An Integrated Tool For Competition Go Kart Track Analysis-PDF Download

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INTRODUCTION Lap time simulation is a very fascinating topic but to become an useful. race engineering tool needs several disciplines to be involved In fact the overall performance. of a racing car that can be well quantified by the lap time is the result of the interaction. between a lot of design and set up parameters and of course of the ability of the driver to. squeeze the characteristics of its car to the limit A lot of research work was devoted to this. matter even if only a little part emerges in the published literature for obvious secrecy. reasons An interesting analysis was recently presented for the race optimisation of AUDI car. in Le Mans 24 hours competition 1 A systematic approach for race car optimisation is. widely discussed in 2 Contributions strictly addressed to lap time analysis for competition. go kart are still not published in technical literature A lot of works are however available. about several topics that concur in lap time analysis. As far as vehicle dynamic is concerned simulation models have been extensively developed. for standard vehicle handling and stability analysis 2 3 Nevertheless the prediction of the. go kart lateral dynamics requires to develop specific models because of the absence of. differential gear and suspension systems and an appropriate approach has to be employed in. simulations instead of classical rigid bodies technique In fact dealing with a so particular. vehicle the elastic behaviour of the chassis has a great influence on road dynamics. Several works have been presented on kart structural aspects and track dynamics Much of. theme regard the structural aspect of the frame like 4 5 Others consider the whole vehicle. behaviour by an means of experimental test 6 or simulating the kart behaviour with. appropriate models by means of commercial multi body software 7 or adapting the single. track model to kart peculiarities 8 9, Also the authors have studied the problem of kart dynamics by means of appropriate. modification of rigid body approach The work described in paper 10 is an investigation on. the powerful and usability of multi body environment to study kart behaviour on track In. paper 11 the effect of driver mass has been examined with multi body technique in order to. highlight the influence of driver position and motion on the whole vehicle dynamics. Furthermore a Fortran code able to simulate kart behaviours in road manoeuvres has been. employed to investigate lateral dynamics taking into account the effect of different frame. geometry configurations 12 Tyre characteristics have been tuned by means of experimental. measures in track sessions, The study of the whole kart dynamics also requires the knowledge of all the contributions to. longitudinal dynamics too i e engine force and aerodynamics resistance Engine simulation. is a widely explored research field and a complete panoramic about set up and design of two. stroke engines can be found in many books such as 13 Several contributions were also. given about simulation of complete motors the authors themselves have worked in this field. about integrated simulation of a complete engine 14 and recently about the design and. optimisation of a reed valve 15, Considering that new kart competition regulations allow almost arbitrary shapes for the. bumpers and other components aerodynamics is going to play a primary role on new kart. design programs Even if wind tunnel measurements continue to be the most common and. extensively used approach with currently available computational equipment the turn around. for numerical simulations is becoming so rapid that is feasible to examine an extremely large. number of variations The employment of numeric approach allows to support the. experimentation and produces a complete description of the three dimensional flow field in. terms of velocity pressure and temperature distribution including other related physical. quantities The importance of an aerodynamic analysis resides not only in predicting drag and. lift forces but also in its influence on vehicle dynamics and engine performance A detailed. study on this topic was presented by the authors in 16 where for the first time the. aerodynamic behaviour of a competition go kart was analysed and simulated. Of course a complete lap time simulation tool requires a virtual driver able to act on steering. throttle and brake in order to maximize the speed in every part of the circuit A review of. various literature approach and a model of automated driver has been presented by Gordon et. al 17 that proposed an algorithm able to follow a planned trajectory. Collecting the aforementioned experiences of the authors an integrated tool for the simulation. of competition go kart was developed and is herein presented. SIMULATION TOOL Several building blocks were prepared and individually checked and. optimised to be suitable for competition go kart simulation vehicle model engine model. aerodynamic model track model The simulation tool developed consists in a software. developed in Windows environment capable to manage the calculation activities of each. Engines parameters were used to launch a one dimensional gas dynamic simulation that. produces as result the working map of the engine in a format suitable for longitudinal vehicle. dynamic analysis However the use of an experimental map in the same format if available. could be inserted, In the same way drag data for various configuration were computed and transferred to the lap. time simulation program since CFD simulations require a lot of CPU time Of course the. same data could be derived experimentally, Vehicle model interacts with the program at two levels The first approach consists in a.
preliminary construction of stationary g g diagrams related to the current vehicle setup such. data are then used by simple dynamic solver based on point mass vehicle model Finer results. could be achieved controlling the full vehicle simulator along the entire lap This approach. requires a virtual pilot to follow the desired path As far as the vehicle simulator is concerned. two solvers are available an internal developed simulation program and a commercial multi. body model Working model 3D, At this stage of development only the first approach is fully working for this reason the. problem of automated driver will not be pursued in this paper. Simulation core is very simple Firstly global input parameters engine vehicle are processed. to obtain engine map and vehicle g g diagram Secondly the trajectory is defined by a set of. control points Speed histories are then calculated imposing a braking and driving law that. maintains the acceleration vector always on the vehicle admissible acceleration diagram. boundary Lap time is then calculated by simple integration To speed up simulation time a. set of vehicle and engine set up can be stored permitting to see in real time the effect of. parameters changes for a given trajectory Furthermore at fixed engine and vehicle set up the. best driving could be found varying trajectory shape parameters Current trajectory is painted. in the graphic view port highlighting the braking point partial times and others interesting. quantities Furthermore a real time animation of the lap is available actual perspective of the. pilot is shown together with a series of configurable instruments that show in real time the. evolution of computed quantities, VEHICLE MODEL The study of kart dynamics needs the development of specific. simulation tools In fact the absence of suspensions and differential gear requires to modify. the typical rigid body approach usually employed in vehicle behaviour simulation In order to. reach good results in applying simulation tools two tasks must be faced Firstly the need of. manage the fixed connection between the rear wheels that impose equal speed for both sides. tyres and hence the presence of slipping during cornering Secondly the necessity of correctly. represent the elastic behaviour of the whole chassis permitting to exactly evaluate the load. transfers and consequently the tyre forces Regarding this second issue several solution have. been carried out by the authors Papers 10 11 12 are based on the condensation of the. whole chassis stiffness into a 4 by 4 matrix Extracting by means of a FE model of the kart. frame the stiffness matrix associated to the dof s representative of vertical displacements of. the wheel hubs is possible to use the stiffness matrix applying such a similitude with. conventional suspension system taking nevertheless into account the coupling between the. dof s considered This approach has been employed both with a model realized in a. commercial multi body environment and with Fortran simulation code named Kart 2D. Further developments have conducted to a larger employment of finite element method to. evaluate load transfers Applying mass loads accelerations in the three direction x y z to a. kart model inclusive of non structural and driver masses is possible to carry out a set of maps. that permit to assess the vertical load acting on each tyre in whatever driving condition. braking cornering accelerating Furthermore the effect of front wheel lift due to steering. cinematic has been considered dealing with it like a load condition Because of the interest to. three wheels equilibrium condition due to the typical rear wheel lift in cornering. manoeuvres both three and four points constraint situations have been examined. Gathering the results of the fem analyses for every single load case 1 g of longitudinal. acceleration 1 g of lateral acceleration 1 g of vertical acceleration 1 mm of front left wheel. vertical displacement 1 mm of front right wheel vertical displacement into matrix and. applying the principle of superposition is possible to assess the vertical load on each tyre. The algorithm also provide for switching between 4 or 3 wheels solution depending by the. presence of a negative vertical load on one of the rear wheels. Once vertical loads on each tyre are known is possible to evaluate longitudinal and lateral. tyre forces A simplified bi linear dependence between traction braking force and longitudinal. slip has been employed basing on literature values to set the model The longitudinal slip is. assessed integrating the equation of motion of the rear axle and comparing the peripheral. speed of the contact point seen as a point in rigid motion with the axle with the velocity of. the vehicle computed taking into account longitudinal speed and yaw rate The engine torque. computed by the engine model is inserted in the code and further also the aerodynamic and. rolling resistance are considered Therefore is possible to simulate the actual ability of the kart. to accelerate, On the other side lateral behaviour of the tyre has been identified by means of track. acquisition The Fortran model has been employed in a set of parametric runs permitting to. carry out the characteristic of lateral force versus tyre lateral slip The simplified formula. adopted is the following,F f max Fz, which presents an almost linear behaviour nearby the zero and a saturation at high values of. slip angle The dependence by vertical load has been estimated basing on the knowledge of. static loads and literature values, Combining all the loads present the equilibrium is computed by time step integration of the.
in plane equations of motion, Kart 2D by itself permits to execute whatever analyses by means of the appropriate input. files Simulation of experimental manoeuvres plots of understeer diagram handling diagram. or g g diagram as well as parametric analyses can be performed In fact in this work the. actual capability of reach combination of longitudinal and lateral acceleration have been. assessed with maps obtained by the outputs ok Kart 2D. ENGINE MODEL A full gas dynamic model was implemented in order to calculate the. effect of setup parameters on engine performance One dimensional non stationary flow. conditions were handled by a total variation diminishing solver previously developed 14. Shocks and thermal discontinuity typical of exhaust flow of two strokes engines are. accurately and robustly resolved using the classical two steps Lax Wendroff solver improved. with a flux correction scheme Open system conservation equations were used to follow the. evolution of thermodynamic variables inside the cylinder the crankcase and the airbox. considering perfect mixing condition Furthermore a simple combustion model represented. by a Wiebe function has been included, Typical engine layout is shown in figure 1 in which the airbox is represented by a reservoir. connected to the external ambient by means of an orifice. EXHAUST CYLINDER,Figure1 Two stroke engine layout, The duct between the airbox and the crankcase was modelled by means of a pipe element that. has with a fixed area orifice at the first boundary and a variable area orifice at the second. boundary Proper values of these areas are imposed adopting a fixed angular base tabled. values for piston ported or rotary disc valve engine or adopting a dynamic model for reed. valve ported engines 15, Crank case and cylinder were connected with a pipe that has a fixed boundary condition at. crankcase side and a variable area connection imposed adopting actual section offered by. ports valves Exhaust line was modelled in a similar manner adopting a one dimensional. Engine simulation is a widely explored research field and a complete panoramic about set up and design of two stroke engines can be found in many books such as 13 Several contributions were also given about simulation of complete motors the authors themselves have worked in this field

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