Research On Formation Mechanism And Variation Law Of Roundness Error In Hydrostatic Bearing Internal Grinding

Ultra-precision machine tools are the base of ultra-precision machining.Hydrostatic spindles are widely used as one of the most important components in ultra-precision machine tools.In the higher accuracy trend of precision and ultra-precision machining,roundness error of hydrostatic bearing bore has gradually become a dominant factor for the accuracy of grinding workpieces.Only from a view of grinding process,spindle system dynamic characteristics can't be reflected to influence forming process of roundness error objectively.Therefore,it is necessary to research the further formation mechanism and the variation law of the roundness error by combining grinding spindle dynamics with grinding process.(1)A dynamic model of the grinding system which is mainly composed of grinding wheel spindle and headstock spindle is established based on theory of Timoshenko beam.Based on the theory of finite element method and rotor dynamic,element matrixes including stiffness,mass and damping are deduced.The dynamic model of spindle-bearing rotor system is constructed by assembling the element matrix.On these basis,natural frequency,vibration mode and dynamic characteristics of the spindle-bearing rotor system dynamic model are calculated by commercial software named 'Matlab'.(2)According to the established mathematical model,a simulation algorithm based on cycles iterative with grinding force and transient removal of workpiece is proposed.The roundness error of bearing bore coupling rotary error of double spindles with grinding process parameters can be calculated quantitatively by the simulation algorithm.A tool is provided for researchion the formation mechanism of roundness error in hydrostatic bearing internal grinding.The main ideas of this algorithm are as follows:1)Important simulation parameters such as spindle speed,infeed time,infeed rate and grinding stiffness,et al.are selected.2)In grinding direction,it follows the equal relationship that total infeed length of grinding wheel is the sum of total removal of workpiece,total wear of grinding wheel,elastic deformation of grinding wheel and workpiece at the contact area and displacement of the double spindle rotors at the contact area.3)The minimum area circle method is selected as the evaluation method of roundness error.(3)A forming mechanism of the roundness error in hydrostatic bearing internal grinding is revealed.The roundness error is a coupling consequent that double spindle system,grinding wheel,grinding process parameters affect the workpiece during grinding process.The influence law of spindle-bearing system,dynamic balance accuracy grade of headstock spindle and grinding wheel,grinding process parameters,et al.on the roundness error of hydrostatic bearing bore are studied quantitatively.The results show that the roundness error could be reduced significantly by diminishing rotary error of grinding wheel and improving dynamic balance accuracy grade of grinding wheel.However,the roundness error can hardly be affected by the dynamic balance accuracy grade of headstock spindle and the damping coefficient of bearing supporting spindle.(4)A hydrostatic bearing grinding experiment table is established.The natural frequency of headstock spindle and the roundness error of hydrostatic bearing bore are measured.The results show that the natural frequency and the roundness error results obtained by numerical calculation and experimental test are in good agreement with each other,which indirectly demonstrates the correctness of numerical results.This thesis enhances the awareness level of people for the formation mechanism of the roundness error in hydrostatic bearing internal grinding.Moreover,it offers important reference significance for exploration the precision limits of hydrostatic spindle and grinding machine further.