Page 444 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 432

432 CAM DESIGN HANDBOOK

FIGURE 13.15. Uniform convolution residual vibration spectrum
envelopes.

FIGURE 13.16. Uniform convolution residual vibration spectrum
envelopes.

k(1 << k < 20p). This portion of R* is shown in more detail in Fig. 13.16. It was obtained
from an FFT analysis of V i *(h) which gave V i *(2pk), k = 0, 1/8, 1/4, 3/8..... The com-
plete residual vibration spectrum for the limiting profile (i.e., v* •) is shown in Fig. 13.17.
A convenient way to express V 1*(h) is in terms of its Fourier series which is as follows
M
v* h () = V *()+ Â [ Re( V * p m)) ◊ cos p mh) - Im( V * p m)) ◊ sin p mh)] . (13.76)
(2
0
2
(2
(2
(2
i i i i
m=1
The Fourier series coefficients for several of the V i*(h) are given in Table 13.4.
When V 0*(h) is chosen as the velocity curve for simple harmonic motion, then the
envelopes of the residual vibration spectra are as shown in Fig. 13.18. The Fourier series
for V 2*(h) is given as