Theoretical And Experimental Study On The Contact Characteristics And Stiffness Of A Wire Race Ball Bearing

As a kind of non-standard bearing, the wire race ball bearing possesses someobvious advantages, including high ratio of stiffness to inertia, high slewing precision,high anti-overturning capability and more flexibility structure design. It has beenextensively used in big radar antennas, aircraft simulating rotary tables, medicalapparatus and instruments and other precision equipments. It can simultaneouslysupport axial loads, radial loads, overturning moment and compound loads. Howeverthere will be frequently cyclic alternating stresses in the contacting surface of wiresunder the external loads. These stresses result in fatigue wear, pitting corrosion, andeven shear failure. It seriously affects the proper function of the equipment. Therefore, itis critical to study the load distribution and stiffness of the bearingFirstly, the relationships between the preload magnitude and the normal contactforce and the deformation were analyzed. On the basis of the contact deformation,mathematical models of the axial load distribution, the radial load distribution and theoverturning moment distribution of the bearing were established by using the cosine law,L’ Hospital’s rule and the non-conforming Hertz contact theory. The curve of loaddistribution and the maximum contact force was obtained by the numerical solution inMATLAB. The influences of the number of the balls and the contact angle on themaximum contact force were discussed.Secondly, a mathematical model on stiffness of the bearing subjected to five-DOF composite loads was developed, based on the principle of superposition, thedefinition of stiffness and the load distribution characteristics of the bearing. Then acomprehensive bearing stiffness matrix was derived. The stiffness matrix was computedwith the numerical arithmetic for a wire race ball bearing used in a certain type ofaircraft simulating rotary table.Finally, in order to verify the theoretical model of the stiffness matrix, theexperimental system was designed to measure the stiffness of the bearing. The axialstiffness, the radial stiffness and the overturning stiffness were calculated by measuringthe relative displacements between the inner and outer frames corresponding to differentexternal loads. The theoretical and experimental results show that: as the load increases,the axial stiffness and overturning stiffness decrease slightly, while the radial stiffnessincreases nearly linearly; the loading method, the deformation of the frame, and theplastic deformation between the ball and wire have significant effects on the stiffnessexperiment. The experimental study provides an effective support to the practicalapplication of the wire race ball bearing.