基于铣削系统动力学响应的球头铣刀铣削表面形貌建模

基于系统动力学响应完成弱刚度球头铣刀铣削系统中铣削表面形貌建模，对于提高表面质量具有重要的理论价值。为此，借助齐次坐标变换原理建立球头铣刀刀齿的运动学轨迹，按照机械建模法提出铣削力的求解方法，根据再生振动理论建立柔性刀具-柔性工件铣削系统的动力学模型，基于全离散法提出考虑变时滞效应的工艺系统动态位移求解方法，并采用线性插值法修正刀齿运动轨迹；综合Z-MAP法和数值法提出球头铣刀铣削表面形貌仿真方法，在完成加工轨迹驱动的表面形貌几何仿真的基础上，实现考虑振动诱导下工艺系统动态位移的表面形貌物理仿真；以硬质合金球头铣刀铣削7050-T6进行验证性实验。实验和仿真结果具有较高的一致性，表明该仿真方法是有效的，可以为实际加工参数的选择和优化提供理论依据。

Modeling and Simulation of Surface Topography under Ball-end Milling Based on Dynamic Response of Milling System

Milling surface topography modeling based on the dynamic response of the weak-stiffness ball-end milling system has an important theoretical value for improving surface quality. To do this, first of all, the kinematic trajectory of the ball-end milling cutter teeth is established by homogeneous coordinate transformation, and a solution for the milling force is put forward according to the mechanical modeling method. A dynamic model for the flexible cutter-flexible workpiece milling system is established based on the regenerative vibration theory. A method for solving dynamic displacement of processes based on the full discrete method with the effect of variable time delay considered is proposed. And a linear interpolation method is adopted to modify the cutter tooth trajectory. Then, a simulation method for the surface topography under ball-end milling is proposed by combining Z-MAP method and numerical method. After completing geometric simulation of the surface topography generated by the machining path, a physical simulation considering the dynamic displacement of the process system induced by vibration is carried out. Lastly, a validation experiment is conducted by milling material 7050-T6 using a carbide ball-end milling cutter. The experiment and simulation results are consistent, indicating that the modeling method is effective and can provide theoretical basis for selecting and optimizing actual machining parameters.