Estimation of temperature distribution in brake shoes is very important in order to prevent thermal damages such as cracks, fading etc. In this research, the thermal model of brake shoe in a train is introduced considering time-dependent frictional heat load in two modes of emergency and continuous braking. The governing heat conduction equation is solved in polar coordinate by using the method of separation of variables combined with Duhamel integral and a closed-form solution is introduced. Results show the good ability of analytical solution to estimate exact temperature profile in composite and cast iron brake shoes. The ability of the solution for estimation of braking situation to prevent from melting criteria is demonstrated. The composite brake shoe will reach to the melting point of 590 °C in continuous braking at the speed of about 120 km/h and the fading limit in cast iron shoe is occurred after 8 sec in emergency braking mode. The introduced thermal model can be applied as a verification branch of other works and can reduced the huge costs of experimental tests of brake shoes.
ModanlooATalaeeMR.Analytical thermal analysis of advanced disk brake in high speed vehicles. Mech Adv Mater Struct2020; 27: 209–217.
2.
KwonSJSeoJWJunHK, et al. Damage evaluation regarding to contact zones of high-speed train wheel subjected to thermal fatigue. Eng Fail Anal2015; 55: 327–342.
3.
PanierSDufrénoyPWeichertD.An experimental investigation of hot spots in railway disc brakes. Wear2004; 256: 764–773.
4.
SawleyKJ.Calculation of temperatures in a sliding wheel/rail system and implications for wheel steel development. Proc IMechE, Part F: J Rail and Rapid Transit2007; 221: 455–464.
5.
MiloševićMSStamenkovićDSMilojevićAP, et al. Modeling thermal effects in braking systems of railway vehicles. Therm Sci2012; 16: 515–526.
6.
AdamowiczAGrzesP.Analysis of disc brake temperature distribution during single braking under non-axisymmetric load. Appl Therm Eng2011; 31: 1003–1012.
7.
TeimourimaneshSVernerssonTLundénR.Modelling of temperatures during railway tread braking: influence of contact conditions and rail cooling effect. Proc IMechE, Part F: J Rail and Rapid Transit2014; 228: 93–109.
8.
NejadRM.Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels. Eng Fail Anal2014; 45: 449–455.
9.
Laguna-CamachoJRJuárez-MoralesGCalderón-RamónC, et al. A study of the wear mechanisms of disk and shoe brake pads. Eng Fail Anal2015; 56: 348–359.
10.
LuBHChenXYQuBZ, et al. Research on wheel-shoe wear for high friction composite brake shoes based foundation brake rigging in railway wagon. Key Eng Mater2016; 667: 530–535. Trans Tech Publications Ltd.
11.
VernerssonT.Temperatures at railway tread braking. Part 2: calibration and numerical examples. Proc IMechE, Part F: J Rail and Rapid Transit2007; 221: 429–441.
12.
VakkalagaddaMRKSrivastavaDKMishraA, et al. Performance analyses of brake blocks used by Indian railways. Wear2015; 328: 64–76.
13.
KimMS.Dynamometer tests of brake shoes under wet conditions for the high speed trains. Int J Syst Appl Eng Dev2011; 5: 143–150.
14.
TudorARadulescuCPetreI.Thermal effect of the brake shoes friction on the wheel/rail contact. Tribol Ind2003; 25: 27–32.
15.
FaccoliMGhidiniAMazzùA.Experimental and numerical investigation of the thermal effects on railway wheels for shoe-braked high-speed train applications. Metall Mater Trans A2018; 49: 4544–4554.
16.
FaccoliMGhidiniAMazzùA.Changes in the microstructure and mechanical properties of railway wheel steels as a result of the thermal load caused by shoe braking. Metall Mater Trans A2019; 50: 1701–1714.
17.
FaccoliMProvezzaLPetrogalliC, et al. Effects of full-stops on shoe-braked railway wheel wear damage. Wear2019; 428: 64–75.
18.
ZhuZCPengYXShiZY, et al. Three-dimensional transient temperature field of brake shoe during hoist’s emergency braking. Appl Therm Eng2009; 29: 932–937.
19.
WangFGuKKWangWJ, et al. Study on braking tribological behaviors of brake shoe material under the wet condition. Wear2015; 342: 262–269.
20.
MazzùAProvezzaLZaniN, et al. Effect of shoe braking on wear and fatigue damage of various railway wheel steels for high speed applications. Wear2019; 434: 203005.
21.
KimMS. Vibration analysis of tread brake block in the brake dynamometer for the high speed train. Int J Syst Appl Eng Dev2011.
22.
WuYKMoJLTangB, et al. Tribological and dynamical analysis of a brake pad with multiple blocks for a high-speed train. Proc IMechE, Part J: J Engineering Tribology2019.
23.
ShigleyJE.Shigley’s mechanical engineering design. New York: Tata McGraw-Hill Education, 2011.
24.
ChipmanJ.Thermodynamics and phase diagram of the Fe-C system. Metall Mater Trans B1972; 3: 55–64.
25.
ChoMHKimSJBaschRH, et al. Tribological study of gray cast iron with automotive brake linings: the effect of rotor microstructure. Tribol Int2003; 36: 537–545.
26.
LadenkGuerinJDWatremezM, et al. Frictional characteristics of Al-SiC composite brake discs. Tribol Lett2000; 8: 237–247.
27.
VernerssonTLundénR.Temperatures at railway tread braking. Part 3: wheel and block temperatures and the influence of rail chill. Proc IMechE, Part F: J Rail and Rapid Transit2007; 221: 443–454.
28.
NasrAMohammadiS.The effects of train brake delay time on in-train forces. Proc IMechE, Part F: J Rail and Rapid Transit2010; 224: 523–534.
29.
TalaeeMRKabiriAKhodarahmiR.Analytical solution of hyperbolic heat conduction equation in a finite medium under pulsatile heat source. Iran J Sci Technol Trans Mech Eng2018; 42: 269–277.
30.
TalaeeMRKabiriA.Exact analytical solution of bioheat equation subjected to intensive moving heat source. J Mech Med Biol2017; 17: 1750081.
31.
TalaeeMAlizadehMBakhshandehS.An exact analytical solution of non-Fourier thermal stress in cylindrical shell under periodic boundary condition. J Eng Solid Mech2014; 2: 293–302.
32.
LukeYL.Integrals of Bessel functions. Chelmsford, MA: Courier Corporation, 2014.
33.
OzisikMN.Heat conduction. New York: John Wiley & Sons, 1993.
