Data-driven chatter detection techniques avoid complex physical modeling and provide the basis for industrial applications of cutting process monitoring. Among them, feature extraction is the key step of chatter detection, which can compensate for the accuracy disadvantage of machine learning algorithms to some extent if the extracted features are highly correlated with the milling condition. However, the classification accuracy of the current feature extraction methods is not satisfactory, and a combination of multiple features is required to identify the chatter. This limits the development of unsupervised machine learning algorithms for chattering detection, which further affects the application in practical processing. In this paper, the fractal feature of the signal is extracted by structure function method (SFM) for the first time, which solves the problem that the features are easily affected by process parameters. Milling chatter is identified based on k-means algorithm, which avoids the complex process of training model, and the judgment method of milling chatter is also discussed. The proposed method can achieve 94.4% identification accuracy by using only one single signal feature, which is better than other feature extraction methods, and even better than some supervised machine learning algorithms. Moreover, experiments show that chatter will affect the distribution of cutting bending moment, and it is not reliable to monitor tool wear through the polar plot of the bending moment. This provides a theoretical basis for the application of unsupervised machine learning algorithms in chatter detection.