Abstract: A first-half combustion period, for example, is estimated/evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. Within a combustion period of an air-fuel mixture, a period from an ignition time FA to a heat generation rate maximum time dQpeakA where the heat generation rate is maximum is defined as the first-half combustion period a that is one of characteristic values of the heat generation rate waveform. The first-half combustion period a is estimated based on an in-cylinder volume at the heat generation rate maximum time, and furthermore by being corrected using an exponential function of the engine rotation speed with a value depending on a tumble ratio as exponent. Thus, the heat generation rate waveform is produced using the estimated first-half combustion period a.

Abstract: Where a relationship between maximum heat release rate timing and a first combustion period length (that is, a reference relationship) in the case where an engine rotation speed of a spark-ignition internal combustion engine is a selected speed and a valve opening characteristic of an intake valve is a reference characteristic is expressed by the function are f=f(?dQpeak) where ?dQpeak denotes the maximum heat release rate timing and aref denotes the first combustion period length, when the valve opening characteristic of the intake valve changes to a specific characteristic from this state, a first combustion period length for selected maximum heat release rate timing is estimated on the basis of the mathematical expression a=f(?2)+?a1 where ?2 denotes the selected maximum heat release rate timing and a denotes the first combustion period length.

Abstract: A combustion speed, for example, is estimated or evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. An increase rate of a heat generation rate relative to a change in a crank angle in a heat generation rate increasing period (e.g., a first-half combustion period a) in which the heat generation rate increases after ignition of an air-fuel mixture is defined as a heat generation rate gradient b/a that is one of characteristic values of the heat generation rate waveform. The heat generation rate gradient is estimated based on a fuel density (e.g., fuel density ?fuel@dQpeak at heat generation rate maximum time) at a predetermined time set in advance in the heat generation rate increasing period so as to produce the heat generation rate waveform using the estimated heat generation rate gradient.

Abstract: A period from ignition timing to maximum heat release rate timing, at which a heat release rate is maximum, within a combustion period of air-fuel mixture is defined as a first combustion period that is one of characteristic values of a heat release rate waveform. The first combustion period is estimated based on a cylinder volume at the maximum heat release rate timing (maximum heat release rate cylinder volume) irrespective of any of an engine load factor, an EGR rate, an air-fuel ratio, an oil or coolant temperature and opening and closing timing of an exhaust valve through correction by the use of the exponential function of an engine rotation speed with an exponent of a value commensurate with a tumble ratio. The heat release rate waveform is calculated by using the estimated first combustion period.

Abstract: A heat generation rate waveform of an internal combustion engine. A period from spark generated by an ignition plug to ignition of an air-fuel mixture is defined as an ignition delay period ? that is one of characteristic values of the heat generation rate waveform. When the ignition time FA of the air-fuel mixture is on the advance side of a compression top dead center of a piston (BTDC), the ignition delay period ? is estimated based on an in-cylinder fuel density ?fuel@SA at the spark time SA, and when the ignition time FA of the air-fuel mixture is on the delay side of the compression top dead center of the piston (ATDC), the ignition delay period ? is estimated based on an in-cylinder fuel density ?fuel@FA at the ignition time FA. Thus, the heat generation rate waveform is produced using the estimated ignition delay period ?.

Abstract: A first-half combustion period, for example, is estimated/evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. Within a combustion period of an air-fuel mixture, a period from an ignition time FA to a heat generation rate maximum time dQpeakA where the heat generation rate is maximum is defined as the first-half combustion period a that is one of characteristic values of the heat generation rate waveform. The first-half combustion period a is estimated based on an in-cylinder volume at the heat generation rate maximum time, and furthermore by being corrected using an exponential function of the engine rotation speed with a value depending on a tumble ratio as exponent. Thus, the heat generation rate waveform is produced using the estimated first-half combustion period a.

Abstract: A combustion speed, for example, is estimated or evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. An increase rate of a heat generation rate relative to a change in a crank angle in a heat generation rate increasing period (e.g., a first-half combustion period a) in which the heat generation rate increases after ignition of an air-fuel mixture is defined as a heat generation rate gradient b/a that is one of characteristic values of the heat generation rate waveform. The heat generation rate gradient is estimated based on a fuel density (e.g., fuel density ?fuel@dQpeak at heat generation rate maximum time) at a predetermined time set in advance in the heat generation rate increasing period so as to produce the heat generation rate waveform using the estimated heat generation rate gradient.

Abstract: A heat generation rate waveform of an internal combustion engine. A period from spark generated by an ignition plug to ignition of an air-fuel mixture is defined as an ignition delay period ? that is one of characteristic values of the heat generation rate waveform. When the ignition time FA of the air-fuel mixture is on the advance side of a compression top dead center of a piston (BTDC), the ignition delay period ? is estimated based on an in-cylinder fuel density ?fuel@SA at the spark time SA, and when the ignition time FA of the air-fuel mixture is on the delay side of the compression top dead center of the piston (ATDC), the ignition delay period ? is estimated based on an in-cylinder fuel density ?fuel@FA at the ignition time FA. Thus, the heat generation rate waveform is produced using the estimated ignition delay period ?.

Abstract: Where a relationship between maximum heat release rate timing and a first combustion period length (that is, a reference relationship) in the case where an engine rotation speed of a spark-ignition internal combustion engine is a selected speed and a valve opening characteristic of an intake valve is a reference characteristic is expressed by the function are f=f(?dQpeak) where ?dQpeak denotes the maximum heat release rate timing and aref denotes the first combustion period length, when the valve opening characteristic of the intake valve changes to a specific characteristic from this state, a first combustion period length for selected maximum heat release rate timing is estimated on the basis of the mathematical expression a=f(?2)+?a1 where ?2 denotes the selected maximum heat release rate timing and a denotes the first combustion period length.

Abstract: A period from ignition timing to maximum heat release rate timing, at which a heat release rate is maximum, within a combustion period of air-fuel mixture is defined as a first combustion period that is one of characteristic values of a heat release rate waveform. The first combustion period is estimated based on a cylinder volume at the maximum heat release rate timing (maximum heat release rate cylinder volume) irrespective of any of an engine load factor, an EGR rate, an air-fuel ratio, an oil or coolant temperature and opening and closing timing of an exhaust valve through correction by the use of the exponential function of an engine rotation speed with an exponent of a value commensurate with a tumble ratio. The heat release rate waveform is calculated by using the estimated first combustion period.