Page 359 - Cam Design Handbook

THB11 9/19/03 7:34 PM Page 347

CAM SYSTEM MODELING 347

in
w
b rin

R pinion
T in
R gear b rout
J load

out
w
(a) Original system.
in req
w b
J eq

T
in
(b) Equivalent system.
FIGURE 11.21. Geared system with damping.

˙
( b w + J w ) w = h( T - b w ) w
rout out laod out out in rin in in
so
1 Ê È w out ˆ ˘
T = Á ˜ b ( w + J w ˙ )+ b w in ˙ .
in Í rout out load out rin
h Î Ë w in ¯ ˚
Since the angular velocities are related by
Ê R pinion ˆ
w = Á ˜ w
out in
Ë R ¯
gear
this can be rewritten as
2 2
J Ê R pinion ˆ Ê b Ê R pinion ˆ ˆ
T = load Á ˜ w ˙ + b + rout Á ˜ ˜ w .
in in Á rin in
h Ë R ¯ Ë h Ë R ¯ ¯
gear gear
Equating this expression with the equation of motion for the equivalent system in
Fig. 11.21b
T = J ˙ w in + b w in
req
eq
in
it is clear that the equivalent inertia and damping terms are