Vehicle Ride 2

Given :-

Total Weight = 1900 kg

F/R distribution = 55% Front

Unsprung mass front = 90 kg

Unsprung mass rear = 60 kg

Solution :-

i)

a) Front sprung mass critical damping = 2 * sqrt (Kr * ms)

Front Ride rate, Kr = (Ks * Kt)/(Ks + Kt)

= (20*250)/(20+250)

Krf = 18.518 N/mm = 18518 N/m

Total mass = 1900 kg

Front mass = 0.55 * 1900 = 1045 kg

Front sprung mass = 1045 - 90 = 955 kg

For a quarter car model, sprung mass at each wheel = 955/2 = 477.5 kg

Front sprung mass critical damping = 2*sqrt(18518*477.5) = 5947.22 N-s/m

b) Rear sprung mass critical damping = 2 * sqrt (Kr * ms)

Rear Ride rate, Kr = (Ks * Kt)/(Ks + Kt)

= (30*250)/(30+250)

Krf = 26.785 N/mm = 26785 N/m

Total mass = 1900 kg

Rear mass = 0.45 * 1900 = 855 kg

Rear sprung mass = 1045 - 60 = 795 kg

For a quarter car model, sprung mass at each wheel = 795/2 = 397.5 kg

Rear sprung mass critical damping = 2 * sqrt (26785 * 397.5) = 6525.96 N-s/m

ii)

a) Front unsprung mass critical damping = 2 * sqrt (Keq * mus)

Front equivalent stiffness, Keq = Ks + Kt = 20 + 250 = 270 N/mm = 270000 N/m

Front unsprung mass = 90 kg

For a quarter car model, unsprung mass at each wheel = 90/2 = 45 kg

Front unsprung mass critical damping = 2 * sqrt (270000 * 45) = 6971.37 N-s/m

b) Rear unsprung mass critical damping = 2 * sqrt (Keq * mus)

Rear equivalent stiffness, Keq = Ks + Kt = 30 + 250 = 280 N/mm = 280000 N/m

Rear unsprung mass = 60 kg

For a quarter car model, unsprung mass at each wheel = 60/2 = 30 kg

Rear unsprung mass critical damping = 2 * sqrt (280000 * 30) = 5796.55 N-s/m

iii)

a) Front sprung mass initial damping coefficient = ζ * Ccf = 0.7 * 5947.22

Front sprung mass initial damping coefficient = 4163.05 N-s/m

b) Rear sprung mass initial damping coefficient = ζ * Ccf = 0.7 * 6525.96

Rear sprung mass initial damping coefficient = 4568.17 N-s/m

iv)

a) Front unsprung mass initial damping coefficient = ζ * Ccf = 0.2 * 6971.37

Front unsprung mass initial damping coefficient = 1394.27 N-s/m

b) Rear unsprung mass initial damping coefficient = ζ * Ccf = 0.2 * 5796.55

Rear unsprung mass initial damping coefficient = 1159.31 N-s/m

v)

Initial damping = Average of rebound and compression damping = (R + C)/2

It is given that Rebound/Compression ratio = 3 (for all speeds) i.e R = 3C

Hence, Initial damping = (3C + C)/2 = 4C/2 = 2C

Therefore, Compression damping = Initial damping/2

a) Front low speed compression damping coefficient = 4163.05/2 = 2081.53 N-s/m

b) Rear low speed compression damping coefficient = 4568.17/2 = 2284.08 N-s/m

vi)

a) Front high speed compression damping coefficient = 1394.27/2 = 697.13 N-s/m

b) Rear high speed compression damping coefficient = 1159.31/2 = 579.65 N-s/m

vii)

From (v),

Rebound damping = 3 * Compression damping

a) Front low speed rebound damping coefficient = 3 * 2081.53 = 6244.59 N-s/m

b) Rear low speed rebound damping coefficient = 3 * 2284.08 = 6852.24 N-s/m

viii)

From (vi),

Rebound damping = 3 * Compression damping

a) Front high speed rebound damping coefficient = 3 * 697.13 = 2091.39 N-s/m

b) Rear high speed rebound damping coefficient = 3 * 579.65 = 1738.95 N-s/m

2.