Analytical model of Johnson–Kendall–Roberts adhesive contact with coating roughness on the release of test mass in TianQin

Abstract

The surface of the coating or substrate structure has a rough topological structure over multiple scales, which significantly affects the actual contact area and adhesion strength. In order to investigate potential interferences during the test mass (TM) release process of the locking and release mechanism in TianQin space-borne gravitational wave detection project, an analytical model of the Johnson–Kendall–Roberts (JKR) adhesive contact with coating roughness between the TM and the release tip has been developed. This work presents the integration of the JKR theory with the Greenwood–Williamson rough surface contact theory to address adhesion challenges and influence of roughness in space-borne gravitational wave detection systems. The comprehensive model can be used to analyze how various factors such as surface shape, material properties, coating thickness and roughness affect adhesion. By introducing a numerical approach based on the Newton down-hill method to solve coupled equations for gap, stress, and load balance, the model achieves high-precision predictions of adhesion behavior under multi-scale roughness effects. By establishing relationships between force, contact half-width, and penetration depth, it provides a theoretical basis for optimizing the TM release process and the design of the locking and release mechanism. Future work will validate predictions via high-precision torsion pendulum experiments.