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Novel Wireless Tire Deformation Sensors for Estimation of Tire Slip Angle and Tire-Road Friction Coefficient

University of Minnesota, Twin CitiesDepartment of Mechanical Engineering

GÜRKAN ERDĞAN, Ph.D.

Objective

� Understanding tire deformations

� Development of wireless, piezoelectric sensors for tire deflection measurements

� Estimation of slip variables and tire-road friction coefficient

GÜRKAN ERDOĞAN, Ph.D.

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� Friction coefficient provides a good measure

of the available tire forces.


Tire Test Rig

( ) zy

V

FF ρα

θδα

=

−=

Force Tire Lateral

AngleSlip


Tire Test Rig


Wireless Data Transmission

Transmitter Circuit


Receiver Circuit

Tire Deformations

� Tread Deformations� Radial� Lateral� Tangential

� Sidewall Deformations� Radial� Lateral� Tangential

Tread Sidewall (Carcass)

Lateral Deformations

Tread

Sidewall (Carcass)


Piezoelectric Sensor Design for Lateral Tread Deflection


Lateral Tread DeflectionRigid Sidewall

Elastic Sidewall


Disadvantages of Tread Deflection Sensors

� Tread deflections are very small.

� PZT piezoelectric material has high sensitivity.

� Sensors are susceptible to the vibrations coming from the roadway.

� Verification of tread deflection measurements is very difficult.

� Lateral and radial sidewall deflections interfere with the measurements.


Coupled Sidewall Deformations

Tangent

Tangential and Lateral Sidewall

Lateral

Tangent



Tangential and Lateral Sidewall



Radial Sidewall Deformation


Decoupled Lateral Sidewall Deflection Sensor Design

Piezoelectric Film


Display of Sensor Performance


Piezoelectric Sensor Measurements

Slip Angles


( ) ( ) os

HP

Lp

HP

HPL V

sR

RV

s

sV

1ˆ

1

1ˆ1 +

++

=ττ

τ LpHP RC=τ

( ) LepHP RCC +=τ̂

Lateral Sidewall Deformation

PIEZOELECTRIC SENSOR

DIGITAL CAMERASlip Angles Slip Angles


Slip Angle Estimation - Tire Kinematic Equations

qqcp

qcp

×++=

+=

ω&&&


α−=∂∂

=∂∂

x

v

x

u0

cgy

cgx

Vs

v

x

vxV

Vs

u

x

uyV

∂∂

+∂∂

−−−=

∂∂

+∂∂

−=

ϕα

ϕ

qqcp ×++= ω&&&

• 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.

Slip Angle Estimation

Line Fit Algorithm Slip Angle Estimations


Slip Angle EstimationSlip Angles

Slip Angles


k

yy

eAyF

n

yB

nn

l

l

l

l

=

+=

Slip Angle Estimation


Contact PatchLocation


Contact Patch Location

δ =k

Fz

1) Another piezoelectric strip can be employed to measure vertical deflection profile. The maximum value of the deflection can be used to find the contact patch.

22 δδ −= Ra

kt

2) Or the second piezoelectric strip can be attached to the center line of the tire to determine the location of the leading and trailing edges of the contact patch.


Friction Coefficient

Slippery Non-Slippery


Measurements at Different Friction Coefficient

Slip Angle = 1.0 [deg] Slip Angle = 2.0 [deg]


Estimation Algorithms – Lateral Force & Aligning Moment

Lateral Deflection Profile of Carcass Inside the Contact Patch:

lat

y

b

yaw

zb

bend

y

bc

Fx

c

Mx

c

Fy +

′+= 2

2

Bend Yaw ShiftSuperposed

2011-01-0095GÜRKAN ERDOĞAN, Ph.D.

Lateral Force EstimationBased on the Sidewall Deflection Measurements

After Parabolic Curve Fit

Slip Angle = 1.0 [deg] Slip Angle = 2.0 [deg]


Friction Coefficient Estimation Based on Brush Model

( )( )

( )( )

( )( )

+−=

slslsl

zy FFαα

αα

αα

µ2

2

tan

tan

3

1

tan

tan1

tan

tan3

( )slz

py

F

acαµ tan

3

2 2

=

Lateral Tire Force :

Friction Coefficient :


Friction Coefficient Estimation Results

Normal Force and Tire Parameters:

Estimation Results:


Summary of Estimation Methodologies

� Slip Angle Estimation

� Find the location of the contact patch

� Measure the lateral sidewall deflection profile.

� Convert the measured deflection profiles into their linear counterparts.

� Estimate the slip angle using the slope of the deflection profile at the leading edge of the contact patch.leading edge of the contact patch.

� Friction Coefficient Estimation

� Estimate the slip angle using the previous technique.

� Estimate the lateral tire force using the sidewall lateral deflection profile measurements inside the contact patch.

� Estimate the sliding slip angle and the friction coefficient using the brush model equations.


Journal Papers

1) G. Erdogan, L. Alexander, R. Rajamani, “Friction Coefficient Measurement for Autonomous Winter Road Maintenance”, Vehicle System Dynamics, Volume 47, No. 4, April 2009, pp. 497 – 512

2) G. Erdogan, L. Alexander, R. Rajamani, “Adaptive Vibration Cancellation for Tire-Road Friction Coefficient Estimation on Winter Maintenance Vehicles”, IEEE Transactions on Control Systems Technology (accepted in June 2009)

3) G. Erdogan, L. Alexander, R. Rajamani, “A Novel Wireless Piezoelectric Tire Sensor for the Estimation of Slip Angle”, Measurement Science and Technology (accepted in October 2009)

4) G. Erdogan, L. Alexander, R. Rajamani, “Closed-Loop Snowplow Applicator Control Using Road Condition Measurements”, Vehicle System Dynamics (submitted in July 2009)

5) G. Erdogan, L. Alexander, R. Rajamani, “Estimation of Slip Angle and Friction Coefficient Using Piezoelectric Sensor and Tire Models” (to be submitted for publication to IEEE sensors)


THANKS FOR LISTENING

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