Abstract: A modified generalized Reynolds equation is derived with the second-order nonlinear slip boundary condition, and the approximate analytic gas film thrust is obtained by solving the nonlinear Reynolds equation with the linear PH method and iterative method. Then, the approximate analytic gas film stiffness is obtained by gas film thrust derivativing of the gas film thickness. Maple program developed with this proposed method is used to compute the gas film stiffness values under the different rotational speed and pressure of an engineering instance, and it is compared to the results obtained with the first-order linear slip boundary conditions and the experimental measurements. The results demonstrate that the gas film stiffness values estimated with the second-order nonlinear slip boundary condition decreases with the gas film thickness increasing, and it is the nonlinear relationship between the stiffness and thickness of gas, and the gas film stiffness increases with the pressure and rotate speed of the medium increasing, and it is the linear relationship between the gas film stiffness and the pressure and rotate speed of the medium, and the gas film stiffness values estimated with the second-order nonlinear slip boundary condition are closer to the experimental values than that estimated with the first-order linear slip boundary condition, and it has the higher calculation accuracy. Especially in low-speed and low-pressure conditions, the estimated values with second-order nonlinear slip boundary condition are significant better than with the first-order linear slip boundary condition. The optimization design by hydromechanics theory with the second-order nonlinear slip boundary condition in shaft dry gas seal of the low-speed and low-pressure conditions can guide engineering application.

Key words: Dry gas seals, Gas film stiffness, Maple program, Nonlinear slip boundary, Spiral groove