Analysis Of Nonlinear Dynamic Characteristics Of Dry Gas Sealed Bellows Diaphragm

As an elastic supporting element in dry gas seal system,metal bellows not only buffer the axial displacement caused by dynamic wear and axial vibration of the system,but also the elastic force of bellows is used to seal the system.The elastic element bellows in the dry gas sealing structure is an important factor affecting the thickness of the sealing film.The nonlinear dynamic characteristics of single arc bellows diaphragms for dry gas seals are analyzed.According to the theory of nonlinear dynamics of plates and shells,ideology of continuous quasi-shell method is used,the single arc bellows diaphragm transformed into circular plate with initial deflection,nonlinear dynamical governing equations are established,boundary conditions and intial conditions of single arc bellows diaphragms are reasonably given.Under the condition of fixed outer edge and free inner edge of the diaphragm,the nonlinear lager deformation of the single arc bellows diaphragm and nonlinear natural frequency of the single arc bellows diaphragm and nonlinear stability of the single arc bellows diaphragm are studied.Firstly,the problem of nonlinear lager deformation of the single arc bellows diaphragm is studied.The single arc bellows diaphragm is regarded as the combined structure of the circular plate with initial deflection by method of simulated shell.By nonlinear large deflection bending theory,the nonlinear large deformation of single circular diaphragm is analyzed.The large deflection equation of the single arc bellows diaphragm is established.Using modified iteration method of theory of plates and shells,the nonlinear large deformation of a single circular arc bellows diaphragm with one end fixed and another end free is solved.By boundary conditions and continuity conditions,quadratic nonlinearity analytical solutions with higher accuracy are obtained.Again,the problem of nonlinear natural frequency of the single arc bellows diaphragm is solved.A mechanical model is established according to the force of the diaphragm.Taking advantage of the Hamiltonian principle,the nonlinear dynamic variation equation and coordination equation of the single circular-arc diaphragm under combined loading are obtained.Selecting the maximum amplitude of the single circular-arc bellows diaphragm as the perturbation parameter,the nonlinear nature frequency of a single circular-arc corrugated pipe diaphragm with one fixed and the other free is solved by using perturbation variation method.The natural frequency of the linear vibration of the single circular-arc diaphragm is obtained through the first approximation.Similarly,the natural frequency of the single circular-arc bellows diaphragm is received by the second approximation and the third approximation respectively.Finally,the problem of the nonlinear stability of the single arc bellows diaphragm is analyzed.Using the nonlinear bending theory of thin shell,the nonlinear dynamic equations of single circular arc diaphragm under synergistic effect of static-dynamic load are obtained.According to the boundary conditions and continuous conditions,the deflection and tension under the synergistic effect of static-dynamic load are obtained.The forced vibration equation of the nonlinear system of single arc bellows diaphragm is obtained based on the Galerkin methods.The bifurcation problem of the system without external excitation is studied and stability of the single arc bellows diaphragm at the equilibrium point is discussed by the Floquet index.The change of the equilibrium position of the system under pure dynamic load and coupling effect of static-dynamic load is considered.