Quantities at each bearing such as deflection, angle of deflection, moment and shearing force are calculated by using equation (1) to (3) and considering the boundary conditions on calculation model.
b. Mobility Method
As shown in figure 8, eccentricity of journal is calculated with bearing load results by mobility method. Mobility equation is given as follows:
In this calculation, equation (4) is solved simultaneously with transfer matrix method.
3.2 Procedure for Theoretical Calculation
Figure 9 shows the procedure of theoretical calculation. In time loop step, crankshaft distortion is calculated beforehand, and then bearing load and journal tilting angle are calculated by transfer matrix method. Based on the bearing load results, the eccentricity of journal is calculated by mobility method. Until the deviation of eccentricity between at 0 deg and at 360 deg of crank angle is less than the convergence criterion, this calculation is repeated. Usually only two repetitions are enough for convergence.
4. COMPARISON OF CALCULATED RESULTS AND MEASURED RESULTS
The journal movement behavior is simulated by the use of the developed theoretical calculation in accordance with the measured engine specification. The main calculated condition is as follows:
Engine load: 100%
Alignment: even alignment,
uneven alignment (see Figure 4)
Comparison with measured results in No.1, No.2, No.4 and No.8 bearing is shown below.
4.1 Journal Movement Behavior Without Uneven Alignment Condition
4.1.1 Journal Center Locus
Figure 10 and figure 11 show the calculated and measured results of journal center loci in the middle of bearing width respectively. The measured result is the average of the locus at fore side and aft side of beating width by referring to figure 5. The plotted values are crank angle assuming that the top dead center of No.1 cylinder is 0 deg.
The horizontal eccentricity of measured result is wider than the calculated result. The reason is presumed that the difference of bearing clearance appeared. While the clearance of the theoretical calculation is assumed circumferential symmetry, the one of the measurement bearing is like lemon shape. The ratio of the side beating clearance to top bearing clearance is between 1.5 and 2.0. Therefore the horizontal eccentricity of measured locus is wider than the vertical in the measurement. Nevertheless, considering the difference of clearance, all calculated loci are agreed qualitatively with all measured results. Furthermore, eccentricity position at each crank angle shows good coincidence with measured results in each comparing measured locus. As a result, the theoretical simulation is effective to predict a journal position at each crank angle in a main beating.
4.1.2 Journal Tilting Angle
Figure 12 shows the journal tilting angle of calculated and measured results in vertical direction. The tendencies of journal tilting angle results almost coincide with each other in all compared measured results. The results indicate that maximum values are obtained at the adjacent cylinder combustion of bearing. The maximum absolute value is approximately agreed with each other. As a result, this model is effective to simulate the journal tilting behavior and to predict the maximum value for practical use.
Using this theoretical calculation model, journal movement behavior under uneven alignment is discussed as follows.
Fig. 9 Procedure of theoretical calculation
