Interpolation Function Research And Error Analysis Of Four-axis Space Intersecting Line Cutting Machine

The intersecting lines of space steel pipes,head ball joints,etc.and pipe joints are mostly space curves.When cutting space intersecting lines,variable bevel cutting is often required according to different positions.When cutting the intersecting line with variable bevel,manual cutting and automatic cutting can be adopted.Manual cutting is difficult to ensure the accuracy of the spatial intersecting line trajectory and the bevel angle.The existing spatial intersecting line cutting equipment is relatively large,and it is not convenient to carry when mobile construction operations are required.In response to the above requirements,this subject has developed a simple and portable spatial intersecting line cutting machine with four degrees of freedom,which can work directly on large diameter round pipes,and can cut intersecting lines without using other platforms to realize the cutting of variable groove intersecting lines and improve cutting efficiency,reducing labor costs,and improving the quality of bevel cutting.For this reason,this article has conducted research from the following aspects:Based on the space intersecting line type and portability requirements,the overall plan for the integration of the supporting mechanism and the cutting machine is determined.The support mechanism adopts a multi-joint manipulator,and each joint is locked after the installation position is determined;the cutting machine has four degrees of freedom of rotation,expansion,lifting and swinging to realize the cutting of spatial intersecting trajectories;the D-H method is used to establish the cutting machine four joint parameters,complete the forward and inverse kinematics solution,determine the spatial pose of the end torch and the parameter relationship between each joint;the dynamic model is established by the Newton-Euler method to provide strength calculation and drive control the theoretical basis was established;the strength of the support frame was checked,and the statics analysis of the whole machine was carried out to make the main components meet the strength requirements.The fitting and interpolation algorithm of spatial intersecting lines is researched.According to the theoretical intersecting line formed by the intersecting of the two pipes,the key point coordinates are extracted,the third-order NURBS curve equation is used to fit the trajectory of the spatial intersecting line,and the cutting torch speed and height at different intersecting line positions are determined Theoretical solution;the interpolation algorithm of the third-order NURBS curve based on Taylor’s expansion is completed,and the influence of the bow height error on the interpolation accuracy is analyzed,and the trajectory of the intersecting line,the interpolation error,the chord length error and the cutting gun end are analyzed the speed is verified by simulation,which provides a theoretical calculation basis for the control system.Considering the end position as an index,the influence of fit error,form and position error,joint rotation angle error and transmission chain error on the cutting accuracy of the spatial intersecting wire cutting machine in the single-joint and multi-joint coupling state is studied based on the control variable method.From the perspective of thermal deformation,the influence of dynamic heat source and ferro-oxygen combustion heat on the actual thickness of the cutting workpiece is analyzed;through the trajectory of the cutting gun end,the influence of the stiffness of the mechanical system on the cutting accuracy of the spatial intersecting wire cutting machine is studied.The experimental results of spatial intersecting line trajectory cutting show that the intersecting curves of the main and branch pipes cut by the intersecting line cutting machine have good contours,good surface effects,and small errors.The main and branch pipes are accurately matched after variable bevel cutting.It is consistent with theoretical analysis and simulation results.The thermal deformation measurement results of the round pipe show that when cutting thin pipes,the cutting speed is too slow will cause large thermal deformation;when cutting thick pipes,the thermal deformation caused by bevel cutting is large;in addition,the secondary cutting Comparing the intersecting line and the groove formed by the first cutting,the effect of the second cutting is good,and the thermal deformation is small.