Comparative of the Mathematical Smoothing Model for Inertial Dynamometer Software 2020-36-0151

The use of dynamometers, especially inertial ones, has been widespread in Brazil in recent years. This increase in the use of the tool has several reasons, among them the greater availability of equipment, price reduction and the appearance of programmable electronic injections. Programmable injections, for better engine performance, must be adjusted in the different conditions of use and in the different points of the injection and ignition maps. This adjustment could be made by driving the vehicle on streets or in a proving ground, however the torque and power gain cannot be measured with sufficient precision to decide the ideal ignition timing and injection time. The inertial dynamometers marketed in the country, and used in repairers or vehicle preparers always bring software that allows the acquisition and registration of the information obtained in the tests. These software are generally proprietary and do not provide detailed information about how smoothing is applied to the torque and power curves. Smoothing is needed especially when rotational speed (RPM) is obtained from a phonic wheel or any other digital encoder. To obtain angular acceleration from rotational speed (and take in account the inertia of the dynamometer) we use differentiation, a mathematical operation that amplifies high frequency noise, including that originated by the finite resolution of the encoder. This paper discusses different ways of circumventing the high frequency noise amplification in differentiation. Data made available by SportDevices, a manufacturer of data acquisition software for inertial dynamometers is used not only to compare the described digital signal processing (DSP) techniques among themselves but also with the resulting torque and power results with those provided by the commercial software. The (DSP) techniques here described are based on moving averages and polynomial fitting, on low-pass filtering, on smoothing splines and on Tikhonov regularization. The conclusions favors the latter smoothing techniques.