Abstract Avoidance of resonance in fluctuation of milling tool is vital for reaching excellence quality and performance of the cutting operation. The cutting tool in resonance condition vibrates with considerable magnitude that causes to increase milling tool wear and manufacturing prices. Analytical study of primary resonances and bifurcation behavior of a micro-milling process, including structural nonlinearities, gyroscopic moment, rotary inertia, velocity-dependent process damping, static and dynamic chip thickness, is chief aim of this article. The milling tool is modeled as a 3-D spinning cantilever beam that is motivated by cutting forces. To get the analytical solution for frequency response function and bifurcation behavior of the system under primary resonances, the method of multiple scales is operated on converted ordinary differential equations that are obtained by applying assumed modes method on nonlinear partial differential equations of tool vibration. The effects of different process parameters and nonlinear terms on the frequency response of the tool tip oscillations are examined. In addition, the effects of detuning parameter and damping ratio on the bifurcation and behavior of the limit cycle under primary resonances are examined. The results shows that these parameters are the bifurcation parameters and Neimark, symmetry breaking, flip, and period-3 bifurcations occur when the detuning parameter is varied.

中文翻译：

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微铣削一次共振条件下的频率响应和分岔分析研究

摘要 避免铣刀波动中的共振对于实现卓越的切削加工质量和性能至关重要。共振条件下的切削刀具以相当大的幅度振动，这导致铣削刀具磨损和制造价格增加。本文的主要目标是对微铣削过程的初级共振和分叉行为进行分析研究，包括结构非线性、陀螺力矩、旋转惯量、速度相关过程阻尼、静态和动态切屑厚度。铣刀被建模为由切削力驱动的 3-D 旋转悬臂梁。为了得到系统在一次共振下的频率响应函数和分岔行为的解析解，多尺度方法是对转换后的常微分方程进行操作的，这些常微分方程是通过对刀具振动非线性偏微分方程应用假设模态方法得到的。检查了不同工艺参数和非线性项对刀尖振荡频率响应的影响。此外，还检查了失谐参数和阻尼比对初级共振下极限环的分岔和行为的影响。结果表明，这些参数是分岔参数，改变失谐参数时会出现内马克、对称破坏、翻转和周期3分岔。检查了不同工艺参数和非线性项对刀尖振荡频率响应的影响。此外，还检查了失谐参数和阻尼比对初级共振下极限环的分岔和行为的影响。结果表明，这些参数是分岔参数，改变失谐参数时会出现内马克、对称破坏、翻转和周期3分岔。检查了不同工艺参数和非线性项对刀尖振荡频率响应的影响。此外，还检查了失谐参数和阻尼比对初级共振下极限环的分岔和行为的影响。结果表明，这些参数是分岔参数，改变失谐参数时会出现内马克、对称破坏、翻转和周期3分岔。