5 - Friction and Braking

Question 1

Define friction

Answer 1

The force between interacting surfaces that hinders their relative tangential motion

Question 2

What is friction influenced by?

Answer 2

Surface geometry
Surface properties (elasticity, roughness)
Running conditions (normal pressure, vibration, temperature)
Lubricants

Question 3

Why is the sign function present in the equation for friction force?

Answer 3

To ensure the friction force always opposes the motion

Question 4

Points about the Coulomb friction model

Answer 4

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)

Question 5

What is the friction coefficient?

Answer 5

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

Question 6

Points about the viscous friction model

Answer 6

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

Question 7

Which friction model is used for rail-wheel contact?

Answer 7

It may be completely dry or very well lubricated, but is usually a combination of the two

Question 8

How is real friction quantified?

Answer 8

Using the adhesion coefficient (the ratio of shear to normal load on the contact)

Question 9

Define braking distance

Answer 9

Distance travelled from beginning braking until the train has stopped

Question 10

What determines braking distance?

Answer 10

Friction level
Track gradient
Brake effectiveness
Driver and train system reaction times

Question 11

For the simple braking distance model, what contributes to the retardation?

Answer 11

Brake force
Air resistance and rolling resistance (propulsive resistance)
Gravity if the train is on a slope

Question 12

Points about the brake force in the simple braking distance model

Answer 12

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

Question 13

When is adhesion coefficient equal to friction coefficient?

Answer 13

Under full slip conditions (not a normal operating point)

Question 14

Points about the gravitational components in the simple braking distance model

Answer 14

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

Question 15

Points about propulsive resistance in simple braking distance model

Answer 15

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)

Question 16

Results of the simple braking distance model

Answer 16

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

Question 17

What makes an even simpler braking distance model?

Answer 17

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

Question 18

Minimum braking decelerations for level track from the European High Speed Interoperability legislation

Answer 18

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

Question 19

Why is there lower deceleration at high speed?

Answer 19

Power dissipation in the brakes is the limiting factor

Question 20

Typical wet and dry traction coefficients

Answer 20

Wet ~ 0.12
Dry ~ 0.30

Question 21

Define creep

Answer 21

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

Question 22

Points about creep curves

Answer 22

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

Question 23

Traction in pure rolling compared to full slip

Answer 23

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

Question 24

Comparison of creep curves

Answer 24

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

Question 25

Application of creep curves

Answer 25

During traction or braking, often the maximum acceleration/deceleration is wanted, but never want to enter very high levels of slip
Under braking, full slip is a wheel slide (wheel locked)
Under acceleration, full slip is a wheel spin
Full slip generates lots of hear input on a concentrated part of wheel/rail
Traction control needs to know how to approach full slip but not reach excessive slip

Question 26

What can braking problems lead to?

Answer 26

Wheel defects

Question 27

What does low adhesion lead to? (+ case study)

Answer 27

Braking problems
London Charing Cross to Hastings failed to stop at Stonegate due to low rail-wheel adhesion
Train ran 5.18km after applying the brakes before stopping
Factors: low adhesion; gradient and lack of sand

Question 28

Early braking systems

Answer 28

Steam pressure or vacuum to create a force
Mechanical application of brake blocks to outside wheel tread
No simple or effective way o link the braking system to attached vehicles
Not fail-safe - without the steam pressure the brakes can’t be applied
Better systems used steam (or vacuum) to hold the brakes off - any failure of the pressure caused the brakes to apply themselves

Question 29

Modern braking systems

Answer 29

Wheel tread braking: used on some passenger vehicles, mainly on freight
Disc brakes: sometimes mounted on the axle; sometimes discs mounted either side of the wheel; electric pneumatic operation with fail-safe design; hydrodynamic and regenerative retarders are present on some fleets

Question 30

Wheel slide prevention systems

Answer 30

Braking systems use knowledge of creep curves to predict the brake force which can be applied without wheel slide
In general, ‘steady’ reduction of speed is expected

Question 31

How to check wheel slide prevention systems

Answer 31

Occasional brake release is usually used on 1 axle to periodically measure real rolling speed, radar systems and others (done automatically, no intervention needed by driver)

Question 32

What happens when a wheel begins to slide?

Answer 32

Rotational speed will slow too rapidly, and will not correlate with vehicle speed
Wheel slide protection system detects a problem
Brake cylinder pressure is reduced
Sliding contact motion reduced - speedometer reads realistic speed
Normal braking resumed