16 - Railway Vehicle Dynamics, Conicity and Stability Flashcards
History of rail and wheel design
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
Current wheel profile design
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
Inclined rails
Aim to keep contact point above rail web
Inclination matches 1:20 inclination of wheel tread
Flange back-to-back spacing
Important for preventing derailment on tight radius curves (checkrail contact) and through switches and crossings
Track gauge
Important to limit wheel set movement and interaction with back-to-back
Basic wheelset
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
Wheelset with conic wheels
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
Kinematic behaviour of a coned wheelset
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
What are the characteristics of motion (wavelength, L) influenced by?
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
Typical conicity range
0.15-0.3
Cyclic patterns of damage in track
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
What is wheelset steering?
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
Disadvantages of wheelset steering
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
Bogie suspensions - real wheelset behaviour
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’
For a wheelset with inertia, which directions do the equations of motion go in?
Lateral - transverse to track
Rotational (yaw) - relative to track
Creep force term in equations of motion depends on
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
Instability - critical speed rises with increase in…
Wheel radius
Track gauge
Bogie stiffness (yaw or lateral stiffness)
Instability - critical speed falls with increase in…
Conicity
Axle mass/rotational inertia
How much vehicle suspensions be designed?
To meet stability for a specified conicity value and vehicle’s maximum speed +10%
P1 wheel profile
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
P8 wheel profile
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
What contributes to conicity?
Wheel profile shape
Rail profile shape
Track gauge
Wheel profile shapes
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
How conicity varies with wheel wear
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
Rail profile shapes
‘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
Track gauge
As gauge tightens, contact point is forced towards flange area of wheel, increasing conicity
How conicity varies with track gauge for different wheel profiles
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
What is a conicity map derived from?
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
Wheelset instability case study
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
Effects of vehicle instability
Poor passenger comfort
Increased forces (damage) imposed on track
In extreme cases, risk of derailment
Solutions to instability
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)
For ideal curving
Low primary stiffness
High conicity
Unstable
For ideal high speed stability
High primary stiffness
Low conicity
Curve wear
