On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage. INTRODUCTION The motivation for this work was to prepare for studies of the dynamic response of bearings with damaged surfaces. The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. One of the calculation methods studied herein was an approach that makes use of a combined finite element and surface integral method for contacting surfaces [1-3]. The method has proven very powerful for studying a variety of gearing and bearing problems. This approach can offer valuable insights for situations when elastic deformations, rigid body movements, and/or wear and damage have significant effects on the shapes and orientations of contacting surfaces [4-8]. Computing speed and memory of personal computers are now of sufficient performance to consider using simulations to study forced vibration response of bearings and gears having pitted surfaces [9]. To prepare for such studies, bearing and gear computing tools including preand postprocessors for the combined finite element and surface integral method have been developed. Studies were selected to exercise and build confidence in the numerical tools. The scope of this work was to analyze two-dimensional models of straight cylindrical roller bearings. Guo and Parker [10] have conducted a study of bearing contact problems using both two-dimensional and three-dimensional models. Guo and Parker were particularly interested in calculating bearing stiffness properties. They noted for certain cases significant differences between the three-dimensional and twodimensional approaches when calculating stiffness properties. Herein, the scope was limited to the two-dimensional approach consistent with the motivations for this study. While Guo and Parker modeled bearings with no damage, bearings with damaged surfaces were considered herein. One must keep in mind the limitations of the two-dimensional approximation when studying the literature and when selecting an approach for a particular study, analysis, or design situation. Even given the limitations, the two-dimensional model can provide useful insights. https://ntrs.nasa.gov/search.jsp?R=20150018925 2018-04-09T08:09:44+00:00Z