摘要
基于非线性振动理论建立了气膜-密封环系统角向摆动的动力学模型,将气膜厚度表示为含有摆角的变量,在介质压力p0=4.5852MPa、转速nr=10380 r/min的特例下计算并拟合非线性气膜的角向刚度,得到了一个含二次、三次项的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问题,分析了螺旋角对系统稳定性的影响,给出了使干气密封系统稳定的螺旋角的范围(α<75°10′34″),并求得在特例下螺旋角α=75°10′34″时系统发生Hopf分岔。这与已有文献中利用Runge-Kutta法研究的结果是一致的,从而验证了本文方法的正确性。改变工况后,对系统分岔问题进行了讨论,得到了系统分岔时的螺旋角数值,结果表明其螺旋角数值基本不变(α为75°9′54″或75°11′1″),说明改变工况后其分岔点位置不变。本文结果可为干气密封的动态优化设计提供理论指导。
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.
出处
《应用力学学报》
CAS
CSCD
北大核心
2013年第4期604-607,651,共4页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(50965010)
关键词
干气密封
非线性
角向刚度
稳定性
分岔
dry gas seals
nonlinear
angular rigidity
stability
bifurcation.
