Dynamic Characteristic Analysis Of Rotor System With Coupling Pseudo-static Analytical Model Of Ball Bearings

As for the processing speed requirements gradually improve,the spindle dynamic characteristics play a more and more important role in affecting the spindle performance and machining process,and the bearing stiffness is the most critical factor in influencing the dynamic characteristics of the spindle.Therefore,there is a great need of a scientific and systematic method for modeling bearings and the whole spindle unit to help the engineers make sure machine tools achieve the optimal design and processing performance without repeatedly testing and error correcting.This paper selected the ball bearing-spindle rotor system as the research object.On the basis of analyzing and calculating some performance parameters of ball bearings,such as,static stiffness,dynamic stiffness,contact angle and contact load between roller and inner/outer ring under rotational condition,this paper integrated the bearing model with the spindle model with the consideration of some dynamic properties of spindle rotor system.And analyze the natural frequency,static deflection,modal shape and critical speed of ball bearing-spindle rotor system.This paper first introduced some basic theories of modeling and solving methods of bearing models,including Hertz contact theory and Newton-Raphson procedure.And analyze the contact problems between roller and inner/outer ring of angular contact ball bearings,according to Hertz contact theory.Next,use the basic theory presented in the previous chapter as foundation,put forward the analytical static bearing model introduced by Demul,which is widely applicable to the analysis of rolling bearings,to analyzing and calculating the static performance parameters of angular contact ball bearings.Then,establish the pseudo-static analytical model of ball bearings,explain the reason of neglecting gyroscopic moment effect and introduce the influences of different boundary conditions that imposed on bearings on the mathematical results during the modeling process.The bearing model is solved using Matlab,dynamic performance parameters of the bearing can be obtained including dynamic stiffness,and explain the centrifugal load effect with combination of the solving results.Meanwhile,further analysis about the influences that applying different bearing boundary conditions have over the solving results is showed.Finally,using the finite element method with combining the Timoshenko beam theory and the theory of rotor dynamics related to bearing-spindle rotor system to establish the bearing-spindle dynamic model.The model takes bearing dynamic stiffness into account,along with the shear effect and gyroscopic moment of spindle shaft.The solving program for the dynamic equations of spindle rotor system is compiled in Matlab,achieving the natural frequency,static deflection and first/second order modal shape.Compare the solution of natural frequency with experimental data in referred literature to verify the correctness and effectiveness of the solving program.In addition,achieve the Campbell diagram of the spindle system,which contains the first order frequency.According to the diagram,engineers can easily get the first-order positive/negative whirl frequency and first order critical speed of the spindle system under different rotational speeds,which has very important reference value for further dynamic analysis of the spindle rotor system.Through the dynamic analysis of bearing and bearing-spindle rotor system,the centrifugal load effect on bearing stiffness is obvious when bearing is running.So in the dynamic analysis of rotor system,it must be taken into consideration,to make sure the analysis result is closer to the engineering practice.