Research On The Geometric And Motion Control Precision Improvement Methods Of Five-axis Machine Tools

Five-axis CNC machining can simultaneously adjust the cutting position and cutting orientation of the tool relative to the workpiece,and thus,becomes one of the most important means for efficiently manufacturing parts with complex sculptured surfaces in the field of aviation,aerospace,navigation and national defense.As the final evaluation index to determine the level of five-axis CNC machining,the machining precision has restricted the improvement of the manufacturing level to a large extent,which in turn determines the development level of the manufacturing industry.However,the kernel algorithms of CNC controller for improving the machining precision have been monopolized by western developed countries for a long time.Besides,there still exist many problems and shortcomings with respect to the current machining precision improvement methods.Therefore,in-depth exploration of the machining precision improvement method is of vital importance to promote the development of advanced CNC system,and improve the overall development level of the manufacturing industry.Focusing on the main factors that affect the machining precision at different stages of the machining process,a series of research work has been conducted on the important research topic "Research on the geometric and motion control precision improvement methods of five-axis machine tools" based on the geometric theory,kinematic theory and control theory.Numerical simulations and experimental verifications are also carried out.To be specific,this thesis establishes a singular trajectory optimization method,a continuous interpolation method of G01 commands,a contour error estimation and control method,a geometric error identification method,and a geometric error compensation method.The main work of this thesis includes:1)Singular trajectory optimization method with minimized induced machining errors is established.An one-to-one projection method is proposed to ensure the unit-vector property of the tool orientations and to transform the three-dimensional singular trajectory optimization problem into a two-dimensional one.Based on this projection method,the concept of "orientation forbidden circle" is proposed,which is treated as the geometrical constraints of the optimization problem to keep the tool orientation trajectory from crossing the singular region.By linearizing the constraints with respect to the changes of control points,the general optimization problem is simplified as the positive definite quadratic programming problem,which possesses one and only global optimal solution.By doing so,the singular problem is avoided and the deformation of the tool orientation trajectory is restricted to the minimum degree,which in turn minimizes the trajectory deformation induced machining errors.2)Continuous interpolation of G01 commands under bounded kinematic constraints is established.A time-optimal discontinuous interpolation of G01 commands is proposed.By overlapping the adjacent kinematic profiles,the one-step continuous interpolation of G01 commands is achieved,and then,the translational motion and the rotary motion are synchronized by establishing a scaling principle.The concept of "admissible area" is proposed and by establishing the ellipse admissible area,the corner errors induced by the continuous interpolation are restricted under the given tolerances.By deriving the Jacobian matrixes and conducting the pre-interpolation,the prediction and correction scheme is established to predict and correct the maximum reachable kinematic constraints.By doing so,kinematic profiles of the interpolated G01 commands are bounded under the given constraints with guaranteed tracking accuracy.3)High precision contour error estimation and predictive-feedback contour error control method are established.Based on the Taylor series expansion,the Frenet-Serret theory and the quaternion spherical linear interpolation method,the tool tip position trajectory and the tool orientation trajectory near the reference tool pose are re-established.A dynamic foot point searching algorithm is proposed to reduce the dependence of the estimation accuracy on the values of tracking error.Based on the PPI controller,a generalized predictive contour error controller is established to integrate the prediction ability and reduce the response time.In order to suppress the "transmission effect" of the feed drive systems,contour error is compensated based on the output motion commands after feeding the compensation motion commands into the feed drive systems.A contour error feedback loop is also established to improve the controller’s robustness against the model parameters’ uncertainties and the system disturbances.4)Equivalent rotary axis(ERA)based non-redundant geometric error identification method for rotary axes is established.Based on the screw theory,the concept of "equivalent rotary axis"is proposed and six non-redundant parameters are selected to fully describe the influences of geometric errors on the rigid body motion of rotary axes.The approximate linear relationship between the ERA parameters and the ball-bar measurement results are established by deriving the Jacobian matrixes,based on which,the ERA parameters are identified.A spherical intersection method is proposed to identify the actual position of the table ball,based on which,the influences of the table ball’s set-up errors and the ball-bar’s sensitive assumption on the identification accuracy are eliminated.By designing and manufacturing a special fixture,the influences of the tool ball’s set-up errors on the identification accuracy are also eliminated.5)Inverse kinematics based generalized analytical geometric error compensation method is established.Based on the location of rotary axes on the kinematic chain,all feasible configurations of five-axis machine tools can be classified as three categories.Then,the generalized actual forward kinematic model of five-axis machine tools is established,based on which,the geometric error compensation problem is transformed into the problem of solving the actual inverse kinematics of five-axis machine tools.The geometric error induced tool tip position error and tool orientation error are compensated in a decoupled way.Based on the rotationconstrained equation,the generalized analytical solution to the inverse kinematics of rotary axes are derived by establishing the Euclidean vector-basis.By introducing the incremental motion commands,the generalized analytical solution to the inverse kinematics of translational axes are derived based on the fact that the multiplication between the incremental motion matrix and the error motion matrix does not depend on the multiplication sequence.The research work in this thesis enriches the current geometric and motion control precision improvement methods of five-axis machine tools.The designed algorithms provide theoretical basis and technical support for both the localization of advanced CNC systems and the precise manufacturing of parts with complex sculptured surfaces,such as the aerospace impellers,the marine propellers,etc.