A Two-Scale Dynamic Friction Model Incorporating Measured Roll Roughness for Mixed-Lubricated Cold Rolling Interfaces

Friction at the cold rolling interface is affected jointly by the surface roughness, lubrication state, local pressure, and relative sliding. A constant friction coefficient is therefore insufficient to describe its non-uniform distribution along the contact arc. Accordingly, this study proposes a macro–micro two-scale mixed-lubrication and dynamic friction model based on the measured roll roughness. First, the measured roll roughness profile was represented within a finite effective scale interval by a scaled and truncated Weierstrass–Mandelbrot (W–M) function. The parameters D and G were obtained as finite-scale W–M roughness parameters and were introduced into a mixed-lubrication load-sharing model to calculate the local mixed-lubrication friction coefficient. The pressure distribution along the contact arc was calculated using the Karman equation, and the local macroscopic pressure was mapped to a representative microscopic contact load. Finally, the mixed-lubrication friction coefficient was used to calibrate the dynamic friction factor separately in the forward-slip and backward-slip zones, and the friction stress distribution along the contact arc was calculated. For the selected effective scale interval and preprocessing procedure, the fitted W–M roughness parameters were D = 1.528 and G = 9.15 × 10−8 m. The W–M parameter D had a more significant influence on the mixed-lubrication friction coefficient and load-sharing behavior than the scale parameter G. Increasing the rolling speed strengthened the oil-film load-carrying effect and reduced the equivalent interfacial friction coefficient. The friction stress was positive in the backward-slip zone and negative in the forward-slip zone, with a direction reversal near the neutral point. Field forward-slip inversion showed that both the simulated and measured equivalent friction coefficients decreased with increasing rolling speed, with a difference of approximately 0.009~0.017. The proposed model can capture the main trend of cold rolling interfacial friction with variations in the rolling speed and contact state.