4569846498

204 Multibody Systems Approach to Vehicle Dynamics
Working in mm and taking the wavelength L as 350 mm and the amplitude
a as 12.5 mm, for a total bump height of 25 mm, gives
x
z 12.5 sin
⎛ ⎞
⎝ 175 ⎠
We are after the vertical velocity of point P which can be expressed as:
dz
dt
where
dx
dt
dz
dx
dx
dt
15 000 mm/s
(4.97)
(4.98)
and
dz
12.5
d 175 cos x
⎛ ⎞
x
⎝175⎠
giving
dz
12.5
x
cos
⎛ ⎞
15 000
dt
175 ⎝175⎠
(4.99)
(4.100)
The maximum value of dz/dt occurs when cos(x/175) 1 and occurs at
values of x 0, 350, 700, . . . giving
⎛ dz⎞
⎝ dt
⎠
The acceleration d 2 z/dt 2 is given by
2
d z
2
dt
max
12.5
15 000 3366 mm/s
175
12.5
2
175
2
sin
⎛ x
⎞
15 000
⎝175⎠
and has a value of zero at x 0, 350, 700, . . .
(4.101)
(4.102)
This provides inputs for the following velocity and acceleration analyses of
V Pz 3366 mm/s
A Pz 0 mm/s 2
The approach taken here is to initially ignore the spring damper assembly
between points C and I shown in Figure 4.67. Solving for the rest of the
suspension system will deliver the velocity {V C } 1 of point C thus providing
a boundary condition allowing a separate analysis of the spring damper to
follow.
Before proceeding with the velocity analysis it is necessary to identify the
unknowns that define the problem and the same number of equations as
unknowns leading to a solution. The angular velocities of the rigid bodies
representing suspension components can be used to find the translational