Experimental investigation of braking dynamics of electric vehicle

EB2013-TM-011

EXPERIMENTAL INVESTIGATION OF BRAKING DYNAMICS OF

ELECTRIC VEHICLE 1Savitski, Dzmitry,

1Ivanov, Valentin,

1Heidrich, Lukas

*, 1Augsburg, Klaus,

2Pütz, Thomas

1Ilmenau University of Technology, Germany,

2TRW Automotive, Germany

KEYWORDS – brake blending, test rig, hydraulic brakes, electro-hydraulic brake system, brake pedal feel

ABSTRACT – One of the most distinctive features of brake architecture for hybrid and full electric vehicles is

an embedded function of brake blending, i.e. a possibility to activate either the electric braking or conventional

friction brakes depending on the actual dynamic state of the vehicle. Development of the brake blending control

requires complex modelling and experimental studies using diverse software tools and testing equipment. Within

this context, the paper relates to such important topics like (i) experimental estimation of brake system dynamics

and (ii) assessment of parameters characterizing the brake blending.

The investigation of the brake characteristics relevant to the brake blending has been realized by the use of the

experimental platform including a complex hardware-in-the-loop (HIL) test rig to investigate dynamic processes

in hydraulic and electro-hydraulic brake systems and an integrated environment connecting the hardware brake

components with the software-based vehicle simulator.

The proposed experimental platform consists of the following elements:

Brake system hardware (both the conventional layout and the decoupled brake-by-wire layout);

Brake robot to control the brake pedal with alterable actuation dynamics;

dSpace real-time components;

Computer simulator of the vehicle and vehicle manoeuvres in IPG CarMaker Software.

The case study introduced in the paper has been performed for the test programme aimed at the definition of the

dynamic characteristics of the brake system by the different velocities of the brake pedal actuation. The obtained

results give a basis for (i) comparison of base brake functions of conventional and decoupled brake systems and

(ii) analysis of brake actuation dynamics on the brake blending.

The obtained results as well as developed experimental technique can find a proper application for advanced

strategies of brake control of electric vehicles with simultaneous improving of the driver comfort and brake

performance.

TECHNICAL PAPER – Development of brake systems for hybrid and full electric vehicles (EV) has a higher

level complexity as compared with the designing procedures for conventional vehicles. This is because the

architecture of the EV brake layout can include both traditional friction brakes and braking functions realized

through electric drive motors. Such dual nature must be taken into account in all the control and operational

modes of the EV brakes: (i) base brake functions; (ii) brake blending and regeneration braking control; (iii) ABS

control; (iv) supporting functions by operation of vehicle dynamics control systems as yaw control or torque

vectoring.

The scope of the presented article is limited by several aspects of base brake functions and brake blending. These

topics were addressed in recent years in many research studies. In particular, fundamentals of brake design for

electric vehicles are expounded by Ehsani, Guo and Emadi in (1). Various strategies of brake torque distribution

control for electric vehicles were investigated by Mutoh (2), Ahn (3), Kim (4), Rosenberger (5) and their co-

authors. Many other publications as well as the scientific and industrial projects can be mentioned within the

framework of discussed context. However, despite a large body of research, some problems of EV brakes need

further development. The subject of this paper directs also to a rare discussed facet of influence of brake pedal

actuation dynamics on the brake blending processes.

The interaction between the brake pedal actuation dynamics and the brake blending (and as consequence the

regenerative braking processes) has a double-sided character because the effect of transition from the friction

braking to the electric braking or vice-versa affects the brake feel perceived by the driver. One more important

point is that the factors of the brake feel can be noticeably more affected in the case of decoupled brake systems

or brake-by-wire (BBW) systems. This subject was appropriately analyzed in works of Sendler, Kirchner and

Augsburg (6, 7). A complex influence of the brake pedal actuation dynamics on the brake feel is also relevant for

decoupled systems leads to the fact that the composition of corresponding brake feel indicators is a subject of

intensive studies. For instance, the work (8) introduces a concept of an impedance surface as function of the

brake pedal force, stroke and velocity. Using this concept, the force control of the BBW pedal simulator can be

organized, and the following design parameters can be derived to characterize the brake feel: pedal force needed

to initiate deceleration; pedal characteristic for the deceleration range z=0,0...0,3 g; pedal force between the

deceleration levels z=0,3 and z=0,6.

More complex approach was proposed by authors from Renault and Ecole Nationale Supérieure des Industries

Alimentaires in (9). This approach uses 11 parameters describing the slopes and stiffnesses in characteristic

sections of the “pedal force / pedal travel” and “vehicle deceleration / pedal travel” relationships. The mentioned

parameters can applied to tune the active pedal feel emulator realized in the BBW system and to formulate the

brake control laws for the different operational modes of the BBW system. The discussed method uses the

Plackett-Burmann design of experiments. The work (10) discussed a number of relative qualitative criteria like

(i) higher free travel at lower deceleration and vice versa and (ii) no jump of brake pressure by low deceleration

demand. Other studies (11-13) proposed different subjective recommendations that can be used for the

characterization of the brake pedal feel: minimization of free pedal travel; small boosting effect at low

deceleration demand; progressive dependence between the pedal force and vehicle deceleration up to z=0,9

inclusive etc.

Analysis of the listed works as well as various customer studies allows to set a reasonable design target that the

brake feel produced by a decoupled brake system should be close to the behaviour of conventional, coupled

brake systems. Accepting this target, the objective of the presented study has been formulated as follows: To

define the reference brake blending dynamics of the electric vehicle. This objective has the following limitations:

The EV has all-wheel drive powertrain with four electric motors.

The target friction brake system of the EV has decoupled electro-hydraulic layout.

The reference friction brake system of the EV has conventional hydraulic layout.

Assessment of the brake blending dynamics is being carried out on qualitative level using experimental

data.

The results presented in the actual study refer to the sport utility vehicle with full mass 2045 kg, Figure 1. The

vehicle has variable powertrain configuration with up to four on-board electric motors, connected gearboxes, and

half-shafts between the drive motors and the wheels. For this configuration, next sections of the paper describe

basic information about realized brake blending approach, experimental technique, and analysis of test results.

Figure 1: The vehicle (as reproduced and edited from (14)) and axial components of electric powertrain (15)

BRAKE TORQUE DISTRIBUTION IN ELECTRIC VEHICLE

Brake blending control refers generally to the distribution of total brake torque demanded by the driver between

the vehicle axles. The distribution algorithm takes usually into account the demanded deceleration level, road

friction, and the safety limitations. The brake blending strategy, applied in this investigation, uses the following

principles:

The distribution control aims at maximum possible engaging of electric brakes to provide the highest

level of energy recuperation according to constraints.

The brake force distribution should tend to the ideal parabolic distribution, Figure 2;

Figure 2: Characteristic segments of brake distribution

In accordance with Figure 2, the brake distribution diagram has three characteristic segments called further in the

text as “0-A”, “A-B” and “B-C”.

Segment “0-A”. Only electric brakes are used and for maximal performance:

em ideal em ideal

bf bf br brF F and F F ,

where Fbfem

and Fbrem

are the brake forces produced by the front and rear electric brakes correspondingly, Fbfideal

and Fbrideal

are the ideal front and rear brake forces correspondingly. After reaching maximal brake force on front

electric brakes Fbfem

max, the rear electric brakes force has to tend the value Fbrideal

(zA).

Segment “A-B”. The front friction brake force Fbffric

is used in addition to the electric brake force Fbfem

. After

reaching the maximum brake force on rear electric brakes Fbrem

max, the front total brake force Fbf has to tend the

value Fbrideal

(zB) by varying the force Fbffric

.

Segment “B-C”. Both electric brake forces are equal to their maximums:

max max em em em em

bf bf br brF F and F F .

Thus maximum energy recuperation is reached and the front Fbffric

and rear Fbrfric

friction brake forces are

enabled.

The relationships between the friction and electric brake forces are summarized in Table 1. The results of mixed

hardware-in-the-loop and software-in-the-loop simulation of the proposed brake blending strategy taking into

account the brake pedal actuation dynamics are presented in next sections of the paper.

Table 1 – Brake forces estimation

Brake force A B B-C em

bfF max

em

bfF max

em

bfF max

em

bfF

em

brF

ideal

brF max

em

brF max

em

brF

fric

bfF

0 max

ideal em

bf bfF F max

ideal em

bf bfF F

fric

brF

0 0 max

ideal em

br brF F

EXPERIMENTAL TECHNIQUE

Within the framework of discussed investigations, the functions of brake systems as well as the brake control

were tested on the test rig having the following features:

Integration of the brake system hardware with the vehicle model;

Possibility of pre-defined and repeatable actuation of the brake pedal for the embedded and stand-alone

operation of the brake system (without connection to other chassis systems / components);

Possibility of the operation both of coupled and decoupled brake systems;

Measurement of brake pressure in each circuits as well as in each brake calliper;

Software realization of electric propulsion system and its components.

Figure 3 presents the corresponding architecture of the HIL test rig and Figure 4 shows its physical

configuration. The layout of the installed decoupled brake system is given on Figure 5. The test rig consists of

three HIL loops. The HIL 1 is responsible for the control on the electro-hydraulic brake robot. The HIL 2

realizes base brake control functions in the vehicle simulator like the brake blending and regenerative braking.

The HIL 3 provides additional functions that embed the operation of a real brake system into software control

circuits of vehicle dynamics control systems, i.e. electronic stability control.

Figure 3: Test rig architecture

Figure 4: The physical configuration of the test rig

Figure 5: Layout of decoupled brake system

The actuation of the brake pedal on the test rig is implemented by using a brake robot. The servo-hydraulic brake

robot constructed at Ilmenau University of Technology has a modular structure and allows the precise and

repeatable automatic actuation of the brake system through pre-defined control sequences. The performance

characteristics of the robot actuators are: pedal actuator force Fpedal from 0 N to >1500 N; pedal actuator

displacement spedal from 0 mm to >100 mm; velocity vpedal from 0 mm/s to >1000 mm/s; admissible measurement

accuracy of the Fpedal-parameter ≤ 10 N (absolute value); data rate up to 4000 Hz.

The test rig uses a number of dSpace devices to process the signals from the pressure sensors and transfer the

processed data to the vehicle simulator, Figure 6. The main processor board (ds1006) is capable to distribute

computing procedures between four core processors. Considering the complexity of every operating unit,

software components of the test rig are divided in two groups related to (i) vehicle dynamics controller and (ii)

multi-body vehicle model with a set of emulated vehicle subsystems. The data processing and observation has

been realized in standard dSpace Control Desk software.

Figure 6: dSpace platform

The information about real pressure in wheel brakes installed on the test rig is forwarded to the vehicle model in

IPG CarMaker. For this purpose, the standard brake model in IPG CarMaker has been replaced with the relevant

input from dSpace / Simulink. Then the resulting brake torques have been used in the user-defined model of the

brake system of the vehicle simulator. Hence the real brake pressure signals are transformed into the brake

torques of the vehicle simulator allowing the further analysis of the brake dynamics of the vehicle at different

manoeuvres.

EXPERIMENTAL COMPARISON OF BRAKE SYSTEMS

The definition of reference characteristics for the development of brake blending control for the target vehicle

requires preliminary comparative analysis of brake dynamics of both possible configurations of brake systems.

For this purpose, the conventional hydraulic brake system and the decoupled BBW system were brought in

operation on the test rig (Figure 4). Both systems can actuate similar friction brakes and brake lines. For this

purpose, a typical test programme was used to collect the experimental data. This programme has covered ramp

application of the brake robot at pedal velocities from 10 to 500 mm/s for brake pressure 15, 40, 60 and 80 bar.

The analysis of the obtained experimental data has resulted in a number of observations that can be of relevance

for the development of the brake blending control from viewpoint of the brake pedal feel in the case of the

decoupled brake system. First of all, typical quasi-static indicators of the brake pedal feel have essential

discrepancy for both considered systems regarding the free travel and the operational travel gradient, Table 3.

Secondly, the BBW system can be rather soft for the driver get accustomed to behaviour of the conventional

brake system (as applied to the specific vehicle).

Table 3 – Comparison of quasi-static brake pedal feel indicators

as measured at the brake pedal velocity 20 mm/sec,

procedure of definition is given in the work (7))

Indicator Conventional

system

Decoupled

system

Preload force Fp, N 22,9 35

Dead travel sd, mm 7,7 1

Free travel sf, mm 51,5 16,5

Free travel gradient Gf, N/mm 1,3 0,97

Operational travel gradient Go, N/mm 24,2 5,4

The next observation relates to the dynamic pedal feel (relation between the pedal force and the pedal travel) of

the decoupled brake system for different application velocities, Figure 7. In general it shows an almost linear/

slightly progressive increase of the pedal force with velocity. This dynamic behaviour is comparable to a

conventional braking system, even though the stationary pedal feel might be different. Noteworthy is the hump

at small pedal displacements emerging at higher application velocities. It needs to be investigated in more detail

to which extent this variation in stiffness is impeding the driver when he is trying to adjust pedal force or pedal

position at low decelerations.

Other observations derived from the analysis of experimental data are out of scope of the presented paper;

however they will be a subject of subsequent publication. Nonetheless, the carried out experiments have

confirmed initial proposition: Development of the brake blending control for a decoupled brake system requires

availability of reference characteristics from a conventional brake system. It is necessary to avoid unusual brake

pedal behaviour felt by the driver during the braking of an electric vehicle. Next section of the article discusses

the definition of such reference characteristics.

DEFINITION OF REFERENCE CHARACTERISTICS FOR BRAKE BLENDING

Using the test rig described in previous sections as well as the software simulator of the target vehicle, the brake

blending processes have been investigated for the following conditions:

Service and full braking of the vehicle on the dry asphalt road;

Brake blending controller operates the hardware-based conventional hydraulic brakes and software-

based electric motors;

Repetition of the tests for the brake pedal actuation velocity 25, 50, and 100 mm/sec.

The diagrams introducing the results for the service braking (the brake pressure 40 bar) are given on Figure 8. It

should be pointed out in this case that the total brake torque demand can be covered by engaging of the electric

brake only. The comparison of “vehicle deceleration – pedal travel” dependencies for the variants of pure

friction braking, Figure 8a, and the braking with the activated brake blending, Figure 8b, indicates an effect of

initial oscillations. Their amplitudes depend distinctly from the velocity of the brake pedal actuations. However

the duration of oscillations (up to 0,3 seconds) is invariant with the pedal velocity. The nature of initial

significant oscillations in wheel torques by the brake blending control is caused by the configuration of the

electric powertrain having half-shafts and gearboxes (see Figure 1).

Figure 7:

Pedal force vs. pedal displacement;

decoupled brake system

a)

b)

c)

d)

e)

Figure 8: Brake diagrams for service braking

(the brake pressure 40 bar)

a) deceleration vs. pedal travel by pure friction

braking;

b) deceleration vs. pedal travel by brake blending;

c) torque distribution at the pedal velocity 25 mm/s;

d) torque distribution at the pedal velocity 50 mm/s;

e) torque distribution at the pedal velocity 100 mm/s

Figure 9 shows the results of brake blending control obtained for the full braking (the brake pressure 80 bar). For

this test manoeuvre, the influence of the brake pedal velocity on the blending point can be clearly evidenced. At

low-speed actuation (25 mm/s), the total brake torque demand is realized through the engaging of electric brakes

only, Figure 9c. With a rise of the pedal velocity the inclusion of the friction brakes becomes a necessity. For

both higher pedal velocities, 50 and 100 mm/sec, the activation of only front friction brakes is required. The

activation point comes into operation earlier at higher pedal velocity. This point corresponds to the transition

from segment “0-A” to the segment “A-B” from Figure 2. The share of friction torque in the total brake torque is

reduced with time. As for service braking, another observation is initial oscillations of brake torques and as a

result the oscillations of the dynamic pedal characteristic. Despite the duration of oscillations at full braking is

shorter as for service braking, this phenomenon need a separate discussion introduced below.

Figures 10 and 11 introduce the powertrain configuration of the target vehicle (see Figure 1). The scheme on

Fig.11 (a) can be simplified to the scheme (b) using the next transformations:

2 2 2

1 2 1 3 2 1 2; ; a b g c g gJ J J J i J J J i i . (1)

a) b)

c) d)

e)

Figure 9: Brake diagrams for full braking

(the brake pressure 80 bar)

a) deceleration vs. pedal travel by pure friction

braking;

b) deceleration vs. pedal travel by brake blending;

c) torque distribution at the pedal velocity 25 mm/s;

d) torque distribution at the pedal velocity 50 mm/s;

e) torque distribution at the pedal velocity 100 mm/s

Tyre

Jw

J3

J2

J1

Electric motorCV - Joints

Half-Shaft

Transmission equivalent play

ig2 ig2

Figure 10: The powertrain

architecture

J3 J1ig2 ig1Te

Ja Jb Jc

ka

Ta

kb

Tb

a)

b)Te

Figure 11: Schematic representation

of powertrain

Using d'Alembert principle, differential equations for rotating masses can be derived:

; 0; 0c c c e b b c b a a bJ T T J T T J T (2)

( ) ( )

( ) ( )

c c c b c c b

b b b a b b a

T c k

T c k

, (3)

where ic are damping coefficients, N/m

2;

ik are stiffnesses, N/m.

The transformation of Eqs. (2) and (3) yields:

( ) ( ) 0

0

c c c c c c c b c b e

b b c b c b b c c c b b a b a

a a b a b a b b b b

J c k c k T

J c c k k c k c k

J c k c k

. (4)

The response of the system of equations (4) on the step brake command is shown on Figure 12 as applied to the

target vehicle model in IPG CarMaker. This simplified example explains generally the nature of oscillations

observed on Figures 8 and 9.

Figure 12: Step response

The fact that initial oscillations are caused by the powertrain configuration can be also clearly recognized in the

case when these systems work separately without blending as it is shown in Figure 13. The maximal torque for

this brake maneuver is equivalent to the corresponding to the torque produced by the conventional brake system.

As the result, these oscillations on the wheel distort the vehicle deceleration that is illustrated in Figure 14 with

the conditions mentioned above. Such kind of brake system behavior influences crucially in a negative way both

on the driver comfort and safety. To resolve in further this problem by the modification of the brake blending

algorithm, oscillation frequency analysis has been done and results are depicted in Figure 15. The low frequency

oscillations up to 20 Hz have the highest amplitudes which lead to the described problematic. As the possible

solution is the implementation of active vibration controller.

a) b)

Figure 13: Torque values in the beginning of brake force application for electric motors (a) and friction brake

system (b); the brake pressure 40 bar

a) b)

Figure 14: Deceleration in the beginning of brake force application for electric motors (a) and friction brake

system (b); the brake pressure 40 bar

a)

b)

Figure 15: Frequency spectrum of torques (a) and deceleration (b) with application only of electric motors

Based on the performed analysis, a number of recommendations can be deduced for the development design of

the brake blending control taking into account the further implementation of the decoupled friction brake system:

Target brake pedal dynamics should corresponds to dynamics of conventional brake system in the wide

range of the brake pedal actuation velocities as far as possible;

Tuning of brake blending functions must aim at eliminating initial oscillation of brake torques caused

by the operation of electric powertrain components;

Brake blending controller should include constraints chosen from the analysis of amplitude-frequency

characteristics of the specific brake system.

CONCLUSIONS

The presented paper has introduced results of investigations on braking dynamic of an electric vehicle with

special attention given to (i) brake blending functions, (ii) influence of brake pedal actuation dynamics on brake

blending and (iii) experimental definition of related brake characteristics. It was also shown that the integrated

HIL environment and software vehicle simulator can be used as an efficient tool for the development design of

the brake controllers. In particular, the experimental acquisition of reference characteristics of brake blending for

conventional and decoupled brake systems has been illustrated with several practical examples. These examples

have confirmed both a necessity to take into account the brake pedal dynamics in the brake blending controller

and impact of blended brake operation on the brake pedal feel.

The introduced preliminary results are receiving the further advancement from viewpoint of the development of

(i) complex methodology for the evaluation of the brake pedal feel for decoupled brake systems and (ii)

integrated brake control systems for electric vehicles. The authors of this article plan to present the

corresponding outcomes in subsequent publications.

ACKNOWLEDGEMENT

The research leading to these results has received funding from the European Union Seventh Framework

Program FP7/2007-2013 under grant agreement no. 284708.

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