Theoretical And Experimental Investigation Of Cage Dynamics In Angular Contact Ball Bearing

Rolling bearing is one of the important basic parts in major equipments,which will directly affect the performance,reliability and security of the whole equipment.Moreover,the bearing performance is greatly influenced by its cage.Unstable cage motion which will cause the cage failure such as the wear and fracture is the urgent issue to be solved.The mechanism and influence factors of the cage motion are so complex,that it is great challenging to investigate the cage motion.Additionally,the effects of complex external loads,cage clearance and unbalances on the cage motion,especially the corresponding influence rules are:inadequate and unclear.Thus,it is vital to investigate the cage motion analytically and experimentally for scientific and engineering practice.In this paper,a dynamic model for cage motion in an angular contact ball bearing is proposed,and a measurement system for cage spatial motion is specially established.Then,the cage motion affected by external loads,its clearances and unbalances,and even rotor unbalances are analytically predicted and experimentally investigated,the main obtained results of this present study are given as follows:A dynamic model of an angular contact ball bearing is developed to analyze the cage motion theoretically,in which the cage is assumed to be three degree-of-freedom(DOF)and the unbalance force is involved,besides the interaction of the cage-balls and the cage-guiding ring.And the differential equations of cage and balls motion,and the equilibrium equations of inner ring are deduced and solved by the Newton-Raphson and Newmark-β method.Finally,the dynamic model of bearing is verified by the typical cases.A non-contact measuring method and a bearing test rig applying the complex loads is developed to measure the spatial cage motion of angular contact ball bearing in axial and radial directions,in which the bearing house and the subpanel are specially designed to fix the eddy transducers.The trajectories,waveforms and spectra of cage motion at typical conditions are constructed and compared with the dynamical simulation results to elucidate its characteristics.The experimental observations of cage motion agree well with the theoretical predictions and verify the dynamic model.Theoretical and experimental investigation of the cage motion are carried out and compared under various rotating speeds and external loads to reveal the varying patterns of the trajectories and spectra.Results reveal that the increment of rotating speeds and axial loads of the bearing gradually make the whirl trajectories of the cage mass center regular,and enlarge its whirl radii.Instead,the whirl trajectories change from well-defined patterns to complicated ones,and its whirl radii and stability reduce when increasing the radial loads and moments.Simulations of cage motion are carried out at different cage pocket and guiding clearances based on the dynamic model of bearing,and then compared with the measured cage motion.The trajectories and spectra of cage motion are compared to research the influence of cage clearances.Results indicate that the cage motion are significantly affected by its clearances.The increment of cage guiding clearance make the whirl trajectories of cage regular.However,the whirl trajectories change from well-defined patterns to complicated ones as increasing cage pocket clearance.In addition,the increment of guiding clearance and pocket clearance can reduce the wear of cage guiding surface after the observation of cage wear surface textures.Investigation of cage motion and wear affected by cage unbalances reveal the inherent relationship between the its motion and wear.And then,the experiments are carried out and obtained the cage motion and wear with additional several cage unbalance.Results show that the increment of cage unbalance masses make the trajectories of cage more regular and enlarge the whirl radii.It is also observed that the amplitudes of the axial and radial motion of cage,particularly corresponding cage rotating frequency and the wear extent of cage guiding surface increase with the cage unbalance values.A dynamic model of the rotor-bearing system with four-DOF based on the Lagrange method is developed to determine the reaction forces due to rotor unbalance,which are introduced as boundary conditions for the supporting bearings.And then,the effect of rotor unbalance on the cage motion is investigated analytically.The cage motion is obtained and compared by measuring the cage motion on the rotor-bearing system.It reveals that the amplitudes of the inner ring rotating frequency and combination frequencies of the cage motion increase with the increment of rotor unbalance values.Besides,the trajectories of cage change from well-defined patterns to complicated and confusing ones.The dynamic model of angular contact ball bearing considering the cage unbalance force is proposed which can effectively analyze the cage motion.Besides,the measuring technique for cage motion which overcomes the limited space of the internal bearing and its installing structure is applied to obtain the authentic data and the varying pattern of the cage motion at multiple complex loads.The effects of rotating speed,external load,cage clearance and cage unbalance on the cage motion are investigated analytically and experimentally,furthermore the investigation of cage motion affected by rotor unbalance on the rotor-bearing system.The researches of this paper are useful references for the dynamic analysis of bearing and the improvement of cage motion used in major equipments.