the point where the pressure angle α max is 30 ° ( φ = 45 ° ) the rise of the follower is 1.96 − 1.56 = 0.40 in. What is the normal force, F n , on the cam? From Formulas (19a) and (19b)
386
preload
yK + + s
W F f e
Wa
+ +
⁄
F
=
sin µ α
n
cos
2
l l
d
h
^
α
−
+ −
µ
1 2
l
2
using φ = 45 ° , h = 1 in., β = 100 ° , and ω = 6 × 900 in Formula (4c) gives a = 5660 in/sec 2 . So that, with W = 2 lbs, y = 0.4, K s = 57, preload = 36 lbs, W f = 2 lbs, F e = 10 lbs, α = 30 ° , μ = 0.05, l 1 = 1.5, l 2 = 4, and d = 0.75,
. 4 005 30 2 15 4 005 075 386 04 57 36 2 2 5660 . . . . sin + # # # # ° + − + + ^ ^ h
110lbs
F
=
=
n
cos
30
# h Note: If the coefficient of friction had been assumed to be 0, then F n = 104; on the other hand, if the follower is too flexible, so that sidewise bending occurs causing jamming in the bushing, the coefficient of friction may increase to, say, 0.5, in which case the calculated F n = 200 lbs. ° − (d) Assume that in the manufacture of this cam an error or “bump” resulting from a chattermark or as a result of poor blending occurred, and that this “bump” rose to a height of 0.001 in. in a 1 ° rise of the cam in the vicinity of φ = 45 ° . What effect would this bump have on the acceleration force R ? One formula that may be used to calculate the change in acceleration caused by such a cam error is:
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