Studies In The Dynamics Of Two And Three Wheeled Vehicles
Karanam, Venkata Mangaraju
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Two and three-wheeled vehicles are being used in increasing numbers in many emerging countries. The dynamics of such vehicles are very different from those of cars and other means of transportation. This thesis deals with a study of the dynamics of a motorcycle and an extensively used three-wheeled vehicle, called an “auto-rickshaw” in India. The commercially available multi-body dynamics (MBD) software, ADAMS, is used to model both the vehicles and simulations are performed to obtain insight into their dynamics. In the first part of the thesis, a study of the two wheeler dynamics is presented. A fairly detailed model of a light motorcycle with all the main sub-systems, such as the frame, front fork, shock absorbers , power train, brakes, front and rear wheel including tire slips and the rider is created in ADAMS-Motorcycle. The simulation results dealing with steering torques and angles for steady turns on a circular path are presented. From the simulation results and analytical models, it is shown that for path radius much greater than motorcycle wheel base, the steering torque and angle can be described by only two functions for each of the two variables. The first function is related to the lateral acceleration and can be determined numerically and the second function, in terms of the inverse of the path radius, is derived as an analytical approximation. Various tire and geometric parameters are varied in the ADAMS simulations and it is clearly shown that steady circular motion of a motorcycle can be reasonably approximated by only two curves–one for steering torque and one for steering angle. In the second part of the thesis, a stability analysis of the three-wheeled “autorickshaw” is presented. The steering instability is one of the major problems of the “auto-rickshaw” and this is studied using a MBD model created in ADAMS-CAR .In an Initial model the frame ,steering column and rear-forks (trailing arms) are assumed to be rigid. A linear eigenvalue analysis, at different speeds, reveals a predominantly steering oscillation, called a “wobble” mode, with a frequency in the range of 5 to 6Hz. The analysis results show that the damping of this mode is small but positive up to the maximum speed(14m/s) of the three-wheeled vehicle. Experiments performed on the three-wheeled vehicle show that the mode is unstable at speeds below 8.33m/s and thus the experimental results do not agree with the model. Next, this wobble instability is studied with an analytical model, similar to the model proposed for wheel shimmy problem in aircrafts. The results of this model show that the wobble is stable at low speeds regardless of the magnitude of torsional stiffness of steering column. This is also not matching with the experimental result. A more refined MBD model with flexibility incorporated in the frame, steering column and the trailing arm is constructed. Simulation results with the refined model show three modes of steering oscillations. Two of these are found to be well damped and the third is found to be lightly damped with negative damping at low speeds, and the results of the model with the flexibility is shown to be matching reasonably well with the experimental results. Detailed simulations with flexibility of each body incorporated, one at a time, show that the flexibility in the steering column is the main contributor of the steering instability and the instability is similar to the wheel shimmy problem in aircrafts. Finally, studies of modal interaction on steering instabilities and parametric studies with payload and trail are presented.
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