Dynamic Modeling And Stability Prediction For Flank Milling Of Curved Thin-walled Components

Curved thin-walled components,such as engine casing,integral impeller and gas wave re-frigeration equipment hub,are key parts of high-end equipment in the fields of aerospace,energy and power,etc.Some parts of these components or their whole often use flank milling mode,and the performance and machining surface quality are extremely demanding.However,due to the thin walls,complex shapes and large amount of material removal,these components not only have weak rigidity,but also have time-varying stiffness and large cutter overhang in the ma-chining process.If the machining parameters are improperly selected,it is easy to cause surface quality degradation,chatter instability and other problems,and it is difficult to meet machining requirements.Therefore,it is of great significance to construct dynamic modeling of the ma-chining system,to put forward accurate methods for predicting the stability limits,and to seek reasonable process parameter combinations,so as to realize the high quality and high efficien-cy machining of curved thin-walled components.This thesis regards the flank milling process of the curved thin-walled components as the research object,studies the issues of machining dynamic modeling and stability prediction with the consideration of the cutter and workpiece flexibilities,deeply reveals the excitation response mechanism of the cutter and the workpiece and their dynamic interaction mechanism,and provides important theoretical basis and technical supports for machining the spatial circuitous flow channels of the gas wave refrigeration equip-ment hub with high machining quality and efficiency.The specific research contents of the thesis are summarized as follows:(1)A multi-point-contact five-axis dynamic cutting force model is established.Firstly,the five-axis flank milling path expression and the transformation relation between the cutter coor-dinate system of and the workpiece coordinate system are given.Position angles of different cut-ting micro-elements under the simultaneous changes of pitch and helical are determined.Then,based on the solid trimming technique,a new extraction method of cutter-workpiece engagement domain is developed.Considering the cutter run-out effect,calculation of the instantaneous un-deformed chip thickness is conducted and the multiple regenerative indexes based on the prin-ciple of minimum static instantaneous undeformed chip thickness is determined.On this basis,the multi-point-contact five-axis dynamic cutting force model is established,and its state space form is given.Finally,a method for calibrating the cutting force coefficients and cutter run-out parameters of variable pitch or helix cutter in parallel is proposed.The established dynamic cut-ting force model can provide the mechanical foundation for the accurate dynamic modeling of the flank milling process.(2)New modal testing and parameter identification methods are proposed for slender cut-ters.Based on the modal analysis theory,a cross-axis and cross-point modal testing method is proposed,which can solve the misalignment problem of the dynamic parameters identified by conventional methods because of ignoring structural cross-axis and cross-point modes to the slender cutter.A parameter identification method matching with the cross-axis and cross-point modal testing method is proposed,and a grouping parameter identification strategy of multiple frequency response functions is given.Then the dynamic parameters of the whole cutter structure are determined.The testing and identification results show that the proposed methods can iden-tify the cutter dynamic parameters with the property of the principle vibration direction,which make up for the deficiency of conventional methods in the aspect of identification accuracy of the structural modal shape vector.The proposed methods can provide accurate and reliable dynamic parameters for the cutter dynamic equation considering the effects of cross-axis and cross-point mode couplings.(3)A flank milling dynamic model considering cutter and workpiece flexibilities is estab-lished.For the flank milling process,a cutter dynamic equation considering the effects of cross-axis and cross-point mode couplings is established,and a parameter matrix assembly method matching with the equation is given.Simulation and experiment results show that the dynam-ic model considering the effects of cross-axis and cross-point mode couplings can significantly improve the prediction accuracy of the stability boundaries.For the process of flank milling of thin-walled workpieces,considering the effects of material removal and static force-induced deformation in the cutting process,the workpiece dynamic equations under the flexibility of the workpiece and double flexibilities of the cutter and the workpiece are established,respectively.A fast method to extract the dynamic parameters of the thin-walled workpiece of the cutting process is given with the consideration of the actual material removal effect,and an iterative method to solve the actual engagement angle boundaries between the cutter and workpiece is proposed considering the effect of static force-induced deformation.Simulation and experiment results show that considering the effect of static force-induced deformation,the prediction ac-curacy of cutting force under the double flexibilities of the cutter and workpiece is improved obviously,and the stability boundary predicted by the dynamic model is more consistent with the experiment results,especially for the thin-walled workpieces with thinner wall thickness.(4)Two milling stability prediction methods with high convergence rates are proposed.For single time-delay milling systems,a second-order SDM based on the PTI algorithm is proposed.This method uses Newton interpolation formula to approximate the time-delay term of Duhamel integral,which can obtain more accurate approximation of the system state response.For solv-ing the large number of exponential matrices and the integrations of the exponential matrices and its product with polynomial functions generated from the approximation process,an effi-cient solution strategy based on the PTI algorithm is presented.For multi-delay milling systems,a multi-step Adams method based on the PTI algorithm is proposed.This method uses the multi-step Adams formula to accurately approximate the dynamic and static components of the system state response,and has the ability to synchronously predict the dynamic displacement and sur-face position errors.In the approximation process,the exponential matrices and the integrations of the exponential matrices and its product with polynomial functions are also solved by the PTI algorithm efficiently.Simulation results show that compared with the international mainstream methods,the second-order SDM and multi-step Adams method have significantly higher con-vergence rates.They can obtain higher computational accuracy under a smaller discretization number.The second-order SDM can improve the computational efficiency of the original first-order SDM by more than 65%.The multi-step Adams method in different step form are faster than the FDMs of different order,and its increase trend of computation time is slower with the growth of the step.(5)The experiment verification of machining a curved thin-wall component is carried out.The proposed flank milling dynamic model and stability prediction method are applied to the flank milling process of the gas wave refrigeration equipment hub,and a process route is formed for machining the spatial circuitous channels which are evenly distributed around the rotor hub.The positioning and clamping schemes with stiffness enhancement function are designed.The process involving the application of variable pitch cutter are divided into different machining stages,and flank milling cutter paths are generated in each machining stage.The effect of vari-able pitch cutter on suppressing machining vibration is analyzed.The optimal selection strategy of flank milling parameters based on the stability lobe diagram is presented.Simulation results show that the critical radial cutting depth can be increased by more than one time by using the variable pitch cutter in some speed ranges.The experiment results show that the process route can effectively avoid and suppress the machining chatter,and can realize the efficient and stable machining of the spatial thin-wall channels of the gas wave refrigerator rotor hub,which verified the feasibility of the proposed model and method in practical engineering application.