Tire Sensors for the Measurement of Slip Angle and Friction
Coefficient and Their Use in Stability Control Systems
Gurkan Erdogan, Sanghyun Hong, Francesco Borrelli, Karl Hedrick
Department of Mechanical Engineering
University of California at Berkeley
Content
Objective
Motivation
Background
Estimation Algorithms
Integration of Tire Sensors and Vehicle Control Systems
Slip Angle
Tire-Road Friction Coefficient
Accelerometer Based Tire Sensor
Lateral Acceleration
FAE Simulations
Surface Transition Tests
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Objective
Understanding Tire Deformations
Developing Estimation Algorithms
Deflection Profiles
Acceleration Profiles
Slip Variables
Friction Coefficient
Tire Forces
Integration of Tire Sensors and Vehicle Control Systems
Stability Control Systems
Traction Control Systems
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Motivation
Estimation of slip angle, slip ratio, tire forces and tire road friction coefficient may
lead to significant improvements in vehicle control systems.
Slip angle is directly related to skidding,
Slip ratio is directly related to loss of traction
Vertical forces are directly related to rollover
Friction coefficient provides a good measure of the available tire forces.
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Motivation
Integration of Tire Sensors and Vehicle Control Systems
Benefit of Friction Estimation
A stability control system enhanced with tire sensors can …
Generate slip angle and yaw rate references based on the friction information
coming from the roadway.
Follow the references smoothly.
EXAMPLE SCENARIO :
Default value of the friction
coefficient inside the controller
is set to a high friction value,
however the driver is executing
a double lane change maneuver
on a slippery road surface with a
low friction coefficient.
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Motivation
Integration of Tire Sensors and Vehicle Control Systems
Benefit of Slip Angle Estimation
Uncertainties of each sensor and observer used in the estimation of tire slip
angles reduce the accuracy and reliability of slip angle estimations.
 v y + L f ψ& 

α f = δ f − tan 
vx


−1
Estimation of the tire slip angles directly from the tire sensor measurements
can improve the accuracy and reliability.
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Tire Deformations
Sidewall Deformations
Radial
Lateral
Tangential
Tread Deformations
Radial
Lateral
Tangential
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Background
G. Erdogan, L. Alexander, R. Rajamani, “Estimation of Tire-Road Friction Coefficient Using a Novel Wireless Piezoelectric
Tire Sensor,” IEEE Sensors, Volume 11, No. 2, pp. 267-279, February 2011.
G. Erdogan, L. Alexander, R. Rajamani, “Measurement of Uncoupled Lateral Carcass Deflections with a Wireless
Piezoelectric Sensor and Estimation of Tire Road Friction Coefficient”, Proceedings of the ASME Dynamic Systems and
Control Conference, Cambridge, MA, September 2010
G. Erdogan, L. Alexander, R. Rajamani, “A Novel Wireless Piezoelectric Tire Sensor for the Estimation of Slip
Angle”, Measurement Science and Technology, Volume 21, No. 1, pp. 015201 , January 2010
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Estimation Algorithms – Slip Angle
p =c+q
p& = c& + q& + ω × q
∂u ∂u 

Vgx =  yϕ −
+  Vc
∂x ∂s 

∂v ∂v 

Vgy =  − α − xϕ − +  Vc
∂x ∂s 

∂u
=0
∂x
∂v
= −α
∂x
• Full Adhesion
• No Turn Slip
• Steady State
• Small Slip Angle
At the beginning of the contact patch, the slope of the deflection curve can be used to
determine the slip angle.
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Estimation Algorithms –
Lateral Force & Aligning Moment
Lateral Deflection Profile of Carcass
Inside the Contact Patch:
yb =
Superposed
Fy
2 cbend
Bend
Fy
M z′
x +
xb +
c yaw
clat
2
b
Yaw
Shift
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Estimation Algorithms – Friction Coefficient
Brush Model
Lateral Tire Force :
tan(α ) 
tan(α ) 1 tan 2 (α ) 
Fy = 3µFz
1−
+

tan(α sl ) 
tan(α sl ) 3 tan 2 (α sl ) 
Aligning Moment :
M z' = − µFz a
Friction Coefficient :
µ=
2c py a 2
3Fz
tan (α )
tan (α )
tan (α ) 2
tan (α ) 3
{1 − 3 |
| +3(
) −|
|}
tan (α sl )
tan (α sl )
tan (α sl )
tan (α sl )
tan (α sl )
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Accelerometer Based Tire Sensor
3D MEMS accelerometer is located at the centerline of the inner liner.
X, Y and Z coordinates of the accelerometer are aligned with the tangential,
lateral and radial directions of the tire, respectively.
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Tire FEA Model
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Coordinate Transformation
FEA results are transformed from inertial frame to accelerometer body
frame in order to simulate the measured lateral acceleration profiles.
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Experimental Verification
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Slip Angle Estimations based on FAE Model
V = 40 km/hr
µ = 0.9
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Friction Estimations based on FAE Model
V = 40 km/hr
α = 2o
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Recent Tests of Tire Sensors on a Vehicle
Lateral acceleration
profiles measured on a
vehicle at a slip angle
close to zero.
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Lateral Deflection and Acceleration Profiles
α = δ − θV
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Lateral Deflection and Acceleration Profiles
α = δ − θV
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Lateral Deflection and Acceleration Profiles - All Four Tires
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Lateral Deflection and Acceleration Profiles - All Four Tires
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Acknowledgements
Pirelli Tyre, SpA
Giorgio Audisio
Riccardo Tebano
Roberto Villa
Marco Sbrosi
Ford Research and Innovation Center
Davor Hrovat
Eric Tseng
Michael Fodor
Mitch McConnell
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Thank you for listening …
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