This paper discusses the evaluation of tool point dynamics using output-only modal analysis methods. As compared to the traditional experimental modal analysis procedures that rely on the input and the output, both being known, output-only methods discussed herein can evaluate modal parameters using only the measured response of the tool subjected to unknown impact-based excitations. Since the input is not known, the estimated shapes are unscaled. To correctly scale shapes, we use the mass-change method. We present analytical models to guide the optimal selection of the mass to be added as well as to guide its placement on the tool. Analytical models systematically characterize errors in scaling the eigenvector and errors due to uncertainties in the estimation of the natural frequencies. The model suggests placement of the mass to be added at the anti-node(s) for the mode(s) of interest. These models guide experiments on two tools – a slender boring bar, and an end mill. Tool point frequency response functions (FRFs) reconstructed with the natural frequencies, damping ratios, and scaled mode shapes evaluated with the output-only mass-change method are compared with and found to be in good agreement with FRFs obtained from the traditional experimental modal analysis procedures. Since output-only methods require one less transducer, and since these methods are robust to uncertainties and inconsistencies in the input, output-only methods promise advantages from the industrial point of view.

本文讨论了仅使用输出模态分析方法对刀具点动力学的评估。与依赖于输入和输出的传统实验模态分析程序相比，两者都是已知的，本文讨论的仅输出方法可以仅使用工具经受未知的基于冲击的激励的测量响应来评估模态参数。由于输入未知，因此估计的形状未按比例缩放。为了正确缩放形状，我们使用质量变化方法。我们提供分析模型，以指导要添加的质量的最佳选择以及指导其在工具上的放置。分析模型系统地表征了特征向量缩放的误差以及由于固有频率估计的不确定性而引起的误差。模型建议将要添加的质量放置在感兴趣模式的波腹处。这些模型指导了两种工具的实验-细长的镗杆和立铣刀。用仅输出质量变化方法评估的自然频率，阻尼比和缩放模式形状重构的工具点频率响应函数（FRF）与通过传统实验模态分析获得的FRF进行了比较，并发现它们非常吻合程序。由于仅输出方法需要较少的传感器，并且由于这些方法对于输入中的不确定性和不一致具有鲁棒性，因此从工业角度来看，仅输出方法具有优势。用仅输出质量变化方法评估的自然频率，阻尼比和缩放模式形状重构的工具点频率响应函数（FRF）与通过传统实验模态分析获得的FRF进行了比较，并发现它们非常吻合程序。由于仅输出方法需要较少的传感器，并且由于这些方法对于输入中的不确定性和不一致具有鲁棒性，因此从工业角度来看，仅输出方法具有优势。用仅输出质量变化方法评估的自然频率，阻尼比和缩放模式形状重构的工具点频率响应函数（FRF）与通过传统实验模态分析获得的FRF进行了比较，并发现它们非常吻合程序。由于仅输出方法需要较少的传感器，并且由于这些方法对于输入中的不确定性和不一致具有鲁棒性，因此从工业角度来看，仅输出方法具有优势。