When the gear generates a nodal mode shape vibration, there are two directions of possible relative displacement between the corresponding points on the contact surface of the damper ring and the damper groove, which are circumferential direction and axial direction respectively. In this paper, the relative displacement of the damper ring and the damper groove are considered in two directions, and the calculation method of energy dissipation is proposed. When the nodal vibration occurs in the gear, due to the existence of the strain difference between the damper ring and the damper groove on the contact surface, circumferential slip of partial area would occur. The energy dissipation in one vibration cycle is accurately determined by analytical solution. Since the aviation gears are mostly thin-walled structures, the axial displacement is large when resonance occurs. Based on the discrete damper ring model which considers interaction between every segment of the ring, the first-order harmonic balance method is used to calculate the axial displacement of the damper ring under the given gear rim amplitude. And then the hysteresis curve area of each discrete segment on the contact surface is summed to obtain energy dissipation in one vibration cycle. In this paper, based on the energy method, the damping effect of the damper ring is predicted. The damping ratio curve obtained by energy dissipation in two directions is compared and analyzed. The occurrence conditions of the two directions of possible relative displacement and the influence of the damper ring parameters on both situations are summarized.