The design of a complex machine like our car seems monumental, right? So, how does one go about starting this process? The beginning of any design is to formulate the outcome using mathematical models. As ideas for new changes are conceived, we instead test their technical feasibility before moving to implement the concept. Similarly, with lap time simulation, we get to stimulate and formulate our powertrain mathematically.
For this purpose, the team developed an indigenous MATLAB model to stimulate a lap using track coordinates and car parameters. The track coordinates were generated through image extraction of the track images of the Formula Bharat and Formula Student Germany tracks. The ideal racing track was generated using the surrogate optimization algorithm in MATLAB. Surrogate optimization attempts to find a global minimum of an objective function using a few objective function evaluations. For this, the algorithm tries to balance the optimization process between two goals: exploration and speed. Exploration to search for a global minimum.
Velocity at all points was computed by taking the maximum velocity permitted by lateral acceleration and the velocity possible with the motor torque produced at that point. The lap time was calculated by assuming uniform acceleration between 2 adjacent points and computing time cumulatively. In addition, we performed iterations in the code with an estimated car mass to find the power needed in our accumulator and changed the estimated mass accordingly until the values converged.
The process, as mentioned above, appears intensive, but does this lead to any help in the actual design? The results from Lap simulation are used in different stages of the powertrain design. The speed and torque profiles for other motors with different final drive ratios are generated. This helps in the motor selection and final drive ratio optimization. Lap simulation results were also used in the thermal modeling of the accumulator, motor, and motor controllers. The voltage, current, and Depth of Discharge curves were also generated, which were used for accumulator design. The best point of the model yet is the flexibility it provides. Before starting the design, we can incorporate different mathematical phenomena into the system to extract the maximum information possible.
Is this the only way to go about doing this? No, but similarly, most student teams use simple techniques with python or Matlab codes, and some even attempt it with Excel. Looking beyond this, the professional teams also prefer to run their modifications on a model to assess their impact before making the change, thus saving time and effort. The significant difference between the two is the software used. They use professional lap time simulation software like ADAMS, VI-Grade, Dymola, and such.
That is not to say this is the end, and many exciting solutions have been found. For example, people have adapted a racing game, rFactor, to run their simulations. Essentially, these codes optimize the chassis setup and the electronics control strategies. While this may seem like only a skeletal replica of the car, it has become evident that it is one of the most vital design strategies employed by a team.