Study On Shape Functions And Optimization Design Theory For Hydrodynamic Journal Bearing

There has always been a huge demand for efficient journal bearings in machines like steam turbines, centrifugal compressors, pumps, and motors. Ideally the bearing achieves good damping, durability, negligible friction, and zero wear in the smallest possible space. However, the starting point for most bearing shape development is still limited to classical geometrical bearing shapes. The radial clearance, the eccentricity ratio, and the attitude angle are all parameters that describe the location between the journal and bush for a given bearing shape. The shape optimized result is therefore limited to cylindrical or elliptical bearings. Using this approach the shape of the bush itself is not modified. In this work a fully generalized film thickness profile was used as the basis for shape optimization. An investigation into the geometrical theory required for hydrodynamic journal bearings was started, the mathematic model was built then optimization methods for shape optimization were used. The main work and results are as follows:①The general Reynolds equation for the shape optimization model of hydrodynamic journal bearings was deduced from lubrication theory with some hypothesis. The Reynolds equation, which is the most importand government formula to express the hydrodynamic pressure generated by bearings, is a non-linear elliptic second order partial differential equation, which does not have a known analytical solution. In this work numerical solutions were found by employing the PDE Toolbox in MATLAB using a finite element method.②Three necessary geometric conditions to generate hydrodynamic pressure were analyzed which were periodicity, non-constant and positive definiteness. Four kinds of general bearing profiles satisfying geometrical conditions were proposed which were the general profile based on points, the general profile based on Tylor series, the general profile based on Bazier functions and the general profile based on Fourier serises. Comparison was made under complexity and accuracy in expression and difficulty in computing, the general bearing profile based on a Fourier series was taken as the most suitable to shape optimization for hydrodynamic journal bearings. Some classical bearing profiles were shown to be a subset of this general bearing profile. Under continuity, three typicall profiles were deduced from the gernal profile based on a Fourier series, which testified that this kind of profiles can not only integrated current shapes but also can create new shapes for hydrodynamic bearings with optimal performance. The new approach based on the general film thickness breaked the limitation in current bearing shapes, which was convenient to analyze directly and adjust reversely. Consequently, arbitrary shapes of bearings can be obtained using optimizing method. The general profile and its parameterization make it possible to investigate the characteristics of bearing profiles. This could potentially be used to improve designs for better performance in industrial applications.③A uniform shape optimization model was created using this general profile. The objective of the optimization had been to maximize the load capacity using the coefficients in the Fourier series as design variables. The lubrication equations had been solved based using the PDE Toolbox in MATLAB. This new method for optimizing the hydrodynamic journal bearings shapes outperformed that of previous publications. The optimization process was carried out using increasing orders of Fourier series to describe the bearing profile. As the order increased the load capacity increased. However the optimized result was almost fully achieved at a profile of order 2. This optimal shape was a single wedge bearing, which proved that a hydrodynamic journal bearing with the largest load capcity had a single wedge.④The necessarity of multi-objective optimization was studied. This paper dealt with multi-objective shape optimization (minimization of side leakage rate, minimization of power loss) and design variables (lubricant viscosity, coefficients of general oil film thickness, slenderness ratio) related to the profile design of a hydrodynamic journal bearing. The aim was to show optimized shapes with better performance proposed here breaks the limitation in existing bearing profiles. The modified Non-Dominant Sort in Genetic Algorithm (NSGA-Ⅱ) can be used as the optimization tool with a penalty to those solutions that violate constraints for bearing shape optimization. The difficulty of selecting the weighting factor was removed in multi-objective journal bearing optimization problems. The Pareto optimal set obtained in this paper was a set of solutions close to the optimal solutions which were diverse enough to represent the true spread of optimal solutions. The multi-objective optimization result was better than single objective optimization one. The relation between designed variables and performance paremters was proved.⑤Experiment was done required by product design and improvement to theory model. The material, processing method, experimental equipment and operation method were studied before the modal was manufactured. Correctless of the shape optimization based on the general profile was testified.This new shape design method provides a new thought for designers in order to design some completely new shape for hydrodynamic bearings with optimal performance. It also plays an important role in mechanism working in hydrodynamic theory and profile theory of transmission devices which make use of micro-clearance to lubricate.