5 - Friction and Braking Flashcards
(32 cards)
Define friction
The force between interacting surfaces that hinders their relative tangential motion
What is friction influenced by?
Surface geometry
Surface properties (elasticity, roughness)
Running conditions (normal pressure, vibration, temperature)
Lubricants
Why is the sign function present in the equation for friction force?
To ensure the friction force always opposes the motion
Points about the Coulomb friction model
Most applicable to dry contacts
Also useful for boundary and mixed lubrication cases (i.e. very thin lubricant layers)
Other than a direction of the friction force there’s no dependence of friction on speed
This is poor for moving contacts (requires a different friction model)
What is the friction coefficient?
Determined experimentally using the same materials and similar loads
Not a material property - depends on both materials in contact, plus on any third body between the surfaces
Points about the viscous friction model
A viscous friction coefficient and force can be defined to depend on the magnitude of velocity, not just direction
Useful for very well lubricated conditions (full film), but often unrealistic for other cases
Which friction model is used for rail-wheel contact?
It may be completely dry or very well lubricated, but is usually a combination of the two
How is real friction quantified?
Using the adhesion coefficient (the ratio of shear to normal load on the contact)
Define braking distance
Distance travelled from beginning braking until the train has stopped
What determines braking distance?
Friction level
Track gradient
Brake effectiveness
Driver and train system reaction times
For the simple braking distance model, what contributes to the retardation?
Brake force
Air resistance and rolling resistance (propulsive resistance)
Gravity if the train is on a slope
Points about the brake force in the simple braking distance model
Real trains are likely to have an unevenly distributed load, and so different brake forces at each wheel, even if adhesion coefficient is equal for all wheels
Adhesion coefficients can differ between wheels (e.g. due to lubrication of only one rail)
Too complex for simple model - assume that total vehicle mass is evenly distributed and adhesion coefficients are all identical
When is adhesion coefficient equal to friction coefficient?
Under full slip conditions (not a normal operating point)
Points about the gravitational components in the simple braking distance model
Railways generally have very shallow gradients (1:50 is steep), but still enough to give accelerating/decelerating forces
Force can be found by resolving weight vector into components parallel and perpendicular to track
Track inclination also slightly reduces normal reaction between wheels and rails - depends on the cosine of the inclination angle, so small angle rule means this effect can usually be ignored
Points about propulsive resistance in simple braking distance model
Defined as sum of rolling resistance and air resistance
Variation in shapes/designs of vehicles and dependence of aerodynamic drag on exact surface form means propulsive resistance is dependent on empirical formulae
Key aspects are journal resistance (axle journal bearing behaviour) and air resistance (often linked to square of speed)
Results of the simple braking distance model
Changing slope ±1:50 can more than double stopping distance
Change of adhesion from dry to wet conditions can multiply stopping distances by 4 times
What makes an even simpler braking distance model?
At slower speeds the velocity dependent terms of retardation are much smaller than the brake force
Can assume uniform retardation so can apply the standard uniform acceleration equations
Minimum braking decelerations for level track from the European High Speed Interoperability legislation
350-300 km/h: a = 0.30 m/s^2
300-230 km/h: a = 0.35 m/s^2
230-0 km/h: a = 0.60 m/s^2
Why is there lower deceleration at high speed?
Power dissipation in the brakes is the limiting factor
Typical wet and dry traction coefficients
Wet ~ 0.12
Dry ~ 0.30
Define creep
Quantifies how much faster or slower the wheel is turning relative to pure rolling
Usually viewed in a high level or macro way
Often expressed as a percentage
Is for the contact overall, so doesn’t attempt to quantify the level of slip or stick happening at specific locations within the contact
Points about creep curves
Plots traction force against creep (slip) in the contact
Important for: designing traction control systems; wheel spin and slide prevention systems and predicting braking distances
Traction in pure rolling compared to full slip
Pure rolling - no traction transmitted by the contact
Full slip - traction level depends on the friction coefficient
In between these extremes is an increasing level of traction as slip builds up
Comparison of creep curves
Lower adhesion conditions allow full slip to develop at much lower creep
Application of mild braking or power under low adhesion conditions can lead to full slip (difficult to control, damaging to track and wheels)
On non-dimensional creep curve plots these would all look the same
