Page 82 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 70

70 CAM DESIGN HANDBOOK

Substituting to find the velocity

v = 22 5. (07767. ) =17 5. ips
A
v = 93 3. (07767. ) = 72 5. ips
B
v = maximum velocity
T
= v + D v
B B to T
+
=
= 72 5 17 5 900 ips
.
.
Also, the maximum acceleration
(
A = 31700 7767 ) = 2460 in sec 2
.
A
The curves may now be plotted in Fig. 3.6b. If they were to be compared with a trape-
zoidal acceleration curve, we would find that this curve has a slightly lower maximum
acceleration and the advantage of lower required cutting accuracy in the initial and final
rise portions. Also, the vibrations induced at high speeds should be slightly smaller than
those of the trapezoidal curve.

3.6 SKEWED MODIFIED TRAPEZOIDAL CURVE

Occasionally, the follower requires a particular velocity and acceleration at some critical
points in the machine motion. This can be accomplished by skewing the acceleration
profile as seen in Fig. 3.7. Neklutin (1969) has treated the modified trapezoidal curve with
unequal periods of acceleration, positive and negative. Ragsdell and Gilkey (1969) have
related the skewed acceleration to a correspondingly symmetrical one. Before skewing is
considered, the follower rise h and angle b have been determined and will be considered
as constants.
Let b 1 and b 2 be the periods during positive and negative acceleration, respectively,
b
and let p = 1 be the skew ratio (Fig. 3.7). Thus
b
2
b + b = b
1 2
h + h = h.
1 2
The velocity match at the transition point that
(y ¢ ) = (y ¢ )
max 1 max 2
Substituting and equating from Eq. (3.9)
2h 1 = 2h 2
b 1 b 2
p
\ b = b
1
+
1 p (3.10)
p
h = h
1
1 p
+