Estimation of the Mean Indicated Pressure from Measurements of the Crankshafts Angular Speed Variation

In recent years much interest has been shown for the possibilities to determine, on-line, the torque or power delivered by an i.c. engine running on site under normal operating conditions.

In this paper, a method is developed which permits to estimate the average value, for the whole engine, of the mean indicated pressure (MIP), based on measurements of the angular speed fluctuations of the crankshaft. In order to establish the correlation between the MIP and some characteristic magnitudes of the angular speed fluctuations, three different ways to solve the system of differential equations of motion for the torsional oscillating system of the shafting are presented and discussed: transfer matrices (TM), direct numerical integration (DI) and modal analysis (MA). A comparison with experiment shows acceptable coincidence between measurements and simulation for all three methods. Every method has its advantages: DI and MA are able to simulate transients while TM may be used only under steady-state conditions but, a reverse calculation according to the TM algorithm is possible and can be used to predict the exciting torque acting on the crankshaft. Proceeding in this way, the simulations have shown that the amplitudes of certain noninteger harmonic orders of the angular motion may be used to predict the MIP. Experiments have demonstrated that in different speed ranges these harmonic orders may be used to estimate the MIP.