Kinematics Planning Of Multi-axis EDM Based On Digitizer/player Architecture

Electrical discharge machining(EDM)has unique advantages in machining high precision components which are made of difficult-to-cut materials.Multi-axis EDM is able to machine components which have complex structures.Shrouded blisks multi-axis EDM and muti-axis wire EDM are two main applications of muti-axis EDM.Shrouded turbine blisks are key components of aero and rocket engines and multi-axis EDM is the main manufacture method for shrouded blisks.However,manufacture of such complex parts is time-consuming.Low machining efficiency of shrouded blisks limits the production capacity of rocket engines.Wire EDM also plays an indispensable role in aerospace mold manufacturing industry.Machining accuracy and efficiency is the criterion for evaluating the performance of machine tools and processing technologies.The aim of this dissertation is to address several key problems in improving the machining accuracy and efficiency of muti-axis EDM.In computer numerical control(CNC)systems,forward kinematics describes the mapping from coordinates in the joint space to those in the workpiece coordinate frame.Kinematics plays a vital role in motion control of axes,both translational and rotational,for a six-axis EDM machine tool for workpieces with complex structures.EDM processes are characterized with profiling processing,jump motion,forward/backward interpolation.In order to achieve a high accuracy as well as a high-efficiency in multi-axis EDM,several novel methods are proposed based on the kinematics of a multi-axis EDM machine.These new methods include feedrate planning,and direct interpolation of parametric curves based on a digitizer/player architecture.The main achievements of this dissertation are summarized as follows:First,to study the rigid motion of an electrode with respect to a workpiece in multi-axis EDM,the kinematics from the tool frame to the workpiece frame is needed.Screw theory is utilized to derive the kinematics of a six-axis EDM machine consisting of three translational axes and three rotational axes.With the rigid transformation of each axis described by an exponential of a twist,the overall kinematics is obtained as a product of exponentials of twists.According to the different configurations in machining shrouded blisks and pump impellers,different forward kinematics maps are analyzed.Based on the kinematics of multi-axis EDM machine,the contour errors of rigid body motions are also analyzed.Second,due to different dimensions of angular and linear velocities,there is a discrepancy between demanded and actual feedrates.This feedrate discrepancy can cause feedrate fluctuations leading to a machining instability,and inaccurate heights of electrode jumps.In order to ensure the machining stability,this dissertation proposes a feedrate planning method for multi-axis EDM of shrouded blisks.In this method,CAD models of both an electrode and a shrouded blisk are utilized to extract characteristic radii for feedrate planning in G-code generations.A feedrate post-processing algorithm(FPPA)for multi-axis EDM for shrouded blisks is proposed to reduce feedrate fluctuations and achieve a proper electrode jump height.The proposed feedrate planning method achieves a better gap status and a higher machining efficiency.Third,to overcome the problems of the sampled data method(SDM)interpolation such as chord error,feedrate fluctuation,the unit arc length increment method(UALI)is adopted for the interpolation of non-circular parametric curves,such as involutes,Archimedes spirals,cycloids,parabolas and B-splines.This interpolation algorithm is applicable in wire EDM for ruled surfaces of a workpiece with different parametric curves in the upper and lower planes.Tool compensation is also considered for both non-tapered workpieces as well as tapered workpieces.Finally,a generalized dual-NURBS interpolation is proposed to interpolate a NURBS curve in the workpiece coordinate frame to position commands in the joint space.The NURBS curve is first interpolated by the UALI algorithm which decomposes the curve into BLUs in the workpiece coordinate frame.To convert the interpolated segments from the workpiece frame into the axial coordinate space,an inverse kinematics is needed.A look-up table approach is adopted to bypass the non-uniqueness in the inverse kinematics problem.Implemented on a digitizer/player architecture,the commands are then coded into a binary stream.Experimental tests show an improved gap status and an decrease by 42.19% in the machining time.