在车削、铣削、钻镗孔等机械加工过程中，由于再生切削效应，刀具-工件系统的运动方程存在时滞环节，导致系统的动力学特性发生改变。以车削过程为工程背景，定量研究了单自由度二阶线性时滞微分系统在受到外激励时的动力学响应。通过推导系统输入输出随时滞刚度及时滞量大小变化的传递函数关系，在参数空间得到了系统的幅频响应曲面。结果显示时滞将使得系统的工作模态发生改变，幅频响应出现多个共振峰，其中时滞刚度主要影响共振峰的峰值，而时滞量则主要影响共振峰的数量。同时，通过解析求解共振峰的脊线簇的方程，得到了共振峰在参数空间的分布规律。此外，数值求解得到了共振峰数目的定量分布图，结果显示，随着时滞刚度与时滞量的增大，共振峰的数目从1呈连续整数增加直至无穷，而系统阻尼对这一增长趋势无明显影响。通过车削试验平台上的模态锤击试验，验证了理论推导的时滞系统时频响应特性的相关结论。该研究在机床工作模态分析、整机动力学响应分析等方面具有潜在的学术与应用价值
Abstract
During the machining process, such as turning, milling and drilling, due to the regenerative cutting effect, the equation of motion of the tool-workpiece system suffers time delay effects, which causes changes in dynamic characteristics of the system.The responses of a linear delay differential system with single degree of freedom were studied when subjected to external excitation.Via deriving the transfer function of the system with time delay and delayed stiffness, the frequency response functions were obtained in the parameter space.The results show that the time delay changes the operating mode of the system, and multiple formants appear on the amplitude-frequency response diagram.The delayed stiffness mainly affects the peak value of the formant, while the time delay amount mainly affects the number of formants.Meanwhile, by analyzing the equations of the ridge clusters of formants, the distribution of formants in the parameter space was presented.In addition, the numerical solution yields a distribution of the number of formants.The results show that as the delayed stiffness and the amount of time delay increase, the number of formants increases from 1 to infinity with a continuous interger increment.Finally, modal hammering tests on a turning test platform verify the relevant conclusions of the time-frequency response characteristics in the paper.The research can serve as a basis in machine tool modal analysis and machine dynamic response analysis.
关键词
时滞系统 /
再生切削 /
工作模态 /
时频特性 /
机床动力学
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Key words
time-delay system /
regenerative cutting /
operational modal /
time and frequency characteristic /
machine tool dynamics
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