滚动轴承打滑动力学模型及振动噪声特征研究
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摘要
滚动轴承是关键基础零件，它直接影响主机的性能与寿命。滚动轴承的打滑，不仅会加速滚动轴承的磨损，破坏滚动轴承的旋转精度，产生异常振动和噪声，而且会造成滚动轴承的划伤和润滑油温度的升高，导致油膜破损，严重影响滚动轴承的性能和寿命。由于滚动轴承内部接触关系与运动关系的复杂性，尤其是考虑滚动体载荷和速度变化的打滑机理，轴承与轴承座耦合的声振计算方法等未得到很好解决，制约了高精度、低噪声和长寿命滚动轴承的研发。目前，关于滚动轴承打滑的动力学模型及算法，打滑对滚动轴承寿命和振动噪声的影响规律等，已成为该领域的关键共性科学问题，亟待予以解决。因此，开展滚动轴承打滑机理、动力学模型和声振耦合计算方法的研究，具有重要的理论意义和实际工程价值。
本论文主要围绕滚动体打滑原因，滚动体进入承载区打滑动力学模型及咬入打滑特性，加速工况滚动轴承打滑动力学模型及打滑特性，打滑对滚动轴承振动特性的影响，轴承声振耦合模型及打滑对轴承噪声的影响等方面展开研究。论文的主要工作如下：
①在滚动体打滑原因及打滑对轴承影响分析的基础上，综合考虑非线性接触、变摩擦系数、游隙及咬入角等非线性因素，建立滚动体进入承载区打滑动力学模型，研究了滚动体进入承载区的咬入打滑特性，以及轴承转速、载荷等对滚动体打滑的影响；
②基于滚动轴承的整体接触模型和滚动体与保持架的相互作用模型，分别推导内圈、滚动体和保持架的运动微分方程，建立加速工况滚动轴承打滑动力学模型，通过与Harris模型计算结果及实验结果的对比，验证了此模型的有效性。研究了加速工况下滚动轴承的打滑特性，以及轴承载荷、内圈角加速度等对轴承打滑特性的影响；
③综合考虑滚动轴承时变刚度、游隙及打滑摩擦力等非线性因素，推导了滚动体非线性接触力和打滑产生的摩擦力，建立了滚动轴承振动模型，获得了滚动体打滑激励下的轴承的振动响应，研究了滚动体进入承载区打滑状态下轴承的振动特征；
④基于动力学模型、有限元模型和边界元模型相耦合的方法，建立了轴承-轴承座声振耦合模型。通过建立轴承-轴承座系统振动模型，获取轴承的振动响应并以此作为轴承座振动噪声的激励；建立轴承座有限元模型，应用完全法对轴承座进行瞬态动力学分析，获得轴承座的振动响应；建立轴承座的边界元模型，将轴承座表面振动响应作为声学分析边界条件，采用直接边界元法求解Helmholtz方程的边界积分公式，获得轴承座的噪声辐射特性。通过轴承噪声实验，验证了本文提出的轴承声振耦合模型的正确性。基于该模型，研究了滚动体进入承载区打滑状态下轴承的噪声特征，为减振降噪提供了理论基础。
Rolling element bearings are key basic elements, which affect the machines’performance and life directly. Skidding of rolling element bearing does not onlyaccelerate the bearing’s wear, destroy rotary precision and lead to vibration and noiseabnormally, but also cause smearing, elevate the temperature of lubricant and evenbreak the lubricant film, so skidding will seriously affect the performance and life ofrolling element bearing. Because of the complexity of contact mechanism and internalmotion of rolling element bearing, especially when considering the skidding mechanismunder variation of load and speed of the rolling element, acoustic-vibration calculationmethods coupling bearing with the pedestal can not be solved very well. And thus itbecomes a barrier for the research and development of rolling element bearings withhigh precision, low noise and long life. Currently, the topics with respct to skiddingdynamic model and algorithm of rolling element bearing, as well as how skiddinginfluences the rolling element bearing’s life, vibration and noise have become keycommon scientific problems which needs to be solved urgently. So, the studies aboutskidding mechanism of rolling element bearing, dynamic model and acoustic-vibrationcalculation methods have great theoretical significance and practical engineering value.
This paper mainly focuses on: the skidding causes of rolling element, dynamicmodel to investigate skidding of rolling element at entry into the loaded zone, dynamicmodel to investigate whole skidding of rolling element bearing during angularacceleration process，the effect of skidding on the vibration characteristic of rollingelement bearing, acoustic-vibration model for bearing noise and the effects of skiddingon the noise characteristics. The main tasks of this paper are listed as follows:
①Based on the analysis of skidding causes of the rolling element and their effectson bearing’s performance, the skidding dynamic model of the rolling element enteringthe loaded zone was built, with taking non-linear contact, variable friction coefficient,clearance, nip angle and other non-linear factors into consideration. Nip skiddingbehavior while rolling element entering the loaded zone was studied, and how theskidding of the rolling element was affected by the bearing’s load and speed was alsoinvestigated;
②The complete contact model of the rolling element bearing and the interactionmodel between rolling elements and cage were established, and then the motion differential equations of the inner race, the rolling elements and the cage were derivedrespectively. The complete skidding dynamic model of the rolling element bearingduring angular acceleration was built. It is validated by comparison with the resultsfrom Harris’s model and experiment. The skidding characteristics of rolling elementbearing during angular acceleration process and how they can be affected by the bearingload and the angular acceleration of inner race were studied;
③The skidding of the rolling element was taken as the excitation of the bearing’svibration. Taking account time-varying stiffness, clearance, skidding of rolling elementsand other non-linear factors, the non-linear contact forces and sliding friction forces dueto skidding were derived. Then, the vibration model of the rolling element bearing wasestablished. The vibration response of the rolling element bearing was obtained, and thevibration features of the bearing under skidding when the rolling elements entering theloaded zone were studied;
④Dynamic model, finite element model and boundary element model werecoupled together to establish the pedestal’s acoustic-vibration model. The vibrationresponse of the outer race was obtained based on the vibration model ofbearing-pedestal system, which was the excitation source of the vibration and noise ofthe pedestal. The finite element model of the pedestal was built, and full method wasused to perform transient dynamic analysis to obtain vibration response of the pedestal.The boundary element model of the pedestal was built, where the pedestal’s surfacevibration response was applied as boundary condition. Direct boundary element methodwas used to solve boundary integral formula in Helmholtz equation, which enables theanalysis of the pedestal’s acoustic characteristics. Validity of the model wasdemonstrated by comparison with experiment results. The noise features of the bearingunder skidding while rolling elements was entering the loaded zone were studied, whichcould provide theoretical basis for the resuction of the vibration and noise.
本论文主要围绕滚动体打滑原因，滚动体进入承载区打滑动力学模型及咬入打滑特性，加速工况滚动轴承打滑动力学模型及打滑特性，打滑对滚动轴承振动特性的影响，轴承声振耦合模型及打滑对轴承噪声的影响等方面展开研究。论文的主要工作如下：
①在滚动体打滑原因及打滑对轴承影响分析的基础上，综合考虑非线性接触、变摩擦系数、游隙及咬入角等非线性因素，建立滚动体进入承载区打滑动力学模型，研究了滚动体进入承载区的咬入打滑特性，以及轴承转速、载荷等对滚动体打滑的影响；
②基于滚动轴承的整体接触模型和滚动体与保持架的相互作用模型，分别推导内圈、滚动体和保持架的运动微分方程，建立加速工况滚动轴承打滑动力学模型，通过与Harris模型计算结果及实验结果的对比，验证了此模型的有效性。研究了加速工况下滚动轴承的打滑特性，以及轴承载荷、内圈角加速度等对轴承打滑特性的影响；
③综合考虑滚动轴承时变刚度、游隙及打滑摩擦力等非线性因素，推导了滚动体非线性接触力和打滑产生的摩擦力，建立了滚动轴承振动模型，获得了滚动体打滑激励下的轴承的振动响应，研究了滚动体进入承载区打滑状态下轴承的振动特征；
④基于动力学模型、有限元模型和边界元模型相耦合的方法，建立了轴承-轴承座声振耦合模型。通过建立轴承-轴承座系统振动模型，获取轴承的振动响应并以此作为轴承座振动噪声的激励；建立轴承座有限元模型，应用完全法对轴承座进行瞬态动力学分析，获得轴承座的振动响应；建立轴承座的边界元模型，将轴承座表面振动响应作为声学分析边界条件，采用直接边界元法求解Helmholtz方程的边界积分公式，获得轴承座的噪声辐射特性。通过轴承噪声实验，验证了本文提出的轴承声振耦合模型的正确性。基于该模型，研究了滚动体进入承载区打滑状态下轴承的噪声特征，为减振降噪提供了理论基础。
Rolling element bearings are key basic elements, which affect the machines’performance and life directly. Skidding of rolling element bearing does not onlyaccelerate the bearing’s wear, destroy rotary precision and lead to vibration and noiseabnormally, but also cause smearing, elevate the temperature of lubricant and evenbreak the lubricant film, so skidding will seriously affect the performance and life ofrolling element bearing. Because of the complexity of contact mechanism and internalmotion of rolling element bearing, especially when considering the skidding mechanismunder variation of load and speed of the rolling element, acoustic-vibration calculationmethods coupling bearing with the pedestal can not be solved very well. And thus itbecomes a barrier for the research and development of rolling element bearings withhigh precision, low noise and long life. Currently, the topics with respct to skiddingdynamic model and algorithm of rolling element bearing, as well as how skiddinginfluences the rolling element bearing’s life, vibration and noise have become keycommon scientific problems which needs to be solved urgently. So, the studies aboutskidding mechanism of rolling element bearing, dynamic model and acoustic-vibrationcalculation methods have great theoretical significance and practical engineering value.
This paper mainly focuses on: the skidding causes of rolling element, dynamicmodel to investigate skidding of rolling element at entry into the loaded zone, dynamicmodel to investigate whole skidding of rolling element bearing during angularacceleration process，the effect of skidding on the vibration characteristic of rollingelement bearing, acoustic-vibration model for bearing noise and the effects of skiddingon the noise characteristics. The main tasks of this paper are listed as follows:
①Based on the analysis of skidding causes of the rolling element and their effectson bearing’s performance, the skidding dynamic model of the rolling element enteringthe loaded zone was built, with taking non-linear contact, variable friction coefficient,clearance, nip angle and other non-linear factors into consideration. Nip skiddingbehavior while rolling element entering the loaded zone was studied, and how theskidding of the rolling element was affected by the bearing’s load and speed was alsoinvestigated;
②The complete contact model of the rolling element bearing and the interactionmodel between rolling elements and cage were established, and then the motion differential equations of the inner race, the rolling elements and the cage were derivedrespectively. The complete skidding dynamic model of the rolling element bearingduring angular acceleration was built. It is validated by comparison with the resultsfrom Harris’s model and experiment. The skidding characteristics of rolling elementbearing during angular acceleration process and how they can be affected by the bearingload and the angular acceleration of inner race were studied;
③The skidding of the rolling element was taken as the excitation of the bearing’svibration. Taking account time-varying stiffness, clearance, skidding of rolling elementsand other non-linear factors, the non-linear contact forces and sliding friction forces dueto skidding were derived. Then, the vibration model of the rolling element bearing wasestablished. The vibration response of the rolling element bearing was obtained, and thevibration features of the bearing under skidding when the rolling elements entering theloaded zone were studied;
④Dynamic model, finite element model and boundary element model werecoupled together to establish the pedestal’s acoustic-vibration model. The vibrationresponse of the outer race was obtained based on the vibration model ofbearing-pedestal system, which was the excitation source of the vibration and noise ofthe pedestal. The finite element model of the pedestal was built, and full method wasused to perform transient dynamic analysis to obtain vibration response of the pedestal.The boundary element model of the pedestal was built, where the pedestal’s surfacevibration response was applied as boundary condition. Direct boundary element methodwas used to solve boundary integral formula in Helmholtz equation, which enables theanalysis of the pedestal’s acoustic characteristics. Validity of the model wasdemonstrated by comparison with experiment results. The noise features of the bearingunder skidding while rolling elements was entering the loaded zone were studied, whichcould provide theoretical basis for the resuction of the vibration and noise.
引文
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