Machinery's Handbook, 31st Edition
2378
CAMS AND CAM DESIGN
180
p ° φ
cos
R h 2 1 max α <
F
d
n
(8d)
− −
min
β
For Cycloidal Motion
180 ° πβ R α ------- 1 [ ( arccot
360 °φ β – cos --------
arctan
(9a) (9b)
φ
α
)] tan α max 360 °
β
180 ° β
φ
α
2
360
°
φ
p
1
cos
<
F
d
n
−
h
β
(9c)
φ φ
2
α max
π
φ
p
sin
360
d
n
°
β
360
1
φ
p ° φ
p
(9d) Radius of Curvature.— The minimum radius of curvature of a cam should be kept as large as possible (1) to prevent undercutting of the convex portion of the cam and (2) to prevent too high surface stresses. Fig. 20(a), (b) and (c) illustrate how undercutting occurs. R h 2 max β π β − − α d n < F min sin
Wanted Path of Follower
Pitch Curve
r f
r f
r f
ρ min
Actual Path of Follower
Pitch Curve
ρ min
ρ min
R c
Cam Surface Left after Undercutting
Cam Surface
(a)
(b)
(c)
Fig. 20. (a) No Undercutting; (b) Sharp Corner on Cam; (c) Undercutting In Fig. 20(a) the radius of curvature of the path of the follower is ρ min and the cam will at that point have a radius of curvature R c = ρ min − r f . In Fig. 20(b) ρ min = r f and R c = 0. Therefore, the actual cam will have a sharp corner which in most cases will result in too high surface stresses. In Fig. 20(c) is shown the case where ρ min < r f . This case is not possible because undercut ting will occur and the actual motion of the roller follower will deviate from the desired one as shown. Undercutting cannot occur at the concave portion of the cam profile (working surface), but caution should be exerted in not making the radius of curvature equal to the radius of the roller follower. This condition would occur if there is a cusp on the displacement diagram which, of course, should always be avoided. To enable milling or grinding of con cave portions of a cam profile, the radius of curvature of concave portions of the cam, R c = ρ min + r f , must be larger than the radius of the cutter to be used. The radius of curvature is used in calculating surface stresses (see following section), and may be determined by measurement on the cam layout or, in the case of radial translating followers, may be calculated using the formulas that follow. Although these formulas are exact for radial followers, they may be used for offset and swinging followers to obtain an approximation.
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