NC Milling Tool Position Control For Ball Head Tools Considering Machine Geometry Errors

The machining accuracy of machine tools is affected by various factors,such as the geometric error of the machine tools caused by the manufacturing and assembly errors of each part of the machine tools and the wear in use,the thermal deformation error affected by the temperature during machine tools operation,the force deformation error under the load of the weight of the machine tools itself and the clamping force and cutting force during the machining process,and the following error generated during the transmission of each moving part.In particular,machine geometry errors are a key factor in machining accuracy when the working temperature does not vary much.In addition,machine geometry errors are stable,repeatable and easy to measure.It is one of the most cost-effective and efficient ways to enhance the machining accuracy of CNC machine tools by modelling and compensating for them.In order to eradicate the impact of the geometric error of the machine tools on the processing accuracy,this paper takes three-axis NC machining of ball-ended knives as the background of research,and maps the geometric error of the machine tools to the position error of the ball-ended knives’ tool centres on the basis of multi-body system theory,flush coordinate transformation theory and rigid body kinematic methods,as well as the topological analysis of the machine tool kinematic chain.Based on the principle of surfaces shaping of the workpiece milled by the ball-end cutter,a forward and backward calculation model between the tool centre curved surfaces and the surface of the component/design surface are constructed,by considering of the mapping correlation between geographical errors of that the machine tool and that of the tool location.This model is used to solve for a programmed tool centre curved surfaces that eliminates the geometrical errors of the machine tools.The surfaces are then imported into CAM software to create a 3D solid model,which are programmed for machining,and the NC machining program that eliminates the geometrical errors of the machine tools is obtained by controlling the movement of the tool position on the surfaces.To this end,the following work is carried out:(1)Take XYFZ type CNC machine tools as the research object,combine the motion transmission relationship of each motion axis in its actual machining process,and carry out geometric errors analysis.On the basis of the theories of multi-body systems and simultaneous coordinate transformations,the error analysis of each kinematic chain of the machine tool is carried out in combination with the transmission relations of the kinematic transmission chain of the machine tools,The result is a matrix of the ideal position,position error,ideal motion and motion error of any adjacent body of the CNC machine tools,and a model of the geometric error of the machine tools in the machine tools referred to the machine tools frame.(2)In the operation of a CMM,the motion of the machine tools when machining a workpiece is defined as the movement of the tools with respect to the workpiece,Taking into account the geometrical errors of the machine,the change of position between each adjacent body of the machine tools,through aligned matrix of coordinate conversions cumulatively transformed along the direction of motion transfer from the workpiece reference coordinate system to the tool reference coordinate system to the change of the ball-end cutter center position,thus,under the workpiece reference coordinate system to construct the ball-end cutter center position error model.(3)Considering the special feature that the surfaces of the ball-end cutter are spherical,the movement of the ball cutter round the center of the sphere will not cause the error of the surfaces of the workpiece milled by the ball-end cutter in three coordinates,the movement of the machine is therefore decomposed into a translation based on the spherical centre of the curved surface of the ball-ended tools and a revolution round the spherical centre.By means of a correspondence between the geometrical error of the machine tools and the position error of the ball-end cutter centre,the actual surfaces of the workpiece under the influence of the geometric errors of the machine tools are obtained according to the principle of forming the surfaces of the workpiece milled by the ball-end cutter,and a forward and reverse calculation model between the tool centre curved surfaces and the workpiece/design surfaces are constructed.(4)The concept of a programmed tool centre curved surfaces for NC milling with a ball-end cutter and a tool position control method to eliminate the influence of machine geometry errors are proposed.The method firstly solves the ideal tool centre curved surfaces and the actual tool centre curved surfaces affected by the geometrical errors of the machine tools,and then establishes a model for solving the programmed tool centre curved surfaces to eliminate the geometrical errors of the machine tools based on the forward and reverse calculation model between the tool centre curved surfaces and the workpiece surface/design surfaces.Finally,the programmed tool centre curved surfaces imported into the CAM software to produce a NC machining program that eliminates the influence of machine geometry errors.(5)The application of the above method of eliminating geometric errors in machine tools is illustrated by the application of a ball-end cutter on an XYFZ CNC machine tools for milling a given design surface of the workpiece.The NC milling surface of the ball-end cutter is used as an example,and transferring the programmed core surface from the solution to the CAM software,and the NC machining program is prepared and simulated based on the surface to verify the feasibility of the method.