Modeling and test study of the radial stiffness of the force-balanced compensators

GAO Xianming; LU Shaohui; XU Hongpeng; LI Yuhan; ZHANG Yanlong

doi:10.16579/j.issn.1001.9669.2026.04.005

Abstract：[Objective]To address the challenge of accurately identifying the mechanical properties of force-balanced compensators in high-thrust liquid rocket engine tests,this study investigates the radial stiffness characteristics of a DN500 force-balanced compensator under various operating conditions.[Methods]Firstly,a mechanical model for the radial stiffness of a single-layer U-shaped bellow was established based on the curved beam model and energy method,and its deformation behavior under load was analyzed.Secondly,a finite element model of the entire compensator was developed using Ansys software to simulate its mechanical response under internal pressurization(0-1.2 MPa)and end-loading conditions.Then,a dedicated experimental setup for mechanical property testing was designed and built,where real working conditions were simulated by pressurizing with liquid nitrogen to conduct loading tests on the compensator.Finally,by combining finite element analysis with experimental results,the correction coefficients in the stiffness model were calibrated.[Results]The results indicate that the compensator initially sinks due to gravity.As the end load increases,it gradually moves upward,and the internal deformation decreases.When the internal pressure ranges from 0 to 1.0 MPa,the terminal radial stiffness of the compensator decreases linearly from 55.03 N/mm to 15.07 N/mm according to finite element analysis,and from 63.49 N/mm to 20.17 N/mm according to experimental measurements,showing a highly consistent trend.The established stiffness model and correction coefficients can effectively predict the radial stiffness of the compensator,providing a reference for the structural optimization design and thrust correction of similar compensators.