盘式制动器外文参考文献
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中英文对照外文翻译文献(文档含英文原文和中文翻译)外文:An Experimental Analysis of Brake Efficiency Using fourFluids in a Disc Brake SystemABSTRACTThe paper studies disc brake failure in Mini-buses using an experimental analysis to test the maximum braking force when different brake fluids such as clean, less dirty, dirty and soapy water solution were used in the braking system. The experimental results clearly showed that the soap solution appears to be the best fluid as far as low viscosity and stability of viscosity with increase in temperature are concerned. However, the soap solution is not compatible with other fluid which makes it difficult to be substitute as a clean brake fluid. The result of the Thepra Universal Brake Testing Equipment used for the braking efficiency test indicated that a pedal brake of 117 kN produce a brake force of 0.96 kN for clean brake fluid, 0.91 kN for the less dirty, 0.85 kN for dirty and 1.44 kN forsoap solution. The value of 1.44 kN which was achieved when the soap solution was used indicated a positive braking force and the indicating that soap solution could be used to produce a high pedal force within a very short time (about 10-30 min) and can therefore be used only in case of emergency. The brake efficiency test indicated that under hot conditions the braking efficiency is reduced and the presence of air in the system renders the braking ineffective because higher pedal force was needed to be able to produce a significant braking force which is noted for causing brake failure.Keywords: Brake fade, brake failure, disc brake, efficiency, pedal force INTRODUCTIONWhen a vehicle is accelerated, energy supplied by the engine causes the vehicle’s speed to increase. Part of this energy is instantly used up in overcoming frictional and tractive resistance but a large amount of it remains stored in the vehicle. According to Heinz (1999) this energy of motion is called the kinetic energy and the existence of kinetic energy is observed when a vehicle is moving and neutral gear is selected. The vehicle does not immediately come to rest; instead it travels for a considerable distance before it becomes stationary. In this case the stored energy is used to drive the vehicle against the resistances that oppose the vehicle’s motion. Relying on these r esistances to slow down a vehicle could cause many problems, so an additional resistance called a brake is needed to convert the kinetic energy to heat energy at a faster rate in order to reduce the speed of the vehicle Mcphee and Johnson (2007). This reduces the speed of the vehicle at a faster rate and brings the vehicle to rest within the shortest possibletime when the brakes are applied.From the point of view of Johnson et al. (2003) most automotive systems in use today utilize front disc brakes, but four-wheel disc systems are also common In disc brakes, the rotor rotates with the wheel and the pads move out to rub the rotor when the brakes are applied. Most disc brakes use floating calipers. The caliper slides in and out as the brakes are applied and released. The piston moves the inside pad out and pushes the outside pad into the rotor by sliding the caliper back toward the rotor.The use of disc brakes to reduce speed or bring the vehicle to rest when in motion cannot be over emphasized if the safety of the occupant is to be guaranteed Heinz (1999). To bring a vehicle to a stop, the disc brakes have to absorb all the energy given to thevehicle by the engine and that due to the momentum of the vehicle. This energy must then be dissipated. In most vehicle disc brakes, the energy is absorbed by friction, converted into heat and the heat dissipated to the surrounding air (Thoms, 1988). As the energy is absorbed, the vehicle is slowed down; in other words, its motion is retarded. The brakes must also pull up the vehicle smoothly and in a straight line to bring the vehicle to a stop position.It is therefore very important that the disc brakes of vehicles operate with the highest efficiency. This couldreduce the rate of accidents due to brake failure so that life and property could be preserved and also to ensure that occupants of these commercial vehicles go about their normal lives without any fear of being involved in an accident. Available crash data in Ghana suggests that about 1,900 persons are killed annually in road traffic crashes (Afukaar et al., 2008) and that more than 40% of the road traffic fatalities are occupants of cars, buses and trucks. Most often than not, some of the road accidents involving commercial vehicles, such as the mini-buses have been attributed to the failure of the disc brakes. The reason for testing the viscosity of these brake fluids, especially that of the soap solution was as a result of the practice of most Ghanaian drivers sometimes using the soapy solution as a substitute to the original brake fluid in the braking system and also using dirty brake fluid which has been used for bleeding purposes. The main objective of this study which is part of a larger work seeks to investigate and establish the reasons for the disc brake failure due to brake fluid also check the efficiency of the four different types of fluids used in the transmission of braking forces. The study looked at the maximum braking force when using clean, less dirty, dirty and soapy water solution in the braking system. It also looked at the braking force when the braking system is with or without servo unit and operating under cold or hot condition with air or without air in the braking systemDISC BRAKESThe disc brake consists of an exposed disc which is attached to the hub flange; the two friction pads arepressed on to this disc to give a braking action. Figure 1a, shows the disk brake system of a car and pad that is separated from wheel assembly to better shows the disk and the pad in sliding contact. As it can be seen, typical disk brake system and caliper assembly of a solid disk brake rotor is completely noticeable. Figure 1b shows schematic form of the disk and the pad in sliding contact assembly.(a) (b)Fig. 1: Disc brakeThe pads are moved by hydraulic pistons working in cylinders formed in a caliper that is secured to a fixed part of the axle. When the hydraulic pressure is applied to the two cylinders held in the fixed caliper, the pistons move; this action forces the friction pads into contact with the rotating cast iron disc. The sandwiching action of the pads on the disc gives a retarding action and heat generated from the energy of motion is conducted to the disc.Greater part of the disc is exposed to the air; therefore heat is easily radiated, with the result that the brake can be used continuously for long periods before serious fade occurs. Since the friction pads move at a right angle to the disc, any drop in the friction value does not affect the force applied to the pad. As a result this type of brake is not less sensitive to heat (Mudd, 1972). The disc brake was developed to minimize the fade problems. When fading occurs, the driver has to apply a much larger effort and in extreme cases it becomes impossible to bring the vehicle to rest. No assistance is obtained from the rotating disc to aid the driver in the application of a disc brake to achieve a given retardation. A disc brake requires a greater pedal pressure and toachieve this pressure required the hydraulic braking system using a good quality brake fluid in its operation.The fluid used in the hydraulic braking systems is a vegetable oil with certain additives. According to Nunney et al. (1998) a good brake fluid should have the following requirements, low viscosity, high boiling point, compatibility with rubber components, lubricating properties, resistance to chemical ageing and compatibility with other fluids. However, mostGhanaian drivers sometimes used other fluid such as dirty brake fluid, less dirty fluid and even soapy water sometimes as a substituted to the original brake fluid. This study among other things will also investigate which of these brake fluid, clean, dirty, less dirty and soapy water will have the best viscosity, high boiling point and less braking force.MATERIALS AND METHODSThe design used for this study was experiment which employed the used of viscometer and Thepra Universal Automotive Brake Testing machine to check the efficiency of the four fluids in the transmission of braking forces.Laboratory analysis: The viscosity tests on the four different liquids were carried out at the Kwame Nkrumah University of Science and Technology (KNUST) Thermodynamics laboratory. The liquids were clean brake fluid, less dirty brake fluid, dirty brake fluid and soap solution. It was necessary to find out how the viscosity of different qualities of brake fluid affected braking efficiency and to find out whether there was any correlation between these and the occurrence of brake failure.Viscosity test on the various fluids used: The viscosity test was carried out on a Redwood Viscometer in Fig. 2 on the four different kinds of fluids to determine their viscosities. The apparatus consists of a vertical cylinder containing the fluid under test which was allowed to flow through a calibrated orifice situated at the centre of the cylinder base. The orifice is closed by a ball valve when it is not being used.Fig. 2: Redwood viscometer used to determine the viscosity of the fluidsThe oil cylinder is surrounded by a water jacket which maintains the lubricant under test at a required temperature by means of a Bunsen burner flame applied to the heating tube. The thermometer for the water in the jacket is mounted in a paddle-type stirrer which can be rotated by hand, using the handle (Zammit, 1987).Procedure for testing various viscosities of the fluids: To test the viscosity of a fluid, the water jacket was filled with water with the orifice ball valve in position. Fluid was poured into the cylinder to the level of the pointer. A 50 mL measuring flask was placed centrally under the orifice. The water was stirred gently until the water and fluid thermometers were the same (room temperature, 30ºC). Thetemperature was recorded. The ball valve was then raised and a stopwatch used to record the time (in seconds) for a 50 mL of fluid to flow into the measuring flask. The test was repeated with the fluid temperatures increasing by 10ºC each time up to 90ºC. All the data for the four differentfluids were recorded as shown in Table 1Thepra universal stand automotive brake testing equipment:The ThepraUniversal Stand Automotive brake testing equipment is structured in such a way that the driven part, such as brake disc, was plugged on to the motor shaft. The brake anchor plate and the caliper are fastened to a flange via a linkage of bar which is connected to the flange. The brake force is measured and displayed on a digital indicator. The individualunits are plugged into the two span-frames which are fastened to both sides. All the brake components used in the testing equipment are original vehicle components. The pedalforce is measured at the actuating linkage of the brake master cylinder and displayed on a digital indicator (Technolab, 2009)RESULTS AND DISCUSSIONExperimental results of viscosity test: Table 1 present the results of viscosity test inan experiment for the four fluids, using the Redwood Viscometer.From the test results obtained using Redwood viscometer, Viscosity-Temperature graphs for the fluids were plotted. Figure 3 shows the plot of viscosity againsttemperature of the four fluids.Table 1: Viscosity testValues of the various viscosities werecalculated using the formula:V = hfρgD232hfvwhere,V : The Viscosityhf : The capillary heightρ : The density of the fluidg : Acceleration due to gravityD : The diameter of the orificev : The velocity (Bird et al., 1960) Fig. 3: Viscosity-temperature relationship of the fluidsFrom Fig. 3 the dirty fluid has the highest viscosity followed by the less dirty fluid, clean fluid and soap solution in that order. From the results shown in Fig. 2 and theviscosity test shown in Table 1, the soap solution appear to be the best fluid as far as lowviscosity and stability of viscosity with increase in temperature are concerned. However, it is less compatible with other fluids, difficult to mix easily with other brake fluids and has a low boiling point which will not make it suitable to be substitute as clean brake fluid (Nunney et al., 1998).The clean brake fluid is next as far as viscosity and stability of viscosity with increase in temperature are concerned. On the other hand, it satisfies all the other requirements of a good fluid for the braking system given in Table 1. According to Mudd (1972) and Nunney et al. (1998), a good brake fluid should have properties such as high boiling point, compatibility with rubber components, good lubrication properties, resistance to chemical ageing (long shelf life) and compatibility with other fluids. The less dirty fluid is very unstable as far as viscosity change with temperature increase is concerned. It is therefore not very reliable in a braking system since its behavior changes as the braking system heats up. The viscosity of the dirty fluid is stable with increase in temperature, however, it is very viscous (235-178 kgs/m3 in the temperature range 30 to 90ºC). It will therefore not be good and effective in brake force transmission. From these results and literature, it is obvious that the clean brake fluid is more suitable for the transmission of braking force as it’s possess all the good brake fluid qualities.Experimental results of the disc brake system:These sections present the results and discussion of the experiments using the four fluids in a Disc brake system under different conditions. Test results for hot and cold conditions of the Disc brake system using a servo system and without using a servo system were considered.Disc brake in cold condition with and without servo unit: The result in Table 2 clearly shows the pedal force and the brake force for clean, less dirty, dirty and soap solution when using disc brake in cold condition with servo unit with the Thepra Universal Brake Testing Equipment. A pedal brake of 117 kN produce a brake force of 0.96 kN for a clean brake fluid,Table 2: Results of disc brake in cold condition with servoTable 3: Results of disc brake in hot condition with servo0.91 kN for the less dirty, 0.85 kN for dirty and 1.44 kN for soap solution. Comparatively, a maximum brake force is achieved when the fluid is clean. When there is the presence of dirt,the brake force decreases and therefore more pedal force is needed to take up thewithout servoloss created by the dirt.Hence the greater the dirt, the greater thepedal force required.The value of 1.44kN which wasachieved when the soap solution wasused indicated a positive braking force compared with all the three fluids at the same pedal force. Subsequent pedal forces applied as shown in Table 2 gave a reduction in the brake force when soap solution was used. The implication was that soap solution could be used to produce a high pedal force within a very short time (about 10-30 min) and can therefore be used in case of emergency.From Table 2, it can be observed that for the same pedal force of 117 KN the soap solution transmitted the highest amount of brake force followed by the clean fluid, less dirty fluid and dirty fluid in that order. This implies that in cold condition using servo, the soap solution performs best followed by the clean, less dirty and dirty respectively.Disc brake in hot condition with servo unit: When the experiment was carried out using a disc brake under the hot conditions with the introduction of a servo, a pedal force of 120 kN gave a brake force of 0.95 kN for clean fluid, 0.90 kN for less dirty, 0.85 kN for a dirty fluid and 0.19 KN for soap solution. The result could be explain that, the clean brake fluid gave the highest brake force follow by less dirty, dirty and soap solution. It was observed that the soap solution perform poorly at this time recording a brake force of 0.19 KN as shown in Table 3.Disc brake in hot condition without servo: Figure 4 shows a plot of disc brake inhot condition without servo unit. It can be observed that, under hot conditions for the disc brake without servo, the trend is generally the same. The soap solution performed very badly compare with the other fluids, unlike its performance under cold conditions. This may be due to evaporation of the fluid making the fluid compressible; as if air was in the braking system. Generally, the clean fluid performed best in terms of transmission of brake force followed by the less dirty, dirty and soap solution in that order.Disc brake with air in system under cold condition: Braking force for this experiment was generally low as compared with the case when air was not trapped in the system as shown in Table 4. When the experiment was conducted with a pedal force of 165 kN, braking force ofTable 4: Results of disc brake with air in system under cold condition with servoFig. 5: Results of disc brake with air in system under hot condition with servo0.32 kN soap solution was obtained, for 0.37 KN for dirty, 0.28 KN for less dirty and 0.30 kN for clean fluid. This is in line with literature because according to Mudd (1972) the presence of air in the braking system makes the system ineffective since much of the drivers effort will be used to compress the air leaving very little for the brake application.Again, the soap solution did not give the least braking force because when the system is cold, soap solution is effective and its density is higher since there is nooccurrence of evaporation of the solution.Disc brake with air in system under hot condition: The Fig. 5 shows the plot of a graph indicating disc brake with air in the system under hot condition clearly shows that, when a pedal force of 152 kN was applied, a brake force of 1.11 kN was obtained for clean, 0.37 kN for less dirty, 0.28 kN for dirty and 0.26 kN for soap solution. It was observed that the maximum brake force was attained when the fluid was clean and on the introduction of dirty fluid, the brake force reduced drastically, though the pedal force was very high at 152 kN in the hot condition.Soap solution provides the least brake force because the air content in the system increases due to evaporation and hence the pedal force compresses air rather than transmitting power. As the system heats up, the air in the system expands thereby reducing the braking efficiency which results in brake failure.CONCLUSIONThe study was conducted using an experiment performed on a Thepra Brake Testing Equipment to check the efficiency of the four fluids in the transmission of braking forces. According tothe viscometer test shown that the soap solution appears to be the best fluid as far as low viscosity and stability of viscosity with increase in temperature is concerned. However, it is less compatible with other fluids, difficult to mix easily with other brake fluids and has a low boiling point which will not make it suitable to be substituted as a clean brake fluid.Again, when air is trapped in the braking system, which results in the brake fluid being compressible, higher pedal force was needed to be able to produce a significant braking force.Also, when brakes are operated under hot conditions its efficiency is reduced, a fault known as brake fade occurs as a result of the heating up of the brakes which creates less frictional resistance between rotating disc and the frictional pads.Finally, Soap solution when used at cold condition produces high braking force but becomes less effective after prolong use due to the presence of heat which evaporates the soap solution.REFERENCESAfukaar, F., K. Agyemang, W. Ackaah and I. Mosi, 2008. Road traffic crashes inGhana, statistics 2007. Consultancy Service Report for National Road SafetyCommission of Ghana.Bird, R., S. Wright and E.N. Light, 1960. Transport Phenomena, Gibrine Publishing Company,Heinz, H., 1999. Vehicle and Engine Technology. 2nd Edn.,Butterworth-Heinemann Publications, Nurumberg, pp: 235-291Johnson, D., B. Sperandei and R. Gilbert, 2003. Analysis of the flow through a vented automotive brake rotor. J. Fluids Eng., 125: 979-986.Mcphee, A.D. and D.A. Johnson, 2007. Experimental heat transfer and flow analysis of a vented brake rotor. Int. J. Thermal Sci., 47(4): 458-467.译文:一个使用四个液体系统分析盘式制动器的制动效率的实验摘要当车辆加速时能量由发动机提供使汽车的速度增加。
( 此文档为 word 格式,下载后您可任意编辑修改!)1.课题研究的目的及意义汽车的设计与生产涉及到许多领域,其独有的安全性、经济性、舒适性等众多指标,也对设计提出了更高的要求。
汽车制动系统是汽车行驶的一个重要主动安全系统,其性能的好坏对汽车的行驶安全有着重要影响。
随着汽车的形式速度和路面情况复杂程度的提高,更加需要高性能、长寿命的制动系统。
其性能的好坏对汽车的行驶安全有着重要影响,如果此系统不能正常工作,车上的驾驶员和乘客将会受到车祸的伤害。
汽车是现代交通工具中用得最多、最普遍、也是运用得最方便的交通工具。
汽车制动系统是汽车底盘上的一个重要系统,它是制约汽车运动的装置,而制动器又是制动系中直接作用制约汽车运动的一个关键装置,是汽车上最重要的安全件。
汽车的制动性能直接影响汽车的行驶安全性。
随着公路业的迅速发展和车流密度的日益增大,人们对安全性、可靠性的要求越来越高,为保证人身和车辆安全,必须为汽车配备十分可靠的制动系统。
车辆在形式过程中要频繁进行制动操作,由于制动性能的好坏直接关系到交通和人身安全,因此制动性能是车辆非常重要的性能之一,改善汽车的制动性能始终是汽车设计制造和使用部门的重要任务。
现代汽车普遍采用的摩擦式制动器的实际工作性能是整个制动系中最复杂、最不稳定的因素,因此改进制动器机构、解决制约其性能的突出问题具有非常重要的意义。
2.汽车制动器的国内外现状及发展趋势对制动器的早期研究侧重于试验研究其摩擦特性,随着用户对其制动性能和使用寿命要求的不断提高,有关其基础理论与应用方面的研究也在深入进行。
目前,汽车所用的制动器几乎都是摩擦式的,可分为鼓式和盘式两大类。
盘式制动器被普遍使用。
但由于为了提高其制动效能而必须加制动增力系统,使其造价较高,故低端车一般还是使用前盘后鼓式。
汽车制动过程实际上是一个能量转换过程,它把汽车行驶时产生的动能转换为热能。
高速行驶的汽车如果频繁使用制动器,制动器因摩擦会产生大量的热量,使制动器温度急剧升高,如果不能及时的为制动器散热,它的效率就会大大降低,影响制动性能,出现所谓的制动效能热衰退现象。
本科毕业设计SQR6468轻型客车前制动器设计某某某燕山大学2015年 6 月22日本科毕业设计SQR6468轻型客车前制动器设计学院:专业:车辆工程学生:某某某学号: 3指导教师:某某某答辩日期: 2015.6.22燕山大学毕业设计任务书摘要本文首先对汽车制动器原理和对各种各样的制动器进行分析,详细地阐述了各类制动器的结构,工作原理和优缺点.再根据轻型客车的车型和结构选择了适合的方案.根据市场上同系列车型的车大多数是滑钳盘式制动器,而且滑动钳式盘式制动器结构简单,性能居中,设计规,所以我选择滑动钳式盘式制动器.本文探讨的是一种结构简单的滑动钳式盘式制动器,对这种制动器的制动力,制动力分配系数,制动器因数等进行计算.对制动器的主要零件如制动盘、制动钳、支架、摩擦衬片、活塞等进行结构设计和设计计算,从而比较设计出一种比较精确的制动器.本文所采用的设计计算公式均来自参考资料。
本设计主要针对轻型客车前制动器设计,首先计算数据,完成二维装配图和二维零件图绘制,然后利用CATIA软件进行三维建模。
以更清楚的表达盘式制动器结构。
关键词盘式制动器;制动力;制动力分配系数;制动器因数;CATIA软件AbstractThis paper first principle of the car brake and brake on a wide range of analysis,a detailed exposition of the structure of various types of brake, and the advantages and disadvantages of working principle. Accordance with Minibus models and structure chosen for the program Under series models on the market with most of the cars leading trailing, and leading trailing simple structure, performance, middling, design specifications, so I chose to receive from the Sliding Disc brake. This paper is a simple structure recipients from the Disc brake, the brake system of this power, braking force distribution coefficient, such as brake factor calculation. brake on the main parts such as brake pan, brake caliper, bracket, friction linings, piston for structural design and design, design and comparison A more precise brake used in the design of this formula are calculated from the reference.This design mainly in view of the light bus front brake design, calculation data first, finish 2 d assembly drawing and 2 d part drawing, And then using CATIA software for 3 d modeling, to more clearly express the structure of disc brake.Key words Disc brakes;Power system;Power distribution coefficient systemBrake factor CATIA software目录摘要 (II)Abstract (II)第1章绪论 (1)1.1 课题背景 (1)1.2 研究目的及意义 (1)1.3 盘式制动器结构形式及其选择 (3)1.3.1 盘式制动器的结构形式 (3)1.3.2 盘式制动器的优缺点 (4)1.3.3 本设计盘式制动器的选择 (5)1.4 浮钳盘式制动器 (5)1.4.1 浮钳盘式制动器的结构 (5)1.4.2 浮钳盘式制动器的工作原理 (6)1.4.3 制动间隙调整原理 (7)1.5 本文研究容 (8)第2章制动系的主要参数及其选择 (9)2.1 任务书给定设计基本参数 (9)2.2 受力分析 (9)2.3 同步附着系数的确定及计算 (13)2.4 制动力、制动强度、附着系数利用率的计算 (15)2.4.1 满载时的情况 (15)2.4.2 空载的情况 (17)2.5 制动器最大制动力矩的计算 (19)2.6 本章小结 (19)第3章盘式制动器的结构设计 (20)3.1 盘式制动器结构设计的任务和步骤 (20)3.2 盘式制动器的主要零部件设计和三维造型 (20)3.2.1 制动盘 (21)3.2.2 制动衬块 (22)3.2.3 制动钳 (23)3.2.4 制动钳支架 (24)3.2.5 盘式制动器总成装配图 (26)3.3 本章小结 (26)第4章盘式制动器的校核计算 (27)4.1 摩擦衬块的磨损特性计算 (27)4.2制动器的热容量和温升的核算 (28)4.3 盘式制动器制动力矩的校核 (29)4.4 本章小结 (32)结论 (33)参考文献 (34)致 (36)附录1 (38)附录2 (364)附录3 (48)第1章绪论1.1 课题背景对制动器的早期研究侧重于试验研究其摩擦特性,随着用户对其制动性能和使用寿命要求的不断提高,有关其基础理论与应用方面的研究也在深入进行。
Frictionally excited thermoelastic instability in disc brakes—Transientproblem in the full contact regimeAbstractExceeding the critical sliding velocity in disc brakes can cause unwanted forming of hot spots, non-uniform distribution of contact pressure, vibration, and also, in many cases, permanent damage of the disc. Consequently, in the last decade, a great deal of consideration has been given to modeling methods of thermo elastic instability (TEI), which leads to these effects. Models based on the finite element method are also being developed in addition to the analytical approach. The analytical model of TEI development described in the paper by Lee and Barber [Frictionally excited thermo elastic instability in automotive disk brakes. ASME Journal of Tribology 1993;115:607–14] has been expanded in the presented work. Specific attention was given to the modification of their model, to catch the fact that the arc length of pads is less than the circumference of the disc, and to the development of temperature perturbation amplitude in the early stage of breaking, when pads are in the full contact with the disc. A way is proposed how to take into account both of the initial non-flatness of the disc friction surface and change of the perturbation shape inside the disc in the course of braking.Keywords: Thermo elastic instability; TEI; Disc brake; Hot spots1. IntroductionFormation of hot spots as well as non-uniform distribution of the contact pressure is an unwanted effect emerging in disc brakes in the course of braking or during engagement of a transmission clutch. If the sliding velocity is high enough, this effect can become unstable and can result in disc material damage, frictional vibration, wear, etc. Therefore, a lot of experimental effort is being spent to understand better this effect (cf. Refs.) or to model it in the most feasible fashion. Barber described the thermo elastic instability (TEI)as the cause of the phenomenon. Later Dow and Burton and Burton et al.introduced a mathematical model to establish critical sliding velocity for instability, where two thermo elastic half-planes are considered in contact along their common interface. It is in a work by Lee and Barber that the effect of the thickness was considered and that a model applicable for disc brakes was proposed. Lee and Barber’s model is made up with a metallic layer sliding between twohalf-planes of frictional material. Only recently a parametric analysis of TEI in disc brakes was made or TEI in multi-disc clutches and brakes was modeled. The evolution of hot spots amplitudes has been addressed in Refs. Using analytical approach or the effect of intermittent contact was considered. Finally, the finite element method was also applied to render the onset of TEI (see Ref.).The analysis of nonlinear transient behavior in the mode, when separated contact regions occur, is even accomplished in Ref. As in the case of other engineering problems of instability, it turns out that a more accurate prediction by mathematical modeling is often questionable. This is mainly imparted by neglecting various imperfections and random fluctuations or by the impossibility to describe all possible influences appropriately. Therefore, some effort aroused to interpret results of certain experiments in addition to classical TEI (see, e.g.Ref).This paper is related to the work by Lee and Barber [7].Using an analytical approach, it treats the inception of TEI and the development of hot spots during the full contact regime in the disc brakes. The model proposed in Section 2 enables to cover finite thickness of both friction pads and the ribbed portion of the disc. Section 3 is devoted to the problems of modeling of partial disc surface contact with the pads. Section 4 introduces the term of ‘‘thermal capacity of perturbation’’ emphasizing its association with the value of growth rate, or the sliding velocity magnitude. An analysis of the disc friction surfaces non-flatness and its influence on initial amplitude of perturbations is put forward in the Section 5. Finally, the Section 6 offers a model of temperature perturbation development initiated by the mentioned initial discnon-flatness in the course of braking. The model being in use here comes from a differential equation that covers the variation of the‘‘thermal capacity’’ during the full contact regime of the braking.2. Elaboration of Lee and Barber modelThe brake disc is represented by three layers. The middle one of thickness 2a3 stands for the ribbed portion of the disc with full sidewalls of thickness a2 connected to it. The pads are represented by layers of thickness a1, which are immovable and pressed to each other by a uniform pressure p. The brake disc slips in between these pads at a constant velocity V.We will investigate the conditions under which a spatially sinusoidal perturbation in the temperature and stress fields can grow exponentially with respect to the time in a similar manner to that adopted by Lee and Barber. It is evidenced in their work [7] that it is sufficient to handle only the antisymmetric problem. The perturbations that are symmetric with respect to the midplane of the disc can grow at a velocity well above the sliding velocity V thus being made uninteresting.Let us introduce a coordinate system (x1; y1)fixed to one of the pads (see Fig. 1) thepoints of contact surface between the pad and disc having y1 = 0. Furthermore, let acoordinate system (x2; y2)be fixed to the disc with y2=0 for the points of the midplane. We suppose the perturbation to have a relative velocity ci with respect to the layer i, and the coordinate system (x; y)to move together with the perturbated field. Then we can writeV = c1 -c2; c2 = c3; x = x1 -c1t = x2 -c2t,x2 = x3; y = y2 =y3 =y1 + a2 + a3.We will search the perturbation of the uniform temperature field in the formand the perturbation of the contact pressure in the formwhere t is the time, b denotes a growth rate, subscript I refers to a layer in the model, and j =-1½is the imaginary unit. The parameter m=m(n)=2pin/cir =2pi/L, where n is the number of hot spots on the circumference of the disc cir and L is wavelength of perturbations. The symbols T0m and p0m in the above formulae denote the amplitudes of initial non-uniformities (e.g. fluctuations). Both perturbations (2) and (3) will be searched as complex functions their real part describing the actual perturbation of temperature or pressure field.Obviously, if the growth rate b<0, the initial fluctuations are damped. On the other hand, instability develops ifB〉0.2.1. Temperature field perturbationHeat flux in the direction of the x-axis is zero when the ribbed portion of the disc is considered. Next, let us denote ki = Ki/Qicpi coefficient of the layer i temperature diffusion. Parameters Ki, Qi, cpi are, respectively, the thermal conductivity, density and specific heat of the material for i =1,2. They have been re-calculated to the entire volume of the layer (i = 3) when the ribbed portion of the disc is considered. The perturbation of the temperature field is the solution of the equationsWith and it will meet the following conditions:1,The layers 1 and 2 will have the same temperature at the contact surface2,The layers 2 and 3 will reach the same temperature and the same heat flux in the direction y,3,Antisymmetric condition at the midplaneThe perturbations will be zero at the external surface of a friction pad(If, instead, zero heat flux through external surface has been specified, we obtain practically identical numerical solution for current pads).If we write the temperature development in individual layers in a suitable formwe obtainwhereand2.2. Thermo elastic stresses and displacementsFor the sake of simplicity, let us consider the ribbed portion of the disc to be isotropic environment with corrected modulus of elasticity though, actually, the stiffness of this layer in the direction x differs from that in the direction y. Such simplification is, however, admissible as the yielding central layer 3 practically does not take effect on the disc flexural rigidity unlike full sidewalls (layer 2). Given a thermal field perturbation, we can express the stress state and displacements caused by this perturbation for any layer. The thermo elastic problem can be solved by superimposing a particular solution on the general isothermal solution. We look for the particular solution of a layer in form of a strain potential. The general isothermal solution is given by means of the harmonic potentials after Green and Zerna (see Ref.[18]) and contains four coefficients A, B, C, D for every layer. The relateddisplacement and stress field components are written out in the Appendix A.在全接触条件下,盘式制动器摩擦激发瞬态热弹性不稳定的研究摘要超过临界滑动盘式制动器速度可能会导致形成局部过热,不统一的接触压力,振动分布,而且,在多数情况下,会造成盘式制动闸永久性损坏。
汽车盘式制动器设计摘要:本文主要是介绍盘式制动器的分类以及各种盘式制动器的优缺点,对所选车型制动器的选用方案进行了选择,针对盘式制动器做了主要的设计计算,同时分析了汽车在各种附着系数道路上的制动过程,对前后制动力分配系数和同步附着系数、利用附着系数、制动效率等做了计算。
在满足制动法规要求及设计原则要求的前提下,提高了汽车的制动性能。
关键词:盘式制动器;制动力分配系数;同步附着系数;利用附着系数;制动效率Automobile disc brake designAbstract:This paper is mainly the disc brake of the classification and various kinds of disc brake of the advantages and disadvantages are introduced, the selection scheme of the chosen vehicle brake was selected and for disc brake do the main design calculation and analysis of the car in a variety of attachment coefficient road on the braking process of, of braking force distribution coefficient and the synchronous adhesion coefficient, utilization coefficient of adhesion, braking efficiency calculated. Under the premise of meeting the requirements of the braking regulation requirement and design principle and improve the braking performance of automobile.Key words: Disc brake,Braking forcedistribution,coefficient,Synchronization coefficient,Synchronous adhesion coefficient,The use of adhesion coefficient,Braking efficiency目录第1章绪论 (5)1.1 制动器的作用 (5)1.2 制动器的种类 (5)1.3 制动器的组成 (6)1.4 制动器的新发展 (7)1.5 对制动器的要求 (7)1.6 工作任务及要求 (9)1.7 制动器研究方案 (10)第2章制动器机构形式的选择 (11)2.1 方案选择的依据 (11)2.2 制动器的种类 (11)2.3 盘式制动器的结构型式及选择 (12)2.4 盘式制动器与鼓式制动器优缺点比较 (15)2.5 雅阁六代车型制动器结构的最终方案 (16)第3章制动器主要参数及其选择 (17)3.1 雅阁六代基本参数确定 (17)3.1.1 轮滚动半径er (17)3.2.2 空、满载时的轴荷分配 (17)3.2.3 空、满载时的质心高度 (18)3.2 制动力与制动力分配系数 (18)3.2 同步附着系数计算 (22)3.3 制动器最大制动力矩 (25)3.4 利用附着系数和制动效率 (27)3.4.1 利用附着系数 (27)3.4.2 制动效率Ef 、Er (28)3.5 制动器制动性能核算 (29)第4章制动器主要零件的设计计算与校核 (31)4.1 制动盘主要参数确定 (31)4.1.1 制动盘直径D (31)4.1.2 制动盘厚度h (31)4.2 摩擦衬块主要参数的确定 (31)4.2.1 摩擦衬块半径和外半径 (31)4.2.2 摩擦衬块有效半径 (32)4.2.3 摩擦衬块的面积和磨损特性计算 (34)4.2.4 摩擦衬块参数设计校核 (36)4.3 驻车制动计算与校核 (37)4.4 液压制动驱动机构的设计计算 (38)4.4.1 制动轮缸直径d与工作容积V (38)4.4.2 制动主缸直径与工作容积 (40)4.4.3 制动踏板力 (40)S (41)4.4.4 踏板工作行程P第5章制动器主要零件的结构设计 (42)5.1 制动盘 (42)5.1.1 制动盘材料及要求 (42)5.1.2 制动盘分类及比较 (42)5.2 制动钳 (43)5.3 制动块 (44)5.4 摩擦材料 (44)5.5 盘式制动器工作间隙的调整 (46)总结 (47)致谢 (48)参考文献 (49)第1章绪论1.1 制动器的作用汽车制动系是用于使行驶中的汽车减速或停车,使下坡行驶的汽车的车速保持稳定以及使已停驶的汽车在原地(包括在斜坡上)驻留不动的机构。
机械工程学院毕业设计(外文翻译)附件外国文献HYDRAULIC BRAKE BASICSAir brakes get more attention, but hydraulic brakes are installed on more vehicles. Understanding how they work is the first step to safe, cost-effective diagnosis and repair.Ever wonder why there can't be just one kind of brake? It's because airand h ydraulic brakes each have operating characteristics that make one or the other ideal for certain applications.In heavy-duty combination vehicles, air is the clear choice because of the large volume of liquid that would be needed to CATIA all the wheel cylinders. Plus, dealing with glad hand and hoses filled with hydraulic fluid would be messy.But for light and medium-duty straight-truck applications, hydraulic brakes offer advantages including:•Brake feel — that is, as the pedal is pressed farther down, effort increases;•High line pressures, which permit the use of lighter, more compact braking components;•Less initial expense, due to smaller and fewer components;•Cleanliness — hydraulic brakes are closed systems;•Ease of locating leaks, since fluid is visible.There are many more permutations of hydraulic brake systems than found in air systems, but all have basic similarities.THE HYDRAULIC SYSTEMAll hydraulic brake systems contain a fluid reservoir, a master cylinder, whichproduces hydraulic pressure, hydraulic lines and hoses to carry pressurized fluid to the brakes, and one or more wheel cylinder(s) on each wheel.The wheel cylinders expand under fluid pressure, and force the brake shoes against the insides of the drums. If disc brakes are used, calipers, with integral cylinders, clamp down on the rotors when pressure is applied.Because a vehicle must be able to stop much more quickly than it can accelerate, a tremendous amount of braking force is needed. Therefore, the retarding horsepower generated by the brakes must be several times that of the engine.In order to develop the forces required to hold the brake linings against the drums or discs, and to achieve controlled deceleration, it is necessary to multiply the original force applied atthe brake pedal.When a hydraulic system is used, the only mechanical leverage is in the foot pedal linkage. However, varying the diameter of the wheel cylinders or caliper diameters, in relation to the master cylinder bore diameter, provides an additional increase in ratio.In a hydraulic system, the pressure delivered by the various wheel cylinders is directly affected by the areas of their pistons. For example, if one wheel-cylinder piston has an area of 2 square inches, and another piston has an area of 1 square inch, and the system pressure is 400 psi,the 2-square-inch piston will push against the brake shoes with a force of 800 pounds. The1-square-inch piston will exert a force of 400 pounds. The ratio between the areas of the master cylinder and the wheel cylinders determine the multiplication of force at the wheel cylinder pistons.Keep in mind that the larger a wheel cylinder's diameter, the more fluid must be supplied by the master cylinder to fill it. This translates into a longer master-cylinder stroke.If the master cylinder bore diameter is increased and the applying force remains the same, less pressure will be developed in the system, but a larger wheel-cylinder piston can be used to achieve the desired pressure at the wheel cylinder. Obviously, a replacement master cylinder, wheel cylinder or caliper must be of the same design and bore as the original unit.Hydraulic brake systems are split systems, comprising two discreet braking circuits. One master-cylinder piston and reservoir is used to actuate the brakes on one axle, with a separate piston and reservoir actuating the brakes on the other axle(s). Although rare, some light-duty brake systems are split diagonally rather than axle by axle.The reason for the split system is that if a leak develops in one hydraulic circuit, the other will stop the vehicle. Of course, the vehicle shouldn't be driven any farther than necessary to havethe brake system repaired.When one of the hydraulic circuits fails, a pressure -differential switch senses unequal pressure between the two circuits. The switch contains a piston located by a centering spring and electrical contacts at each end. Fluid pressure from one hydraulic circuit is supplied to one end of the pressure-differential switch, and pressure from the other circuit is supplied to the other end. As pressure falls in one circuit, the other circuit's normal pressure forces the piston to the inoperative side, closing the contacts and illuminating a dashboard warning light.POWER ASSISTPower assist units, or boosters, reduce operator effort at the brake pedal. Vacuum boosters, popular on light-duty vehicles, make use of an engine vacuum on one side of a diaphragm, and atmospheric pressure on the other side. A valve allows the vacuum to act on the diaphragm in proportion to brake pedal travel. This assists the pedal effort, and allows increased pressure onthe brake fluid, without an undue increase in pedal effort.Other types of boosters use hydraulic pressure — either from the vehicle's power steering pump or from a separate electric pump, or both — to assist pedal effort. As the brake pedal is depressed, a valve increases hydraulic pressure in a boost chamber to apply increased pressure to the master cylinder pistons.Some systems use both vacuum and hydraulic assist. In other systems, air pressure from an onboard compressor is used to generate hydraulic system pressure.VALVINGValves commonly found in hydraulic brake systems include: Proportioning, orpressure-balance valves. These restrict a percentage of hydraulic pressure to the rear brakes when system pressure reaches a preset high value. This improves front/rear brake balance duringhigh-speed braking, when some of a vehicle's rear weight is transferred forward, and helps prevent rear-wheel lockup. Some proportioning valves are height-sensing. That is, they adjustrear-brake pressure in response to vehicle load. As a vehicle's load increases (decreasing height) more hydraulic pressure to the rear brake s is allowed;Metering valves. These hold off pressure to front disc brakes to allow rear drum brake shoes to overcome return-spring pressure and make contact with the rear drums. This prevents locking the front brakes on slippery surfaces under light braking applications. These valves do not come into play during hard braking.PARKINGThe parking function varies greatly among hydraulic brake systems. Many light-duty vehicles with rear drum brakes use a passenger-car type lever-and-cable setup. A ratcheted lever or foot pedal pulls a cable, which, in turn, pulls a lever assembly at each rear wheel end. The lever forces the brake shoes apart, and they are mechanically held against the drums until the ratchet is released.Other parking systems include spring chambers, like those used onair-brake systems. These are spring-engaged, but are disengaged by hydraulic pressure instead of air.ANTILOCKOn many hydraulically braked light-duty trucks, brakes are used on the rear wheels to preserve braking stability when these vehicles are lightly loaded. Front and rear-wheel is usually an option, except for vehicles over 10,000 pounds GVWR, which are required to have steer and drive-axleIn current hydraulic systems, a dump valve releases pressurized hydraulic fluid into an accumulator in the event of an impending wheel lockup.An electronic control box receives speed signal(s) from sensors in the transmission and/or at the wheels. When the brakes are applied, the control box senses the decrease in rear wheel speed, and activates the dump valve(s) if the rate of deceleration exceeds a predetermined limit.The control box energizes the dump valve with a series of rapid pulses to bleed-offwheel hydraulic pressure. Continuing in mode, the dump valve is pulsed to keep the wheels rotating, while maintaining controlled deceleration.At the end of such a stop, the valve and any fluid in the accumulator is returned to the master cylinder. Normal brake operation resumes.FOUNDATION BRAKESFoundation brakes in hydraulic systems can be either drum or disc. In many applications, discs are used on the front axle and drums on the rear.Drum brakes are said to be self-energizing. That's because when the brake shoes expand and contact a rotating drum, the leading, or forward, brake shoe is pushed against the trailing shoe by the force of the moving drum. This results in higher lining-to-drum pressure than would be produced by the wheel cylinder alone.As brake linings wear, the shoes periodically must be moved closer to the drums to ensure proper contact during braking. While some older drum brake assemblies are manually adjusted, most are automatic. These use a star wheel or ratchet assembly, which senses when the wheel cylinder has traveled beyond its normal stroke, and expands the pivot point at the other end ofthe brake shoes.In addition to being one of the friction elements, the brake drum or rotor also acts as a heat sink. It must rapidly absorb heat during braking, and hold it until it can be dissipated into the air. The heavier a drum or rotor is, the more heat it can hold.This is important, since the hotter the brake linings get, the more susceptible they are to heat fade. Heat fade is induced by repeated hard stops and results in reduced lining-to-drum/rotor friction and increased vehicle stopping distance. As a rule, high-quality linings will display less heat fade than inferior ones. Also, are far more resistant to heat fade than drum brakes.Another type of fade that brakes are susceptible to is water fade. Drum brakes, with their large surface areas, apply fewer pounds per square inch of force between lining and drum during a stop than disc brakes. This, added to the drum's water-retaining shape, promotes hydroplaning between shoe and drum under wet conditions. The result is greatly increased stopping distance.Disc brakes, with their smaller friction surfaces and high clamping forces, do a good job of wiping water from rotors, and display little reduction in stopping capability when wet.中文翻译液压制动基础空气制动系统得到更多的关注,但更多的车辆上安装液压制动器。
盘式制动器制动系统原理外文文献翻译、中英文翻译、外文翻译制动系统原理摩擦力是指抵抗两个物体之间相对运动的力。
在制动系统中,通过产生摩擦力来使汽车停止运动或减速行驶。
摩擦力的大小取决于物体表面粗糙度和接触面所受压力的大小。
当发生摩擦运动时,动能就会转化为热能。
因此在刹车时,必须尽量减少热量的产生,以避免制动系统故障。
摩擦力和制动系统在制动系统中,摩擦力的大小是由控制器控制的。
通过改变摩擦力,可以使汽车停止运动或以不同的速度行驶。
控制器通过制动蹄或制动板传递给旋转的制动鼓或制动盘。
当驾驶员踩在制动脚踏板上的力增大时,摩擦力也会随之增加。
车轮在制动摩擦力的作用下逐渐停止转动,但轮胎和地面之间也会产生摩擦力。
制动器上产生的摩擦力必须与轮胎与地面之间产生的摩擦力大小相匹配,避免车轮锁死或打滑的现象。
为了控制车轮在减速时出现打滑的现象,现在广泛使用电脑控制的制动器。
鼓式制动器的基本操作原理鼓式制动器由一个铸造鼓和连接在制动板上的制动蹄构成。
铸造鼓固定在车轮上,随车轮一起转动。
制动器内还有液压缸、弹簧和连接杆等部件。
制动蹄和摩擦材料连接在一起,制动器工作时,摩擦材料贴附在制动鼓的内表面,制动蹄在力的作用下紧贴在制动鼓的内表面,产生摩擦力。
制动器的工作原理是通过液压缸控制制动蹄的运动,使其紧贴在制动鼓上,从而实现制动效果。
在刹车系统开始工作时,盘式制动器的制动片会被推向制动盘。
制动片与制动盘之间的摩擦力会使得车轮减速或停止旋转。
制动盘通常是由铁制成的,而制动片则通常是由摩擦材料制成的。
制动片与制动盘之间的摩擦力是由制动液压缸内部的液压力驱动的。
这种液压力是由操纵者的脚踏板产生的。
盘式制动器的优点是可以承受更高的温度和更大的力量,因为它们的制动面积更大。
此外,盘式制动器的制动片更容易被更换和维护。
缺点是盘式制动器比鼓式制动器更昂贵,并且更容易受到灰尘和水的影响。
总的来说,盘式制动器是一种高效、可靠的刹车系统,适用于高速行驶和紧急制动。
International Journal of Automotive Technology , Vol. 11, No. 1, pp. 133−138 (2010)DOI 10.1007/s12239−010−0018−0Copyright ©2010KSAE 1229−9138/2010/050−18133STRESS ANALYSIS OF VENTILA TED BRAKE DISCS USING THE FINITEELEMENT METHODY . YILDIZ and M. DUZGUN *Mechanical Department, Faculty of Technical Education, Gazi University, Ankara 06500, Turkey(Received 9 July 2008; Rrevised 21 January 2009)ABSTRACT −One of the most common problems related to ventilated brake discs are crack formations, particularly under high brake loads or from the associated stresses during braking. In this study, three different ventilated brake discs, the cross-drilled disc, the cross-slotted disc, and the cross-slotted with a side groove disc, were manufactured, and their braking force performances were investigated experimentally together with a solid disc. Stress analyses were subsequently performed by the finite element method. Analyses results showed that the maximum stress generations were formed on the ventilated discs in comparison to the solid disc. However, these comparisons indicate that the application of varying force distributions along brake pads reduces the stresses on ventilated discs by 8.8% to 19.1%.KEY WORDS :Stress analysis, V entilated brake discs, Finite element method, Crack formations1. INTRODUCTIONVentilated brake discs or rotors are known as high perfor-mance brakes, and they are produced by making hollows or slots (or both) of different shapes on the disc surface and side edges. Ventilated brake discs were originally tested on racecars in the 1960s, and different designs have been employed widely in the automotive and railway industry (Chatterley and Macnaughtan, 1999; Patrick, 2002). For example, Zuber and Heidenreich manufactured three different ventilated brake disc constructions from CMC (Carbon fiber reinforced ceramic matrix composites) material and compared their strength (Zuber and Heidenreich, 2006).During braking, kinetic energy is converted to heat.Around 90% of this energy is absorbed by the brake disc and then transferred to the ambient air. Solid brake discs dissipate heat slowly. Therefore, ventilated discs have been used to improve cooling by facilitating air circulation (Hudson and Ruhl, 1997; Breuer and Bill, 2008). It has been noted that ventilated disc brakes generally exhibit convective heat transfer coefficients that are approximately twice as large as those associated with solid discs (Limpert, 1999).Antanaitis and Rifici (2006) proved that the 90-hole cross-drilled pattern improved the heat rejection capability of the disc by 8.8% to 20.1%, depending on the vehicle speed.Aleksendric and coworkers demonstrated the ability of ventilated disc brake rotors in dissipating thermal flow by FEA (finite element analysis) (Aleksendric et al., 2006).Venkitachalam and Maharudrappa performed a flow and heat transfer analysis of six different types of disc configu-rations by CFD (computational fluid dynamics), and they suggested operation guidelines for ventilated discs of high-speed vehicles (Venkitachalam and Maharudrappa, 2008).Brake fade improvement and higher braking performance in wet conditions are other advantages of ventilated brake discs.However, there are some disadvantages associated with ventilated brake discs. Cracking is one, and this phen-omenon has been specifically correlated to stresses during braking. It has been shown that stresses could lead to cracks around the outside edges of the drilled holes near the edge of the disc under severe conditions due to metal fatigue (Brecht and GmbH, 1998). These and similar cracks were also proved by FEA. For example, Kim et al. showed the maximum von-Mises stress generations where the actual fatigue cracks were located on a ventilated disc brake of railway vehicles via thermal stress analysis (Kim et al.,2008). Similarly Bagnoli et al. performed FEA to deter-mine the temperature profile and to estimate the von-Mises stress distributions that arise during braking for fire fight-ing vehicles (Bagnoli et al., 2009). Liu et al. established a general subsurface crack propagation analysis methodology for wheel/rail rolling contact fatigue by using FEM (Liu et al., 2007). Consequently, cracking is a particular inevitable difficulty for ventilated brake discs. Decreasing the braking temperatures and/or re-designing the hub-rotor unit were some methods proposed by Mackin et al. to eliminate cracking in brake rotors (Mackin et al., 2002).In this study, three different ventilated brake discs were designed and manufactured, and their performances of braking force were investigated experimentally in addition to those of a solid disc. Afterwards, stress analyses were*Corresponding author . e-mail: mduzgun@.tr134Y. YILDIZ and M. DUZGUNperformed by FEA. In these analyses, a different approach,the variable loading on brake pads, was also introduced. It was found that this approach remarkably reduced the stresses on ventilated discs. Hence, this unique approach could be an improvement for eliminating crack formations in ventilated brake discs.2. EXPERIMENTAL PROCEDUREFigure 1 shows the brake discs employed in this study.Ventilated brake discs were manufactured from the ATE (Alfred Teves) solid discs. In these products, a propeller-shaped design was selected for the hole and slot locations.For the CD (cross-drilled) disc, five holes of 5.2 mm in diameter were arranged at equal intervals of 60.54 mm on an arc. These holes were duplicated in groups of twenty on the disc surface. Thus, a hundred holes overall were drilled on the disc surface for the CD disc. In producing the CS (cross-slotted) shape, twenty channels 6.9 mm wide and 67.3 mm long were machined on a solid disc surface.Finally, a CS-SG (cross-slotted with side groove) disc was manufactured additionally by making a groove 4 mm wide and 15 mm deep on another CS disc edge. Hence, a path opening to the outside of the disc side edge was obtained to facilitate air circulation. The CD and CS discs were manufactured on a 3-axis CNC Vertical Machining Center.The side groove for the CS-SG disc was made on a CNC Turning Center.The braking force outputs were measured on brake test equipment as shown in Figure 2. The measurements were performed by piezoelectric sensors that were set on pedal and caliper mechanisms in this instrument. The power,speed, and output torque of the motor are 4 kW, 34 rev/min,and 450 Nm, respectively. The disc rotation was clockwise (CW). ATE 501 FF brake pads were used in the tests.Experiments were conducted on continuous braking condi-tions at a constant pedal force of 250 N. Eight periodic measurements of the braking force outputs were executed at 30 s, 60 s, 90 s, 120 s, 150 s, 180 s, 210 s, and 240 s.3. FINITE ELEMENT METHODThree-dimensional (3D) constructions of brake discs and brake pads and their assembly designs were modeled at a 1/1 scale in related modules of the CATIA P3 V5R17version. These designs were converted into “stp ” format,and they were imported in ANSYS 11.0 software for FEA.Figure 3 shows the mesh models of the disc-pad systems.Parts were meshed with element types of 10 Node Quadratic Tetrahedron (Solid 187) and 20 Node Quadratic Hexahedron (Solid 186). The accuracy and computational efficiency of these types of mesh generations have been previously studied (Han et al., 2008). A frictional contact pair was defined between disc-pad interfaces. The element types used were Quadratic Quadrilateral Contact (Conta 174) and Quadratic Quadrilateral Target (Targe 170). The mechanical properties of the most common disc brakes (grey cast iron) and pad materials used in the analysis are given in Table 1. Design characteristics of the parts are also provided.Two groups of analyses were performed to investigate stress formations. The temperature effect was neglected in these analyses. In the first group, a uniform force distri-bution was applied on brake pad surfaces, and stress formations were compared. For the second group, alter-natively, thirteen different loading cases were variably applied to brake pad surfaces for just a disc on which maximum stresses were observed in the first group. Hence,the most convenient condition in terms of stress formationFigure 1. (a) Solid (SL) disc; (b) Cross-drilled (CD) disc;(c) Cross-slotted (CS) disc; (d) Cross-slotted with sidegroove (CS-SG) disc.Figure 2. Brake test equipment.STRESS ANALYSIS OF VENTILATED BRAKE DISCS USING THE FINITE ELEMENT METHOD135was determined. A general comparison was then made between all disc configurations. Analyses were simulated according to the equivalent (von-Mises) stress distributions. In these analyses, a 9689N equivalent to 250N pedal force was applied on each top surface of the brake pads at a revolution speed of 200 km/h (or angular velocity of 397.56 rad/s). It was assumed that the disc rate was con-stant and the time that was required for a complete stop is 240 s. The value of the pedal force extracted is taken from equation (1) (Heisler, 1999), where the F f is the force on each front cylinder piston, F is the force on foot-pedal, A f is the cross-sectional area of front pistons, A m is the cross-sectional area of master-cylinder, p n is the number of pistons, 2.3 is the pedal leverage ratio, and 2.75 is the effect of servo unit. This computation was made related to the test equipment used in the experiments. The pedal force leverage ratio and the servo unit effect are the values from the test equipment.(1) 4. RESULTS AND DISCUSSIONFigure 4 shows the experimental and finite element analy-sis results. The best performance in terms of braking force outputs was obtained with the CS-SG disc. Braking force generations with the CS-SG disc were higher (between 18.7% and 29.9%) than the SL disc. For example, while the brake force output was 5.26 kN with the CS-SG disc, the brake force output was 3.86 kN with the SL disc after 120 s of braking. Therefore, it can be concluded that the best braking or stopping performance would be obtained by the CS-SG disc. On the other hand, the maximum stressesF f = F A f×p n× 2.3× 2.75×A m-------------------------------------------------Figure 3. Finite element mesh visualizations for the stress analysis, (a) SL disc; (b) CD disc; (c) CS disc; (d) CS-SG disc.Table 1. Mechanical property and design characteristics of the brake discs and brake pads.Mechanical property Disc PadYoung's Modulus (E) (N/mm2)1080001029Poisson's ratio (v)0.350.25Mass density (kg/mm3)7.1e-006 2.1e-006 Coefficient of friction0.350.35Design characteristics SL disc CD disc CS disc CS-SG disc PadV olume (mm3)7.305e+0057.05e+005 6.217e+005 5.811e+0050.5502e+005 Area (mm2) 1.87e+005 2.03e+005 2.03e+005 2.19e+0050.13e+005 Mass (kg) 5.742 5.541 4.887 4.5680.488Figure 4. (a) Braking force generations; (b) maximumstress formations.136Y. YILDIZ and M. DUZGUNwere formed on the same disc, as expected (Figure 4(b)).Figure 5 shows simulated stress formations for all disc configurations. Stress formations around the holes and channels on ventilated discs were indicators of the initial of crack regions. For this reason, Figure 6 is an important proof in terms of actual cracks demonstrated experimental-ly in the study of Antanaitis and Rifici (2006) and shows the beginning regions of these cracks simulated by stress analysis in this study. Similarly, Bagnoli et al. showed that these stresses were mainly localized based on the radial direction of the friction surface of the disc around the edge of the cooling holes and channels (Bagnoli et al., 2009). In addition, according to Ripley and Kirstein, such stress formations have the tendency to increase the tensile-strains,particularly for the grey cast iron, which is the most common disc material (Ripley and Kirstein, 2006).4.1. Variable Force ApplicationThe above analyses show that the stresses generated on the outer and inner regions of discs were larger than those in the middle region for uniform force application to the brake pad surfaces. A variable loading force to the brake pads may produce different results. Therefore, in this group analysis, the same force value of 9689N was applied vari-ably to each pad surface under thirteen different conditions as shown in Table 2. This kind of force application to brake pad surfaces was inspired from a study by Kim et al.,although they used this force application to test the reliability of disc thermal analysis (Kim et al., 2008). Each disc pad surface was divided into three regions for variable loading as shown in Figure 7. The areas were 1433 mm 2 for the outer, 1443 mm 2 for the middle, and 1367 mm 2 for the inner regions. The differences between these areas are due to the original shapes of the brake pads. Thus, thirteen different loadings, having the same uniform force distri-butions on all regions (Case 1), some having the same force distributions on two regions (Case 2, Case 3, Case 4, Case 5, Case 6 and Case 7), and others having different force distributions on all regions (Case 8, Case 9, Case 10, Case 11, Case 12, Case 13), were analyzed. However, these conditions were applied only to the CS-SG disc because the maximum stresses were observed on its channels in thefirst analyses.Figure 5. Simulation of analysis results, (a) SL disc; (b) CD disc; (c) CS, disc; (d) CS-SG disc.Figure 6. Actual cracks and simulated stresses around the holes on the ventilated discs.STRESS ANALYSIS OF VENTILATED BRAKE DISCS USING THE FINITE ELEMENT METHOD 137Figure 8 shows graphs of the analysis results for the variable loading cases. It can be shown that Cases 4, 12 and 13 reduced the maximum stresses when compared to Case 1 (uniform loading). However, there were no considerable differences between Cases 4, 12, and 13. Therefore, only Case 4 as shown in Figure 9 was applied to the all discconfigurations for the general comparison. Figure 10 shows graphs of these comparison results. When compared to Case 1, a 50.4% increase in stress formation was seen for the SL (solid) disc with Case 4. However, the application ofTable 2. Conditions of variable force distributions.Force distribution cases on abrake pad surfaceOuter region force (ORF)ratioMiddle region force (MRF)ratioInner region force (IRF) ratioTotal force (F) distribution on a brake pad surface (N)Case 1 (ORF=MRF=IRF)1/3F 1/3F 1/3F 9689Case 2 (ORF=MRF<IRF)1/4F 1/4F 1/2F 9689Case 3 (ORF=IRF<MRF)1/4F 1/2F 1/4F 9689Case 4 (ORF>MRF=IRF)1/2F 1/4F 1/4F 9689Case 5 (ORF<MRF=IRF)1/5F 2/5F 2/5F 9689Case 6 (ORF=IRF>MRF)2/5F 1/5F 2/5F 9689Case 7 (ORF=MRF>IRF)2/5F 2/5F 1/5F 9689Case 8 (ORF<MRF<IRF)1/7F 2/7F 4/7F 9689Case 9 (ORF<MRF, MRF>IRF, ORF<IRF)1/7F 4/7F 2/7F 9689Case 10 (ORF>MRF, MRF<IRF, ORF<IRF)2/7F 1/7F 4/7F 9689Case 11 (ORF<MRF, MRF>IRF, ORF>IRF)2/7F 4/7F 1/7F 9689Case 12 (ORF>MRF, MRF<IRF, ORF>IRF)4/7F 1/7F 2/7F 9689Case 13 (ORF>MRF, MRF>IRF, ORF>IRF)4/7F2/7F1/7F9689Figure 7. Variable force application regions on a brake pad.Figure 8. Maximum stress generations according to differ-ent loading cases.Figure 9. Application of Case 1 and Case 4 to the brake padsurfaces.Figure 10. Stress formations on discs.138Y. YILDIZ and M. DUZGUNCase 4 to the ventilated discs reduced the stress formations on discs from 8.8% to 19.1%. As a result, it can be inferred that variable force application to the brake pads is not convenient for the solid discs, but it can reduce the stress formations on ventilated discs.5. CONCLUSIONSThe following conclusions can be drawn from the above analyses:(1) The CS-SG disc showed the best performance in termsof braking force output. However, the maximum stress generations were shown on the same disc for the uniform force applications to the pad surfaces. (2) FEA results demonstrated that the maximum stressesmainly localized outwardly in the radial direction of the friction surface around the edge of the cooling holes and channels on the ventilated discs.(3) Alternatively, thirteen variable loading cases on the padsurfaces were examined. They were applied only for the CS-SG disc because it had the maximum stresses under the uniform loading conditions. The most conv-enient conditions were determined by Cases 4, 12, and13 (from Table 2). There were no significant differ-ences between them, so only Case 4 was applied to the ventilated discs, which reduced the stress formations from 8.8% to 19.1%, whereas it increased the stresses on the solid disc.The practicability of using such a variable loading case on brake pads is not convenient for modern brake systems. However, it should be considered because of its ability to reduce the stress formations on ventilated brake discs, which means that the possibility of crack formations would be reduced.ACKNOWLEDGEMENTS−The authors would like to thank the editors and the two anonymous reviewers for their helpful comments and contributions.REFERENCESAleksendric, D., Duboka, C., Gotowicki, P. F., Mariotti, G. V. and Nigrelli, V. (2006). 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