Modeling and Simulation of Automobile Braking System Based on Kinetic Energy Conversion

Modeling and Simulation of Automobile Braking System Based on Kinetic Energy ConversionWenjuan Li, Xudong Wang, Xue Leng, and Meng WangCollege of Electrical & Electronic Engineering, Harbin University of Science & Technology, Harbin, China.Email: lwenjuan@Abstract—Fatal traffic accidents are related with the overlength braking distance and sideslip when the automobile is braked in an emergency. It is very important to study and improve the braking ability of the automobile. The anti-lock braking system (ABS) is the active method of increasing the braking ability. The ABS controller is the key to ABS. The modeling and simulation of the automobile braking system can be used in designing the ABS controller. The general braking model is built by analyzing the forces on the automobile body and it is difficult to be understood.A new method which establishes the braking model is presented in this paper. When the automobile is braking, the kinetic is worn down by frictions that come from the wheels and road, the wheels and the braking block. A single wheel mathematical model is deduced with this principle. The simulation models of this braking system and ABS are established. Simulations under Matlab/ Simulink are made. The braking distances obtained by the simulation are compared with the known data. The results show that the braking model based on the kinetic energy conversion is reliable. This method can provide a new way to analyze the automobile braking process.Keywords—Braking model; Kinetic energy; Anti-lock braking systemI.I NTRODUCTIONThe automobile is one of the most important vehicles. The security and comfort are the focuses concerned by the people. The braking ability is the main index representing the security of the automobile which is running on the road. Fatal traffic accidents are related with the overlength braking distance and sideslip when the automobile is braked in an emergency, as in [1]. With the increase of the quantity and running speed of the automobile the damages brought to people by the traffic accidents are more serious. It is very important to study and improve the braking ability of the automobile. Ref. [2] pointed out that the anti-lock braking system (ABS) is the active method of increasing the braking ability. The ABS controller is the key to ABS. The modeling and simulation of the automobile braking system can be used in designing the ABS controller.The general braking model is built by analyzing the forces on the automobile body and is difficult to be understood, as in [3] and [4]. A new method which establishes the braking model is introduced in this paper. The kinetic is worn down by frictions that come from s and road, the wheel and braking block when the automobile is braking. A single wheel mathematical model is deduced with this principle. In order to validate this model, simulations with ABS and no ABS model are done in the Matlab/Simulink environment.II.E STABLISHMENT OF M ATHEMATICAL M ODEL OFB RAKING S YSTEMThe braking model depends on the decrease of kinetic energy when the automobile is braking. It consists of the kinetic energy dissipating model, speed model, fluid braking model and slip rate versus adhesion coefficient model.A.Kinetic Energy Dissipating ModelThe kinetic energy of the automobile body is mostly dissipated by the frictions between the wheel and the ground, the brake sheet and brake disc in the braking process.The initial kinetic energykE of the automobile body is22mvE k=, (1) where m is the mass of the automobile in kilograms (kg) and v0 is the initial speed (m/s).From 0 to t, the energy 1Q dissipated by the friction between the wheel and the ground is given bymgdtRvQtv01)(μω∫−= , (2) where t is the braking time in seconds(s); v v is the automobile body speed in the braking process (m/s); ω is the angular velocity of the wheel (rad/s); μ0 is the friction coefficient between the wheel and the ground;R is the radius of the brake disc (m).From 0 to t, the energy 2Q dissipated by the brake can be expressed in mathematically,RdtpSQtmωμ∫=2, (3) where p is the pressure within the wheel cylinder (MPa); S is the area of wheel cylinder (m2); μm is the friction coefficient between the brake sheet and brake disc. According to the law of conservation of energy the following equation is obtained,2/221vk mvQQE=−−, (4) that is978-1-4244-1849-7/08/$25.00○C2008 IEEESlip Rate2)(2200020v tm t v mv rdt pS mgdt R v mv =−−−∫∫ωμμω . (5)Equation (5) is the kinetic energy dissipating model of the automobile.B. Slip Rate Versus Adhesion Coefficient ModelThe braking process of the automobile is influenced by the adhesive force between the ground and the wheel. This force is associated with the adhesion coefficient. The adhesion coefficient is the ratio of the adhesive force to the vertical load which acts on the wheel. The adhesion coefficient is mostly determined by roads, tires and the slip rate.The slip rate λ is calculated by vv v Rv ωλ−=. (6) The relationships between the slip rate and adhesion coefficient on different roads are illustrated in Fig. 1, as in [5].C. Speed ModelThe speed of the wheel is represented byωω=+∫dt R m T tw ]2[020 , (7)where ω0 is the initial angular velocity; m w is the mass of the wheel (kg); T is the resultant moment of the wheel (N.m), it meets⎪⎩⎪⎨⎧≤>=>>=−>>−=),0,0(0),0,0()0,0(0000r pS mg Ru v r pS mg R v r pS mg R v r pS mg R T m v m v m v m μωμμωμμωμμ .(8)Therefore the speed model of the automobile can be described by (7).D. Fluid Braking ModelThe pressure within the wheel cylinder determines the braking moment and it can be written inz lpl p dtdp C p =+ , (9) where p z is the pressure within the brake pipe between the wheel cylinder and ABS controller (MPa); p l is the pressure within the wheel cylinder without braking(MPa) ;C p is the constant that is mainly decided by the caliber of the brake pipe and the viscosity coefficient of the braking fluid.III. S IMULATION E XPERIMENTSIn order to validate the above braking model established by the kinetic energy conversion, simulation experiments are done in the Matlab/Simulink environment.The simulation model of this braking system is made in terms of the deduced mathematical model of the braking system. Fig. 2 illustrates this model.M2 is the kinetic energy module dissipated by the wheel and ground; M3 describes the slid rate calculation module; M4 denotes the kinetic energy module dissipated by friction between the brake sheet and disc; M5 stands for the fluid braking module; M6 shows the moment module. The initial speed uses C symbol, it is set by the input. The body speed, braking distance and wheel speed of the automobile are observed by simulating with this model. ABS controller can be considered in this model. It is able to be added into the fluid braking module. Fig. 3Body0shows the internal structure of the fluid braking module.inertial element is similar to a first-order inertial element. The input In1 represents the slid rate of the wheel. The pressure within the brake pipe is the output. The object of the ABS controller is to regulate the slid rate at the 20%, as in [4]. Seen in Fig.1, the adhesion coefficient reaches maximum at this time. The approach controlling the slid rate in this simulation is PID.IV. S IMULATION R ESULTS AND A NALYSISBased on the simulation models of this braking system and ABS, simulations under Matlab/ Simulink are made. Fig. 4 shows the braking curves of the wheel speed and the body speed varying with the time at the braking speed 28m/s. The curve of the wheel speed 1 is achieved by using the braking model presented in this paper. The curve of the wheel speed 2 is obtained by using the general braking model used in the most papers. It can be seen that two curves are almost overlap, the wheel is locked at 0.3s and the braking time is 4.3s.For comparison with the data in [6], simulations with ABS have been bone. The ABS approach is the PID control to the slid rate. The curves are shown in Fig.5. Curves of wheel speed 1 and wheel speed 2 are the same meaning with those in Fig. 4. The figure illustrates the wheel is unlocked and the braking time is 3.9s. The effect of ABS is also verified.Comparison results are given in Table I. It shows that the simulation braking distances based on the built model are consistent with the results in [6]. kinetic energy conversion is right and can be used in the research on the automobile braking ability.V. C ONCLUSIONSBased on the kinetic energy conversion, the mathematical model of the automobile braking system is deduced in this paper. The simulation models of this braking system and ABS are established. Simulations under Matlab/ Simulink are made. The braking distances obtained by the simulation are compared with the known data. The results show that the braking model based on the kinetic energy conversion is reliable. This method can provide a new way to analyze the automobile braking process.R EFERENCES[1] Farmer, C. M., “New evidence concerning fatal crashes ofpassenger vehicles before and after adding anti-lock braking systems”, Accident Analysis and Prevention , vol. 33, pp. 361–369, 2001.[2] J.Broughton, C. Baughan, “The effectiveness of anti-lock brakingsystems in reducing accidents in Great Britain”, Accident Analysis and Preventio , vol. 34, pp. 347–355, 2002.[3] Jeonghon Song, “Performance evaluation of hybrid electric brakesystem with a sliding mode controller”, Mechatronics , vol. 15, pp. 339–358, March 2005.[4] M. C. Wu, M. C. Shil, “Simulated and experimental study ofhydraulic anti-lock braking system control using sliding-mode PWM control”, Mechatronics , vol.13, pp. 331–351,May 2003. [5] R ．Jeffery, “Fuzzy learning control for antislid braking system”,IEEE Trans. on Control System Technology , vol. 1, pp. 122–129, February 1993.[6] /c/2001/5/31/a75125.htm052530。