Roll Rate, Tramp Rate, and Roll Center Location

Branch ID: 220 Request Number: 50000220

Table 1.
Component Unit Comment
1 (X): Suspension Roll Rate N-m/deg The change in axle moment per change in axle roll angle (excluding tires) or:

track = abs((right wheel center y) - (left wheel center y))

roll rate = track^2/(C(3,3)-C(3,9)-C(9,3)+C(9,9))/rtod/1000
2 (Y): Total Roll Rate N-m/deg The change in axle moment per change in axle roll angle (tires in series) or:

track = abs((right wheel center y) - (left wheel center y))

deltaz = C(3,3)-C(3,9)-C(9,3)+C(9,9)+2/(tire stiffness)

roll rate = track^2/deltaz/rtod/1000
3 (Z): Tramp Rate N-m/deg The change in axle moment per change in axle roll angle (tires in parallel) or:

track = abs((right wheel center y) - (left wheel center y))

deltaz = (C(3,3)-C(3,9))*1/(tire stiffness)/

(C(3,3)-C(3,9)+1/(tire stiffness))+

(C(9,9)-C(9,3))*1/(tire stiffness)/

(C(9,9)-C(9,3)+1/(tire stiffness))

tramp rate = track^2/deltaz/rtod/1000
4 (RX): Roll Center Height mm The suspension roll center is found by intersecting the line connecting the left tire patch and the left tire patch front view instant center with the line connecting the right tire patch and the right tire patch front view instant center. The roll center height is defined as the difference between the roll center z coordinate and the average tire patch z coordinate.

ltpdz = C(3,3)-C(3,9) + 1/(tire stiffness)

rtpdz = C(9,9)-C(9,3) + 1/(tire stiffness)

Orientation A:
ltpdy = C(2,3)-C(2,9) + slr*(C(4,3)-C(4,9))
rtpdy = C(8,9)-C(8,3) + slr*(C(10,9)-C(10,3))
Orientation B:
ltpdy = -C(2,3)+C(2,9) + slr*(-C(4,3)+C(4,9))
rtpdy = -C(8,9)+C(8,3) + slr*(-C(10,9)+C(10,3))
m1 = -ltpdy/ltpdz
m2 = -rtpdy/rtpdz
rcy = (ltpz-rtpz+m2*rtpy-m1*ltpy)/(m2-m1)
rcz = ltpz+m1*(rcy-ltpy)
roll center height = rcz - (ltpz+rtpz)/2
5 (RY): Roll Center Lateral mm The roll center lateral location is defined as the roll center y coordinate. See comment for Component 4 for equations.
6 (RZ): Not Used Not Used Not Used