滚动轴承动特性及轴承—转子系统动力学模型研究
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摘要
滚动轴承支承的转子系统广泛应用于工业领域,滚动轴承的动特性在很大程度上决定着轴承-转子系统的动力学性能。对于滚动轴承支承的转子系统动力学性能研究的关键是如何精确计算滚动轴承的刚度和阻尼的数值、弄清轴承结构刚度及其对转子系统刚度的影响。以往的研究在计算滚动轴承的刚度和阻尼时,没有同时考虑轴承变形和油膜的影响,在进行转子振动模型研究中,将滚动轴承简化为具有径向刚度和阻尼的一个点。这样的做法使得目前对实际滚动轴承-转子系统的振动问题的研究精度不高,难以进行有效的理论分析和计算。
本文分别以球轴承、圆柱滚子轴承和圆锥滚子轴承为对象,首次提出了综合刚度概念和计算思想,通过受力分析和EHL研究,建立了考虑润滑油膜、内外圈弹性变形和滚动体弹性变形的滚动轴承综合刚度的解析计算模型,并详细研究了滚动轴承的滚子长度、滚子直径、滚子个数、径向载荷、转动速度等因素对轴承综合刚度的影响规律,并对这些规律进行了分析和讨论；首次提出了综合阻尼的概念和计算思想。通过对球轴承、圆锥滚子轴承和圆柱滚子轴承的受力和变形分析,以及对Reynolds方程进行二次积分,建立了球轴承、圆锥滚子轴承和圆柱滚子轴承的综合阻尼的计算模型。依据该模型分别研究了圆柱滚子、圆锥滚子和球轴承的结构参数对轴承综合阻尼的影响规律,并对这些影响规律进行了理论分析。以滚动轴承支承的Jeffcott转子和链式悬臂转子系统为研究对象,利用新建立的滚动轴承综合刚度和综合阻尼模型进行动力学分析,系统研究了滚动轴承结构参数(滚子长度、滚子半径等)和工作状态参数(转速、外载荷)对于转子系统临界转速和转子系统不平衡响应的影响规律,研究了圆柱滚子轴承的滚子长度、悬臂长度、轴承间距等结构参数对链式悬臂转子的临界转速、振动响应等振动性能的影响规律,并进行了分析讨论。
通过对圆柱滚子轴承、圆锥滚子轴承、球轴承的结构力学分析,建立了滚动轴承的结构刚度计算模型,将滚动轴承结构刚度计算模型引入转子振动分析过程,建立了滚动轴承单元两端的新型传递关系,并将此传递关系引入整个轴承-转子系统的传递矩阵中,建立了考虑轴承具体结构的新型传递矩阵；依据新建立的传递矩阵构建了滚动轴承-转子系统的振动计算模型,并对一实际轴承-转子系统进行了计算研究,系统分析了滚动轴承结构参数对轴承-转子系统的模态振型、临界转速和不平衡响应的影响规律。研究表明,滚动轴承(尤其是圆柱滚子轴承和圆锥滚子轴承)的几何结构对转子系统的模态振型有较大的影响,尤其是对于靠近轴承两端的模态振型有明显的影响,对转子系统不平衡响应的临界转速影响不大,对不平衡响应的振幅有一定程度的抑制作用,其中圆柱滚子轴承对响应振幅的抑制十分明显。
将本文建立的新型滚子轴承刚度模型、阻尼模型、轴承结构刚度模型以及新型转子传递矩阵模型应用于某一核电站风机转子的振动分析,计算得到了风机系统的模态振型、临界转速以及风机叶轮中心处的不平衡响应曲线,分析了轴承结构对该风机转子系统的振动性能的影响规律。并利用有限元法对同一算例进行分析计算,计算结果表明,用有限元法计算的结果与应用本文所建立的刚度模型、阻尼模型、轴承结构刚度模型所计算的结果具有良好的一致性,表明本文所建立的刚度模型、阻尼模型、轴承结构模型、对传递矩阵的修改具有良好的工程应用的可行性和可信性。
通过本文的研究,构建了关于滚动轴承刚度、阻尼的新型计算模型,构建了关于轴承结构刚度的计算模型和新型传递矩阵计算模型,这些模型不仅在计算精度上有了很大的提高,而且计算过程十分方便。本文的研究成果将为滚动轴承支承的转子系统动力学性能研究提供有益的借鉴。
Rolling element bearing-rotor systems are widely used in industry. Their dynamic characteristics depend on bearings to some extent. The key of studying rolling element bearing-rotor systems lies in calculating bearing stiffness and damping accurately and understanding the influences of bearing structure stiffness on whole system. In past studies on rolling element bearing stiffness and damping, the influences of bearing material and lubrication film on stiffness and damping are not considered simultaneously. Therefore bearings are usually simplified to be a point on the shaft with radial stiffness and damping coefficient. According to the simplification, the computational accuracy for studying real rolling element bearing-rotor system decreased and the studies on bearing-rotor system is difficult to be acknowledged.
In this dissertation, ball bearing, cylindrical roller bearing and tapered roller bearing are studied respectively and the concept of overall stiffness is proposed for the first time. Analytical model for calculating overall stiffness of rolling element bearing is established through stress EHL analysis, and the new model includes the influences of both lubrication and elastic deformation of roller and raceways. By use of the model, the influences of roller length, roller diameter, roller number, radial load and rotating speed on bearing overall stiffness are studied in detail and significant results are obtained and discussed. The concept of overall damping is also proposed for the first time. A new model for calculating the overall damping of rolling element bearing is established through analysis on load, deformation and implementation of Reynolds equation. By use of the new model, the influences of rolling element bearing structure on bearing overall stiffness are studied and some significant results are obtained and discussed. Also, by using the new stiffness and damping model, Jeffcott and chain-linked cantilever rotor supported by rolling element bearing are studied. The influences of bearing structure (roller length and roller diameter etc.) and working conditions (rotating speed and radial load etc.) on the critical speed and unbalanced response of Jeffcott rotor, and the influences of roller length of cylindrical, cantilever length, and bearing distance on dynamic characteristics of chain-linked bearing-rotor system are studied and discussed.
By structure and mechanics analysis on cylindrical roller bearing, tapered roller bearing and ball bearing, the bearing-structure-stiffness model is proposed for rotor vibration dynamics analysis, new state vector relationships between ends of rolling element bearing are obtained, and the relationships are applied in the whole transfer matrix of the bearing-rotor system to built a new transfer matrix and vibration equations. A real bearing-rotor example is studied by using the new method, influences of rolling element bearing structure on modal shape, critical speed and unbalanced response are studied, and results show that the influences of rolling element bearing structure (especially cylindrical roller bearing and tapered roller bearing) on rotor dynamic modal shapes are significant, the influences of bearing structure on critical speed are faint, bearing structure reduce the unbalanced respond amplitude of the system, especially for cylindrical roller bearing supported rotor.
Utilizing the new calculating models of stiffness, damping, bearing structure stiffness and the new transfer matrix, the dynamic characteristics of a nuclear air blower is studied. The influences of bearing structure on modal shape, critical speed and unbalanced response of the blower are calculated by use of the new transfer method. FEM is also used to calculate the same example to verify the new transfer method. Calculating results by use of FEM and by use of the new transfer method are quite close to each other. It indicates that the new stiffness model, damping model, bearing structure stiffness and the new transfer method established in this paper are quite credible.
The new calculating models of stiffness and damping of rolling element bearings in this paper are more accurate than before, what is more, these models are easier for practical application. The established rolling element bearing structure stiffness model and the new transfer method also increase the accuracy of the dynamic chacteristics of the rolling element bearing rotor system. The research conclusions obtained in this dissertation will be very helpful for the further application and studies of rolling element bearing and its supported rotor.
本文分别以球轴承、圆柱滚子轴承和圆锥滚子轴承为对象,首次提出了综合刚度概念和计算思想,通过受力分析和EHL研究,建立了考虑润滑油膜、内外圈弹性变形和滚动体弹性变形的滚动轴承综合刚度的解析计算模型,并详细研究了滚动轴承的滚子长度、滚子直径、滚子个数、径向载荷、转动速度等因素对轴承综合刚度的影响规律,并对这些规律进行了分析和讨论；首次提出了综合阻尼的概念和计算思想。通过对球轴承、圆锥滚子轴承和圆柱滚子轴承的受力和变形分析,以及对Reynolds方程进行二次积分,建立了球轴承、圆锥滚子轴承和圆柱滚子轴承的综合阻尼的计算模型。依据该模型分别研究了圆柱滚子、圆锥滚子和球轴承的结构参数对轴承综合阻尼的影响规律,并对这些影响规律进行了理论分析。以滚动轴承支承的Jeffcott转子和链式悬臂转子系统为研究对象,利用新建立的滚动轴承综合刚度和综合阻尼模型进行动力学分析,系统研究了滚动轴承结构参数(滚子长度、滚子半径等)和工作状态参数(转速、外载荷)对于转子系统临界转速和转子系统不平衡响应的影响规律,研究了圆柱滚子轴承的滚子长度、悬臂长度、轴承间距等结构参数对链式悬臂转子的临界转速、振动响应等振动性能的影响规律,并进行了分析讨论。
通过对圆柱滚子轴承、圆锥滚子轴承、球轴承的结构力学分析,建立了滚动轴承的结构刚度计算模型,将滚动轴承结构刚度计算模型引入转子振动分析过程,建立了滚动轴承单元两端的新型传递关系,并将此传递关系引入整个轴承-转子系统的传递矩阵中,建立了考虑轴承具体结构的新型传递矩阵；依据新建立的传递矩阵构建了滚动轴承-转子系统的振动计算模型,并对一实际轴承-转子系统进行了计算研究,系统分析了滚动轴承结构参数对轴承-转子系统的模态振型、临界转速和不平衡响应的影响规律。研究表明,滚动轴承(尤其是圆柱滚子轴承和圆锥滚子轴承)的几何结构对转子系统的模态振型有较大的影响,尤其是对于靠近轴承两端的模态振型有明显的影响,对转子系统不平衡响应的临界转速影响不大,对不平衡响应的振幅有一定程度的抑制作用,其中圆柱滚子轴承对响应振幅的抑制十分明显。
将本文建立的新型滚子轴承刚度模型、阻尼模型、轴承结构刚度模型以及新型转子传递矩阵模型应用于某一核电站风机转子的振动分析,计算得到了风机系统的模态振型、临界转速以及风机叶轮中心处的不平衡响应曲线,分析了轴承结构对该风机转子系统的振动性能的影响规律。并利用有限元法对同一算例进行分析计算,计算结果表明,用有限元法计算的结果与应用本文所建立的刚度模型、阻尼模型、轴承结构刚度模型所计算的结果具有良好的一致性,表明本文所建立的刚度模型、阻尼模型、轴承结构模型、对传递矩阵的修改具有良好的工程应用的可行性和可信性。
通过本文的研究,构建了关于滚动轴承刚度、阻尼的新型计算模型,构建了关于轴承结构刚度的计算模型和新型传递矩阵计算模型,这些模型不仅在计算精度上有了很大的提高,而且计算过程十分方便。本文的研究成果将为滚动轴承支承的转子系统动力学性能研究提供有益的借鉴。
Rolling element bearing-rotor systems are widely used in industry. Their dynamic characteristics depend on bearings to some extent. The key of studying rolling element bearing-rotor systems lies in calculating bearing stiffness and damping accurately and understanding the influences of bearing structure stiffness on whole system. In past studies on rolling element bearing stiffness and damping, the influences of bearing material and lubrication film on stiffness and damping are not considered simultaneously. Therefore bearings are usually simplified to be a point on the shaft with radial stiffness and damping coefficient. According to the simplification, the computational accuracy for studying real rolling element bearing-rotor system decreased and the studies on bearing-rotor system is difficult to be acknowledged.
In this dissertation, ball bearing, cylindrical roller bearing and tapered roller bearing are studied respectively and the concept of overall stiffness is proposed for the first time. Analytical model for calculating overall stiffness of rolling element bearing is established through stress EHL analysis, and the new model includes the influences of both lubrication and elastic deformation of roller and raceways. By use of the model, the influences of roller length, roller diameter, roller number, radial load and rotating speed on bearing overall stiffness are studied in detail and significant results are obtained and discussed. The concept of overall damping is also proposed for the first time. A new model for calculating the overall damping of rolling element bearing is established through analysis on load, deformation and implementation of Reynolds equation. By use of the new model, the influences of rolling element bearing structure on bearing overall stiffness are studied and some significant results are obtained and discussed. Also, by using the new stiffness and damping model, Jeffcott and chain-linked cantilever rotor supported by rolling element bearing are studied. The influences of bearing structure (roller length and roller diameter etc.) and working conditions (rotating speed and radial load etc.) on the critical speed and unbalanced response of Jeffcott rotor, and the influences of roller length of cylindrical, cantilever length, and bearing distance on dynamic characteristics of chain-linked bearing-rotor system are studied and discussed.
By structure and mechanics analysis on cylindrical roller bearing, tapered roller bearing and ball bearing, the bearing-structure-stiffness model is proposed for rotor vibration dynamics analysis, new state vector relationships between ends of rolling element bearing are obtained, and the relationships are applied in the whole transfer matrix of the bearing-rotor system to built a new transfer matrix and vibration equations. A real bearing-rotor example is studied by using the new method, influences of rolling element bearing structure on modal shape, critical speed and unbalanced response are studied, and results show that the influences of rolling element bearing structure (especially cylindrical roller bearing and tapered roller bearing) on rotor dynamic modal shapes are significant, the influences of bearing structure on critical speed are faint, bearing structure reduce the unbalanced respond amplitude of the system, especially for cylindrical roller bearing supported rotor.
Utilizing the new calculating models of stiffness, damping, bearing structure stiffness and the new transfer matrix, the dynamic characteristics of a nuclear air blower is studied. The influences of bearing structure on modal shape, critical speed and unbalanced response of the blower are calculated by use of the new transfer method. FEM is also used to calculate the same example to verify the new transfer method. Calculating results by use of FEM and by use of the new transfer method are quite close to each other. It indicates that the new stiffness model, damping model, bearing structure stiffness and the new transfer method established in this paper are quite credible.
The new calculating models of stiffness and damping of rolling element bearings in this paper are more accurate than before, what is more, these models are easier for practical application. The established rolling element bearing structure stiffness model and the new transfer method also increase the accuracy of the dynamic chacteristics of the rolling element bearing rotor system. The research conclusions obtained in this dissertation will be very helpful for the further application and studies of rolling element bearing and its supported rotor.
引文
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