In order to investigate the rotational speed ratio at equilibrium,tribological properties,and oil film pressure distribution of the floating ring bearing of an 215.9 mm cone bit with an inner and outer gap ratio under bottom pressure of well,Reynolds boundary conditions were modified by considering the actual downhole environmental pressure of the floating ring bearings and the seal pressure difference of the cone bit.The Reynolds equation of floating ring bearings was numerically solved by using the PDE Toolbox in MATLAB,and the influence of the internal and external gap ratios on the rotational speed ratio at equilibrium,oil film pressure,and friction coefficient of floating ring bearings was analyzed.The results show that when the ambient pressure is 60 MPa and the seal pressure difference is 20 MPa,the equilibrium rotational speed ratio of the floating ring increases first and then decreases with the increase of the inner and outer clearance ratios.Taking the bearing′s friction coefficient and oil film pressure as a comprehensive evaluation index,when the internal and external gap ratio of floating ring bearings is 2.0,the friction coefficient of the bearing is smaller,the pressure of the oil film is higher,and the overall performance of the bearing is better.When the internal and external gap ratio is 2.0,with the rise of environmental pressure,the torque and friction coefficient of the floating ring bearing increase,thereby accelerating the wear of the bearing.This study provides basic theoretical support for structural parameter optimization and performance improvement of cone-bit floating ring bearings under special boundary conditions.