Design/methodology/approach A two-dimensional orthogonal cutting thermo-mechanical coupled finite element model is established in this study. The tanh material constitutive model is used to simulate the mechanical properties of the material. Velocity-dependent friction model between the workpiece and the tool is considered. Material characteristics such as material damage, stiffness degradation, equivalent plastic strain and temperature field during cutting are evaluated through computation. Contact pressure and shear stress on the tool surface are extracted for friction analysis. Findings Speed-dependent friction models predict cutting force errors as low as 8.6%. The prediction errors of various friction models increase with increasing cutting forces and depths of cut, and simulation results tend to be higher than experimental data. Social implications The current research results provide insights into understanding and controlling tool-chip friction in metal cutting, offering practical recommendations for friction modeling and machining simulation work. Originality/value The originality of this research is guaranteed, as it has not been previously published in any journal or publication. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0162/