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Top1. Introduction
A rolling-element bearing is a bearing which carries a load by placing round elements between two pieces. A common kind of rolling-element bearing is the ball bearing. The bearing has inner and outer races and a set of balls. Each race is a ring with a groove where the balls rest. The groove is usually shaped so the ball is a slightly loose fit in the groove. The ball contacts each race at a single point. In actual practice, the ball deforms slightly where it contacts each race. The race also dents slightly where each ball presses on it. Thus, the contact between ball and race is of finite size and has finite pressure. Because of this deformation of balls, there is little sliding with pure rolling. All parts of a bearing are subject to many design constraints. For example, the inner and outer races are of complex shapes which make them difficult to design and manufacture. Balls and rollers, though simpler in shape, are small since they bend sharply where they run on the races, the bearings are prone to fatigue. The loads within a bearing assembly are also affected by the speed of operation.
Very limited work was reported in the past for the design optimization of rolling element bearings. Seireg (1972) reviewed some examples of the use of optimization techniques, in the design of mechanical elements and systems. These included gears, journal bearings, rotating discs, pressure vessels, shafts under bending and torsion, beams subjected to the longitudinal impact and problems of the elastic contact and load distributions. Changsen (1991) presented the optimization of rolling element bearings for five different objective functions namely, maximum fatigue life, maximum wear life, maximum static load rating, minimum frictional moment and minimum spin to roll ratio. Gradient based numerical optimization technique was implemented for the optimization of bearing. However, only the basic concepts and solution techniques were introduced without any illustrations.
Hirani et al., (2000) proposed a design methodology for an engine journal bearing. The procedure of selection of the diametral clearance and the bearing length was described by limiting the minimum film thickness, the maximum pressure and the maximum temperature. The research was concerned mainly with the journal bearing design. However, internal geometries of journal bearings are far simple as compared to rolling bearings.
Choi and Yoon (2001) used genetic algorithms (GA) in optimizing the automotive wheel-bearing unit, by considering the maximization of life of the unit as the objective function. Periaux (2002) discussed in detail the applications of GA to the aeronautics and turbo machineries. Chakraborthy et al., (2003) described a design optimization problem of rolling element bearings with five design parameters, by using genetic algorithms based on requirements of the longest fatigue life. The authors had presented bearing internal geometrical parameters resulted from the optimized design of different bearing boundary dimensions. However, only single objective function was used and some of the constraints were unrealistic. Also, assembly angles were assumed and values of certain constraint constants were chosen arbitrarily.
Rao and Tiwari (2007) described ten different design variables for the design of rolling element bearings of which five design variables were associated with the constraints. Dynamic capacity was maximized using a genetic algorithm (GA). Also the variation of design variables (associated with the constraints) with dynamic capacity were presented. A convergence study for the GA was also presented by taking different number of generations and population size with different crossover and mutation probabilities.