Research On High Speed Milling Stability Of Variable Cross-Section Scroll Teeth Based On Lagrangian Interpolation Full Discrete Method

Variable section scroll teeth made up of a combination of profiles are deep groove thin walled parts,which require high tolerances on the shape and surface roughness of the teeth during machining.In the machining process,due to the small diameter of the tool and the large extension length,tool let-off and chattering tend to occur,and there is a problem of limited accuracy of the scroll tooth machining.In order to solve the above processing problems,this paper uses the regenerative chatter theory to construct a milling dynamics model,and uses the second-order Lagrangian interpolation full discrete method to study the stability of high-speed milling of variable-section volute teeth.The details of the study are as follows:(1)Firstly,the geometric model of variable-section volute teeth was established by analyzing the design principle of volute tooth profile with three base circular involutes as the research object.Then,the cutting force model of milling variable-section volute teeth was constructed to form the calculation theory of total cutting force of the tool.Finally,the tool trajectory during the actual milling of volute teeth was solved by combining the geometric model of variable-section volute teeth,and the actual machining trajectory of the tool based on the instantaneous undeformed cutting thickness based on the actual tool trajectory is obtained.(2)The dynamics model of the milled scroll tooth with regenerative chattering is established and characterized as a system of time-lag differential equations.The second-order Lagrangian interpolation full dispersion method is used to fit the state and time lag terms in the integral term of the equation set,and the transfer matrix is derived and the leaflet diagram of milling flutter stability is obtained.The results show that a)as the cutting width of the cutter teeth increases,the ultimate depth of cut of the main leaflet stability region gradually decreases and the stability region gradually moves to the right,b)compared with the first-order full dispersion method,the second-order Lagrangian interpolation full dispersion method has more advantages in terms of computational accuracy and convergence speed,and is more accurate in predicting the stability of the milling model.(3)A set of parameters was selected in the stable,critical and chattering zones of the flap diagram,and the simulation was used to mill the variable-section scroll tooth.The results showed that a)when the parameters selected in the stable zone of the flap diagram were used for machining,the cutting force curve changed gently and the milling process was stable,b)when the parameters selected in the critical zone were used for machining,the cutting force curve fluctuated greatly,the milling process was not stable and chattering occurred easily,c)when the parameters selected in the chattering zone were used for machining,the cutting force curve fluctuated strongly,the milling process was unstable and chattering occurred.When the parameters of the critical zone are selected for machining,the cutting force curve fluctuates sharply,the milling process is unstable and chattering occurs.The analysis of the experimental data shows that the trend of the cutting force obtained from the experiment is consistent with the simulation results,which verifies the stability of the milling process.In this dissertation,the stability of the high-speed milling process of variable-section scroll teeth is studied through theoretical analysis,mathematical modeling,machining simulation and experimental verification,which provides an effective solution for the reasonable selection of parameters and avoidance of milling chatter during the actual machining of variable-section scroll teeth.