Curving and stability of a Railway wheelset

Question 1

What are the 2 reasons railway vehicles are ‘coned’?

Answer 1

• To provide a centralising action on a straight track

- To allow a rigid wheelset to negotiate a curve without slip

Question 2

What are the 2 degrees of freedom for a railway wheelset?

Answer 2

Yaw angle and sideways displacement

Question 3

How do you find the rolling radius of railway wheels?

Answer 3

They equal the original radius +/- y*tanΣ
y- sideways displacement
Σ- cone angle/effective conicity

Question 4

What is the no slip condition?

Answer 4

u = rω

Question 5

Equation for angular velocity of wheelset

Answer 5

((u1 - u2) / 2d where u represents the speed of each wheel, so angular velocity is derived from the relative velocity of each wheel

Question 6

How do you get the equation of motion for a wheelset?

Answer 6

There are 2 unknown states, y and θ (yaw and slideways disp), make equations for θdot and ydot. Differentiate ydot to acceleration, which will allow you to substitute for θdot and thus create a equation of motion in SHM form ydouble dot + ωn^2*y = 0, giving you the natural frequency of the oscillations.

Question 7

How do you get the wavelength of the oscillations of a railway wheelset, and what is this also called?

Answer 7

Take the natural frequency from the equation of motion, then use the average speed equation u = rω, and v = fλ to get λ

λ is also called the kinematic wavelength

Question 8

What is the lateral creep velocity of a railway wheel?

Answer 8

y(dot) + uθ
u- average forward speed
y(dot)- velocity due to lateral tracking error
uθ- velocity due to yaw angle θ

Question 9

What is the longitudinal (creep) velocity for a railway wheel?

Answer 9

Outer wheel:
u + d( θ(dot) + γ(dot) ) - r2 u/r
u- average forward speed
θ(dot) + γ(dot) - sum of angular velocities of the wheelset yaw θ(dot) and the turning motion around an instantaneous centre γ(dot)
d- half the wheelset width
r2 u/r - longitudinal slip term (gives the actual velocity at the base of the wheel, subtracting this from the average forward speed u is the normal longitudinal slip velocity equation)

Get inner wheel equation as the same as the outer but with the sign changed for the rotational velocity term and the rolling radius changed to r1.

Question 10

How do you get the lateral force for a railway wheel?

Answer 10

You take the lateral creep velocity and divide by the average forward speed u to get the lateral creep ratio α, then just multiply by the coefficient of creep C to get the lateral force on the wheel (multiply by 2 if you want the force on the whole wheelset.

Question 11

What are the conditions for steady state curving of railway set?

Answer 11

y(dot) = θ(dot) = 0