Research Of A Polishing Machine For Freeform Surface Based On A Six Degrees Of Freedom Serial-Parallel Mechanism

The eternal objective of manufacturing technology is to sufficiently fulfill the demands of industry by improving its quality and efficiency.Nowadays,many freeform surfaces are still polished manually,which result in a low efficieny,accuracy and stability of the process.For these reasons,this dissertation focuses on the development of an automatic polishing machine for freeform surfaces.A novel design scheme of the polishing machine is proposed by integrating the technologies of ultra-precision polishing,serial robot,parallel robot and CNC.A series of theoretical analyses and investigations about the polishing machine are conducted,including kinematics,static stiffness,error calibration and off-line programming.On these bases,a prototype of the polishing machine is designed and developed.The validity of the theoretical analysis and the practicality of the developmed machine are verified by calibration experiments and polishing experiments,respectively.The main contributions and innovations of this dissertation can be concluded as follows:Driven by the practical demands of freeform surface polishing,a novel design scheme of a polishing machine is proposed based on a six degrees-of-freedom(DOF)serial-parallel mechanism.It mainly comprises a two DOF serial mechanism for orientating the polishing tool and a three DOF parallel mechanism for positioning the workpiece.An elastic spherical polishing head is adopted as the polishing tool and its spherical center is installed coincidently at the intersection point of the two rotation axes in the serial mechanism,so the position and the orientation adjustments of the polishing tool with respect to the workpiece are decoupled during the synchronized movements.Considering the features reflected in the structural independence and motion decoupling,a systematic kinematics analysis of the serial mechanism and parallel mechanism in the scheme are conducted based on the spatial closed-loop vector method and the exponential product formula,which include position,velocity,singularity,workspace and dexterity analysis.Due to the horizontal configuration of the polishing machine,a semi-analytical static stiffness modeling method of the serial-parallel mechanism is proposed considering the effects of gravity.By disconnectting the serial-parallel mechanism at active joints and passive joints in turn,the whole machine can be split into several sub-assemblies and each sub-assembly contains one or a group of active joints or passive joints.Considering the effects of external force on the end-effector and the gravity force on each moving part,the constraining force at each joint can be derived by using static force analysis.Assisted by the compliance matrix of each sub-assembly in its local coordinate system,the elastic deformations of the endeffoctor caused by the deformation of every sub-assembly can be obtained through the virtual work principle.Under the premise of small deformation,the total deformation of the end-effoctor can be calculated by using the linear superposition principle,and the stiffness model of the serial-parallel mechanism considering the effects of gravity can be obtained.To deal with the geometric errors of the machine,a comprehensive error calibration method is proposed with the distance information measured by ball-bar.The error models of the parallel mechanism and the serial mechanism are established based on the spatial closed-loop vector method and the exponential product formula,respectively.For these two error models,the geometric errors that affects the position error and the orientation error are explicitly separated.According to the measuring principle of the ball-bar,the relationship between the geometric errors of the whole machine and the length varations of the ball-bar is established by using the two position error models.After eliminating the redundant parameters,an error model that simultaneously satisfyies the requirements of completeness,minimality and continuity are obtained,which enables that the geometric errors can be quickly identified with the least squares method.In order to correct the pose error in the machine operating space,a step-by-step decoupling error compensation strategy is proposed,which simplifies the error compensation process and solves the coupling problem caused by the synchronized motions of the serial and parallel mechanism.To generate the NC program during the polishing of freeform surfaces,an offline programming method with geometric error compensation is proposed for the polishing machine.According to the information of freeform surfaces,polishing strategy,polishing path,polishing process parameters,etc.,the trajectory of the polishing head represented in the workpiece frames is generated.Combining the geometric error compensation strategy and the nominal kinematic model,a special post-processor for the polishing machine is developed,which can convert the modified tool path data in the operation space into the motion of each independent driving actuator.Taking into account the characteristics of the CNC system and the format of the motion data,corresponding auxiliary information are added to generate the synchronized NC program.Based on the these steps,an off-line programming software is developed to realize the automatic conversion of freeform surfaces information and process parameters to NC programs.According to the design scheme of the serial-parallel polishing machine,the mechanical system,control system and electrical system of the machine are designed in detailed.On this basis,a prototype of the polishing machine is developed by completing the system integration and debugging work.For the developed machine,calibration experiment is performed to identify the geometric errors by using a ball-bar.With the help of the developed off-line programming software,NC programs are generated and the machine is controlled to polish flat and curved surfaces.During the experiment,the polishing tool can move according to the planned path and the tool compression is stable.As a result,the correctness of the calibration algorithm and the off-line programming algorithm can be verified.After polishing,the experimental results show that the surface roughness and the maximum profile height of the workpieces with different materials and surfaces are all greatly reduced.As a result,the effectiveness and practicality of the polishing machine can be verified.