Parametric modelling and CFD analysis of maxi scooters: a Design Of Experiment approach CONTI, Paolo (1); ARGENTO, Marco (2) (1) Università degli studi di Perugia, Italy Dipartimento di Ingegneria Industriale e-mail: coxti@unipg.it (2) Università degli studi di Perugia, Italy Dipartimento di Ingegneria Industriale e-mail: m.argento@unipg.it ABSTRACT In the last decade the market of maxi scooters is continually increasing. Any constructor must develop new models, new design, new concepts. Due to this fast evolution, the possibility to cope at each step aesthetics and functionality, during the whole design process, may be a crucial aspects. The present work displays a methodology to integrate in the conceptual design process many aerodynamic aspects. Four main points are considered: - Aesthetic design - Comfort - Safety - Performances All these aspect have mutual influence and require many interactions between different skills during the design process. This work displays an integrated approach based on both experimental and numerical analyses (CFD) to scooter design. The goal of the work is to point out the interactions among the different aspects involved in aerodynamic behaviour and to identify their mutual influence together with their relative influence with DOE (Design of Experiments) techniques. As a conclusion the paper points out the importance of embedding aerodynamic skills into the very initial conceptual design of a scooter, and the method proposed tries to answer to this need. Key words: Modeling, Simulation, Design of Experiment Grupo tematico: Proyectos de Ingeniería: Métodos innovadores en el Proyecto Industrial. 1. INTRODUCTION The traditional preliminary design process of new scooters, up to now, is still a sequential process; the preliminary shape definition is decided on aesthetical basis with poor attention to technical aspects and then the development of the vehicle is build up around this preliminary design. After the definition of the shape design, a full scale mock-up is constructed and it becomes a reference for the mechanical systems and other components. The mechanical designers begin their work at this step and they are asked to fit their solutions into the preliminary design. This design philosophy was suitable until few years ago as scooters were characterised by low speed and aerodynamic did not play a central role.
Presently, with increasing engine power and overall performances, modern scooter are very prone to aerodynamic effects as, because of their shape, scooters safety and stability can become critical. In this context, as the preliminary design heavily influences the performance of the vehicle [1], it is of a primary importance to take into account at the very early stages all the design aspects as fitting technical solution into an existing shape can lead to very critical issues. The introduction of virtual prototypes at very early stages and the analysis of the interaction between shape and safety in a simplified scooter virtual mock-up, may help the preliminary designer in defining the shape and drive him towards more sound solutions. Up to now, few studies are available on conventional motorcycles [2 4] but nearly nothing is available on scooters. In the present work, an integrated aesthetic/ aerodynamic/ mechanical approach is shown. Fig.1 shows the link existing among the different aspects of preliminary design. Lets examine in deeper details these aspects. Aerodynamic efficiency Aesthetics Comfort SHAPE DESIGN Cooling Safety Fig.1: Links between different activities Links between aesthetics and aerodynamics are evident: the shape controls the aerodynamics of a vehicle. Safety is linked to aerodynamics as aerodynamic loads have important issues on scooter stability [1,2]: because of their shape they are prone to upward lift and pitching moment which both reduce the load on front wheel. Moreover, discontinuous and unstable vortices are generated at the lateral edges of the windscreen and result in self sustained dangerous oscillations of the steering handle bars. Comfort is an important aspect. In opposition to traditional motorcycle riders, scooter users particularly are aware about comfort. We do not intend only comfort under ergonomic point of view, but also under noise level, loads on the rider s head and shoulders, mud drag on rider s legs, heating in winter. All these aspects depend on shape design and aerodynamics. With engine power increase in confined closed shells, large heat radiators must be used and their position together with the air path downstream the radiator becomes critical. The radiator have an important aesthetic impact and its design is the result of a trade off between efficiency and aesthetics. 2. DESIGN APPROACH In order to analyse and take into account all these aspects at early design stage, a rough virtual prototype of the vehicle can be created and can be used for comparing results from different CFD analyses of different solutions. At this step, a very useful tool for driving the designer to a wise choice is Design of Experiments technique (DOE) applied to virtual prototypes (Appendix A).
The parametric virtual model can also be used to obtain response surface for different values of the parameters [7-9]. This result can usefully be used by the designer to decide the most effective parameters choice Figure 2 displays the overall procedure diagram. In the figure the roles of DOE and response surface are shown Choice of parameters and methodology Response surface Planning tests and performing the analysis DOE design matrix Pareto diagram Norm. plot Residual analysis Results analysis Regression model implementation Error analysis and estimation Checking model reliability Point prediction and new test definition Graphical representation And Global trend Checking the influence and the adequacy of the parameters trend and effect analysis Optimization Fig. 2: Preliminary design process The use of a very simple parametric model allows to point out only the most relevant aspects of the shape design unbiased by secondary effects. Moreover, some experimental evaluations can be carried out to verify the numerical results obtained with virtual prototyping. 3. CASE STUDY The design procedure has been tested in developing a particular scooter. First, a simplified parametric virtual model was created with the scope of analysing the mutual influence of the driver position and the shape of the front shield of the vehicle on the overall performances. The analyses yielded the numerical figures corresponding to different parameters arrays. The objective functions to optimise were two numerical values, pitching moment and drag force, and two qualitative aspects, load on the driver head and load on driver shoulders. The two later aspects are linked to the airflow closure behind the driver and have important comfort issues. The more these load increase, the more the driver feels uncomfortable. Fig. 3 shows the complete set of ergonomic variables.
As an example, in the following, the link amomg chest inclination and front shield geometry will be analysed in detail. A simplified model of a scooter is defined. Two geometrical parameter are selected as process factor and one regarding the position of the driver. These are the length p, the height h and the gamma angle showed in the figure 4. Aerodynamic loads and performances of this kind of Fig. 3: Ergonomic variables vehicle are the objective of the analysis. The pitching moment (e.g. stability of the vehicle) and the loads affecting the driver (e.g. aerodynamic comfort) are chosen as responses. A 2 k full factorial design is selected. The analysis methodology is based on a numerical approach using a commercial CFD software. Fig 4: The model and the parameters The model is composed of several planar surfaces. Their relative position can be modified in order to obtain different configuration. The driver is modelled using simple features (loft, protrusion) assembled by parametrical relations. The human body size are obtained by a statistical software. The above figure shows an example of how this geometric parameterisation can be used and the variable selected for the analysis. A single replicate full factorial design is selected and an eight runs design is performed. Generally a numerical calculation is not affected by experimental errors (such as errors in measure, environment, people) and replicate a run is useless without a perturbation on the boundary conditions. The responses to investigate in this example are the global pitching moment and the aerodynamic loads affecting the head and the shoulders of the pilot. Once the calculations are completed the ANOVA analysis on each response can be performed.
The first step is select the effects (main effects and interaction effects) that are able to vary the response over a fixed statistical value. Then the F-test and the residual analysis are used to test the significance of the model. A normal plot of the effect is useful to achieve this goal. Fig 5a: normal plot of the effects (response is load on head) Fig 5b: residuals vs. predicted values (response is load on head) In the figure below is shown the ANOVA table for the load on head response. It is the output table of a commercial software. Fig 6: ANOVA table
Once the model or the models (one for each response) are verified it s possible to analyse the influence of the parameter selected on the performances and comfort of the vehicle. Fig 7a: main effect plot (pitching moment) Fig 7b: Interaction plot (load on head) The figure 7a shows the effect on pitching moment due to the variation of parameter h. The evidence is that a lower nose can reduce the moment allowing the stability of the vehicle. The figure 7b shows that there are no interaction effect between the height and the length regarding the load on head response because the two straight line of the factor h and p are parallel. The regression model obtained for each response also can be used to plot the response surface. These 3D diagrams can give an evaluation of the overall performances of the vehicle within the whole design space. Fig 8a: Response surface (pitching moment) Fig 8b: Response surface (load on shoulders) Fig 8c: Response surface (load on head) Looking at the figures 8a, b, c it s already achievable to have an idea on how optimise the shape of the scooter. The last step of the analysis is an approach to multi objective optimisation using a technique due to Derringer and Such [5] who made use of a desirability function. According to this approach, each response y i has to be converted into a corresponding desirability function d i.
So that d i = 1 when the related response y i is equal to its target value, while d i = 0 when the response value lies outside the user-defined acceptable region. Common goal types are, according to [3]: target, within range, minimum, maximum. Each of those goals is linked to its own desirability function. In the following example, is chosen a minimum goal type for all the responses in order to minimizing all the aerodynamic loads affecting the driver and the stability of the vehicle. Fig 9: desirability function vs. height and length The maximum value obtained for the desirability function is not much high. A value over 0.9 is generally more acceptable. Nevertheless, in order to have a suggestion about the trend of how the selected parameters are influencing the response prefixed it is a good results. With respect the position of the nose of the scooter the conclusion is that a lower and more protruding nose can reduce the actions and can increase stability and comfort. The parametric virtual CFD prototype, doubled with DOE, can also be effectively used to Fig. 10: Design of details : mudguard and radiator analyse some shape detail. In fig.10 some aspects of the mudguard and the radiator shape optimisation are displayed. The scope was the analysis of the mutual influence between the
radiator geometry, its position and the mudguard design. As a result, the DOE analysis provided to the designer some trends which were very useful in designing the frontal details. 4 - CONCLUSIONS Because of the continually increasing performances of modern scooters, a new design approach must be followed. For safety and comfort reasons, it is necessary to embed into the first preliminary design many aspects depending on aerodynamics. Up to now, in the technical bibliography, there is a lack of information on these subjects. Some information are available on conventional motorcycles [2,3] but no data are available on scooters. With the intent of developing some basic knowledge on the main trends of the aerodynamic behaviour of the scooters, a modular virtual CFD prototype of the vehicle has been developed and, with the concourse of DOE, the influence of the main geometric parameters has been studied. The modular approach allows a top - down evaluation which is useful in designing the shape details. The scope of this approach is to yield to the designer some "feeling" about the consequences of the shape choices he is making and to create a "data base" of the aerodynamic effectiveness of different shapes in scooter design. The use of a virtual wind tunnel and the analysis of the numerical "experiments" with DOE seem to be a cheep approach which can be very useful during the first steps of the overall design. APPENDIX A Design of experiments is the simultaneous study of several variables. By combining several variables in one study instead of creating separate study for each, the amount of testing required will be drastically reduced and greater process understanding will result. This is in direct contrast to the typical one-factor-at-a-time approach (OFAT), which limits the understanding and wastes data. Additionally, OFAT studies can not be assured of detecting the unique effect of combination of factors (a condition later to be defined as an interaction). The objective of a DOE analysis are [5]: - to learn how a process can be move in the desired direction - to learn how to reduce process variation - to learn how to make a process robust (make the process insensitive to the unknown variables) - to learn which variables are important to control and which are not. The DOE methodology spans a wide range of analytical approach developed for different situation or final target. In a preliminary evaluation a 2 level factorial approach can be used. The variables, factors, assume only two values, named levels (low an high), so the final number of test which a complete analysis needs is 2 k, where k is the number of process variables chosen. This is named a 2 k full factorial design. The experimental design is the collection of trials to be run in the experiment that result form the combination of the low and high levels assumed by the factor. The design space is a geometrical representation of the treatments to perform and the design matrix resumes the order of runs and the treatments combination to perform [6]. In the design space a treatment is represented by the presence of a lower case letter indicates the high level of a variable and by the absence of the letter referred to the low level of a variable. The treatment associated with all the low level combination of the factors is represented as (1). In the design matrix the two levels are represented with a plus (high) and minus (low) sign. So if we have three factors named A, B and C the notation is shown in the next figures.
Fig APP.1 Once designed the runs to perform and the treatments combination the results obtained by the experimental analysis are processed to obtain a regression model. References [1] Conti P., Malerba M., Hippoliti R.,: "Aerodinamica su due ruote". Il progettista industriale, Novembre 2002. 1996). [2] J. BRADLEY, The racing motorcycle (Whitby GB: Broadland Leisure Publications, [3] W.H. HUCHO, Aerodynamic drag of passenger cars, in Aerodynamics of road vehicles (W.H. Hucho editor, SAE International Editions,1998). [4] K.R. COOPER, The effect of Aerodynamics on the Performance and stability of high speed motorcycles. AIAA Symposium on Aerodynamics of Sport Automoiles, Los Angeles, CA, 1974. [5] L. B. Barrentine, An introduction to design of experiment, ASQ Quality Press, Milwaukee, Wisconsin, 1999. [6] NIST/SEMATECH e-handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/index.htm [7] Myers R H, Montgomery D C, Response Surface Methodology, John Wiley and Sons Inc., 2002 [8] Montgomery D C, controllo statistico della qualità, McGraw-Hill, 2000. [9] Derringer G, Suich R, Simultaneous Optimization of Several Response Variables, Journal of Quality Technology, 12, 1980