Page 331 - Cam Design Handbook

THB11 9/19/03 7:33 PM Page 319

CAM SYSTEM MODELING 319

the “natural frequency” of the system. A stiffer spring (higher spring constant k) results in a
higher natural frequency while a larger mass produces a lower natural frequency.
More complex systems consisting of multiple masses will possess several frequencies
at which components will vibrate. This basic idea of simple harmonic motion and natural
frequencies can be adapted to more complex systems by considering individual modes of
vibration. Figure 11.2 provides an example of a two-mass system commonly used to rep-
resent the suspension at one corner of an automobile for ride quality analysis (Gillespie,
1992). Mass M represents the vehicle body (the “sprung mass”) while mass m represents
the tire and wheel assembly (the “unsprung mass”). These masses are both clearly lumped
parameters that combine masses of a number of individual components on the car. Asso-
ciated with these two masses are two position coordinates (or degrees of freedom) and
two second-order differential equations describing the motion. These equations of motion
can be put into the form
Mx ˙˙ t ()+ Kx t () = 0 (11.8)

where
È M 0 ˘ È K s -K s ˘
M = Í ˙ K = Í ˙ (11.9)
Î 0 m ˚ - Î K s K s + K t ˚

M
x s

K s

m
x t

K t

FIGURE 11.2. Quarter car suspension model.