S-transformation based on diagnostic of machining operations from displacement, velocity, torque, and force data is proposed. Damping ratio was calculated from the time-frequency-amplitude plots of the s-transformation. The values were called damping index by considering the influence of the window functions on the calculations. Variance of the damping index in a small band around the first natural frequency of the system was found an effective chatter detection tool. The s-transformation of all the signals considered had similar characteristics and the sharp drop of the variance of the damping index indicated chatter development.