Based on the lubrication analysis model and dynamic characteristics mathematical model of foil dynamic pressure gas bearing,the dynamic equation of foil dynamic pressure gas bearing-rotor system was established combining Newton’s mechanical equation,and the calculation method of the stiffness and damping coefficient was studied.The vibration and speed of the foil dynamic pressure gas bearing-rotor system was tested,and the stiffness and damping coefficient was calculated.The linear and nonlinear instability phenomena of the foil dynamic pressure gas bearing-rotor system during the acceleration process was analyzed combining the mapping method,and the influence of speed on the stiffness and damping coefficient was studied.The results show that the main stiffness coefficient of the foil dynamic pressure gas bearing rotor-system increases with the increase of speed,while the cross stiffness decreases with the increase of speed and the trend of change is relatively gentle.The damping coefficient decreases with the increase of speed.The damping of the system suppresses disturbances and the accumulation of low-frequency energy,avoiding foil vibration and effectively improving the stability of the system operation.The proposed dynamic characteristic coefficient calculation method,combined with gas lubrication theory and dynamic model,and combined with experimental testing,can effectively obtain the dynamic characteristics of the bearing-rotor system.