Vehicle Vibration 1

Question 1

what is quarter-car analysis

Answer 1

• a way of modelling a vehicle
• consisting of one wheel and the surrounding car infrastructure

Question 2

what does the diagram for a quarter-car analysis look like

Answer 2

• a point on the road coupled to a mass m_u above it with a spring k_t
• the mass m_u is then coupled to another mass m_s above it with a spring k and a damper c

Question 3

what do the masses m_u and m_s represent

Answer 3

• m_u = unsprung mass for the wheel station
• m_s = sprung mass for the quarter of the vehicle

Question 4

what do the displacements z_r, z_u and z_s represent

Answer 4

• z_r = vertical displacement of road surface (at the point on the road)
• z_u = vertical displacement of unsprung mass m_u
• z_s = vertical displacement of sprung mass m_s

Question 5

what do the springs k_t and k and the damper c represent

Answer 5

• k_t = tyre spring stiffness
• k = suspension spring stiffness
• c = suspension damping

Question 6

what are the two types of road roughness and what type does the course focus on

Answer 6

• discrete roughness from potholes, steps and kerbs
• random roughness due to the road laying process and the Earth’s topography
• the course focuses on random road roughness

Question 7

what is the formula for calculating the mean square value E[x^2]

Answer 7

• Datasheet

Question 8

what is the relationship between the frequency content of a signal x(t) and its mean square spectral density, MSSD, S_x(w)

Answer 8

• x(t) can be represented by S_x(w) by calculating S_x(w) from x(t) using Fourier analysis

Question 9

what is the formula in the datasheet S_y(w) = |H(w)|^2 * S_x(w) saying in words

Answer 9

• the MSSDs of the excitation x(t) and the response y(t) of a single input linear system are related by the transfer function H(w) in that way

Question 10

for a plot of the displacement MSSD against the wavenumber, how would you calculate the mean square displacement

Answer 10

• by calculating the area under the MSSD line

Question 11

for such a plot, what is the analytical representation of the road profile S_zr(n) and what are the variables

Answer 11

• S_zr(n) = Kn^-w
• S(n) = single-sided MSSD (m^3/cycle)
• K (kappa) = roughness
• n = wavenumber (cycle/m)
• w = downwards ‘slope’ of the MSSD (dimensionless), typically 2.5

Question 12

what is the formula for the frequency w as a function of the wavenumber n

Answer 12

• w = 2pinV
• V = speed of the vehicle

Question 13

for vehicle response calculations, the MSSD of a profile needs to be defined in terms of angular frequency. The math is done in the notes, but what is the formula for the MSSD S_zr(w) from S_zr(n) = Kn^-w (in this case, angular frequency is w and the downwards slope is m)

Answer 13

• S_zr(w) = K(2pi*V)^(m-1) * w^-m

Question 14

what does Newland show and what is its relevance

Answer 14

• the second expression in the datasheet: S_x_dot(w) = w^2 * S_x(w)
• its involved in making the input spectral density be white noise so S_zr_dot(w) is constant with w
• to increase the efficiency of the calculation of the vehicle response