钢丝滚道球轴承的接触力学特性及其相关技术研究
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摘要
近10来年,钢丝滚道球轴承(Wire race ball bearing, WRBB)以其径向尺寸大、轴向尺寸小的结构特点,被广泛地应用于大型雷达天线和飞行器仿真转台等国防科技领域、数控回转工作台、建筑机械、医疗器械以及纺织工业。它被认为是具有高刚惯比和高抗倾覆能力的轴系支承系统技术,已经成为解决许多存在几何空间限制、质量约束和惯量约束的工程设计与制造等方面问题的优选方案。该类轴系支承可同时承受轴向载荷、径向载荷、倾覆力矩及其组成的多种形式的复合载荷。然而,接触体间循环交变的接触应力及残余不平衡力矩往往导致疲劳、磨损及点蚀在钢丝滚道表面发生,影响系统的运转平稳性和回转精确度。针对该现象国内外目前相关研究不足。因此,本文提出将其视为接触问题进行对待,运用接触力学、摩擦学和材料学知识,采用解析法、弹-塑性有限元法及试验,考虑几何非线性、材料非线性、复合载荷分布以及摩擦等接触边界条件,对WRBB轴系的预紧、支承刚度和接触破坏进行全面研究。
适当的预紧有利于提高轴系的支承刚度;过大的预紧导致塑性变形和接触破坏;故WRBB的预紧是首先需要研究的内容。
为了克服相关行业目前WRBB轴系预紧的调试方法极其依赖工程师个人经验的问题,本文对其轴系进行力学分析,然后基于非协调性Hertz接触理论建立了确定其轴系预紧量范围的数学模型,通过MATLAB?编程形成一套数值计算方法。数值求解得到了法向接触力、接触变形、最大接触压力以及椭圆形接触区域的长、短半轴,并获得了WRBB轴系预紧量合理的范围。以某型号飞行仿真转台中直径为1000mm的WRBB为例,组建了预紧测量系统,实验结果与理论结果吻合良好。
为了能够准确定位并确定WRBB轴系的预紧量,本文在对其轴系的空间力系进行分析的基础上,基于库伦定律、滚动摩阻定律和空间力偶等效定理,建立了其起动力矩与预紧量关系的数学模型。通过MATLAB?编程并进行数值求解,得到该数学模型的理论曲线。此后通过实验系统对理论结果进行了实验验证,获得了良好效果,为实际工程中WRBB轴系预紧量的调节与控制提供了有效的方法。
刚度计算是振动理论和结构稳定性分析的重要环节,研究大型WRBB的刚度特性对提高其使用性能具有实际意义。为此,本文首先对WRBB的接触载荷分布进行了分析,然后根据非协调性Hertz接触理论、虚位移原理、余弦定理、极限定理中的洛必达法则、刚度和柔度的数学定义以及Stribeck的载荷分布理论分别建立了WRBB的轴向支承刚度、径向支承刚度和翻转支承刚度的数学模型。分别设计了加载机构并组建了轴向支承刚度、径向支承刚度和翻转支承刚度的测量系统,实验验证了上述支承刚度数学模型的正确性。对理论与实验结果进行对比和分析,获得了良好效果,为WRBB今后进一步的接触动力学分析奠定了基础,为工程实际提供了参数依据。
接触问题的求解是一个高度非线性且相当耗费计算资源的问题。常规接触分析的方法主要基于经典Hertz弹性接触理论,而且未考虑接触体的几何与材料非线性。因此,本文充分考虑接触体的几何与材料非线性,在Instron-5569万能电子拉伸机上测得工程中常用的两种钢丝(牌号均为T8MnA;一种是国产质地偏软的,称其为I号钢丝;另一种是日本进口质地偏硬的,称其为II号钢丝)的应力-应变曲线。然后,在ANSYS?中运用APDL语言建立了球-钢丝滚道的3D接触子模型,对I号钢丝-钢球、II号钢丝-钢球、I号钢丝-Si3N4陶瓷球以及II号钢丝-Si3N4陶瓷球4种接触模型的弹-塑性接触分析进行了求解,得到了接触体的von Mises应力、弹性应变、塑性应变以及接触斑的形状和尺寸。最后,与弹性接触分析的结果进行了对比。结果表明:(1)考虑接触体的应力-应变曲线的弹-塑性接触分析的结果比不考虑应力-应变曲线的纯弹性接触分析的结果更接近实际;(2)采用子模型技术和多尺度有限元分网方法有效地节约了接触分析的计算成本,提高了计算效率和求解精度。
另外,目前尚不明确接触载荷、接触体的几何尺寸和材料属性参数对接触特性的影响关系以及接触体的磨损及点蚀的特征和规律。鉴于此,本文首先分析了接触载荷、接触体的几何参数和材料属性参数对接触特性的影响关系。然后,分别对钢球-I号钢丝、钢球-II号钢丝、Si3N4陶瓷球-I号钢丝和Si3N4陶瓷球-II号钢丝4种接触方式进行了接触破坏试验。最后,对接触区用扫描电子显微镜(SEM)进行了表征和分析,揭示了接触体发生接触破坏的特征、规律和机理,为有效控制钢丝滚道发生接触破坏的难题和钢丝滚道的新材料、新工艺研究奠定了理论和技术基础。
In recent 10 years, the wire race ball bearing has been extensively used, including in the field of weapon equipments, like the big antenna of radar and the aircraft simulating rotary table; the field of numerical control slewing machines, the field of building machineries, the medical apparatus and instruments, and the field of the textile industry. It has been regarded as a technique of the supporting system with high ratio of stiffness to inertia and high resistance capability to overturning moment. It has become the optimal proposal for solving the engineering design and manufacture problem with limitation in spatial dimension, and with restriction in mass and inertia. This kind of bearing can simultaneously support axial loads, radial loads, overturning moment and compound loads. However, the alternating stress and the residual unbalanced moment often result in fatigue, wear and pitting corrosion on contacting surfaces of wires. They have significant effects on the precision and dynamic stability of the system. No effective method has been reported. Hence, we present that this problem can be treated as a contact problem. According to the corresponding theories of contact mechanics, tribology and material science, by the analytical method, elastic-plastic finite element method and experiments, with taking the geometric nonlinearity, the material nonlinearity, the compound load distribution and the friction into account, the preload of the wire race ball bearing, the supporting stiffness and the contact failure were investigated in detail.
Reasonable preload can improve the supporting stiffness; while excessive preload results in plastic deformation and contact failure. Therefore, the research on preload is critical.
In order to eliminate the problem of the traditional method for adjusting the preload which relies heavily on personal experience of engineers, the mechanical equilibrium conditions were analyzed firstly. Then, the preload mathematical model of a wire race ball bearing was built based on the non-conforming Hertz contact theory. And a numerical method was developed in MATLAB?. The normal contact forces, contact deformation, contact pressure distribution and the semi axes of the contact ellipse were obtained. Further, the appropriate range of preload for a wire race ball bearing was achieved. Finally, the preload measuring system was constructed by employing an example of a wire race ball bearing with a diameter of 1000 mm used in a certain type of aircraft simulating rotary table. The experimental results are in good agreement with the theoretical results.
To exactly determine the preload magnitude of the wire race ball bearing, in the present dissertation, the mathematical model of the relationship between the starting torque and the preload magnitude was built, based on the analysis of the spatial force system, Coulomb’s law, the law of rolling resistance and the theorem of equivalent spatial couple. The theoretical curve of the above model was obtained by the numerical solution in MATLAB?. Finally, the experiments were performed to validate the theoretical results. It shows that the theoretical and experimental results are very close. The investigation provides an effective method for the adjusting and controlling of preload in a wire race ball bearing in practice.
It is paramount that the stiffness characteristic should be exactly described for being the foundation of the vibration theory and the structure stability analysis. Hence, firstly, the load distribution of the wire race ball bearing was analyzed. According to the non-conforming Hertz contact theory, the principle of virtual displacement, the cosine law, L’Hospital’s rule and the definition of stiffness and flexibility and Stribeck’s load distribution, the mathematical models of the axial supporting stiffness, the radial supporting stiffness and the overturning supporting stiffness were developed. Finally, the loading mechanisms were designed. The measuring systems of the above supporting stiffness were built. The experimental results are in good agreement with the theoretical results, which demonstrates the validity of the above supporting stiffness mathematical models. It provides basis for the contact dynamics analysis and parametric support for engineering application of the wire race ball bearing.
The solution of contact problems is highly nonlinear and requires significant computer resources. The conventional contact analysis is mainly based on the classical Hertz elastic contact theory and the geometric and material nonlinearity are not considered. Hence, firstly, the geometric and material nonlinearity of 2 kinds of wires named No. I and No. II were taken into account by using the real stress-strain curve of the wire tested on the Instron-5569 universal electron tension tester. Secondly, the ANSYS Parameter Design Language (APDL) was used to model and solve the contact analysis of 4 kinds of 3-D contact sub-models, namely steel ball-wire race of No. I, steel ball-wire race of No. II, Si3N4 ceramic ball-wire race of No. I and Si3N4 ceramic ball-wire race of No. II. The von Mises stresses, the elastic strain, the plastic strain and the shape and sizes of contact ellipses were achieved. Finally, comparison between the elastic-plastic contact analysis and the elastic contact analysis shows that the elastic-plastic contact analysis is exacter and closer to the fact in practice; and the sub-modeling technology and the multi-size mesh method greatly contribute to the saving of the computing cost, and the improvement of the computational efficiency and precision.
In addition, the influences of the contact load, the geometric parameters and the material property parameters on the contact characteristic are not clear. Furthermore, the characteristic, regularity and mechanism on wear and pitting corrosion are ambiguous. Therefore, firstly, the influnces of the contact load, the geometric parameters and the material property parameters on the contact characteristic were analyzed theoretically. Secondly, the contact failure experiments for the 4 types of contact, namely steel ball-wire race of No. I, steel ball-wire race of No. II, Si3N4 ceramic ball-wire race of No. I and Si3N4 ceramic ball-wire race of No. II were carried out. Finally, the contact zones of the contact bodies were characterized by the scanning electronic microscopy (SEM). The results reveal the characteristic, regularity and mechanism on contact failure. The present work provides theory and technology for effectively preventing the wire from contact failure and studying on the new material and the novel processing.
适当的预紧有利于提高轴系的支承刚度;过大的预紧导致塑性变形和接触破坏;故WRBB的预紧是首先需要研究的内容。
为了克服相关行业目前WRBB轴系预紧的调试方法极其依赖工程师个人经验的问题,本文对其轴系进行力学分析,然后基于非协调性Hertz接触理论建立了确定其轴系预紧量范围的数学模型,通过MATLAB?编程形成一套数值计算方法。数值求解得到了法向接触力、接触变形、最大接触压力以及椭圆形接触区域的长、短半轴,并获得了WRBB轴系预紧量合理的范围。以某型号飞行仿真转台中直径为1000mm的WRBB为例,组建了预紧测量系统,实验结果与理论结果吻合良好。
为了能够准确定位并确定WRBB轴系的预紧量,本文在对其轴系的空间力系进行分析的基础上,基于库伦定律、滚动摩阻定律和空间力偶等效定理,建立了其起动力矩与预紧量关系的数学模型。通过MATLAB?编程并进行数值求解,得到该数学模型的理论曲线。此后通过实验系统对理论结果进行了实验验证,获得了良好效果,为实际工程中WRBB轴系预紧量的调节与控制提供了有效的方法。
刚度计算是振动理论和结构稳定性分析的重要环节,研究大型WRBB的刚度特性对提高其使用性能具有实际意义。为此,本文首先对WRBB的接触载荷分布进行了分析,然后根据非协调性Hertz接触理论、虚位移原理、余弦定理、极限定理中的洛必达法则、刚度和柔度的数学定义以及Stribeck的载荷分布理论分别建立了WRBB的轴向支承刚度、径向支承刚度和翻转支承刚度的数学模型。分别设计了加载机构并组建了轴向支承刚度、径向支承刚度和翻转支承刚度的测量系统,实验验证了上述支承刚度数学模型的正确性。对理论与实验结果进行对比和分析,获得了良好效果,为WRBB今后进一步的接触动力学分析奠定了基础,为工程实际提供了参数依据。
接触问题的求解是一个高度非线性且相当耗费计算资源的问题。常规接触分析的方法主要基于经典Hertz弹性接触理论,而且未考虑接触体的几何与材料非线性。因此,本文充分考虑接触体的几何与材料非线性,在Instron-5569万能电子拉伸机上测得工程中常用的两种钢丝(牌号均为T8MnA;一种是国产质地偏软的,称其为I号钢丝;另一种是日本进口质地偏硬的,称其为II号钢丝)的应力-应变曲线。然后,在ANSYS?中运用APDL语言建立了球-钢丝滚道的3D接触子模型,对I号钢丝-钢球、II号钢丝-钢球、I号钢丝-Si3N4陶瓷球以及II号钢丝-Si3N4陶瓷球4种接触模型的弹-塑性接触分析进行了求解,得到了接触体的von Mises应力、弹性应变、塑性应变以及接触斑的形状和尺寸。最后,与弹性接触分析的结果进行了对比。结果表明:(1)考虑接触体的应力-应变曲线的弹-塑性接触分析的结果比不考虑应力-应变曲线的纯弹性接触分析的结果更接近实际;(2)采用子模型技术和多尺度有限元分网方法有效地节约了接触分析的计算成本,提高了计算效率和求解精度。
另外,目前尚不明确接触载荷、接触体的几何尺寸和材料属性参数对接触特性的影响关系以及接触体的磨损及点蚀的特征和规律。鉴于此,本文首先分析了接触载荷、接触体的几何参数和材料属性参数对接触特性的影响关系。然后,分别对钢球-I号钢丝、钢球-II号钢丝、Si3N4陶瓷球-I号钢丝和Si3N4陶瓷球-II号钢丝4种接触方式进行了接触破坏试验。最后,对接触区用扫描电子显微镜(SEM)进行了表征和分析,揭示了接触体发生接触破坏的特征、规律和机理,为有效控制钢丝滚道发生接触破坏的难题和钢丝滚道的新材料、新工艺研究奠定了理论和技术基础。
In recent 10 years, the wire race ball bearing has been extensively used, including in the field of weapon equipments, like the big antenna of radar and the aircraft simulating rotary table; the field of numerical control slewing machines, the field of building machineries, the medical apparatus and instruments, and the field of the textile industry. It has been regarded as a technique of the supporting system with high ratio of stiffness to inertia and high resistance capability to overturning moment. It has become the optimal proposal for solving the engineering design and manufacture problem with limitation in spatial dimension, and with restriction in mass and inertia. This kind of bearing can simultaneously support axial loads, radial loads, overturning moment and compound loads. However, the alternating stress and the residual unbalanced moment often result in fatigue, wear and pitting corrosion on contacting surfaces of wires. They have significant effects on the precision and dynamic stability of the system. No effective method has been reported. Hence, we present that this problem can be treated as a contact problem. According to the corresponding theories of contact mechanics, tribology and material science, by the analytical method, elastic-plastic finite element method and experiments, with taking the geometric nonlinearity, the material nonlinearity, the compound load distribution and the friction into account, the preload of the wire race ball bearing, the supporting stiffness and the contact failure were investigated in detail.
Reasonable preload can improve the supporting stiffness; while excessive preload results in plastic deformation and contact failure. Therefore, the research on preload is critical.
In order to eliminate the problem of the traditional method for adjusting the preload which relies heavily on personal experience of engineers, the mechanical equilibrium conditions were analyzed firstly. Then, the preload mathematical model of a wire race ball bearing was built based on the non-conforming Hertz contact theory. And a numerical method was developed in MATLAB?. The normal contact forces, contact deformation, contact pressure distribution and the semi axes of the contact ellipse were obtained. Further, the appropriate range of preload for a wire race ball bearing was achieved. Finally, the preload measuring system was constructed by employing an example of a wire race ball bearing with a diameter of 1000 mm used in a certain type of aircraft simulating rotary table. The experimental results are in good agreement with the theoretical results.
To exactly determine the preload magnitude of the wire race ball bearing, in the present dissertation, the mathematical model of the relationship between the starting torque and the preload magnitude was built, based on the analysis of the spatial force system, Coulomb’s law, the law of rolling resistance and the theorem of equivalent spatial couple. The theoretical curve of the above model was obtained by the numerical solution in MATLAB?. Finally, the experiments were performed to validate the theoretical results. It shows that the theoretical and experimental results are very close. The investigation provides an effective method for the adjusting and controlling of preload in a wire race ball bearing in practice.
It is paramount that the stiffness characteristic should be exactly described for being the foundation of the vibration theory and the structure stability analysis. Hence, firstly, the load distribution of the wire race ball bearing was analyzed. According to the non-conforming Hertz contact theory, the principle of virtual displacement, the cosine law, L’Hospital’s rule and the definition of stiffness and flexibility and Stribeck’s load distribution, the mathematical models of the axial supporting stiffness, the radial supporting stiffness and the overturning supporting stiffness were developed. Finally, the loading mechanisms were designed. The measuring systems of the above supporting stiffness were built. The experimental results are in good agreement with the theoretical results, which demonstrates the validity of the above supporting stiffness mathematical models. It provides basis for the contact dynamics analysis and parametric support for engineering application of the wire race ball bearing.
The solution of contact problems is highly nonlinear and requires significant computer resources. The conventional contact analysis is mainly based on the classical Hertz elastic contact theory and the geometric and material nonlinearity are not considered. Hence, firstly, the geometric and material nonlinearity of 2 kinds of wires named No. I and No. II were taken into account by using the real stress-strain curve of the wire tested on the Instron-5569 universal electron tension tester. Secondly, the ANSYS Parameter Design Language (APDL) was used to model and solve the contact analysis of 4 kinds of 3-D contact sub-models, namely steel ball-wire race of No. I, steel ball-wire race of No. II, Si3N4 ceramic ball-wire race of No. I and Si3N4 ceramic ball-wire race of No. II. The von Mises stresses, the elastic strain, the plastic strain and the shape and sizes of contact ellipses were achieved. Finally, comparison between the elastic-plastic contact analysis and the elastic contact analysis shows that the elastic-plastic contact analysis is exacter and closer to the fact in practice; and the sub-modeling technology and the multi-size mesh method greatly contribute to the saving of the computing cost, and the improvement of the computational efficiency and precision.
In addition, the influences of the contact load, the geometric parameters and the material property parameters on the contact characteristic are not clear. Furthermore, the characteristic, regularity and mechanism on wear and pitting corrosion are ambiguous. Therefore, firstly, the influnces of the contact load, the geometric parameters and the material property parameters on the contact characteristic were analyzed theoretically. Secondly, the contact failure experiments for the 4 types of contact, namely steel ball-wire race of No. I, steel ball-wire race of No. II, Si3N4 ceramic ball-wire race of No. I and Si3N4 ceramic ball-wire race of No. II were carried out. Finally, the contact zones of the contact bodies were characterized by the scanning electronic microscopy (SEM). The results reveal the characteristic, regularity and mechanism on contact failure. The present work provides theory and technology for effectively preventing the wire from contact failure and studying on the new material and the novel processing.
引文
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