动静压轴承非线性轴心轨迹的计算与仿真
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摘要
滑动轴承的轴心轨迹反映了轴承的工作状态。通过对轴心轨迹的研究,可以确定轴承的回转精度和最小油膜厚度,可以判定轴承转子系统的稳定性和轴承设计参数的合理性。通过对动静压轴承采用主动控制技术,可以实现轴颈轴心做预定椭圆运动,进而可以实现非圆异性零件的加工。本文以四油腔有回油槽的动静压轴承为研究对象,建立了非线性轴心轨迹的计算模型,计算了一定工况下毛细管节流的动静压轴承油膜压力分布和非线性轴心轨迹,研究了转子转速、供油压力、轴承半径间隙对非线性轴心轨迹的影响,计算了动载荷下轴心轨迹的变化规律,并对轴心轨迹正弦激振实验进行了仿真。
首先,建立了动静压轴承数学模型,根据雷诺方程和流量平衡方程,采用有限差分法,计算了毛细管节流的动静压轴承油膜压力分布。基于非线性油膜力,轴颈惯性力和动载荷三者之间的平衡关系,建立了轴承转子系统的运动方程,建立了非线性轨迹计算模型。采用欧拉方法计算出了非线性轴心轨迹。为了便于比较非线性模型,采用油膜力线性化方法,建立了轴心在平衡位置附近小位移涡动的线性分析模型,采用差分法计算了轴心在平衡位置时的油膜刚度系数和阻尼系数,再根据线性化运动方程计算了线性轴心轨迹。
其次,分别计算了在不同转速,不同供油压力,不同轴承半径间隙下其他工况条件不变时毛细管节流动静压轴承的非线性轴心轨迹,分析了它们对轴心平衡位置的影响,计算出了轴承系统的临界转速。
接着,研究了阶跃载荷、矩形脉冲载荷、正弦脉冲载荷作用下轴心非线性轨迹,轴心非线性位移,最大油膜压力等主要参数随时间的变化规律。轴承系统稳定的情况下,阶跃载荷使得轴心收敛于新的平衡位置,由于矩形脉冲和正弦脉冲载荷作用在轴上的时间短,载荷消失后,轴心轨迹仍然收敛到原来的平衡位置。
最后,以动静压轴承转子系统为研究对象,仿真了在虚拟正弦激振力下系统的动态特性和共振现象,采用MATLAB计算仿真了正弦载荷激励下系统的幅频特性,得出系统的幅频特性曲线和激振响应共振频率
The journal centre motion trajectory reflects the working condition of the bearing. Based on the research of the journal centre motion trajectory, we can determine the bearing rotation accuracy and minimum oil film thickness, we can judge the stability of rotor and the rationality of the bearing design parameters. By using Hybrid Bearing Active Control Technology, journal centre doing predetermined elliptical motion can be achieved, and we can also achieve the machining of Non-circular complex parts. So we take the four oil cavity Hybrid bearings with the oil grooves as the research object; calculated the oil film pressure distribution and non-linear journal centre motion trajectory of Capillary restrictor under the certain conditions; and researched the influence of the rotor speed, oil pressure, bearing radius clearance for non-linear journal centre motion trajectory, the author also calculated the variation of non-linear journal centre motion trajectory under dynamic loading,and simulated the vibration experiment of the journal centre motion trajectory
Firstly, the Hybrid Bearing mathematical model is established. Using the finite difference method, calculate the hybrid bearing of capillary throttling oil film pressure distribution by the Reynolds equation and flow equilibrium equations. The equation of motion of the rotor-bearing system is established, which is based on the nonlinear oil film force, journal inertial force and dynamic load. The nonlinear journal centre motion trajectory is calculated by using the Euler method. In order to compare the nonlinear model with the linear model, we established the linear model; calculated the stiffness and damping coefficients using finite difference method and calculated the linear journal centre motion trajectory which is eddy's moving near the equilibrium position for small displacement by using the oil film force linearization method.
Secondly, nonlinear journal centre motion trajectory is calculated under different speed, different oil pressure and different bearing radius clearance. We also analyzed their influence on journal centre equilibrium position, and calculated the critical speed of the bearing system.
Thirdly, we researched change rule of nonlinear journal centre trajectory, nonlinear journal centre trajectory displacement, the maximum film pressure and minimum film thickness under step load, rectangular pulse load, sinusoidal pulse load over time. Step load makes the journal centre converge to a new equilibrium position. Because of the short time of rectangular pulse and the sinusoidal pulse to the journal, the journal centre motion trajectory will still converge to the original equilibrium position with the load disappearing.
Finally, taking the Hybrid bearing system as the research object, system dynamics process and the resonance phenomenon are studied under sinusoidal excitation force. We simulated the system's amplitude-frequency characteristics and obtained amplitude-versus-frequency curve and the resonance frequencies using MATLAB under virtual sinusoidal force.
首先,建立了动静压轴承数学模型,根据雷诺方程和流量平衡方程,采用有限差分法,计算了毛细管节流的动静压轴承油膜压力分布。基于非线性油膜力,轴颈惯性力和动载荷三者之间的平衡关系,建立了轴承转子系统的运动方程,建立了非线性轨迹计算模型。采用欧拉方法计算出了非线性轴心轨迹。为了便于比较非线性模型,采用油膜力线性化方法,建立了轴心在平衡位置附近小位移涡动的线性分析模型,采用差分法计算了轴心在平衡位置时的油膜刚度系数和阻尼系数,再根据线性化运动方程计算了线性轴心轨迹。
其次,分别计算了在不同转速,不同供油压力,不同轴承半径间隙下其他工况条件不变时毛细管节流动静压轴承的非线性轴心轨迹,分析了它们对轴心平衡位置的影响,计算出了轴承系统的临界转速。
接着,研究了阶跃载荷、矩形脉冲载荷、正弦脉冲载荷作用下轴心非线性轨迹,轴心非线性位移,最大油膜压力等主要参数随时间的变化规律。轴承系统稳定的情况下,阶跃载荷使得轴心收敛于新的平衡位置,由于矩形脉冲和正弦脉冲载荷作用在轴上的时间短,载荷消失后,轴心轨迹仍然收敛到原来的平衡位置。
最后,以动静压轴承转子系统为研究对象,仿真了在虚拟正弦激振力下系统的动态特性和共振现象,采用MATLAB计算仿真了正弦载荷激励下系统的幅频特性,得出系统的幅频特性曲线和激振响应共振频率
The journal centre motion trajectory reflects the working condition of the bearing. Based on the research of the journal centre motion trajectory, we can determine the bearing rotation accuracy and minimum oil film thickness, we can judge the stability of rotor and the rationality of the bearing design parameters. By using Hybrid Bearing Active Control Technology, journal centre doing predetermined elliptical motion can be achieved, and we can also achieve the machining of Non-circular complex parts. So we take the four oil cavity Hybrid bearings with the oil grooves as the research object; calculated the oil film pressure distribution and non-linear journal centre motion trajectory of Capillary restrictor under the certain conditions; and researched the influence of the rotor speed, oil pressure, bearing radius clearance for non-linear journal centre motion trajectory, the author also calculated the variation of non-linear journal centre motion trajectory under dynamic loading,and simulated the vibration experiment of the journal centre motion trajectory
Firstly, the Hybrid Bearing mathematical model is established. Using the finite difference method, calculate the hybrid bearing of capillary throttling oil film pressure distribution by the Reynolds equation and flow equilibrium equations. The equation of motion of the rotor-bearing system is established, which is based on the nonlinear oil film force, journal inertial force and dynamic load. The nonlinear journal centre motion trajectory is calculated by using the Euler method. In order to compare the nonlinear model with the linear model, we established the linear model; calculated the stiffness and damping coefficients using finite difference method and calculated the linear journal centre motion trajectory which is eddy's moving near the equilibrium position for small displacement by using the oil film force linearization method.
Secondly, nonlinear journal centre motion trajectory is calculated under different speed, different oil pressure and different bearing radius clearance. We also analyzed their influence on journal centre equilibrium position, and calculated the critical speed of the bearing system.
Thirdly, we researched change rule of nonlinear journal centre trajectory, nonlinear journal centre trajectory displacement, the maximum film pressure and minimum film thickness under step load, rectangular pulse load, sinusoidal pulse load over time. Step load makes the journal centre converge to a new equilibrium position. Because of the short time of rectangular pulse and the sinusoidal pulse to the journal, the journal centre motion trajectory will still converge to the original equilibrium position with the load disappearing.
Finally, taking the Hybrid bearing system as the research object, system dynamics process and the resonance phenomenon are studied under sinusoidal excitation force. We simulated the system's amplitude-frequency characteristics and obtained amplitude-versus-frequency curve and the resonance frequencies using MATLAB under virtual sinusoidal force.
引文
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[2]王朝晖,张来斌,万波.基于轴心轨迹的滑动轴承承运行稳定性综合评价方法[J].煤炭学报,2007,32(12)：1328-1333
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[4]肖圣光.旋转机械轴心轨迹识别方法研究[J].中国测试,2009,35(2)：7-10
[5]邓中亮,王先逵.异形零件的几种车削加工方法[J].机械制造,1994,(1)14-16
[6]张凯,胡德金,马浩全.新型活塞异形销孔加工方法[J].上海交通大学学报,2003,(37)29-32
[7]张凯,胡德金,杨亚川.异形销孔加工及控制方法研究[J].机械设计与研究,2004,20(1)：58-59
[8]邓中亮.非圆截面工件加工法的发展[J].制造技术与机床,1996,(9)：48-50
[9]王海峰,胡德金.基于磁悬浮主轴的活塞异形销孔加工原理研究[J].内燃机工程,2006,27(3)：54-57
[10]邬义杰,项占琴.基于超磁致伸缩材料的活塞异形销孔加工原理研究[J].浙江大学学报,2004,38(9)：1185-1189
[11]刘学忠.主动混合滑动轴承-转子系统运动轨迹控制技术研究[D].山东大学博士学位论文,2008.10：1
[12]B.Tower,First Report on Friction Experienments[C].Proc,Inst,Mesh,Engrs.1883.36-58
[13]SommerfeldA.Zur Hydrodynamischen Theorie der Schmiermittlreibung.Z Math u physic.1904,50:97-105
[14]Reynolds O. On the Theory of Lubrication and its Applications to Mr.Beauchamp Tower's Experiments including an Experimental Determination of the Viscosity of Olive Oil[J].Phil Trans Roy Soc.1886,177 (1):157-234
[15]Kingsbury A.Trans[C].ASME 1931,53-59.
[16]Christopherson D G. Proc[C].Institutions of Mech.Eng,1942,146
[17]Dubois G B, Ocvirk F W. Analytical Derivation and Experimental Evaluation of Short Bearing Approximations for full Journal of Tribology.1993,(115):355-363
[18]Sternlicht, Michel A G.Trans[C].ASME 1929,51,53
[19]Guo, Zenglin, Hirano, Toshio, et al. Application of CFD analysis for rotating machinery, part 1:Hydrodynamic, hydrostatic bearings and squeeze film damper[C].American Society of Mechanical Engineers, International Gas Turbine Institute, Turbo Expo (Publication) IGTI, 2003,4:651-659
[20]高庆水,刘松平,蒋小文等.基于CFD方法的液体动压滑动轴承动特性研究[J].润滑与密封,2008,33(9)：65-67
[21]刘松平,基于计算流体力学方法的动静压轴承研究[J].铜业工程,2008,4：64-66
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