Brake torque analysis of fully mechanical parking brake system: Theoretical and experimental approach

Accepted Manuscript Brake torque analysis of fully mechanical parking brake system: Theoretical and experimental approach Mohd Razmi Ishak, Abd Rahim Abu Bakar, Ali Belhocine, Jamaludin Mohd Taib, Wan Zaidi Wan Omar PII: DOI: Reference:

S0263-2241(16)30487-0 http://dx.doi.org/10.1016/j.measurement.2016.08.026 MEASUR 4304

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

2 June 2016 20 July 2016 23 August 2016

Please cite this article as: M.R. Ishak, A.R.A. Bakar, A. Belhocine, J.M. Taib, W.Z.W. Omar, Brake torque analysis of fully mechanical parking brake system: Theoretical and experimental approach, Measurement (2016), doi: http:// dx.doi.org/10.1016/j.measurement.2016.08.026

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BRAKE TORQUE ANALYSIS OF FULLY MECHANICAL PARKING BRAKE SYSTEM: THEORETICAL AND EXPERIMENTAL APPROACH Mohd Razmi Ishak1), Abd Rahim Abu Bakar1), Ali Belhocine2)* Jamaludin Mohd Taib1) and Wan Zaidi Wan Omar1) 1)

Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia 2) *Faculty of Mechanical Engineering, University of Sciences and the Technology of Oran, USTO, L.P 1505 El-Mnaouer, 31000 Oran, Algeria

Abstract: The effect of the drum brake temperature reduction on the clamping force of the parking brake system has not been well addressed despite the fact that it may result in vehicle roll away. In view to this, a parking brake model that takes into account the temperature reduction of the drum brake has to be developed and more importantly, it must comply with the applicable standards or regulations such as Federal Motor Vehicle Safety Standard (FMVSS) 135. This paper develops a one dimensional (1D) model of leading-trailing drum-type parking brake model. This brake model is then verified with experiments carried out on a test bench that has been verified with the hand brake system in the vehicle. The results from the experiments show a good correlation with the predicted results from the brake model. It is also found that the existing parking brake design meets the standard requirements. Another finding is that the brake torque slightly increases as the drum temperature increases. With the verified brake model, parametric studies can be carried out as one of the tools during the design process. From the studies, it is found that rollaway will not happen even with the maximum vehicle weight and friction coefficient at drum/lining interface above 0.2.

Key Words: Parking brake model, Torque, Drum brake, Temperature, Rollaway

*

Corresponding author Tel* : +213556803713 Email* : [email protected]

1

1. Introduction Brakes are one of the most important safety systems in a motor vehicle. The main functions are to decelerate, to maintain the speed during downhill operation, and finally to park the vehicle stationary either on a flat or sloped road condition. The first two functions are related to the service brakes, while the last function is referred to the secondary or parking brakes as cited in [1]. The basic principle of the brake system is to provide clamping force between the disc/pad and drum/lining. Insufficient clamping force may cause the vehicle fail to decelerate or stop as intended. This can expose danger to the vehicle, driver, passengers, pedestrians, and other road users. In ground vehicles, mechanical parking brake is a mechanism to hold the vehicle stationary either on a flat or sloped road. It consists of a cable that is directly connected to the brake unit on one end and to an actuating lever on the other end. This actuating mechanism is often a hand-operated lever or a pull handle, or a footoperated pedal as mentioned [1]. The European Economic Community (EEC) regulation [2] specified that the handbrake system of a laden vehicle in class M1 (passenger cars comprising no more than eight seats in addition to the driver's seat) must be able to hold the vehicle in 20% gradient. Thiessen [3] suggested that parking brake is designed to hold a vehicle stationary over any desired time period. In addition, the parking brake should be able to hold a vehicle stationary on 30% gradient with a maximum applied force on the parking brake pedal of 445 N for a vehicle with hand-operated parking brake lever. Federal Motor Vehicle Safety Standard (FMVSS) 135 [4] specified that, for standard passenger vehicles with weight of 3500 kg and below, the vehicle should be able to stay stationary on 20% grade road for 5 minutes in both forward and reverse

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directions, with 400 N or less force applied at the hand control of the parking brake mechanism. To date, a lot of literatures have discussed the braking performance of the service brakes [1, 5-14], but only a handful focuses on the parking brakes. For instance, McKinlay et al. [15-17] investigated the conventional parking brake performance in term of vehicle rollaway for the disc brakes through laboratory tests and theoretical approaches. In the theoretical approach, one-dimensional (1-D) lumped parameter model of disc-type parking brake system using simple linear spring element had been proposed to predict the clamping force. A laboratory parking brake test rig was then developed to measure the clamping force of the parking brake system, which is used to validate the results from the 1-D model. In their study, they did consider the thermal effects on the braking torque and vehicle rollaway. Recently, Rozaini et al. [18] investigated mechanical parking brake system in terms of torque performance using combined analytical-experimental approach without considering thermal effects. They developed one dimensional rigid parking brake model and validated the model by comparing brake torque versus hand-brake lever force over measured data. To the authors’ knowledge, there is no information available in the public domain to investigate the torque performance of a drum-type parking brake system with thermal effect. Thus, the current work attempts to establish a theoretical model of the drum parking brake and validate the results against test results measured from parking brake test bench. 2. Parking brake tests In this work, parking brake test bench [18] for a typical fully mechanical hand lever operated drum-type parking brake system as shown in Fig. 1 was used. The test bench consists of a set of parking brake mechanism connected to a pair of rear-drum brake

3

unit, two hydraulic pumps, an actuator, a flywheel, a 5.5 kW DC motor with speed controller, and one load cell. One of the hydraulic pumps is used to supply brake pressure to the drum brake to simulate the brake in normal operations, which heat up the brake unit, whilst the other one is connected to the actuator, which is used to pull a cable that connects to the flywheel and the load cell. This will measure the brake torque produced by the drum brake unit when the hand lever is being pulled [15]. To engage the parking brake, force on the hand lever is applied using deadweight that is connected to the hand lever using cable and pulley. The DC motor rotates the drum brake and as the drum rotates, the friction force will create heat and the heat increases over a time period.

Fig. 1. Parking brake test bench [18]

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After the test bench was built, verification and calibration process was carried out by comparing the force of the load cell with the applied force to lift the hand lever of an actual car. Having been satisfied with the calibration process, the test bench was ready to be used. In this work, the test was conducted by heating up the drum brake for different hand-brake applied forces until it reached the maximum temperature of 250

0

C. The standard initial temperature to test the effect vehicle rollaway

phenomenon stated by McKinlay [15] is 300°C. However, using the available motor, the temperature level is difficult to achieve. This is because, during the dragging process, as the drum and lining temperature increases drastically, the coefficient of friction at the lining to drum interface increases. When the friction coefficient is too high, the torque produced by the drum brake is much higher than the torque of the DC motor. This causes the DC motor to stop. Due to this problem, the dragging process could only be performed until the drum surface temperature reaches around 250°C. After the dragging process, a delay time was allocated to set up the connection between the cable actuator with the drive wheel to allow the external torque to be applied to the drive shaft after the rear drum unit was heated. The delay time caused the drum temperature to drop. Therefore, this test was run with the initial temperature at approximately 200°C only. The temperature of the outer surface of the drum was measured using a non-contact temperature sensor (Brand: Cole-Parmer N-08406-00). Since the outer surface of the drum is exposed to the ambient air, it is expected that the drum will be cooled down at a faster rate than the shoes and hence, the drum would shrink earlier than the shoes. Thereafter, the parking brake torque was measured at five minute intervals [18] for up to one hour.

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3. Analysis of brake torque In the parking brake analysis, two models are used i.e. parking brake model and onslope vehicle model. The first model is employed to calculate brake torque produced by the parking brake system, whilst the vehicle model is used to determine torque that needs to hold the vehicle stationary. Rolled away phenomena starts if the torque from the vehicle model exceeds the torque from the parking brake model. 3.1. Parking brake model Fig. 2 shows the arrangement of a parking brake system used in this work. This arrangement is schematically represented as one dimensional model using linear spring as shown in Fig 3. The model is based on McKinlay model [15] and it has been modified to suit this study. The derivation of the parking brake torque starts from hand-brake lever and it is transmitted through brake cable. Engagement of the handbrake lever cause tension Fc in the cable, which always depend on the force applied Fhb to the lever and the hand lever arm length, la. This is reacted by the force in the cable and the cable lever arm length, lb. Fig. 4 illustrates the forces on hand-brake lever, the length of hand lever arms, la and the length of the cable lever arm, lb.

Fig. 2. Typical parking brake system.

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Fig. 3. One dimensional model of parking drum brake system.

u1

A B

u2

Fig. 4. Forces at hand-brake lever (A is the pivot point and B is the cable attachment point).

Then, from Fig. 5, ratio of reaction forces at the brake shoe is

Fs l f u 6   Fl le u5

(1)

7

Fig. 5. Forces at (a) secondary brake shoe, (b) strut, and (c) parking brake lever

When the brake shoe pushes the drum brake, lining (u6) and drum brake (u7) will deform. This deformation can be used to calculate the force. The force of deformable component is generally governed by

Fc 

Ac Ec c lc

(2)

where Fc (N) is the cable load, Ac (m2) as the cross sectional area, Ec (Nm-2) is modulus of elasticity, δc (m) is linear deformation and lc (m) is the initial thickness of the component. When the reaction force of the brake lining is equal to the drum brake interface force resulted from the deformation of both parts due to force reaction and thermal effect, the force between the interfaces will be derived as

F  F d

where

(3)

l

F

d

is described as the summation force reaction on drum surface and

F

l

is described as the summation force reaction on lining surface.

8

As the radial load F l and thermal load FT are taken into account, Eq. (3) will transform into Eq. (4);

 F  (

l

  d )  F  T d   F  l  F  T l

(4)

By substituting F from Eq. (2) into Eq. (4), the equation will expand to

 Al El Ad Ed   Ad Ed   Al El   Al El     l ,d    T ,d    l ,l    T ,l lod   lol  lod   lol   lol 

(5)

where  l ,d and  T ,d is drum displacement due to radial load and thermal reactions respectively.  l ,l and  T ,l represent the displacements of lining due to radial and thermal loads, respectively. As illustrated in Fig. 3, the radial deformation against the lining is u 6 and the radial deformation at the drum/lining interface is u 7 . Assuming that the drum and lining are homogeneous, the deformations of both components in relation to the thermal change

 T is proportional to both the temperature change and the thickness of the component. Hence,

 T   T l

(6)

where  is a constant characteristic of the material, called the coefficient of thermal expansion. Temperature change ΔT is the increment of drum temperature Tt at the specific time t in relation to its initial temperature, To, which is the temperature when the handbrake lever was initially applied. Thus, the temperature change will be

T  Tt  To

(7)

With the assumption of convection is dominant in the cooling process [21], the temperature at certain time Tt is

9

Tt  To  Tamb e

 hAt     pcpV 

 Tamb

(8)

where Tamb is ambient temperature, h is the heat transfer coefficient, A is the surface area where heat being transferred, ρ is the density of the drum, cp is drum specific heat capacity per unit mass and V is the volume of the drum. After all the deformations in Eq. (5) are substituted, the equation becomes

A E A E  A E AE  A E u 7  l l  d d   d d  d Tlod   u6  l l   l l  l Tlol  lod  lod  lol  lol  lol

(9)

To cancel out the denominators in Eq. (9), lol lod is multiplied to the equation. A new force equation is formed as follows;

u7  Al El lod  Ad Ed lol   Ad Ed  d Tlollod   u6 Al El lod  Al El  l Tlollod  By rearranging Eq. (10) to solve for

(10)

which is the displacement between brake

shoe/drum brake interfaces, it can be represented as: u7 

u 6 Al El lod  Al El  l Tlol lod   Ad Ed  d Tlol lod   Al El lod  Ad Ed lol 

(11)

With equation of deformation, the radial force at the frictional interface is represented by;

Fl 

AE AE  l l

 

AE l

 

T

 s  

AE l

 

T

 u7 

(12)

By replacing the thermal deformation and force deformation into the equation, the force at the interface becomes;

Fl 

Ad Ed l od

 u6 Al El l od  Al El  l Tlol lod   Ad Ed  d Tlol lod   d Tlod    Al El lod  Ad Ed lol   

(13)

Cancelling out the original drum thickness in the equation, the normal force without installation gap will be given as

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 u A E  Al El  l Tlol   Ad Ed  d Tlol  Fl  Ad Ed  d T  6 l l   Al El lod  Ad Ed lol   

(14a)

If the installation gap (lg) between the lining and drum exists, then the normal force becomes

 u6 Al El  Al El  l T (lol  l g )   Ad Ed  d T (lol  l g  Fl  Ad Ed  d T   Al El lod  Ad Ed (lol  l g   

(14b)

In order to calculate the torque generated at drum brake, Tqgen the radial force at the interface, Ff is multiplied by the radius of the drum brake, rd.

Tq gen  F f rd

(15a)

Tq gen   d Fl rd

(15b)

where, F f  d Fl

(15c)

Due to design configurations of the drum brake, the applied force at the handbrake lever differs when the vehicle is parked facing uphill or downhill. This can be seen from the forces acting on the brake shoe as depicted in Figs. 6(a) and 6(b).

Ff

Ff lg

lg

O

(a)

O

(b)

Fig. 6. Forces acting on the brake shoe: (a) vehicle facing downhill, (b) vehicle facing uphill

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From the figures, the total moment at point 0 is; For vehicle facing downhill,

Fs le  Fl l f  F f l g

(16)

For vehicle facing uphill,

Fs le  Fl l f  F f l g

(17)

By substituting Eqs. (1), (7) and (8) into Eqs. (16) and (17), The handbrake applied force, Fhb can be given as; For vehicle facing downhill, For vehicle facing uphill,

Fl (l f  d l g ) lc ( ) le ld Fl (l f  d l g ) lc Fhb  ( ) le ld

Fhb 

(18) (19)

3.2. Vehicle model on a slope Fig. 7 shows a vehicle with mass m is parked on gradient θ. The weight (mg) of the vehicle is assumed at the centroid of the vehicle with normal force (N) reacts perpendicular to the road at each tyre. The frictional force is assumed only at the rear tyre because the parking brake system is attached at the rear wheels. Resolving all the forces along the road, x’ direction and perpendicular to the road, y’ direction, the frictional force equation in x’ direction is Ffric  r Fr  mg  sin 

(20)

As the braking torque of the tyre is equal to the multiplication of frictional force at the tyre and the radius of the wheel, the torque required at the center of the rear wheel to hold the vehicle stationary [15] is

Tqreq   r Fr Rwheel  mg sin   Rwheel

(21)

where  r is the friction coefficient between road and tyre, Fr is a normal force at rear tyre and Rwheel is radius of the tyre.

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Fig. 7. Vehicle on a slope in the uphill direction [18]

4. Results and discussion In this section, the results are discussed; starting with the verification of the test bench, followed by the prediction of temperature and torque generated by the drum brake. Finally, the parametric study is carried out. 4.1. Verification and calibration of the test bench Prior to carrying out the experiment on the test bench, the test bench must closely behave as the actual parking brake performance. Verification of the test bench is done by comparing the applied force on the actual hand lever in the vehicle with the dead weight applied on the test bench. Thus, to achieve identical applied force between vehicle and test bench, calibration of the cable tension must be carried out. This can be done by adjusting the screw-nut mechanism to increase or decrease the cable tension. The applied forces on both hand-brake levers were based on the number of ratchet teeth the arm went through. The maximum number of ratchet teeth for current handbrake lever design is 13. The in-vehicle hand-brake force is measured using a

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spring scale, which is hooked to the handle of the hand-brake and the scale is positioned perpendicular to the lever. The reading was taken once the ratchet pawl slips. In the vehicle, the maximum applied force can reach up to 500 N. However, in the test bench, available deadweight used to pull the hand-brake lever can only provide handbrake force up to 340 N. Fig. 8 shows result of the two tests and the results show there is a close correlation between them. This indicates that the test bench can be used in replacing the vehicle test.

Fig. 8. Correlation of applied force on hand-brake lever between vehicle test and test bench.

4.2. Prediction of temperature and parking brake torque Predictions of temperature and parking brake torque are made based on Eq. (8) and Eq. (15b), respectively. All the parameters and their values used to predict the temperature and torque are given in Table 1. Most of the parameters are measured

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values of the brake components and some of them are taken from other resources as stated in Table 1. Fig. 9(b) shows that the measured temperature varies with cooling time after the wheel rotated with the brake applied until an approximate temperature of 200oC was reached. Small variations in the initial temperature are noticed due to the measurement approach as stated in Section 2. These small variations however will not give any significant effect on the parking brake torque. It is seen that a quick temperature drop occurs at the start of cooling time before 500 s and then, the temperature drop is more gradual. The quick initial temperature drop shows that the whole brake system is not fully heated (or not fully heated to the maximum heat absorptive capacity). Thus the heat initially spread to the parts that are cooler. When the whole system had reached a more equal temperature which is lower than the initial maximum value, then the heat lost would be to the atmosphere, which occurs at a lower rate. A similar trend of temperature profiles of brake disc also reported by McKinlay [15]. It is also observed that there is no significant difference in the cooling temperature curve for all cases of hand-brake applied forces. In addition, similar temperature curves are also predicted for the downhill and uphill direction. The prediction results in Fig. 9(a) are almost identical to the results obtained in the experiment as shown in Fig. 9(b). From the cooling temperature curve, the normal force in Eq. (13) can be calculated and later, the parking brake torque can also be predicted. From the experiment, it is found that u6 in Eq. (13) can be represented by

u6 = 3.89 x 10-7 * Fhb - 1.5 x 10-5

(20)

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Table 1. Parameters and values used in the parking brake model. Parameters

Value

Unit

Value

Unit

27

°C

Modulus Young of lining, El

2.1 x 108 [22]

Nm-2

Mass of vehicle, m

1250

kg

Surface area of drum, Ad

2.2×10-3

m2

Mass of driver, md

70

kg

Surface area of lining, Al

4.8×10-3

m2

Volume of drum, V

7.7 x 10-4

m3

Thermal expansion coefficient of drum, αd

1.1 × 10-5 [1]

°C-1

Radius of drum, rd

0.09

m

Thermal expansion coefficient of lining, αl

1.2 × 10-5 [20]

°C-1

Specific heat capacity of drum, cp

586 [20]

J kg-1 °C-1

Drum thickness, lod

0.008

m

Density of drum, ρ

7100 [21]

kg m-3

Lining thickness, lol

0.004

m

0.3

m

Friction coefficient (shoes/drum)

0.3~0.6

1.1 × 1011 [22]

Nm-2

Initial gap between lining and drum

1

Ambient Temperature, Tamb

Radius of wheel, Rwheel Modulus Young of drum, Ed

Parameters

mm

16

Drum surface temperature, T ( oC)

250 FhbC=160N FhbC=250N FhbC=340N FhbC=400N

200

150

100

50

0

500

1000

1500

2000

2500

3000

3500

4000

time, t (s)

(a) Calculated

Drum surface temperature, T ( oC)

250 Fhb=160N Fhb=250N Fhb=340N

200

150

100

50

0

500

1000

1500

2000

2500

3000

3500

4000

Time, t (s)

(b) Measured Fig. 9. Brake temperatures being cooled over time

Having known the relationship of temperature change and cooling time, the torque generated by the parking brake can be obtained for various hand-brake applied forces. Fig. 10 depicts the parking brake torque curves calculated from Eq. (15b) in the downhill direction and it can be seen that a good correlation is achieved against measured data. From this correlation, parking brake torque for FhbC = 400 N can be predicted using the same equation. A good correlation is also achieved for the uphill direction as plotted in Fig. 11. From these two plots, it shows that parking brake

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torque generated is much higher in the downhill direction than the uphill direction with the same applied force of Fhb = 400 N. This is due to the design of the drum brake leading-trailing shoe mechanism [1] and is also supported by Eqs. (18) and (19). The significant observation in the results as shown in Fig. 10 and Fig. 11 is that the drum brake torque is not very much affected by temperature variations of the brake. This is differed with the finding of McKinlay [15] for the disc brake. The reason can be due to the curved shape of the brake shoes and drum compared to the flat shape of the brake pads and disc. The brake pad can easily be detached from the disc surface during the cooling process. Another possible reason is that the normal brake pad movement is much smaller compared to the brake shoes, thus would have a larger ratio of disengagement when the disc cools off. For these two reasons, the clamping force and brake torque will be reduced significantly.

Fhb=160N Fhb=250N Fhb=340N FhbC=160N FhbC=250N FhbC=340N FhbC=400N

Torque generated, Tgen (Nm)

1400

1200

1000

800

600

400

200

0

500

1000

1500

2000

2500

3000

3500

4000

Time, t (s)

Fig. 10. Parking brake torque for vehicle facing downhill (Fhb=measured,FhbC=calculated)

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1000 Fhb=160N Fhb=250N Fhb=340N FhbC=160N FhbC=250N FhbC=340N FhbC=400N

Torque generated, Tgen (Nm)

900 800 700 600 500 400 300 200

0

500

1000

1500

2000

2500

3000

3500

4000

Time, t (s)

Fig. 11. Parking brake torque for vehicle facing uphill (Fhb=measured, FhbC=calculated)

According to FMVSS 135 [4], a vehicle weighing 3500 kg and below should be able to remain stationary on 20% or 11.3o grade road for 5 minutes in both forward and reverse direction when 400N or less force is applied at the hand control mechanism. From Fig. 12, the torque generated by the parking brake in the downhill and uphill direction at Fhb = 400 N is much higher than the torque required for a slope of 11.3o. This indicates that the current parking brake design that is used in this work complies with FMVSS 135 regulation.

19

1500 Tg at FhbC=400N Treq at Slope=11.3o

1400

Brake Torque, Tq (Nm)

1300 1200 1100 1000 900 800 700 600

0

500

1000

1500

2000 time, t (s)

2500

3000

3500

4000

(a) Downhill 1500 Tg at FhbC=400N Treq at Slope=11.3o

1400

Brake Torque, Tq (Nm)

1300 1200 1100 1000 900 800 700 600

0

500

1000

1500

2000 time, t (s)

2500

3000

3500

4000

(b) Uphill Fig. 12. Calculated parking brake torque performance It is also interesting to see the effect of temperature on parking brake torque performance at different handbrake applied force. From Fig. 13 and Fig. 14, it can be seen that parking brake torque is not very much affected by the temperature and this similar brake torque – temperature curve was also reported by Limpert [1]. There is

20

only slight increase in the brake torque as the temperature increases from 50 oC to 200oC. For instance, at applied force of 340 N, the brake torque increases from 944 N to 973 N for vehicle facing downhill and from 740 N to 774 N for vehicle facing uphill. A similar brake torque performance profile is also observed for 160 N and 250 N applied forces. A good agreement is also observed in the generated torque between measured and calculated results.

Fig. 13. Parking brake torque against temperature for vehicle facing downhill (Fhb=measured, FhbC=calculated, values given are from measured data)

Fig. 14. Parking brake torque against temperature for vehicle facing uphill (Fhb=measured, FhbC=calculated, values given are from measured data)

21

4.3. Parametric studies After the parking brake model is validated, the model can be used to predict brake torque performance due to changes in some of the parameters of the brake components and the vehicle. They are the drum/lining coefficient of friction and the vehicle weight. The effect of installation gap between the shoes and the drum is not considered because the motivation of this work is to investigate thermal effect which requires the shoes always in contact with the drum. To ensure a vehicle in a stationary state, the torque generated by the parking brake must always be higher than the torque required for certain road slope (Tgen > Treq). This is shown by Fig. 15 that the vehicle is in a stationary condition on the slanting road when the friction coefficient between drum and lining is above 0.2. 1800

Tgen (µ=0.1) Tgen (µ=0.2) Tgen (µ=0.3) Tgen (µ=0.4) Tgen (µ=0.5)

1600

Torque, Tq (Nm)

1400

Treq (slope=11.3o)

1200 1000 800 600 400 200

0

500

1000

1500

2000 time, t (s)

2500

3000

3500

4000

Fig. 15. Brake torque performance for different friction coefficients

Fig. 16(a) and Fig. 16(b) show the brake torque performance with various vehicle weights in the downhill and uphill direction, respectively. These results are based on 400 N handbrake applied force, but the maximum force that can be applied by the

22

driver is up to 500 N. As stated in Table 1, the weight of the vehicle is 1250 kg and the passenger weight is assumed to be 70 kg per person. It shows that the vehicle will not roll away in the uphill and downhill direction, even though there are five passengers inside the vehicle. This is because the torque generated by the parking brake is much higher than the torque required with five passengers.

1500 Tgen (Fhb=400 N) Treq (m = car only) Treq (m = car + driver) Treq (m = car + 2p) Treq (m = car + 3p) Treq (m = car + 4p) Treq (m = car + 5p)

1400

Torque, Tq (Nm)

1300 1200 1100 1000 900 800 700 600

0

500

1000

1500

2000

2500

3000

3500

4000

Time, t (s)

(a) Downhill 1000

Tgen (Fhb=400 N) Treq (m = car only) Treq (m = car + driver) Treq (m = car + 2p) Treq (m = car + 3p) Treq (m = car + 4p) Treq (m = car + 5p)

950

Torque, Tq (Nm)

900 850 800 750 700 650 600

0

500

1000

1500

2000

2500

3000

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Time, t (s)

(b) Uphill Fig. 16. Brake torque performance in various vehicle weights

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5. Conclusion This paper attempts to establish validated parking brake model in order to predict its torque performance with the aim to avoid vehicle roll away phenomena from the parked condition. In doing so, parking brake test bench was firstly developed with the intention to validate the parking brake model. To ensure the validity of the bench, a comparison was made against vehicle test data and a very good agreement was demonstrated between them. Then, a one dimensional parking brake model with consideration of temperature effect is proposed. A good correlation of temperature change and parking brake torque between the model and the test bench was also demonstrated. In addition, the parking brake unit used in this work was found to comply with the FMVSS 135 regulation. The result also shows that the torque generated by the parking brake in the downhill direction is much higher than in the uphill direction. This is due to the leading-trailing shoe type used in the drum brake mechanism. It is observed that the drum brake torque is not very much affected by temperature reduction. Thus, temperature effect on the drum parking brake is not an issue for vehicle rollaway. From the parametric studies, it is seen that the vehicle will not roll away when the friction coefficient of the brake lining is above 0.2 and that the parking brake can hold the vehicle stationary with five occupants inside it.

Acknowledgement The authors would like to thank the Ministry of Science, Technology and Innovation Malaysia (MOSTI) and Universiti Teknologi Malaysia (UTM) for their continuous

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Highlights ► We developed a one-dimensional drum-type of parking brake model. ►We studied the thermal effect on the parking brake torque performance. ► We conducted experiments using parking brake test bench. ►We obtained good correlation between the model results and the test data.

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