Harmonic analysis of the torque of autotractor engines by speed and load modes of operation

¹ Kazan National Research Technical University named after A. N. Tupolev - KAI, 10, K. Marx St., Kazan, 420111, Russian Federation
² Kazan State Agrarian University, 65, K. Marx St., Kazan, 420015, Russian Federation

^* Corresponding author: khaliullin_kai_adis@mail.ru

Abstract

When assessing the cause of torsional vibrations on the crankshaft of tractor engines, forced vibrations are taken into account, which are provoked by torques arising from each cylinder and transmitted to the connecting rod necks, taking into account the order of operation of the cylinders. Researchers have only calculated or experimental values of the torque for different angular positions of the crankshaft with a certain sampling step. The algorithm for solving the torsional vibration problem involves the decomposition of discrete values of the torque of one cylinder into a harmonic series in order to determine its amplitudes and phase shifts. The adequacy of the resulting decomposition is determined by the number of harmonics taken into account and, as a rule, includes 10-12 harmonics. At the same time, it is necessary to perform such decompositions for each speed and load mode, which increases the amount of calculations. An algorithm is proposed that considers these modes separately, and depending on the values of the gas and inertial forces, allows using the characteristics of the nominal operating mode and the decomposition with a smaller number of terms. In this case, the results of the expansions have a satisfactory convergence. The proposed method for determining the parameters of motor harmonics of exciting moments under changing speed and load modes of the internal combustion engine, can be useful in the design of new and fine-tuning dampers of torsional vibrations of crankshafts.