meca0494 : braking systems · meca0494 : braking systems pierre duysinx ... is a parabola in the...
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MECA0494 : Braking systems
Pierre DuysinxResearch Center in Sustainable Automotive
Technologies of University of Liege
Academic Year 2017-2018
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MECA0494 Driveline and Braking Systems
Monday 23/10 (@ULG)
AM: Braking performance P. Duysinx (ULg)
Thursday (XXX)
High performance braking systems J. Bouchain (Optesi)
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Bibliography
T. Gillespie. « Fundamentals of vehicle Dynamics », 1992, Society of Automotive Engineers (SAE)
J.Y. Wong. « Theory of Ground Vehicles ». John Wiley & sons. 1993 (2nd edition) 2001 (3rd edition).
R. Bosch. « Automotive Handbook ». 5th edition. 2002. Society of Automotive Engineers (SAE)
R. Bosch. « Automotive Brake Systems ». R. Bosch Publishers. 1995.
R. Bosch. « Safety, Comfort, and Convenience Systems. Function regulation and components. » Bentley Publishers 2006.
« An introduction to modern vehicle design ». J. Happian-Smith ed. Butterworth-Heinemann. 2002
“Automotive Engineering: powertain, Chassis system, and vehicle body”. D. Crolla ed. Butterworth-Heinemann. 2009 3
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Braking system architecture
Introduction
Braking performance
Weight transfer
Optimal braking distribution
Non ideal braking
Brakes devices
Drum brakes
Disk brakes
Braking systems
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INTRODUCTION
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Introduction
Brakes are primarily used to decelerate a vehicle beyond its road resistance and the braking drag of the engine
Brakes generally transform the kinetic energy of the vehicle into heat
Brakes can also be used to:
Keep a constant speed
Keep the vehicle at standstill
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Introduction
One distinguishes the different categories of braking systems
Service brake system: generally decreases the speed while driving
Emergency brake system: has to take over the function of the service brake system when failing
Parking brake system: prevents unwanted motion of the vehicle when parked
Continuous service braking systems: for longer uninterrupted braking and frequent stops for instance in urban heavy vehicles
The service, emergency and parking brake systems directly work on the wheels
The brake elements of the continuous service generally act on the driveline
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Introduction
A common brake system includes
Control device: pedals / hand-brake lever
An energy source which generates, stores and releases the energy required by the braking system
Transmission device: components between the control device and the brake
The wheel brake or foundation brakes generate the forces opposed to the vehicle motion
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BRAKING PERFORMANCE
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EQUILIBRIUM WHILE BRAKING
Wong Fig 3.47: equilibrium while braking
Deceleration: a<0
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b
c
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EQUILIBRIUM WHILE BRAKING
Newton’s second law
Front and rear wheel braking
Rolling resistance
Aerodynamic drag
Grading resistance
Resistance due to friction in drivetrain
Acceleration:<0 if braking
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Braking forces
Braking forces developed by the braking system
The brake must also absorb the rotation inertia of the wheels and of the rotating parts (driveline).
When there is no slip of the tyres, the inertia of the wheels and the rotating components can be modelled as an additional fictitious translational mass and an effective mass. The correction factors is about 1.03 to 1.05
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Simplified braking motion
If the adhesion friction is constant, the braking forces is constant and
Speed and distance as a function of time
Reduction of the kinetic energy of the vehicle and the work dissipated by the brakes
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Simplified braking motion
Motion till rest V2=0:
Time to stop
Stopping distance
Taking care of the reaction time of the driver and the braking system
ta + td takes into account for the reaction time of the driver (from 0.5 to 2 s) and for the development of the braking forces in the braking system
Energy dissipated during braking
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Example
Passenger car: mass 1400 kg, v0 = 120 km/h, ax=6 m/s²
Energy to be absorbed by the braking system
Time and distance to stop
Average power dissipated by the braking
Peak power = 2 * average power = 282 kW
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Distribution of braking forces
Pitch equilibrium: weight transfer
Longitudinal equilibrium
a<0 if decelerationFb>0 if deceleration16
b
c
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Distribution of braking forces
Weight under the axles
Or using weight transfer DW
Fb>0 if braking
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Distribution of braking forces
The maximum braking forces depends on the weight on the wheels and on the friction coefficient µ:
Ideal braking distribution: both axles reach simultaneously the friction limits, which happens for a unique front / rear braking distribution
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Distribution of braking forces
Example
Light duty vehicle: 68% of the weight on the rear axles
b/L = 0.68, c/L=0.32,
h/L =0.18,
µ = 0.85, f=0.01
The ideal braking distribution is:
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The vehicle braking characteristics
The braking characteristics (‘I’ curve) is the relation between the maximum braking forces on the front and rear wheels in ideal conditions
Distribution of braking forces
Let’s neglect the rolling resistance forces (f=0)
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The vehicle braking characteristics
Let’s eliminate the friction coefficient µ:
It comes
Reorganizing the terms
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The vehicle braking characteristics
The equation
is a parabola in the braking forces plane Fbf et Fbr whose major axes are the bisectors
Intersection with the axes
With axis Fbr=0
With axis Fbf=0
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b>c
b=c
b<c
Reminder:Fb>0 if braking
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The vehicle braking characteristics
It is interesting to calculate the maximum braking force on the front axles for a given rear braking force
That is
And
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The vehicle braking characteristics
Similarly one gets the maximum braking force on the rear axle in terms of a prescribed front wheel braking force
So
And
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Slope
Intersection with axis
Slope
Intersection with axes
b>c
b=c
b<c
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The vehicle braking characteristics
Rear wheel Lock up
Front wheel lock up
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The vehicle braking characteristics
The straight lines of the max braking forces are intersecting on the characteristic parabola
The intersection point is a function of the friction coefficient
The intersection gives the ideal ratio between front and rear wheels.
Iso-value of the deceleration is related to the friction coefficient
Constant deceleration along the line
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The vehicle braking characteristics
Other presentation of the same results (see Gillespie)
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Braking under non ideal conditions
One generally does not brake under ideal conditions. So what happens?
If the front wheels lock first, we have a loss of directional control
The vehicle slides following a straight line and the centrifugal accelerations are naturally reduced so that the driver can recover the control of its machine non dangerous vehicle
The rear wheels lock first: Loss of stability
The rear of the vehicle loses its ability to develop any lateral forces and the lateral acceleration leads to an uncontrolled increase of the yaw speed.
This is a dangerous behaviour to avoid…
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Braking under non ideal conditions
Wong (1993)Fig 1.33a et 1.34
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Braking under non ideal conditions
Wong. Fig 3.48. Los of control with rear wheels lock-up
Wong. Fig 3.49: Angular yaw deviation for front and rear wheel lock-up
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Braking under non ideal conditions
Prediction of the wheel locking under non ideal braking conditions and the resulting deceleration
Neglect the aerodynamic forces and the grading forces
It comes
ax<0
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Braking under non ideal conditions
For a fixed braking distribution between the front and rear wheels, let’s calculate which wheels are subject to the locking first
The braking efforts on the front wheels
And rear wheels
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Braking under non ideal conditions
Lock-up of the front wheels if
Locking condition of the front wheels
So
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Braking under non ideal conditions
Similarly, the locking condition of the rear wheels
The front wheels are locking before the rear wheels if
Or vice-versa
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Braking under non ideal conditions
Example: µ =0,8
f = 0,01
h/L = 0,15
Kbf= 0,6
Kbr=1-kbf=0,4
b/L = x
c/L=1-x
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0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
1 2 3 4 5 6 7 8 9 10
Acce
léra
tio
n m
en
an
t a
u b
loca
ge
(a/g)f
(a/g)r
b/L
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Braking under non ideal conditions
Example: µ =0,8
f = 0,01
h/L = 0,15
Kbf= x
Kbr=1-x
b/L = 0,4
c/L=0,6
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kbf0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8
Accélération donnant lieu au blocage
en fonction de la fraction de freinage sur l'avant kbf
(a/g)f (a/g)r
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Braking under non ideal conditions
These formulae show the large influence of the weight distribution (and position of CoG) over the optimal braking distribution
Vehicle with no freight: braking distribution is stronger on the front to have a wheel blocking in the front first
Design approach: find the right compromise point 1
Wong: Fig 3.50 39
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Braking under non ideal conditions
For passenger cars, the influence is lesser than on duty vehicle
Design approach: find the right compromise point 1
Wong: Fig 3.51 40
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Braking under non ideal conditions
Remark: One recovers the ideal braking conditions on the braking ratio by assuming :
f r
a a
g g
a/g
kbxf
Issue: these curves depend strongly on the geometry, the position of the CoG, and the friction coefficient
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BRAKING DISTANCE UNDER NON IDEAL CONDITIONS
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Braking efficiency
Our reference: all wheels are reaching simultaneously the friction limit:
One obtains the maximum deceleration:
In these ideal conditions, one compares the actual braking deceleration that is measured to the reference deceleration rate:
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Braking distance
To calculate the braking distance, we start from Newton equation
The effective mass factor is gb which is between 1.03 and 1.05 in braking since the clutch is open
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Braking distance
The aerodynamic forces write:
It comes
The stopping distance till rest (V2=0)
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Braking distance
The best stopping distance: the brakes are just producing the forces to necessary reach the friction coefficient (as well as the force to absorb the braking of the driveline)
If we have a lower braking efficiency, one ca use the coefficient
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Braking distance
One can further add some time related to :
Reaction time necessary to the driver to react tc : generally between 0.5 and 2 s
The lead time of the braking system,
The rise time of the braking system to develop full braking forces, generally around tr = 0.3 s
During this time the vehicle is still driving at initial speed so that the stopping distance gets longer:
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