热耗散变形下干气密封系统轴向振动稳定性分析

Stability analysis on axial vibration of dry gas seal system under the thermo-elastic deformation considering the thermal dissipation

基于非线性振动理论,建立了气膜-密封环系统轴向振动模型,同时考虑了热耗散有热弹变形对气膜厚度和刚度的影响。在特定的工况下,求解并拟合了非线性气膜的轴向刚度和阻尼,获得了一个非线性受迫振动微分方程。在无外激励情况下,通过求解Floquet指数,讨论了系统分岔的问题,分析了螺旋角对系统稳定性的影响,得到了干气密封系统稳定运行的螺旋角范围,并求得螺旋角为75°54′36″时系统发生Hopf分岔。将数据结果与无热耗散有热弹变形、无变形下的数据进行比较。研究结果表明:考虑热耗散有热弹变形下的系统稳定的螺旋角范围比无热耗散有热弹变形和无变形的螺旋角范围更大。热耗散热弹变形下发生Hopf分岔的分叉点位置相比无热耗散有热弹变形和无变形的分岔点更加突出。这与先前利用龙格-库塔法研究的结果一致,从而验证该方法的正确性。其结果说明,热耗散有热弹变形对干气密封系统的稳定运行有一定的干扰,对工程实际具有一定应用价值。

Based on the nonlinear vibration theory,the axial vibration model which is about the film and seal rings in the system of dry gas seals is established.In this model,the influence of the gas film thickness and gas film stiffness are considered by the thermal dissipation and thermal-elastic deformation.A forced vibration differential equation containing nonlinear terms is derived in consideration of the nonlinear axial rigidity and damping of the gas film for the specific working conditions.The bifurcation behavior in the dry gas seal system is discussed by the Floquet exponent in the case of without external excitation.Then the influence of the spiral angle on the stability of the dry gas seal system is is analyzed.According to the above data,the range of the spiral angle that guarantee the dry gas seal system stable is given.When the spiral angle is 75°54′36″,Hopf Bifurcation occurrs.The result is compared with those of thermal-elastic deformation without thermal dissipation and of non-thermal-elastic deformation,when the Hopf Bifurcation occurres as well.The results show that the range of the spiral angle which makes the dry gas seal system stable,under thermal-elastic deformation with thermal dissipation is different from that under the thermalelastic deformation without thermal dissipation and under non-thermal-elastic deformation.What＇s more,the range of the spiral angle which makes the dry gas seal system stableunder thermal-elastic deformation without thermal dissipation is closer to that under the thermal-elastic deformation with thermal dissipation.And the position of the Hopf bifurcation under thermal-elastic deformation with thermal dissipation is clearer than that under thermal-elastic deformation without thermal dissipation and nonthermal-elastic deformation.The result agree well with the result which is obtained by using the Runge-Kutta method,through which the validity of the method confirmed.Accordingly,in the future,the thermal-elastic deformation with thermal dissipation will become one of aspects which affect the stability of the dry gas seal system and will have application to the engineering practice.