Modeling and sensitivity analysis of an ABS hydraulic modulator

The components of the hydraulic modulator of an anti-lock braking system (ABS) are modeled using the bond graph methodology. The analysis includes the solenoid valve, the return pump, and the accumulator. The inputs are the pressure exerted from the brake master cylinder and the commands of the electronic control unit (ECU). The bond graph is analyzed and the state equations, that describe the modes of operation, are derived and solved numerically. Sensitivity analysis is applied to investigate the influence of the design parameters on the dynamics of the 3/3 solenoid valve. The results show that during the pressure build-up mode, the initial forces in both the main and auxiliary springs are the major parameters that affect the opening of the intake valve. During the pressure reduction period, the armature dynamics are sensitive to the armature mass and to the auxiliary spring stiffness. The influence of mechanical friction on the armature motion can be conceivably strong in the case of armature block. The volume of flow to the wheel-brake cylinders depends mainly on the capacitance of the brake. This volume is sensitive to both the hydraulic resistance and the size of the filters.