Prediction of Spark Timing to Achieve a Specified Torque Profile in Spark-Ignition Engines Using Time-Dependent Metamodeling

The internal combustion engine is a source of unwanted vibration on the vehicle body. The unwanted vibration comes from forces on the engine mounts which depend on the engine torque during a transient maneuver. In particular, during a tip-in or a tip-out maneuver, different torque profiles result in different magnitudes of vibration. A desired engine torque shape can be thus obtained to minimize the unwanted vibration. The desired torque shape can be achieved by controlling a set of engine calibration parameters. This paper provides a methodology to determine the spark timing profile to achieve a desired engine torque profile during a tip-out maneuver. The spark timing profiles are described by a third-order polynomial as a function of time. A set of coefficients to define a third-order polynomial (design sites) are first generated using design of experiments (DOE). Each design site defines a spark timing profile which is then used to generate an engine torque profile using a CAE tool. The set of design sites and the corresponding engine torque profiles are used to construct time-dependent metamodels using Singular Value Decomposition (SVD) and Kriging. An example shows that the appropriate spark timing profile to achieve a desired engine torque profile can be successfully determined. The results are validated using the GT-Power engine software.