Page 406 - Cam Design Handbook

THB12 9/19/03 7:34 PM Page 394

394 CAM DESIGN HANDBOOK

F = ( + 1 y 2 + F cosa
k y y - )cosa
h
p
n
F p
and for y ≥+ 1 , separation occurs, thus
y y +
2
k
h
F = 0.
n
F p
Therefore, we may regard y =+ 1 as providing the least contact separation.
y y +
2
k h
To calculate the contact force, the spring stiffness k h for contact between the cam and
the roller should be defined. We recall that for two cylinders having thickness w, the width
of the rectangular contact area, 2b, can be obtained from Chap. 9, the hertzian stress
formula. Thus,
È 1 - m 1 2 1 - m 2 ˘
Í 2 P E + E ˙
b = Í 1 1 ˙
Í p w Ê 1 + 1 ˆ ˙
Í Î Á Ë r 1 r 2 ˜ ¯ ˙ ˚
where
m 1 , m 2 = Poisson’s ratio of materials for the roller and the cam, respectively
E 1 , E 2 = the modulus of elasticity of materials for the roller and the cam, respectively
r 1 , r 2 = the radius of the roller and the cam, respectively
Note that r 2 varies according to the contact position and is given
2 32
È 2 Ê ds ˆ ˘
Í (r o + ) +s Ë d q ¯ ˙
r = Î ˚
2 Ê ds 2 ds
2
2
(r + ) + 2 ˆ -(r + ) s
s
o Ë d q ¯ o d q 2
where r o = r b + r 1 , R b is the base circle radius. Also, with reference to the geometry of
Chap. 9, the depth of deformations
h = r - r 2 - b 2
1 1 1
2
h = r 2 - r 2 2 - b .
2
P
Since k = , and by assuming unity P, we finally get
h
H
1
k = .
h
h + h
1 2
The frictional forces between the follower stem and the follower guide can be calculated
at
F = m N 1
1
F = m N
2 2
where m is the coefficient of friction between the follower and its guide. From static force
equilibrium,