Thermal FE analysis of a one side brake block test equipment ( Part 2 )

The paper includes the second part of an investigation of the braking process of railway vehicles, dealing with the temperature distribution of a brake block in various load cases and the FE analysis of the phenomenon of thermal elastic deformation. Thermal expansion calculations pointed out to the fact that in case of the contact area, the radius of the operating surface of the brake block increases as a result of warming up. In the course of braking, the brake block of increased radius wears off to the size of the wheel, and after cooling down the radius of the operating surface will be smaller than the radius of the wheel, therefore at the next braking phase the two edges of the brake block will first contact with the wheel. The paper deals with the thermal expansion of a worn brake block as well to compare the FE results with the measured worn data. It was found that the thermal expansion of the brake block is less significant than the effect of the wear on the deformation of the brake block profile.


Introduction
In addition to a precise description of friction conditions, it is essential to explore the (elastic and plastic) contact and thermal conditions of the brake block and the wheel rim in friction for the design and dimensioning of railway brake blocks.Braking characteristics depend on load, motion and material properties.By drawing on adequate information, braking friction and wear processes can be forecasted and the wear speed of the friction pair can be reduced, which is an important expectation in regard to the economy of railway operation.The complex phenomenon of braking was investigated through the analysis of a brake block test equipment operated at the Department of Railway Vehicles of Budapest University of Technology and Economics (BME).Research commenced by determining the thermal state of the equipment.The heat distribution of the equipment was determined by a thermal FE model in a steady state at a given braking power; in addition, transient tests were performed to track the process of heating up.In order to take heat conduction precisely into consideration, thermal contact resistances were applied inside the bearing boxes.A 3D model is required to be applied to model the actual heat-up process [1].Calculation parameters were validated by temperature measurements.The CosmosWorks software was used for FE calculations; measurements were performed at BME Department of Railway Vehicles.

Test equipment
The testing equipment developed in the 1980's is suitable for examining the friction, heat and wear processes of a railway brake block vs. wheel rim on a scale of 1:4.Fig. 1. shows a photo about the test equipment.
Fig. 2 shows the dimensions of the brake block and the braked wheel.

Material properties
The brake block is made of P14 cast iron with high phosphorous content.The mechanical and thermal properties of this material in function of the temperature had been determined during the cooperation of the Department of Railway Vehicles of Budapest University of Technology and Economics (BME) and  The test wheel was made of carbon steel A38.Its material properties used for calculations are contained by Tab. 1.The materials of further components were defined with simplifications, namely that the material of all components was set as normal structural steel (Tab.1).The scope of the model was determined in a way that only those parts were removed from the testing equipment which do not heat up in a consolidated temperature state, either.As the measurement was validated by a single brake block design, the geometric model also contains only 1 brake block.The SKF SN 510 type bearing houses were taken into consideration with a simplified geometry, taking care of the fact that the size of heat convection surfaces and the mass of the bearing house should correspond to the respective characteristics of the actual bearing house.The heat insulation effects of bearings were taken into account with contact thermal resistances in the thermal model.Fig. 6. shows the armature taken out of the complete geometric model, together with the three bearing houses and the two brake block holders.The braked wheel in the test equipment is driven by a steel friction disk to model the contact between wheel and rail.The flat disk rotating in the middle of the shaft enables the investigation of disk brakes.
10-node second order tetrahedron elements were used in the FE model, with an average element size of 2 mm along surfaces in friction and 8 mm elsewhere.Fig. 7 shows the entire model examined and the FE mesh refinement on the surfaces in friction of the brake block and the wheel.
The thermal load of the FE model was determined based on the operating conditions of the test equipment.The total heat power generated in the course of braking (Q) can be determined where F N is the normal force acting on the brake block; F S is the friction force generated on the brake block; µ is the average friction coefficient; v is the average sliding speed; A S is the operating surface of the braking block; and p N is the average surface pressure.It was assumed that the F N and µ and also the sliding speed (v), furthermore the Q remain constant during the test process.Tab. 2 summarizes the operation conditions and the initial data associated therewith.and for the rotating wheel, Rolling bearings constitute a significant obstacle in terms of thermal conductivity, and this may fundamentally influence the process of heating up and the heat distribution to be produced.The "heat insulation" impact of bearings, that is, contact heat transfer can be modelled by a fictitious convective heat transfer coefficient.The value of which in the thermal model was selected to be α * = 10000W/m 2 K, [3].In the CosmosWorks software, the inverse of contact heat transfer, the so-called thermal contact resistance must be specified: the value of which is: h c = 0.0001 m 2 K/W.

Location of measurement and control points in the model
The results of numerical calculations were checked on the test equipment by temperature measurements.Measurement points were designated for controllability, where the calculated temperatures were checked by measurement.Figs.9-11 illustrate and Tab. 3 summarizes the locations of the temperature measurement points.

Transient calculations
The model is "thermally loaded" by the friction energy (converted into heat power) generated at the points of contact of the brake block and the wheel.According to Tab. 2, the value thereof is 446 W. The problem was solved by distributing the heat load by heat partitions, meaning that the total heat generated must be distributed between the brake block and the wheel so that the temperature of the surfaces in friction of the two components should be identical [4].(In case of transient FEA calculations, this condition must be met at each iteration step.)In the FEA simulations the wheel was separately analyzed by using the distributing heat source model [5].At the same time step the rest of the model formed a separate model, there was not any physical contact connection between the wheel and the brake block.For both models the heat power followed the given heat partitions to fulfil the contact temperature condition [4].In calculations for a steady state, distribution of the total heat between the two components is the result of a calculation of iteration, according to which 89% of the total heat generated falls on the wheel side and 11% to the brake block side.As a result of this heat partition, the temperature of the two surfaces in friction is identical with proper approximation.In case of a transient calculation, the measures of heat partition are a bit different at each time step, for example ate the beginning of the simulation the 86% of the total heat power acted on the wheel and 14% on the brake block.Transient heat partitions were specified with iteration in every 60 seconds in the transient simulations in order to fulfil the condition of Block [4].Fig. 12 shows the temperature of the surfaces in friction of the wheel and the brake block.The Figure indicates that the temperature of the brake block and the wheel practically coincide, evidencing the correct proportions of distributing the heat generated.
Fig. 12 shows the thermal distribution of the entire model and the small environment of the brake block and the wheel at given moments of time.In order to illustrate the temperature development the temperature values was presented according to the same temperature chart at each moment, i.e. the maximum temperature was set to 120 • C in Fig. 12.

Comparison of measurement and calculation results
In the test, the measurement configuration contained 1 brake block where the load was 100 N, the rpm of the wheel was 913, and the environment temperature was 25 ˚C.At the designated places of measurement (Tab.3, temperatures were measured by two types of thermometers (Brenner type Thermo Control laser temperature, TM-25 type Thermometer).In the course of the measurement, both thermometers were used for measurements at each measurement location (8 measured points).Obviously, only laser measurements could be applied at point 4 on the braked wheel.It can be stated in general that the contact thermometer measured 2-3 • C lower temperatures than the laser one.Likely reasons for this include the thermal contact resistance between the tip of the thermometer and the surface as well as the thermal inertia of the sensor.The comparison of the measured and calculated temperature values are shown in Figs.14-17.
Unfortunately, the contact temperature can not be measured directly.Control points 5 and 6 are near the contact surfaces illustrated the heat generation in the vicinity of the contact area (see Fig. 11 and Fig. 16.These measured and calculated temperature values are in good agreement near the contact area.

Conclusion
Based on simulations using the 3D transient thermal FE model of the equipment to simulate a complete brake block and wheel connection, it can be stated that in the course of the braking process, the measurement and calculation results coincide in their characteristics, with temperature values varying at certain parts of the equipment.The nature of the different temperatures calculated and measured on the braked wheel (point 4) are similar: measured values are systematically lower -by 10 ˚C -than those calculated.The presumable reason for this can be that laser temperature measurements were performed on moving surfaces, which is "not recommended" according to the operating manual of the instrument.A common characteristic feature of the places of measurement on the platform part is that calculated temperatures are lower than those measured.This may be due to the fact that the ball bearings built in the test equipment act as heat sources themselves at the tested rpm, and this must be taken into consideration in the calculation model as well.

Fig. 1 .Fig. 2 .
Fig. 1.Small sample test equipment with one side brake block configuration

Fig. 3 .
Fig. 3. Temperature dependence of elastic modulus and the thermal expansion coefficient of cast iron P14

Fig. 4 .
Fig. 4. Temperature dependence of elastic modulus and the thermal expansion coefficient of cast iron P14

Fig. 5 .
Fig. 5. Geometric model of the test equipment

Tab. 1 .Fig. 6 .
Fig. 6.Test equipment model with bearings and arms to hold brake block

Tab. 3 .
Fig.8shows the location of contact heat resistances in the thermal model.

Fig. 13 .
Fig. 13.Temperature distribution of the entire model and the immediate surroundings of the brake block and the wheel at discrete moments of time

Fig. 14 .
Fig. 14.Measurement and calculation results at measured points 1 and 2

Fig. 15 .
Fig. 15.Measurement and calculation results at measured points 3 and 4

Fig. 16 .
Fig. 16.Measurement and calculation results at measured points 5 and 6

Fig. 17 .
Fig. 17.Measurement and calculation results at measured points 7 and 8