development and modelling of an electropneumatic brake system

7/30/2019 Development and Modelling of an Electropneumatic Brake System

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Development and Modelling of an Electropneumatic Brake SystemP. Karthikeyan and Shankar C. Subramanian

Abstract-The brake system is the primary system in anautomobile which ensures its safety on the road. The idealb rake system should opera te with the least effort from thedriver and should stop the vehicle within the minimum possibledistance. This paper deals with the ai r brake system which iswidely used in commercial vehicles such as trucks, buses andtractor-trailers. One of the important parameters which affectthe stopping distance of a vehicle is the brake response time.The work presented focuses on the development of anelectropneumatic brake which would decrease the responsetime of the air brake system thereby providing a reducedstopping distance. A mathematical model that correlates thepressure transients in the brake chamber to the voltage inputprovided to the electropneumatic brake has been developed.The efficacy of this model is tested by comparing its resultswith experimental data obtained from various test runs.

I. INTRODUCTIONThe brake system is one of the critical components in

ensuring the safety of any vehicle on the road. The brakesystem must ensure the safe control of a vehicle during itsnormal operation and must bring the vehicle to a smoothstop within the shortest possible distance under emergencyconditions. It should also permit the safe operation of avehicle while descending down a grade and also be able tohold a vehicle stat ionary once it comes to rest [1]. Existingbrake systems typically use either brake fluid (hydraulicbrakes) or compressed air (air brakes) as their energytransmitting medium. The hydraulic brake system is widelyused in passenger cars while the air brake system is widelyused in commercial vehicle such as trucks, buses andtractor-trailers [2].The existing air brake system used in commercial vehicles

can be broadly divided into two subsystems - the pneumaticsubsystem and the mechanical subsystem [3]. The pneumaticsubsystem includes compressor, storage reservoir, treadlevalve (brake application valve), brake lines, relay valve,quick release valve and brake chambers. The mechanicalsubsystem consists of push rods, slack adjusters, S-cams,brake pads and brake drums.In a vehicle equipped with an air brake system, the driver

applies the brake by pressing the brake pedal attached to thetreadle valve. This action meters out the compressed airManuscript received December 13, 2008. This work was supported bylIT Madras under the grant EDD/06-071181/NFSC/CSSH.P. Karthikeyan is with the Department of Engineering Design, IndianInstitute of Technology Madras, Chennai 600 036, INDIA.Shankar C. Subramanian (Corresponding Author) is with theDepartment of Engineering Design, Indian Institute of Technology Madras,Chennai 600 036, INDIA (Phone: +91-44-22574705; Fax: +91-4422574732; E-mail: [email protected]).

from the storage reservoir to the brake chambers. Thetreadle valve has inlet ports, which when open, providecompressed air from the storage reservoirs to the brakechambers. It also has exhaust ports, which when open,discharge compressed air from the brake chambers to theatmosphere. When the brake is not applied, the exhaust portsin the treadle valve are open and the inlet ports are closed.When the brake pedal is displaced, the exhaust ports of thetreadle valve are fITst closed and then the inlet ports areopened. Then, the compressed air travels through air hosesto the brake chambers mounted on the axles. These actionsresult in a time lag between the application of the brakepedal and the increase in pressure in the brake chambers.This time lag affects the speed of response of the air brakesystem and thus the stopping distance of the vehicle. Thus,one of the objectives of this research work is towardsdeveloping an electropneumatic brake in order to reduce thistime lag.An electropneumatic brake will have electronically

operated valves, which will respond faster thanmechanically operated valves. This will ensure that theresponse time of the brake system will reduce leading to areduction in the stopping distance of the vehicle. A welldesigned electropneumatic brake will also reduce thenumber of pneumatic l ines present in the air brake systemthereby reducing its complexity. Additionally, it will alsoreduce the amount of brake pedal force to be provided bythe driver.In this research work, the treadle valve in the exist ing air

brake system is replaced by an electropneumatic regulator.A voltage signal is provided as input to thiselectropneumatic regulator and it supplies compressed air tothe brake chamber corresponding to this voltage input. Amathematical model has been developed to predict thepressure transients in the brake chamber and is presented inthis article. This mathematical model will be used towardsmodel-based control and fault diagnosis of theelectropneumatic brake.The tradit ional pneumatic and hydraulic brake systems

have been extensively studied and models for them havebeen developed by many authors. Khan et al. [4] developedmodels for hydraulic brake system components such asbrake pedal, vacuum booster, master cylinder andproportioning valves using the bond graph technique.Gerdes et al. [5] developed a model for the hydraulic brakesystem considering the master cylinder seal friction, washerhysteresis, etc. Subramanian et al. [6] developed anexperimentally corroborated model for the pneumatic

978-1-4244-3504-3/09/$25.00 2009 IEEE 858


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Air CompresSGr

S-CamFig. 2. The S-cam foundation brake

Parking Brake ~ - - ~Control Valve Rear Service and SpringBrake Chambers

Front ServiceBrakeChamben

QuickRelease Valve

with the brake drum. This action results in the decelerationof the rotating brake drum. When the brake pedal is releasedby the driver, air is exhausted from the brake chamber andthe push rod strokes back into the brake chamber therebyrotating the S-cam in the opposite direction. The contactbetween the brake pads and the brake drum is now brokenand the brake is thus released.

Fig. 1. General layout of a 2-axle commercial vehicle air brake system

III. AIM AND SCOPE OF THE PROBLEMThe long term aim is to develop and integrate an

electropneumatic brake in commercial vehicles. Such abrake would reduce the time lag of existing air brakesystems thereby reducing the vehicle stopping distance. Itwill also reduce the braking effort that needs to be appliedby the driver. One of the long term objectives is to developmethods for controlling the electropneumatic brake toachieve a desired braking force. This would be helpful incase of future commercial vehicle technology such as anAdaptive Cruise Control (ACC) system. Another long termobjective is to develop fault diagnostic schemes to monitorthe electropneumatic brake system.The fITst step in achieving these objectives is to develop a

mathematical model for the electropneumatic brake systemand this is the scope of this article. This model will correlatethe voltage input provided to the electropneumatic regulatorto the pressure transients in the brake chamber. The resultsfrom this model will be corroborated with experimental dataobtained from various test runs.

subsystem of an S-cam air brake system. They haveintegrated models of the treadle valve, the flow of air in thesystem and the brake chamber. Xing-Dong et al. [7]developed models for the individual components of an airover-hydraulic brake system. Natarajan et al. [8] developeda model for the relay valve which is used in the air brakesystem. Lindemann et al. [9] discussed the feasibility andcompatibility of an electronically controlled brake systemfor a tractor-trailer combination. Wrede and Decker [10]provide a broad discussion of electronically controlledbraking systems for commercial vehicles and their potentialbenefits.In the above studies, the authors have developed

mathematical models for existing traditional brake systems.A model for an electropneumatic brake has not yet beendeveloped. A main objective of this research work istowards developing a mathematical model for anelectropneumatic brake and experimentally corroboratingthe same.The organization of this article is as follows. In section 2,a brief description of the existing air brake system and the

operation of its various components are presented. Section 3outlines the aim and scope of the problem under study. Thedetails of the experimental setup developed at lIT Madrasare provided in section 4. The mathematical model for theelectropneumatic brake is developed in section 5. Sections 6and 7 provide the details of the corroboration of the modeland concluding remarks respectively.II. A BREIF DESCRIPTION OF THE AIR BRAKE SYSTEMA general layout of the air brake system found in a typical

two axle commercial vehicle is presented in Fig. 1. Anengine driven compressor provides compressed air which iscollected in a storage reservoir. Compressed air is providedto the brake chambers through the treadle valve via twocircuits - the primary circuit is used to apply the brakes onthe rear wheels through the relay valve and the secondarycircuit is used to apply the brakes on the front wheelsthrough the quick release valve. The primary circuit isactuated via pedal force and the secondary circuit is actuatedby the compressed air delivered from the primary circuitunder normal operating conditions. The advantage of thisdual circuit treadle valve is that partial braking is stillpossible in the event of failure of one of the two circuits.The foundation brakes are mounted on the axles. The S-camdrum foundation brake is widely used in existing air brakesystems and is illustrated in Fig. 2. The compressed airenters the brake chamber and acts against the diaphragm,generating a force resulting in the motion of the push rod.The motion of the push rod serves to rotate a splined shaftthrough the slack adjuster.The other end of the splined shaft has a cam in the shape

of an S mounted on it. The ends of two brake shoes rest onthe profile of the S-cam. The rotation of the S-cam pushesthe brake shoes outward so that the brake pads make contact

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IV. THE EXPERIMENTAL SETUPAn experimental set up of an air brake system with S-cam

foundation brakes has been developed and is i llustrated inFigs. 3 and 4. The front axle of a commercial vehicle isrigidly fixed to a custom made fixture. It has a Type 20brake chamber along with a manual slack adjuster at eachwheel. A compressor provides compressed air to the brakesystem with the maximum possible supply pressure being900 kPa (gauge). A storage reservoir with a capacity of 90ltrs is integrated with the compressor and a pressureregulator is used to regulate the pressure of air beingprovided from the storage reservoir. The compressed air istransmitted through the brake system using hoses.

Fig. 3. A schematic of the experimental facility

Fig. 4. A photograph of the experimental facilityA pressure sensor is mounted at the entry point of each

brake chamber to measure the pressure of air in the brakechamber. A linear potentiometer is fixed to the push rod on acustom made fixture and is used to measure the stroke of thepush rod. An electropneumatic regulator (EPR) has beeninstal led to meter out the compressed air from the storagereservoir to the brake chamber. In this study, the outlet portof the EPR is directly connected to one of the two brakechambers. This regulator is controlled by providing ananalog voltage between 0-10 VDC. The sensors and theregulator are interfaced with a computer through a PCI(Peripheral Component Interconnect) mounted DataAcquisition board. In this setup the mechanical subsystemremains the same as in the existing commercial vehicles.

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V. MATHEMATICALMODEL OF THE SYSTEMThe mathematical model developed in this section

correlates the voltage input provided to the EPR and thepressure transients in the brake chamber. The EPR isdesigned to provide a pressure output between 5-900 kPa(gauge) in response to an analog voltage input between 0-10VDC. The EPR was calibrated by providing a range ofvoltage inputs and measuring the pressure of air delivered.This calibration curve is provided in Fig. 5.

1,000900

'2 800C 700600500

i 400C/.l 3002001000 2 4 5 6 7 9 10Input voltage (V)

Fig. 5. Calibration curve of the electropneumatic regulatorIt can be observed that the relationship between the input

voltage and the output pressure is almost linear. From thiscurve, the relationship between the voltage input to theregulator (V,eg) and the output pressure from the regulator(P,eg) is obtained as

P,eg = 90v,eg + Palm' (1)where Palm is the atmospheric pressure. When a voltageinput is provided to the EPR, a port is opened in theregulator and air is metered out from the storage reservoir tothe brake chamber. This port remains open as long as theoutput pressure is not the one corresponding to the voltageinput provided to the regulator. The following assumptionsare made in the development of the lumped parametermathematical model for the electropneumatic brake. Theport in the EPR is considered as a nozzle. I t is assumed thatair behaves like an ideal gas. The flow through the regulatorport is assumed to be one-dimensional and isentropic. I t isalso assumed that the fluid properties are uniform at all thesections in the nozzle. Figure 6 shows the simplifiedpneumatic subsystem of the electropneumatic brake underthe above assumptions.Applying the balance ofmass to the brake chamber,m=puAp , (2)

where m is the time rate of change of the mass of air in thebrake chamber, p is the density of air inside the brakechamber at any instant of time, u is the velocity of air at theexit section of the nozzle and Ap is the cross-sectional areaof the regulator opening.


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Fig. 6. The simplified pneumatic subsystem when the brake is applied (11)

(12)

/I/

0.050.0450.04g 0.035o 0.030.025e 0.02=0.0150.010.005o 100 200 300 400 500 600 700

Brake chamber pressure (kPa)

Now, from the ideal gas equation of state, the mass of airinside the brake chamber is~ ~m =--b RT 'b

where ~ is the volume of air inside the brake chamber and~ is the temperature of air inside the brake chamber.Differentiating this equation with respect to time and

using the isentropic process relations (Eq. (8)), we obtain. 1 ~ ~ ~ ~mb =---+--.r R ~ R ~

Fig. 7. Push rod stroke and brake chamber pressureat 720 kPa supply pressure

Let us now determine the relationship between the brakechamber pressure and the push rod stroke. Figure 7illustrates the variation of the push rod stroke with respect tothe brake chamber pressure for a test run. The overalltransients in the brake chamber during its operation can bebroadly divided into three phases/modes. It can be observedthat the push rod starts to move only after a "thresholdpressure" (denoted by is reached in the brake chamber.Let us refer to this phase as "Mode 1". After this, the pushrod starts to move and the clearance between the brake padsand brake drum starts to decrease. The brake pads makecontact with the brake drum only when the brake chamberpressure reaches the "contact pressure" (denoted by ) . Letus denote this phase as "Mode 2". Once contact between thebrake pads and the brake drum is established, further motionof the push rod occurs due to the deformation of themechanical components in the brake with increasing brakechamber pressure. Let us refer to this phase as "Mode 3".From Fig. 7, the relationship between the push rod stroke

(xb ) and the brake chamber pressure can be written as{ M ] ~ +N] if ~ ~ < ~ t 'xb = . > (13)M 2 ( ~ - ~ t ) + M ] ~ t +N] if ~ - ~ t '

(9)

~ ~ : : i P u s h Rod

BrakeChamber

PoTn

Compressor andStorage Reservoirs

The area of the regulator opening is modeled usingk ( 9 0 ~ e g + ~ t m - ~ )Ap = , (3)9 0 ~ e g + Palm

where ~ is the pressure of air in the brake chamber and kis a constant parameter which is determined fromexperiments.

The energy equation for the flow of air can be writtenas [11]

h+!...u 2 =ho ' (4)2where ho is the specific stagnation enthalpy at the entrancesection of the nozzle, h is the specific enthalpy at the exitsection of the nozzle and u is the velocity of air at the exitsection of the nozzle.Since air is considered to be an ideal gas, its specificenthalpy at any point in the flow region can be written as

h = CpT, (5)where Cp is the specific heat of air at constant pressure ( Cpis assumed to be constant) and T is the local temperature ofair at that point.Using Eq. (4) and Eq. (5) we obtain

u = ~ 2 C p ( T o - T ) , (6)The ideal gas equation of state is given by

P( p) = pRT, (7)where R is the gas constant of air.For isentropic flow of an ideal gas, the pressure, densityand temperature are related byp p(r;IJ

-=Consfanf , - -=Consfanf , (8)pY Twhere r is the ratio of the specific heats and is assumed tobe constant.Now, Eq. (6) can be re-written as

where ~ and Po are the pressure and density of air in thestorage reservoir respectively.Substituting Eq. (9) in Eq. (2), and including a dischargecoefficient CD in order to compensate for losses that occurduring the flow, we obtain

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(14)

TABLE IVALUES OF PARAMETERS

Value298K1.40.82

0.00047136 mlkPa0.00003038 mlkPa-0.05716359 m

Parameteralue0.0129 m20.0002 m3101.356 kPa118 kPa180.96 kPa0.287 kJlKgK0.00025

Parameter

where the constants M], M 2 and N] are obtained from thecalibration curve. From the above relation, the volume of thebrake chamber for each phase is given by

1VOl i f Pb

development and modelling of an electropneumatic brake system

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