detection of tire lateral force based on a resolver ......r&d review of toyota crdl vol. 40 no....

R&D Review of Toyota CRDL Vol. 40 No. 4

14

Detection of Tire Lateral Force Based on a Resolver MechanismTakaji Umeno

ResearchReport

AbstractTo observe the frictional state of a tire and

improve the active safety control system of avehicle, it is necessary to sense the tire-generatedforces.

This paper presents a technique for detecting alateral tire-force. This is based on the resolvermechanism that is used as a rotational speedsensor for a wheel. It is realized simply byreplacing a conventional wheel speed sensor, andcan detect tire lateral force by magnetically

sensing the positional offset of the rotating shaftthat occurs due to the stiffness of the shaft andaxle hub bearing. Therefore, there is no need forcomplex machining and the system canaccommodate variations in the tire characteristicscaused by changes in temperature, inner pressure,aspect ratio, and so on. The principle of thetechnique has been confirmed by experiments ona tire test machine and on a test vehicle.

Keywords Resolver, Lateral force, Differential phase shift, Stiffness, Moment

Special Issue Estimation and Control of Vehicle Dynamics for Active Safety


1. Introduction

To observe the frictional state of a tire andimprove the active safety control system1) of avehicle, it is a necessary to sense tire-generatedforces such as the longitudinal force, self-aligningtorque, and lateral force. Of these forcecomponents, the longitudinal force and self-aligningtorque can be sensed by vehicle control equipment,such as the ABS hydraulic pressure sensor and theEPS torque sensor. The tire lateral force, however,has always been assumed to be difficult to detectusing conventional sensors.

Many methods of detecting tire-generated forceshave been proposed. One typical method involvesdetecting the tire-generated forces by embedding astrain gauge in a suspension knuckle,2) while anothermethod uses a magnetic marker on the surface of thetire to detect tire deformation.3) Unfortunately, bothof these methods require complex machining of theknuckle or tire, and lack wide applicability. Also,the detection accuracy is poor and they cannot beregarded as being reliable.

This paper presents a tire lateral force detectiontechnique that is based on the resolver mechanismthat is used as a rotational speed sensor for a wheel.It can be realized simply by replacing a conventionalwheel speed sensor, and detects tire lateral forces bymagnetically sensing the positional offset of therotating shaft that occurs due to the stiffness of theshaft and axle hub bearing. Therefore, it needs nocomplex machining and can accommodate variationsin the tire characteristics resulting from changes intemperature, inner pressure, aspect ratio, and so on.The validity of this method has been confirmed byexperiments on a tire test machine and on a testvehicle.

2. Detection mechanism

2. 1 Principle of the resolverFigure 1 shows the configuration of a rotary

transformer resolver. It features a rotary transformeron the rotor and multiple coils on the stator that arelaid out such that the phase difference in the outputsignals is π/2. When a high frequency AC voltageE sin ωt is applied to the rotary transformer, voltagesexpressed by the following equations are induced in

the stator coils by electromagnetic induction.Ec = KE cos θ sin ωtEs = KE sin θ sin ωt

,• • • • • • • • • • • • • • • • • • • • • • • • • • (1)

where, K is a coupling coefficient. The magnitudesof the induced voltages vary in accordance with therotational angle θ of the rotor.

The R/D converter shown in Fig. 2 determines andthen outputs the angular position of the rotor fromEs and Ec. It has two multipliers and a subtracterthat generate a signal, as follows:

KE sin ωt sin (θ - φ). • • • • • • • • • • • • • • • • • • • • • • • • • • (2)Then, the synchronous commutator removes thesin ω t from the above signal. The voltage controloscillator (VCO) outputs counter up-down pulsescorresponding to the magnitude of the voltageKE sin (θ - φ), and adjusts the value of φ such that itcoincides with the rotational angle θ, namely, θ = φ.As a result, digital output angle φ becomes equal tothe actual angle position θ of the rotor.

2. 2 Differential phase shift (DPS)To detect the lateral force of a tire, the rotary

transformer is mounted on a drive shaft and thestator coils are fixed to the knuckle. When thelateral force Fy occurs as shown in Fig. 3, a momentMx, which is a product of Fy and the tire radius R, is

15

tE sin tKEEc sincos=

tKEEs sinsin=

Rotor Stator

ElectromagneticInduction

Rotary Transformer

Change in amplitude in accordance with rotational angle

Fig. 1 Configuration of resolver.

VCOCounter

tE sin

)sin(sin

)sincoscos(sinsin

-=

-

tKE

tKE

sin

cos

)sin( -KE

tE sin

Es

Ec

Resolver

SynchronousCommutator

Output

Fig. 2 R/D Converter.

applied to the rotating shaft and bearing. Then, theposition of the shaft is offset by γ due to the stiffnessof the shaft and bearing.

In this case, the voltages induced in the resolver,Ec and Es, are as follows:

Ec = KE cos (θ + δc)sin ωtEs = KE sin (θ + δs)sin ωt

. • • • • • • • • • • • • • • • • • • • (3)

Then, VCO and the counter of the R/D converterdetermine the digital output angle φ, such that

sin(θ - δs)cosφ − cos(θ + δc)sinφ 0 • • • • • • • • (4)Equation (4) derives

,

which can be approximated to

• • • • • • • • • • • • • (5)

by assuming that δc, δs<<1.Here, the speed change rate is obtained by

differentiating Eq. (5), as follows:

, • • • • • • • • • • • • • • • • • • • • • • • • • • (6)

where is the detected speed and ν is the truespeed. Since ν cannot be measured, the averagespeed during one rotation is used instead of ν. Thisequation indicates that if a lateral force is generated,the rate of change of the speed fluctuatesperiodically in the magnitude of (δc + δs) and at afrequency equal to twice the rotational speed of thewheel.

Generally, given that the number of magneticpoles is P, the period of the speed change rate is Ptimes the number of rotations of the wheel:

. • • • • • • • • • • • • • • • • • • • • • • • • • • (7)

Since (δc + δs) indicates the difference between the

v vv

Pc s− = +( )δ δ θsin

^

v̂

v vv c s− = +( )δ δ θsin 2

^

φ θ δ δ δ δ θ= + −( ) − +( ){ }12

2c s c s cos

sin tansincos

φθ δθ δ

−−( )+( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=−1 0s

c

phase shift in the voltage induced in the two coils, itis defined as the "Difference Phase Shift (DPS)" inthis paper.

The lateral force can be detected from Eq. (7),provided the characteristic relationship between DPSand the lateral force, namely the stiffness of the shaftand bearing, has been determined in advance.

3. Experiment using a tire test machine

To confirm the lateral force detection principle, weperformed an experiment using a tire test machine.

3. 1 Experimental systemA general view of the tire test machine and the

resolver installed on the axle hub is shown in Fig. 4.To sense the actual forces, we used a six-axis forcesensor. The resolver used in this experiment haseight poles and is of the variable reluctance type.This has the same characteristics to the rotarytransformer type shown in Fig. 1.

3. 2 Detection of DPSThe algorithm used to detect the lateral force using

DPS is shown in Fig. 5. According to Eq. (7), DPScan be detected as the magnitude of the speed

16


Rotating shaft

tKEEc c sin)cos( +=

tKEEs s sin)sin( -=

c

s

Rotating shaft is offsetby due to the moment

Stator coil

Fy

R

MomentMx = R Fy

Fz

Bearing

Resolver

Stator coil

Fig. 3 Moment and phase shift of resolver.

6-axis force sensor

drum

6-axis force sensor

drum ( 1m )

Knuckle

Stator coilRotor

Fig. 4 Tire test machine and resolver.

change rate. The rotational speed is obtained asfollows:

Normally, the R/D converter is designed so as tohave an angular resolution of 16 bits per rotation byusing a 16-bit register in the counter. If we look atthe time series signal of each bit of the register, wesee that a signal of one pulse rises at MSB within asingle rotation, and that 215 pulses rise at LSB. Inthis experiment, the bit position to be measured isselected so that 256 pulses rise in one rotation. Bymeasuring the interval between the rising or fallingedges (the period of the pulse), the rotational speed

in Eq. (7) can be obtained.Figure 6 shows the results of measuring the wheel

speed for a case in which the lateral force is almostzero (slip angle 0 deg) and a case in which a lateralforce is generated (slip angle 4 deg). We can showthat the fluctuation of the wheel speed clearlyappears to have eight periods in one rotation when alateral force is generated.

DPS δ(Ν), which is the value at the Nth pulse inone rotation, is calculated by using the followingequations:

R N i Pi

I N i Pi

ei N

N

m

( ) ( )sin( / )

( ) ( ) cos(

=

=

= −∑1

1282 256

1128

2

255α π

α π // )

( ) ( ) ( ) ( ) ( )( ) (

256255

2 2

i N

N

c s e m

f f f

N N N R N I NN K N

= −∑

= + = += −

δ δ δδ δ 11 1 0 1) ( ) ( ),+ − < <K N Kf fδ

v̂

where,

and δf(Ν) is the output from the lowpass filter. Thelowpass filter suppresses noise from the loadsurface.

A simple Fourier transform is applied in the abovesteps to extract the periodic component from thespeed change rate α(Ν).

3. 3 ResultsFigure 7 shows the results of an experiment inwhich the vehicle weight Fz and the wheel speedwere varied and the lateral force was set to zero. Inthis figure, we can see that DPS has a certain offset

v N v i N v N v Nv Ni N

N

( ) ( ), ( ) ( ) ( )( )

= = −= −∑1

256 255α^

^

17


32

33

34

35

36

37

38

10 10.1 10.2 10.3 10.4 10.5

32

33

34

35

36

37

38

10 10.1 10.2 10.3 10.4 10.5

Slip angle: 0 deg, Fy : 130 N

Slip angle: 4 deg, Fy : 1670 N

1 rotation 1 rotation

Time (s)

Time (s)

Whe

el s

peed

(ra

d/s)

(Wheel load: 2000 N, Speed: 40 km/h)

Whe

el s

peed

(ra

d/s)

Fig. 6 Wheel speed signal from resolver.

0

0.01

0.02

0.03

0.04

0.05

10 20 30 40 50 60

Fz = 500 N

Fz = 2000 N

Fz = 3000 N

Fz = 4000 N

0

Slip angle: 0 deg

Offset Dif

fere

ntia

l pha

se s

hift

(ra

d)

Rotational speed (rad/s)

Fig. 7 Offset of resolver.

Measure period of pulse from resolver

Detect rate of speed change with respect to the averageover one rotation for each pulse period

Apply Fourier transform to rate of change of each pulse periodwith respect to rotational angle

Calculate of DPS

Convert moment Mx andcompute tire lateral force Fy

Fig. 5 Lateral force detection algorithm.

• • • (8)

value, but it is not affected by either Fz or the wheelspeed. It is believed that this offset is derived fromthe alignment accuracy and electrical imbalancebetween the two coils in the stator.

Since this offset is fixed regardless of the changein Fz and the wheel speed, a corrected DPS can beobtained by subtracting the offset from the actualDPS. Figure 8 shows the results obtained from anexperiment that uses the corrected DPS with respectto the moment Mx(=FyR) which is applied to thebearing center. In this case, the vehicle weights Fzare 2000N and 3000N, and each wheel speed is setto 20, 40, and 60 km/h. This figure indicates that thecorrected DPS depends on Mx or Fy and is notaffected by any other parameters.

Therefore, if the relationship between Mx(or Fy)and the corrected DPS are known in advance, thelateral force can be detected from DPS.

4. Experiment using a test vehicle

The test vehicle was a rear-drive car with theresolver installed on the axle hub of the right-front

wheel. For this experiment, we used a rotarytransformer resolver.

Figure 9 shows the wheel speed detected by theresolver when the test vehicle was run through aslalom. We can see that the fluctuation in thedetected speed increased as the lateral accelerationincreased. This fluctuation appears to be caused bythe previously mentioned differential phase shift.

Figure 10 shows the relationship, experimentallydetermined in advance, between the DPS andmoment Mx applied to the bearing center of the axlehub. The estimated values of Mx and Fy obtainedfrom filtered DPS δf by using the characteristicshown in Fig. 10 are depicted in Fig. 11. In thisfigure, Fy is computed by simply dividing theestimated moment Mx by the tire radius R. To

18


Slip angle: 0, 1, 2, 4 degSpeed: 20, 40, 60 km/h

0

0.01

0.02

0.03

0.04

0 100 200 300 400 500 600

Fz = 2000NFz = 3000N

Determined by shaftand bearing stiffness

Moment Mx (Nm)

Cor

rect

ed d

iffe

rent

ial p

hase

shi

ft (

rad)

Fig. 8 Moment vs. corrected DPS.

30

35

40

45

0 5 10 15 20-0.8

-0.4

0

0.4

0.8Resolver outputActual speed

Lateral acceleration

Lat

eral

acc

eler

atio

n (G

)

Whe

el s

peed

(ra

d/s)

Time (s)

Fig. 9 Resolver output during slaloming.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 200 400 600 800Moment Mx (Nm)

Cor

rect

ed d

iffe

rent

ial p

hase

shi

ft (

rad)

Measured

Determined

Fig. 10 Relationship between Mx and DPS of testvehicle.

0

500

10001500

2000

2500

3000

0 5 10 15 20

0

200

400

600

800

0 5 10 15 20

MeasuredEstimated

Measured

Estimated

Outer wheel

Innerwheel

Time (s)

Time (s)

Lat

eral

for

ce F

y(N

)M

omen

t Mx

(Nm

)

Fig. 11 Results of estimation.

compare this with the measured value, the filteredabsolute values of Mx and Fy as sensed by the 6-axisforce sensor are shown in this figure. The highlyaccurate detection can clearly be seen, especially inthat area when the right-front wheel is the outerwheel in a turn.

5. Conclusion

This paper has presented a tire lateral forcedetection technique that is based on a resolvermechanism. It can be realized simply by replacing aconventional wheel speed sensor, and detects the tirelateral force by magnetically sensing the positionaloffset of the rotating shaft that occurs as a result ofthe stiffness of the shaft and the axle hub bearing.Therefore, it needs no complex machining and canaccommodate variations in the tire characteristicsdue to the change in the temperature, inner pressure,aspect ratio, and so on. The method has beenconfirmed by experiments in a tire test machine andon a test vehicle.

Currently, this method is software-based and canonly detect the absolute value of the lateral force. Inthe future, we aim to develop a hardware-basedmethod that can directly detect signed forces.

References

1) Hattori, Y., et al. : "Force and Moment Control withNonlinear Optimum Distribution for VehicleDynamics'', Proc. AVEC'02, (2002), 595, JSAE

2) Miyazaki, N. : Examined Patent Pub. H04-331336 (in Japanese)

3) Giustino, J. : US Patent No. US 6550320 B1(Report received on Sep. 22, 2005)

19


Takaji UmenoResearch fields : Vehicle state estimation

and controlAcademic degree : Dr. Eng.Academic society : Inst. Electr. Eng. Jpn.,

Soc. Instrum. Control Eng., IEEE,Soc. Automot. Eng. Jpn.

Awards : IEEE/IES Outstanding PaperAward, 1994Robomec'94 Best Poster Award,1995R&D 100 Award, 1997SICE Chubu Chapter Award forOutstanding Technology, 2002Paper Award of AVEC'02, 2002

detection of tire lateral force based on a resolver ......r&d review of toyota crdl vol. 40 no....

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