A Hyperbolic Contact Surface Winkler Contact Force Model for Spherical Clearance Joints

Spherical clearance joints are essential for the successful deployment of space structures. When the clearance is small enough, the contacts will be considered conformal contact, which probably leads to inaccuracies in existing contact force models. To address the limitation, this paper proposes a novel hyperbolic contact surface Winkler model. First, a new fundamental formula incorporating a modified variable exponent is presented. Based on the surrogate modeling method, an optimized surrogate function for the variable coefficient is developed. In the optimization process, the finite element and response surface methods (RSMs) are introduced to improve the precision and reliability of the model. Compared with previous models, this paper organizes a detailed discussion and evaluation to validate the accuracy and application of the new proposed model, after which a dynamic example demonstrates the model's effectiveness. The results highlight the model's accuracy and practical efficacy, showing a strong correlation and minimal margin of error, especially when compared to finite element method (FEM) results. This improvement is attributed to the refined variable exponent, which accurately characterizes the relationship between contact force and penetration depth, and the optimized variable coefficient, which fine-tunes the contact force magnitude. Additionally, the model's versatility extends beyond the geometric properties of the contact bodies, offering a broad application scope. As a foundation of precise impact modeling, it is crucial to address the structural dynamic challenges inherent in high-precision space structures.