Method of estimating the MFB50 combustion index and the instantaneous torque generated by the cylinders of an internal combustion engine

1. A method of estimating the MFB50 combustion index, namely the crank angle at which 50% of the fuel mass has been burnt in the cylinders of an internal combustion engine provided with a drive shaft and a pair of phonic wheels, each keyed to one respective end of the drive shaft wherein a first phonic wheel is keyed to the end of the drive shaft at a flywheel, and a second phonic wheel is keyed to the end of the drive shaft at a timing belt and wherein each phonic wheel is provided with a number of teeth and is coupled to a respective position sensor which detects the time elapsed between the passage of two consecutive teeth; the estimation method comprising the steps of:

capturing the signals coming from the at least one pair of position sensors;

determining an instantaneous relative torsion (Δθ) of the drive shaft based on the signals coming from the at least one pair of position sensors;

conducting a frequency analysis of the instantaneous relative torsion (Δθ) of the drive shaft to determine a first harmonic (Ω 1 ) of the instantaneous relative torsion (Δθ) signal by its own module (|Ω 1 |) and by its own phase (Arg(Ω 1 ));

estimating the MFB50 combustion index of each cylinder based on the phase (Arg(Ω 1 )) of the first harmonic (Ω 1 ) of the instantaneous relative torsion (Δθ) signal and the instantaneous relative torsion (Δθ) of the drive shaft generated during the combustion along the angular arc corresponding to a combustion phase of each cylinder;

for each cylinder, during a preliminary set-up phase, determining a first correlation coefficient (P i ) between the MFB50 combustion index of each cylinder and the instantaneous relative torsion (Δθ) of the drive shaft;

wherein the first correlation coefficient (P i ) is expressed as follows:

P i =MFB50 i /Arg(Ω 1 ) i with i= 1 . . . n , where

MFB50 i represents the combustion index based on the ith cylinder;

Arg (Ω 1 ) 1 represents phase Arg (Ω 1 ) of the first harmonic (Ω 1 ) of the instantaneous torsion (Δθ) signal;

Pi represents the first correlation coefficient between the MFB50 combustion index and the phase Arg (Ω 1 ) of the first harmonic (Ω 1 ) of the instantaneous relative torsion (Δθ) signal; and

n represents the number of cylinders; and

once the first correlation coefficient (P i ) for each cylinder is determined, the first correlation coefficient (P i ) can be used during the normal operation of the internal combustion engine to determine a real (MFB50 real ) combustion index for each cylinder;

and wherein at least one cylinder is provided with a pressure sensor housed in the combustion chamber and the method further comprises the steps of:

for each cylinder, during a preliminary set-up phase, determining a first correlation coefficient (P i ) between the estimated MFB50 combustion index and the instantaneous relative torsion (Δθ) of the drive shaft;

determining an actual MFB50 combustion index of the cylinder based on the signal coming from the pressure sensor housed in the combustion chamber;

determining an estimated MFB50 combustion index of the cylinder based on the instantaneous relative torsion (Δθ) of the drive shaft;

comparing the actual MFB50 combustion index of the cylinder with the estimated MFB50 combustion index;

correcting the first correlation coefficient (P i ) of the cylinder based on the comparison between the actual MFB50 combustion index and the estimated MFB50 combustion index and correcting the first correlation coefficient (P i ) of the remaining cylinders without pressure sensors within the pressure chambers based on the comparison between the actual MFB50 combustion index and the estimated MFB50 combustion index.

2. A method according to claim 1 and comprising the further steps of:

determining the angular speed (ω) of the drive shaft based on the signals coming from the at least one pair of position sensors; and

determining the instantaneous relative torsion (Δθ) of the drive shaft based on the angular speed (ω) of the drive shaft.

3. A method according to claim 2 , wherein the position sensors are encoders or phonic wheel sensors; the method comprising the steps of:

associating an angular reference of a first pair of position sensors with each angular reference of a second pair of position sensors;

determining the instantaneous relative torsion (Δθ) of the drive shaft based on the difference between the time instant in which the passage of the angular reference of the first position sensor is detected and the time instant in which the passage of the angular reference of the second position sensor is detected.

4. A method according to claim 1 , wherein the step of carrying out a frequency analysis comprises applying the Fourier transform to the instantaneous relative torsion (Δθ) of the drive shaft.

5. A method according to claim 1 , wherein each cylinder is interposed between a pair of position sensors; the method comprises, for each cylinder, the steps of:

capturing the signals coming from the two position sensors adjacent to said cylinder;

determining the instantaneous relative torsion (Δθ) of the drive shaft generated during the combustion along the angular arc corresponding to the combustion phase of said cylinder based on the signals coming from the two position sensors adjacent to said cylinder; and

estimating the MFB50 combustion index of each cylinder based on the instantaneous relative torsion (Δθ) of the drive shaft generated during the combustion along the angular arc corresponding to the combustion phase of said cylinder.