TECHNOLOGY – SIMULATION
Equations 1
F
L = ! kb p
2
ka = initial coefficient of friction
kb = drop off of coefficient with load
Fz = load on the tyre 2
A l c p. = c p. =
P F
T Z
A .c p wt
Ac.p = contact patch area (m2) Fz = vertical load on the tyre (N)
wt = width of the tread (m) lcp = length of the contact patch (m)
3 µ= fn(P V T, L , s IN )T
u = coefficient of friction of the tyre
PL = local tyre pressure applied at the tyre
Vs = sliding velocity of the tyre
TINT = core temperature of the tyre
4 5
TC = fn F fn P RAD Z ΔFFFACT ΔFFFACT = _ ⋅ y ref _ ( ) ( )t
a _y cur − ay ref w adf
= change in force factor
ay_cur = measured lateral acceleration for the
change
ay_ref = measured lateral acceleration for the
base set up
wdf = weight distribution at the front
"a 2D model gives you a
good broad brush stroke, but lacks fidelity"
60
www.racecar-engineering.com • January 2012 Figure 2: an illustration of what you obtain from a 2D tyre model
Table 1: typical V8 Supercar set up Parameter
Value
Front roll centre Rear roll centre Front wheel rate Rear wheel rate
Front bar wheel rate Rear bar wheel rate Front track / rear track Front tyre spring rate Rear tyre spring rate c of g height
100mm 240mm 60N/mm 60N/mm 40N/mm 10N/mm
1.6m/1.6m 305N/mm 305N/mm 0.45m
y = k (1" kb ! F ! 1
a z ) Fz
Figure 1: typical 2D tyre modelling correlation using ChassisSim
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