Longitudinal location of bounce and pitch nodes with respect to H-point and the natural frequencies of bounce and pitch modes.
Computed by:
SVCNOD
Input Variables Used:
■Hip point marker id | ■Front and rear suspension ride rates |
■Wheel center id's of left and right front wheels | ■Front and rear unsprung mass |
■Global marker id | ■Total force applied to the front and rear tires |
■Sprung mass pitch inertia | ■Wheel base |
Method:
SVC solves the equation of motion of the bounce and pitch displacements of the sprung mass. It first 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 bounce and pitch 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 = (Kf + Kr)/M
b = (Kf*fdis - Kr*rdis)/M
g = (Kf*fdis*ldis + Kr*rdis*rdis)/J
Where:
Kf - total front ride rate
Kr - total rear ride rate
M - total sprung mass
J - moment of inertia of sprung mass about pitch axis
fdis - distance between front springs and sprung mass C.G
rdis - distance between rear springs and sprung mass C.G
The solutions for the above equations are in the form:
z = Z *coswt
q = Q*coswt
substituting these in the equations of motions and solving for w will give the natural frequencies for the bounce and pitch motions.
Node points with respect to C.G of the sprung mass are:
rmd1 = -b/(a - w12)
rmd2 = -b/(a - w22)
where, w12 = Natural Frequency of Pitch
w22 = Natural Frequency of Bounce
Node furthest from the C.G represents the bounce node.
Node points with respect to H-point are:
dhp = (dhp1+dhp2)/2.0 - rllf
Where,
dhp1 - distance between H-point and left wheel center in global X direction.
dhp2 - distance between H-point and right wheel center in global X direction.
rllf - distance between front wheels and sprung mass C.G location.
hpt1 = rmd1 - dhp
hpt2 = rmd2 - dhp
Where,
hpt1 and hpt2 are node point locations with respect to H-point.