Fuel injector calibration and trimming

Abstract

A method for correcting injection behavior of a fuel injector includes calculating a nominal value of a fuel injector family characteristic for an average fuel injector from a family of fuel injectors as a multi-variable function of engine operating conditions, calculating a corrected value of the fuel injector family characteristic as a function of the nominal value, and employing the corrected value when actuating the fuel injector to inject fuel.

Claims

1. A method for correcting injection behavior of a fuel injector that injects a gaseous fuel in an internal combustion engine comprising: (a) conducting a fuel injector family calibration phase for a family of fuel injectors, said family calibration phase comprising: (i) operating a set of fuel injectors from said family at a first predetermined number of engine operating conditions, each engine operating condition defined by a gaseous fuel rail pressure, a liquid fuel rail pressure and a cylinder pressure; and (ii) determining a multi-variable function of said gaseous fuel rail pressure, said liquid fuel rail pressure and said cylinder pressure based on measurements of performance of said set of fuel injectors, said multi-variable function determining a nominal value of a fuel injector family characteristic based on said gaseous fuel rail pressure, said liquid fuel rail pressure and said cylinder pressure; (b) conducting a fuel injector calibration phase prior to installation of said fuel injector in said internal combustion engine, said fuel injector calibration phase comprising: (i) operating a fuel injector from said family of fuel injectors at a second predetermined number of engine operating conditions; and (ii) determining a function of said nominal value based on measurements of performance of said fuel injector, said function of said nominal value determining a corrected value of said fuel injector family characteristic for said fuel injector; (c) conducting a fuel injector trimming phase during operation in said internal combustion engine, said trimming phase comprising: (i) operating said fuel injector at an engine operating condition; (ii) calculating said nominal value of said fuel injector family characteristic from said multi-variable function of said gaseous fuel rail pressure, said liquid fuel rail pressure and said cylinder pressure; (iii) calculating said corrected value of said fuel injector family characteristic from said function of said nominal value; and (iv) employing said corrected value when actuating said fuel injector to inject said gaseous fuel.

2. The method of claim 1, wherein said gaseous fuel is a main fuel, and said fuel injector family calibration phase, said fuel injector calibration phase and said fuel injector trimming calibration phase are conducted for a pilot fuel and for said main fuel.

3. The method of claim 1, wherein said fuel injector family calibration phase further comprises, for each fuel injector and engine operating condition: (iii) measuring performance of said fuel injector when injecting; and (iv) determining an actual value of said fuel injector family characteristic as a function of said measurements of said performance; (v) grouping said engine operating conditions and said actual values for each fuel injector into a set of points; and (vi) determining said multi-variable function by employing surface fitting techniques on said sets of points.

4. The method of claim 1, wherein said fuel injector calibration phase further comprises, for each engine operating condition: (iii) measuring performance of said fuel injector when injecting; (iv) determining an actual value of said fuel injector family characteristic as a function of said measurements of said performance; (v) calculating said nominal value of said fuel injector family characteristic from said multi-variable function; (vi) grouping said actual value and said nominal value for each engine operating condition into a set of points; (vii) determining said function of said nominal value by employing curve fitting techniques on said set of points; (viii) determining parameters representative of said function of said nominal value; and (ix) associating said parameters with said fuel injector.

5. The method of claim 1, wherein said fuel injector injects accurately metered quantities of said gaseous fuel and a liquid fuel.

6. The method of claim 1, wherein each engine operating condition is further defined by a hydraulic pulse width.

7. The method of claim 1, wherein said fuel injector family characteristic is one of opening delay, closing delay and hydraulic pulse width correction factor.

8. The method of claim 7, further comprising correcting said injection behavior for said fuel injector by determining corrected values for each of said opening delay, closing delay and hydraulic pulse width correction factor.

9. The method of claim 1, wherein said function of said nominal value comprises a first equation of a first line representative of a relationship between said nominal value and said corrected value.

10. The method of claim 9, wherein said first equation of said first line is characterized by coefficients associated with said fuel injector.

11. The method of claim 9, wherein said first equation is an equation for a straight line characterized by coefficients comprising a slope and a y-intercept.

12. The method of claim 11, further comprising determining said slope and said y-intercept during fuel injector calibration and associating said slope and said y-intercept with said fuel injector.

13. The method of claim 9, wherein said function of said nominal value further comprises a second equation of a second line representative of a relationship between said nominal value and said corrected value, said first equation representative of a high load and/or speed region and said second equation representative of a low load and speed region of said engine operating conditions.

14. The method of claim 13, wherein when an engine operating condition is between said low load and speed region and said high load and/or speed region, said method further comprises interpolating between corresponding corrected values in said low load and speed region and said high load and/or speed region to determine said corrected value.

15. An apparatus for correcting injection behavior of a fuel injector that injects a gaseous fuel in an internal combustion engine, the apparatus comprising an electronic controller operatively connected with said fuel injector, wherein said electronic controller is programmed to: (a) calculate a nominal value of a fuel injector family characteristic for a family of fuel injectors from a multi-variable function of engine operating conditions defined by gaseous fuel rail pressure, liquid fuel rail pressure and cylinder pressure, said multi-variable function determined in a fuel injector family calibration phase performed at least once for a set of fuel injectors from said family of fuel injectors; (b) calculate a corrected value of said fuel injector family characteristic for said fuel injector from a function of said nominal value; said function of said nominal value determined during a fuel injector calibration phase prior to installation of said fuel injector in said internal combustion engine; and (c) employ said corrected value when actuating said fuel injector to inject said gaseous fuel.

16. The apparatus of claim 15, wherein said engine operating conditions are further defined by hydraulic pulse width.

17. The apparatus of claim 15, wherein said fuel injector family characteristic is one of opening delay, closing delay and hydraulic pulse width correction factor.

18. The apparatus of claim 15, wherein said electronic controller is further programmed to correct said injection behavior for said fuel injector by determining corrected values for each of said opening delay, closing delay and hydraulic pulse width correction factor.

19. The apparatus of claim 15, wherein said gaseous fuel is a main fuel, and said fuel injector is actuated to introduce a pilot fuel separately and independently from the main fuel.

20. The apparatus of claim 19, wherein said electronic controller is programmed to perform steps (a), (b) and (c) for said pilot fuel and for said main fuel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic view of a fuel system according to one embodiment.

(2) FIG. 2 is a plot of an electronic control signal, a corresponding hydraulic pressure signal employed to activate a fuel injector in the fuel system of FIG. 1, and a mass flow signal representing the rate of mass flow through the fuel injector due to the hydraulic pressure signal.

(3) FIG. 3 is a schematic view of a fuel injector trim apparatus for the fuel system of FIG. 1.

(4) FIG. 4 is a plot of opening delay (OD) for a fuel injector versus a fuel injector family characteristic (x.sub.OD) representative of a nominal value of opening delay for an average fuel injector from a family of fuel injectors and determined as a function of engine operating conditions.

(5) FIG. 5 is a plot of closing delay (CD) for a fuel injector versus a fuel injector family characteristic (x.sub.CD) representative of a nominal value of closing delay for the average fuel injector from the family of fuel injectors and determined as a function of engine operating conditions.

(6) FIG. 6 is a plot of fuel trim (FTM) for a fuel injector versus a fuel injector family characteristic (x.sub.FTM) representative of a nominal value of fuel trim for the average fuel injector from the family of fuel injectors and determined as a function of engine operating conditions.

(7) FIG. 7 is a plot of opening delay (OD) for a fuel injector versus a fuel injector family characteristic (x.sub.OD) representative of a nominal value of opening delay for the average fuel injector from the family of fuel injectors showing a low load/speed trend and a high load/speed trend.

(8) FIG. 8 illustrates a plot of load versus speed illustrating a high load region, a low load region and a transition region for an internal combustion engine employing the fuel system of FIG. 1.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENT(S)

(9) FIG. 1 shows fuel system 10 for a high pressure, direct injection internal combustion engine. Only the components relevant for the understanding of the present technique are shown; there are other components associated with a fuel system which are not shown. Although the disclosure herein is directed at a direct injection system, the technique described applies to any type of fuel injector. Gaseous fuel supply apparatus 20 delivers pressurized gaseous fuel to gas rail 30 through piping 40. In the present disclosure gas refers to gaseous fuel. Gaseous fuel pressure in rail 30 is monitored by pressure sensor 50 which sends a signal to electronic controller 60 such that the controller commands apparatus 20 to pump gaseous fuel to maintain the pressure in rail 30 at a set point pressure within a predetermined range of tolerance as a function of engine operating conditions. Liquid fuel supply apparatus 70 delivers pressurized liquid fuel to rail 80 through piping 90. The liquid fuel pressure in rail 80 is monitored by pressure sensor 100 which sends a signal to electronic controller 60 such that the controller commands apparatus 70 to pump liquid fuel to maintain the pressure in rail 80 at a set point pressure within a predetermined range of tolerance as a function of engine operating conditions. In other embodiments a bias pressure between gaseous fuel pressure in rail 30 and liquid fuel pressure in rail 80 can be mechanically controlled, for example by a dome loaded regulator, such that by controlling the pressure of one fuel the other is automatically determined by the bias pressure. As is understood by those familiar with the technology, there are other related techniques for controlling pressure in rails 30 and 80.

(10) In some preferred embodiments, fuel injectors 110 are hydraulically actuated direct injectors that inject a pilot fuel and a main fuel, which can be actuated to introduce the pilot fuel separately and independently from the main fuel. In the present embodiment the pilot fuel is the liquid fuel in rail 80 delivered through piping 120 and the main fuel is the gaseous fuel in rail 30 delivered through piping 130. Control bus 140 from controller 60 comprises control lines 140a, 140b, 140c, 140d, 140e, 140f which actuate respective fuel injectors 110 to inject gaseous fuel. Similarly, control bus 150 from controller 60 comprises control lines 150a, 150b, 150c, 150d, 150e, 150f which actuate respective fuel injectors 110 to inject liquid fuel.

(11) Referring now to FIGS. 1 and 2, the actuation of fuel injectors 110 is described in more detail in relation to control line 140a of one such fuel injector. Controller 60 (from FIG. 1) actuates the fuel injector to introduce gaseous fuel by generating control signal 143a (shown in FIG. 2) sent over control line 140a which energizes an actuator in the injector (not shown) to initiate a pressure change of hydraulic fluid characterized by hydraulic fluid pressure signal 144a. Control signal 143a is an electrical control signal shown in its ideal form, such as a voltage or current signal for example. Hydraulic fluid pressure signal 144a actuates mechanisms of the injector to introduce gaseous fuel into combustion chambers (not shown) of the internal combustion engine, and the mass flow of the gaseous fuel into the combustion chambers is illustrated in FIG. 2 as mass flow signal 145a. Mass flow signal 145a is representative of the rate of fuel flowing into the combustion chambers. Control signal 143a is characterized by electronic pulse width (ePW), and mass flow signal 145a is characterized by hydraulic pulse width (hPW). The timing for electronic pulse width (ePW) begins at the rising edge of control signal 143a indicated as electronic start of injection (eSOI). The timing for hydraulic pulse width (hPW) begins at the rising edge of mass flow signal 145a indicated as hydraulic start of injection (hSOI), and begins a period of time known as opening delay (OD) after electronic start of injection (eSOI). Hydraulic start of injection (hSOI), which is an important parameter to control for improved combustion quality, correlates to the time fuel starts flowing through the injector into the combustion chamber, in direct injector embodiments. For this reason it is advantageous to know the opening delay (OD) for each fuel injector such that the time when fuel is introduced can be known with improved accuracy. Similarly, closing delay (CD) is the timing difference between the falling edge of control signal 143a and the corresponding falling edge in mass flow signal 145a. Opening delay (OD) and closing delay (CD) are characteristics of each fuel injector that vary from injector to injector. For the purposes of this disclosure, in FIG. 2, it is arbitrary whether opening delay (OD) is greater than, equal to or less than closing delay (CD). Depending upon the design and operating characteristics of a particular fuel injector, as well as the engine system operating conditions, opening delay (OD) could be greater than, equal to, or less than closing delay (CD).

(12) Fuel injectors exhibit other characteristics that vary from part to part. For a given hydraulic pulse width (hPW) the actual quantity of fuel delivered from each fuel injector varies from a nominal value for the family of fuel injectors for a variety of reasons, including the dimensional variances introduced by the permitted manufacturing tolerances. As used herein a family of fuel injectors comprises like fuel injectors. To compensate for this variation the hydraulic pulse width (hPW) can be corrected by increasing or decreasing the width. In the present disclosure the hydraulic pulse width is corrected by multiplying it by a correction factor called fuel trim (FTM). The present disclosure provides a technique to calibrate fuel injectors 110 such that a reduced amount of trim information is provided to electronic controller 60 whereby opening delay (OD), closing delay (CD) and fuel trim (FTM) can be determined for each fuel injector 110 as function of engine operating conditions as a function of the particular characteristics of each individual fuel injector.

(13) Referring now to FIG. 3 fuel injector trim apparatus 200 comprises opening delay (OD) module 220, closing delay (CD) module 230, fuel trim (FTM) module 240 and correction module 250. As used herein, the terms module, algorithm and step refer to an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. In some preferred embodiments the modules, algorithms and steps herein are part of electronic controller 60. Apparatus 200 operates to determine electronic start of injection (eSOI) and electronic pulse width (ePW) based on a desired hydraulic start of injection (hSOI) and a desired hydraulic pulse width (hPW). Hydraulic start of injection (hSOI) and hydraulic pulse width (hPW) are nominal values for a nominal fuel injector and are determined as a function of engine operating conditions to achieve a desired nominal fueling at a desired nominal timing. For the purposes of this disclosure start of injection (SOI) refers to crank angle degrees (CA) before top dead center (BTDC). Conventionally, controller 60 looks up in a map a corresponding electronic pulse width (ePW) as a function of hydraulic pulse width (hPW) and a corresponding electronic start of injection (eSOI) as a function of hydraulic start of injection (hSOI). In the present disclosure modules 220, 230 and 240 correct opening delay (OD), closing delay (CD) and hydraulic pulse width (hPW) respectively, such that electronic start of injection (eSOI) and electronic pulse width (eSOI) can be determined according to correction module 250.

(14) Each module 220, 230 and 240 comprises a model representative of the family of fuel injectors 110 in the form of a multi-variable function that outputs a value as a function of engine operating conditions that is common to fuel injectors in that family. Referring first to opening delay module 220, Eqn. 1 below illustrates the multi-variable function that determines a value (x.sub.OD) representative of the opening delay for an average fuel injector from the family of fuel injectors as a function of gaseous fuel rail pressure (GFRP), liquid fuel rail pressure (LFRP) and in-cylinder pressure (P.sub.CYL). The derivation of the multi-variable function in EQN. 1 will be described in more detail below, in addition to the derivation of multi-variable functions EQNS. 3 and 5 discussed in relation to closing delay (CD) and fuel trim (FTM). The value (x.sub.OD) can be a nominal opening delay for the average fuel injector from the family of fuel injectors, or can be a nominal value having dimensions (units) that have no physical meaning but which is correlated, and therefore representative of the nominal opening delay. A corrected value for opening delay (OD) for a particular fuel injector can be determined by substituting the value (x.sub.OD) into EQN. 2, which is a function comprising constants (m.sub.OD, b.sub.OD) that are characteristic of the particular fuel injector. EQN. 1 represents a relationship for the family of fuel injectors 110, and EQN. 2 represents a relationship for the particular fuel injector. The constants (m.sub.OD, b.sub.OD) for each fuel injector are determined in a calibration phase during manufacturing. When the family of fuel injectors is the type that are hydraulically actuated direct injectors that inject a pilot fuel and a main fuel, which can be actuated to introduce the pilot fuel separately and independently from the main fuel, there are a set of EQN. 1 and EQN. 2 for the pilot fuel portion of the fuel injector and a set of EQN. 1 and EQN. 2 for the main fuel portion of the fuel injector. EQN. 1 for the pilot fuel may not be a function of GFRP.
x.sub.OD=f(GFRP,LFRP,P.sub.cyl)EQN. 1
OD=m.sub.ODx.sub.OD+b.sub.ODEQN. 2

(15) Referring now to closing delay module 230 in FIG. 3, Eqn. 3 below illustrates the multi-variable function that determines a value (x.sub.CD) representative of the closing delay for the average fuel injector from the family of fuel injectors as a function of gaseous fuel rail pressure (GFRP), liquid fuel rail pressure (LFRP), in-cylinder pressure (P.sub.CYL) and hydraulic pulse width (hPW). The value (x.sub.CD) can be a nominal closing delay for the average fuel injector from the family of fuel injectors, or can be a nominal value having dimensions (units) that have no physical meaning but which is correlated, and therefore representative of the nominal closing delay. A corrected value for closing delay (CD) for a particular fuel injector can be determined by substituting the value (x.sub.CD) into EQN. 4, which is a function comprising constants (m.sub.CD, b.sub.CD) that are characteristic of the particular fuel injector. EQN. 3 represents a relationship for the family of fuel injectors 110, and EQN. 4 represents a relationship for the particular fuel injector. The constants (m.sub.CD, b.sub.CD) for each fuel injector are determined in the calibration phase during manufacturing. When the family of fuel injectors is the type that are hydraulically actuated direct injectors that inject a pilot fuel and a main fuel, which can be actuated to introduce the pilot fuel separately and independently from the main fuel, there are a set of EQN. 3 and EQN. 4 for the pilot fuel and a set of EQN. 3 and EQN. 4 for the main fuel. EQN. 3 for the pilot fuel may not be a function of GFRP.
x.sub.CD=f(GFRP,LFRP,P.sub.cyl,hPW)EQN. 3
CD=m.sub.CDx.sub.CD+b.sub.CDEQN. 4

(16) Referring now to fuel trim module 240 in FIG. 3, Eqn. 5 below illustrates the multi-variable function that determines a value (x.sub.FTM) representative of the fuel trim for the average fuel injector from the family of fuel injectors as a function of gaseous fuel rail pressure (GFRP), liquid fuel rail pressure (LFRP), in-cylinder pressure (P.sub.CYL) and hydraulic pulse width (hPW). The value (x.sub.FTM) can be a nominal fuel trim for hydraulic pulse width for the average fuel injector from the family of fuel injectors, or can be a nominal value having dimensions (units) that have no physical meaning but which is correlated, and therefore representative of the nominal fuel trim. Fuel trim (FTM) is a correction factor that scales hydraulic pulse width (hPW) due to variations in fueling from injector to injector when identical hydraulic pulse widths are employed to actuate the injectors. A corrected value for fuel trim (FTM) for a particular fuel injector can be determined by substituting the value (x.sub.FTM) into EQN. 6, which is a function comprising constants (m.sub.FTM, b.sub.FTM) that are characteristic of the particular fuel injector. EQN. 5 represents a relationship for the family of fuel injectors 110, and EQN. 6 represents a relationship for the particular fuel injector. The constants (m.sub.FTM, b.sub.FTM) for each fuel injector are determined in the calibration phase during manufacturing. When the family of fuel injectors is the type that are hydraulically actuated direct injectors that inject a pilot fuel and a main fuel, which can be actuated to introduce the pilot fuel separately and independently from the main fuel, there are a set of EQN. 5 and EQN. 6 for the pilot fuel and a set of EQN. 5 and EQN. 6 for the main fuel. EQN. 5 for the pilot fuel may not be a function of GFRP.
x.sub.FTM=f(GFRP,LFRP,P.sub.cyl,hPW)EQN. 5
FTM=m.sub.FTMx.sub.FTM+b.sub.FTMEQN. 6

(17) Referring now to correction module 250, electronic start of injection (eSOI) and electronic pulse width (ePW) are calculated according to EQNS. 7 and 8 below. Electronic start of injection (eSOI) and hydraulic start of injection (hSOI) have units of crank angle degrees before top dead center, and electronic pulse width (ePW) and hydraulic pulse width (hPW) have units of crank angle degrees in the present disclosure however other units are possible. Closing delay (CD) and fuel trim (FTM) can be combined into a single correction parameter in other embodiments since they both act to adjust hydraulic end of injection (hEOI) seen in FIG. 2. When the family of fuel injectors is the type that are hydraulically actuated direct injectors that inject a pilot fuel and a main fuel, which can be actuated to introduce the pilot fuel separately and independently from the main fuel, there are a set of EQN. 7 and EQN. 8 for the pilot fuel and a set of EQN. 7 and EQN. 8 for the main fuel.
eSOI=hSOI+ODEQN. 7
ePW=hPW*FTM+ODCDEQN. 8

(18) The multi-variable functions EQN. 1, 3 and 5 can be determined theoretically and empirically. In a preferred embodiment these equations are determined empirically according to the following technique. For a sample set of fuel injectors, from the same family of fuel injectors, fuel injection tests are conducted for each of the injectors for a predetermined number of engine operating conditions by varying at least the following parameters: liquid fuel rail pressure, gaseous fuel rail pressure, in-cylinder pressure and hydraulic pulse width. Preferably, the sample set of injectors are from a lot of fuel injectors obtained from a manufacturing facility. For each of the predetermined engine operating conditions opening delay (OD), closing delay (CD), hydraulic pulse width and actual quantity of fuel injected are measured. Fuel trim (FTM), that is the hydraulic pulse width correction factor, is determined based on the measured quantity of fuel injected, measured hydraulic pulse width, desired quantity of fuel injected and desired hydraulic pulse width. The predetermined engine operating conditions and corresponding measured data form sets of points {(GFRP, LFRP, P.sub.cyl, hPW, OD)}, {(GFRP, LFRP, P.sub.cyl, hPW, CD)}, and {(GFRP, LFRP, P.sub.cyl, hPW, FTM)} which when plotted in multi-dimensional space form multi-dimensional surfaces respectively. For each of these surfaces, known surface fitting techniques are employed to determine the multi-variable functions EQN. 1, 3 and 5 respectively. In other embodiments instead of employing actual fuel injectors in real physical tests, models of the fuel injector and of the test environment can be employed to determine the sets of points described above. Preferably, the models of the fuel injectors take into consideration dimensional variations due to manufacturing tolerances. In the event that trim information is not provided for an actual fuel injector, for example trim information was not entered during injector replacement in the field, then the values (x.sub.OD, x.sub.CD, x.sub.FTM) can be employed in EQNS. 7 and 8 in place of opening delay (OD), closing delay (CD) and fuel trim (FTM) respectively. The values (x.sub.OD, x.sub.CD, x.sub.FTM) in this situation are normalized to represent the average opening delay, the average closing delay and the average fuel trim for the average fuel injector from the family of fuel injectors. By this technique an actual fuel injector for which trim data is not provided is operated as an average fuel injector, instead of an ideal fuel injector, which statistically reduces fueling errors.

(19) Referring now to FIGS. 4, 5 and 6 the derivation of the constants (m.sub.OD, b.sub.OD), (m.sub.CD, b.sub.CD) and (m.sub.FTM, b.sub.FTM) during a calibration procedure in manufacturing will now be described in more detail. After each fuel injector 110 is assembled it can be installed into a testing apparatus (not shown) in which it can be actuated to inject fuel or a fluid with like properties. The testing apparatus comprises equipment and instrumentation to take measurements such that mass flow signal 145a and the actual injected quantity of fuel can be determined. A predetermined number of engine operating conditions are selected, and for each operating condition the fuel injector is actuated and OD, CD and FTM are determined from the measurements taken with the test equipment. The x.sub.OD, x.sub.CD and x.sub.FTM values for each of the predetermined engine operating conditions are calculated according to EQN. 1, EQN. 3 and EQN. 5 respectively, and are paired with respective OD, CD and FTM measurements. The pairs of points (x.sub.OD,OD), (x.sub.CD,CD) and (x.sub.FTM,FTM) are assembled into sets {(x.sub.OD,OD)}, {(x.sub.CD,CD)} and {(x.sub.FTM,FTM)} respectively, and these sets are plotted in graphs in FIGS. 4, 5 and 6 to illustrate the relationship between the points. Curve fitting techniques are employed to determine the best fit lines 300, 310 and 320 through the sets {(x.sub.OD,OD)}, {(x.sub.CD,CD)} and {(x.sub.FTM,FTM)} respectively. For each of the lines 300, 310 and 320 the slopes (m.sub.OD, m.sub.CD, m.sub.FTM) and y-intercepts (b.sub.OD, b.sub.CD, b.sub.FTM) are determined and stored on recording apparatus 160, as seen in FIG. 1, of fuel injector 110. In some preferred embodiments, recording apparatus 160 for each fuel injector 110 is encoded with slopes (m.sub.OD, m.sub.CD, m.sub.FTM) and y-intercepts (b.sub.OD, b.sub.CD, b.sub.FTM) characteristic for that fuel injector. Recording apparatus 160 can be a bar code, a memory or an integrated circuit, as well as other components capable of storing information such that the information can be retrieved or displayed. The slopes (m.sub.OD, m.sub.CD, m.sub.FTM) and y-intercepts (b.sub.OD, b.sub.CD, b.sub.FTM) are employed in EQNS. 2, 4 and 6 during operation of the engine to determine opening delay (OD), closing delay (CD) and fuel trim (FTM) as a function of engine operating conditions (GFRP, LFRP, P.sub.CYL, hPW).

(20) It is noteworthy to mention that, in other embodiments, lines 300, 310 and 320 can have shapes other than straight lines, such as lines that are parabolic or hyperbolic in shape, or lines that require a more complex polynomial or other functions to represent them. Factors influencing the shape of lines 300, 310 and 320 are the size of the sets {(x.sub.OD,OD)}, {(x.sub.CD,CD)} and {(x.sub.FTM,FTM)}, the number of variables in the multi-variable functions EQNS 1, 3 and 5 and the characteristics of the family of fuel injectors for which calibration is performed, and therefore coefficients other than slope and y-intercept can be determined and stored on recording apparatus 160. In general, EQNS 2, 4 and 6 have a representation that is characteristic of the shape of the lines 300, 310 and 320 respectively.

(21) Referring now to FIG. 7, a plot of the set {(x.sub.OD,OD)} is illustrated for another embodiment. There exist similar plots (not shown) for the sets {(x.sub.CD,CD)} and {(x.sub.FTM,FTM)}. In this embodiment the characteristic behavior of fuel injectors 110 exhibit different trends between low load/speed, such as idle, and high load/speed which refers to a load and speed above low load/speed. Straight line 330 is the best fit line for the set {(x.sub.OD,OD)} at high load/speed and is characterized by slope m.sub.H,OD and y-intercept b.sub.H,OD according to EQN. 9. Straight line 340 is the best fit line for the set {(x.sub.OD,OD)} at low load/speed and is characterized by slope m.sub.L,OD and y-intercept b.sub.L,OD according to EQN. 10. Opening delay (OD) for a particular fuel injector at high load/speed can be determined by substituting the value (x.sub.OD) from EQN. 1 into EQN. 9, and opening delay (OD) at low load/speed can be determined by substituting the value (x.sub.OD) from EQN. 1 into EQN. 10. There are corresponding equations for closing delay (CD) and fuel trim (FTM).
OD.sub.H=m.sub.H,ODx.sub.OD+b.sub.H,ODEQN. 9
OD.sub.L=m.sub.L,ODx.sub.OD+b.sub.L,ODEQN. 10

(22) When the engine is operating at a load/speed between low load/speed and high load and/or speed the values for opening delay (OD), closing delay (CD) and fuel trim (FTM) can be interpolated between their low load/speed and high load and/or speed values. A preferred interpolation technique is described herein but there are other known interpolation techniques which can be employed. The plot in FIG. 8 illustrates the regions of the load/speed map for the engine applicable to straight lines 330 and 340. Region 350 is a high load and/or speed region characterized by slope m.sub.H,OD and y-intercept b.sub.OD. Region 360 is a low load/speed region characterized by slope m.sub.L,OD and y-intercept m.sub.L,OD. Region 370 represents a transition region between regions 350 and 360. In a preferred embodiment, the engine spends little time operating in transition region 370, for example 1-2% and is normally operating in region 350. Although FIG. 8 illustrates a two dimensional view, in other embodiments there can be other transition zones between other axes, for example between gas rail pressure and speed, and gas rail pressure and load. Line 400 represents the speed idle limit (S.sub.IL) and line 410 represents the speed non-idle limit (S.sub.NIL), the region between lines 400 and 410 represents the speed transition region associated with transition region 370. Line 420 represents the load idle limit (L.sub.IL) and line 430 represents the load non-idle limit (L.sub.NIL), the region between lines 420 and 430 represents the load transition region associated with transition region 370. When operating at a load/speed point in region 370, for example at point (S.sub.1,L.sub.1) in FIG. 8, the following technique can be performed to determine opening delay (OD), closing delay (CD) and fuel trim (FTM). The fraction that point (S.sub.1,L.sub.1) has entered speed transition region from speed idle limit (S.sub.IL) and the fraction that point (S.sub.1,L.sub.1) has entered load transition region from load idle limit (L.sub.IL) are calculated according to EQNS. 11 and 12 below respectively. A fractional value from EQNS. 11 and 12 that is less than zero is interpreted as zero, and when more than two axes are employed (load, speed, gas rail pressure) a fractional value that is greater than one is interpreted as one. Of the two fractions F.sub.S and F.sub.L maximum fractional value F.sub.M is selected according to EQN. 13. Opening delay (OD), closing delay (CD) and fuel trim (FTM) are then calculated according to EQNS. 14, 15 and 16. Values x.sub.OD, x.sub.CD and x.sub.FTM are determined according to EQNS. 1, 3 and 5, based on engine operating conditions at point (S.sub.1,L.sub.1), such that opening delays (OD.sub.L, OD.sub.H), closing delays (CD.sub.L, CD.sub.H) and fuel trims (FTM.sub.L, FTM.sub.H) in EQNS. 14, 15 and 16 can be determined. In EQN. 14, OD.sub.L is the opening delay corresponding to the value x.sub.OD in low load and speed region 360, and OD.sub.H is the opening delay corresponding to the value x.sub.OD, in high load and/or speed region 350. In EQN. 15, CD.sub.L is the closing delay corresponding to the value x.sub.CD in low load and speed region 360, and CD.sub.H is the closing delay corresponding to the value x.sub.CD in high load and/or speed region 350. In EQN. 16, FTM.sub.L is the fuel trim corresponding to the value x.sub.FTM in low load and speed region 360, and FTM.sub.H is the fuel trim corresponding to the value x.sub.FTM in high load and/or speed region 350.

(23) $\begin{array}{cc}{F}_S=\frac{S_1-S_{\mathrm{IL}}}{S_{\mathrm{NIL}}-S_{\mathrm{IL}}}& \mathrm{EQN}.11\\ F_L=\frac{L_1-L_{\mathrm{IL}}}{L_{\mathrm{NIL}}-L_{\mathrm{IL}}}& \mathrm{EQN}.12\end{array}$
F.sub.M=max(F.sub.S,F.sub.L)EQN. 13
OD=OD.sub.L+F.sub.M(OD.sub.HOD.sub.L)EQN. 14
CD=CD.sub.L+F.sub.M(CD.sub.HCD.sub.L)EQN. 15
FTM=FTM.sub.L+F.sub.M(FTM.sub.HFTM.sub.L)EQN. 16

(24) While particular elements, embodiments and applications of the present invention have been shown and described, it will be understood, that the invention is not limited thereto since modifications can be made by those skilled in the art without departing from the scope of the present disclosure, particularly in light of the foregoing teachings.