Development of a model for an air brake system with leaks

Brake systems in trucks are crucial for ensuring the safety of vehicles and passengers on the roadways. Most trucks in the US are equipped with S-cam drum brake systems and they are sensitive to maintenance. Brake defects such as leaks are a major cause of accidents involving trucks. Leaks in the air brake systems affect braking performance drastically by decreasing the maximum braking pressure and also increasing the time required to attain the same, thereby resulting in longer stopping distances. In this paper, we present a mathematical model for an air brake system in the presence of leaks with a view towards developing a diagnostic system based on this model in the near future. The model that has been developed builds on earlier research at Texas A&M University in which the pressure evolution in the brake chamber was determined as a function of the brake pedal input in the absence of any leaks in the air brake system. A leak may be characterized by its location and size. Since the connecting pipes are short, the location of the leak does not significantly affect the evolution in the brake pressure as much as its size. We provide a constitutive relationship for the leak and we estimated the associated parameter, namely, the ldquoeffective areardquo of the leak from the experimental data. The supply pressure and effective area of leak comprised the inputs to the model along with the displacement of the brake pedal (treadle valve plunger). We also provide a simple leak detection scheme and estimates of the severity of the leak in terms of the mass flow rate of leaking air based on the input measurements of brake pressure for a full application of the brake pedal and the supply pressure. This scheme can be implemented using a simple look-up table.