Establishment and verification of real gas multivariate index model for hydro-pneumatic suspension system

One of the problems in the analysis of the dynamics performance of off-road vehicles is the effect of the accuracy of the hydro-pneumatic suspension model. However, the accuracy of the model for the polytropic process of nitrogen in the gas-charged hydraulic accumulator is one of the key factors, which affects the accuracy of the model for the hydro-pneumatic suspension systems. The traditional approach based on the energy equation and the Benedict-Webb-Rubin equations deduces the well-known thermal time constant model. However, researchers indicate that the thermal time constant varies with the change in the accumulator size and operating cases. Other researchers attempt to modify the multivariate index to model the real gas behavior, but the hysteresis loop representing the energy losses in a cycle can’t be described because the multivariate index is treated as a constant value. In this paper, an attempt was made to describe the hysteresis loop by adopting a variable multivariate index. On the accumulator rig, some tests excited by the sinusoidal displacement with four different amplitudes and frequencies respectively were carried out. The plots of the gas pressures versus the gas volume ratio and the gas volume rate respectively were made according to the experimental data from the accumulator test by using the Matlab software. A comprehensive analysis of experimental data showed that the relationship between the gas pressure and both the volume compression ratio and the volume compression rate were very close. To analyze the relationship between the multivariate index and the two parameters respectively, the formula of the multivariate index was deduced based on the ideal gas approach and multivariate index. By substituting the experimental data from the accumulator test into the formula, the plots of the multivariate index versus the two parameters respectively were also made. The plots illustrated that the multivariate index was closely proportional to the two parameters, respectively. Based on the analysis, a novel method was proposed to build a multivariate index model with the two parameters to describe the real gas behavior. In order to verify the correctness and the accuracy of the proposed multivariate index model, the two coefficients in the model were identified by using the experimental data from the previous accumulators test, and the coefficient of the volume compression ratio in the model was 2.4 for the test accumulator, and the coefficient of the volume compression rate was 1.5. Moreover, substituting the values of the two parameters, which were determined by the different operating cases, into the proposed multivariate index model with the two identified coefficients gave a comparison with these experimental data. Furthermore, a co-simulation model, which was based on the multivariate index model, for six hydro-pneumatic suspension systems was built to check the application of the multivariate index model in the hydro-pneumatic suspension systems of the overall vehicle. And a platform for the hydro-pneumatic suspension systems of the overall vehicle invented and designed by our laboratory, which was the first platform with the capability to test the comprehensive characteristics of multiple suspension systems, was used to test the rolling characteristics of the six hydro-pneumatic suspension systems. Several tests were carried out under the sinusoidal displacements with four different amplitudes and frequencies, respectively. The comparison of the co-simulation results and experimental data showed that the average discrepancy was equal to 5.12% and the maximum discrepancy was less than 10.9%. Therefore, a good correlation was achieved. It further demonstrated that the proposed multivariate index model can describe the behavior of the real nitrogen in the accumulator. But the proposed model should be further verified by using more experimental data from much higher frequency tests, and the influence of dissipated energy on the two coefficients in the proposed model should be explored.