Multi-mass trammel pendulum model of fluid lateral sloshing for tank vehicle

To deeply investigate the lateral dynamics of tank vehicle, the equivalent mechanical model of fluid lateral sloshing for a tank with elliptical (circular) sectional shape was studied.The predicting precision of the trammel pendulum (TP) model was evaluated by the computational fluid dynamics (CFD) software FLUENT, and the effects of fill level, tank sectional ellipticity, and excitation frequency on the model's predicting precision were analyzed.A generalized multi-mass TP model was proposed, the mass and distance between each part of fluid pendulum were reasonably distributed to adapt to the variations in tank sectional ellipticity and fill level.The dynamics equation for the generalized multi-mass TP model was derived based on the Lagrange approach.The method to determine the parameters of mass ratio and distance between the two masses, and the fitting formulas of double mass TP (DMTP) model were presented.The predicting precision of theproposed DMTP model was evaluated by the CFD method.Analysis result shows that the sloshing moment gained from the TP model is generally less than that computed by the CFD method, and the predicting error generally increases as the fill level increases.The predicting error of the peak sloshing moment increases from 15%to 65% when the fill level increases from 30%to 80%.This is mainly because the TP model is fitted under the conditions of small initial fluid incline angle and free sloshing.When the fill level and sloshing frequency are relatively high, both the length of pendulum arm and the sloshing fluid mass are less than the actual cases.The proposed DMTP model presents a relatively stable and high predicting precision in most conditions of fill levels, tank sectional ellipticities and excitation frequencies.Comparing with the TP model, when excitation frequency is 0.2 and 0.3 Hz, respectively, the mean value of the root mean square error (RMSE) of the predicted maximum sloshing moment in the DMTP model decreases by 54.2% and 43.9%, respectively, and the standard deviation decreases by 45.1% and 31.2%, respectively.The predicting precision of the proposed DMTP model is obviously higher than that of the TP model, and the DMTP model can especially well make up for the deficiency of low predicting precision of the TP model in the case of high fill level.