# Project Overview

The suspension design of a two-Wheeler is a fairly difficult task. The first problem to take into account is the influence of the rider, considering that his weight is the same order of magnitude as the vehicle's. In addition, the presence of a passenger causes a large increase of the static load on the rear suspension, and weight shift may be up to 100%, i.e. wheeIie in high acceleration and reverse wheelie in hard braking conditions. In addition, Front and rear suspensions have to be efficient in all conditions, allowing wheels to remain in contact with ground. Another problem is the strength of the suspension components. Oversizing should be avoided, because the unsprung masses must be kept as low as possible in order to have a good dynamic behaviour. On the other end, for obvious safety reasons, they must be failure free. Up to now, in PIAGGIO V.E., the suspension design procedure has been the following:
• Strength design according to empirical formulas.
• Basic springs and dampers sizing according to self-developed one-dimensional computer programs.
• Bench and road tests to check components strength.
• Road tests for suspension set trimming.

The empirical formulas basically are scale coefficients to be applied to static loads. Those coefficients and the strength tests, coming from a long time experience in vehicle mass production, lead to failure free components, but may result in some oversizing. In fact, maximum stresses occur in dynamic conditions, e.g. passing over bumps and potholes, during which suspension components undergo the very high but brief accelerations peaks typical of shock loads. Reducing those dynamic conditions to an equivalent static load for the whole structure obviously leads to inaccuracies. In addition, not knowing the correct input loads dramatically reduces the utility of doing accurate FEM strength analyses of each component.

The one-dimensional model used for the first basic sizing of springs and dampers is based on the DE CARBON theory. This model is not accurate enough for a fine suspension trimming, that has to be done by trial and error experimental tests. It is basically a two mass two degrees of freedom model, whose mathematical formulation is very simple and therefore does not require either sophisticated algorithms or HPC. Intensive parametric studies can be carried out on a PC in one working day. The advantage of this model, besides its simplicity, is that it is able to provide very quickly the transfer function between road disturbance and vehicle body acceleration. The plot of this function versus frequency is a significant indicator of the vehicle comfort. The use of multibody simulation could be very profitable. The kinematics and dynamics of multibody systems is an important part of what is referred to as MCAE (Mechanical Computer Aided Engineering). The name multibody stands as a general term that encompasses a wide range of mechanical systems as automotive steering and suspension systems, robotic arms, industrial machinery, satellites and~loyable antennas, heavy machinery and many others. The mechanisms used in all these applications suffer large displacements and their geometric configuration shows large variations under normal service conditions. Sometimes accelerations may be very high, causing large inertia forces. The advantage of computer simulations carried out using MCAE tools is that they show the kinematic and dynamic behaviour of all types of multibody systems in great detail during all the design stages, from the first design concepts to the final prototypes. At any stage of the design process, computer-aided analysis provides an important amount of data to study the influence of the different design parameters, since it allows to carry out a large number of simulations quickly and economically, even before the construction of any physical device or prototype.

At the present time, several general purpose programs for kinematic and dynamic analysis of multirigid body systems are available in the market. Among them COMPAMM , developed in the last decade by the Computational Mechanics Group at CElT. These programs include collections of built-in elements (such as kinematic joints, force elements, springs, dampers, etc.) that allow the user to define the charactenstics of the system being anaIysed. Usually, this system description is written in a data file on disk that also includes the initial conditions and other parameters of interest in the simulation. Most of the simulation programs carry out the analysis as a batch process and provide a graphic interface to visualise the magnitudes requested to the analysis module. Summarising, it can be said that all the currently available multibody codes are not design tools but analysis tools. They simulate the behaviour of a multibody system once all of its geometric and dynamic characteristics have been defined. If an intensive parametric study were to be carried out by one of these codes, it would take some days of continuos work for one engineer, who should define the model for each set of the input parameters, run the simulation and review the results. In addition, to obtain the transfer function of the vehicle acceleration versus input road disturbance, which is very important for comfort studies, these programs need special custom post processing routines.

In the design process, engineers are interested in visualising a whole set of successive responses of the mechanical system, they want to know how changes on design parameters affect the system behaviour and they need the answer in a short time. In fact, when a new vehicle is nothing more than a blueprint, it is more important to have the possibility of doing many quick simplified investigations rather than a single detailed analysis. The aim of HlPERCOMBATS is to develop a new design tool that will allow to carry out in a working day a complete parametric study of the vehicle suspensions, with the accuracy of a detailed multibody analysis. The software will be run on a workstation network, which is currently available in PIAGGlO V.E. These requirements impose the use of very efficient and sophisticated algorithms, as well as the most adequate parallel computer implementation. In order to create an interactive code, an efficient user interface must be developed. For pre-processing, the user will be prompted for the input of each physical quantity characterizing the vehicle dynamics, in order to allow him/her to quickly assemble a two-dimensional model of the vehicle. When a parametric analysis is requested, the user will specify the range of variation of parameters. Two calculation modules will allow different analyses to be carried out. The Ride Comfort Module will allow to study the steady state response to an external sinusoidal input in the frequency domain. The input will be based on the Power Spectrum Density measured on the test tracks used by PIAGGlO V. E., which represent the typical roads that can be found in the allay use of this kind of vehicles. This module must be develop linearizing the more general equations of motion use in the multibody analysis programs. The Dynamic Simulation Module will allow to evaluate the transient dynamic loads on the vehicle chassis that originate in several operating conditions (bumps, potholes). This module may be regarded as a subset of the COMPAMM code, with the addition of appropriate submodules to represent the tire behaviour and the rider and passenger. The Post-Processing Module will be very powerful and flexible. The user will be able to plot the time histories of transient analyses, as well as the steady state response in the frequency domain for stochastic input loads. When comparing different suspension arrangements, overlaying of several plots will be possible. When parametric analyses are being carried out, it will be possible to plot any output quantity versus the varying parameters.