Ride Handling and Braking

BAJA SAE-INDIA 2011 WorkshopSPCOE, Bhavan Campus, Mumbai, 23rd - 24th July 2010

Manish Jaiswal, PhD

John Deere Technology Center India (JDTCI, Pune)

TerminologyHandling - more of a human judgment, based on the response or feel of the vehicle over a range of driving conditions.

Stability - ability of a vehicle to perform in a manner consistent with driver inputs or against disturbances over a wide range of driving conditions. A directionally stable vehicle returns to a steady state condition within a finite time, following a disturbance.

Braking - to convert the kinetic energy possessed by the vehicle at any one time into heat energy by means of friction. Apart from braking efficiency, stability induced by braking has become an important parameter, determining the safety of a vehicle.

Ride - tactile and visual vibrations in low frequency domain, experienced by passengers. Being subjective in nature its an important performance parameter, determining the way ride quality is perceived by the passengers.

Handling

Vehicle Axis System - SAE

Fig source - 8

Bounce - the vertical displacement Pitch - rotation about the Y axis Roll - rotation about the X axisWarp - combined rotation about the Y and X axisYaw - rotation about the Z axis

Steady-State Cornering

Steady-state cornering is concerned with the directional behaviour of a vehicle under time invariant conditions.

The vehicle, in this case, will have two simultaneous motions –rotation about its own CG and revolution around the centre of turn, both at a constant angular velocity.

Main factors controlling the steady-state handling of a vehicle are the weight distribution (including load transfer) and the cornering stiffness of the tyres.

The steady-state cornering is mostly related with small values of lateral acceleration.

Slip Angle and Cornering ForceThe relationship between lateral force or cornering force and slip angle (at low slip) is linear and can be expressed

yF Cα α= ⋅

The slip angle α in a tire is primarily because of its lateral deformation at the contact patch. The tire moves along a path at an angle α with the wheel plane.

The coefficient Cα is known as the cornering stiffness and represents the slope of the lateral force and slip angle curve at α =0. The cornering stiffness of a tire is primarily dependent on the load and inflation pressure.

Fig Source - 11

Steer angle depends on the wheel base, turning radius, forward speed, and the under-steer coefficient.

( )( )

( )( )

2f f f

2r r r

W C U gR

W C U gR

α

α

α

α

=

=

f f r wδ - L Rα α+ =

( )2w usfδ L R K U gR= +

Under-Steer Coefficient

Neutral steer - Kus = 0

Under-steer - Kus >0

Over-steer - Kus <0 Fig Source - 3

( )us f f r rK W C - W Cα α=

Under-Steer Coefficient (Cont..)

Fig Source - 1

Fig Source - 1

wcrit usU 57.3L g K−=

Critical Speed

Characteristic Speed

wchar usU 57.3L g K=

Yaw Velocity Gain

( )w

2us w

U Lrδ 1 K U 57.3L g+=

Force and Moment during Cornering

trf trf

FzR

FyR FyL

ϕ

hf O

h1

FzL

Fy

( ) ( )L Rz y yr r

1 hΔF K C p - F F2t 2tϕ ϕϕ= + +

Load transfer can be found by equating the suspension roll moment with moments generated by the vertical and lateral tyre forces.

During cornering, weight transfer happens from inside to outside tires

During braking, weight transfer happens from rear to front tires, while during acceleration, weight is transferred from front to rear.

Fig Source - 3

Roll Center Height

Roll center can be determined by the intersection of the centerline with the line joining the contact patch center to the instantaneous center.

The roll moment is determined by the roll center to CG height.

With suspension travel, the roll center is displaced or migrated.

Low roll center height leads to reduction in jacking forces.

Vehicle Roll – Anti Roll Bar

f f

1

f f

2

roll wheelroll

rf

roll wheelroll

rf

KF -

t

KF

t

ϕ ϕ

ϕ ϕ

⋅ +=

⋅ +=

( )

( )

The anti-roll bar forces at the front wheels can be expressed as

Fig Source - 3

Vehicle RolloverStages of Rollover

Pre-rollover – from the start of the control loss to lift offLift off - airborne phase starting from the wheel lift off to the body contacting the groundRoll phase - from the ground contact to vehicle coming to rest

Static Stability Factor (SSF = T/2H) is used to determine rollover propensity

Rollover is predicted if for sustained period of time, ΣF>W* (T/2H)

or if lateral acceleration α/g > T/2H

or if coefficient of friction μ > T/2H

Critical Sliding Velocity (CSV) is another estimate for rollover propensity, which determines the minimum sideways velocity required for a vehicle to just barely tip over

Fig Source - 7

Steering Kinematics

Camber Angle γ

Lateral InclinationAngle λ

η

υp

γ

CasterAngle ν

Kingpin Axis

Scrub radius

Fig Source - 3

Steering Kinematics (Cont..)

Camber – Results in lateral force development at the contact patchLesser force in comparison to the force generated by slip angle

Caster – Allows the wheels to self-center by generating a self-centering force

Positive when steering axis is ahead of the contact patch center

Steering Axis Inclination – Like caster, provides directional stabilityReduces steering effort by reducing scrub radius

Scrub Radius – Distance between the steering axis andthe center of the contact patchNegative scrub radius helps in reducing steering sensitivity to braking inputs

Toe – Compensates for the turning behaviour of a cambered wheel Easy to adjust as compared to caster or camber

a

δ1

b

trr2

trr2

δ2

trf2

trf2

Lw

δ1 δ0δ2

D

1 2

3 4

Ackerman Steering Geometry

1 0 0w

trf 2δ δ (1 δ )L

≈ ⋅ ⋅- 2 0 0w

trf 2δ δ (1 δ )L

≈ ⋅ + ⋅

( )1 0 0

w

Pa trf 2δ δ (1 δ )

L⋅

≈ ⋅ ⋅-

( )2 0 0

w

Pa trf 2δ δ (1 δ )

L⋅

≈ ⋅ + ⋅

If Pa is the proportion of Ackerman, then δ1 and δ2 become:

The steer angle at the front wheels can be expressed in terms of the centralvehicle axis and its distance from the centre of turn.

Fig Source - 3

Braking

Brake Force

Apart from braking force developed at the friction element, the vehicle experiences the retarding forces from the rolling resistance of tires, aerodynamic and transmission resistance, and grade resistance at slope.

Fxtyre

Mb

VXw

dFz

FR

ro

ωTd

rwKtyre

Road Surface

Fzo

d x R wb

wheel

T (F F ) rMI ω

⋅=

⋅- -

Fig Source - 3

Conventional Braking System

The pressurized fluid is forced out of the master cylinder and into the wheel cylinders, through the brake lines.

The flow into the rear brake cylinders is passed through proportioning valves.

The hydraulic pressure at the wheel cylinder is translated into the friction pads, which eventually applies the brake torque at the disk / drum.

Driver presses the brake pedal.

The force from the pedal after being multiplied by the pedal/lever ratio reaches the brake booster.

The hydraulic or pneumatic brake booster further amplifies it by a gain.

The booster exerts a force against the piston in the master cylinder, thus pressurizing the brake fluid.

Braking System - Vacuum BoosterApply Chamber

Vacuum ChamberDiaphragm

Power Piston

Pushrod

Return Spring

Master Cylinder

Valve Springs

Check Valve

Firewall

Seal

Reaction Washer

Fig Source - 5

The vacuum booster located on the vehicle’s firewall acts like a force amplifier, enhancing the force applied by the driver pedal by exploiting the pressure differential between the atmosphere and the engine manifold vacuum.

Fout

Primary Piston

Pmcp

Master Cylinder

Secondary Piston

Brake Lines

Brake DiskWheel Cylinder

Prr Plr

Prf

Pmcs

Seal

Plf

Master Cylinder

Master Cylinder and Friction Element

Fig Source - 3

Fig Source - 9

Fig Source - 10

Split Circuit Braking System – required for safety reasons so that if one circuits fails the other can function.

Front/Rear Split – circuit is divided between front and rear axle, where the primary piston connects the front and the secondary piston connects the rear.

Diagonal Split –the right front and left rear are connected by one piston while the left front and the right rear are connected by the second piston.

Brake Force DistributionProportioning Valve – reduces the pressure in the rear brakes so as to prevent the rear brakes from locking before the front ones, during high level of deceleration. The front brakes receives higher proportion than the rear ones.

Metering Valve – required when the vehicle has both drum and disk brakes. As the disk brakes engage quicker than the drum brakes, the metering valve does not allow the disk brakes to engage before the drum brakes.

Brake Force Distribution – to achieve optimum braking according to the dynamic weight distribution. During high deceleration, If the front brake torque exceeds the dynamic front weight, then it may lead to front wheels locking before the rear. The opposite happens (rear locking before the front), if the rear brake torque exceeds the dynamic rear weight.

Over the years, the advances in brake technology has led to development of various active safety systems such as Electronic Brake force Distribution system (EBD), Anti-lock Braking System (ABS), Brake Assist System (BAS), Electronic Stability Control (ESC) and many more…..

Anti-Lock Braking System (ABS)

μ-slip curve as a function of slip angle Typical ABS braking cycleFig Source - 4Fig Source - 6

An ABS system would detect incipient locking at one or more wheels in time, and react by modulating the brake pressure on individual wheels, so as to prevent it from locking and keep the tyre slip within a desired range.

Ride

Quarter Vehicle Model

( ) ( ) ( ) ( )z

wheel body wheel body tyre wheel 0 tyre wheel 0 wheel wheel

F

-K z - z - C z - z -K z - z - C z - z - M z 0 ⋅ ⋅ ⋅ =

body wheel body wheel sprung body- K [z - z ] - C [W - z ] - M z 0⋅ ⋅ ⋅ =

Equation for sprung mass can be obtained by balancing the suspension and the inertia forces

The unsprung mass forces include suspension forces, inertia forces of wheel and tyre vertical load (after road excitation)

Fig Source - 3

Z0

Quarter Vehicle Model (Cont..)

For undamped system, equation of motion for free vibration can be reduced to

body wheel sprung body- K [z - z ] - M z 0⋅ ⋅ =

( ) ( )wheel body tyre wheel 0 wheel wheel-K z - z - K z - z - M z 0 ⋅ ⋅ =

The undamped natural frequencies of the sprung and unsprung mass can be expressed as:

tyre tyre tyre

sprung tyre

tyre

wheel

K K (K K ) K K1 , where represents the ride rate2 M (K K )

K K12 M

sprung

unsprung

f

f

π

π

⋅ + ⋅= ⋅

+

+= ⋅

Overall, the quarter vehicle model can be used to a good effect for studying the initial estimate of vehicle vibration in relation with the mass, stiffness and damping characteristics, along with the realistic road inputs.

2-DOF Model for Bounce and Pitch

Fig Source - 2

The equation of motion for free vibration for bounce is

sprung f 1 r 2 - M z - K [z - ]- K [z ] 0ι θ ι θ+ =

The equation of motion for pitch is

y f 1 1 r 2 2I - K [z - ] K [z ] 0θ ι ι θ ι ι θ+ + =

In comparison to the quarter vehicle model, this slightly detailed pitch plane dynamics model could be used to a good effect for studying vehicle vibration during coupled bounce and pitch motions.

Human Response to Vibration

Limits of whole-body vibration for fatigue or decreased proficiency in vertical direction (foot-to-head), ISO 2631-1:1997

Fig Source - 2

Human Response to Vibration (Cont..)

Limits of whole-body vibration for fatigue or decreased proficiency in transverse direction (back to chest or side to side), ISO 2631-1:1997

Fig Source - 2

References1. Gillespie, T.D. , Fundamentals of Vehicle Dynamics, SAE, Warrendale, 1999

2. Wong, J.Y., Theory of Ground Vehicles, John Wiley & Sons, New Jersey, 2008

3. Jaiswal, M., PhD Thesis, The Interaction of Tyre and Anti-lock Braking in Vehicle Transient Dynamics, School of Mechanical Engineering, Loughborough Univeristy, 2009

4. Bauer, H. Driving-safety systems, 1999 (Robert Bosch GmbH, Stuttgart).

5. Gerdes, J. C. and Hedrick, J. K., Brake System Modeling for Simulation and Control, Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, Vol. 121, 1999

6. Austin, L. and Morrey, D., Recent advances in antilock braking systems and traction control systems, IMechE, Part D, Journal of Automobile Engineering, Vol- 214, No-6, 2000

7. Transportation Research Board, NHTSA’s Rating System for Rollover Resistance, An Assessment, Special Report No 265, 2001.

8. http://www.carsim.com/applications/education.php

9. http://www.familycar.com/Classroom/Images/Brake_Disk_Brake.gif

10. http://www.familycar.com/classroom/Images/Brake_Drum_Brake.gif

11. http://features.evolutionm.net/imageview.php?image=1537

Thanks