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Linear and Nonlinear Analysis of Ride and Stability of a Three-Wheeled Vehicle Subjected to Random and Bump Inputs Using Bond Graph and Simulink Methodology
ISSN: 1946-391X, e-ISSN: 1946-3928
Published June 07, 2021 by SAE International in United States
Citation: Sharma, R., Sharma, S., Sharma, N., and Sharma, S., "Linear and Nonlinear Analysis of Ride and Stability of a Three-Wheeled Vehicle Subjected to Random and Bump Inputs Using Bond Graph and Simulink Methodology," SAE Int. J. Commer. Veh. 15(1):65-79, 2022, https://doi.org/10.4271/02-15-01-0001.
Bond graph framework, established with MATLAB/Simulink, has a dual objective: analyze the system using bond graph and develop the system equations in symbolic form. This approach is a combination of the simulation skill of the MATLAB/Simulink and the modelling skill of the bond graph. In this analysis, a nine-degrees-of-freedom (9 DoF) three-wheeled vehicle model integrated with a 5 DoF human subject model is formulated using bond graph methodology and simulated using the Simulink toolbox. The present work is divided into two linear and nonlinear analyses of the dynamic behavior of sprung mass subjected to random and bumps inputs, respectively. The linear analysis evaluates the ride comfort of the vehicle and human subject model under the International Organization for Standardization (ISO) and ISO-2631-1 criterion, and the stability of the vehicle is evaluated through on eigenvalues obtained from a single-order state-space form of differential equations obtained from the Simulink toolbox. The nonlinear analysis excludes the human biodynamic model and evaluates the sprung mass bounce acceleration and displacement response and pitch acceleration response under bump inputs. From the linear analysis, vehicle ride is found to be in the “very uncomfortable” range, and above 74 km/h vehicle is found to be unstable. The nonlinear analysis suggests that a semi-active magnetorheological (MR) damper with a fuzzy logic control policy is superior compared to a conventional passive suspension when the vehicle is subjected to bump inputs. The present work is validated with a comparison between the vehicle sprung mass center vertical-lateral power spectral density (PSD) acceleration response simulated through the Simulink software tool and the same received from field tests.