滑动轴承非线性轴心轨迹的瞬态与周期特性研究
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摘要
轴心轨迹是滑动轴承工作状态的综合反映。通过轴心轨迹,可以确定轴承的回转精度和最小油膜厚度,判断转子系统的稳定性和轴承设计参数的合理性；通过控制可以实现具有特殊用途的期望轴心轨迹。本课题针对滑动轴承的复杂受力状态,开展非线性轴心轨迹的瞬变及周期特性研究,对旋转机械的精度和稳定性控制及期望轴心轨迹的实现具有重要意义。
首先,基于轴颈惯性力、非线性油膜力和动载荷之间的平衡,建立了滑动轴承轴心轨迹的非线性分析模型。同时,为便于比较,根据油膜力线性化方法,建立了轴心在平衡位置附近作小位移涡动的线性分析模型。
其次,提出了非线性轴心轨迹的位置配置计算方法。步骤是：由初始条件,先求解该瞬时轴心位置的Reynolds方程,根据油膜压力分布积分得到油膜合力,然后求解运动方程,得到轴心的瞬时加速度,再由欧拉方法计算出轴心的下一个位置参数,如此循环迭代,直到得到完整的轴心轨迹。
接着研究了阶跃、矩形脉冲、正弦脉冲和三角脉冲复杂载荷作用下,轴心轨迹的瞬态特性、最大油膜压力及最小油膜厚度等主要参数的变化规律,分析比较了四种载荷对主要参数的影响。轴承在稳定工作而受到瞬变载荷作用时,主要参数都有较大的变化。时域中变化剧烈的阶跃和矩形脉冲载荷,比正弦脉冲和三角脉冲载荷对轴心轨迹及主要参数的影响大。由于脉冲载荷的作用时间有限,随着其消失,轴心乃收敛于原平衡位置,而阶跃载荷则使轴心收敛于新的平衡位置。
研究了不平衡旋转载荷作用下,轴心轨迹的周期特性,分析比较了在小不平衡载荷作用下轴心轨迹非线性分析与线性分析之间的误差,即轴心轨迹中心的位置误差与位移幅值误差。当不平衡载荷较小时,可以作为小扰动载荷处理,轴心轨迹的非线性分析可以用线性分析代替,二者误差较小。
当不平衡载荷增大时,轴心轨迹的中心偏离原平衡位置向轴承中心移动,且涡动位移随载荷非线性增大,轴心轨迹的非线性分析与线性分析之间的误差增大。对轴心轨迹特性及动态油膜力进行了频谱分析,表明轴心位移及油膜力不仅包含基频成分,而且包含二倍频及三倍频等高频成分,且基频力随不平衡载荷的增加具有明显的线性增加特征。
基于非线性轴心轨迹和油膜合力的频谱特征,提出了大扰动不平衡载荷作用下轴心轨迹的准线性分析方法：将油膜力基频部分表示为位移、速度的线性函数,采用LMS方法识别出一组当量刚度和当量阻尼系数,再以此刚度、阻尼系数和载荷对轴心轨迹进行准线性分析。比较了非线性分析与准线性分析的误差,完全能够满足工程要求。用准线性分析代替非线性分析,可大大减少计算时间。
研究了不平衡载荷与阶跃载荷对轴心临界涡动轨迹的影响。不平衡载荷的存在,使临界转速降低,临界涡动提前,半频涡动和基频涡动同时存在。不平衡载荷小时以半频涡动为主,不平衡载荷大时以基频涡动为主。只有不平衡载荷在-定范围时,轴心涡动轨迹才为“内8形”。当轴承处于临界涡动时,如果给轴施加一个阶跃载荷,可以调整轴心的工作位置,抑制临界涡动的发生。
最后,根据非圆轴心轨迹的应用要求,研究了椭圆轴心轨迹的成形方法。建立了轴心预定轨迹计算模型,计算了轴心同步进动时,实现不同轴心轨迹所需的控制力,并比较了“期望轨迹”与“检验轨迹”之间的误差。从控制力的波形看,圆轨迹所需的控制力优于椭圆轨迹的控制力。从“期望轨迹”与“检验轨迹”的误差看,圆轨迹的误差小于椭圆轨迹的误差。相比同步正进动,轴心作同步反进动时,轴心轨迹的抗扰动能力强,即使在临界转速时,“检验轨迹”都能较好地复现“期望轨迹”。
论文详细地研究了滑动轴承非线性轴心轨迹的瞬态和周期特性,揭示了轴心轨迹变化的内在规律,为旋转机械的精度、稳定性控制及期望轴心轨迹的实现奠定了理论基础。
需要指出的是,论文建立的非线性轴心轨迹计算模型,提出的非线性轴心轨迹计算方法,并未涉及具体的轴承结构,因而适用于所有滑动轴承,包括静压轴承和动静压轴承。
本课题为国家自然科学基金资助项目课题(项目编号：50275089,51075242)。
Journal centre motion trajectory is a comprehensive behavior of journal bearing working condition. Journal centre trajectory analysis can be used to ascertain index repeatability and the least oil film thickness that to judge stability of rotor and rationality of the bearing design parameters. Directed towards complex stress state of journal bearing, the transient and periodical feature of nonlinear journal centre trajectory is studied in this dissertation, which is significant to precision and stableness control of rotating machinery.
In the first place, the non-linear analysis model of journal centre trajectory is establish, which based on equivalence of neck journal inertial force, non-linear oil film force and dynamic load. Synchronously, based on linearization technique of oil film force the linear model that journal center whirl around its static equilibrium position is established for conveniently analyze.
Secondly, an algorithmic method is proposed that locate the center position of journal centre trajectory. The following is the procedure, first solve the Reynolds equation of transient bearing center position according to initial conditions, resultant force of oil film can be got by integral of oil film force distribution, then acceleration of journal centre can be got by solve move equation, the next calculate parameters of next position by using Euler method, iteration in this method until acquire a completed journal centre trajectory.
Thirdly, instantaneous characteristic of journal centre trajectory, maximum oil film force and minimum depth of oil film under step, square wave pulse, sinusoidal pulse and triangular pulse transient load are calculated separately, variation of main parameters is analyzed and also the influence to these parameters caused by different types of loads. Transient load applied to steady working journal bearing will cause the main parameters significantly changed. Step and square wave pulse load fluctuate considerable in time domain such as sinusoidal pulse and triangular pulse signals influence journal centre trajectory and main parameters notably. Owing to action time of impulse load is finite the shaft center will go back to its equilibrium position that the load applied before, on the other side step load will cause the shaft center transit to another equilibrium position.
The cyclophysis of journal centre trajectory under unbalanced rotating load is investigated. Linear analysis and non-linear analysis of journal centre trajectory that affected by small disequilibrium load are compared, and both journal centre trajectory center position error and displacement amplitude error are studied. Under the condition of disequilibrium load is small, it can be taken as small disturbance, that non-linear analysis of journal centre trajectory can be taken placed by linear analysis, and the error between these two methods is small.
When the load increased, the center of journal centre trajectory departs its equilibrium position and moves towards to journal center, and whirling displacement increases nonlinearly to the load, and the error between methods of Linear analysis and non-linear analysis will increase too. Spectral analysis is carried out to journal centre trajectory characteristic and dynamic oil film force, results show that shaft center displacement and oil film force not only contain the fundamental frequency component, but also second-harmonic generation and upper, and fundamental frequency force will increase linearly to the unbalanced load.
Based on spectral features of nonlinear journal centre trajectory and oil film force, an idea of quasi-linear analysis method of journal centre trajectory under large disequilibrium load is proposed, which expresses the fundamental frequency part of oil film force as linear function of displacement and velocity, identify stiffness coefficient and damping coefficient of the bearing by LMS method, and then use these coefficient to analysis journal centre trajectory. The error between non-linear and quasi-linear analysis is calculated, results show that the latter can meet engineering demands and its computer time is much less.
Finally, according to application of noncircular locus, method of shaping elliptic locus is investigated. The computational modeling of desired trajectories is established, and the control force is calculated that used to force the journal center to move along desired locus when the journal is rotating, the error between desired trajectory and test trajectory is worked out. After analysis the wave pattern, it can be concluded that the force needed to form a circle locus surpasses that to form an ellipse, besides the error is smaller to shape a circle than an ellipse. The ability of resist disturbance of backward precession is stronger than forward precession, even in the condition of critical whirl the locus of backward precession can reproduce desired trajectory accurately.
Transient and periodical characteristic of nonlinear journal centre trajectory are investigated minutely in this dissertation, that to exposit inherent law of variation of it, these all lay the foundation for precision realization of rotating machinery, stableness control and acquiring desired trajectory.
It is to be remarked that both the establishment of nonlinear journal centre trajectory calculating model and the proposing of its computing method are not concerned with concrete bearing structure, so all these methods can be used to all types of journal bearings such as hydrostatic bearing and hybrid bearing.
This project is supported by National Natural Science Foundation of China (No.50275089,51075242)
首先,基于轴颈惯性力、非线性油膜力和动载荷之间的平衡,建立了滑动轴承轴心轨迹的非线性分析模型。同时,为便于比较,根据油膜力线性化方法,建立了轴心在平衡位置附近作小位移涡动的线性分析模型。
其次,提出了非线性轴心轨迹的位置配置计算方法。步骤是：由初始条件,先求解该瞬时轴心位置的Reynolds方程,根据油膜压力分布积分得到油膜合力,然后求解运动方程,得到轴心的瞬时加速度,再由欧拉方法计算出轴心的下一个位置参数,如此循环迭代,直到得到完整的轴心轨迹。
接着研究了阶跃、矩形脉冲、正弦脉冲和三角脉冲复杂载荷作用下,轴心轨迹的瞬态特性、最大油膜压力及最小油膜厚度等主要参数的变化规律,分析比较了四种载荷对主要参数的影响。轴承在稳定工作而受到瞬变载荷作用时,主要参数都有较大的变化。时域中变化剧烈的阶跃和矩形脉冲载荷,比正弦脉冲和三角脉冲载荷对轴心轨迹及主要参数的影响大。由于脉冲载荷的作用时间有限,随着其消失,轴心乃收敛于原平衡位置,而阶跃载荷则使轴心收敛于新的平衡位置。
研究了不平衡旋转载荷作用下,轴心轨迹的周期特性,分析比较了在小不平衡载荷作用下轴心轨迹非线性分析与线性分析之间的误差,即轴心轨迹中心的位置误差与位移幅值误差。当不平衡载荷较小时,可以作为小扰动载荷处理,轴心轨迹的非线性分析可以用线性分析代替,二者误差较小。
当不平衡载荷增大时,轴心轨迹的中心偏离原平衡位置向轴承中心移动,且涡动位移随载荷非线性增大,轴心轨迹的非线性分析与线性分析之间的误差增大。对轴心轨迹特性及动态油膜力进行了频谱分析,表明轴心位移及油膜力不仅包含基频成分,而且包含二倍频及三倍频等高频成分,且基频力随不平衡载荷的增加具有明显的线性增加特征。
基于非线性轴心轨迹和油膜合力的频谱特征,提出了大扰动不平衡载荷作用下轴心轨迹的准线性分析方法：将油膜力基频部分表示为位移、速度的线性函数,采用LMS方法识别出一组当量刚度和当量阻尼系数,再以此刚度、阻尼系数和载荷对轴心轨迹进行准线性分析。比较了非线性分析与准线性分析的误差,完全能够满足工程要求。用准线性分析代替非线性分析,可大大减少计算时间。
研究了不平衡载荷与阶跃载荷对轴心临界涡动轨迹的影响。不平衡载荷的存在,使临界转速降低,临界涡动提前,半频涡动和基频涡动同时存在。不平衡载荷小时以半频涡动为主,不平衡载荷大时以基频涡动为主。只有不平衡载荷在-定范围时,轴心涡动轨迹才为“内8形”。当轴承处于临界涡动时,如果给轴施加一个阶跃载荷,可以调整轴心的工作位置,抑制临界涡动的发生。
最后,根据非圆轴心轨迹的应用要求,研究了椭圆轴心轨迹的成形方法。建立了轴心预定轨迹计算模型,计算了轴心同步进动时,实现不同轴心轨迹所需的控制力,并比较了“期望轨迹”与“检验轨迹”之间的误差。从控制力的波形看,圆轨迹所需的控制力优于椭圆轨迹的控制力。从“期望轨迹”与“检验轨迹”的误差看,圆轨迹的误差小于椭圆轨迹的误差。相比同步正进动,轴心作同步反进动时,轴心轨迹的抗扰动能力强,即使在临界转速时,“检验轨迹”都能较好地复现“期望轨迹”。
论文详细地研究了滑动轴承非线性轴心轨迹的瞬态和周期特性,揭示了轴心轨迹变化的内在规律,为旋转机械的精度、稳定性控制及期望轴心轨迹的实现奠定了理论基础。
需要指出的是,论文建立的非线性轴心轨迹计算模型,提出的非线性轴心轨迹计算方法,并未涉及具体的轴承结构,因而适用于所有滑动轴承,包括静压轴承和动静压轴承。
本课题为国家自然科学基金资助项目课题(项目编号：50275089,51075242)。
Journal centre motion trajectory is a comprehensive behavior of journal bearing working condition. Journal centre trajectory analysis can be used to ascertain index repeatability and the least oil film thickness that to judge stability of rotor and rationality of the bearing design parameters. Directed towards complex stress state of journal bearing, the transient and periodical feature of nonlinear journal centre trajectory is studied in this dissertation, which is significant to precision and stableness control of rotating machinery.
In the first place, the non-linear analysis model of journal centre trajectory is establish, which based on equivalence of neck journal inertial force, non-linear oil film force and dynamic load. Synchronously, based on linearization technique of oil film force the linear model that journal center whirl around its static equilibrium position is established for conveniently analyze.
Secondly, an algorithmic method is proposed that locate the center position of journal centre trajectory. The following is the procedure, first solve the Reynolds equation of transient bearing center position according to initial conditions, resultant force of oil film can be got by integral of oil film force distribution, then acceleration of journal centre can be got by solve move equation, the next calculate parameters of next position by using Euler method, iteration in this method until acquire a completed journal centre trajectory.
Thirdly, instantaneous characteristic of journal centre trajectory, maximum oil film force and minimum depth of oil film under step, square wave pulse, sinusoidal pulse and triangular pulse transient load are calculated separately, variation of main parameters is analyzed and also the influence to these parameters caused by different types of loads. Transient load applied to steady working journal bearing will cause the main parameters significantly changed. Step and square wave pulse load fluctuate considerable in time domain such as sinusoidal pulse and triangular pulse signals influence journal centre trajectory and main parameters notably. Owing to action time of impulse load is finite the shaft center will go back to its equilibrium position that the load applied before, on the other side step load will cause the shaft center transit to another equilibrium position.
The cyclophysis of journal centre trajectory under unbalanced rotating load is investigated. Linear analysis and non-linear analysis of journal centre trajectory that affected by small disequilibrium load are compared, and both journal centre trajectory center position error and displacement amplitude error are studied. Under the condition of disequilibrium load is small, it can be taken as small disturbance, that non-linear analysis of journal centre trajectory can be taken placed by linear analysis, and the error between these two methods is small.
When the load increased, the center of journal centre trajectory departs its equilibrium position and moves towards to journal center, and whirling displacement increases nonlinearly to the load, and the error between methods of Linear analysis and non-linear analysis will increase too. Spectral analysis is carried out to journal centre trajectory characteristic and dynamic oil film force, results show that shaft center displacement and oil film force not only contain the fundamental frequency component, but also second-harmonic generation and upper, and fundamental frequency force will increase linearly to the unbalanced load.
Based on spectral features of nonlinear journal centre trajectory and oil film force, an idea of quasi-linear analysis method of journal centre trajectory under large disequilibrium load is proposed, which expresses the fundamental frequency part of oil film force as linear function of displacement and velocity, identify stiffness coefficient and damping coefficient of the bearing by LMS method, and then use these coefficient to analysis journal centre trajectory. The error between non-linear and quasi-linear analysis is calculated, results show that the latter can meet engineering demands and its computer time is much less.
Finally, according to application of noncircular locus, method of shaping elliptic locus is investigated. The computational modeling of desired trajectories is established, and the control force is calculated that used to force the journal center to move along desired locus when the journal is rotating, the error between desired trajectory and test trajectory is worked out. After analysis the wave pattern, it can be concluded that the force needed to form a circle locus surpasses that to form an ellipse, besides the error is smaller to shape a circle than an ellipse. The ability of resist disturbance of backward precession is stronger than forward precession, even in the condition of critical whirl the locus of backward precession can reproduce desired trajectory accurately.
Transient and periodical characteristic of nonlinear journal centre trajectory are investigated minutely in this dissertation, that to exposit inherent law of variation of it, these all lay the foundation for precision realization of rotating machinery, stableness control and acquiring desired trajectory.
It is to be remarked that both the establishment of nonlinear journal centre trajectory calculating model and the proposing of its computing method are not concerned with concrete bearing structure, so all these methods can be used to all types of journal bearings such as hydrostatic bearing and hybrid bearing.
This project is supported by National Natural Science Foundation of China (No.50275089,51075242)
引文
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