INTRODUCTIONBrake judder is a vibration that is felt at the steering wheel, brake pedal and vehicle body when the brakes are applied softly during mid to high speed (30 to 140 km/h) travels. It is perceived as one of the most notorious failures that can occur in a brake system and has led to recalls.

Depending on the cause and vibration frequencies, judder can be categorized into cold and hot (or thermal) judder. The majority of judder vibration is cold judder, which has one to two oscillations per wheel rotation. Cold judder is principally attributable to geometrical irregularities in rotors, such as runout, thickness variations and

friction variations on the brake lining and rotor surface [1]. On the other hand, hot judder has a higher vibration frequency (typically between six to twenty oscillations per wheel rotation) and is caused by uneven thermal deformations and expansions in rotors [1, 2]. Note that both cold and hot judders are caused by the irregularities on rotor, leading to brake torque variation (BTV) [3]. The BTV then may excite the resonance vibration modes of the suspension and steering column, causing judder vibration.

Due to the detrimental implications of judder in brake and vehicle manufacturers, major development and manufacturing resources are often spent to lower the occurrence of judder. Existing studies on the

Active Brake Judder Compensation Using an Electro-Hydraulic Brake System

Chih Feng LeeLinköping Univ

Dzmitry SavitskiIlmenau Technical Univ

Chris ManzieUniv of Melbourne

Valentin IvanovIlmenau Technical Univ

ABSTRACTGeometric imperfections on brake rotor surface are well-known for causing periodic variations in brake torque during braking. This leads to brake judder, where vibrations are felt in the brake pedal, vehicle floor and/or steering wheel. Existing solutions to address judder often involve multiple phases of component design, extensive testing and improvement of manufacturing procedures, leading to the increase in development cost.

To address this issue, active brake torque variation (BTV) compensation has been proposed for an electromechanical brake (EMB). The proposed compensator takes advantage of the EMB's powerful actuator, reasonably rigid transmission unit and high bandwidth tracking performance in achieving judder reduction.

In a similar vein, recent advancements in hydraulic system design and control have improved the performance of hydraulic brakes on a par with the EMB, therefore invoking the possibility of incorporating the BTV compensation feature of the EMB within hydraulic brake hardware.

In this paper, the typical characteristics of electromechanical and electro-hydraulic brake systems are presented. Based on the experimental results, the feasibility of active BTV compensation on the electro-hydraulic brake (EHB) systems is discussed. Furthermore, a BTV compensation algorithm designed for the EMB is presented and is shown to be applicable to the EHB. Using an experimentally validated model of BTV, the compensation was performed on a hardware in-the-loop EHB test rig. The preliminary results demonstrate the potential of using an EHB to compensate for brake judder.

CITATION: Lee, C., Savitski, D., Manzie, C., and Ivanov, V., "Active Brake Judder Compensation Using an Electro-Hydraulic Brake System," SAE Int. J. Commer. Veh. 8(1):2015, doi:10.4271/2015-01-0619.

2015-01-0619Published 04/14/2015

Copyright © 2015 SAE Internationaldoi:10.4271/2015-01-0619saecomveh.saejournals.org

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reduction of brake judder using conventional hydraulic and electro-hydraulic brake systems mainly focus on passive approaches, such as reducing the sensitivity and the transmission of judder by modifying the brake composition [4, 5] and suspension elements [6, 7, 8]. These are costly processes, both monetarily and time-wise, as they involve multiple phases of component design, extensive testing and improving manufacturing tolerance.

Although the aforementioned activities significantly reduce the occurrence of brake judder, judder may arise due to wear during usage. When judder is detected, the after-market resolutions include replacing or resurfacing the rotor and using softer brake pads [9]. Unfortunately when action is taken at this stage, the driver has already had the undesired experience of judder vibration.

To address this issue, an active judder attenuation solution utilizing an electromechanical brake (EMB) is proposed in [10, 11, 12]. Compared to conventional hydraulic brakes, the EMB offers better fidelity in clamp force regulation, higher bandwidth in clamp force tracking and reconfigurable control software platform. Taking advantage of these strengths, novel BTV compensation algorithms are designed to regulate the EMB actuation and to produce a brake torque that is free from oscillations introduced by the geometrical irregularities in rotor. Furthermore, the proposed approach potentially relaxes the manufacturing tolerance requirements. Additionally, an early warning system can be developed to prompt the driver for servicing the brake when the rotor wear is severe, even before judder is felt. Note the proposed method eradicates judder directly from the source, as opposed to modification of the vibration transfer paths using an active suspension [13] or active steering system [14].

The proposed active BTV compensation approach imposes several performance requirements on the brake actuator which are lacking in conventional hydraulic brakes, in particular a high system bandwidth and tracking fidelity. Therefore judder can only be handled with the passive methods described previously when conventional hydraulic brakes are used. However, recently developed electro-hydraulic brake (EHB) systems [15, 16] have improved system bandwidths compared to the conventional hydraulic brake systems, therefore opening the possibility of incorporating the proposed active judder attenuation functionality in an EHB.

As alluded before, existing judder reduction methods have drawbacks in terms of high cost and bad user experience. To address these shortfalls, this paper evaluates the potential of using an EHB to actively compensate for judder. The hardware-in-the-loop test rig presented in [17] is utilized to experimentally obtain the system characteristics of a modern EHB system and to assess its potential for judder compensation.

The structure of the paper is as follows. The next section describes validated linearized models for EMB and EHB, which serve as the basis for compensator design. Then, an overview of the adaptive BTV

compensator is presented in a form applicable to both EMB and EHB. This is followed by presenting the experimental setups for both braking systems before results are presented and discussed.

LINEARIZED BRAKE MODELS

Linearized model for electromechanical brakeAn EMB consists of an electric motor, planetary gears, a ball screw, a floating caliper and control electronics. An experimentally validated EMB model is presented in [18], and a procedure for identification of the system parameters is presented in [19]. Furthermore, a high-bandwidth controller design for an EMB is presented in [20, 21].

The EMB can be considered as a system that takes in clamp force reference command as input and outputs an actual clamp force. By further assuming a clamp force operating region in the vicinity of a fixed or slowly varying clamp force level, which is the operating condition corresponds to judder, the following linearized EMB model can be adopted [10, 12]:

(1)

where Fcl, Fcl,ref, and θm are the brake clamp force, clamp force reference, linearised lumped stiffness coefficient, and motor position respectively. The parameters kp, kd are related to the system characteristics and can be modified by tuning the clamp force controller gains, where detailed tuning guidelines are provided in [12, 21].

Linearized model for electro-hydraulic brakeFor the controller design purposes, a linearized model of the EHB system is utilized. Considering the system frequency response and recommendations in [22] for low pressures, it is possible to derive a complete system dynamics as a second-order transfer function with delay of the form:

(2)

where pi and pi,ref respectively refer to the actual and reference hydraulic brake line pressures for caliper i. KG, ζ, ωn and τ are system characteristic parameters obtained experimentally.

Since judder occurs during the application of low brake pressure, cases with pressures of up to 25 bars are considered. The parameterized second-order transfer function produces step responses that match well with experimental results depicted in Figure 1.

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Figure 1. Validation of the linearized EHB model using low pressure references.

Note that (2) can be expressed as the following state-space equation, with clear synergies to (1):

(3)

The normal force, Fni is produced by the caliper pressure between the brake pad and disk rotor on each wheel, and can be written as:

(4)

where dcyl, p0 and ηc are the diameter of brake piston, pushout pressure and wheel cylinder efficiency respectively.

OVERVIEW OF BRAKE TORQUE VARIATION COMPENSATOR DESIGNThe brake torque, Tb is generated by applying a clamp force on both surfaces of a disk rotor via brake pads. For the EMB, the brake torque can be calculated as

(5)

where , rd, Tbtv, Td and θd are the estimated coefficient of friction between brake pads and disk rotor, effective rotor radius, BTV, discrepancy in brake torque resulted from friction coefficient estimation error and disk rotational position respectively. Similarly, the brake torque generated by the EHB can be calculated as

(6)

A brake torque profile with variations due to disk thickness variation is shown in Figure 2. It can be seen that the torque varies periodically with respect to the disk rotation, where the first harmonic has the

largest amplitude, followed by smaller amplitudes of the second and third harmonics. Taking advantage of the periodicity of the signal, a disturbance model can be constructed [10, 12]:

(7)

where ak and ϕk represent the amplitude and phase-shift of the k-order harmonic respectively. The amplitude and phase-shift are unknowns, but are assumed to be time-invariant or slowly varying in the proceeding compensator design.

In the following, the structure of the adaptive BTV compensator design first proposed in [10] is briefly presented. Note that detailed derivation and analysis of the proposed compensator can be found in [12].

For the EMB, the adaptive compensator carries the form of:

(8)

Note g is the compensator gain, ωi is the disk rotational velocity and eb is the brake torque tracking error, given by:

(9)

where Tb,ref is the brake torque reference. Additionally, the parameterized compensator gains are given by:

(10)

(11)

(12)

The components in the diagonal matrix, Φ(θd) are given by:

(13)

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Figure 2. (a) Brake torque variation measurements with its mean and the first three orders of approximations. (b) Amplitude spectrum of the brake torque variation profile.

Since both the EMB model (1) and the EHB model (3), (4) are second-order linear systems, their respective compensators have similar structure, although with different gain matrices. Assuming small pushout pressure, p0=0 and high wheel cylinder efficiency, ηc=1, the adaptive compensator for the EHB system can be written as

(14)

where Acyl is the area of the piston cylinder,

(15)

Additionally, the feedforward gain matrix can be obtained as:

(16)

where

(17)

In order to evaluate the soundness of the assumptions in practical conditions, experiments were conducted and the results are presented in the following sections.

EXPERIMENTAL SETUPS

Electromechanical brake systemA dynamometer of a production-ready prototype EMB shown in Figure 3 is adopted for experimental investigations of the proposed BTV compensator. The experimental setup comprises a PC laptop, a data acquisition system, a 42 V power supply, an EMB and a brake dynamometer. The proposed compensator is implemented on the PC with sampling rate of 250 Hz. The PC is configured to record measurements and to deliver clamp force reference to the EMB in real-time. Additionally, the communication between the PC and the EMB is established using a CAN bus. Furthermore, communications between the PC and the brake dynamometer is achieved using the analog input/output ports of the data acquisition card. Note that the brake torque and disk rotational position measurements are available in real-time, and the dynamometer speed can be changed online.

Figure 3. EMB and brake dynamometer.

Electro-hydraulic brake systemThe electro-hydraulic brake system is represented by TRW Slip Control Boost (SCB) system, which consists of a master cylinder, electro-hydraulic control unit (EHCU), four brake assemblies, and pressure sensors mounted directly before the brake calipers (Figure 4).

The main difference of this system compared to the conventional analogues is that the brake pedal is hydraulically decoupled for the complete system. In the normal mode, pedal feedback force is generated artificially and realized by brake pedal simulator, therefore providing independent brake pedal characteristics [17].

Figure 4. Hardware-in-the-loop test platform with mounted EHB.

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The operating principle of the EHB can be described as follows. Brake pedal travel sensor transmits the signal to the vehicle control unit (VCU). The generated torque demand request is based on lookup tables and further sent to the internal controller of EHCU, which is responsible for the estimation and realization of the appropriate pressure level in each caliper. To provide a better system performance, the hydraulic accumulator has a preload pressure up to 180 bar, which is supplied by the hydraulic pump.

In the case of a VCU failure, the internal controller of the EHB takes control over the system. It realizes not only base-brake function, but can also provide anti-lock braking (ABS) operation during the panic braking. In the worst case scenario, where both VCU and internal controllers have failed, hydraulic coupling between the brake pedal and system is established without loosing the booster function.

RESULTS AND DISCUSSIONSIn this section, a recap of the experimental results for BTV compensation using an EMB presented in [10] is first presented. This establishes a baseline for comparing the BTV compensation using an EHB.

BTV compensation for a fixed rotational speed using compensators of various orders are compared in Figure 5. For this preliminary test case, the frequency of BTV is 1 Hz. The first-order compensator showed a 50% reduction in BTV. Furthermore, the second and third-order compensators are capable of reducing the amplitude of BTV by 70%. Note that a typical BTV that causes cold judder has one to two oscillations per wheel rotation, therefore it is expected that a second-order compensator produces attenuation signal that sufficiently compensates for a typical BTV waveform. Furthermore, the first-order compensator is the compensator design with the lowest computational requirements, albeit having slightly lower compensation performance compared to the second-order compensator. Note the computation load increases with the order of compensator.

Figure 5. Brake torque variation compensation performance of an EMB using the first, second and third-order compensators.

As illustrated in the above examples of using the EMB for BTV compensation, the first-order compensator provides sufficient reduction of BTV while requiring less computational load compared to the higher order compensators. To assess the compensation effectiveness using an EHB, a first-order compensator is implemented, and rotor velocity is varied from 1 Hz to 5 Hz. Due to the absence of a dynamometer in the EHB test rig, the total brake torque is calculated from the measured brake pressure, and added by an experimentally obtained BTV signal shown in Figure 2. The BTV compensator is then used to produce a brake pressure such that the calculated total brake torque matches the reference.

During experiments, technical difficulties were encountered for maintaining a low hydraulic pressure (5 bars to 8 bars) while providing enough tracking precision. Therefore, a higher brake torque reference of 500 Nm was adopted in the experiments involving EHB. The total brake torque without compensation is shown in Figure 6, and with compensation as illustrated in Figure 7. The root-mean square (RMS) errors of the BTV compensation are calculated and listed in Table 1. The application of the first-order compensator reduced the RMS tracking error from 20% up to 40% for 5 and 1 Hz respectively, demonstrating the capabilities of EHB to compensate for low-frequency periodic oscillations.

Figure 6. Brake torque variation using an EHB without compensation at various frequencies.

Figure 7. Brake torque variation compensation using an EHB at various frequencies.

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Table 1. Compensation performance of an EHB using compensator of the first-order at various frequencies

It is noticed that the compensation performance deteriorates as the frequency increases. This may be due to the modeling error in the EHB system. Note that the current linearized model is based on a second-order state-space system (3), (4), and delay is not taken into account explicitly. Furthermore, since the low level controller of the EHB is not currently assessable at the time of writing, it is unclear if the existing codes for the low level embedded controller hindered the tracking precision at low hydraulic pressure.

Figure 8 compares the simulated judder compensation performance of an EMB and EHB with a brake torque reference of 500 Nm, where the RMS of BTV are listed in Table 2. It is shown that the compensation performance of the EMB and EHB are comparable, as they have similar braking capabilities. Note that apart from the compensation algorithm, the compensation performance is dependent on hardware limitations, such as the closed-loop bandwidth and the maximum braking force. The EMB and EHB employed in this study have similar closed-loop bandwidth at about 15 Hz. Furthermore, they also produce similar maximum brake clamp force at 40 kN. This clamp force level corresponds to approximately 150 bars for the EHB.

Figure 8. Simulated brake torque variation compensation using an EMB and EHB at torque reference of 500 Nm and various frequencies.

By comparing the simulated and experimental compensation performance of the EHB, it is noticed that the experimentally obtained performance deteriorates as frequency increases, which could be due to the inaccuracy of the low order control oriented EHB model used during the compensator design. Nevertheless, both simulation and experiment results obtained in this investigation show reduction in BTV, therefore proving the concept that an EHB can be used to attenuation low-frequency periodic oscillations.

Table 2. Simulated compensation performance of an EMB and EHB using compensator of the first-order at various frequencies

CONCLUSIONSA novel method for brake judder attenuation using an electro-hydraulic brake is investigated. The proposed method utilizes a brake torque variation compensator developed for an electromechanical brake to regulate brake pressure actively such that the resultant brake torque is free from oscillations caused by irregularities on the brake rotor.

The proposed brake torque variation compensator was implemented in an electro-hydraulic brake system and experimentally demonstrated a reduction in BTV, where the RMS tracking error was reduced by 40% and 20% for 1 Hz and 5 Hz oscillations respectively.

The obtained results give a clear view on the capabilities of hydraulic brake systems to handle low-frequency periodic oscillations. Therefore, this study sheds light on a potentially promising solution to deal with judder actively, in addition to the conventional methods that rely on passive vibration attenuation.

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10. Lee, C. and Manzie, C., “Adaptive Brake Torque Variation Compensation for an Electromechanical Brake,” SAE Int. J. Passeng. Cars - Electron. Electr. Syst. 5(2):600-606, 2012, doi:10.4271/2012-01-1840.

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CONTACT INFORMATIONChih Feng LeeDivision of Vehicular SystemsDepartment of Electrical EngineeringLinköping UniversityLinköping, Sweden 58183chih.feng.lee@liu.se

Dzmitry Savitski, Valentin IvanovIlmenau University of TechnologyDepartment of Automotive EngineeringEhrenbergstraße 15, Ilmenau, Germany 98693dzmitry.savitski@tu-ilmenau.de

valentin.ivanov@tu-ilmenau.de

Chris ManzieDepartment of Mechanical EngineeringUniversity of MelbourneParkville, Victoria 3010Australiamanziec@unimelb.edu.au

ACKNOWLEDGMENTSThis research relates to the research group PORT at Ilmenau University of Technology funded by the European Social Fund ESF (project No. 2011 FGR 0120).

DEFINITIONS/ABBREVIATIONSABS - Anti-lock braking system

BTV - Brake torque variation

EHB - Electro-hydraulic brake

EHCU - Electro-hydraulic control unit

EMB - Electromechanical brake

RMS - Root-mean square

VCU - Vehicle control unit

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