Nonlinear dynamic modeling and parameter identification of air springs in the ultra-low frequency range considering thermal hysteresis

The nonlinear dynamic performance of a constrained rolling-lobe air spring (CRLAS) is measured using a servo-controlled hydraulic test rig. Experimental results indicate that in the ultra-low frequency range (0.002–1 Hz), the dynamic stiffness increases sharply, while the loss angle increases firstly and then decreases. However, current literature exhibits two primary limitations regarding the nonlinear dynamics of air springs at ultra-low frequencies: 1) parameter identification methods for the heat transfer coefficient are absent, 2) efficient frequency-domain models analyzing the thermodynamic processes of air inside the air spring at ultra-low frequencies are not well developed. To address these gaps, a nonlinear time-domain model considering friction and thermal hysteresis generated by air pressure inside the air spring is established to analyze the hysteresis characteristics in ultra-low frequency range. The heat transfer coefficient is inversely identified using the perturbation amplitude of the measured pressure inside the air spring, and the proposed identification method is easy to apply in engineering applications. Secondly, the time-domain model is linearized by Taylor expansion, and the force versus displacement estimated by nonlinear and linearized models are compared with the measurement. Subsequently, a frequency-domain model is established by Laplace transformation of the linearized time-domain model to calculate the dynamic stiffness and loss angle of the air spring, demonstrating good agreement with experimental results at ultra-low frequencies. Finally, in the ultra-low frequency range, it is revealed by the proposed models that the hysteresis of the air spring is determined by friction and thermal hysteresis, and the thermodynamic process transitions from isothermal to adiabatic.