International Conerence on Applied Science and Engineering Innovation (ASEI 5) Simulation Optimization Design on Vehicle Disk Brake Pengei Duan, a Dept. o Equipment Support, Bengbu Automobile NCO Academy, Bengbu, China a duanpengei@sina.com Keywords: Disk brake, Optimization design, Simulation Abstract. The braking perormance is one o the most important active saety perormances o vehicle, which plays a key role in the traic saety. It is necessary to research on braking eiciency and it becomes a hotspot to express the braking perormance scientiically and rationally. To improve braking capability and eiciency o vehicle disk brake, a multi-objective optimization model with the lowest braking temperature and the largest braking torque as the objective unction was proposed. The model was on the basis o property indexes and restraints needed or disk brake designing. The example to veriy its itness was provided and Genetic Algorithm (GA) in Matlab optimization toolbox was used or solving ideal result. Introduction Design o vehicle disk brake should be considered comprehensively and optimized to avoid brake deterioration caused by temperature rising in the practical application process. Disk brake is widely used in engineering machinery and various automobiles or its advantages o simple and compact structure, braking capability, good thermal and water stabilities. Given the same braking torque, disk brake is smaller in size and weight than drum brake. According to related materials, the accidents caused by brake system ailure accounted or 45% in that caused by problems o vehicle itsel. Furthermore, long braking distance and brake slip oten leads to atal accidents in the emergency braking, which indicates key role o rake to ensure mechanical device security. The vehicle braking system aims at grasping vehicle start and stop, controlling speed, dealing with incidents and maintaining vehicle in accordance with needs o drivers. Its high quality and excellent perormance are important guarantee or vehicle saety. Thus, all newly designed or modiied vehicles should carry out brake perormance tests. It is o signiicance to improve vehicle braking perormance, design and manuacture level, which has increasingly become an important topic in the ield o vehicle researches [-]. The existing researches just uses the shortest braking time and the thinnest braking disc as the objective unction, but the weighting actors o sub-objectives not been normalized, resulting in the dierences in magnitudes o sub-objectives and in turn aects the optimization. It will lead to bad braking eect because o the heat o riction plate, and even the brake disc will crack taking the shortest braking time as objective unction but not take the rising temperature o brake into account in practical applications. To improve braking capability and eiciency o disk brake, a multi-objective optimization model with the lowest braking temperature and the largest braking torque as the objective unction is designed in this research, which is based on the analysis o property index and restraint that designing a disk brake requires, then genetic algorithms o MATLAB optimization toolbox are used or optimization solution so as to arrive at good results. The paper is organized as ollows: section provides related works; section mainly perorm mathematic calculation related to disk brake design; section 4 proposes the optimization design model; section 5 gives design example; section 6 concludes our work. elated Works 5. The authors - Published by Atlantis Press 89
The development o vehicle braking technology is always around the basic unction and security perormance o braking system. It is o importance to research brake and its perormance targeting at developing new mode with low cost and high repetition utilization. Traditional design methods need large amount o test and repeated changes, so it is extremely diicult or product development. With the continuous development o simulation technology in recent years, the new development mode that analyze brake system perormance with various modeling methods attracted more and more attention. Qin et al carried on multi-objective uzzy optimization design on disc brakes on the car [4]. Ding et al addressed to uzzy optimization design on disk brake o construction machinery [5]. The simulation methods to analyze braking process mainly based on heat conversion in the automobile braking process. The brake model was established with in Matlab/Simulink. The obtained brake distance was compared with known data to arrive at good result. The ABS combined simulation model is constructed which consists o ABS mechanical dynamics model or cars simulation using ADAMS sotware and ABS control simulation model using Matlab/Simulink. sotware.the thresholds o ABS regulated parameters are determined using Matlab sotware [6]. The Matlab and ADAMS were also utilized or co-simulation to establish integrated mechatronic system model, so as to complete brake perormance simulation test in the virtual environment and arrived at good result [7]. The co-simulation technology was used or uzzy control o semi-active suspension system, namely damping-adjustable shock absorber model is built with EASYS sotware, and mechanism model o suspension system is built with ADAMS sotware and control model based on uzzy arithmetic is built with Matlab sotware, so as to reduce vehicle vibration and improve vehicle ride comort characteristics. The paper mainly emphasizes on perormance computation and optimization o disk brake. Disk Brake Design Calculation Brake torque calculation. In calculation, it is considered that riction surace o pads get in touch with brake disc, and that unit pressure p is evenly distributed, as shown in the Fig.. θ α θ Fig. Brake torque calculation o disc brake Take an area o dα d rom riction surace o pads as rectangular ininitesimal. The resulting brake torque or brake disc center is dm = pdαd, is the riction actor between riction pads and brake disc. Obviously, brake torque o riction pad on one side or brake disc center is M θ = p d d p( ) α = θ θ,, are the inner and outer radius o brake pad; θ is a hal o the corner o brake pad. So, the total brake torque o disk brake M is: 4 M = p( ) θ. () 9
Set liquid pressure o the brake cylinder as p, so the unit pressure p between riction surace o brake pad and brake disc contact area is: pa = p p d, () 4 d is the role diameter o brake cylinder piston; A is the eective area o riction pad on one side, θ A= π ( ) = θ ( ). π Take the above equation into (), and the unit pressure p between riction surace o and brake disc contact area is: p d p = P. () θ ( ) Take () into (), so the brake torque that two sides o riction pads produce is p ( ) ( ) ( ) ( ) ( ) ( ) M = p d = d p. (4) 4 6 Set e = p as the eective radius o disc brake. Wear characteristics calculation. The working process o riction type o brake can be understood as a process o converting mechanic energy into heat energy. Most o the kinetic energy o automobile is consumed by brake within a short time, while the rest o the kinetic energy can be consumed by resistance rom tire rolling and air. So brake is heated up, which is called energy load o brake. Energy load o brake is usually evaluated by using speciic energy dissipation rate that physically means the energy consumed by unit area o riction plate in unit o time with the international unit o β δ mv W / m. The speciic energy dissipation rate o single ront wheel brake is deined as e =. ta Where, β is the distribution ration o ront and rear braking orce; δ m is the total vehicle mass including conversion rotating mass; A is the aected area o ront wheel riction pad; t is braking duration. When strong braking in an emergency happens, braking deceleration j is taken as constant, v v t = ; setting j as.6g. j The speciic energy dissipation rate o disk brake is much bigger than drum brake, but it is better not to exceed 6 W / mm. Otherwise, riction pad will be worn more quickly, and brake disc will also crack. Unit pressure calculation. To guarantee that riction pad is resistant to wearing and can be used or a long time, the unit pressure between riction pad and brake disc must be limited within a certain range. Set the normal pressure that one side riction pad o ront brake gets as N, and unit pressure p is N evenly distributed. So p =, total brake torque o ront brake (two riction pads) is M = Ne. A Meanwhile, the ground brake orce o ront axle has the relation: = β mj, So, r β mjr p = < [ p] =Mpa. ea Heat capacity and temperature increase calculation. The working process o riction type o brake can be understood as a process o converting mechanic energy into heat energy. Most o the kinetic energy o automobile is consumed by brake within a short time, while the rest o the kinetic energy can be consumed by resistance rom tire rolling and air. So brake is heated up, which is called M 9
energy load o brake. In engineering, α can be used to express the proportion o kinetic energy that brake absorbs in the process, with α set as.9~.9. Friction pad is usually made o non-metallic materials, so it has a poor property in heat conduction. Much o the heat is absorbed by metal brake disc. The more energy load o brake, the more seriously riction plate is worn. Thereore, the heat capacity and temperature increase o brake must be calculated. According to the theory o conservation o energy, kinetic energy beore braking is E = mv. Temperature increase o checking brake disc is cm d d t> α E. In this ormula, c d is the speciic heat capacity o brake disc metal material, taking 48 J ( kg K) o cast iron, 88 J ( kg K) o aluminum. The md is the weight o brake disc; v is the speed o brake disc; t is the temperature increase o brake disc. Usually, braking should be completed when the initial velocity o braking reaches km/h, with the temperature increase not more than 5 degrees Celsius. It is diicult to calculate the weight o brake disc at the beginning o design, so it can be seen as regularly shaped discoid parts. The weight o brake disc m d can be calculated approximately as md = ρd πdb. In this ormula, ρd is the density 4 o brake disc material, set as 75kg/ m ; D is the outer diameter o brake disc and b is the thickness o brake disc. Optimization Model Establishment Objective unction. Brake torque is the key target parameter to the unction o brake. Thereore, in much o the research literature, biggest brake torque is set as optimization objective unction. According to engineering experience, special attention should be paid to the controlling o temperature increase o brake disc while considering the biggest brake torque. Otherwise, the service time o brake will be greatly reduced. In this paper, biggest brake torque and smallest temperature increase o brake disc are set as objective unction to achieve optimization. Based on the above theoretical analysis, to get the biggest brake torque total brake torque o a disc brake is: ( ) max M = max p d p. (5) 6 ( ) To get the smallest temperature increase o brake, we can get the ollowing result rom cm d d t= α E: α E α ( mv ) min t = = min. (6) cm d d cm d d The two objective unctions belong to two dierent classes, getting the biggest or the ormer but the smallest or the latter. Thus, multiplication and division can be used to make a balance: ( ) M min obj x = min t. (7) Designing variable. Ater studying structures and property parameters related to disc brake, set the ollowing seven parameters as designing variables. X = [ x x x x4 x5 x6 x7] = [ D b d p θ ] (8) The D is the outer diameter o brake disc; b is the thickness o brake disc; d is the diameter o brake cylinder; p is oil pressure; is the inner diameter o riction pad; is outer diameter o riction pad; θ is the central angle o riction pad. Constraint unction. The constraint on properties includes the ollowing parts. The irst is constraint on unit pressure between riction pad and brake disc. The second one is constraint on temperature increase o brake. The last one is constraint on speciic energy dissipation rate. 9
Above three constraints will not be discussed at length, since detailed derivation about them has already been made in the above analysis. The constraint on brake torque: in order to prevent wheel lock, braking orce should be smaller than traction on ground. For example: λt < mmgβ r (9) The constraint on brake oil pressure: the highest oil pressure o hydraulic brake lines is generally not more than Mpa. p < p () [ ] The constraint on structural parameters o disc brake: D<.78D h ; D +. < ; +.4 < ; Dg.7.6 < <. Optimization Design Example Set D h =.6, Dg =.m, v = km / h, λ =.6, r =.47m, e= 6 W / m, µ =.66, =.7, ρ = 7499 kg / m. The initial values o design variables o disc brake structure and properties are shown in the Table. Table The initial values o design variables o disc brake structure and properties D b d ρ θ.64m.4m.55m.mpa.6m.5m 6 According to the theoretical analysis, the optimizer can be written. We can get the ollowing results i the main unction optimization is operated. Disc brake torque beore optimization is 8.7 N m; Brake disc weight beore optimization is 5.68 kg; Disc brake torque ater optimization is 7.58 N m; Brake disc weight ater optimization is 5.5kg. As can be seen rom Table, by optimizing the design, under the conditions o ensuring small temperature rise while braking strongly, disc brake torque increases to a certain extent, the weight o the brake drops at the same time, reducing the overall weight o the brake, achieving the purpose o optimization. Table The optimized contrast values o design variables o disc brake θ Brake torque Parameters D b d ρ Initial values.64m.4m.55m.mpa.6m.5m 6 8.7N m Optimized values.58m.m.5m.5mpa.86m.m 5. 7.58N m Conclusion Aiming at the problem o existing brake optimization design that using shortest braking time and minimum thickness but not plan weight coeicient o sub-objective, the paper established multi-objective optimization model to arrive at minimum brake temperature rising and maximum brake torque. Simulation example showed that it can achieve ideal optimization result. As the disk brake is a complex integrated hydraulic and mechanical dynamics, there are many actors aecting brake eectiveness. Some parameters directly or indirectly aect system result and the impact is 9
mutual. Thereore, its structure and mechanism should be thoroughly researched and discussed. The parameters should also be determined to establish more accurate model, which will be our next research ocus in the uture. eerences [] Peijiang Chen, Study on vehicle braking perormance detection system, Proceedings o IEEE Fith International Conerence on Advanced Computational Intelligence (ICACI),, pp. 9-. [] Lu Yinding, He Wenhua, Hou Mingyang, Yao Jiansong, Emulation and Experimental Study o Drum Dynamometer or Simulating the Vehicle's oad Braking, Proceedings o Third International Conerence on Measuring Technology and Mechatronics Automation (ICMTMA),, pp. 7-4. [] Zhang Xiaolong, Peng Jiankun, Xia Ping, Design o roadway test system or motor vehicle brake perormance and its evaluation methods, Proceedings o International Conerence on Computer, Mechatronics, Control and Electronic Engineering (CMCE),, pp. 9-95. [4] Qing Liyi, Xu Degang, Multiple objective optimized design or disc brake, Machine Design and Manuacturing Engineering, vol. 5,, pp. 7-8. [5] Ding Weidong, Liu Ming, Zhong Bingdi, Fuzzy optimal design or disk brake on construction machines, Construction Machinery and Equipment, Computer Simulation, vol.,, pp. 9-. [6] Song Ming, Liu Zhaodu, Liang Pengxiao, Co-simulation o ABS or cars in ADAMS and SIMULINK, Computer Simulation, Vol., no., 4, pp. 6-66. [7] Feng Jihe, Sun Wei, Ma Weibiao, Hu Yunhua, Application o Co-simulation technique in Fuzzy Control o vehicle semi-active suspension system, Journal o Academy o Armored Force Engineering, vol., no., 7, pp. 4-44. 94