Modeling and Simulation Vehicle Air Brake System

Transcription

1 Moeling an Simulation Vehicle Air Brake System Li He, Xiaolong Wang, Yunqing Zhang, Jinglai Wu, Liping Chen CAD Center, Huazhong University of Science an Technology, China Abstract Air brake system has been wiely use in heavy trucks an intercity buses for its great superiority over other brake system. The practical performance of air brake system may be greatly ifferent from if we analyze it with static theory. Thus, it is necessary to buil an integrate air brake system moel to simulate the process of brake accurately. However, the ynamic mathematic moel of air brake system is very complicate, which makes the moel har to be solve. In this paper, the components of air brake system are ecompose to several basic stanar pneumatic components, an then buil the system base on these basic stanar pneumatic components. The stanar pneumatic components which are built in the software- MWorks base on Moelica language inclue cyliner, nozzle, air reservoir, volume, an air pipe. An air brake system which contains brake valve, relay valve, brake chambers an pipelines is mae base on the stanar pneumatic components. The simulation results show the ynamic characteristics of air brake system. Keywors: air brake system; ynamic moel; Moelica 1 Introuction Brake system affects the safety of automotive irectly. The theories of brake system have been well stuie [1, 2, 3]. However, the theories of brake system are almost limite to analyze the system s static characteristics such as the istribution of brake force between the front an rear axle, brake efficiency an so on. There is little literature focus on the ynamic characteristics of brake system. The vehicle brake system can be generally ivie into hyraulic brake system an air brake system. In fact, most tractor-trailer vehicles with a gross vehicle weight rating (GVWR) over lb, most single trucks with a GVWR over lb, most transit an intercity buses, an about half of all school buses are equippe with air brake systems [4]. Generally, the air brake system will show longer elay time than the hyraulic brake system for the response of air pressure is relative slowly to hyraulic pressure. In fact, the elay time for the pressure response has enormous influence on the performance of the vehicle brake system. Also the quick pressure response is one of the most imant inispensible working conitions for the anti-brake system (ABS) which has been wiely use in automotives. Thus, to shorten the pressure response time is necessary. Roulf [1] has given an empirical equation to calculate the elay time for the pressure response in air brake system, which correlate with the brake chamber volume an the length of pipelines. However, in practice we often nee a more accurate moel to research the elay time more exactly. So the moel of air brake system which can accurately preict the pressure transmits from reservoir along the brake pipelines to the brake valve, relay valve an brake chamber shoul be buil. The mathematic moel for ynamic responses of air brake system is very complicate since many ifferential equations nee to be solve an many parameters may be correlate with each other, especially the parameters for the key components, such as brake valve, relay valve an pipelines. A non-linear moel of the pneumatic subsystem of the air brake system which relates the pressure in the brake chamber to the brake valve plunger isplacement an the supply pressure to the brake valve has been evelope in [5,6]. The mathematic moel is very compli-

2 cate, which leas it har to be solve. Wu [7] stuie the robust of pneumatic brake system in commercial vehicle, where the ynamics moel is built in software-amesim. In this paper, we use the Moelica language [8, 9] to construct the mathematic moel, an we o not nee to focus on the solver, which simplifies the work largely. In this stuy, the pneumatic brake system moel are built an simulate base on the Moelica language. In section 2, the constitutions of air brake system are presente; the air brake system moel is introuce in section 3. The simulation results are shown in section 4, an some conclusions are presente in the last section. 2 Air brake system components An essential layout of the air brake system of a commercial vehicle is shown in Fig.1. The air brake system contains air compressor, storage reservoirs, brake valve, relay valve, brake chambers an some brake lines. Front Brake Top Air Compressor Brake Valve Supply Wet Reservoir Rear Reservoir Front Reservoir Supply Control Relay Valve Rear Brake Figure. 1 Schematic representation of an air brake system The river applies the brake by pressing the brake peal on the brake valve. This action makes the compresse air flow from the supply of the brake valve to its elivery. For the front circuit, the compresse air travels from the elivery in bottom chamber of the brake valve through pipelines to the front brake chambers mounte on the front axles. For the rear circuit, the compresse air travels from the elivery in top chamber of the brake valve through pipelines to the control of relay valve, which opens the supply of relay valve an makes the air flow to the rear brake chambers mounte on the front axles. 2.1 Brake Valve The structure of brake valve is shown in Fig. 2. x p Rubber Circuit x tp Exhaust Port x tv Inlet Port Plunger C t C b Fp D tpl D tps D tvl Exhaust Stem Spring Figure. 2 Structure of brake valve Top Piston Top Piston Top Valve Assembly Top Supply Top Valve Piston Supply Valve Valve Assembly There are two supply s, two elivery s, an an exhaust in the brake valve. The top supply an bottom supply are connecte to rear reservoir an front reservoir respectively, while the top elivery an bottom elivery are connecte to relay valve an front chambers respectively. For the top chamber, when the river applies peal force to the plunger, the force transmits to top piston compressing the rubber plunger spring. If the force acte on top piston is larger than the preloa an friction, the top piston will move own. The exhaust will be close when the top piston touches the top valve, an the inlet will open if the force transmitte to top valve can overcome the preloa on top valve. Then the compresse air in rear reservoir can flows into top chamber, which makes the pressure in top chamber increasing. The compresse air in top chamber will prouce a force that makes the top piston an top valve move up, an the inlet will be close graually. The pressure keeps constant for both the inlet an exhaust are close, thus the air pressure in top chamber

3 keeps constant. If the river reuces peal force, the balance of top piston will be broken. The top piston moves up for the force mae by compresse air larger than peal force, which make the exhaust opene. Thus, the compresse air flow to atmosphere an reuces the pressure. The apply process of bottom chamber is similar to the top chamber. The flow areas of inlet an exhaust have imant effect on the characteristics of brake valve. The positions of top piston an top valve etermine the flow areas of inlet an exhaust, expresse by the following equations. A A in ex 0 xtp Ct = π Dtvl ( xtp Ct ) xtp > Ct ( ) π Dtps Ct xtp xtp Ct = 0 xtp > Ct (1) (2) Where C t enotes the exhaust clearance, D tvl an D tps are the geometry imensions shown in Fig. 2, x tp is the isplacement of top piston. 2.2 Relay Valve The structure of relay valve is similar to the brake valve, shown in Fig. 3. Relay Control Exhaust Relay Piston Relay Valve Relay Supply Figure. 3 Structure of relay valve The ifference between the brake valve an relay valve is that the control signal for brake valve is the force supplie by peal while the control signal for relay valve is the compresse air from the brake valve. Relay valve can shorten the elay time for the rear brake chambers which are far from the brake valve. 2.3 Brake Brake chamber is the component transiting air pressure to mechanical force. When the compresse air flows to the brake chamber, the air pressure pushes the push ro move, an then the mechanical force is transmitte to brake rum which makes the vehicle ecelerate. In this paper, we simplify the rear service an spring brake chamber as the front service brake chamber (see Fig. 4). Brake Compresse Air Diaphrgam Push Ro Figure. 4 Structure of brake chamber 3 Moeling vehicle air brake system 3.1 Stanar pneumatic components The stanar pneumatic components inclue air volume, cyliner, nozzle, an pipe. We assume that the air temperature in volume is constant, an the thermal ynamic process is calle isothermal. When the air flows to a constant volume, the pressure in the volume can be escribe by: P = mrt V (3) Where P enotes the pressure, m enotes the air mass in the volume, R enotes the ieal gas constant, T is the temperature, an V is the volume. The cyliner is still assume as isothermal, but the volume is not constant. The volume can be expresse as V= V0 + As c p (4) Where V 0 enotes the initial volume of cyliner chamber, A c is the effective area of piston, an s p enotes the isplacement of piston.

4 The nozzles in pneumatic system can be moele as restrictions. The air flows from highpressure chamber (upstream) to low-pressure chamber (ownstream), the mass flow rate for the nozzle can be expresse by Pu m = ACqC (5) m T u The bottom chamber of brake valve is shown in Fig. 6. Here, A is the flow area of nozzle, an C q is the flow coefficient which can be expresse as 2 3 p p p Cq = pu pu pu 4 5 p p pu pu (6) C m is the flow parameter can be expresse by [7, 8,10,11] 2 2 > = R 1 P P P + 1 Cm = = R P 1 P P, if Pcr u u u 1 1 P 1, if Pcr Pu. (7) Where enotes the specific heat ratio, P cr entoes critical pressure ratio, P an T enote the pressure an temperature respectively, subscript u an enote upstream an ownstream respectively. The pipelines can also be moele as restriction. 3.2 Air brake components Figure. 6 Structure of bottom chamber The structure of relay valve is the same as the bottom chamber of brake valve, so we woul not repeat it. Buil the brake chamber base on the stanar pneumatic moel, shown in Fig. 7. Figure. 7(a) Structure of brake chamber Buil the air brake components moels base on the stanar pneumatic moel in software- MWorks. The top chamber of brake valve is shown in Fig. 5. Figure. 7(b) Icon of brake chamber 3.3 Air brake system Base on the components of air brake system, construct the air brake system shown in Fig. 8. Figure. 5Structure of top chamber

5 Figure. 8 Air brake system 4 Simulation results Take the plunger force (enlarge peal force) as input signal an the pressure of air in brake chamber as the output signal. Figure.9 shows a specifie plunger force variation curve. The plunger force increases to 1200N from 0N uring the perio between 0 secon an 0.4 secon (apply phase), keep the force unchange until the time at 4 secon (hol phase), an reuce the force to 0N uring the perio between 4 secon an 4.4 secon (exhaust phase). Figure. 10 Pressure in brake chamber From the simulation results, we fin that the pressure in brake chamber is consistent with the plunger force, but the pressure variation elays to the plunger force. Through the simulation, we can research the ynamic response of air brake system further. 5 Conclusions The ynamic moel of air brake system is presente in this paper. The mathematic moels of some stanar pneumatic components are introuce an built in software- MWorks. The key components of air brake system such as brake valve, relay valve, an brake chamber are constructe base on the stanar pneumatic components. The integrate air brake system is also built using the key components, an the simulation results show ynamic characteristics of air brake system. Through the ynamic simulation, the elay time of brake system can be obtaine more accurately, which has helpful to improve the performance of air brake system. Figure. 9 Plunger force The pressure in brake chambers are shown in Fig. 10. The blue line enotes the pressure in front brake chamber, an re line enotes the pressure in rear brake chamber. Acknowlegement This work was supe by the National High-Tech R&D Program, China (No. 2009AA044501). References [1] Limpert. R. Brake Design an Safety. SAE Orer No. R-198, 1999.

6 [2] Limpert. R. Engineer Design Hanbook, Analysis an Design of Automotive Brake Systems. US Army Material Development an Reainess Comman, DARCOM-P , [3] Bert. B, Karlheinz. H. Brake Technology Hanbook. SAE Orer No.R-367, [4] Williams. S. F, Knipling. R. R. Automatic Slack Ajusters for Heavy Vehicle Air Brake Systems. Nat. Highway Traffic Safety Aministration, Washington, DC, Tech. Rep. DOT HS , Feb [5] Subramanian. S. C, Darbha. S, an Rajagopal. K. R. A Diagnostic System for Air Brakes in Commercial Vehicles. IEEE Transactions on Intelligent Transation Systems, Vol.7, No.3, September 2006, pp [6] Subramanian. S. C, Darbha. S, an Rajagopal. K. R. Moeling the Pneumatic Subsystem of an S-cam Air Brake System. Trans. of the ASME, J. of Dynamic Systems, Measurement, an Control, Vol.126, 2004,pp [7] Wu. J, Zhang. H, Zhang. Y, Chen. L. Robust esign of pneumatic brake system in commercial vehicles. SAE, [8] Fritzson P., Vaim V. Moelica -- A Unifie Object-Oriente Language for System Moeling an Simulation. Proceeings of the 12th European Conference on Object- Oriente Programming, 1998, pp [9] Zhou F, Chen L. an Wu Yi., etc. MWorks: a Moern IDE for Moeling an Simulation of Multiomain Physical Systems Base on Moelica. Moelica 2006, September 4th 5 th, pp [10] Bowlin. C. L, Subramanian. S. C, Darbha. S, an Rajagopal. K. R. Pressure Control Scheme for Air Brakes in Commercial Vehicles. IEE Proc. Intelligent Transation Systems, Vol. 153, No.1, March 2006, pp [11] Peter. B. Pneumatic Drives. Springer-Verlag Berlin Heielberg, [12] Burrows C R, Peckham R G (1977) Dynamic characteristics of a pneumatic flapper valve. Journal Mechanical Engineering Science. 19(3):