Statistical Correlation Between the Crankshaft’s Speed Variation and Engine Performance—Part I: Theoretical Model

Abstract

The goal of this two-part paper is to develop a methodology using the variation of the measured crankshaft speed to calculate the mean indicated pressure (MIP) of a multicylinder engine and to detect cylinders that are lower contributors to the total engine output. Both the gas pressure torque and the crankshaft’s speed are, under steady-state operating conditions, periodic functions of the crank angle and may be expressed by Fourier series. For the lower harmonic orders, the dynamic response of the crankshaft approaches the response of a rigid body and that makes it is possible to establish correlations between the amplitudes and phases of the corresponding harmonic orders of the crankshaft’s speed and of the gas pressure torque. The inherent cycle-to-cycle variation in the operation of the cylinders requires a statistical approach to the problem. The first part of the paper introduces the statistical model for a harmonic component of the gas pressure torque and determines the correlation between the amplitudes and phases of the harmonic components of the gas pressure torque and the MIP of the engine. In the second part of the paper the statistical model is used to calculate the MIP and to detect deficient cylinders in the operation of a six-cylinder four-stroke diesel engine.