1756 ieee sensors journal, vol. 13, no. 5, may 2013 …coejgyi/pdfs/ieeesensorsj_2013.pdf · ·...

1756 IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013

Embedded Flexible Force Sensor for In-SituTire–Road Interaction Measurements

Yizhai Zhang, Student Member, IEEE, Jingang Yi, Senior Member, IEEE, and Tao Liu, Member, IEEE

Abstract— In-situ sensing the tire–road interactions such aslocal contact friction force distributions provides crucial infor-mation for building accurate friction force models for vehiclesafety control. In this paper, we report the development of anembedded, flexible local force sensor for measuring the tirelocal friction forces and their distributions. A new pressure-sensitive, electric conductive rubber (PSECR) sensor is usedand embedded inside the tire rubber layer to extract the multi-dimensional local friction forces on the tire contact patch. Thelow-cost, flexible PSECR sensor is oriented in certain directions,and is sensitive to multiple compressive forces. To interpret thesensor measurements, we use a beam-spring model for the tire–road interactions to extract the local contact friction forces.The experimental results of stick–slip interaction testing on amotorcycle tire demonstrate the effective and good performanceof the PSECR-based tire force sensor.

Index Terms— Contact model, pneumatic tire, stick–slip inter-actions, tactile sensing, tire sensors.

I. INTRODUCTION

PNEUMATIC tires are widely used for ground vehicles.Tire-road interactions such as tire friction forces play

an extremely important role for safe operation of these vehi-cles. Building high-fidelity tire-road friction models is crucialfor vehicle dynamic simulations and active safety control[1]–[3]. Non-intrusive, in-situ sensing of the tire-road interac-tions provides direct information about the local force distrib-utions on the tire contact patch and helps build friction forcemodels [4]. It is however challenging to measure the localfriction forces on the tire contact patch. It is a challenging taskto develop a sensing system to measure the contact frictionforces of deformable rubber tires. Due to the highly couplingeffects between the longitudinal and lateral friction forcesand the normal contact force, extracting and obtaining all3-D forces simultaneously adds further modeling challengesto interpret sensor measurements.

Manuscript received November 3, 2012; revised December 25, 2012;accepted January 10, 2013. Date of publication January 18, 2013; date ofcurrent version April 2, 2013. This work was supported in part by the U.S.National Science Foundation under Award CMMI-0856095. The associateeditor coordinating the review of this paper and approving it for publicationwas Prof. Elena Gaura. (Corresponding author: J. Yi.)

Y. Zhang and J. Yi are with the Department of Mechanical and AerospaceEngineering, Rutgers University, Piscataway, NJ 08854 USA (e-mail:[email protected]; [email protected]).

T. Liu is with the Department of Intelligent Mechanical Systems Engi-neering, Kochi University of Technology, Kochi 782-8502, Japan (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2013.2241051

The US Congress TREAD Act requires the mandatoryinstallation of a tire pressure monitoring system (TPMS) inall US automobiles and light trucks for safety reasons [5].However, the TPMS is not designed for obtaining the frictionforces. Tire rubber deformation and stresses contain the mostdirect information for understanding and modeling tire-roadinteraction forces [1], [3], [4]. Various tire sensors are devel-oped to measure the rubber tread deformation and stresses.In [6], [7], a tire sensor has been developed to measure thetire tread deformation. There is however no further reportedevaluation on tire-road friction forces from the measuredtread deflection. Surface acoustic wave (SAW) sensors areproposed for the “smart tire” application in [8]. Strain andcapacitance sensors have been developed for monitoring thetire tread deformation [9], [10]. In [11], [12], accelerometersare placed inside tires for friction force estimations. Opticalsensors are also developed for measuring tire deformation [13].The optical sensing system is complicated and might not bevery robust for varying tire running environments and for real-time applications. Piezoelectric sensors such as polyvinylidenefluoride (PVDF) has been proposed and used for measuringthe stresses on the inlet surface of the tire [14]. The stressmeasurements are interpreted through a friction force model.The results in [14] demonstrate the feasibility of the PVDF-based tread deformation sensor. In [15], a differently config-ured PVDF-based deformation sensor is designed to measurethe tire sidewall deformation and then to estimate the tire slipangle. Built on these measurements, the tire lateral frictionforce is estimated using an analytical force model. A similarPVDF-based deformation sensor is also reported in [16].

Although the above discussed tire sensors provide mea-surements of the forces and the deformations, few resultsare reported to capture the local friction forces and theirdistributions. Moreover, these tire sensors cannot captureall aspects of the tire/road interaction forces. For example,the piezoelectric tire sensors such as PVDF cannot capturethe static loading and forces. It is also challenging to usestrain and capacitance sensors to measure multi-directionalforces. In this paper, we present the development of a newpressure-sensitive, electric conductive rubber (PSECR) sensorto directly measure local friction forces during tire/road stick-slip interaction. Comparing with the existing reported tire sen-sors, we choose the PSECR sensor to measure the local frictionforces between the tire and the road because of its attrac-tive properties such as multi-sensing cells within one smallunit, flexibility, high sensitivity to both static and dynamic

1530-437X/$31.00 © 2013 IEEE

ZHANG et al.: EMBEDDED FLEXIBLE FORCE SENSOR FOR IN-SITU TIRE–ROAD INTERACTION MEASUREMENTS 1757

(a) (b)

O

Rc

(c)

10 mm

Tire center line

xy

zπ1

π2

(d)

Fig. 1. (a) PSECR sensor. (b) Motorcycle tire used in experiments. (c) Cross section of the tire. (d) PSECR sensor embedded inside the tire.

forces, and low-cost [17]. To interpret the PSECR sensormeasurements and obtain the local friction forces, we use andextend the beam-spring network model developed in [18] tobuild the sensor model. The sensor system development is alsoinspired by the fingertip tactile sensing for robotic manipu-lation applications [19]. We finally demonstrate the PSECRsensor performance through applications and experiments tostudy the local friction forces and their distributions during thestick-slip interactions between the stationary tire and the firmroad. Measuring stick-slip interaction friction forces is used asthe sensor application for several reasons. First, understandingthe stick-slip interaction provides the foundation to capturethe dynamic tire-road interactions. Second, obtaining the localfriction forces and their distributions in stick-slip interactionsis a challenging task due to large rubber deformation andcomplex normal load distributions, etc. Finally, although wepresent the sensor development for stick-slip friction forcemeasurement, the sensor model can be extended to dynamictire sensing.

The main contribution of this work lies in the new localforce sensor prototype and modeling development for study-ing friction contact problems in tire-road interactions. Theproposed sensor directly measures and captures the localfriction forces. The local friction sensing model can also bepotentially used for other mechanical systems in which a largedeformation exists between a flexible thin layer and a rigid. Tothe best of our knowledge, there are no sensing, modeling andexperimental studies that reveal the contact force distributionsbetween the tire and the road, or in general a deformable thinlayer and a rigid. The sensing system developed in this workfills the gap of such knowledge.

The rest of the paper is organized as follows. In Section II,we discuss the embedded PSECR sensor development. InSection III, we present the sensing model to extract the localfriction forces. The PSECR sensor calibration and experi-ments are presented in Section IV. We conclude the paperin Section V.

II. EMBEDDED TIRE SENSORS

A. PSECR Sensor

The PSECR sensor (from Pongpara Codan Rubber Technol-ogy Company, Thailand) is shown in Fig. 1(a). The circularsensor is around 12-mm in diameter and is flexible. In one sen-sor unit, there are four sensing cells that generate independent

measurement outputs. The output voltage of each sensor cellis proportional to the compressive pressure perpendicularlyapplied on the sensor surface. Due to the thin-film packaging,the PSECR sensor cannot work under applied tensile stress.The details of the PSECR sensor are described in [17].

We use a motorcycle tire to embed the PSECR sensor.The motorcycle tire is shown in Fig. 1(b) and the tire hassmooth outer surfaces. The cross-section of the tire has acircular shape as shown in Fig. 1(c). For the torus-shapetire, it is straightforward to obtain that the tire-road contactpatch forms an elliptical shape [20]. We choose this typeof motorcycle tires with simple geometry and structure suchthat we can focus on the fundamental mechanical contactproperties without distraction by the influences of other factorssuch as tire treads and grooves etc. Although we choosethis simple-geometry tire, as shown in experiments in thispaper and in [18], the contact properties such as the normalcontact pressure distribution follow the similar pattern as thoseobtained by using actual automobile tires reported in [21],[22].

The sensor is embedded at the center line of the contactpatch; see Fig. 1(d). To minimize the destructive effects, cut-ting and gluing process is carefully conducted. The small cutis created using a scalpel. The 3M Scotch-Weld Neoprene highperformance rubber glue is used to maintain the homogeneousrubber property within the cut area. As we will show in thelater sections, the consistent comparison results between thesensor measurements and the model predictions confirm thatthe destructive effect on the tire structure due to cutting isnegligible.

B. “Smart Tire” Testing Platform

Fig. 2 shows the “smart tire” testing platform. A treadmillis modified to act as a firm foundation to hold the tire supportplate. To study tire-road stick-slip interactions for PSECRsensor testing, we replace the treadmill belt with a thicktransparent plate. The plate is supported by three individuallycomputer-controlled jacks. Three load cells (from TransducerTechniques Inc.) are positioned under the plate to measure thetotal normal load between the tire and the plate.

To generate friction forces along the x- and y-axis direc-tions, we use two steel cables to pull the tire: one appliedon tire rim for the longitudinal (x-axis) direction and theother applied on the transparent plate for the lateral (y-axis)direction. The total friction forces along x- and y-directions


Comp. RIO

sensor

Amplifier

plate

Pulling force

Transparent

PSECR sensorPulling forcesensor

F fx

F fy

Fig. 2. “Smart tire” testing platform with an embedded force sensor insidethe tire. We use force sensors to measure the total friction forces on the tirecontact patch.

are respectively measured by two force sensors as shown inFig. 2. The data collection and the normal force control areimplemented through a real-time NI CompactRIO embeddedsystem. The details about the setup are presented in [20].

III. SENSOR MODELS

In this section, we first briefly review the beam-spring modelfor the tire-road interactions. Then we present the model tointerpret the sensor measurements and to extract the localfriction forces on the tire contact patch. Finally, we discussthe optimal orientation of the embedded sensor inside the tirerubber layer.

A. Beam-Spring Tire–Road Interaction Models

Fig. 3(a) shows the schematic of the tire-road contact. Wedenote the contact patch as P and the thickness of the rubberlayer as 2h. A coordinate system is set up with the origin at thecenter of P with a vertical distance of h to the road surface.The x-axis is along the tire center with the positive directiontowards the leading edge of P , that is, the direction where thetire tends to move forward. We denote the total longitudinaland lateral friction forces as F f x and F f y , respectively. Theresultant of F f x and F f y is defined by F f . We denote the tirenormal contact pressure distribution on P as Pn(x, y) with theinflation air pressure Pair and the total normal force Fz . Wedenote the friction force distribution at point (x, y) on P asP f (x, y) with the x- and y-axis components as Pf x(x, y) andPf y(x, y), respectively. Therefore, we have

Fz =∫P

Pn(x, y) d S, F f =∫P

P f (x, y) d S

where d S is an infinitesimal area on P .For stationary tire-road contact, when total friction force

F f increases, the contact goes through a stick-to-slip tran-sition [18]. The stick contact refers to no locally relativemovement between the tire and the road, while in slip contact,local relative tire-road motion exists. During the stick-to-sliptransition, some contact points at certain locations on P begin

(a) (b)

Fig. 3. (a) Schematic diagram of the tire–road contact patch. (b) Schematicdiagram of the beam-spring network model for stick–slip interactions.

(a) (b)

Tire rubber layer

σ2z

σ2x

τ2x

Pn(x)

Pair

Pfx

Pfx

Pfy

π1π1π2

C1

C1

C2

C2

C3

C4

2hhC1

hC2

x

x

y

z

z

α

α

β

P

Fig. 4. Embedded PSECR sensor configuration. (a) Configuration diagramsof the four sensor cells. (b) Side view schematic diagram of the embeddedsensor inside the rubber layer.

deforming and slipping while other points remain stickingto the road. The slipping region grows as the applied forceincreases. We use a beam-spring network modeling approachto capture the stick-slip interactions.

Fig. 3(b) illustrates the beam-spring network modelingapproach. We partition the tire-road contact into N virtualcantilever beams and each of them has a height of 2h anda square cross-section. Linear springs are assumed to connecteach pair of neighboring beams. During the stick-to-slip tran-sition, dynamic motions of the beams are negligible. For thei th beam inside the interior of P , i = 1, . . . , N , the followingforce equilibrium is obtained.

f if + f i

b + f ie = 0 (1)

where f if is the tire contact friction force, fb

i is the bendingforce that captures the shear deformation, and f i

e is the resultantnet elastic force from the adjacent beams. In [18], we havediscussed how to obtain fb

i and f ie such that we can then

use (1) to calculate f if .

In the following, we describe how to use the beam-springnetwork model to extract the friction forces on P from themeasured forces by the PSECR sensor inside the tire rubber.

B. PSECR Sensor Output Model

To obtain the multi-directional local friction forces, thesensor is embedded with a special orientation as shown inFig. 4. If being positioned horizontally, the PSECR sensoris not sensitive to local friction forces on P . Moreover, thePSECR sensor only functions under compressive forces inside


the rubber layer and thus, it cannot be placed along the verticaldirection since horizontal tensile stresses exist during the stick-to-slip transition. By tilting the sensor with a certain angle, theexistence of the internal compressive normal stress preventsthe sensor from exposing to tensile forces.

To extract both the local x- and y-axis directional frictionforces, we separate the four sensor cells into two groups: C1and C2 are placed on plane π1, while C3 and C4 lie in planeπ2. The tilting angles of π1 and π2 with respect to the x- andy-axis directions are denoted as α and β, respectively. We willdiscuss how to determine the optimal values for α and β inSection III-C.

Let Pf x and P f y denote the local friction stresses at location(x, y) on P along the x- and y-axis directions at the sensorlocation, respectively; see Fig. 4(a). Pf x and Pf y can beconsidered as the x- and y-axis components of the spatiallynormalized friction force f i

f given in the beam-spring networkmodel in (1); see Fig. 3(b). Due to symmetry of P and forpresentation clarity, we consider locations on P along the tirecenter line (e.g., at y = 0) and varying x coordinate so thatthe force variables are only functions of x . Let σ l

k and τ lk

denote the normal and shear stresses along the k-axis for Cl ,k = x, y, l = 1, 2, 3, 4, respectively. Note that σ l

k correspondsto the spring elasticity effect and is considered as the spatiallynormalized spring force in the beam-spring network model.Similarly, τ l

k is related to the bending effect at the sensorlocation. We denote the normal stress along the z-directionat the sensor location as σ l

z .Let Fl

s denote the resultant compressive force applied to Cl

and V ls be its measured output voltage. Then we have V l

s =Kl Fl

s , where Kl , l = 1, 2, 3, 4, are the output gains for sensorcells Cl [17]. The sensor output Vs under Pf x and Pf y consistsof two portions: one portion V0 is due to the rubber bendingand the other portion comes from the existence of σ l

k and τ lk

due to the friction forces on P . Thus, output V ls can be written

as

V ls =

{V l

0 + Kl As(−σ lx + τ l

x) sin α, l = 1, 2,

V l0 + Kl As(−σ l

y + τ ly) sin β, l = 3, 4,

(2)

where

V l0 =

{Kl As(−σ l

z cos α − σ lx0 sin α), l = 1, 2,

Kl As(−σ lz cos β − σ l

y0 sin β), l = 3, 4,(3)

where As is the area of each sensor cell, and σx0 and σy0are the shell-to-plate bending stresses along the x- and y-axis,respectively.

The goal of building a sensor model is to extract Pf x

and P f y information from measurements V ls in (2). We first

obtain a model for V l0. By the assumption of the unchanged

length of neutral line during the shell-to-plate bending [23]and considering the thin rubber layer, we estimate

σ lx0 ≈ − EhCl

Ro − h, l = 1, 2, and σ l

y0 ≈ − EhCl

Rc − h, l = 3, 4,

where hCl is the z coordinate of cell Cl . To obtain σz(z), weobtain the following relationship

σz(z) = [Pn(x) − Pair ]

(1

4h3 z3 − 3

4hz

)− Pn(x) + Pair

2,

(4)

where Pn(x) is the contact normal pressure and can be esti-mated empirically [20]. The derivation of the above equationis given in Appendix I. Combining the above results for σ l

x0,σ l

y0 and σ lz = σz(hCl ) and from (3), we obtain V l

0 in (2).We need to build the relationship between σ l

k , τ lk and

Pf x , Pf y . In the following discussion, we only present thedevelopment of such relationships for C1 and C2 to extractPf x and the similar results can be obtained along the y-axisdirection for C3 and C4 to obtain Pf y .

We denote the spatially normalized net spring force f ie and

beam bending force f ib along the x-axis direction as σPx

and τPx , respectively. We normalize (1) spatially, take themagnitude of the normalized stress equation along the x-axisdirection, and then obtain

P f x = τPx + σPx . (5)

Notice that τPx corresponds to the shear stress τ lx and σPx is

related to the normal stress σ lx . Both σ l

x and τ lx can be extracted

from the sensor measurements through (2) for C1 and C2.First, the sensor cells are spatially close each other and in thelocal area of C1 and C2, σ l

x , l = 1, 2, are treated approximatelythe same because of the small sensor size. Therefore, we have

σ 1x = σ 2

x = σx . (6)

To further build the relationship between τ lx and τPx , we

consider that τPx is the boundary shear stress at z = h and τ lx ,

l = 1, 2, are the shear stresses at the sensor locations zl = hCl .We assume that the shear deflection of the rubber layer followsthe virtual beam deflection. Using the Euler-Bernoulli beamtheory, the deflection w(z) of a cantilever beam under bendingforce fbx is

w(z) = fbx (z + h)2(5h − z)

6E I

and the (maximal) deflection at the tip is δx = fbx (2h)3

3E I . Byeliminating fbx , we obtain

w(z) = δx

16h3 (−z3 + 3hz2 + 9h2z + 5h3)

and τ lx is then calculated by

τ lx = G

∂w(z)

∂z

∣∣∣z=hCl

= γl G∂w(z)

∂z

∣∣∣z=h

= γlτPx , (7)

where γl = 14h2 (−h2

Cl+2hCl h+3h2), l = 1, 2. Eq. (7) implies

that τ lx varies along the z-direction.

Using (2), (6) and (7), we obtain[V 1

s − V 10

V 2s − V 2

0

]

︸︷︷︸V

=[−K1 As sin α K1 Asγ1 sin α−K2 As sin α K2 Asγ2 sin α

]︸︷︷︸

K

[σx

τPx

]︸︷︷︸

σ

. (8)

The coefficient matrix K is invertible if γ1 �= γ2, that is,C1 and C2 are not at the same depth, which is satisfied inthe design. σx and τPx are then uniquely determined as σ =K−1V. The linear model in (8) is derived based on the Euler-Bernoulli beam assumption and other modeling approachesmight lead to the similar conclusion. Instead computing Kin (8) from a set of the model parameters, we conduct acalibration process to obtain K in practice for high accuracy.


Therefore, the final results of obtaining coefficient K are notrestricted by knowing the beam model parameters.

We still need to obtain σPx to calculate Pf x by (5). Wetake an empirical approach to calculate σPx : if the sensor liesin the stick region, we take the following relationship

σPx = κx |σx |mx , (9)

where we use the absolute value of σx because σx can benegative and σPx is always positive. The coefficients κx andmx are obtained by calibration in experiments. When thesensor lies in the location where the local contact slips, σPxsaturates at the value σ 0

Px . We detect slipping when τPx issaturated and at this moment, we denote σx = σ 0

x . Then σ 0Px

is calculated by (9) for the given σ 0x .

Summarizing the above discussion, we obtain

Pf x ={

τPx + σPx locally stick,

τPx + σ 0Px locally slip

(10)

where τPx and σPx are respectively obtained by (8) and (9)with a calibrated PSECR sensor, and σ 0

Px = κx |σ 0x |mx with

σ 0x is captured by sensor measurements as discussed above.

C. Optimal Sensor Orientation

The tilting angles α and β of the PSECR sensor canbe optimized for enhancing force measurements. Due to thesymmetry, we discuss how to obtain the optimal value for αand the similar conclusion is applicable to obtain the optimalvalue for β.

From (8), angle α should be maintained as large as possibleto have a superior sensitivity and resolution for stresses σ .Furthermore, from the first equation in (3), a large α alsohelps minimize the influences of the variations of V l

0 inmeasurements due to the small σ l

x0 term. On the other hand,the PSECR sensor only works under compressive stresses anda large α potentially risks elongation stresses applied to thesensor because of the possible tensile stress distribution insidethe rubber layer (see Fig. 12(a)). We thus enforce the constraintV l

s ≥ 0 to guarantee always compressive forces on the sensor.With the above considerations, we formulate the followingoptimization problem:

maximize α (11a)

subject to −σ lz cos α + (−σ l

x + τ lx) sin α ≥ 0, (11b)

0 ≤ α ≤ 90◦, l = 1, 2. (11c)

The constraint (11b) is obtained by plugging (2) into V ls ≥ 0

and neglecting the term σ lx0 because of its negligible value.

The constraint should be satisfied for all possible stresses σ lz ,

σ lx and τ l

x on P . We consider the fact that σ lz < 0 and the only

possibility of having elongation stresses on the sensor existswhen −σ l

x + τ lx < 0. Therefore, we solve (11) by considering

the case of τ lx < σ l

x , and obtain

αmax = minl

{min tan−1

(−σ l

z

σ lx − τ l

x

)}, τ l

x < σ lx (12)

for l = 1, 2. In the above equation, we take the minimalvalue of all possible cases of τ l

x < σ lx for both C1 and C2.

Calibration fixture

x−axis localfriction force

friction force

sensor

y−axis local

Embeded PSECR

Pfx

Pfy

Fig. 5. PSECR sensor calibration fixture.

To illustrate a typical value of αmax, we consider a case ofPair = 69 kPa and Fz = 267 N (used in experiments), andobtain αmax = 41 degs. Due to the small size of the PSECRsensor and the thin rubber layer thickness (2h = 7 mm), wecannot install the PSECR sensor at αmax = 41 degs. Instead,α = 21 degs and β = 26 degs are the largest possible valuesthat satisfy (11) and that are obtained to embed the PSECRsensor.

IV. EXPERIMENTS

In this section, we present the experiments to calibrate thePSECR sensor, validate the sensor models, and demonstratethe sensor performance through an example of the tire-roadstick-slip interactions.

A. PSECR Sensor Calibration and Model Validation

The sensor calibration processes for the x- and y-directionforces are similar and we here only describe the x-directioncase. We first obtain the σx measurements right after the sensoris glued on one side inside the tire rubber. We use a forcegauge (model FDK 80 from Wagner Inc.) to press on C1and C2 to generate σx . Fig. 6(a) shows the outputs of C1and C2 under various σx measurements. The sensor outputsdemonstrate a strong linear relationship with σx .

After the sensor is completely glued inside the tire, weapply τPx to the local area where the PSECR sensor isembedded using a calibration fixture. The fixture is designedand fabricated with a comparable size to that of the PSECRsensor [20]; see Fig. 5. The fixture is directly mounted on thetransparent plate of the testing platform (Fig. 2). The use of thecalibration fixture guarantees that the friction force lie locallyat the location where the sensor is embedded. We put a leathercover on the fixture surface to generate high friction forcesand prevent the contact from sliding. Therefore, shear forcedominates the interaction and we assume that the local frictionforce P f x is fully contributed by τPx . The calibration resultswith varying τPx are shown in Fig. 6(b). A linear relationshipbetween the sensor outputs and τPx is clearly obtained, similarto the model prediction by (7). Moreover, the results also showthat the two sensor cells have different sensitivities to τPx , asthe model (7) predicts due to the different γl at locations ofCl , l = 1, 2.


0 1 2 3 4 5 6

x 105

0

0.5

1

1.5

2Sensor cell 1

Sensor cell 2

Linear fitting Cell 1


Vs(V

)

σx (Pa)(a)

0 2 4 6 8 10

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

Sensor cell 1

Sensor cell 2



Vs

(V)

τPx (Pa)(b)

0 1 2 3 4 5 6

x 104

0

1

2

3

4

5

6x 10

4

ExperimentData fitting

σx (Pa)

σP

x(P

a)

(c)

Fig. 6. Sensor cells C1 and C2 calibration results. (a) Sensor output voltage with various σx . (b) Sensor output voltage with various τPx . (c) Gain κx(between σPx and σx ) calibration.

0 1 2 3 4 5 6

x 105

0

0.5

1

1.5

2

2.5

Sensor cell 4

Sensor cell 3



Vs(V

)

σy (Pa)

(a)

0 2 4 6 8 10

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sensor cell 4

Sensor cell 3



Vs

(V)

τPy (Pa)

(b)

0 1 2 3 4 5

x 104

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

ExperimentData fitting

σy (Pa)

σP

y(P

a)

(c)

Fig. 7. Sensor cells C3 and C4 calibration results. (a) Sensor output voltage with various σy . (b) Sensor output voltage with various τP y . (c) Gain κy(between σP y and σy ) calibration.

In experiments, multiple repeated calibrations are con-ducted. Given M1 measurements of σ x = (σx)M1 and M2measurements of τPx = (τPx )M2 , we form a stress measure-ment matrix σm ∈ R

2×(M1+M2) and the corresponding sensoroutput matrix Vm ∈ R

2×(M1+M2) respectively as

σm =[

σ x 0M2

0M1 τPx

]and Vm =

[V 1

s − V 10

V 2s − V 2

0

],

where 0M ∈ R1×M is the zero row vector. From the rela-

tionship V = Kσm in (8), we estimate K in the x-directionas

K̂x = Vmσ+m = Vmσ T

m(σmσ Tm)−1, (13)

where σ+m = σ T

m(σmσ Tm)−1 is the pseudo-inverse of σm . The

mean and the standard deviation values of the calibrated Kx

are respectively as

K̂x =[−3.01 2.73−3.02 4.84

]V/MPa

and

σ̂Kx =[

0.09 0.180.10 0.23

]V/MPa.

By substituting K̂x into the sensor output model, we thencalibrate coefficients κx and mx in (9) with measurementsσx and σPx , where σPx = P f x − τPx and P f x is obtainedagain from the calibration fixture without the leather cover; seeFig. 5. Fig. 6(c) shows the calibration curve. The calibration

values of estimated κx and mx are κ̂x = 29.74 and m̂x = 0.68,respectively. The standard deviations of the estimated κx andmx are σ̂κx = 1.97 and σ̂mx = 0.01, respectively.

A similar calibration process is conducted for the y-direction force sensor cells C3 and C4. The calibration resultsare shown in Fig. 7 and the calibration coefficients in the y-direction are

K̂y =[−3.32 2.97−3.33 5.03

]V/MPa, κ̂y = 32.40 and m̂ y = 0.66

respectively. The standard deviations for the estimated Ky , κy

and my are respectively as

σ̂Ky =[

0.13 0.220.11 0.24

]V/MPa, σ̂κy = 1.91 and σ̂my = 0.01.

To validate the sensor model, we conduct multiple repeatedvalidation tests by varying P f x and Pf y at the sensor locationand then compare with the sensor measurements. Fig. 8 showsthe comparison results for both Pf x and Pf y in one validationtest. The root mean square differences are 1.1 × 104 Pa (forthe x-direction stress) and 0.9 × 104 Pa (for the y-directionstress). Fig. 9 shows the statistical errors of the multiplevalidation tests. The maximum errors are consistently less than1.5 × 104 Pa in both the x- and y-direction. We also comparethe measured voltage V0 with the model prediction (3) asshown in Fig. 10. The values for the V0 model parameters arelisted in Table I. The model predictions show a clear agreementwith the experiments for V0.


0 5 10 15 18

x 104

0

5

10

15

18x 10

4

Actual Pfx (Pa)

Mea

sure

dP

fx

(Pa)

(a)

0 5 10 15

x 104

0

5

10

15x 10

4

Actual Pfy (Pa)

Mea

sure

dP

fy

(Pa)

(b)

Fig. 8. Friction force measurement validations. (a) Pf x measurements.(b) Pf y measurements.

2 4 6 8 10 12 14 16

x 104

0

0.5

1

1.5

2x 10

4

2 4 6 8 10 12 14

x 104

0

0.5

1

1.5

2x 10

4

erro

r(P

a)er

ror

(Pa)

Pfx (Pa)

Pfy (Pa)

Fig. 9. Statistical mean errors and their standard deviations of sensormeasurements.

−4 −2 0 2 40

0.5

1

1.5

2

2.5

3

3.5 Cell C1 (Exp)

Cell C1 (Model)

Cell C2 (Exp)

Cell C2 (Model)

Cell C3 (Exp)

Cell C3 (Model)

Cell C4 (Exp)

Cell C4 (Model)

x (cm)

V0

(V)

Fig. 10. Comparison of the prediction of the static bending stress (representedby V0) with the experiments.

B. Friction Force Distributions in Stick-to-Slip Transition

We use the calibrated PSECR sensor to measure the frictionforce distribution on P during the stick-to-slip transition.We compare the experiments with the prediction resultsfrom the model in [18] to validate the sensor measurementsand demonstrate the sensor performance.

0

5

10

15x 10

4

0

5

10

15x 10

4

0 2 4 6 8 10 120

100

200

Partial slip at sensor location

Full slip onentire patch

(Pa)

Time (s)

σ0x

σx

τPx

Pf

x(P

a)F

fx

(N)

Fig. 11. PSECR sensor measurements and stress estimation at the sensorlocation during the stick-to-slip transition.

TABLE I

PSECR SENSOR AND TIRE PARAMETERS

E(MPa) Ro(m) h(mm) As (cm2) K1(V/N) K2(V/N) K3(V/N) K4(V/N)

11.7 0.128 3.5 0.16 0.56 0.54 0.53 0.53

To observe the stick-to-slip transition and the local frictionforce evolutions for a point on P , we rotate the tire to locatethe sensor around the middle point between the trailing edgeand the center of P (Fig. 2). An increasing F f x is generatedby pulling the cable until the tire completely slips at aroundF f x = 160 N. Fig. 11 shows the sensor measurements at thelocal area where the sensor is embedded. Shear stress τPxstarts to increase with the increasing F f x . Once the partialslip at the sensor location starts around t = 8.8 s, τPx stopsincreasing and keeps flat. This observation agrees with thefriction model in which Pf x saturates when partial slip starts.The observation of τPx becoming flat is used to predict themoment when the partial slip happens at the sensor location.We estimate σ 0

x = 6×104 Pa and therefore, σ 0Px = κ̂x |σ 0

x |m̂x =5.76 × 104 Pa.

After the partial slip starts, σx keeps increasing with theincreasing F f x and the slip region propagates towards theinterior portion of P . Pf x shown in the middle plot of Fig. 11is the local friction force measurement during the stick-to-sliptransition. When the full slip of the entire patch starts aroundt = 11 s, σx , τPx and P f x drop rapidly.

To illustrate σx (x) and Pf x(x) distributions under F f x ,we conduct a set of scanning experiments by moving theembedded sensors at various locations along the tire center line(i.e., y = 0), while pulling the tire until completely slipping.Fig. 12(a) demonstrates the comparison results between theexperiments and the model predictions for local stress σx (x).The results show a clear agreement between the sensor mea-surements and the model calculations. The results in Fig. 12(a)show that σx(x) has larger values close to the edge of Pthan those around the center of P . Notice the sign changeof σx (x), at the leading edge the rubber is under compression


−4 −3 −2 −1 0 1 2 3 4−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5x 10

5

Ffx

=44.5N (model)

Ffx

=44.5N (exp)

Ffx

=89N (model)

Ffx

=89N (exp)

Ffx

=133.5N (model)

Ffx

=133.5N (exp)

x (cm)

σx(x

)(P

a)

(a)

−4 −3 −2 −1 0 1 2 3 40

5

10

15x 10

4

Ffx

=44.5N (model)

Ffx

=44.5N (exp)

Ffx

=89N (model)

Ffx

=89N (exp)

Ffx

=133.5N (model)

Ffx

=133.5N (exp)

x (cm)

Pf

x(x

)(P

a)

(b)

Fig. 12. Comparison results between the sensor measurements of stressdistributions and the model prediction on P under various friction forcesF f x . (a) σx (x) and (b) P f x (x).

(i.e., negative σx (x)), while at the trailing edge portion it isunder elongation (i.e., positive σx (x)). This phenomenon alsomatches the rubber deformation distribution reported in [18].Fig. 12(b) shows the local friction stress Pf x(x) along thecenter line of P . Again, the sensor measurements fit thenumerical calculations.

Fig. 13 shows the consistent matching results betweenthe experiments and the model predictions for P f y(x) alongthe center line of P under lateral force F f y . Similar to Pf x (x),the sensor measurements of Pf y(x) match the model predic-tion. We also conduct experiments under the existence of bothF f x and F f y and the results consistently show the agreementsbetween the sensor measurements and the model predictions.These results confirm the capability of the PSECR sensor tocapture the local friction forces and their distributions on P .

Some discrepancies exist between the sensor measurementsand the model predictions. These differences mainly comefrom several sources. Due to the physical constraints, thesensor is not installed at the optimal orientation for superiorsensitivity. The imperfect numerical model calculations alsocontribute partially to the discrepancies. The complex rubberhyper-elastic property also results in sensor prediction errors.The accuracy limitation of the low-cost PSECR sensor isanother source of the measurement errors.

−4 −3 −2 −1 0 1 2 3 40

2

4

6

8

10

12x 10

4

Ffy

=26.5N (model)

Ffy

=26.5N (exp)

Ffy

=53.5N (model)

Ffy

=53.5N (exp)

Ffy

=89N (model)

Ffy

=89N (exp)

x (cm)

Pf

y(x

)(P

a)

Fig. 13. Comparison results of the sensor measurements and the modelprediction for P f y (x) distribution under applying various friction forces F f yalong the center line.

V. CONCLUSION

We presented a new, flexible force sensor to capture thein-situ tire local friction force distributions in stick-slip tran-sition. The flexible force sensor is made of the pressuresensitive, electric conductive rubber (PSECR). The PSECRsensor has four independent sensing cells within one unit andthese spatially distributed sensor arrays enabled us to extractthe multi-dimensional local friction forces simultaneously. Weanalyzed and interpreted the PSECR sensor measurements byusing the beam-spring network model. The sensor calibrationprocess and results were presented and the performance wasalso demonstrated through experiments to extract the localfriction forces in tire-road stick-slip interactions. The sensormeasurements showed high agreements with the numericalresults for the friction force distributions. The PSECR sensorhas the potentials to capture local friction forces in contactbetween a flexible thin layer and a rigid in other applications.

APPENDIX ICALCULATION OF σz(z) INSIDE THE RUBBER LAYER

Fig. 4(b) illustrates the configuration of the tire rubber layer.We first decompose Pn(x) by a Fourier series.

Pn(x) = P0 +∞∑

m=1

Am sin (λx) +∞∑

n=1

Bm cos (λx) , (14)

where P0 is the constant term and λ = mπLx

and Lx is themajor axis length of the elliptical P . By superposition, weconsider the contribution of each term in (14) to the internalstress σz(z). The particular solution of σz(z) when Pair andP0 are applied on each side of the tire rubber layer is givenby (page 41 of [23])

σ sz (z) = P0 − Pair

4h3 z3 − 3(P0 − Pair )

4hz − P0 + Pair

2.

To calculate the contribution of the first harmonic termAm sin (λx) in (14) to σz(z), we introduce an Airy func-tion φm(x, z) = sin (λx) fm(z) in the form of the Fourier


series [23]. Plugging φm(x, z) into bi-harmonic condition∇4φm(x, z) = 0, we obtain

λ4 fm(z) − 2λ2 f ′′m(z) + f (4)

m (z) = 0.

The general solution for fm(z) is

fm(z) = D1ch(λz)+D2sh(λz)+D3zch(λz)+D4zsh(λz) (15)

where sh(x) := sinh(x) and ch(x) := cosh(x) for x .Considering that σz = ∂2φm

∂x2 and τxz = ∂2φm∂x∂z and the

boundary conditions: τxz = 0, σz = −Am sin λx for z = h,and τxz = 0 and σz = 0 for z = −h, we obtain coefficientsDi in (15). Therefore, the contribution of the term Am sin (λx)in (14) for Pn(x) is given by σm

s as

σms = −Am sin(λx)

×{ [λhch(λh) + sh(λh)]ch(λz) − λzsh(λz)sh(λh)

sh(2λh) + 2λh

+[λhsh(λh) + ch(λh)]sh(λz) − λzch(λz) cos(λh)

sh(2λh) − 2λh

}.

(16)

Similarly, for the term Bm cos (λx) in (14) for Pn(x), thecontribution to the stress distribution is given by σm

c as

σmc = −Bm cos(λx)

×{ [λhch(λh) + sh(λh)]ch(λz) − λzsh(λz)sh(λh)

sh(2λh) + 2λh

+[λhsh(λh) + ch(λh)]sh(λz) − λzch(λz) cos(λh)

sh(2λh) − 2λh

}.

(17)

For Lx � h, using the approximations sh(x) ≈ x + x3

6 + x5

120

and ch(x) ≈ 1 + x2

2 + x4

24 for small x , Eqs. (16) and (17) arereduced respectively to

σms ≈ Am sin(λx)

(1

4h3 z3 − 3

4hz − 1

2

)and

σmc ≈ Bm cos(λx)

(1

4h3 z3 − 3

4hz − 1

2

).

By superposition, we add all the above calculated stressterms together and using (14), we obtain

σz(z) = σ sz (z) +

∞∑m=1

σms +

∞∑m=1

σmc

= [Pn(x) − Pair ]

(1

4h3 z3 − 3

4hz

)− Pn(x) + Pair

2

for a given x . This completes the calculation of (4). The abovederivation is readily extended to the two-dimensional case (i.e.,including stress along the y-axis direction) if L y � h.

ACKNOWLEDGMENTS

The authors would like to thank Prof. L. Liu of RutgersUniversity for various helpful discussions. We are also gratefulto A. Allen and the Rutgers “smart tire” senior design teamin 2009 for designing, fabricating, and improving the originaltesting platform.

REFERENCES

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[2] J. Yi, L. Alvarez, and R. Horowitz, “Adaptive emergency brake controlwith underestimation of friction coefficient,” IEEE Trans. Control Syst.Technol., vol. 10, no. 3, pp. 381–392, May 2002.

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[4] Intelligent Tyre Systems—State of the Art and Potential Technologies,Technical Research Centre of Finland (VTT), Espoo, Finland, 2003.

[5] “Federal motor vehicle safety standard: Tire pressure monitoringsystems, controls, and displays,” NHTSA, Washington, DC, USA,Tech. Rep. 2000–8572, 2000.

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Yizhai Zhang (S’11) received the B.S. degree andthe M.S. degree in information and communicationengineering from Xi’an Jiaotong University, China,in 2005 and 2009, respectively. He is currentlypursuing the Ph.D. degree in mechanical andaerospace engineering at Rutgers University,Piscataway, NJ, USA. His research interests includeautonomous robotic systems, dynamic systems andcontrol, intelligent sensing and actuation systems,and mechatronics.

Mr. Zhang is a student member of AmericanSociety of Mechanical Engineers (ASME). He received the Best StudentPaper at the 2012 IEEE/ASME International Conference on AdvancedIntelligent Mechatronics and the 2012 ASME Dynamic Systems and ControlConference.

Jingang Yi (S’99-M’02-SM’07) received the B.S.degree in electrical engineering from Zhejiang Uni-versity, Hangzhou, China, in 1993, the M.Eng.degree in precision instruments from Tsinghua Uni-versity, Beijing, China, in 1996, and the M.A. degreein mathematics and the Ph.D. degree in mechani-cal engineering from the University of California,Berkeley, in 2001 and 2002, respectively. He iscurrently an Assistant Professor of Mechanical Engi-neering at Rutgers University. His research interestsinclude autonomous robotic systems, dynamic sys-

tems and control, mechatronics, automation science and engineering, withapplications to biomedical systems, civil infrastructure and transportationsystems.

Dr. Yi is a member of American Society of Mechanical Engineers (ASME).He is a recipient of the 2010 US NSF CAREER Award. He has co-authoredpapers that have been awarded the Best Student Paper at the 2012 IEEE/ASMEInternational Conference on Advanced Intelligent Mechatronics and the2012 ASME Dynamic Systems and Control Conference, the Kayamori BestAutomation Paper at the 2005 IEEE International Conference on Roboticsand Automation, and several Best Paper finalists at the 2007 and 2008 IEEEInternational Conference on Automation Science and Engineering and the2008 ASME Dynamic Systems and Control Conference. Dr. Yi currentlyserves as an Associate Editor for the IEEE TRANSACTIONS ON AUTOMATION

SCIENCE AND ENGINEERING and the IEEE Robotics and Automation SocietyConference Editorial Board (since 2008). He also served as a Guest Editor forthe IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING

in 2009 and an Associate Editor for the ASME Dynamic Systems and ControlDivision Conference Editorial Board from 2008 to 2010.

Tao Liu (M’08) received the M. Eng. degrees inmechanical engineering from the Harbin Institute ofTechnology, Harbin, China, in 2003 and the Doc-torate degree in engineering from Kochi Universityof Technology, Kochi, Japan, in 2006. From 2003to 2006, he was a Research Assistant at the KochiUniversity of Technology, where during 2007, hewas a Postdoctoral Fellow in the Department ofintelligent Mechanical Systems Engineering. He hasbeen an Assistant Professor in the Department ofIntelligent Mechanical Systems Engineering, since

2008. He was a recipient of the Japan Society of Mechanical EngineersEncouragement Prize (2010).

Dr Liu is also an inventor of one Japan patent about wearable sensors forgait analysis, which was commercialized. He has been serving as EditorialBoard Member and Reviewer of multiple international journals, and servingas Program Committee member and Session Chair of multiple internationalconferences. His current research interests include wearable sensor systems,rehabilitation robots, biomechanics, and human motion analysis.

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