# Analysis of processing methods for combustion pressure measurement in a diesel engine

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## Abstract

This paper analyzes combustion chamber pressure data processing methods related to the number of cycles averaged, top dead center referencing and pressure referencing (pegging). A total of 1000 consecutive engine cycles were measured in a four-cylinder diesel engine. The number of cycles that minimizes the influence of cycle-to-cycle oscillations depends on engine operating conditions and the parameters under analysis. The top dead center (TDC) referencing, using the motored curve, revealed that the thermodynamic loss shifts the peak pressure − 0.4 °CA from TDC. Four pegging methods were compared—least-squares, fixed-point, three-point and two-point—introducing as main novelty the fact they have not been previously investigated on the same baseline conditions. The least-squares based method showed the lowest sensitivity to random noise, but with longer processing time, and the fixed-point method presented higher dispersion in the heat release analysis. The three-point referencing method considers a variable polytropic coefficient, but suffers from noise sensitivity, and the two-point referencing method presented close values and higher dispersion in comparison with the least-squares method. The choice of which method to use depends on the type of analysis, signal quality and processing time available.

## Keywords

Diesel engine Combustion pressure Processing methods Cycle-to-cycle variation Pegging methods## 1 Introduction

The treatment of combustion pressure data consists of pressure referencing, crank angle phasing, cycle averaging and experimental signal filtering [1]. The accuracy of combustion and performance parameters obtained from pressure data are also affected by the number of cycles used for the calculations. There are several sources of error that affect the signal quality and cycle-to-cycle variations [2], motivating the proposition of data metrics for the quality of combustion pressure measurement [3]. Several works used different numbers of cycles to obtain the average cycle and remove the effects of cyclic variations. The optimal number of cycles to be averaged depends on several factors such as engine type, engine operating condition and data acquisition system [1]. Cyclic variations are caused by chemical and physical phenomena, as they are related to mixture composition, cycle cylinder charging and in-cylinder mixture motion [4].

The minimum number of cycles for an accurate calculation of the average pressure varies from 25 to 2800 [4]. From tests in a spark ignition engine operating at different conditions, 50 cycles were reported to be sufficient to provide accurate averaged values [4]. Elsewhere, the optimum number of cycles for tests in a homogeneous charge compression ignition (HCCI) engine was taken as 500, and increasing the number of cycles for averaging from this value did not improve the precision of the results [1].

There are various methods of pressure pegging, but no single method is an ideal solution for every situation. The main methods can be grouped in two strategies [5, 6]. The first one references the pressure signal to a known point, measured by a fast-response piezoresistive pressure transducer capable of measuring the absolute pressure in the intake manifold [7]. Alternatively, it can be assumed that the pressure at bottom dead center (BDC) after the intake stroke is equal to the mean intake manifold pressure [4, 8, 9], based on the assumption that with piston velocity variation near zero, while the valve is still significantly open, the pressure drop across the intake port and valve will be near zero [10]. In the other strategy, the compression stroke is modeled assuming a fixed polytropic coefficient, using the least-squares [11, 12] or the two-point [13] referencing methods, or assuming a variable polytropic coefficient [14]. Each method presents advantages, limitations and accuracy levels [15]. The inlet manifold is the region with the lowest pressure in the engine cycle, being this the major problem with pressure referencing in this location as linearity errors and signal noise can be very large in comparison with other regions [15]. The inlet manifold and polytropic index pressure referencing methods produced similar performance when applied to a gasoline engine operating under different conditions.

There is also the so-called real pegging strategy, where a piezoresistive transducer is installed in the lower barrel of the cylinder liner to measure the pressure at bottom dead center (BDC) [16]. The main limitation of this method is the requirement to create a passage for the transducer in the engine block, which is an additional installation difficulty. Also, the piezoresistive transducer at this condition highly suffers from temperature-dependent characteristics, such as zero-line shift, change of linearity and varying sensitivity [17]. This will need extra signal treatment and conditioning to obtain accurate results.

The two-point referencing (2ptR), three-point referencing (3ptR) and least-squares method (LSM) were compared with a modified LSM with a variable polytropic coefficient as pegging methods to a diesel engine [14]. The 2ptR and LSM methods assume a fixed polytropic coefficient for all engine cycles, while the 3ptR and modified LSM methods assume a variable polytropic coefficient. The modified LSM method presented the lowest standard deviation for the polytropic coefficient. The LSM and the modified LSM methods produced the lowest peg drift, which is determined by the changes in the sensor offset from one cycle to the next. The least-squares-based methods produced the lowest variation in the center of gravity (COG) of pressure difference and reduced sensitivity to random noise. It was concluded that the assumption of a fixed polytropic coefficient for all engine cycles could result in an erroneous calculation of the sensor offset and that the modified least-squares method has the least sensitivity to random measurement noise [14].

This work aims to analyze pressure referencing, cycle averaging and TDC referencing as combustion pressure data processing methods. Experiments were carried out in a four-cylinder engine with different engine loads to evaluate the influence of the number of cycles averaged on combustion pressure and indicated mean effective pressure (IMEP) standard deviation. Referencing to TDC was done using the engine motored curve from a thermodynamic method. A comparative study on four different pegging methods was done, analyzing the polytropic coefficient, pressure shift value and influence on heat release rate. The main novelties of this work are the evaluation of four different pegging methods from the same baseline experiments, and the presentation of updated recommended values for the optimized number of averaged cycles and the thermodynamic loss angle of TDC.

The group of pegging methods here analyzed are different from the ones investigated in previous works [18, 19]. A comparison has previously been made between the three-point referencing method, its variant with five-point averaging, a linear and a nonlinear least-squares method [18]. Elsewhere, a comparison between least-squares methods with a fixed polytropic coefficient, variable polytropic coefficient and polytropic coefficient with cyclic learning has been reported [19]. Here, a comparison is made between the fixed-point referencing (1ptR), 2ptR, 3ptR and LSM methods.

## 2 Methodology

### 2.1 Experiments

Diesel engine and generator details

Equipment | Parameter | Type or value |
---|---|---|

Engine | Model | MWM D229-4 |

Cycle | Four strokes | |

Diesel oil injection | Direct | |

Bore × stroke | 102 mm × 120 mm | |

Number of cylinders | 4, in line | |

Total displacement | 3.922 L | |

Compression ratio | 17:1 | |

Intake system | Naturally aspirated | |

Rated power | 44 kW | |

Intake valve open (IVO) | 0 °CA ATDC | |

Intake valve close (IVC) | 210 °CA ATDC | |

Exhaust valve open (EVO) | 510 °CA ATDC | |

Exhaust valve close (EVC) | 720 °CA ATDC | |

Number of poles | 4 | |

Voltage | 220 V | |

Generator | Number of phases | 3 |

Rated power | 55 kVA | |

Frequency | 60 Hz |

The experiments were performed with load power of 10.0 kW, 20.0 kW, 27.5 kW and 35.0 kW. These points were chosen to cover most of the engine operational range, from about 20% to 80% of the rated power. The measurements were performed at steady state condition, after stabilization of the inlet and outlet coolant water temperatures and exhaust gas temperature at a set load condition. The results shown in the forthcoming sections are the average of three sets of experiments performed at each load condition. At motored engine conditions, the cylinder with the pressure sensor installed was operated without fuel injection, while the other three cylinders were fired. The experimental procedure to make the measurements was the same as adopted when load was applied.

The combustion pressure was measured by a Kistler model 6061B water-cooled piezoelectric transducer installed in the first engine cylinder. The cooling system conferred stability to the sensor and reduced the thermal drift [17]. The transducer was connected to a Kistler 5037B3 charge amplifier, to convert the electric charge into analog voltage signal. The pressure transducer operation was in the range from 0 to 250 bar with a sensitivity of − 25.6 pC/bar, linearity ≤ ± 0.5% of full-scale output, natural frequency ≈ 90 kHz and sensitivity shift ≤ ± 0.5%.

A 60-2 crank trigger wheel and a magnetic sensor were used to synchronize the pressure data with the first cylinder at TDC. The time-based technique was used for the in-cylinder pressure phasing with crank angle, resulting in an angular resolution of 0.1 °CA with an acquisition rate of 100 kHz. As the engine had four cylinders and was operated at constant speed (1800 RPM), the crank angle phasing errors due to instantaneous crankshaft speed fluctuations were reduced [20]. The analog signal from the magnetic sensor was conditioned by a LM1815 adaptive variable reluctance amplifier to turn it into a digital signal and eliminate noise. The pressure and magnetic data were simultaneously acquired using a National Instruments Data Acquisition system (NI USB-6211) with an acquisition rate of 100 kHz. A fourth-order low-pass Butterworth filter with a frequency of 1 kHz was used to remove high-frequency noise. The delay between the filter output and input signals was determined by plotting the unfiltered and filtered signals against the crankshaft position. The filtered pressure signal was then advanced by the delay time of 25 μs to be consistent with the unfiltered pressure signal.

### 2.2 Combustion pressure processing

*θ*

_{loss}) that shifts the peak pressure due to thermodynamically non-ideal compression and expansion processes resulting from heat transfer, crevice and blow-by effects [22] was calculated. To calculate

*θ*

_{loss}, which is the angular difference of the mechanical TDC position and thermodynamic TDC position, the motored curve was bisected at equidistant points of − 14 to − 4 °CA and 4 °CA to 14 °C. From each symmetrical point, a straight line was connected and the center position was derived from that line. Using linear regression, a straight line was calculated through the central points and the intersection of this line with the crank angle axis determined

*θ*

_{loss}and, therefore, the thermodynamic TDC [20]. The absolute pressure at a crank angle position

*p(θ)*was obtained from the shift of the measured pressure

*p*

_{meas}

*(θ)*by the zero-line shift ∆

*p*[17]:

In this study, four different pegging methods were compared: fixed-point referencing (1ptR), two-point referencing (2ptR), three-point referencing (3ptR) and least-squares method (LSM).

In the 1ptR method [23], the in-cylinder pressure at BDC, at the end of the intake process, was considered equal to the intake manifold absolute pressure. The whole in-cylinder pressure curve was shifted until, at the fixed-point, the reference pressure was achieved. This method is not suitable for tuned intake system or high engine speed [14]. It is considered very accurate procedure in naturally aspirated engines, but is limited by signal noise that can lead to inaccurate referencing for the total cycle [14, 23, 24]. In this work, the average pressure of 78 kPa in the inlet manifold was used as pressure referencing, as adopted by other authors [23].

*κ*and used the pressure at two points,

*θ*

_{1}and

*θ*

_{2}, related to the cylinder volume by:

*p*shift can be written as:

The recommended crank angle values for diesel engines are 100 °CA BTDC ≤ *θ*_{1} ≤ 80 °CA BTDC and 40 °CA BTDC ≤ *θ*_{2} ≤ 30 °CA BTDC [18], or *θ*_{1} = 100 °CA BTDC and *θ*_{2} = 65 °CA BTDC [21]. The main uncertainty of this method is based on the use of a constant polytropic exponent. To minimize this influence, the crank angle interval must be as large as possible. This method is frequently used due to its simplicity and good level of accuracy [17].

Equation (4) was expanded in a first-order Taylor series to calculate the polytropic coefficient. The value of ∆*p* was calculated from Eq. (3):

*c*

_{p}/

*c*

_{v},

*p*is the cylinder pressure (Pa),

*V*is the cylinder volume (m

^{3}) and \(\theta\) is the crank angle ( °CA).

## 3 Results and discussion

*σ*

_{IMEP}(kPa) and its mean value [25], and it was here used to evaluate the influence of the number of cycles on the cyclic variability. It can be observed that the optimum number of cycles for this parameter depends on the engine operating condition. The COV of IMEP was stabilized after a certain number of cycles at a given load and did not significantly change with additional cycles. There was an increase in COV of IMEP with the decrease in engine load, indicating a higher engine instability at low loads. The cyclic variability increases with increasing relative air–fuel ratio [4], explaining the need for less cycles to be acquired at high engine loads when increased fuel amounts are utilized. At a given load and increasing the number of cycles, stabilization was considered to occur when the ratio of the COV of IMEP to the COV of IMEP of 1000 cycles reached a value lower than 3%. The stabilization of COV of IMEP was achieved at the number of cycles of 500, 700, 250 and 250, for the loads of 10.0 kW, 20.0 kW, 27.5 kW and 35.0 kW, respectively.

*θ*

_{loss}). This angle was determined applying the FEV method to the in-cylinder pressure of the motored engine, averaged from 1000 cycles. The calculations resulted in a

*θ*

_{loss}of − 0.4 °CA, which is near the reported values of − 1.0 °CA [26], 0.35 °CA [27] and 0.7 °CA [28]. The small differences may be accounted to some dependence of

*θ*

_{loss}on engine configuration, which ranged from 4-cylinder spark ignition [27] to 6-cylinder supercharged diesel engine [28]. Figure 5 shows the in-cylinder pressure and volume of the motored engine, and

*θ*

_{loss}.

The pegging methods were evaluated analyzing the effects on the polytropic coefficient, shift value, heat release rate and CA50, which represents the crank angle at which 50% of the cumulative heat release occurred [29, 30]. The calculations of each pegging method were done cycle-by-cycle for 1000 cycles, and then the in-cylinder pressure mean and standard deviations were calculated using a program developed in MATLAB^{®} software. Comparing the processing time of each method, the calculation using the LSM method took the longer processing time, followed by the 3ptR, 2ptR and 1ptR methods. For all methods, the processing time was of the order of milliseconds.

Polytropic coefficients (*κ*) and standard deviations (*σ*) of 3ptR method

Load | | |
---|---|---|

Motored | 1.33 | 0.02 |

10.0 kW | 1.32 | 0.02 |

20.0 kW | 1.32 | 0.02 |

27.5 kW | 1.31 | 0.03 |

35.0 kW | 1.31 | 0.05 |

Pressure shift and standard deviation of the different pegging methods with varying engine load

Method | 10.0 kW | 20.0 kW | 27.5 kW | 35.0 kW | ||||
---|---|---|---|---|---|---|---|---|

\(\overline{\Delta p}\) (kPa) |
| \(\overline{\Delta p}\) (kPa) |
| \(\overline{\Delta p}\) (kPa) |
| \(\overline{\Delta p}\) (kPa) |
| |

1ptR | 832.6 | 17.7 | 812.5 | 16.8 | 1100.1 | 14.3 | 962.1 | 16.0 |

2ptR | 854.0 | 17.9 | 834.5 | 17.2 | 1124.9 | 15.7 | 988.2 | 18.2 |

3ptR | 856.8 | 18.0 | 837.8 | 17.2 | 1131.9 | 15.8 | 992.3 | 18.3 |

LSM | 854.9 | 18.0 | 834.2 | 16.9 | 1121.9 | 15.0 | 989.4 | 16.7 |

CA50 and deviations for the different pegging methods and engine loads

Method | 10.0 kW | 20.0 kW | 27.5 kW | 35.0 kW | ||||
---|---|---|---|---|---|---|---|---|

CA50 ( °CA) |
| CA50 ( °CA) |
| CA50 ( °CA) |
| CA50 ( °CA) |
| |

1ptR | 5.3 | 0.2 | 6.7 | 0.2 | 8.3 | 0.3 | 11.1 | 0.5 |

2ptR | 5.5 | 0.2 | 7.3 | 0.4 | 9.1 | 0.4 | 12.0 | 0.6 |

3ptR | 5.5 | 0.2 | 7.4 | 0.4 | 9.4 | 0.5 | 12.2 | 0.7 |

LSM | 5.5 | 0.2 | 7.3 | 0.4 | 9.0 | 0.4 | 12.0 | 0.5 |

Total HR and deviations for the different pegging methods and engine loads

Method | 10.0 kW | 20.0 kW | 27.5 kW | 35.0 kW | ||||
---|---|---|---|---|---|---|---|---|

HR (J) |
| HR (J) |
| HR (J) |
| HR (J) |
| |

1ptR | 3419 | 244 | 6163 | 272 | 8058 | 319 | 10,215 | 396 |

2ptR | 3581 | 235 | 6528 | 272 | 8566 | 307 | 10,849 | 385 |

3ptR | 3549 | 236 | 6603 | 274 | 8734 | 311 | 10,956 | 396 |

LSM | 3592 | 221 | 6521 | 246 | 8494 | 263 | 10,842 | 350 |

## 4 Conclusions

The optimum number of cycles to minimize cycle-to-cycle variation effects on calculated parameters from cylinder pressure measurement was shown to be dependent on engine operating conditions and the analyzed parameter. For the engine tested, higher engine loads reduced the number of cycles required for the standard deviation of in-cylinder pressure and heat release analysis, ranging from 250 to 800 cycles. The TDC position was adequately determined from a thermodynamic method using the motored curve method, and a shift of − 0.4 °CA of the peak pressure in relation to TDC was calculated. From the pegging methods compared, the least-squares-based method showed the lowest standard deviation in relation to the shift value and the CA50 parameter and less sensitivity to random noise, but with longer processing time, which is critical for online analysis. The fixed-point method presented higher dispersion for CA50 determination and differences in the heat release analysis, in comparison with the other methods, being the least recommended, as it does not consider in-cylinder variations. The 3ptR method considered a variable polytropic coefficient, but suffered from noise sensitivity, and the 2ptR method presented values close to those presented by the LSM, but with higher dispersion. The LSM was proved to be the most recommended pegging method for the tested engine and operating conditions, showing the lowest sensitivity to noise and lowest dispersion.

## Notes

### Acknowledgements

The authors thank CAPES, CNPq 304114/2013-8 Research Project and FAPEMIG TEC PPM 0385-15 Research Project, for the financial support to this work.

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