Computing the main journal bearings dynamic coefficients in a six-cylinder in-line diesel engine 2007-01-1968
A finite element method (FEM) basing on rectangular isoparametric element for evaluating the stiffness and damping coefficients of hydrodynamic bearings is presented. The domain of whole journal bearing working space, which is discretize with rectangular isoparamentric element, is modeled from 0 to 2π in the circumferential direction, and from -1 to 1 in the non-dimension axial direction. The non-dimension Reynolds equation is solved only once by FEM method. There are several cavitation conditions, such as the Gümbel condition, Reynolds condition, JFO (Jakobsson-Floberg and Olsson) condition and Elrod algorithm etc. The Gümbel condition is the simplest, the Reynolds condition is more accurate, and the JFO condition and Elrod algorithm are the most accurate. In this paper, considering both the accurate and the calculation speed, the Gümbel condition is chosen.
The main solving process is shown below. First, the variation of the Reynolds equation should be obtained. Second, this variation equation is represented by using the element parameters, and then total stiffness matrix is formed. Third, using the common method of FEM, the pressure distribution of the journal bearings is solved from the governing equation. The convergence of this process is discussed at the same time. At last, the stiffness and damping coefficients can be calculated from the formula easily. An example of analytical results of a short bearing is used to compare with the results from the present calculation. Using the method mentioned above, the dynamic coefficients of the journal bearing in a six-cylinder in-line diesel engine were gotten. All these results are proven that the method is well used.