R. Nejat TUNCAY2
The Scientific and Technologic Research Council of TURKEY (TUBITAK) Marmara Research Center (MRC) Energy Institute, PK.21 41470 Gebze-Kocaeli, TURKEY
Mekatro R&D, TUBITAK MRC Technology Free Zone Section B No:18 41470 Gebze-Kocaeli, Turkey
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. . . 
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.
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.
2-Quarter Car Model
Figure 2 Wheel longitudinal dynamics
Fx = μ.m.g/4
Figure 1 Forces acting on the vehicle
Fx is tire braking force and μ can be calculated based on a Pacejka magic tire formula  or taken from a table of μ 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.
wv − ww max(wv,ww)
where wv and ww represents vehicle and wheel Forces acting on one wheel of a vehicle; Fw = ct.m.g.cosα/4 Fs = m.g.sinα/4 Fa= 0.5.cr.δ.Af.V2/4 Facc = (m/4).dV/dt (1) (2) (3) (4) Tire model can be given as; angular speeds respectively. For this study μ is calculated based upon the following graph in Figure 3, which represents a dry road condition.
where ct, m, α, cr, δ, 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.
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 )
Tire rolling resistance Coef. (cr) Aerodynamic resistance Coef. (ct) Wheel inertia (kg.m2)
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:
Figure 3 μ vs. s graph
k τ.s + 1
where for this study k and τ are selected as 100 and 0.01 respectively....