基于非线性动态特性的轴承–转子系统振动分析
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摘要
随着空气静压主轴在超精密加工过程中的广泛应用,对主轴的运动精度的要求不断提高,如何准确预测和提高主轴运动精度是十分必要的。基于空气静压轴承的非线性动态特性,研究空气静压主轴的振动特性和预测模型,探索非线性动态特性分析对主轴回转精度的影响。首先,对空气静压径向轴承的动态特性进行分析,建立气膜动态流动模型,采用扰动法求解模型得到轴承的非线性动刚度与动阻尼系数。将空气静压轴承内的气膜作为弹簧阻尼系统建立轴承–转子系统,并通过动力学分析建立了轴承–转子的动态振动模型。将轴承的非线性动态特性参数引入振动模型,结合MATLAB对模型进行求解,得出了空气静压主轴径向跳动误差曲线、偏转误差曲线和径向总振动误差曲线,并通过FFT数据处理对振动进行频域分析。通过对比分析得到非线性分析对空气静压主轴径向振动误差的影响。最后,搭建了空气静压主轴径向回转误差测量试验台,得到主轴实时回转误差信号,实现轴承–转子系统的振动动力学模型分析的实验验证。从空气静压径向轴承的动态分析可以看出,轴承的动刚度和动阻尼均呈非线性变化,随着偏心率的增加动刚度不断增加,而动阻尼不断减小。从轴承–转子系统的振动分析可以看出:1)非线性分析对主轴偏角振动误差有明显影响,而对径向跳动误差的影响不明显,说明非线性分析主要通过影响主轴的偏角误差从而影响径向总误差。2)定值分析时偏角误差的最大振幅基本稳定,而非线性分析时偏角误差的最大振幅存在一个增加过程并最终趋于稳定,并且非线性分析时最大振幅明显大于定值分析时的振幅。3)在供气开始一段时间内,非线性分析与定值分析下的径向总误差基本一致,但随着时间的增加,非线性分析下的最大振幅大于定值分析下的最大振幅,说明开始供气时非线性分析对径向跳动误差和偏角误差没有造成明显影响,当供气稳定时非线性的动刚度与动阻尼会对主轴转子振动幅度产生明显影响。4)从频域上看,非线性分析最大振幅处的共振频率为964 Hz,定值分析最大振幅处共振频率为986 Hz,非线性分析使最大振幅处的共振频率有所下降。5)非线性分析和定值分析在频率高于1 500 Hz时,转子的振幅变化都很小,说明频率大于1 500 Hz之后,转子振动比较稳定,此时气膜的振动频率与固有频率不容易发生共振。空气静压主轴回转误差实验的结果表明,基于非线性分析所得的主轴径向回转误差的误差率比定值分析所得主轴径向回转误差的误差率降低了1.43%～6.54%。因此,将空气静压径向轴承内气膜作为弹簧阻尼系统施加于转子之上可以实现轴承–转子系统的耦合振动分析,轴承非线性动态特征参数的引入实现了轴承动态性能对主轴动态振动的影响,通过基于非线性动态特性的轴承–转子系统的振动分析可以更加准确地研究和预测空气静压主轴的径向振动误差。
With the wide application of the aerostatic spindle in the ultra-precision machining process, the requirements for the kinematic precision of the spindle are increasing. It is necessary to predict and improve the precision of the spindle motion accurately. Based on the nonlinear dynamic characteristics of the aerostatic bearing, the vibration characteristics and prediction model of the aerostatic spindle were studied, and the influence of the nonlinear dynamic characteristic analysis on the spindle rotary precision was explored. Firstly, the dynamic flow model of the gas film of the aerostatic journal bearing was established, the nonlinear dynamic stiffness and damping coefficients were obtained by the perturbation method. The gas film was used as the spring-damping system to build the bearing-rotor system, and the dynamic vibration model of bearing-rotor system was established by dynamic analysis. Then nonlinear dynamic parameters were introduced into the vibration model, and the curve of the radial runout error, the deflection error and the total error of radial vibration were obtained by solving the model with MATLAB. The frequency domain analysis were conducted on the vibration signal. Finally, Rotation Error Measurement experimental of spindle was performed to inspect the results of vibration error analysis. From the dynamic analysis of the aerostatic journal bearings, the dynamic stiffness and dynamic damping of the bearing are all nonlinear, and the dynamic stiffness increases with the increase of eccentricity, and the dynamic damping decreases. From the vibration analysis of the bearing-rotor system, the following conclusions can be obtained. 1) The nonlinear analysis has an obvious influence on the deflection error, but the influence on the radial runout error is not obvious. It shows that the nonlinear analysis mainly affects the deflection error of the spindle and thus affects the total radial error. 2) The maximum amplitude of the deflection error is basically stable when the fixed value analysis is analyzed, while the maximum amplitude of the deflection error has an increase process and tends to be stable at the time of nonlinear analysis, and the maximum amplitude of the nonlinear analysis is obviously larger than the amplitude of the constant value analysis. 3) The total radial error of the nonlinear analysis and the constant value analysis is basically the same at the beginning of the gas supply, but with the increase of time, the maximum amplitude under the nonlinear analysis is larger than the maximum amplitude under the constant value analysis, which shows that the nonlinear analysis has no obvious effect on the error of radial runout and the deviation angle when the gas supply is started. When the gas supply is stable, the nonlinear dynamic stiffness and dynamic damping will obviously affect the vibration amplitude of the rotor. 4) From the frequency domain, the resonance frequency at the maximum amplitude of the nonlinear analysis is 964 Hz, and the resonance frequency at the maximum amplitude of the constant value analysis is 986 Hz, and the nonlinear analysis reduces the resonance frequency at the maximum amplitude. 5) When the frequency is higher than 1 500 Hz, the amplitude change of the rotor is very small, which shows that the vibration of the rotor is more stable when the frequency is greater than 1 500 Hz, and the vibration frequency of the gas film is not easy to resonate with the natural frequency. Experimental results indicated that the error of radial rotation error of the spindle based on nonlinear analysis is reduced by 1.43% to6.54% compared to the constant value analysis. Therefore, the coupled vibration analysis of the bearing-rotor system can be achieved by applying the gas film as the spring-damping system to the rotor. The introduction of nonlinear dynamic characteristic parameters of bearing realizes the effect of bearing dynamic performance on spindle dynamic vibration. Based on nonlinear dynamic characteristics, the vibration analysis of the bearing-rotor system can more accurately analysis and predict the radial vibration error of the aerostatic spindle.
With the wide application of the aerostatic spindle in the ultra-precision machining process, the requirements for the kinematic precision of the spindle are increasing. It is necessary to predict and improve the precision of the spindle motion accurately. Based on the nonlinear dynamic characteristics of the aerostatic bearing, the vibration characteristics and prediction model of the aerostatic spindle were studied, and the influence of the nonlinear dynamic characteristic analysis on the spindle rotary precision was explored. Firstly, the dynamic flow model of the gas film of the aerostatic journal bearing was established, the nonlinear dynamic stiffness and damping coefficients were obtained by the perturbation method. The gas film was used as the spring-damping system to build the bearing-rotor system, and the dynamic vibration model of bearing-rotor system was established by dynamic analysis. Then nonlinear dynamic parameters were introduced into the vibration model, and the curve of the radial runout error, the deflection error and the total error of radial vibration were obtained by solving the model with MATLAB. The frequency domain analysis were conducted on the vibration signal. Finally, Rotation Error Measurement experimental of spindle was performed to inspect the results of vibration error analysis. From the dynamic analysis of the aerostatic journal bearings, the dynamic stiffness and dynamic damping of the bearing are all nonlinear, and the dynamic stiffness increases with the increase of eccentricity, and the dynamic damping decreases. From the vibration analysis of the bearing-rotor system, the following conclusions can be obtained. 1) The nonlinear analysis has an obvious influence on the deflection error, but the influence on the radial runout error is not obvious. It shows that the nonlinear analysis mainly affects the deflection error of the spindle and thus affects the total radial error. 2) The maximum amplitude of the deflection error is basically stable when the fixed value analysis is analyzed, while the maximum amplitude of the deflection error has an increase process and tends to be stable at the time of nonlinear analysis, and the maximum amplitude of the nonlinear analysis is obviously larger than the amplitude of the constant value analysis. 3) The total radial error of the nonlinear analysis and the constant value analysis is basically the same at the beginning of the gas supply, but with the increase of time, the maximum amplitude under the nonlinear analysis is larger than the maximum amplitude under the constant value analysis, which shows that the nonlinear analysis has no obvious effect on the error of radial runout and the deviation angle when the gas supply is started. When the gas supply is stable, the nonlinear dynamic stiffness and dynamic damping will obviously affect the vibration amplitude of the rotor. 4) From the frequency domain, the resonance frequency at the maximum amplitude of the nonlinear analysis is 964 Hz, and the resonance frequency at the maximum amplitude of the constant value analysis is 986 Hz, and the nonlinear analysis reduces the resonance frequency at the maximum amplitude. 5) When the frequency is higher than 1 500 Hz, the amplitude change of the rotor is very small, which shows that the vibration of the rotor is more stable when the frequency is greater than 1 500 Hz, and the vibration frequency of the gas film is not easy to resonate with the natural frequency. Experimental results indicated that the error of radial rotation error of the spindle based on nonlinear analysis is reduced by 1.43% to6.54% compared to the constant value analysis. Therefore, the coupled vibration analysis of the bearing-rotor system can be achieved by applying the gas film as the spring-damping system to the rotor. The introduction of nonlinear dynamic characteristic parameters of bearing realizes the effect of bearing dynamic performance on spindle dynamic vibration. Based on nonlinear dynamic characteristics, the vibration analysis of the bearing-rotor system can more accurately analysis and predict the radial vibration error of the aerostatic spindle.
引文
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[10]Chen X D,Zhu J C,Chen H.Dynamic characteristics of ultra-precision aerostatic bearings[J].Advances in Manufacturing,2013,1(1):82-86.
[11]Jia Chenhui,Meng Xiao,Qiu Ming,et al.Nonlinear dynamic characteristics and stability prediction of aerodynamic bearings[J].Lubrication Engineering,2016,41(10):8-12.[贾晨辉,孟肖,邱明,等.气体动压轴承非线性动力学行为和稳定性预测[J].润滑与密封,2016,41(10):8-12.]
[12]Yu P,Chen X,Wang X,et al.Frequency-dependent nonlinear dynamic stiffness of aerostatic bearings subjected to external perturbations[J].International Journal of Precision Engineering&Manufacturing,2015,16(8):1771-1777.
[13]Zhao Guang,Liu Pannian,Yu Hechun,et al.Research on gas film force of aerostatic gas bearing and its coupled dynamics with rotor[J].Journal of Aerospace Power,2012,27(2):472-480.[赵广,刘盼年,于贺春,等.静压气体轴承气膜力及其与转子耦合动力学特性研究[J].航空动力学报,2012,27(2):472-480.]
[2]Li Qi,Fang Haiyan.Rotation accuracy measurement of magnetic suspension spindle[J].Machine Tool&Hydraulics,2004(8):156-158.[李旗,方海燕.磁浮主轴回转精度的测试[J].机床与液压,2004(8):156-158.]
[3]Chen Dongju,Dong Lihua,Zhou Shuai,et al.Dynamic performance analysis and experiment research of aerostatic spindle under the rarefaction effects[J].Journal of Sichuan University(Engineering Science Edition),2016,48(5):180-185.[陈东菊,董丽华,周帅,等.稀薄效应下空气静压主轴动态特性分析及试验研究[J].四川大学学报(工程科学版),2016,48(5):180-185.]
[4]Zhang S J,To S,Wang H T.A theoretical and experimental investigation into five-DOF dynamic characteristics of an aerostatic bearing spindle in ultra-precision diamond turning[J].International Journal of Machine Tools&Manufacture,2013,71(8):1-10.
[5]Zhang S J,To S,Cheung C F,et al.Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning[J].International Journal of Machine Tools&Manufacture,2012,62(1):1-12.
[6]Osborne D A.Comparison of rotordynamic analysis predictions with the test response of simple gas hybrid bearings for oil free turbomachinery[J].Journal of Engineering for Gas Turbines&Power,2003,128(3):619-632.
[7]Huang P,Lee W B,Chan C Y.Investigation of the effects of spindle unbalance induced error motion on machining accuracy in ultra-precision diamond turning[J].International Journal of Machine Tools&Manufacture,2015,94:48-56.
[8]Cappa S,Reynaerts D,Al-Bender F.Reducing the radial error motion of an aerostatic journal bearing to a nanometre level:theoretical modelling[J].Tribology Letters,2014,53(1):27-41.
[9]Al-Bender F.On the modelling of the dynamic characteristics of aerostatic bearing films:From stability analysis to active compensation[J].Precision Engineering,2009,33(2):117-126.
[10]Chen X D,Zhu J C,Chen H.Dynamic characteristics of ultra-precision aerostatic bearings[J].Advances in Manufacturing,2013,1(1):82-86.
[11]Jia Chenhui,Meng Xiao,Qiu Ming,et al.Nonlinear dynamic characteristics and stability prediction of aerodynamic bearings[J].Lubrication Engineering,2016,41(10):8-12.[贾晨辉,孟肖,邱明,等.气体动压轴承非线性动力学行为和稳定性预测[J].润滑与密封,2016,41(10):8-12.]
[12]Yu P,Chen X,Wang X,et al.Frequency-dependent nonlinear dynamic stiffness of aerostatic bearings subjected to external perturbations[J].International Journal of Precision Engineering&Manufacturing,2015,16(8):1771-1777.
[13]Zhao Guang,Liu Pannian,Yu Hechun,et al.Research on gas film force of aerostatic gas bearing and its coupled dynamics with rotor[J].Journal of Aerospace Power,2012,27(2):472-480.[赵广,刘盼年,于贺春,等.静压气体轴承气膜力及其与转子耦合动力学特性研究[J].航空动力学报,2012,27(2):472-480.]
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