Investigation of Mode Superposition as Modelling Approach for Crankshaft Torsion

Abstract: With tougher emission standards for heavy duty trucks, good control of the engine is of importance. By taking into consideration the torsional vibrations occurring in the crankshaft, the engine control can be improved. This could be done by implementing a torsion model that would give feedback to the engine control unit to reduce the cycle-to-cycle variations in the cylinders, which is partly due to the torsion in the crankshaft. It is therefore of interest to determine if a torsion model can be developed with a reduced computational complexity and still have sufficient accuracy. In this thesis a model was developed in Matlab for estimation of torsion in the crankshaft of an inline 6 cylinder diesel engine. By applying Newtons second law, the equations of motion that describe the torsional vibrations in the crankshaft were set up. The equations of motion were transformed using modal analysis and with the use of mode superposition it was investigated how reducing the number of vibrational modes in the model, affected the models accuracy in its estimation of torsion. Two model reductions were evaluated where the first three and four vibrational modes were used to calculate the torsional displacement between the flywheel and the cylinders. Using measured pressure curves for a number of operating points of the engineas input to the model, results were produced for different crank angle intervalsshowing deviations between the developed torsion models and a reference models estimation of torsion. Due to the damping approximation used in the model, high initial deviations could be found at certain operating points beforereducing the number of vibrational modes. These initial deviations weregreatest for the first two cylinders. Results from the model reductions showed that using the first three vibrational modes in the torsion model, is sufficient for estimating the torsional displacement between the flywheel and all cylinderswith an accuracy of within 0.1 degrees, with the exception of the first two cylinders for the early and late combustion interval.