Nonlinear stability analysis of angular wobbly in the dry gas seals system

Using the nonlinear oscillation theory,the dynamic angular wobbly model of the gas film and seal rings in the system of dry gas seals is established.Thickness of gas film is expressed as variable contains swing angle,then the nonlinear forced vibration differential equation contains the second and the third order is derived while the nonlinear angular rigidity of the gas film is calculated and simulated under the conditions of p 0 =4.5852MPa and n r =10380r/min.The bifurcation question is discussed through the solution of Floquet exponent,and the stability influenced by spiral angle is analyzed in the system,the range of the spiral angle α < 75 °1 0′ 3 4′′enable system stable is given on the condition of without outer excitation,when spiral angle α at 75°10′34″ the Hopf bifurcation occurs in the system.The method is verified as the result keeps consistent with the result by Runge-Kutta method.The bifurcation problem is discussed by changing conditions in the system,the value of the spiral angle when bifurcation occurred is obtained,the spiral angle value α = 75 °9 ′ 5 4′′and α = 75° 1 1′ 1′′is almost invariant.The result obtained shows that the bifurcation point unchanged as the condition change and it may provide guidance for the dynamic optimization in the dry gas seals system.