Page 181 - Cam Design Handbook

THB6 8/15/03 2:40 PM Page 169

ELEMENTS OF CAM PROFILE GEOMETRY 169

+ )
SN ==01 F - AN + ( A B N - m N W + m N W. (6.17)
q 2 1 1 2
Solving these equations and eliminating m c N 1 W and mN 2 W, whose differences are negligi-
ble, gives

BL
F = (6.18)
B+ 2 mmm (2 A B)
+
l -
c
-
(m Al L )
N = c (6.19)
2
A B)
B 2+ mmm ( 2 +
l -
c
AB) - ]
[m ( 2 + l L
N = c . (6.20)
1
l -
A B)
B 2 mmm ( 2 +
+
c
For best action, the overhang A (which varies through the complete cycle) should be as
small and rigid as possible and the coefficient of friction m c should be kept as small as
possible, such as by a good lubricant and minimization of contaminants.
6.4 CAM RADIUS OF CURVATURE
6.4.1 Radius of Curvature
In the previous discussion, we saw that the pressure angle and cam size are directly related
and the size of the cam should be as small as possible. However, as the cam size is reduced,
another design parameter, radius of curvature is affected. The radius of curvature has a
limiting value for the following reasons:
1. Undercutting could be introduced to yield an erroneous cam shape.
2. Surface contact stresses may be exceeded.
3. Heat treatment could produce cracks.
In other words, the cam surface radius of curvature will have a minimum allowable design
value that will satisfy the other design factors. The shape of a curve at any point (its flat-
ness or sharpness) depends on the rate of change of direction called curvature. We may
construct for each point of the curve a tangent circle whose curvature is the same as that
of the curve at that point. The radius of this circle is called radius of curvature. Figure 6.8
shows the center C of the radius of curvature of a point p of the curve. Note that the
radius of curvature is continuously changing as we move toward other points on the
curve.
From calculus we know that if the curve is in the Cartesian coordinate form y = f(x),
the radius of curvature
¢()] }
{1 +[ fx 2 32
r = . (6.21)
f ¢¢() x
If a curve is given in polar coordinate form r = f(q), the radius of curvature
q }
{ f 2 q ()+[ f ¢()] 2 32
r = 2 2 . (6.22)
q
f
[ f q ()] + [ f ¢()] - f q () ¢¢()
2
q