Research On Geometric Modeling And Stability Of Cutting Force In Five-axis Machining Of Toroidal Cutter

At present,numerical control(NC)machining technology is developing as a highly accurate,precise,efficient,and reliable core of digital manufacturing.Two rotational degrees of freedom are added in the five-axis NC machining.Thus,the position and pose of the cutter can be continuously adjusted according to the change of the shape of the machined surface.Therefore,this technology is widely used in free-form surface machining.Achieving the multi-axis precision machining of complex surface has become an urgent problem to be solved in the field of NC technology.At present,studies on precision machining mostly focus on ball-end milling cutter.However,the multi-axis precision machining with non-ball-end milling cutter has not yet formed a mature theory and a perfect technical system.Toroidal cutter,as a typical non-ball-end milling cutter,is characterized by high processing efficiency and good processing quality.It has remarkable application prospects in the processing of complex surface.Therefore,this work aims to perform an in-depth study on cutting force modeling,tool path planning,and cutting stability in the five-axis machining of complex surface with toroidal cutter and other issues.The specific studies are presented as follows:1)Establish the workpiece,cutter,and local coordinate systems in the five-axis machining;construct the surface equation of the toroidal cutter according to the geometric structure of the toroidal cutter;and derive the trajectory equation of any point on the edge of toroidal cutter cutter in milling process based on the principle of differential geometry and the transformation relationship among coordinate systems.2)Taking the complex surface as the research subject,the lowest and highest points on the cutting edge at any cutting time are solved by using envelope theory and surface intersection method,respectively.Calculate the effective cutting length at any time.This work analyzes and simulates the effects of different pose angles of the cutter on the effective cutting length.The results show that the effect of the lead angle on the effective cutting length is not obvious.Compared with the solid method,the calculation efficiency is higher and the solution accuracy is higher than that of the discrete method.The instantaneous undeformed chip thickness in the cutting process is solved by using the actual motion trajectory equation of the cutting edge.The model is substituted into the traditional cutting force integration model,and the validity of the model is verified by simulation and experiment.3)The tool path planning technology in five-axis NC machining for complex surfaces is investigated.An equal bow height error interpolation method with tool step length is proposed by using osculating plane theory in differential geometry and calculating the corresponding cutter contact points on the adjacent cutter paths in the geodesic direction according to constant scallop-height for the generation of the corresponding cutter paths.The simulation and experiment results show that the proposed equal bow height error interpolation method in this work can ensure that all interpolation points fall on the machined surface and greatly decrease under the premise of satisfying the interpolation accuracy,thereby improving the speed of the interpolation operation.In addition,the actual bow height error of two adjacent cutter contacts varies uniformly,and these contacts are stable near the allowable bow height error,thereby enabling the machined surface to have improved surface quality compared with the traditional isoparametric method.4)A new interference detection and avoidance method is proposed in this paper using toroidal cutter as cutting tool aiming at the global interference of cutters and workpieces in five-axis machining of complex surface.The boundary of the detection area is rapidly established by four extreme planes.Then,the detection points in the detection area are effectively screened to determine the maximum interference points through interference judgment and subdivision technology.The example of interference in the complex surface by five-axis end milling of annular milling cutter is simulated by using Matlab and Vericut simulation software to verify the correctness of the method to provide a new method for off-line detection interference before milling.5)The stability of the five-axis processing is investigated.Aiming at dynamic equation in milling,HAMM and IAM methods are adopted to construct the state transfer matrix,and Floquet theory is used to determine the stability of the system to determine the stability lobes of the system.Matlab simulation and experiment results show that HAMM and IAM have higher computational accuracy and reliability than 1st-SDM method and 2nd-FDM method,respectively.These methods are effective in predicting milling stability.Moreover,the simulation result is consistent with the experiment result.The research findings will provide a theoretical basis for the selection and optimization of process parameters in the five-axis highly efficient precision machining.However,the prediction accuracy of IAM method is higher than that of HAMM method for two-degree-of-freedom milling dynamics model.