Determination of TDC in internal combustion engines by a newly developed thermodynamic approach

Abstract

In-cylinder pressure analysis is nowadays an indispensable tool in internal combustion engine research & development. It allows the measure of some important performance related parameters, such as indicated mean effective pressure (IMEP), mean friction pressure, indicated fuel consumption, heat release rate, mass fraction burned, etc.. Moreover, future automotive engine will probably be equipped with in-cylinder pressure sensors for continuous combustion monitoring and control, in order to fulfil the more and more strict emission limits. For these reasons, in-cylinder pressure analysis must be carried out with maximum accuracy, in order to minimize the effects of its characteristic measurement errors. The exact determination of crank position when the piston is at top dead centre (TDC) is of vital importance, since a 1° degrees error can cause up to a 10% evaluation error on IMEP and 25% error on the heat released by the combustion: the position of the crankshaft (and hence the volume inside the cylinder) should be known with the precision of at least 0.1 crank angle degrees, which is not an easy task, even if the engine dimensions are well known: it corresponds to a piston movement in the order of one tenth of micron, which is very difficult to estimate. A good determination of the TDC position can be pursued by means of a dedicated capacitive TDC sensor, which allows a dynamic measurement (i.e. while engine is running) within the required 0.1 degrees precision [1, 2]. Such a sensor has a substantial cost and its use is not really fast, since it must be fitted in the spark plug or injector hole of the cylinder. A different approach can be followed using a thermodynamic method, whose input is in-cylinder pressure sampled during the compression and expansion strokes: some of these methods, more or less valid, can be found in literature [5,6,7,8,7,8]. This paper will discuss a new thermodynamic approach to the problem of the right determination of the TDC position. The base theory of the method proposed is presented in the first part, while the second part deals with the assessment of the method and its robustness to the most common in-cylinder pressure measurement errors. BASE THEORY OF THE METHODThe compression and expansion processes in a motored (i.e. without combustion) engine can be described observing the energy transformations regarding the unity mass which remains in the cylinder. The first law of thermodynamics states that:where dq represents the elementary specific heat received by the gas from the cylinder walls, p and v represent the gas pressure and specific volume, and u the specific internal energy. The gas involved in the process is air and can be assumed to be a perfect gas, thus the following equations are also valid:being T the gas temperature, c P and c V the constant pressure and constant volume specific heat, and R' the gas constant. The compression-expansion process in a motored engine can be assumed to be frictionless, hence the second law of thermodynamics states that the specifi...

A New Method for Simultaneous Determination of the TDC Offset and the Pressure Offset in Fired Cylinders of an Internal Combustion Engine

“…Unlike for the TDC variation, where a TDC offset resulted in ROHR deviation with the same sign in compression and expansion regions, it can be observed that for a pressure offset variation, ROHR curves feature deviations with different signs in compression and expansion regions, which coincides with the results from the Table 1. Figures 2 and 4 thus in addition to the governing equations in Section 2.3 and results generated thereof confirm the basic hypothesis of the proposed method stating that ROHR features different characteristic deviations in the compression phase and the expansion phase when subjected to the TDC and the pressure offset. This further proves the hypothesis that, considering assumption stated after Equation (18) in Section 2.3, it is possible to determine both offset simultaneously using Equations (17) and (18) It can be observed in Figure 1 that for a positive TDC offsets, ROHR curves feature negative values in the compression and the expansion phase, whereas an inverse trend is observed for negative TDC offsets. This observation confirms results, presented in the Table 2 for crank angles in compression and expansion phases.…”

“…In the Figure 2 ROHR values calculated using Equation (4) are presented. Vertical red lines in compression and expansion regions represent selected integration intervals used in Equations (17) and (18), which will be kept constant for all cases in the presented paper. Integration interval in the compression phase is from −70 to −40 • CA, whereas in expansion phase it is from 90 to 120 • CA.…”

“…Using k com,p , k com,TDC , k exp,p and k exp,TDC as well as I com and I exp , determined in items 3 and 4, pressure and TDC offset values are calculated using Equations (17) and (18). As coefficients in item 3 were calculated with shifted pressures traces their values deviate from the values that would have been calculated for zero TDC and pressure offset.…”

Practical research of the angle of thermodynamic losses when indicating pressure in the cylinder diesel engine

“…23) is calculated, varies in the range ±5°C compared to the measured value of 74°C, as illustrated in Fig.7. This feature of the applied method could give an advantage over the similar, "more accurate" methods that are designed so that they search for the values of components of the ATL in parallel, such as the method disclosed in reference [4]. In this reference there is a more detailed approach to the analysis of the expression for the change in entropy, where it is called a function of loss.…”

“…The establishment of ties between the change in entropy and relative volume changes, the terms for explicit calculation of the ATL with the statement that it is possible to achieve accuracy of 0.1 degrees on the angle of rotation of the crankshaft, have been proposed. Calculation according to the method described in [4] is not carried out by these authors, primarily because it was estimated that in the turbo engine, the required initial conditions (temperature and the gas pressure at the time of closing of the intake valve) can hardly be determined with the necessary accuracy. Another reason is that the parallel use of empirical data according to [2] and the results of calculations according to [6] show a more than satisfactory match on the basis through which a fairly realistic insight on the required ATL can be acquired.…”