Rolling bearings. Cylindrical roller bearings, separate thrust collars. Boundary dimensions

1995 ◽  
2009 ◽  
Vol 131 (5) ◽  
Author(s):  
K. Sunil Kumar ◽  
Rajiv Tiwari ◽  
P. V. V. N. Prasad

The long fatigue life is the one of the most important criterion for the design of rolling bearings, however, due to complex and diverse internal geometries, each type of rolling bearings require a different design formulation. To increase the life of cylindrical roller bearings, the profile (or the crowning) of the roller plays an important role. A flat profile of the rolling element results in the edge stress concentrations at roller ends. A circular crowning of roller eliminates the edge stress concentration at the lower and moderate loads only; however, it develops edge stress concentrations at heavy loads. The logarithmic profile of the roller results in no edge stress concentration at the low, medium, and heavy loads; distribution of contact stresses is also nearly uniform along the length of the roller. A design methodology for the optimum design of cylindrical roller bearings with the logarithmic profile has been outlined. A nonlinear constrained optimization problem has been formulated for the design of cylindrical roller bearings with logarithmic profiles and is optimized by using real-coded genetic algorithms. The change in roller profile has not been accounted for explicitly in the standard definition of the dynamic capacity; hence, for the present case directly the Lundberg–Palmgren life equation has been chosen as an objective function. Design variables include four bearing geometrical parameters and the two logarithmic profile generating parameters are considered. In addition to these, another five design constraint constants are also included, which indirectly affect the fatigue life of cylindrical roller bearings. The five design constraint constants have been given bounds based on the parametric studies through initial optimization runs. The effective length of the roller is taken corresponding to the standard roller diameter, which has standard discrete dimensions. Constraint violation study has been performed to have an assessment of the effectiveness of each of the constraints. A convergence study has been carried out to ensure the global optimum point in the design. A sensitivity analysis of various geometric design parameters has been performed using the Monte Carlo simulation technique, in order to see changes in the fatigue life of the bearing. Illustrations show that the multiplier of the logarithmic profile deviation parameter has more effect on the fatigue life as compared with other geometric parameters.


Author(s):  
Eugenio Dragoni

The design of compact and inexpensive mechanical drives and gearboxes can take advantage from the use of custom rolling bearings in which the rolling elements are directly in contact with the shaft and the housing containing them. The custom construction is particularly convenient for the case of roller bearings, either cylindrical or tapered, because these elements are easily manufactured and provide a remarkable loading capacity. Starting from the standard load rating equations available in the literature (ISO standards), this paper develops a step-by-step design procedure for the geometric optimization of radial bearings with cylindrical rollers. The procedure includes constraints on the geometry and leads to the optimal bearing with the maximum static and dynamic load ratings compatible with the space available.


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