TDC Offset Estimation from Motored Cylinder Pressure Data based on Heat Release Shaping

Abstract

Finding the correct Top Dead Center (TDC) offset for an internal combustion engine is harder than it seems. This study introduces a novel method to find the TDC offset based on the simple assumption that the heat loss power through the combustion chamber walls is constant for motored cycles in a narrow Crank Angle interval around TDC. The proposed method uses nonlinear least squares optimization to find the combination of specific heat ratio and TDC offset that makes the heat loss power as constant as possible. An important subproblem is to determine the peak pressure location with high accuracy. Fitting a third order Fourier series to the motored cylinder pressure allows the pressure maximum to be estimated with a standard deviation of 0.005° Crank Angle (CA) and it can also be used instead of the measured pressure to reduce the uncertainty of the TDC estimate by approximately 50%. The standard deviation of a single-cycle TDC estimate is approximately 0.025° CA when using a crank resolution of 0.2° CA for the measurements. The bias of the TDC estimate is in the 0-0.02° CA range both when comparing to measurements with a TDC sensor and with simulated motored cycles. The method can be used both for calibration and on-board diagnostics purposes e.g. during cranking, fuel cut-off or engine switch-off. The third order Fourier series fit comes with a significant computational penalty but since it is only applied very intermittently this does not have to be a serious issue.