Theoretical research regarding the active safety systems.

Beles, Horia ; Preda, Ion ; Dragomir, George 等

1. INTRODUCTION

The passenger car safety represents its capacity to prevent accidents and to diminish the consequences of an accident produced by other causes than technical break downs. (Bosch 2004) This safety comprises two major categories:

* Active safety.

* Passive safety.

The active safety consists in prevention or avoidance of some accidents that take place as a consequence of an improper operation of the passenger car, and the passive safety consists in reducing the effects of an accident on passengers.

The main characteristic of active safety systems consists in maintaining the directional stability and manoeuvrability of the passenger car in critical rolling conditions as: wheels locking on a slippery surface, skidding in curves, the unexpected appearance of some obstacles.

2. THE MODEL FOR ABS (ANTI-LOCK BRAKING SYSTEM) SIMULATION

2.1 The dynamic model of ABS

To check the ABS working algorithm and to emphasize the different influences on the braking process, with and without ABS, a planar dynamic model was used for a single wheel of the vehicle. The selected model has two inertial elements: a wheel and a mass in translational movement (the vehicle).

The influences of the suspension and direction mechanisms weren't explicitly considerate. (Preda 2005) Also were neglected the jerk and jumping movements of the wheel, respectively the lift up and pitch movements of the translational mass. These simplifications were realised deliberately to highlight the anti-lock braking system parameters that influence the braking process. In these conditions, the dynamic model has only two degrees of freedom: the wheel rotation around the spindle and the translation of the mass sustained by this wheel (including the wheel mass) on the travelling direction (longitudinal) (Preda 1997).

2.2 The Simulink model of ABS

Simulink is a work module of the general mathematical calculus program Matlab (Mathworks Inc.). It is suitable for the simulation of technical systems because it has some very valuable qualities (Simulink 2007):

* It allow the description of the modelled system using block diagrams interconnected with signal lines; from here results the ease in creation, understanding and use.

* The block diagrams can be hierarchically grouped, which permits the description of some assemblies and subassemblies of great complexity.

* The writing of the algebraic and differential equations with initial values that constitute the mathematical model of the system is done automatically.

* For solving the mathematical model more advanced methods of numerical integration are available.

[FIGURE 1 OMITTED]

In figure 1 it is presented the main diagram of the Simulink model realised for the simulation of the ABS operating mode. The blocks that compose it are defined so that it permit the identification and understanding of the ABS functioning.

The "Wheel" and "Vehicle" blocks correspond to these two degrees of freedom of the dynamic model--wheel rotation and "quarter" vehicle translation. These two movements are connected through the grip between the wheel and the road ("Adherence" block) that depends on the road properties defined in the "Road" block.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The comparator (the round block from the left side of the figure) calculates the difference between the desired values of the slip (the "Desired Slip" block) and the real slip (calculated in the "Adherence" block). Using this difference, the "Controller" block that simulates the operation mode of the adjustment algorithm implemented in the ABS computer will establish what kind of command must be executed by the ABS hydraulic assembly (modelled by "Hydraulic Modulator" block). The pressure generated by this is finally applied to the brake (modelled by the "Brake" block).

The "Ctrl off / Ctrl on" block was introduced in the inverse connection path (to enable or disable the feedback loop) in order to simulate with the same model both an anti-lock braking system (ABS) and a classic braking system (without ABS).

Even if it is very simple, the model was realized in a systemic vision, chasing the accentuation of the functional links between the different components of the ABS.

2.3 Simulation of braking with a pressure of 90/75 bar

The simulation parameters for braking with the pressure inside the hydraulic circuit of 90/75 bar, figure 2 and 3 (Beles 2007):

* Three states controller (able to increase, maintain or decrease the braking pressure).

* The pressure in the hydraulic circuit is 90/75 bar.

* The vehicle mass is 300 kg per wheel.

* The inertia moment of the wheel is 0.75 kg[m.sup.2].

* The velocity from which the braking starts is 25 m/s.

* The road surface used for the simulation begins with a portion of 5 m with dry asphalt with an adherence coefficient equal with 1, then a portion of 2 m with snow with adherence coefficient equal with 0.2, then again dry asphalt.

3. THE COMPARATIVE ANALYSIS OF THE THEORETICAL AND EXPERIMENTAL RESULTS

Experimental data was acquired on an experimental ABS system fitted on a Daewoo Nubira passenger car.

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Comparing the experimental results with the theoretical results obtained from simulation, it can be seen that the results obtained with the mathematical model have similar evolutions with those determined experimentally. This proves that the simulation model realized and presented in this paper surprise accurately enough the phenomena related to the passenger car braking dynamics. Thus, the main objective of this work was achieved: the one to realize a simplified mathematical model of the vehicle that permits the simulation of the braking process, able to reproduce with enough accuracy the ABS behaviour.

The simulation parameters on a road with dry asphalt figure 4 and 5:

* The pressure in the hydraulic circuit is 90 bars.

* Three states controller (able to increase, maintain or decrease the braking pressure).

* The pressure in the hydraulic circuit is 90 bars.

* The vehicle mass is 300 kg per wheel.

* The inertia moment of the wheel is 0.75 kg

* The velocity from which the braking starts is 25 m/s.

* The road surface used for the simulation is with a grip coefficient equal with 1 corresponding to a road with dry asphalt.

The experimental conditions for braking:

* Rectilinear braking (with ABS), with warm brakes on dry asphalt.

* Constant grip coefficient, equal with 1 (dry asphalt) for all the wheels.

* The velocity from which the braking starts is 22.8 m/s.

4. CONCLUSION

The paper presented a dynamic and mathematic model realised with the idea of simplicity, but still able to generate results with enough accuracy, that permit to put in evidence the main influences of each ABS subsystems. Experimental results acquired during road tests on a car ABS permitted to tune and validate the simulation model. The model can be easily adapted for different subsystems or for an entire vehicle.

5. REFERENCES

Beles, H. (2007). The research regarding the development of active safety for passenger cars in order to reduce the accidents with serious consequences, Doctoral thesis (in Romanian), "Transilvania" University, Brasov.

Bosch R. GmbH (2004). Automotive handbook--6th Edition, Plochingen

Matlab Simulink tutorial (2007). Modelling an Anti-Lock Braking System

Preda, I.; Todor, I.; Ciolan, Gh. (2005). Contributions to the simulation of vehicle longitudinal dynamics. In: Bulletin of the "Transilvania" University of Brasov, vol.12 (47), Seria A1, p.177-186, ISSN 1223-9631, Brasov

Preda, I. si Ciolan, Gh.--Wheel-road interaction modelling. CAR Pitesti, 1997, pg. 85-90.