Torsional vibration feature extraction method from lateral vibrations based on decomposed forward and backward whirl motions

•A way to extract torsional features from lateral vibration signals is proposed.•The forward whirl signals perform better in torsional vibration extraction.•Harmonics can amplify the torsion angle by the factor of the vibration order.•Results of experiments and simulations confirm the accuracy of the method.•Machines without torsion meters can monitor torsional vibration via this method.