APPLICATION NOTE ON REGENERATIVE BRAKING OF ELECTRIC VEHICLES AS ANTI-LOCK BRAKING SYSTEM Okan TUR1 Okan. Tur@mam. gov. tr 1 Ozgur USTUN2 oustun@mekatro. com R. Nejat TUNCAY2 ntuncay@mekatro. com The Scientific and Technologic Research Council of TURKEY (TUBITAK) Marmara Research Center (MRC) Energy Institute, PK. 21 41470 Gebze-Kocaeli, TURKEY 2 Mekatro R&D, TUBITAK MRC Technology Free Zone Section B No:18 41470 Gebze-Kocaeli, Turkey Abstract Anti-locking brake systems (ABS) are well known in the automotive industry and studied under safety heading.
ABS improves vehicle safety by reducing longitudinal breaking distance. This occurs by on-off control of the wheel slip. In this study, a basic modeling approach has been introduced on a quarter car model by using ANSOFT Simplorer for the following braking modes; hydraulic braking and all electric vehicle regenerative braking concept. This paper starts with development of quarter car model (QCM). First a hydraulic ABS model is A car braking system is one of the major factor for the driving safety.
The introduction of the AntiLock Braking Systems has contributed to improve the security of modem cars decisively by automatically controlling the brake force during braking in potentially dangerous conditions such as braking on iced or wet asphalt, panic braking, etc. . . [1] Keywords: ABS, Electric vehicle, Quarter Car Model applied to the QCM. Later modification of permanent magnet (pm) brushed dc machine model for field weakening region is introduced. 1-Introduction
Electric or hybrid electric vehicles propose not only better fuel economy and less environmental pollution but also superior performance of braking, traction control and stability control systems employing motoring and regenerative braking capability of electric machines. Finally this model is applied to QCM to investigate regenerative braking performance of electric vehicles by means of ABS. 1 2-Quarter Car Model Figure 2 Wheel longitudinal dynamics Fx = ?. m. g/4 Figure 1 Forces acting on the vehicle (6) Fx is tire braking force and ? an be calculated based on a Pacejka magic tire formula [2] or taken from a table of ? vs. slip ratio (s). Slip ratio is defined as; Forces acting on a vehicle is shown in Figure 1, which are wheel friction force (Fw), aerodynamic drag force (Fa), slope friction force (Fs) and force due to vehicle inertia (Facc). Fx denotes the tire braking force. s= wv ? ww max(wv,ww) (7) where wv and ww represents vehicle and wheel Forces acting on one wheel of a vehicle; Fw = ct. m. g. cos? /4 Fs = m. g. sin? /4 Fa= 0. 5. cr.?. Af. V2/4 Facc = (m/4). dV/dt (1) (2) (3) (4) Tire model can be given as; angular speeds respectively.
For this study ? is calculated based upon the following graph in Figure 3, which represents a dry road condition. where ct, m, ? , cr, ? , Af and V are wheel rolling resistance coefficient, total vehicle mass (kg), slope angle (rad), aerodynamic coefficient, air density (kg/m3), vehicle frontal area and vehicle speed (m/s) respectively. Fx. r-Tb = J. d? dt (8) where r, Tb, J and w are wheel radius, braking torque, wheel inertia and wheel angular velocity respectively. Longitudinal vehicle dynamics of quarter car during braking can be given as;
Tabel 1 Vehicle Parameters used in model Vehicle Weight (m) Wheel radius (r) 2 1700 kg 0. 325 3. 1 0. 3 0. 01 0. 5 m dV -Fx-Fw-Fs-Fa = . 4 dt Vehicle Frontal Area (m ) (5) Tire rolling resistance Coef. (cr) Aerodynamic resistance Coef. (ct) Wheel inertia (kg. m2) 2 For the control of the ABS, optimum slip ratio is entered to the controller as reference value. Slip error then is feed to hydraulic actuator. The dynamic model of hydraulic fluid lag of braking system is used as the following first order transfer function: G(s) = Figure 3 ? vs. s graph k ?. s + 1 here for this study k and ? are selected as 100 and 0. 01 respectively. Finally, quarter car model during braking is represented in the following figure. For this model, definition of initial speeds is crucial. Initial speed is selected as 100 km/h for both vehicle and wheel for all of the simulations. Then braking torque is simply achieved by integrating the hydraulic fluid and multiplying by a constant as show in figure 5. Figure 5 Hydraulic ABS model Integration of the hydraulic ABS model and QCM is given in figure 6. Figure 4 Quarter car model during braking -Hydraulic ABS Braking The purpose of ABS is to optimize the braking effectiveness and maintain vehicle stability under various road conditions. It is achieved by controlling the slip ratio at the point where maximum braking force can be applied to the wheels. 3 Figure 6 Integration of hydraulic ABS to QCM During braking simulation, maximum braking torque of the system is limited to 1500 Nm. Reference slip value is entered as 0. 2 seeing that maximum braking force occurs at this point as seen in figure 3. In figure 7, vehicle and wheel speeds (km/h) are plotted during simulation.
Total braking time is 3. 5 s. Around 1. 5 s, wheel slip ratio reaches 0. 2 where maximum braking force is achieved as indicated in figure 8 (m on the wheel slip axis indicates 10-3). Total distance traveled during braking is 57. 27 m shown in figure 9. Figure 9 Vehicle speed and traveled distance Figure 10. Braking power and torque vs. speed Braking power and torque vs. wheel rotational Figure 7. Vehicle and wheel speeds vs. time speed is plotted in figure 10. As can be seen from the figure nominal power is 75 kW at 530 rpm and nominal applied braking torque is around 1400 Nm. -Modification of PM Brushed DC Machine Model for Field Weakening Region Electric vehicle applications require high constant power to constant torque ratio, typically in the Figure 8. Wheel slip vs. time range of 3 to 5 for better performance at lower power consumption [3]. 4 For simplification of the overall electric traction system modeling, a dc motor model will be used looking from system engineering point of view. Conventional permanent magnet stator dc machine model simplified equations can be modified as below to simulate the constant power region of field oriented controlled ac machines;
Va = Ea + Ri. Ia + Li. dia/dt Ea = ke(? r).? r Te = kt(? r). Ia (9) (10) (11) where Va, Ea, Ri, Li, ke, kt and ? r represent supply voltage, back EMF voltage, winding resistance, winding inductance, back EMF constant (rotor flux), torque constant and rotor speed respectively. Considering electromechanical power equality; Te. ?r = Ea. Ia kt(? r). Ia. wr = ke(? r).? r Ia kt(? r)= ke(? r) (12) (13) (14) Figure 11 Modification of rotor flux Code entered under equation section of the block for the rotor flux calculation is given below; IF(INPUT[0] INPUT[1]) AND (INPUT[0]
