6837092899

14    Diagnostyka’ 4(48)/2008

KEKEZ, AMBROZIK, RADZISZEWSKI, Modeling of Cylinder Pressure in Compression Ignition Engine ...

°CA

fuzzy system for engine work modeling, 3) development of methodology for "timing" tliis model for other fuels.

2.    TEST STAND

Experimental research was madę on the test stand (presented in Part 1) built of diesel engine Perkins AD3.152UR, water brake and control cubicle. The cylinder pressure was measured by piezoelectric transducers. Measured values were recorded in function of cranksliaft angle degrees (°CA). The engine was fueled by FAMĘ. Measurements were done when engine operated in extemal speed cliaracteristic regime with the crankshaft speeds 1000. 1200, 1400, 1600, 1800 and 2000 rpm. Cylinder pressure values were recorded eveiy 1.4 °CA (exactly 512 measurements for one working cycle of 4-stroke engine). At each measurement point. values of parameters were recorded. for 50 consecutive working cycles. Indicator diagrams. acquired in tliis way, were averaged.

3.    RESULTS OF EXPERIMENTAL

RESEARCH AND MODELING OF

PRESSURE CURVE

Fig. 1 shows acquircd indicator diagrams of cylinder pressure. for engine work at different rotational speeds and for ranges 180-540 and 340-390 °CA. For the latter rangę, the differences between pressure curves for different rotational speeds are noticeable. Fast pressure increase (for FAMĘ fuel) starts at 3.3 to 3.9 MPa. and 351° to 357° CA. When rotational speed increases, maximum cylinder pressure decreases, but the cranksliaft angle. at which it appears. increases. Maximum value of slope of the tangent linę to tlie pressure curve decreases with increase of rotational speed from 1400 to 2000 rpm [4]. Knowledge of first and second derivative of pressure curie with respect to crankshaft angle allows detennining the start of self-ignition.

The calculations were madę by means of GFSm system [4], proposed by the authors. which can be described as a method of generation of fuzzy models by means of genetic algoritlun [2, 3], GFSm creates Mamdani fuzzy' model (Fig. 2) or Takagi-Sugeno fuzzy model. The model describes relations between input \ ariables and output \ariable. which describe given phenomena or process. Model produced by GFSm predicts cylinder pressure for all possible rotational speeds in AD3.152UR engine fueled by diesel oil - this was presented in Part 1 of paper. In order to predict pressure for another fuel (like FAMĘ), we added two scaling functions: one for input scaling and one for output scaling (Fig. 2).

a)

pc, MPa 9

b)

pc, MPa

- 2000

0

340    350    360    370    380    390

°CA

Fig. 1. Indication diagram of cylinder pressure in diesel engine working at extemal speed cliaracteristic and fueled by FAMĘ. in function of crankshaft angle. for several CA speeds: a) in the rangę 180° - 540°. b) in the rangę 340° - 390°

Parameters of these functions are different for each fuel. In order to find these values, we measured cylinder pressure curve for one rotational speed (1200 rpm) when engine was fueled by FAMĘ. Later. we used this curve to obtain parameters of scaling functions.

Fig. 2. Mamdani-type fuzzy model (with scaling functions). which has two input variables x_t and x₂, and one output \ ariable y