16 - Railway Vehicle Dynamics, Conicity and Stability

Question 1

History of rail and wheel design

Answer 1

Early iron rails had flange mounted on rail to guide conventional wagon wheels
Evolved to wheels with flanges for easier rail construction (less material) and cylindrical wheel treads
Evolved again for wheels to have tapered profile of tread - easier to manufacture by forging, reduces rolling resistance on curves as tapered profiles provide some ‘steering’ ability

Question 2

Current wheel profile design

Answer 2

Very closely defined with tight tolerances
Railway Group Standards specify allowable shapes for wheel tread
Specify flange shape for safety - derailment resistance and behaviour through switches and crossings

Question 3

Inclined rails

Answer 3

Aim to keep contact point above rail web
Inclination matches 1:20 inclination of wheel tread

Question 4

Flange back-to-back spacing

Answer 4

Important for preventing derailment on tight radius curves (checkrail contact) and through switches and crossings

Question 5

Track gauge

Answer 5

Important to limit wheel set movement and interaction with back-to-back

Question 6

Basic wheelset

Answer 6

Axle with 2 wheels fixed to rotate with it
Cylindrical tread profiles
Runs well on straight track
No guidance provided on curves
No mechanism for wheel to know the rails are moving laterally and they should follow them
High derailment risk, even with flange providing guidance - high lateral forces

Question 7

Wheelset with conic wheels

Answer 7

Allows wheel radius to vary, depending on location of contact point
Rolling radius of each wheel depends on how far wheelset is from track centre
Steering movement of wheelset is controlled by ‘Rolling Radius Difference’ between two wheels
Slope of graph of RRD function is twice the semi-cone angle (conicity) of wheelset

Question 8

Kinematic behaviour of a coned wheelset

Answer 8

For ‘typical’ conicity wheel on 1500m radius curve, equilibrium rolling line is 2.009mm from track centre line
This is how much the wheelset needs to move laterally over rail to get to ideal curving position

Question 9

What are the characteristics of motion (wavelength, L) influenced by?

Answer 9

L increases with track gauge, 2l
L decreases as conicity increases
L is independent of the initial offset of the wheelset from the track centre
The wheelset will always steer itself back towards the centre line of the track

Question 10

Typical conicity range

Answer 10

0.15-0.3

Question 11

Cyclic patterns of damage in track

Answer 11

Clusters of RCF cracks or rail side wear
Lateral track alignment irregularities
Often appear in cyclic manner at 7-10m intervals
Caused by natural kinematic motion of wheelset

Question 12

What is wheelset steering?

Answer 12

When a wheelset encounters a curve it becomes offset from the centre line of the track and the rails move under it
The increase in RRD will cause the wheelset to ‘yaw’ or steer to follow the centre of the track

Question 13

Disadvantages of wheelset steering

Answer 13

On straight track, if wheelset becomes displaced from track centre line, sinusoidal motion will be set up (with wavelength given by Klingel equation)
Wheelset continuously overshoots track centre line
Often referred to as ‘hunting’ - very undesirable
Imposes large lateral forces on track
Increases risk of derailment
Poor passenger comfort

Question 14

Bogie suspensions - real wheelset behaviour

Answer 14

Expression for kinematic motion of wheelset (Klingel equation) is too simplistic - considers only an ‘unconstrained’ wheelset
In reality, wheelset is attached to bogie frame/vehicle through series of springs and dampers
These allow wheelset to yaw (rotate about vertical axis) when curving, but need to be stiff enough to hold wheelset steady if it tries to start ‘hunting’

Question 15

For a wheelset with inertia, which directions do the equations of motion go in?

Answer 15

Lateral - transverse to track
Rotational (yaw) - relative to track

Question 16

Creep force term in equations of motion depends on

Answer 16

Creepage - relative velocities of wheel and rail
Contact patch size and shape
Creep force terms are ‘Kalker coefficients’ that describe relationship between contact patch, creepage and creep force

Question 17

Instability - critical speed rises with increase in…

Answer 17

Wheel radius
Track gauge
Bogie stiffness (yaw or lateral stiffness)

Question 18

Instability - critical speed falls with increase in…

Answer 18

Conicity
Axle mass/rotational inertia

Question 19

How much vehicle suspensions be designed?

Answer 19

To meet stability for a specified conicity value and vehicle’s maximum speed +10%

Question 20

P1 wheel profile

Answer 20

1:20 cone
No contact on gauge shoulder
Very small changes in contact position
Little variation in RRD
Low conicity - large lateral movement gives small RRD, but long natural wavelength
Good stability on straight track, poor curving

Question 21

P8 wheel profile

Answer 21

Worn P1 profile
Contact across more of profile
Larger variations in RRD
Moderate conicity - small lateral movement gives larger RRD, but short natural wavelength of oscillation
Good curving

Question 22

What contributes to conicity?

Answer 22

Wheel profile shape
Rail profile shape
Track gauge

Question 23

Wheel profile shapes

Answer 23

P1: 1:20 cone; traditional for old passenger stock
P8: derived from worn P1; almost universal on modern passenger stock
P12: new variation on P8; developed to try to reduce risk of RCF developing
RD9: variation on P8 but with thinner flange; attempt to reduce conicity on track with tight gauge
P5, P10: used on freight vehicles
Once in service, wheel will wear to a new shape depending on vehicle type and route it operates
Changes to wheel shape changes its conicity
GM/RT/2466 specifies limits for wear - tread depth and flange thickness

Question 24

How conicity varies with wheel wear

Answer 24

Conicity generally increases as wheel mileage (i.e. wear) increases
For passenger vehicles, wheelset maintenance interval is often governed by conicity (leading to poor ride), rather than limits of wear allowable in Railway Group Standards

Question 25

Rail profile shapes

Answer 25

‘Bullhead’ and BR109 profiles - higher gauge corners which contact well into root of wheel between tread and flange
113A (and CEN56E1, CEN60E2) - profiles have lower gauge corners so lower conicity than bullhead
Ground rail profile has even lower gauge corner

Question 26

Track gauge

Answer 26

As gauge tightens, contact point is forced towards flange area of wheel, increasing conicity

Question 27

How conicity varies with track gauge for different wheel profiles

Answer 27

P1 gives similar conicities
P8 wheel gives much higher conicity on bullhead rail because of higher gauge corner - can lead to wheelset stability ‘hunting’ problems
P10 profile gives very low conicity on 113A rail for most track gauge values - very poor steering, lots of flange wear

Question 28

What is a conicity map derived from?

Answer 28

Measured rail profiles
Measured track gauge
For different wheel profiles measured from vehicles running over route
Very high conicity calculated for track sections where instability occurs for worn wheel shapes
Acceptable conicity achieved on older rail sections and for new wheel profiles

Question 29

Wheelset instability case study

Answer 29

Thirsk, 31st July 1967
Derailment of 4-wheel wagon due to ‘hunting’
45mph
Worn wheels
Before vehicle dynamics and stability fully appreciated
Instability in some vehicles occurring at speeds as low as 30mph
Derailed wagon struck by passenger train on adjacent line

Question 30

Effects of vehicle instability

Answer 30

Poor passenger comfort
Increased forces (damage) imposed on track
In extreme cases, risk of derailment

Question 31

Solutions to instability

Answer 31

Change vehicle design - stiffer suspension
Reduce vehicle speed - impose speed restriction
Reduce conicity - improve track gauge, grind rail profile (relieve gauge corner area to reduce RRD) or correct wheel profile (choose new, lower conicity profile or, if problem due to heavily worn wheels, return wheels to design profile)

Question 32

For ideal curving

Answer 32

Low primary stiffness
High conicity
Unstable

Question 33

For ideal high speed stability

Answer 33

High primary stiffness
Low conicity
Curve wear