Geometric Error Identification And Compensation Of Five-axis CNC Machine Tool Based On Dual Quaternion

Compared with the three-axis CNC machine tool,the five-axis CNC machine tool has two rotation axes,which make it more suitable for the processing of precision parts and complex surfaces in the aerospace,transportation,and automotive industries,and also has higher requirements for machining accuracy.Due to the complex structure of the five-axis machine tool,the error sources that affect the machining accuracy have increased significantly,and the rotary axis is the main error contributing axis.In order to identify the geometric error of the machine tool rotation axis,this paper studies the AC five-axis CNC machine tool with double-rotation table and the BC five-axis CNC machine tool with a tilting head and a rotary table from three aspects: machine tool error modeling,rotation axes error identification experiment and geometric error compensation.The main research contents are as follows:(1)The error modeling of five-axis CNC machine tools is studied.Different from the existing geometric error modeling methods,this paper establishes the ideal kinematics model and actual error model of AC and BC five-axis CNC machine tools based on Dual Quaternion.The establishment of the machine tool model adopts the global coordinate system,and only the Plücker parameters of the machine reference coordinate system,workpiece coordinate system,tool coordinate system and other axis systems in the reference coordinate system are required.Based on the principle and algorithm of dual quaternion,the position-independent geometric errors of three linear axes and three rotary axes of a five-axis machine tool are redefined.Each rotation axis is defined as two displacement errors,one rotary angle error and one axis ratio error,and each linear axis is defined as one rotary angle error and one axis ratio error.The establishment of the entire machine tool space motion model does not include the calculation of the homogeneous matrix,which simplifies the calculation parameters and improves the calculation efficiency.The proposed modeling method is not limited to the five-axis CNC machine tools mentioned in this paper,but is also applicable to other five-axis CNC machine tools.(2)The measurement method of the geometric error of the rotary axis of a five-axis CNC machine tool is studied.Based on the double ball-bar measuring device,a newly defined measuring trajectory only involving both rotary axes coordinated motion is proposed to measure the position-independent geometric errors of the two rotation axes of a five-axis CNC machine tool.The proposed error measurement method requires only one installation,which avoids the influence of installation error and repeatability in multiple installation measurements.The geometric error of the two rotary axes of the five-axis CNC machine tool is measured by trajectory involving the simultaneous movement of two rotating axes,the linear axis always remains stationary,which eliminates the influence of linear axis geometric errors.Aiming at the irregular spherical trajectory during the use of the double ball-bar,a synchronization matching algorithm for double ball-bar sampling and machine tool motion is proposed,which solves the problem that the distance between the two bases is not constant and the relative movement speed is not synchronized during the course of the double ball-bar running trajectory,and effectively improves the accuracy of the error detection experiment.Based on the pseudo-inverse matrix,the position-independent geometric errors of the rotation axis of the machine tool are decoupled.(3)The geometric error compensation of the rotary axis of a five-axis CNC machine tool is studied.Based on the established dual quaternion space transformation model,the direction error and position error of the rotation axis of the five-axis CNC machine tool are compensated respectively.The direction error of the two rotation axes is compensated by surrounding the actual axis of the rotation axis,and the displacement error of the rotation axis is compensated by the movement of the linear axis of the machine tool itself.In terms of direction error compensation,two compensation strategies are proposed,namely,separate compensation and simultaneous compensation,and MATLAB is used to simulate the two compensation strategies.Based on the method of modifying the NC code,the effect of error compensation is verified by machining deep holes on the arc surface and double ball-bar experiments.The results show the effectiveness of the proposed compensation strategy.