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

For the safety problem of heavy duty vehicles running on long downhill sections, a model was built for the application of engine brake and service brake combination based on test results. And a model of brake temperature rise for heavy duty vehicles running on long downhill sections was also established. For different braking modes, gear positions, speed and downhill slopes, brake temperature rising to 250°C was used as the index. And then simulation of brake temperature rise and downhill distance was researched. Simulation results show that the combined braking of low gear and high speed should be adopted for heavy duty vehicles running on long downhill sections.


INTRODUCTION
The implementation of develop-the-west strategy has provided positive conditions for regional economy.The center of road construction is moving from eastern plains to western mountain areas [1].Considering factors of cost, environment and natural conditions, critical parameters of design standard were chosen when designing and constructing the roads, so that the roads were steep and the slope was continuous [2][3][4].As a result, safety driving on the continuous and steep mountain roads is a key scientific issue to be solved at the present stage in traffic safety field.
When vehicle runs on continuous downhill roads, gravitational energy translates to kinetic energy, so the vehicle speed increases.In order to ensure safety, certain brake force is required for the vehicle.However, with the increase of downhill distance and brake temperature, brake performance degrades [5,6].Therefore, certain continuous brake force is required when driving on downhill roads.And if continuous brake force fails to meet the need of braking requirements, service brake starts working.Driving performance of the combination of engine brake and service brake for heavy duty truck is discussed in this paper.

FUNDAMENTAL OF ENGINE CONTINUOUS BRAKE
Common continuous brake methods include engine brake, exhaust brake, JieKebo brake, eddy current retarder, hydrodynamic retarder and so on [7][8][9][10].Compared with other ways, engine brake is easier to operate and costs less.Other assisted components are also unneeded for engine brake.As a result, engine brake is widely used as a continuous brake method.
Engine brake is a term used when the gas pedal is released, supply of fuel is cut, clutches meet each other and the transmission is not in neutral gear, engine is rotated by high speed vehicle.Brake effect is generated by compression resistance, internal friction, air intake and exhaust resistance on driving wheels at the engine compression stroke.

Brake Temperature Rise Model
When vehicle was running on downhill road and braking measurements were taken, vehicle decelerated with service brake force, rolling resistance, air resistance, and continuous brake force.The stress analysis figure for vehicle braking on downhill road is shown in Fig. (1).When brake measures were taken on downhill road, altitude and vehicle speed decreased.Gravitational energy and kinetic energy were also decreased.The energy translated to thermal energy of service brake in addition to the work of rolling resistance, air resistance, and continuous brake force [11].According to work and energy principle in the vehicle brake process, kinetic energy and gravitational energy translated to the energy consumed by service brake, rolling resistance, air resistance and continuous brake force.That is to say, 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, where, T 0 is the initial temperature, m g 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), 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].
Based on equation ( 4), the mathematical model of brake drum temperature fall was established.
where, A can be calculated as follows,

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.
The function relation between engine braking torque and vehicle speed obtained from experiment is formulated as equation (7), and the value of The function relation between the sum of rolling resistance and air resistance and vehicle speed obtained from experiment is shown as equation ( 8) Based on equation ( 6), ( 7) and ( 8), the brake temperature rise model is,

Parameters for Simulation Model
Driving performance on continuous downhill road was researched with DongfengTianlong DRL4251A9 truck, which was established as a simulation object.Simulation parameters of the test vehicle are shown in Table 2.

Simulation Results
Aimed at different brake methods, different gear position, different vehicle speed and different gradient, brake temperature rise model of heavy duty truck driving on continuous downhill road was researched.Downhill road distance was used as index of downhill driving performance when the temperature of brake rises to 250℃.Comparisons were made between the usage of service brake only and the usage of combined brake, which included engine brake and service brake.Comparisons were made between driving performance on downhill road at the 9th gear and 10 th gear.Comparisons were also made for downhill driving performance with different vehicle and different gradient.
In the simulation process, assumed that initial temperature of brake was 30℃, and the temperature around brake was 35 ℃ .The mathematical value of brake temperature was obtained with different vehicle speed, gear position, brake method and gradient.
(1) Brake temperature rise simulation result under the circumstance of the application of engine brake and service brake at 9th gear, 50km/h.
(2) Brake temperature rise simulation result under the circumstance of the application of engine brake and service brake combination at 9th gear, 60km/h.
(3) Brake temperature rise simulation result under the circumstance of the application of engine brake and service brake combination at 10 th gear, 50km/h.
(4) Brake temperature rise simulation result under the circumstance of the application of service brake only at 10 th gear, 50km/h.

Contrastive Analysis of Simulation Results
(1) According to Figs.
(2, 3), if engine brake and service brake were applied together, vehicle travelled on 5% downhill road in the 9th gear at 50km/h.When the brake temperature rose to 250℃ and driving distance reached was 8055.56m.Vehicle run on 5% downhill road at the speed of 60km/h and the distance reached was 8516.67m.

Fig. (2).
Result of brake temperature rise with the application of combined brake at 9th, 50km/h.

Fig. (3).
Result of brake temperature rise with the application of combined brake at 9th, 60km/h.

Fig. (4).
Result of brake temperature rise with the application of combined brake at 10 th , 50km/h.
(2) According to Figs. (2,4), if engine brake and service brake were applied together, vehicle run on 5% downhill road in the 9th gear at 50km/h.When the brake temperature rose to 250℃ and driving distance reached was 8055.56m.Vehicle ran on 5° downhill road in the 10 th gear at 50km/h and the distance reached was 6805.56m.

Fig. (5).
Result of brake temperature rise with the application of service brake only at 10 th , 50km/h.
(3) According to Figs. (4,5), if engine brake and service brake were applied together, vehicle run on 5% downhill road in the 10 th gear at 50km/h.When the brake temperature rose to 250℃ and the driving distance reached was 6805.56m.If service brake was applied only, vehicle run on 5% downhill road in the 10 th , at 50km/h and the distance reached was 5972.22m.
(4) According to Fig. (4), if engine brake and service brake were applied together, vehicle run on 3% downhill road in the 10 th gear at 50km/h.When the brake temperature rose to 250℃ and driving distance reached was 20555.56m.Vehicle run on 4% downhill road and the distance reached was 10138.89m.Vehicle run on 5% downhill road and the distance reached 6805.56m.
(5) According to Fig. ( 5), if service brake was applied only, vehicle run on 3% downhill road in the 10 th gear at 50km/h.When the brake temperature rose to 250℃ , driving distance reached was 14583.33m.Vehicle run on 4% downhill road and the distance reached was 8472.22m.Vehicle run on 5% downhill road and the distance reached was 5972.22m.

CONCLUSION
Aimed at safety problem of heavy duty vehicle running on continuous downhill road, the model of combination of engine brake and service brake is established and analyzed.The brake temperature rise model was built, and then brake temperature rise and downhill distance was researched according to different vehicle speed, gear position, brake method and gradient.Conclusions were made as follows through comparative analysis of simulation results. (1) When combined brake was applied under the circumstance of same gradient and vehicle speed.If higher gear position was chosen, continuous brake force was smaller, the speed of brake temperature rise was faster and downhill distance was shorter.If lower gear position was chosen, continuous brake force was bigger, the speed of brake temperature rise was slower and downhill distance was longer.
(2) When combined brake was applied under the circumstance of same gradient and gear position.If the vehicle speed was lower, continuous brake force was smaller, the speed of brake temperature rise was faster and downhill distance was shorter.If the vehicle speed was higher, continuous brake force was bigger, the speed of brake temperature rise was slower and downhill distance was longer.
(3) Under the circumstance of same gradient, vehicle speed and gear position, the speed of brake temperature rise was slower and downhill distance was longer if combined brake was applied.The speed of brake temperature rise was faster and downhill distance was shorter if service brake was applied only.
(4) Under the circumstance of same brake method, vehicle speed and gear position, the speed of brake temperature rise was faster and the downhill distance was shorter if the gradient was larger.
As a result, combined brake method should be chosen for heavy duty vehicle when it runs on continuous downhill road at low gear position and high speed.