Dynamic behaviors of a wedge disc brake

Applied Acoustics xxx (2017) xxx–xxx

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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

Dynamic behaviors of a wedge disc brake Khaled R.M. Mahmoud a,b,⇑, M. Mourad a, A. Bin Mahfouz c a

Mechanical Dept., Faculty of Eng., Minia University, 61111 Minia, Egypt Mechanical Dept., Faculty of Engineering, University of Jeddah, Jeddah, Saudi Arabia c Chemical Eng Dept., University of Jeddah, Jeddah, Saudi Arabia b

a r t i c l e

i n f o

Article history: Received 31 July 2016 Received in revised form 26 April 2017 Accepted 7 June 2017 Available online xxxx Keywords: Disc brake dynamic behavior Friction coefficient Brake shoe factor Wedge angle Self-energized brake

a b s t r a c t Mathematical models to study the dynamic behavior of a wedge disc brake are presented in this article. The friction coefficient has a significant role in the brake system dynamics especially, self-energized. A set of experiments have been conducted to formulate mathematical equations relating the friction coefficient, normal force and sliding speed. The effect of main operational parameters of a wedge disc brake such as normal force, sliding speed and wedge angle on the dynamic behavior and their comparisons with conventional disc brake system are investigated. Setting time and frequency response are the main performance indicators to investigate the dynamic behavior of a disc brake. The results indicate that friction coefficient significantly influence the resonance frequency and setting time of wedge disc brake shoe factor. However, the coefficient of friction has a negligible effect on setting time or resonance frequency of conventional disc brake. The effect of sliding speed on a wedge disc brake dynamics is somewhat considerable but it has a little effect on the dynamics of a classical disc brake. Moreover, the wedge angle has a considerable effect on the wedge disc brake dynamics. The normal force has negligible influence on dynamic characteristics of wedge and conventional disc brakes. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Many researchers are trying to develop the vehicle disc brakes that may ensure better performance under severe service conditions. The expanding necessities identified with high safety, and better ride comfort of modern vehicles makes them turn out to be more perplexing. These high and principally assorted necessities are to a great extent thought about the car stopping mechanism, and specifically on its brakes [1–3]. Friction is the prime factor that may be considered for the dynamic behavior of disc brake systems. In uphill case, the braking process is basically a conversion of kinetic or potential energy into heat through friction. Many research works illustrated that the coefficient of friction is affected by several parameters such as the surface area topography, disc and pads properties, temperature, sliding speed, and normal force [4]. There were many efforts to accurately determine the coefficient of friction and its variation with normal force, sliding speed and contact temperature. This leads to the observation that the coefficient of friction is varying with the brake time. There exists a relationship between the sliding speed and the coefficient of friction especially under extreme ⇑ Address: Mechanical Dept., Faculty of Eng., Minia University, 61111 Minia, Egypt. E-mail address: [email protected] (K.R.M. Mahmoud).

loads. Many studies such as Blau [5] concluded that the sliding friction greatly increases with the decrease of the sliding speed. Also, it is observed that the coefficient of friction decreased with the increase of the sliding speed [6]. Blau [5] also researched to form the relation between the sliding speed and the coefficient of friction under extreme loads. The results indicate that the coefficient of friction decreases with the increase of the sliding speed. Eriksson et al. [7] have experimentally investigated the relation between the coefficient of friction and the sliding speed. They used five different types of brakes, and each brake had a trend that differed from the others, however, the coefficient of friction decreased with the sliding speed in all the brakes that were investigated in their study. The brake shoe factor C⁄ is known as the ratio between friction (brake) force on the shoe to the applied force at the tip of the shoe. Whereas, the brake force between the rotor and the pad is as a result of the friction process, [8,9]. The shoe factor C⁄ depends mainly on the value of the coefficient of friction. The selfenergized brakes are characterized by high brake shoe factor but at the same time they have high sensitivity to the friction coefficient variations. From the other side, conventional disc brake has low brake shoe factor but it is less sensitive to the change of friction coefficient [10,11]. Wedge disc brake is introduced in different shapes by many investigators such as Dietrich et al. [12] who invented it first,

http://dx.doi.org/10.1016/j.apacoust.2017.06.005 0003-682X/Ó 2017 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Mahmoud KRM et al. Dynamic behaviors of a wedge disc brake. Appl Acoust (2017), http://dx.doi.org/10.1016/j. apacoust.2017.06.005

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K.R.M. Mahmoud et al. / Applied Acoustics xxx (2017) xxx–xxx

Fig. 1. Photo of brake dynamometer test setup and measurement instrumentation.

Data acquissition

Electro--mechanical actuator

indicate that disc brake topography has a significant effect on dynamic characteristics as well as squeal generation. Petry et al. [20] have investigated the effect of the brake disc waviness of the self-energized disc brake on its dynamic behaviors. Their results indicate that friction coefficient has a considerable effect on brake force and setting time. Also, Balogh et al. [3] have modelled self-energized disc brake to study its dynamic behaviors. Their results indicate that there was good validation between theoretical and experimental results. Moreover, the coefficient of friction has a significant role on setting time values. In the present work, a set of experimental tests are conducted to formulate the mathematical equations to relate the coefficient of friction with sliding speed and normal force for wedge and conventional disc brakes. Then, Matlab Simulink models are created for wedge and conventional disc brakes to study their dynamic behaviors in terms of time and frequency responses. The main parameters of the evaluation are setting time that determines the

Amplifier Load cell Rotor AC Motor

gearbox 1

gearbox 2

Wed dge

Abutm ment

Brake pad

Wedge inclination α Fig. 2. Brake dynamometer test setup and measurement instrumentation.

and Hartmann et al. [13]. In any case, all the innovations that are introduced depend mainly on the providence of the disc brake with an electromechanical system as well as to apply the selfamplification in the disc brake, [14]. Many design forms of wedge disc brake were introduced to increase the brake effectiveness by changing its configuration. For example, an adaptive wedge disc brake is presented by Roberts et al. [15] which is provided by a variable wedge angle to maintain the brake shoe factor at constant and high values. In the last few years, many designs of wedge disc brakes were presented but until now they are still in the research stage. These designs are still at an early development stage and requires further investigation, [9,16]. Most of the previous studies used brake dynamometers to evaluate the brake performance. The brake dynamometer is the most famous mechanism that has been widely used to study the influence of different operational conditions mainly for good understanding of the brake system characteristics during braking process and at the same to present the better solutions, [17,18]. It is important to investigate the dynamic characteristic of vehicle’s brake. For example, C´irovic´, and Aleksendric´ [19] have presented a study aimed to investigate the thermal and mechanical behaviors of disc brake using finite element analysis. Their results

Table 1 Conventional and wedge disc brakes parameters. Parameters

Symbol

Value

Piston arm mass, kg Piston arm stiffness, N/m Piston arm damping coeff., Ns/m Brake pad mass, kg (Wedge and brake pad) mass, kg Brake pad damping coeff., Ns/m Brake pad stiffness, N/m Bearing mass, kg Bearing damping coeff., Ns/m Bearing stiffness, N/m

ma ka ca mp mw cp kp mb cbx and cby kbx and kby

0.033 107 116 0.2 0.2 89 106 0.2 282 107

Fig. 4. Coefficient of friction variations with normal force.

Fig. 5. Coefficient of friction variations with sliding speed.

Fig. 3. Disc brake mathematical models (a- conventional b-wedge).



frequency response of the system to avoid the brake noise generation. The effect of coefficient of friction, wedge angle, normal force and sliding speed on wedge and conventional disc brake dynamic behaviors have been investigated.

2. Experimental setup The test rig, as shown in Fig. 1, is designed to provide the brake system with the simulated mechanical power. Disc revolution and

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motor power as well as applied force are the main system input signals. While the brake force and coefficient of friction between disc and pads are the output signals to data acquisition system. The test rig is divided into driving unit, braking unit and measurement facilities. An electromechanical actuator is used to generate the required applied force. The braking force as required output is measured using load cell. The wedge inclination angle is maintained at 30°. The input and output data are collected by fourchannel data acquisition system. The driving unit consists of an 18.56 kW AC motor operating at 1500 rpm, that rotates the driving

Fig. 6. Linear analysis of wedge disc brake shoe factor with wedge inclination angle variations (a: step response b: frequency response).

Fig. 7. Linear analysis of conventional disc brake shoe factor with coefficient of friction variations (a: step response b: frequency response).


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shaft at different rotating speeds. The braking unit comprises the new wedge disc brake assembly, as shown in Fig. 2. The instruments for measurement include rotational speed (tachometer), applied pressure (a pressure gauge) and tangential force (load cell). 3. Wedge disc brake modelling Two Matlab Simulink models for conventional and wedge disc brakes are designed according to the following mathematical equa-

tions. Fig. 3 show the mathematical models for conventional and wedge disc brakes. All parameters used in these models such as brake pad mass, brake pad stiffness. . .etc., have the same values for both conventional and wedge disc brakes. Table 1 shows the operating parameters used in the conventional and wedge disc brake models. First, for conventional disc brake, the equations of motion can be expressed as follow:-

ma €xa þ ca ðx_ a x_ p Þ þ ka ðxa xp Þ ¼ F app

ð1Þ

Fig. 8. Linear analysis of wedge disc brake shoe factor with coefficient of friction variations (a: step response b: frequency response).

Fig. 9. Linear analysis of conventional disc brake shoe factor with sliding speed variations (a: step response b: frequency response).



mp €xp ca ðx_ a x_ p Þ ka ðxa xp Þ þ cp x_ p þ kp xp ¼ 0 cp x_ p þ kp xp ¼

R

ð2Þ ð3Þ

l

Second, for wedge disc brake, the equations of motion can be expressed as follow:-

ma €x1 þ ca ðx_ 1 x_ 2 Þ þ ka ðx1 x2 Þ ¼ F app

ð4Þ

mb €x2 ca ðx_ 1 x_ 2 Þ ka ðx1 x2 Þ þ cbx x_ 2 þ kbx x2 ¼ 0

ð5Þ

€1 þ cby ðy_ 1 y_ 2 Þ þ kby ðy1 y2 Þ ¼ 0 mb y

ð6Þ

€2 cby ðy_ 1 y_ 2 Þ kby ðy1 y2 Þ þ cp y_ 2 þ kp y2 ¼ 0 mw y

ð7Þ

cp y_ 2 þ kp y2 ¼

R

ð8Þ

l

4. Results and discussions The effect of normal force on the coefficient of friction for wedge and conventional disc brake at 1 m/s sliding speed is shown in Fig. 4. From this Figure it can be noticed that the higher the normal force, the slightly lower is the coefficient of friction for both brake types. These results are in agreement with Blau and McLaughlin [18] who have also established that with low contact pressure, the chemistry of the contact areas plays key role in the variations of the coefficient of friction. With high normal force,

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many factors can be affected by many parameters such as surface softening by friction heating, increased blowing in the softer materials, and enhanced heat transfer and oxide film formation. The experimental results could be expressed with an acceptable error as follow:

l ¼ lo 0:00033F N 0:00031F 2N

ð9Þ

where l is the coefficient of fiction, lo is the static friction coefficient and FN is normal force in N. Fig. 5 shows the effect of sliding speed on the friction coefficient of wedge and conventional disc brakes. As it can be seen from the current work results that sliding speed increases with the decreases of coefficient of friction for both types. These results are in agreement with many researchers such as [9,5]. At high sliding speed, friction coefficient is influenced by the heat generated which is proportionally increased with increase of sliding speed and oxide film formation. It is difficult to identify which parameter plays the main role on the coefficient of friction variations. The experimental results could be represented with an acceptable error as follow:

l ¼ l0 0:1v þ 0:009v 2

ð10Þ

where v is sliding speed in m/s. Figs. 6a and b illustrate the brake shoe factor C⁄ of wedge disc brake as time and frequency response with different wedge angles. As the wedge angle a decreases the brake shoe factor C⁄ increases. The high value of brake shoe factor is characterized by a delay in setting time of as high as about 0.8 s at an inclination angle of

Fig. 10. Linear analysis of wedge disc brake shoe factor with sliding speed variations (a: step response b: frequency response).


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Fig. 11. Linear analysis of conventional disc brake shoe factor with normal force variations (a: step response b: frequency response).

Fig. 12. Linear analysis of wedge disc brake shoe factor with normal force variations (a: step response b: frequency response).



30°. On the other hand, the resonance frequency is strongly influenced by the wedge inclination angle. Change in the wedge angle from 30° to 60° leads to a decrease in the resonance frequency from 105 to 80 Hz. It can be observed that the resonance frequency values are low which means it is more likely due to the vibrations and noise occurrence. These results could be attributed to wedge disc brake configuration, which has four degrees of freedom as compared to two in the case of conventional disc brake. this caused the delayed in response of the system and as a result, the resonance frequency decreases. Also, the high sensitivity of wedge disc brake to the inclination angle and coefficient of friction leads to extreme vulnerability in the dynamic characteristics as also concluded by [17,15]. The effect of the coefficient of friction on the conventional disc brake shoe factor as step time and frequency response is shown in Fig. 7a and b respectively. The dynamic value of brake shoe factor was affected by the coefficient of friction such that it increases with increase of coefficient of friction the brake shoe factor also increases. However, there is no effect on step time or frequency response with the change in friction coefficient. On the other hand, the effect of friction coefficient on shoe factor of wedge disc brake as step time and frequency response is shown in Fig. 8a and b respectively. It can be noticed that brake shoe factor increases significantly as the friction coefficient increases from 0.3 to 0.5. However, the higher the value of coefficient of friction delays the setting time and the lowers the resonance frequency Increase in friction coefficient from 0.3 to 0.5 is accompanied with a reduction of the resonance frequency from about 83 to 40 Hz and an increase of transient time from about 0.2 to 1.2 s. By comparing these results with conventional disc brake, the transient time of conventional disc brake is much less than the wedge one for the same friction coefficient value. Therefore, the resonance frequency of conventional disc brake is much more than the wedge disc brake system. The effect of sliding speed on conventional and wedge disc brake shoe factors are shown in Figs. 9 and 10 respectively. From these figures, it can be seen that brake shoe factor decreases with the increase in sliding speed for both brake types. But still, the conventional disc brake is less sensitive than wedge disc brake to sliding speed variations. The response time and resonance frequency of conventional disc brake aren’t being affected by the variations of sliding speed. While, the response time and resonance frequency are greatly influenced by the change in sliding speed. In other words, the resonance frequency remains the same for conventional disc brake and increases markedly with the increase in sliding speed. The resonance frequency of wedge disc brake increases from about 65 to 84 Hz when the sliding speed is increased from 1 to 5 m/s. But, the resonance frequency of conventional disc brake remains constant at about 220 Hz with the same sliding speed variations. This means that not only the resonance frequency of wedge disc brake is affected by sliding speed variations but also it was lower than the case of conventional disc brake. These findings are in agreement with the results of [5,21,9]. For brake pads materials, the friction at the start is low and remains at its initial value for some time and the factor mainly responsible for this low friction phenomenon is the presence of a layer of foreign material between brake pad and disc. The effect of normal force on the step and frequency responses for conventional and wedge disc brakes is shown in Figs. 11 and 12 respectively. From these figures, it can be concluded that there is no big difference between the effect of sliding speed and normal force except that the normal force is less effective on brake shoe factor C⁄. Change of normal force has no effect on the step or the

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frequency responses of conventional disc brake. However, in the case of wedge disc brake, it appears that there is a noticeable but small effect of normal force on step and frequency responses. By increasing the normal force from 400 to 2000 N, the setting time decreases from 0.9 to 0.7 s and the resonance frequency increases from about 55 to 63 Hz. These results are in agreement with the results of [22]. This may be attributed to the fact that the strength of these materials is greater at higher shear strain rates which results in a lower real area of contact and a lower coefficient of friction in dry contact conditions. 5. Conclusion Series of the experimental tests were carried out to investigate the effect of sliding speed and normal force on the coefficient of friction between brake pad and disc. The coefficient of friction has a considerable effect on disc brakes dynamics; however, this effect was more noticeable with wedge disc brake mechanism as compared to the conventional disc brake system. Wedge disc brake shoe factor response is very late as compared to the conventional disc brake and the delay increases with the increase of the coefficient of friction and the decrease of wedge inclination angle. On the other hand, the wedge disc brake pad resonance frequency strongly decreases compared to that of conventional disc brake pad that has the same properties. This decrease is magnified as the coefficient of friction increases or the wedge inclination angle decreases. The normal force has relatively little effect on wedge disc brake dynamics and has a negligible effect on classical disc brake dynamics. The sliding speed has a considerable effect on disc brake dynamics; however, it affects more in the case of wedge disc brake. References [1] Talati F, Jalalifar S. Analysis of heat conduction in a disk brake system. Heat Mass Transfer 2009;45:1047–59. [2] Mostafa MM, Gawwad KA, Mahmoud KR, et al. Optimization of operation parameters on a novel wedge disc brake by Taguchi method. Am J Vehicle Des 2013;1(2):21–4. [3] Balogh L, Stréli T, Németh H, et al. Modelling and simulating of self-energizing brake system Vehicle System Dynamics. Int J Vehicle Mech Mob 2006;44:368–77. [4] Mostafa MM, Nouby, M.G., Gawwad, K. A. A. E., et al. A preliminary experimental investigation of a new wedge disc brake. Int. J. Eng Research and Applications.; 3(6): p. 735–744. [5] Blau PJ. Friction science and technology. New York: Dekker Mechanical Engineering; 1995. [6] Eriksson M, Bergman F, Jacobson S. Surface characterisation of brake pads after running under silent and squealing conditions. Wear 1999;232:163–7. [7] Eriksson M, Bergman F, Jacobson S. On the nature of tribological contact in automotive brakes. Wear 2002;252:26–36. [8] Durali L. A new self-contained electro-hydraulic brake system waterloo. University of Waterloo; 2015. [9] Mahmoud KRM. Theoretical and experimental investigations on a new adaptive duo servo drum brake with high and constant brake shoe factor. Paderborn: University of Paderborn; 2005. [10] Liermann M. Self-energizing electro hydraulic brake aachen: RheinischWestfaelischen Technischen Hochschule Aachen; 2008. [11] Mitschke M, Sellschopp J, Braun H. Regelung der Bremsen an Kraftfahrzeugen. unterkritischen Bereich VDI-Verlag GmbH. Düsseldorf; 1995. [12] Dietrich J, Gombert B, Grebenstein M, inventors; Dietrich J, Gombert B, Grebenstein, M. Elektromechanische Bremse mit Selbstverstärkung. Germany patent DE 198 19 564 C2; 2000. [13] Hartmann H, Schautt M, Pascucci A, et al. The mechatronic wedge brake. SAE; 2002. 2002-01-2582. [14] Yu L et al. Magnetorheological and wedge mechanism-based brake-by-wire sys-tem with self-energizing and self-powered capability by brake energy harvesting. IEEE/ASME Trans Mechatron 2016;21(5):2568–80. [15] Roberts R, Schautt M, Hartmann H, et al. Modelling and validation of the mechatronic wedge disc brake. SAE; 2003. [16] Ghazaly NM, Makrahy MM, Gwwad KAAE, et al. Experimental evaluation of an empirical model for wedge disc brake using box-behnken design. Int J Vehicle Struct Syst 2014;6(3):58–63.


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