Vibration- Roll plane analysis

Question 1

How many DOF does the roll plane model have?

Answer 1

6

Question 2

What assumption allows for one degree of freedom to be removed from the roll plane model?

Answer 2

The fact that there is no relative lateral motion of the masses at the roll centre, therefore we can reduce the model to 6 DOF (vertical displacement and roll of sprung and unsprung masses, and lateral displacement of vehicle centre point and the connection point between the spring and damper model for later tyre performance)

Question 3

What is the equation for damping coefficient c(lat)?

Answer 3

c(lat) = F(lat) / αU
(recall equation for a damper that force=damping x velocity)
α-slip angle
U-forward speed
therefore αU = lateral force due to lateral velocity

Recall from other dynamics lecture, F(lat)=αC where C is the lateral creep coefficient. Therefore c(lat) = C/U

Note that as the velocity of the vehicle increases to inf, c(lat) and thus F(lat) decreases to 0, and the damping is infinite at 0 speed)

Question 4

For a series spring damper model of a tyre, what do you know about the lateral for generated

Answer 4

It is equal to both the force in the spring (kx) and the force in the damper (c(lat)*relative velocity)

Question 5

For a series spring damper model of a tyre, what do you know about the rate of change of lateral force generated? (NOT SURE ABOUT THIS ONE)

Answer 5

It is only contributed by the spring and thus is equal to the rate of compression/extension * k

Question 6

What is the time constant of a series spring-damper?

Answer 6

τ(lat) = c(lat) / k(lat)

time constant = damping/stiffness) increases with increasing damping to stiffness ratio

Question 7

What is the relaxation length of the tyre?

Answer 7

The distance the tyre rolls for the lateral force to reach 63.2% of its steady state value, following a step change in slip angle or lateral velocity.

Lrelax = C / k(lat)
C-lateral creep coefficient

Question 8

What characteristics occur with a step change in lateral force Flat applied to a tyre?

Answer 8

There will be a step change in deflection from the spring, and a steady velocity from the damper

Question 9

What change to the inputs makes the response calculation much easier for the roll model?

Answer 9

considering the input as a combination of the average vertical input (average of the left and right input) and a roll contribution

Question 10

What does it mean if two signals are uncorrelated?

Answer 10

That if we know the value of x at any instant, we cannot predict the corresponding value of y.

Question 11

What is the equation used for mod(G(n)) ^2 for a high pass filter, and how does this relate to the MSSDs of average vertical input and roll input?

Answer 11

mod(G(n)) ^2 = n^2 / (n(c)^2 + n^2)
n(c) = cut off wavenumber that depends on wheel track width, typically n(c) = 0.2 cycles/m

mod(G(n)) ^2 is derived to equal MSSD of roll input / MSSD of average vertical input