A Ubiquitiform Model for Thermo-elastoplastic Normal Contact Stiffness at Micro/Macro Scales in Thermal Machinery

Existing fractal contact models for normal stiffness suffer from the scale paradox, rely on parameters that are difficult to measure, and yield unstable predictions under thermo-mechanical loads. To overcome these issues, this study systematically extends the ubiquitiform theory to thermo-elastoplastic contact stiffness modeling. Methodologically, the proposed approach proceeds in three steps: (1) starting from the thermo-mechanical elastoplastic analysis of a single asperity, the supremum (maximum contact area) and infimum (minimum contact area) of the ubiquitiform framework are extended from 1D profiles to 2D contact domains, where the infimum is directly linked to machining accuracy or instrument resolution; (2) based on the standard area-distribution density function of asperities, the stiffness contributions of all elastically deformed asperities are integrated over the range [α c , α l ], enabling a rigorous micro-to-macro scale transition; (3) a mechanical load proportionality coefficient f 1 is introduced to obtain a more compact analytical expression, and an explicit model incorporating the real contact area A is further constructed. The derived closed-form solution shows that the overall stiffness k n is linearly proportional to ΔT and (2 f 1 +1), follows a power-law decay with G, and exhibits negligible dependence on the supremum α l . Over the parameter ranges examined (ΔT = 50~300 K, D= 1.2~1.8, f 1 = 0.2~10), k n increases significantly with A, D, and ΔT, and decreases with G Compared with the classical fractal model, the ubiquitiform prediction is consistently lower, effectively removing the overestimation caused by non-physical infinitesimal asperities. This study provides a new theoretical tool for calculating the thermo-elastoplastic normal contact stiffness of such joints, with the model featuring measurable parameters, physical soundness, and computational robustness.