DEVELOPMENT OF A METHOD FOR DETERMINING PARAMETERS OF THE HEAT LOAD OF FRICTION PAIRS OF VEHICLE BRAKE SYSTEMS

ABSTRACT

This paper examines the influence of specific factors related to hot climate conditions, particularly the combination of high temperature and elevated dust content in the air, on materials, equipment, and technical-economic indicators of vehicles. The proposed method is quite universal since it is based on the analysis of patterns inherent to braking mechanisms in use. During the operation of braking devices, their friction pairs experience wear with varying intensities. To study the cooling and heating of components, representing a special form of non-stationary heat transfer, it is necessary to distinguish several stages of thermal loading of brake friction pairs. The heating and cooling of the brake drum are described by Fourier’s differential equation of thermal conductivity. Thermal effects on the drum rim (not less than 100°C or higher) cause its thermal deformation, which, due to the low efficiency of natural cooling, persists longer than mechanical effects. The provided data on the thermal load of working parts of vehicle brakes allow for establishing the influence of geometric (diameter, thickness, and width of the brake drum rim, installation gap between friction pairs, coefficient of mutual overlap of interacting pairs) and thermophysical coefficients, thermal conductivity and diffusivity of the materials of the drum rim and friction lining, their surface temperatures, and accumulating a priori information on heat management.

АННОТАЦИЯ

В данной работе рассматривается влияние некоторых факторов жарких климатических условий, в частности сочетания высокой температуры и высокой запыленности воздуха, на материалы, оборудование и технико-экономические показатели транспортных средств. Предлагаемый способ достаточно универсален, поскольку основан на анализе закономерностей процессов, характерных для используемых тормозных механизмов. При эксплуатации тормозных устройств их пары трения подвергаются износу с различной интенсивностью. Считалось, что для изучения охлаждения и нагрева кузовов, представляющих собой особую форму нестационарного теплообмена, необходимо различать некоторые стадии тепловой нагрузки пар трения тормозов. Нагрев и охлаждение тормозного барабана описывались дифференциальным уравнением теплопроводности Фурье. Тепловое воздействие на обод барабана (не ниже 100°C и более) вызывает его термическую деформацию, которая из-за низкой эффективности естественного охлаждения действует в течение более длительного периода времени, чем механическое. Приведенные данные о тепловой нагрузке рабочих частей тормозов транспортных средств позволяют установить влияние геометрических (диаметр, толщина и ширина обода тормозного барабана, установочный зазор между парами трения, коэффициент взаимного перекрытия взаимодействующих пар) и теплофизических коэффициентов, теплопроводности а также теплопроводность материалов обода барабана и фрикционной накладки, параметры, температуру их поверхности и накапливают априорную информацию об управлении теплом.

Keywords: friction pairs, thermal load, braking properties, vehicles, factors, braking systems, temperature.

Ключевые слова: пары трения, тепловая нагрузка, тормозные свойства, транспортные средства, факторы, тормозные системы, температура.

Introduction. In recent years, there has been a steady increase in the number of vehicles capable of developing high speeds. Improvements in road quality have led to increased average traffic speeds, especially on urban routes. At the same time, traffic intensity and density have grown, increasing the likelihood of road accidents. Therefore, the task of improving road safety, in particular ensuring reliable braking properties of vehicles, remains highly relevant.

Problem Statement. Although the industry produces a large number of machines, most designs are not adapted to the operating conditions in hot climates. Therefore, assessing the working conditions of machines in dry and hot climatic zones with high air dust content is of great interest.

Method Description

Theoretical Basis

The potential operational properties of vehicles are realized under specific operating conditions. Knowledge of the factors affecting these conditions and their impact on vehicle characteristics enables purposeful management of quality indicators during design and operation stages.

The developed method takes into account the patterns of heating and cooling processes of friction pairs of braking mechanisms, as well as the influence of geometric and thermophysical parameters.

Detailed Mathematical Models

To assess drum deformation and thermal load, the following key formulas are used:

1. Calculation of force load and deformation of the drum:

=(∑)

where:

∑K_Mo ​ — a combination of constructive parameters of the cylindrical rim of the brake drum (thickness, diameter, width),

H_o— load on the drum rim, N,

P_Mo ​ — parameters of the drum construction,

T_No ​ — temperature change parameter of the rim.

2. Deformation considering the lining parameters:

W₁=φ₂​(W₁​:∑K_Mδ​:H_b​:P_Mδ​:T_Mδ​)

where:

∑K_Mδ ​ — lining parameters,

H_b​ — load on the linings,

P_Mδ, T_Mδ— thermally related lining parameters.

Practical Example

Consider a drum with diameter D=300 mm, thickness b=20 mm, load H_o=1000 N, and heating temperature T_No=150^∘C. With ∑K_Mo=1.2, P_Mo=0.8 and φ₁=0.5 the calculated deformation is:

W₁=0.5×(1.2×1000×0.8×150)=72000 conditional units

Similarly, parameters for linings are calculated.

Modeling of the Thermal Process

The heating and cooling of the drum are described by Fourier’s heat conduction equation:

= ()

where α_oδ​ is the temperature diffusivity coefficient of the material, and T2=T2(x,y,z,t) is the temperature at a point in the body.

The solution reduces to a sum of exponential terms:

T_δ​=A₁​U_1​e^−m1​t+A₂​U_2​e^−m2​t+A₃​U_3​e^−m3​t

In practice, only the first term is considered due to the rapid decrease of others.

Physical and Mechanical Meaning of Parameters

T_δ — excess temperature of the drum above ambient temperature,

A_i, U_i​ — constants and functions defining initial temperature distribution,

m_i​ — parameters characterizing cooling rate, dependent on shape, size, and material properties.

Novelty of the Method

The proposed method stands out from classical approaches by:

• Considering specific hot climate conditions with high dust load affecting heat transfer and wear;
• Incorporating nonlinear thermal loading and deformation processes, which are not addressed in traditional linear models;
• Introducing a comprehensive analysis of geometric and thermophysical parameters of the drum and friction linings, including mutual overlaps and gaps.

Compared to traditional methods that typically model stationary and isolated processes, this new method offers a more accurate description of temperature and deformation regimes, enhancing reliability in predicting brake system behavior under real operating conditions.

Experimental Verification

To verify the model, experimental studies were conducted in a climatic chamber with controlled temperature and dust content.

• Ambient temperature was maintained at 60°C, dust concentration at 3 g/m³.
• Surface temperatures of the drum and linings were measured using thermocouples and infrared pyrometers.
• Drum deformation was recorded with a laser sensor.

Results showed that calculated data matched experimental results within a 5% error margin, confirming the practical applicability of the method.

Figure 1 illustrates the dependence of the heating and cooling time of the drum rim on the natural logarithm of the excess temperature ln T_δ​

Conclusion

The developed method for determining thermal load parameters of friction pairs in vehicle braking systems allows:

• Considering the influence of climatic factors (high temperature, dust load) on thermal processes and wear;
• Evaluating the impact of geometric and thermophysical parameters on thermal deformation;
• Modeling non-stationary heating and cooling processes using Fourier’s heat conduction equation;
• Using the results to manage thermal regimes of braking systems and improve their reliability under extreme operating conditions.

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