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Control and Power Portfolio Partnership
Control and Stability Analysis of Two-Wheeled Road Vehicles
REPORTS
The "Sharp 1971" motorcycle
model
The "Sharp 1994" motorcycle model
Animation of the "SL2001" motorcycle model
Thesis by Simos Evangelou
The "Sharp 1971" motorcycle model
Linear and nonlinear models are developed for the "Sharp 1971" motorcycle model using the multi-body modelling package, Autosim. The nonlinear part of the code uses Autosim to produce a FORTRAN program which solves the nonlinear equations of motion thereby producing time histories of the motorcycle behaviour as it evolves from an arbitrary, but given initial condition. We have studied the behaviour associated with small initial roll angles. The linear part of the code generates linearised equations of motion and produces a MATLAB file that contains a state-space model in symbolic form. The MATLAB code is used to generate a plot of the real parts of the eigenvalues of the motorcycle system for a sequence of forward speeds. By making minor changes to the MATLAB plotting code, it is possible to present these same stability results in root-locus form with speed the varied parameter.
Download the report in PDF format.
The "Sharp 1994" motorcycle model
Linear and nonlinear models are developed for the "Sharp 1994" motorcycle model using the multi-body modelling package, Autosim. The nonlinear part of the code uses Autosim to produce a FORTRAN program which solves the nonlinear equations of motion thereby producing time histories of the motorcycle behaviour as it evolves from an arbitrary, but given initial condition. We have studied the behaviour associated with small initial roll angles. The linear part of the code generates linearised equations of motion and produces a MATLAB file that contains a state-space model in symbolic form. The MATLAB code is used to generate root-locus stability plots with speed the varied parameter. The hands-on and hands-off cases are studied via the adjustment of a few parameter values.
Download the report in PDF format.
Animation of the "SL2001" motorcycle model
The task of an animator is to generate a visual representation of the dynamic operation of complex multi-body systems such as road vehicles. This is done by generating a wire-frame image of the constituent parts of the mechanism and then "driving" it with the output of a simulation programme. The Autosim animator can be downloaded from our website and is the one we will make use of in this report. The animator must be supplied with two files. The first is a parsfile (PAR) that contains keyword-based text data that defines all the mechanism parts together with other information such as programme settings. The second file is an ERD file generated by an Autosim simulation programme. It contains time history data associated with each of the vehicle bodies. The time histories comprise six degrees-of-freedom data associated with each body in global co-ordinates. The time histories in the ERD file are used to drive the various parts of the motorcycle. The aim of this report is to supplement, in a motorcycle specific context, the animator description that can be found in Chapter 6 of the CarsimEd manual. The manual can be downloaded from http://www.trucksim.com/download/carsimed/cseoverview.html. The vehicle used to demonstrate the animator is the "SL2001" motorcycle.
Download the report in PDF format.
Thesis by Simos Evangelou
The multibody dynamics analysis software, AUTOSIM, is used to develop automated linear and nonlinear models for the hand derived motorcycle models presented in (R.S. Sharp (1971), The stability and control of motorcycles, Jour.Mech.Eng.Sci. 13(5), 316-329), (R.S. Sharp (1994), Vibrational modes of motorcycles and their design parameter sensitivities, Vehicle NVH and Refinement, Proc Int Conf., Birmingham, Mech. Eng. Publications, London, pp. 107-121). A more comprehensive model, based on previous work (R.S. Sharp and D.J.N. Limebeer (2001), A motorcycle model for stability and control analysis, Multibody System Dynamics 6(2), 123-142), is also derived and extended. One version of the code uses AUTOSIM to produce a FORTRAN or C program which solves the nonlinear equations of motion and generates time histories, and a second version generates linearised equations of motion as a MATLAB file that contains the state-space model in symbolic form. Local stability is investigated via the eigenvalues of the linearised models that are associated with equilibrium points of the nonlinear systems. The time histories produced by nonlinear simulation runs are also used with an animator to visualise the result. A comprehensive study of the effects of acceleration and braking on motorcycle stability with the use of the advanced motorcycle model is presented. The results show that the wobble mode of a motorcycle is significantly destabilised when the machine is descending an incline, or braking on a level surface. Conversely, the damping of the wobble mode is substantially increased when the machine is ascending an incline at constant speed, or accelerating on a level surface. Except at very low speeds, inclines, acceleration and deceleration appear to have little effect on the damping or frequency of the weave mode. A theoretical study of the effects of regular road undulations on the dynamics of a cornering motorcycle with the use of the same model is also presented. Frequency response plots are used to study the propagation of road forcing signals to the motorcycle steering system. It is shown that at various critical cornering conditions, regular road undulations of a particular wavelength can cause severe steering oscillations. The results and theory presented here are believed to explain many of the stability related road accidents that have been reported in the popular literature. The advanced motorcycle model is improved further to include a more realistic tyre-road contact geometry, a more comprehensive tyre model based on Magic Formula methods utilising modern tyre data, better tyre relaxation properties and other features of contemporary motorcycle designs. Parameters describing a modern high performance machine and rider are also included.
Download the thesis in PDF format.