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In this study, the formula to calculate the impact factor of fluid–solid coupling (ξ) was proposed in order to describe the fluid–solid strong coupling relationship of the whole system in a more realistic way based on the strong fluid–solid coupling problem between magnetorheological fluid and the surface of a brake disc due to the shearing friction in braking process. The magnetorheological fluid was considered using a Herscher–Bulkley model according to the structural features and fluid properties of the magnetorheological braking system with double coils placed on the side housing. Next, a correlation between the constitutive equations of the mechanical and thermal fields was established by analyzing their interaction parameters. The numerical simulation of the distribution disciplinarian of the mechanical and thermal fields in strong coupling was studied using COMSOL Multiphysics software. Experimental results have been compared with the simulations in terms of the surface temperature in braking process. The mathematical expression on the impact factor of coupling (ξ) depending on braking time (t) has been obtained by a numerical analysis. Simulation results revealed that the impact factor of coupling (ξ) decreased with the braking time (t). However, the change rate of function decreases first and then increases with time. There also exists an inflection point at t = 1.9025 in the function ξ of t and a strong nonlinear coupling relationship between the mechanical and thermal fields based on the inflection point properties of the function is found. In addition, all the maximum relative errors are less than 5%, which also reveals that there is a good agreement between the simulation and experimental results. This work can provide insights useful to solving complex multi-physics problems with strong coupling.

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