# Research of Driving Performance for Heavy Duty Vehicle Running on Long Downhill Road Based on Engine Brake

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2 476 The Open Mechanical Engineering Journal, 2014, Volume 8 Zhao et al. resistance, air resistance and continuous brake force. That is to say, 1 2 m(u 2 t ) mgssinθ = (F b F f F b _ motor )s (1) where, the symbol u t is final velocity, u 0 is initial velocity, m is vehicle mass, F b is service brake force, F f is rolling resistance, F w is air resistance, F b _ motor is engine brake force, θ is gradient, s is driving distance. According to energy fundamental, brake temperature rise model was built as follows, T = T 0 n (1 2 m(u 2 t ) mgssinθ-(f f F b _ motor )s) where, T 0 is the initial temperature, is brake drum mass, c g is brake drum specific heat capacity, ε is correction factor, which is related with axle load and the gap between brake shoe and brake drum Brake Temperature Fall Model According to thermodynamic theory, the ways for cooling are heat conduction, heat convection and thermal radiation [12]. Among them, heat convection plays an important role while the effect of heat conduction and thermal radiation can be ignored in the process of braking. Heat convection is that fluid goes over the solid surface and if temperature is different heat transfer takes place between fluid and the solid surface. According to Newton cooling formula, brake drum temperature falls due to radiating of the surrounding air [13], Heat flux of heat convection can be calculated with equation (3), P d = h r A 2 ( T T a ) (3) where, h r is strength coefficient for heat convection between brake drum and air, T is brake drum temperature, T a is the average temperature around brake drum, A 2 is the area of extended surface for brake drum. Formula (4) was made according to energy conservation of brake drum temperature fall [14]. ΔT = P Δt (4) Based on equation (4), the mathematical model of brake drum temperature fall was established. T = ( T 0 T a )e At T a (5) where, A can be calculated as follows, ( A = u a e u a ) A 2 (2) 3.3. Establishment of Brake Temperature Rise Model for Heavy Duty Truck Running Downhill Brake temperature changes included the process of brake temperature rise and brake temperature fall. According to equation (2) and (5), the model of brake temperature rise when vehicle running downhill was as follows. T = T 0 T T = 2T 0 n (1 2 m(u 2 t ) mgssinθ-(f f )s F b _ motor s) ((T 0 T a )e At T a ) The function relation between engine braking torque and vehicle speed obtained from experiment is formulated as equation (7), and the value of D 1, E 1, F 1 is shown in the following Table 1 T b _ motor = D 1 u a 2 E 1 u a F 1 (7) Table 1. (6) Coefficient of function relation between engine braking torque and vehicle speed. Gear Position 1 st Gear 2 nd Gear 3 rd Gear 4 th Gear D E F Gear Position 5 th Gear 6 th Gear 7 th Gear 8 th Gear D E F Gear Position 9 th Gear 10 th Gear 11 th Gear 12 th Gear D E F The function relation between the sum of rolling resistance and air resistance and vehicle speed obtained from experiment is shown as equation (8) F f F w = 0.371u a u a (8) Based on equation (6), (7) and (8), the brake temperature rise model is, T = 2T 0 n {1 2 m(u i 2 t )mgs 1 i 2 -[( 0.371D 1 ) u 2 a ( E 1 ) u a ( F 1 )] s} (9) ( T 0 T a )e At T a

5 Research of Driving Performance for Heavy Duty Vehicle The Open Mechanical Engineering Journal, 2014, Volume [6] D.K. Whiteford, NCHRP Synthesis 178. Truck Escape Ramps. A synthesis of highway practice. Transportation Research Board, vol. 5, [7] R. Xiao, Y. Ye, X. Zhou, and D. Liu, Critical slope length computation of engine brake inefficacy, Journal of Traffic and Transportation Engineering, vol. 6, no. 4, 122-6, [8] Q. Yu, Y. Chen, J. Ma, R. Guo, and Y. Zhang, Research on engine brake performance of passenger car, Journal of Xi an Highway University, vol. 19, no. 4, pp.90-92, [9] C. Hu, J. Shen, and Y. Chen, Temperature-rising Laws of Drum brake pad for truck on long downgrades, Journal of Traffic and Transportation Engineering, vol. 9 no. 44, 49-55, [10] R. Xiao, X. Zhou, and Y. Ye, Calculation of criticalvalue for downhill road driving distance of vehicle brake failing with exhaust brake applied, Journal of Safety and Environment, vol. 7 no. 6, pp , [11] J. Jancirani, S. Chandrasekaran, and P. Tamilporai, Design and heat transfer analysis of automotive disc brakes Conference, American: American Society of Mechanical Engineers, vol. 4 no. 1, pp , [12] X. Mou, Vehicle Theory. Chongqing, Chongqing University Press, pp , [13] S. Jin, and B. Du, Prediction model ofbrake temperature oftruck on long and steep downgrade Journal of Highway and Transportation Research and Development, vol. 28, no. 2, pp , [14] A.J. Day, The dissipation of frictional energy from the interface of an annular disc brake, Proc Instn Mech Engrs, vol. 198, no. 11, pp , Received: September 10, 2014 Revised: November 5, 2014 Accepted: November 5, 2014 Zhao et al.; Licensee Bentham Open. This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License ( by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

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