Vehicle Vibration 3

Question 1

what is the lateral force F_lat

Answer 1

• F_lat = αC
• C = lateral creep coefficient

Question 2

for roll-plane analysis, what is the damping coefficient c_lat for a vehicle moving with speed U

Answer 2

• c_lat = F_lat / αU
• F_lat = lateral force applied by a vehicle to a tyre
• αU = steady lateral velocity from slip angle α

Question 3

knowing what F_lat is, what is the simplified version of the damping coefficient c_lat

Answer 3

• c_lat = C / U

Question 4

what is the time constant for a series spring-damper T_lat

Answer 4

• T_lat = c_lat / k_lat

Question 5

what is the lateral spring stiffness k_lat

Answer 5

• k_lat = C / T_lat*U

Question 6

what is the relaxation length of the tyre L_relax

Answer 6

• L_relax = C / k_lat

Question 7

what is the ratio of the roll MSSD S_zφ(n) and the vertical MSSD S_zv(n) defined as

Answer 7

• |G(n)|^2 = S_zφ(n) / S_zv(n)

Question 8

what is the high-pass filter expression for |G(n)|^2

Answer 8

• |G(n)|^2 = n^2 / (n_c^2 + n^2)
• n_c = cut-off wavenumber that depends on the wheel track 2T

Question 9

what is the vertical MSSD S_zv(n) in terms of single wheel track profile MSSD S_z_L,R(n)

Answer 9

• S_zv(n) = S_z_L,R(n) / (1 + |G(n)|^2)

Question 10

what is the roll MSSD S_zφ(n) in terms of single wheel track profile MSSD S_z_L,R(n)

Answer 10

• S_zφ(n) = S_z_L,R(n)*|G(n)|^2 / (1 + |G(n)|^2)

Question 11

what is the suspension roll stiffness T_s

Answer 11

• T_s = 2k_s*S^2

Question 12

what is the suspension roll damping n_s

Answer 12

• n_s = 2c_s*S^2

Question 13

what is the axle to ground roll stiffness T_t

Answer 13

• T_t = 2k_t*T^2

Question 14

what does n_c usually equal for T = 0.75m

Answer 14

• n_c = 0.2 cycle/m for T = 0.75m

Question 15

what is z_φ

Answer 15

• z_φ = φT

Question 16

what is z_L and z_R

Answer 16

• z_L = z_v - z_φ
• z_R = z_v + z_φ

Question 17

what is z_v

Answer 17

• z_v = z_L + z_R / 2

Question 18

what is z_L,R

Answer 18

• z_L,R = z_L = z_R = z_v +/- z_φ

Question 19

what is S_z,L,R(n) from z_L,R and why

Answer 19

• S_z,L,R(n) = S_z,L(n) = S_z,R(n) = S_z,v(n) + S_z,φ(n)
• the +/- changes to + because of the ‘uncorrelation’ expression in the datasheet
• S_x+y = S_x-y = S_x + S_y

Question 20

if the vertical acceleration of the sprung mass is z_s,dd and its angular acceleration is θ_s,dd, what is the vertical acceleration at the seat position z_p,dd

Answer 20

• z_p,dd = z_s,dd + p*θ_s,dd
• p usually = T

Question 21

what is the MSSD of z_p,dd, S_z_p,dd

Answer 21

• S_z_p,dd = S_z_s,dd + p^2*S_θ_s,dd

Question 22

how would you calculate S_z_s,dd and S_θ_s,dd

Answer 22

• S_z_s,dd is calculated from the TFs in the quarter car model
• S_θ_s,dd is calculated from the TFs of the lateral-roll model
• using the single input to single output expression in the datasheet