COUPLED VERTICAL - LATERAL DYNAMICS OF THREE - WHEELED MOTOR VEHICLES

Abstract

With the growing fuel costs, significant pressure has been put on automotive industries to develop more fuel-efficient passenger vehicles. Due to safety, emissions and economy requirements, automotive transportation will be undergoing vast changes in the next few decades. Obviously, the automobile will become smaller and lighter in search for better fuel economy. As a result, the designs based on three-wheeled motor vehicles are likely to be the most popular mode of public and private transport not only in India but in other countries as well. The three - wheeled vehicles operating in India have their front steering with one wheel similar to those of motorcycles and motor-scooters, the two rear wheels are the driving wheels with a differential and a suspension, which are similar to those of automobiles. The three-wheeled vehicle in this research study has been modeled as four and five mass system consisting of a sprung mass, a solid rear axle dependent suspension system in case of Vikram vehicle and rear wheel independent suspension system in case of Bajaj vehicle comprising the rear unsprung mass, steering arm and front wheel unsprung mass. In the present work the results, of an analytical study of 9 degrees-of-freedom (DOE) coupled motion of two commercial three - wheeled motor vehicles of Bajaj-rear engine (RE) with independent suspension and Vikram-front engine (FE) with dependent suspension moving on roads of different roughness values are presented. The equations of motion are obtained for an assumed 9-DOF model of vehicle - tyre system using Lagrangian dynamics approach. In this research work, an experimental set-up for measuring tyre structure vertical, lateral, longitudinal and torsional rigidity has been developed and reported [132]. Measurements of tyre properties and contact patch area for six different bias - ply tyres from two ply to eight ply ratings have been carried out and effects of normal load and inflation pressure are presented in the form of power law. 11 The primary forces and moments that affect the directional control properties of wheeled vehicles are those between the road and the rolling tyre. These force and moment characteristics are nonlinear functions of lateral slip, longitudinal slip, normal load etc. In this work, an analytical approach for determining tyre tractive force, lateral force, aligning torque and overturning moment characteristics due to combined slips has been presented. The present analytical model predicts these steady state forces and moments as a function of longitudinal, lateral and vertical stiffnesses of the tyre and contact patch area. The required tyre lateral force and aligning torque characteristics due to lateral slip and camber angle, are obtained by using the above described analytical model and are finally used in the equations of vehicle motion. Mass and inertia parameters, of the two vehicles as reported by Singh et al. [165], Goel et al. [65] and others [44, 66, 83 and 129] have been used in the analysis. The vehicle suspension elements are modeled with equivalent linear stiffness and damping parameters. The damping characteristics of suspension systems and geometrical parameters are obtained from the manufacturers. The measurements of front and rear suspension vertical stiffnesses are carried out by the author on a set-up for Bajaj three - wheeled vehicle. The suspension stiffness properties for the Vikram vehicle are taken from the Goel et al. [65]. The operating parameters (rolling dynamic stiffness and damping) related to the tyres used in the present work are taken from Saran and Goel [143], which also outlines the procedure to measure these parameters in the laboratory. The present work also deals with the development of a profile measuring trailer unit and analysis technique to evaluate the road roughness, which could be defined as vertical deviation of the surface from a true planar surface. A profile measuring trailer unit has been designed and developed. Measurements of road roughness were taken on five types of institute roads that are similar to different Indian roads and one smooth mosaic floor (for academic interest only) using a PC (Personal Computer) based system. The results are represented by power spectral density (PSD) and compared with the standard values specified by ISO [80], Van Deusen [182] and Wong [188] to classify the type of road. The results iii represented in the form of power law equation have been used as road inputs in vehicle models for evaluation of ride behaviour. In practice the road roughness measurements are often available for a single track. In the present analysis the road roughness is treated as a stationary, ergodic and Gaussian random function of vehicle position. It is modeled using improved technique, considering both the auto- and cross-spectra between the input points. The assumptions, that the road profile is homogeneous and isotropic, have been proposed as a way for generating the required information from the characteristics of a single profile. The assumption initially was proposed many years back by several researchers [47, 73 to 75 and 84 - 85], but has been put to extensive testing only recently [10] and improvements in the procedure have been suggested [19]. The assumption of the road as homogeneous random isotropic surface thus implies that auto-spectra for heights on parallel tracks are identical and that cross - spectra between them is real. An eigenvalue analysis has been done to determine the rigid body modes, damping ratios and natural frequencies for Bajaj and Vikram vehicles. The vertical and lateral acceleration response for Vikram and Bajaj vehicles at a constant speed of 45 km/hr is presented over a set of known straight roadway roughness profiles. The acceleration responses are presented in terms of PSD and root mean square acceleration response (RMSAR) values at sprung mass center of gravity (c.g.) for both vehicles in vertical and lateral directions in the frequency range of 0.1 - 80 Hz for institute and international rough roads [80]. Since these vehicles are mainly used for city transport, it is sufficient for the purpose of ride comfort, to consider ISO fatigue boundary for 1 hour (H) only. The analysis indicates that the lateral response of Vikram is better than that of Bajaj and is well within the ISO limits. Vikram vehicle has also better ride behaviour than Bajaj in low and high frequency range with slight penalty in the mid frequency range. Vikram vehicle has slightly better ride behaviour than Bajaj in vertical direction, however ride behaviour for both vehicles on international, institute and Indian roads [131] are below the ISO mark and improvements in suspension design are required. The results of the analysis also indicate that ride behaviour of these