Page 311 - Cam Design Handbook

THB10 9/19/03 7:28 PM Page 299

CAM MANUFACTURING 299

Ê w ˆ 2
˙˙ y @± 2 s . (10.5)
s Ë D q ¯
Equations (10.3) through (10.5) provide the actual cam profile deviation from the theo-
retical cam shape. A smoother acceleration curve can be found by utilizing average
weighted values (Olderfield, 1958).
In Fig. 10.12 the cam acceleration curves of a high-speed aircraft engine valve gear
linkage are shown. Superimposed on this curve—Fig. 10.12a—is the acceleration trace of
a cam profile with a single smooth nonperiodic error of 0.0005in in 0.020in length of
cam profile. Furthermore, the error was introduced at the top of the cam rise and the
acceleration profile trace shows that this error is only slightly larger than other profile
imperfections.
In Fig. 10.12b we see the acceleration trace of a cam having a more abrupt 0.002in
error in the same profile length of 0.020in. This magnitude of error causes a more appre-
ciable disturbance in the acceleration curve.
It is suggested for satisfactory performance at high speeds that the allowable acceler-
ation error be
˙˙ y £ (1020to % ˙˙ y ) (10.6)
s m
where y m = maximum follower acceleration, in/sec 2
¨
Obviously, the error location with respect to the theoretical cam acceleration curve may
affect the performance and life of a cam-follower surface. In a cycloidal cam as an
example, an error of a few thousandths of an inch in initial and final stages of the rise will
definitely affect the follower performance.
Many types and sizes of errors were investigated to determine the correlation of the
two techniques of obtaining cam-follower acceleration curves. The test cams employed
the cycloidal curve as a theoretical shape. The example in Fig. 10.13 shows a cam that
rotates at 300rpm in 45° of cam falling action from the dwell position. The greatest error
exists at about the 40° cam angle. Correlation is observed between the finite difference
and experimental results. The theoretical maximum acceleration was calculated from the
cycloidal formula to be 19.5g and the maximum acceleration of the cam with errors is
about 34g. On a broad average the maximum acceleration difference for the error is 12g
per 0.001in error at a speed of 300rpm.

EXAMPLE By finite differences, verify the test results of Fig. 10.13.
¨
Solution In Fig. 10.12a, the 0.0005in error has a measured acceleration y s =
2
8400in/sec . By Eq. (10.5)
Ê w ˆ 2
˙˙ y @± 2 s
s Ë D q ¯
2
¥
Ê 3402 p ˆ
@± ( 2 . 0 0005 )Á ˜ = 7400 in sec 2
¥
3
¥
p
Ë 60180 ¯
4
This shows good correlation between test and calculated values. In Fig. 10.13b, the
2
0.002in error has a measured acceleration y s = 45,000in/sec . Again substituting in
¨
Eq. (10.5)
¥
Ê 5402 p ˆ 2
˙˙ y @± ( 2 0 .002 )Á ˜ = 29 ,600 in sec 2
s 3
¥
p
¥
Ë 60180 ¯
4