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Analysis of emergency braking performance with particular consideration of temperature effects on brakes

Abstract

During vehicle deceleration due to braking there is friction between the lining surface and the brake drum or disc. In this process the kinetic energy of vehicle is turned into thermal energy that raises temperature of the components. The heating of the brake system in the course of braking is a great problem, because besides damaging the system, it may also affect the wheel and tire, which can cause accidents. In search of the best configuration that considers the true conditions of use, without passing the safety limits, models and formulations are presented with respect to the brake system, considering different braking conditions and kinds of brakes. Some modeling was analyzed using well-known methods. The flat plate model considering energy conservation was applied to a bus, using for this a computer program. The vehicle is simulated to undergo an emergency braking, considering the change of temperature on the lining-drum. The results include deceleration, braking efficiency, wheel resistance, normal reaction on the tires and the coefficient of adhesion. Some of the results were compared with dynamometer tests made by FRAS-LE and others were compared with track tests made by Mercedes-Benz. The convergence between the results and the tests is sufficient to validate the mathematical model. The computer program makes it possible to simulate the brake system performance in the vehicle. It assists the designer during the development phase and reduces track tests.

Brake; Braking; Temperature; Thermal Analysis; Vehicles


Analysis of Emergency Braking Performance with Particular Consideration of Temperature Effects on Brakes

Silvia Faria Iombriller

Antônio Carlos Canale

Universidade de São Paulo

Escola de Engenharia de São Carlos

Departamento de Materiais, Aeronáutica e Automobilística

During vehicle deceleration due to braking there is friction between the lining surface and the brake drum or disc. In this process the kinetic energy of vehicle is turned into thermal energy that raises temperature of the components. The heating of the brake system in the course of braking is a great problem, because besides damaging the system, it may also affect the wheel and tire, which can cause accidents. In search of the best configuration that considers the true conditions of use, without passing the safety limits, models and formulations are presented with respect to the brake system, considering different braking conditions and kinds of brakes. Some modeling was analyzed using well-known methods. The flat plate model considering energy conservation was applied to a bus, using for this a computer program. The vehicle is simulated to undergo an emergency braking, considering the change of temperature on the lining-drum. The results include deceleration, braking efficiency, wheel resistance, normal reaction on the tires and the coefficient of adhesion. Some of the results were compared with dynamometer tests made by FRAS-LE and others were compared with track tests made by Mercedes-Benz. The convergence between the results and the tests is sufficient to validate the mathematical model. The computer program makes it possible to simulate the brake system performance in the vehicle. It assists the designer during the development phase and reduces track tests.

Keywords: Brake, Braking, Temperature, Thermal Analysis, Vehicles

Introduction

With the increasing technological development in the area of motors and materials, heavy transport vehicles (trucks) and the buses (urban and highway) have been suffering an increase in size and consequently in load capacity. The development of compatible and even more efficient brakes has become necessary with these alterations. One must take into account that a great part of these vehicles are submitted to conditions that overload the projected brake system, such as overloading, bad use by the driver and slow traffic, amongst others.

Braking can occur in different ways:

- Mountain descent- treats the use of continuous braking over a period on a steady slope

- Frequent stops - treats braking within the urban perimeter

- Emergency - treats sudden braking

In all these cases there is the problem of overheating, however, during emergency braking, which occurs within a short space of time, practically all the kinetic energy of the vehicle is turned into thermal energy in the brakes, with a small dissipation of heat to the atmosphere and only 5% of the generated heat is absorbed by the linings.

Usually, it is the temperature during an emergency braking that defines the physical properties of the lining and those of the drum, since despite the lesser period of use of the brake than in all other types of braking, there is maximum heating of the brake, with the least possibility of the flow of heat out of the system.

Due to the short time of emergency braking, one can conclude that heat conduction into the closest components in the system will be small, just like heat convection to the environment. Considering the temperatures involved, the effect of radiation will not be considerable in this process. This work aimed at emergency braking for medium to high speed, assuming all thermal energy to be absorbed by the drum, since the effects of heat flow are small and the heat absorbed by the lining is small because of its insulating characteristics.

Nomenclature

A = area of the brake cylinder [m2]

b = deceleration [m/s2]

c = adjustment lever [m]

c* = braking factor of the vehicle

cp = specific heat of the drum material [J/kg.oC]

dcs = diameter of the came-s [m]

dt = internal diameter of the drum [m]

e = braking efficiency [%]

E = energy involved in the braking [J]

Fc = transmitted force of the cylinder to the came-s [N]

Fe = forces that the came-s transmits the linings [N]

FF = braking force [N]

Fi = initial force on the brake cylinder [N]

FN = normal force [N]

Fs = attrition force between the linings and the drum [N]

g = acceleration due to gravity [m/s2]

hcg = height of the center of gravity [m]

L = distance between axles [m]

Ld = distance of the front axle to the center of gravity [m]

Lt = distance of the rear axle to the center of gravity [m]

m = mass of the vehicle [kg]

mt = mass of the drum [kg]

P = pressure in the brake cylinder [bar]

Pf = maximum pressure in the brake cylinder [bar]

Pi = low pressure in the brake cylinder [bar]

Rd = dynamic radius of the wheel [m]

Ri = inertia force [N]

T = temperature [oC]

Ti = initial temperature before braking (temperature of cold brake) [oC]

Vf = speed at the end of braking [m/s]

Vi = speed at the beginning of braking [m/s]

W = weight of the vehicle [kgf]

h = output of the brake system

mo = standard coefficient of adherence of the track

m = coefficient of adherence

d = subscript appended to a symbol to assign the corresponding variable to the front axle

t = subscript appended to a symbol to assign the corresponding variable to the rear axle

Modeling

Many researchers have been concerned about the thermodynamic analysis of brakes, several models have been used for this, including the most restricted and specific models in some cases.

The reason for the use of several models is the problem of choosing the most appropriate for the situation under study, evaluating costs, ease of use and the area of application.

It is important to remember that the brake is a component that is not easy to model for different configurations and possible uses. However, a great part of the studies made were accompanied by track tests or on the dynamometer, in this way looking for validation of the chosen model.

Basically the methods of calculation may be separated into continuous, discreet and empirical methods. Although there is normally predominance of one of these methods, it is observed that in practice, one of the methods chosen always predominates over the others, either during the calculations or simply in the validation of the model.

Among the researchers of this area the following stand out: Limpert (1992), Winkler (1976), Gillespie, Fancher and Johnson (1978), Sartori (1972), Ramachandra Rao, Ramasubramanian and Seetharamu (1989), Pauletti (1993), Morgan and Dennis (1972), Canale (1989), Sheridan, Kutchey and Samie (1988) and Ritz, Adas and Francisco (1995).

Observing the studied modelings the conclusion is reached that the method that should be chosen is the best adapted to the conditions of the process of appraisal of the braking, as well as of the contour conditions considered.

In this work emergency braking was evaluated using the plate model through the method of the conservation of energy, shown by Canale (1989), because in this braking condition a very small portion of energy is dissipated to the atmosphere.

On highways, due to the high speeds reached, the concern with safety is also higher. For this, the vehicle chosen for this work was a long distance bus, where the safety of a number of people is taken into account.

The chosen vehicle was a Mercedes-Benz long distance bus (OHL1635), with two axles, load capacity for 44 passengers and luggage, adding up to a maximum weight of 18 tons. Equipped with drum brake system, of the simplex type with came-s.

An algorithm was then developed as represented in figure 1, which became a computer program.


The physical, mechanical and loading characteristics of the vehicle were used as entry data.

Varying the speed of the vehicle for a chosen pressure in the cylinder of the brake and having the mass of the vehicle known, it is possible to calculate the total quantity of energy involved in braking.

However, one must consider that the total energy varies according to the distribution of braking forces in the balance of braking system.

Starting at a initial temperature, knowing the material of the drum and its respective specific heat and also knowing the area of the surface of contact between lining and drum, the use of the equation used by Canale (1989) leads to the values for temperatures which are reached after each emergency braking in each axle.

By using the results of tests in dynamometer carried out by FRAS-LE*, the brake factor (c*)** (Limpert, 1992) was calculated depending on temperature, pressure and speed involved in braking. Figure 2 shows the variation of brake factor in relation to temperature for the vehicle, which was studied, since temperature was considered to be the most prevalent factor on the variation of the brake factor during tests.


In modelings, the brake factor is frequently found to be considered constant. In this work, however, its actual behavior, which varies mainly on the temperature, was aimed at.

The points, which are indicated in figure 2, were obtained in tests and a polynomial function of third power was used for interpolation. This function was used to simulate the bus braking within the program for the computer.

A mathematical model was devised according to Fernandes (1994), which is described as follows; using the Laws of Newton applied in the balance of forces and balance of force momentum. Figures 3 and 4 show respectively the forces in the system of braking and the forces acting in the vehicle. The braking forces were then calculated in both axles of the vehicle and their respective normal forces.



Considering the braking forces, the mass of the vehicle and the decelerations of the vehicle were as displayed.

Relating the normal forces and the braking forces to the coefficient of adhesion of each axle, which was calculated up to the skidding point of the vehicle, in other words, when this coefficient is equal to the adherence offered by the track.

In this case, the efficiency of the brake system was calculated, defined as the ratio between the maximum deceleration during braking and the maximum adhesion coefficient in the contact between tires and pavement, without any axle slip, according to Limpert (1992).

The computer program, which was developed, has as output the decelerations, forces and normal reactions during the braking, braking distribution, temperatures of the brake drums and coefficients of adhesion, showing the point at which the vehicle begins to skid.

In order to compare the theoretical results obtained by the computer program, Mercedes-Benz of Brazil supplied results of their track tests executed using the bus under study.

Results

Figure 5 shows the temperature variations depending on the initial speed of braking to total stopping, comparing the final temperatures obtained theoretically with the experimental results. The experimental results belong to internal reports of Mercedes-Benz of Brazil.


In this case the vehicle was used with maximum total weight, in order to consider an ordinary loading situation. The front axle was evaluated, because it suffers the highest workload. It is still possible to observe in figure 5 the braking time, which is very low.

Figure 6 shows the variation observed among the final theoretically obtained temperatures and the results of the track tests. It can be seen that the theoretical temperatures are a little higher than the experimental results, which proves that the initial consideration that during emergency braking the heat dissipated to the atmosphere is very small.


Figures 7 and 8 show the braking forces in the front and rear axles varying with the decrease of the speed during the braking process, for the vehicle with maximum weight and different total applied pressures to the brake system.



The normal reactions on the front and rear axles are shown in figures 9 and 10, varying the speed during braking, for different pressures in the brake system and with maximum total weight of vehicle.



With the braking forces and the mass of the vehicle it is possible to obtain the decelerations of the vehicle, varying with the pressure of the brake system, resulting in typical curves, as seen in figure 11.


However, during track tests, only the average deceleration between the beginning and end of braking is evaluated. In order to compare the theoretical and experimental results, the average deceleration, which was calculated by the computer program, has used. Figure 12 shows this comparison.


Figures 13 and 14 show the behavior of the coefficient of adherence with the increase of brake pressure. The point of skidding can be observed, when the coefficient of the front axle reaches the maximum coefficient offered by the track, considered in this case as 0.8. It is noticed that in practice, the front axle is the first to skin.



At the moment of skidding, in other words, when the coefficient of adherence of the axle is equal to the coefficient of adherence offered by the track, the braking efficiency was obtained, linking the coefficients of adherence of the axle and of the vehicle.

The braking efficiency was calculated, as seen in table 1, for the vehicle in different operational conditions, for the empty vehicle and with maximum total weight.

Conclusions

Observing figure 5 it can be seen that there is a convergence between the theoretical and the experimental values obtained on the track test for the brake temperatures.

In relation to the temperatures, it is noticed that although the theoretical values are slightly superior to the practical values. It is concluded that this small difference is due to the heat dissipated to the surroundings, confirming the initial hypothesis of conservation of energy during emergency braking.

The average decelerations obtained theoretically were similar to those obtained in track tests for 60km/h, as can be observed in figure 12.

The fall in deceleration during braking, shown in figure 11, is due to the influence of the temperature on the brake factor, as seen in figure 2.

It may be concluded that through the convergence of temperatures and decelerations, the use of the mathematical model was validated.

Based on the values of braking efficiency, it can be observed that the vehicle was designed to have its best performance when loaded, since it is a highway vehicle, because with the empty vehicle the braking efficiency decreases.

It was also observed in figure 2, that in the vehicle that was studied, the brake factor decreases with the increase in temperature and thus the braking efficiency does not vary, since in the calculations the pressure at constant braking is considered, as demanded by the norms of track tests. However, it is expected that the use of another system of brakes with a different curve for the variation of the brake factor, would provoke alteration in the braking efficiency, besides, it is known that in practice, through the pedal, the driver during braking provokes a variation in the pressure on the brake system.

The development modeling applied in the computer program allowed the analysis of the performance during the braking of the vehicle, for different operational conditions and different systems of brakes.

The results that were obtained can be useful both to the planners of the brake system and to those who should adapt them to the vehicle. In this way it is possible to obtain a forecast of the performance of the brake system on the vehicle and if it is necessary to modify the configuration before submitting it to the track tests, track time maybe reduced, consequently reducing the costs involved in the project.

Acknowledgements

Thanks are due to the companies Mercedes-Benz of Brazil and FRAS-LE, for the concession of the experimental data used in this work.

Manuscript received: November 1999. Technical Editor: Átila P. S. Freire.

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Publication Dates

  • Publication in this collection
    28 Sept 2001
  • Date of issue
    2001

History

  • Received
    Nov 1999
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