INTRODUCTIONBrake judder is a braking-induced vibration which is

perceived by the driver as a vibration at the steering wheel,brake pedal or vehicle body during light braking, typicallyduring mid to high speed traveling (30 to 140 km/h). It is oneof the most commonly occurring faults in braking systemsand has resulted in major recalls, warranty claims anddetrimental effects to the company reputation. Furthermore,the associated vibrations may also provoke additional wearand prompt components fracture, hence resulting in shorterservice life and higher operating costs.

Brake judder is caused by the irregularities in the brakedisk, and can be categorized into cold and hot (or thermal)judder [1]. Cold judder is induced by geometricalirregularities due to mounting, machining, uneven wear,uneven corrosion and uneven friction film generation [2].Geometrically, these irregularities resemble disk runout ordisk thickness variation (DTV). Disk runout may induceuneven wear and further generates DTV [3], whichcontributes to the brake pressure variation (BPV) and braketorque variation (BTV). For most manufacturers, themanufacturing tolerances for disk runout and DTV are lessthan 80 μm and 10 μm respectively [4]. However, a slightincrease in DTV to 15 μm can cause brake judder in certainvehicles [2], therefore raising the need for bettermanufacturing tolerances. Other non-thermal related sourcesof judder include uneven surface film transfer.

Hot judder is induced by thermal deformation (e.g. coningand waving), uneven thermal expansion or phase

transformation of the disk material [2]. Unlike cold judder,hot judder does not require large amplitude permanent diskirregularities for its initialization. When exposed to brakingpressure, permanent irregularities (both with low and highamplitudes) cause a localized rise in the contact pressure fieldand temperature, leading to hot spot generation [5,6,7]. Thehot spots result in instantaneous DTV and spatial frictionvariation, causing brake pressure and brake torque pulsationsduring braking. Additionally, large thermal gradients maylead to disk cracking, warping and buckling [6,8], and furtherdeteriorate the disk condition. Compared to cold judder,thermally excited judder is of higher order (with respect tothe wheel speed), typically between six to twenty times thewheel rotational speed [9].

Both hot and cold judder lead to BPV and BTV, whichare the primary excitation mechanisms for judder vibrations.The generated BPV are further transmitted to pedal viahydraulic systems, resulting in pedal vibration. Furthermore,the vibration excited by the BTV is transmitted to the vehiclechassis, vehicle body and the steering system through thewheel suspension system, causing noise and vibrations in thevehicle compartment and steering wheel. The vibration isalso amplified when its frequency is within the resonance ofthe suspension and steering systems [10,11]. In particular, thefront wheel suspensions of most passenger cars have fore-aftvibration mode resonance in the range of 10 to 20 Hz [2].This frequency range corresponds to a maximal amplitude ofvibrations at a critical vehicle speed of between 60 to 140

2012-01-1840Published 09/17/2012

Copyright © 2012 SAE Internationaldoi:10.4271/2012-01-1840

saepcelec.saejournals.org

Adaptive Brake Torque Variation Compensation for anElectromechanical Brake

Chih Feng Lee and Chris ManzieThe University of Melbourne

ABSTRACTA novel method for attenuation of brake judder directly at the source is proposed, utilizing an electromechanical brake

to actively compensate for the variation in brake torque that causes judder. Taking advantage of the high-bandwidthclosed-loop clamp force tracking performance offered by an electromechanical brake, an adaptive compensator is designedto estimate the brake torque variation (BTV), and to produce a compensating clamp force command to cancel it. Thecompensator is tested over fixed and varying BTV frequencies by employing a production-ready prototype EMB. It isdemonstrated that significant BTV attenuation is obtained using the proposed approach.

CITATION: Lee, C. and Manzie, C., "Adaptive Brake Torque Variation Compensation for an Electromechanical Brake,"SAE Int. J. Passeng. Cars - Electron. Electr. Syst. 5(2):2012, doi:10.4271/2012-01-1840.

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km/h for the first-order judder, and 30 to 70 km/h for thesecond-order judder.

Gassmann and Engel [12] investigated the excitation andtransfer mechanism of brake judder experimentally in street-going vehicles, and determined the interactions betweenexcitation and transfer mechanism. Based on this result, aholistic approach to the attenuation of brake judder wassuggested in [13] by considering the total system, includingthe brakes, the suspension and the steering system. Brakejudder attenuation strategies can be categorized intominimization of the judder excitation and modification of thetransfer path as summarized in Table 1.

Table 1. Existing and proposed strategies for brakejudder attenuation.

Minimization of the judder excitation can be achievedthrough BPV and BTV reduction, attained by reducing diskrunout, DTV and thermal effects. Initial disk runout and DTVcan be improved by adopting better assembly and machiningtolerances, albeit resulting in higher manufacturing costs.Subsequent disk resurfacing can be performed if the DTVlevel exceeds the disk specifications due to wear. However,this leads to higher operating costs. Furthermore, in order tominimize DTV generation, residual drag can be reduced byincreasing clearance, optimizing sliding pin and piston sealrollback characteristics of the caliper [14,15], which mayadversely affect pedal feel characteristics. Jacobsson [16]analytically showed that a heavier caliper reduced judder, butthis creates conflicting design requirements for improvedassembly weight and fuel economy. Other methods include:reducing thermal deformation of the disk through improvedair flow and heat transfer characteristics, reducing unevendisk wear and reducing non-uniform deposition of transferfilm on the disk [14,17]. Decreasing pad stiffness was alsosuggested in [18,19,20], although leading to the increase ofpedal travel, deteriorating ABS performance and decreasingpad wear life. Lower coefficient of friction was suggestedalso by [21], albeit compromising braking effectiveness.

The judder transfer path can be optimized by shifting theresonance frequencies of suspension and steering systemsoutside of the first wheel order excitation [22]. In particular,Zhang et al. [23] reported that the suspension bush bearingscharacteristics greatly affect the resonance amplitude. Judderattenuation performance can be improved by increasing the

rubber bush bearing stiffness [20] and adopting a hydraulicbush bearing with higher damping [24]. Furthermore, Gruberet al. [25] suggested using an active wheel suspension to shiftthe resonance frequency online to dampen judder, while vonGroll et al. [26] proposed using an active steering system tocompensate for judder.

The current approaches suggested above are either ofcorrective measures (applied after the driver has experiencedjudder), or may affect vehicle handling performance, or arelocally isolating the vibration (as the source of vibration isstill exists). These approaches have been the only possiblesolutions under hydraulic braking system due to the lowbandwidth of the closed-loop system.

On the other hand, brake-by-wire (BBW) offers highclosed-loop bandwidth and fine clamp force control fidelitywhich provides the opportunity to eradicate judder at thesource. Due to the mechanically decoupled construction ofthe brake pedal in BBW system using the pedal feel emulator,pedal pulsation during judder is eliminated. However, theresultant BTV that causes judder is not dealt with. The designflexibility offered by BBW through software upgrades invitesinvestigation into value added functions, such as a brakejudder attenuation.

This work proposes a novel method to activelyattenuation the brake torque variation using anelectromechanical brake (EMB), taking advantages of theoffered high closed-loop bandwidth, and therefore reducingthe judder phenomenon. This would reduce the need for abetter manufacturing tolerance and extend components life.

The organization of the paper is as follows. The nextsection describes a linearized closed-loop EMB model thatserves as the basis for the proceeding BTV compensatordesign. A model of the BTV is first presented, followed bythe derivation of the compensator, whereby a flexiblecompensator structure for attenuation of multiple harmonicsis proposed. Then, experimental results on a brakedynamometer will be presented and discussed. Theconclusion encompasses the main results and establishesfurther work required for real world implementation.

LINEARIZED CLOSED-LOOP EMBMODEL

A production-ready EMB prototype shown in Figure 1 ischosen in this work to demonstrate the proposed brake torquevariation compensator. The EMB consists of a three phase,permanent magnet synchronous motor, a gear reductionstage, a ball screw, a floating caliper and control electronics.An experimentally validated simulation model for the EMB ispresented in [27,28]. Furthermore, the flexible clamp forcecontroller design proposed in [28] is utilized to design theclosed-loop controller, whereby the available motor capacitygenerates a high-bandwidth clamp force response.

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Figure 1. The production-ready prototypeelectromechanical brake used in this work.

The EMB takes in a clamp force command in real-timeand outputs an actual clamp force. Since the brake judderoccurs during light braking, it is assumed that thecompensator operates in vicinity of a small clamp forceregion. By linearizing the closed-loop nonlinear EMB andcontroller models with respect to a small clamp force, theinput-output relationship of the EMB is governed by thefollowing dynamics:

(1)

where Fcl, Fcl,r, kp, kd, , x1 and x2 represent brake clampforce, clamp force reference, proportional gain, derivativegain, linearized lumped stiffness coefficient, motor positionand velocity respectively. By linearizing the stiffness modelin the vicinity of the commanded motor position, x1r, the

linearized lumped stiffness coefficient, , is given by

(2)

The proportional and derivative gains can be tunedaccording to design specifications for the clamp forcetracking performance, such as rise-time and maximumovershoot. In [28], a near-time-optimal control (NTOC)structure and tuning procedure are introduced whereby thegains are chosen to achieve high closed-loop bandwidthperformance. Specifically, the proportional and derivativegains are given by

(3)

where Tmmax and J are the maximum motor torque andeffective moment of inertia about the EMB motor rotational

axis respectively. Additionally, ks, ssat, x2sat and ξ (0) are theauxiliary tuning parameters that set the region in x1-x2 phaseplane where the clamp force controller output is non-saturated. The reader is referred to [28] for further details ofthe high-bandwidth clamp force controller.

The brake torque, T generated by the clamp force is thengiven by

(4)

where d(t), rd and μ are BTV, effective brake disk radius andcoefficient of friction between brake pad and brake diskrespectively. The numerical values used in (1),(2),(3),(4) areprovided in Table 2. As indicated in (4), brake torque ismodeled as a static function of brake force. This implies thatthe mounting of the caliper is sufficiently rigid such that themovement of the caliper is fast compared to the brake torquegeneration. Due to this assumption, in addition to thelimitation of EMB clamp force bandwidth, we only considercompensation for low order judder, which is a commonlyoccurring type of judder.

Furthermore, it is noted that BTV is often periodic withrespect to the brake disk rotation, i.e. d(t)=d(xd), where xd isthe disk rotation. Additionally, the mean is assumed to besmall using a floating type caliper. In the subsequent section,we consider a BTV model using a sum of sinusoidal signalsof zero mean.

Table 2. Linearized EMB Model Parameters

TORQUE VARIATIONCOMPENSATOR

Disturbance ModelAs eluded in the introduction, it is evident that since BTV

is caused by the geometry irregularities of the brake disk, itmust be periodic to the disk rotation, xd, and may beapproximated using an n-order Fourier series expansion

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(5)

where Ai, ωi, and ϕi represent the amplitude, frequency andphase-shift of the i-order harmonic, while xd represents theangular position of the brake disk. The frequenciescorrespond to the periodicity with respect to the diskrotations, denoted by positive integers, that is ωi = {1,2,…,n}. The amplitude and phase-shift are unknowns, but areassumed to be time-invariant in the proceeding compensatordesign. However, in practice, these quantities may varyslowly relative to the disk rotations.

It is noted that (5) can be written as

(6)

where

(7)

are unknowns and needed to be estimated online. Acompensator structure will be introduced in the proceedingsection to estimate these quantities.

Compensator DesignThe underlying idea of the proposed BTV compensator is

to produce the compensating clamp force command thatattenuates the BTV. The inputs of the compensator are braketorque command, Tr, measured brake torque, T and diskangular position, xd. The output is the clamp force commandFcl,r (Figure 2).

Figure 2. BTV compensator structure.

Before deriving the compensator law, brake torquetracking error is first considered, which is given by

(8)

We then consider the brake torque tracking error dynamicby substituting (8) into (1). After repeated differentiation andminor algebraic manipulations, the error system can beshown to be described by:

(9)

Equation (9) governs the dynamics of the brake torquetracking error in the influence of clamp force command, Fcl,r,BTV, d and brake torque command Tr. The aim is to find anappropriate Fcl,r online such that the tracking errordiminishes with time. It is assumed that the brake torquecommand is slowly varying relative the disk position tocapture the most common occurrence of judder. Under this

assumption, . Therefore, (9) can be rewritten as

(10)

where

(11)

It may be observed that the error dynamics are internally

stable, which means has negative eigenvalues.This implies that the brake torque tracking error willconverge to zero if the last three terms sum to zero. Byscrutinizing the last three terms in (10) and let their sum to bezero, this suggests the following compensator structure:

(12)

where current estimate of (11) is given by

(13)

Noted that and are the estimates of and

respectively. These quantities are estimated using thefollowing adaptive control law:

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(14)

where g > 0 is the compensator gain. Finally, (12),(13),(14)form the compensator equation. To assess the validity of theassumptions in practical situations, experimental results willbe presented in the following section.

RESULTS AND DISCUSSIONSExperimental investigation of the proposed compensator

is conducted on a dynamometer of a production-readyprototype EMB shown in Figure 3. The experimental setupconsists of a PC laptop, a data acquisition system, a 42 Vpower supply, an EMB and a brake dynamometer. Theproposed compensator is implemented on the PC withsampling rate of 250 Hz. The PC sends clamp force referenceand logs the measurements from the EMB onboard sensors inreal-time, communicating via a CAN bus. Furthermore,communications between the PC and the brake dynamometeris established using the analog input/output ports of the dataacquisition card, where brake torque and disk rotationalposition measurements are available in real-time, and thedynamometer speed can be varied online.

Figure 3. Brake dynamometer.

A disk with disk thickness variation (DTV) as shown inFigure 4 is employed in this study. Geometrical measurementof the disk indicates that the disk possesses a DTV ofapproximately 18 microns, which is significant enough tocause judder when included in a vehicle chassis. Furthermore,Fourier analysis of the DTV waveform revealed that the firstharmonic has the largest amplitude, followed by smalleramplitudes of the second and the third harmonics. Thissuggests that BTV compensators of up to three orders aresufficient in implementation for this case.

Figure 4. (Top) Measured and approximated diskthickness variation. (Bottom) Amplitude of Fourier

components.

From the implementation point of view, a lower ordercompensator is preferred, due to lower requirements formemory and computation. Figure 5 shows the brake torquecompensation for fixed disk rotational speed for compensatorof various orders. The first-order compensator, whichrepresents the simplest compensator design, demonstrates a50% reduction in BTV. Furthermore, the second and thirdorder compensator is capable of reducing the amplitude ofBTV by 70%, which is achieved within three disk rotations. Itis observed that the amplitude of the clamp force increaseswith the compensator order in order to better approximate theBTV. While the third-order compensator may approximatethe BTV with better accuracy, its incremental compensationperformance is insignificant in implementation, as it can beseen from the RMS value listed in Table 3. This suggests thata second-order compensator is adequate in this case, andwarrants further investigation using this setup.

Figure 5. Brake torque variation compensationperformance for compensator of various orders.

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Table 3. Compensation performance for compensator ofvarious orders.

Figure 6 shows the brake torque compensation under avarying disk rotational speed, starting from 31.4 rad/s whilesimulating a light braking event with 2 rad/s2 deceleration. Itis demonstrated that the second order compensator achieves70% attenuation in amplitude even under varying rotationalspeed.

Figure 6. Comparison of brake torque (top figure) undercompensation using a second order compensator (solid)

and without compensation (dotted). Measured clampforce and dynamometer speed are shown in the middle

and bottom figures respectively.

CONCLUSIONSA novel method for brake judder attenuation is

investigated, employing the high-bandwidth clamp forceperformance of an electromechanical brake. To this end, abrake torque compensator is proposed which estimates theBTV, and then generates a compensating clamp forcecommand online. Preliminary experimental investigationsdemonstrate favorable results that warrant furtherinvestigation into this concept, whereby the proposed methodreduces BTV by up to 70% in a few disk rotations.

However, it is noted that the current design is takingadvantage of brake torque and disk angular positionmeasurements from the dynamometer, which may be lackingin actual implementation in a production vehicle. While it isnot uncommon to have brake torque measurement setup inprototype vehicles, equipping this sensor in a near future

production vehicle is not expected. Nevertheless, braketorque may be estimated using the available vehicleacceleration measurements. Furthermore, disk position maybe approximated by integrating the measured wheel speed.

Further research directions include the construction ofbrake torque and disk position estimators, as well asinvestigation into the relationship between the compensationperformance and power requirement of an EMB.

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CONTACT INFORMATIONChih Feng LeeDepartment of Mechanical EngineeringThe University of MelbourneParkville, Victoria 3010Australia.Tel.: +61(3) 8344 6661c.lee33@pgrad.unimelb.edu.au

ACKNOWLEDGMENTSThis research was in part supported by the Australian

Research Council through the grant FT100100538.

LIST OF NOTATIONFcl - Clamp force

Fcl,r - Clamp force reference

J - Lumped moment of inertia about EMB motor rotationalaxisk1, k2 - Stiffness coefficients for EMB

- Stiffness coefficient for linearized EMB modelkp, kd - EMB clamp force controller gains

rd - Brake disk radius

Tmmax - EMB motor torque limit

x1, x2 - Angular position and velocity of EMB motor

x1r - EMB motor position reference

xd - Angular position of brake disk

μ - Coefficient of friction between brake pad and brake disk

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