Numerical Prediction Of Static Form Errors In The Peripheral Milling Of Thin-Walled Workpiece

Milling is a widely used manufacturing process in aeronautic and aerospace industries for machining monolithic thin-walled workpiece. Due to the weak rigidity of the workpiece, form errors induced by the cutter/workpiece deflection constitute a common problem that influences extremely the accuracy and the surface quality of the workpiece. In the worst case, form errors will violate the dimensional tolerance and lead to useless products. Consequently, investigation on the prediction and control of the deflection during the milling process of thin-walled workpiece is of great significance to select appropriate values for the process parameters at the process planning stage. Based on numerical simulations combining the finite element method with cutting mechanics, the following efforts are focused on the predicting approach of the cutting deflection and other associated techniques in the peripheral milling process of thin-walled workpiece:(1) Finite element modeling methods of the cutter-workpiece system are studied. The cutter and workpiece are modelled separately, i.e., coordinate systems, meshing methods and element types are selected independently. The helical end mill is modelled as a cantilevered elastic cylindrical beam with equivalent diameter. 3D irregular finite elements of different shapes such as tetrahedral elements, prismatic elements, hexahedral elements or a combination of them are adopted in practical modelling of the workpiece firstly. This idea provides a general way of discretizing the workpiece with complex structure. The coherence description equation of cutter-workpiece system is generated through a series of coordinate transformations. Based on the study, mathematical formulations are established for equivalently discretizing the cutting forces into the cutter nodes and the workpiece nodes.(2) On the basis of the above study, three models i.e. rigid model, flexible model with invariable rigidity of workpiece and flexible model with variable rigidity of workpiece, are developed to predict the cutting deflection and the static form errors. In the rigid model, it is assumed that deflections of the cutter and of the workpiece don't affect the magnitude of cutting forces and that the influence of the material removal on the rigidity of the workpiece is ignored. A new coupling algorithm is established based on correction factor in the flexible model with invariable rigidity of workpiece, in which the rigidity change of the workpiece induced by the materialremoval is not considered. In the flexible model with variable rigidity of workpiece, both the cutter/workpiece deflections and the rigidity change of the workpiece are taken into account. Based on the idea of the artificial power law used in structural topology optimization, the rigidity variation of the workpiece due to the material removal is updated by correcting the element stiffness without remeshing. Especially, the three models are independent of finite element modeling methods of the cutter-workpiece system so that they have good capability in the application of complex thin-walled workpiece.(3) Efficient finite element analyses method is studied. As for the fact that a large number of finite element analyses is needed in the flexible models in which numerous nodes and load cases exist, the unit load method of finite element method based on the assumption of linear elasticity is applied to predict the defection of the workpiece. Besides, cantilevered beam theory is used to calculate the deflection of the cutter. With these techniques, the CPU time is dramatically reduced so that the computing efficiency is improved.Based on the typical cutting case with Aluminum and Titanium alloy, numerical results obtained are compared with experimental results. It is shown that the approaches proposed in the study have a good validity to predict the form errors in the peripheral milling process of thin-walled workpiece.