基于库伦摩擦效应的径向气体箔片轴承-转子系统振动特性
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摘要
动压气体箔片轴承较滚动轴承具有的运转速度高、无污染、回转精度高、运行寿命长、高温低温等极限环境适应性强等诸多优点使其在航空航天、低温制冷等关键领域具有广阔的发展前景和重要的应用价值。波箔型径向气体箔片轴承的弹性表面自适应性以及箔片结构内部干摩擦给轴承带来高转速、强稳定性等优点的同时也给轴承箔片结构理论建模带来了难度。本文针对轴承箔片结构内部的摩擦问题展开研究，从箔片轴承理论建模和数值计算方法等基本问题出发，分析了箔片结构内部摩擦效应对轴承静动态特性的影响，并在此基础上搭建了轴承性能测试试验台和轴承-转子系统特性试验台，对箔片轴承进行试验研究,为气体箔片轴承箔片结构摩擦特性提供新的研究方法和手段。
基于有限单元法建立了充分考虑箔片结构内部摩擦效应的波纹箔片刚度理论计算模型，研究了摩擦效应对波纹箔片刚度特性的影响，分析结果表明箔片结构的库伦摩擦效应在一定程度上增大了波纹箔片的刚度，波纹箔片库伦摩擦模型具有比文献线性弹簧更复杂的刚度特性。
在建立了考虑平箔片剪切刚度和箔片结构摩擦效应的箔片结构有限元模型的基础上，采用有限单元法（FEM）和有限差分法（FDM）耦合求解Reynolds方程和气膜厚度方程，研究了平箔片剪切刚度以及箔片结构库伦摩擦效应对轴承静态特性的影响，并将计算结果与NASA试验数据对比验证了箔片结构模型以及数值仿真方法的正确性。
基于小扰动法，结合气体Reynolds方程、气膜压力、气膜厚度和箔片变形之间的数学关系推导出轴承动力学特性系数计算微分方程，通过有限差分法对其进行求解得到不同箔片结构摩擦系数条件下轴承动力学特性系数，获得了波纹箔片摩擦效应对轴承气膜刚度和阻尼系数的影响规律。
根据有限元法建立实际的波箔型径向气体箔片轴承-转子系统模型，结合轴承在各个转速下的刚度和阻尼系数，通过求解转子系统频率方程分析了箔片结构摩擦效应对箔片轴承-转子系统前三阶临界转速的影响。利用Newmark数值计算方法分析了轴承-转子系统的动力学稳定性，结果表明轴承支承处振动幅值随着转速的升高而降低，虽然高速转速较低转速时振动出现低频分量，但轴心轨迹重复性好，并且波纹箔片和轴承壳之间摩擦系数越小，轴承-转子系统稳定性越高。
设计并建立了波箔型径向气体箔片轴承特性测试试验台，通过改变轴承壳圆柱孔内表面粗糙度，提出了一种研究箔片结构摩擦效应对波箔型径向气体箔片轴承特性影响的试验方法，并对箔片轴承静刚度、起飞转速、极限承载力和轴承动力学特性系数进行了测试，结果表明降低轴承壳圆柱孔内表面粗糙度能够减小轴承静刚度，使得箔片轴承的悬浮转速降低，减少了轴承启停时表面磨损，延长了轴承寿命，同时还能够有效提高轴承极限承载力，为提高箔片轴承承载力提供新的思路。
设计并搭建了波箔型径向气体箔片轴承-转子系统试验台，基于振动频率和平箔片温度测量准确判断了转子起飞转速，重点分析了波纹箔片和轴承壳之间摩擦效应对转子系统动力学特性的影响。通过降低轴承壳内表面粗糙度有效消除了转子高频振动，提高了转子系统运行稳定性，为提高箔片轴承-转子系统运行稳定性提供了新的方法。
Because of its many outstanding advantages compared with rolling bearingssuch as high speed, pollution free, high precision turning, long operating life, limitenvironment adaptability like high and low temperature, the hydrodynamic gas foilbearings have vast potential for future development and important valuableapplication in those fields including avigation, aerospce engineering, cryogenics andrefrigeration. The elastic surface self-adaptivity and foil structural dry fricition notonly make the bearing run in high speed and have strong rotating ability, but alsomake it difficult to establish theoretical model of bearing foil structure. In this paper,the internal friction effects in bearing foil strucure are investigated. Firstly, the foilbearing theoretical model is established and numerical algorithm analytical solutionis presented. Based on it the effects of internal friction in foil structure on static anddynamic characteristics of foil bearing are analyzed. Furthermore, the experimentalstudy of static and dynamic charactristics of foil bearing and dynamic performanceof bearing-rotor system provides a new method for research of frictioncharacteristics of foil structure in gas foil bearing.
The theoretical calculation model of bump foil stiffness including foilstructural internal friction effects is developed by finite element method and theeffects of Coulomb friction on stiffness of bump foil are studied. The results indicatethat Coulomb friction force can enhance the stiffness of bump foil and the stiffnesscharacteristic of bump foil Coulomb friction model is more complex than linearspring stiffness model that in literatures.
On the basis of establishing the foil structural finite element model with theconsideration of shear stiffness in top foil and foil structural friction effects, thecompressible gas lubricated Reynolds equation and film thickness equation aresolved together by using finite element mothod and finite difference method, thenthe effects of shear sthiffness in top foil and Coulomb friction in foil structure onbump foil static performance are studied. The accuracy of foil structural model andnumerical algorithm analytical solution are verified via comparing numerical resultswith test data from NASA.
Differential equations for calculation of bump foil bearing dynamiccharacteristics are derived from air Reynolds equation, air pressure, gas filmthickness and bump foil deformation by using perturbation method. The effects ofCoulomb friction in foil structure on bump foil stiffness and damping coefficientsare studied via comparing of dynamic characteristics of bump foil bearing withdifferent foil structural friction coefficients.
The practical bump type gas foil journal bearing-rotor system model is built.The critical speeds of rotor system are solved and the effects of foil structure frictionon critical speeds of rotor system are studied by solving rotor system frequencyequation combined with stiffness and damping coefficients of bearing at variousspeeds. The hydrodynamics of bearing-rotor system are analyzed by using Newmarkmethod. It shows that the vibration values at bearing supports decrease with theincreasing of rotor speed. Although some low frequency components occur at highrotating speed, but the shaft orbit has good repeatability and gas foil bearing-rotorsystem has good rotating stability at high speed.
A bump type gas foil journal bearing performance test-bed is designed and built.A test method for studying effects of foil structure friction on performance of bumptype gas foil journal bearing is proposed by changing the roughness of bearinghousing cylindrical hole surface. The bearing performance including bearing staticstiffness, lift-off speed, limiting load capacity and dynamic coefficients are test andit indicates that reducing roughness of bearing housing cylindrical hole surface canweaken the bearing static stiffness, decrease the lift off speed, reduce the bearingsurface wear at start and stop stage and extend bearing life. Furthermore, decreasethe foil structural friction force can enhance bearing limiting load capacityeffectively and it can provide a new idea to improve the capacity pf gas foil bearing.
A test-bed is developed for bump type gas foil bearing-rotor system. Thevibration frequency and foil temperature measurement can both determine thelift-off speed. The effects of friction between bump foil and bearing housing ondynamic performance of rotor system are analyzed. Reducing roughness of bearinghousing cylindrical hole surface can effectively eliminate high frequency vibrationand improve the stability of rotor system and it provides a new approach to improvethe stability of foil bearing-rotor system.
基于有限单元法建立了充分考虑箔片结构内部摩擦效应的波纹箔片刚度理论计算模型，研究了摩擦效应对波纹箔片刚度特性的影响，分析结果表明箔片结构的库伦摩擦效应在一定程度上增大了波纹箔片的刚度，波纹箔片库伦摩擦模型具有比文献线性弹簧更复杂的刚度特性。
在建立了考虑平箔片剪切刚度和箔片结构摩擦效应的箔片结构有限元模型的基础上，采用有限单元法（FEM）和有限差分法（FDM）耦合求解Reynolds方程和气膜厚度方程，研究了平箔片剪切刚度以及箔片结构库伦摩擦效应对轴承静态特性的影响，并将计算结果与NASA试验数据对比验证了箔片结构模型以及数值仿真方法的正确性。
基于小扰动法，结合气体Reynolds方程、气膜压力、气膜厚度和箔片变形之间的数学关系推导出轴承动力学特性系数计算微分方程，通过有限差分法对其进行求解得到不同箔片结构摩擦系数条件下轴承动力学特性系数，获得了波纹箔片摩擦效应对轴承气膜刚度和阻尼系数的影响规律。
根据有限元法建立实际的波箔型径向气体箔片轴承-转子系统模型，结合轴承在各个转速下的刚度和阻尼系数，通过求解转子系统频率方程分析了箔片结构摩擦效应对箔片轴承-转子系统前三阶临界转速的影响。利用Newmark数值计算方法分析了轴承-转子系统的动力学稳定性，结果表明轴承支承处振动幅值随着转速的升高而降低，虽然高速转速较低转速时振动出现低频分量，但轴心轨迹重复性好，并且波纹箔片和轴承壳之间摩擦系数越小，轴承-转子系统稳定性越高。
设计并建立了波箔型径向气体箔片轴承特性测试试验台，通过改变轴承壳圆柱孔内表面粗糙度，提出了一种研究箔片结构摩擦效应对波箔型径向气体箔片轴承特性影响的试验方法，并对箔片轴承静刚度、起飞转速、极限承载力和轴承动力学特性系数进行了测试，结果表明降低轴承壳圆柱孔内表面粗糙度能够减小轴承静刚度，使得箔片轴承的悬浮转速降低，减少了轴承启停时表面磨损，延长了轴承寿命，同时还能够有效提高轴承极限承载力，为提高箔片轴承承载力提供新的思路。
设计并搭建了波箔型径向气体箔片轴承-转子系统试验台，基于振动频率和平箔片温度测量准确判断了转子起飞转速，重点分析了波纹箔片和轴承壳之间摩擦效应对转子系统动力学特性的影响。通过降低轴承壳内表面粗糙度有效消除了转子高频振动，提高了转子系统运行稳定性，为提高箔片轴承-转子系统运行稳定性提供了新的方法。
Because of its many outstanding advantages compared with rolling bearingssuch as high speed, pollution free, high precision turning, long operating life, limitenvironment adaptability like high and low temperature, the hydrodynamic gas foilbearings have vast potential for future development and important valuableapplication in those fields including avigation, aerospce engineering, cryogenics andrefrigeration. The elastic surface self-adaptivity and foil structural dry fricition notonly make the bearing run in high speed and have strong rotating ability, but alsomake it difficult to establish theoretical model of bearing foil structure. In this paper,the internal friction effects in bearing foil strucure are investigated. Firstly, the foilbearing theoretical model is established and numerical algorithm analytical solutionis presented. Based on it the effects of internal friction in foil structure on static anddynamic characteristics of foil bearing are analyzed. Furthermore, the experimentalstudy of static and dynamic charactristics of foil bearing and dynamic performanceof bearing-rotor system provides a new method for research of frictioncharacteristics of foil structure in gas foil bearing.
The theoretical calculation model of bump foil stiffness including foilstructural internal friction effects is developed by finite element method and theeffects of Coulomb friction on stiffness of bump foil are studied. The results indicatethat Coulomb friction force can enhance the stiffness of bump foil and the stiffnesscharacteristic of bump foil Coulomb friction model is more complex than linearspring stiffness model that in literatures.
On the basis of establishing the foil structural finite element model with theconsideration of shear stiffness in top foil and foil structural friction effects, thecompressible gas lubricated Reynolds equation and film thickness equation aresolved together by using finite element mothod and finite difference method, thenthe effects of shear sthiffness in top foil and Coulomb friction in foil structure onbump foil static performance are studied. The accuracy of foil structural model andnumerical algorithm analytical solution are verified via comparing numerical resultswith test data from NASA.
Differential equations for calculation of bump foil bearing dynamiccharacteristics are derived from air Reynolds equation, air pressure, gas filmthickness and bump foil deformation by using perturbation method. The effects ofCoulomb friction in foil structure on bump foil stiffness and damping coefficientsare studied via comparing of dynamic characteristics of bump foil bearing withdifferent foil structural friction coefficients.
The practical bump type gas foil journal bearing-rotor system model is built.The critical speeds of rotor system are solved and the effects of foil structure frictionon critical speeds of rotor system are studied by solving rotor system frequencyequation combined with stiffness and damping coefficients of bearing at variousspeeds. The hydrodynamics of bearing-rotor system are analyzed by using Newmarkmethod. It shows that the vibration values at bearing supports decrease with theincreasing of rotor speed. Although some low frequency components occur at highrotating speed, but the shaft orbit has good repeatability and gas foil bearing-rotorsystem has good rotating stability at high speed.
A bump type gas foil journal bearing performance test-bed is designed and built.A test method for studying effects of foil structure friction on performance of bumptype gas foil journal bearing is proposed by changing the roughness of bearinghousing cylindrical hole surface. The bearing performance including bearing staticstiffness, lift-off speed, limiting load capacity and dynamic coefficients are test andit indicates that reducing roughness of bearing housing cylindrical hole surface canweaken the bearing static stiffness, decrease the lift off speed, reduce the bearingsurface wear at start and stop stage and extend bearing life. Furthermore, decreasethe foil structural friction force can enhance bearing limiting load capacityeffectively and it can provide a new idea to improve the capacity pf gas foil bearing.
A test-bed is developed for bump type gas foil bearing-rotor system. Thevibration frequency and foil temperature measurement can both determine thelift-off speed. The effects of friction between bump foil and bearing housing ondynamic performance of rotor system are analyzed. Reducing roughness of bearinghousing cylindrical hole surface can effectively eliminate high frequency vibrationand improve the stability of rotor system and it provides a new approach to improvethe stability of foil bearing-rotor system.
引文
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