Objectives  This paper aims to analyze the thermal equilibrium performance of a piston hydraulic damper in a stable working state so as to solve the problem in which the oil circuit of the hydraulic damping system of a longitudinal vibration-reduction thrust bearing is closed and the external disturbance input is unknown.

  Methods  To this end, a micro-mechanism for the heat production calculation of piston friction loss and hydraulic fluid loss is applied to the thermal analysis of the hydraulic damping system in order to deduce the formula of the power loss calculation of the piston vibration and the reciprocating flow of the hydraulic oil. Meanwhile, the piston friction loss and head loss of the model are calculated, and the heat production variation of the hydraulic damping system with dynamic frequency and piston stroke is analyzed. In addition, the input power of the external disturbance is ascertained and the thermal finite element model of the bearing part established, allowing the steady temperature rise and heat flow distribution of the structure to be calculated.

  Results  The calculation results show that the input power of the external disturbance is roughly equal to the sum of the thermal power of each part, the steady temperature rise of the system is fairly low and the heat flow division is reasonable.

  Conclusions  The results show that the heat production calculation method described in this paper is quite feasible. Furthermore, the calculated temperature rise of the system is within the permissible range, and corresponding effective measures can be taken to reduce local temperature rise at intensive heat flow parts according to the heat flow division diagram of the system.