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The rolling process is a strategical industrial and economical activity that has a large impact among world-wide commercial markets. Typical operating conditions during the rolling process involve extreme mechanical situations, including large values of forces and tensions. In some cases, these scenarios can lead to several kinds of faults, which might result in large economic losses. Thereby, a proper assessment of the process condition is a key aspect, not only as a fault detection mechanism, but also as an economic saving system. In the rolling process, a remarkable kind of fault is the so-called chatter, a sudden powerful vibration that affects the quality of the rolled material. In this paper, we propose a visual approach for the analysis of the rolling process. According to physical principles, we characterize the exit thickness and the rolling forces by means of a large dimensional feature vector, that contains the energies at specific frequency bands. Afterwards, we use a dimensionality reduction technique, called t-SNE, to project all feature vectors on a visual 2D map that describes the vibrational states of the process. The proposed methodology provides a way for an exploratory analysis of the dynamic behaviors in the rolling process and allows to find relationships between these behaviors and the chatter fault. Experimental results from real data of a cold rolling mill are described, showing the application of the proposed approach.