The Study On Modeling And Dynamic Property Analysis Of Linear Rolling Bearing Based On The Contact Mechanics

The determination of connection parameters between different parts and components inmanufacturing equipments are of great importance for the design of a machine tool capableof high-precision and high-speed machining. It is a hot topic in mechanical system designand analysis and becomes a frontier research field for the dynamical system. Linear rollingbearing is one of the most important connecting components in manufacturing equipments. Itis difficult to effectively and precisely characterize the physical properties of the linearrolling bearing because of its complex configuration. Linear rolling bearing is characterizedby the contact problem between the raceway and rolling elements. Because of thecomplexity of this type of problem, the modeling for linear rolling bearing is generally eitherover-simplified or ignored. It is one of the resons for the difficulty in precisely predicting thedynamic performance for the manufacturing equipments in the design stage. Therefore, it isnecessary to study the static and dynamic properties associated with the linear rollingbearing. It is significant for revealing the nature of the dynamical behavior of the linearrolling bearing and has great potential for developing the high-speed, high-precision and lownoise manufacturing equipment.An efficient and straightforward technique based on the improved Gauss-Jacobiquadrature rule for solving elastically dissimilar contact problems under sliding condition isproposed in the thesis. The efficiency has been well validated by a rough stamp with sharpcorners frictionally sliding on an elastically dissimilar half-plane. This work investigates anddemonstrates the effects of frictional coefficient on the contact pressure distributionsbetween the generallied punch and the elastically dissimilar half-plane. The possible reasonsfor crack initiation associated with fatigue and fracture of the contacting components are alsoelaborated.Based on the Hertzian contact theory and elastic beam theory, a theoretical model of thevertical stiffness of preloaded linear rolling bearing considering the flexibility of the carriageis established. The calculated outward carriage deformations match the finite element analysis results well. Clearly, the theoretical model could deal with the vertical stiffness ofpreloaded linear motion guide more accurately compared with the traditional rigid model.Based on the rigidity model of a linear rolling bearing incorporating the flexibility of thecarriage, a modal analysis method of a linear rolling bearing using finite element analysismethod is proposed. A three dimensional finite element model of a linear rolling bearing hasbeen established. The finite element modal analysis is conducted and the modal frequenciesand vibration modes are presented. The modal testing experiment was conducted on the typeof linear rolling bearing. For the occurrence of the modes, the finite element analysis resultsbased on the presented method match the experimental results well. It should be pointed outthat, because of the nonlinear property of the contact stiffness, the variance of the amplitudeof the exciting force would result in the fluctuation of the eigenfrequency and lead to themeasurement error.Prediction of machine dynamics at the design stage is a challenge due to lack of adequatemethods for identifying and handling the nonlinearities in the linear rolling bearing, whichappear as the nonlinear restoring force function of relative displacement and velocity acrossthe joint. This thesis discusses identification of such a nonlinear restoring force function fora linear rolling bearing. An innovative test rig is designed and the nonlinear parameters ofthe linear rolling bearing are extracted from the measurements of the applied random forceand the resultant response based on the Volterra and Wiener theories. The identified model isvalidated by comparing the frequency response function calculated from the identified modeland that from the mearsurment. Good agreement is achieved. The identified model can befurther used to predict the dynamic performance of the manufacturing equipment.The problem of updating a finite element model representing a family of linear rollingbearings and its associated uncertainties by utilizing measured modal parameters isaddressed using a Bayesian statistical framework that can handle the inherentill-conditioning and possible nonuniqueness in model updating applications. The objective isnot only to give more accurate response predictions for the finite element model representinga family of linear rolling bearings but also to provide a quantitative assessment of thisaccuracy. The quantification of model uncertainties is carried out by means of the predictionerror. The results point out that an improvement of the prior model can be achieved and the prediction error variance provides a means for bridging the remaining gap between themeasured data and the computed output. The updated, i.e. improved, finite element modelcan be used for more reliable predictions of the structural performance in the targetmechanical environment.