Modeling and compensation method for hysteretic attribute of rubber bellows for air spring

The hysteretic attribute of rubber bellows and its model parameters characteristics varying with time at different pressures result in air springs characteristics alike, which affects the accuracy of the air suspension control systems. To solve this issue, a feedforward compensation control method for the rubber bellows based on its inverse model is proposed. Firstly, a modified Bouc-Wen pressure correlation model composed of a fractional order pressure correlation model and a general Bouc-Wen pressure correlation model of rubber bellows is put forward. Subsequently, a pressure correlation unified model of rubber bellows hysteretic attribute is constructed. The inverse models are derived from the modified Bouc-Wen pressure correlation model. Then, specific compensator structures are come up with. The results indicated that the mean absolute percentage error of hysteresis loops between the calculation and the test of the air spring is less than 1%. Moreover, the nonlinear error of hysteretic loops between the output force and input displacement of rubber bellows is reduced to 0.03% after compensation. Finally, a quarter-vehicle suspension model equipped with an air spring is established. After compensating for the hysteretic attribute of rubber bellows, the root mean square (RMS) of body acceleration is reduced by a maximum of 13.8%, the RMS of suspension dynamic travel is reduced by a maximum of 18.6%, and the RMS of tire dynamic load is reduced by a maximum of 13.5% under bump excitation, sinusoidal excitation, and B-class road random excitation, respectively. The results provide theoretical support for compensating the hysteretic attribute of rubber and cord multilayer composite viscoelastic elements and for accurately controlling air suspension systems.