The wheel hop and tramp natural frequencies are determined by assuming the tire and suspensions springs act in parallel. For independent suspensions, only the wheel hop frequencies of left and right side suspensions are determined. For dependent suspensions, the wheel hop and tramp frequencies are determined.
Computed by:
SVCNOD1
Input variables:
■Unsprung mass of solid axle suspension
■Solid axle roll rate
■Left and right tire rate
■Left and right wheel rate
■Unsprung mass inertia about roll axis for solid axle
■Left and right unsprung masses for independent suspension
Method:
For independent suspensions the hop natural frequency is
frq = sqrt(1000.0 * lrr/lmass)/(2*pi)
where:
■lrr - left suspension ride rate
■lmass - left unsprung mass
For solid axle suspension, SVC solves the equation of motion of the wheel hop and tramp and displacements of the unsprung mass. It first determines the distance between the suspension springs by taking the roll rate into account.
Total distance between both the springs is:
dis = roll rate/ride rate
It then determines the total ride rate at the spring center, total ride rate per unit rotation of the sprung mass, and the angular rate of the body. These values are inserted into the equation of motion to determine the wheel hop and tramp natural frequencies.
The equation of motion for the bounce and pitch motions are:
zacc + az + bq = 0
qacc + gq + bz/r*r = 0
where:
a,b,g are the rates defined above and r is the radius of gyration.
a = (Kl + Kr)/M
b = (Kl*ldis - Kr*rdis)/M
g = (Kl*ldis*ldis + Kr*rdis*rdis)/J
Kl - left ride rate
Kr - right ride rate
M - total unsprung mass
J - moment of inertia about roll axis
ldis - location with respect to axle CG at which effective spring rate acts.
rdis - location with respect to axle CG at which effective spring rate acts.
The solutions for the above equations are in the form:
z = Z *coswt
q = Q*coswt
Substituting these in the equations of motion and solving for w gives the natural frequencies for the wheel hop and tramp motions.