牙轮钻头圆柱滚子轴承接触力学性质及弹流润滑理论研究
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摘要
要加快我国石油天然气的勘探开发速度,提高钻井工程技术的国际竞争能力,提高钻头尤其是牙轮钻头的工作性能和工作寿命十分重要。现阶段应综合应用接触力学、润滑理论等学科的知识,对滚子凸度设计、空心圆柱滚子及其润滑状态等关键问题进行深入研究,进而研制开发长寿命、高转速的滚动轴承牙轮钻头。
本文首先针对Hertz点接触问题的求解方法进行了研究,得到了关于点接触问题精确高效的完全数值算法；从计算速度、计算精度和计算方便性等方面对几种典型算法进行了对比研究,得出了各算法在不同条件下的适用情况；并将完全数值算法应用于牙轮钻头滚动轴承中的全圆弧凸型滚子,分析了其接触参数在不同条件下的变化。然后,采用MSC.Marc有限元软件对迄今常见代表性凸型滚子的应力分布规律和特点进行了分析,提出采用多段变曲率圆弧组合替代Lundberg理论对数凸型的工程化模拟技术,给出了较为合理的圆弧组合数目；分析了空心圆柱滚子及其进行凹端处理后的应力分布规律。结果表明,合理的空心度可减小接触应力的边缘效应,但等效应力在滚子两端的应力集中始终存在；在相同空心度下,等效应力和接触应力随载荷的变化规律不同；且不同载荷作用下,最佳空心度的理论值不同；空心度较大时,滚子内壁等效应力会超过外壁成为危险区域,同时应考虑弯曲应力的影响,避免滚子内壁发生弯曲疲劳断裂；较之普通空心滚子,凹端空心圆柱滚子有效克服了滚子端部的应力集中现象。最后,采用多重网格法对牙轮钻头实心圆柱滚子和空心圆柱滚子的弹流润滑情况进行了分析,通过对无限长滚子线接触弹流润滑问题的研究,揭示了实心圆柱滚子油膜压力和膜厚随载荷参数、速度参数和材料参数的变化规律；空心圆柱滚子空心度的变化会引起速度参数和载荷参数的变化,但并没有引起接触区域中部油膜厚度以及最小膜厚的明显变化；空心度的增加可以降低油膜压力,但合理空心度的选取应考虑其对滚子内壁应力分布的影响。有限长线接触弹流润滑中最大油膜压力和最小膜厚都位于滚子端部,故滚子端部为易破坏部位；滚子中部润滑状况与无限长滚子几乎一致,可按无限长处理；空心度对滚子端部润滑情况的影响与中部相同,由于端部油膜压力大于中部,故二次峰值和最小油膜厚度较之中部都更靠近出口区。
本文的研究成果为国内自主实现滚动轴承牙轮钻头的长寿命和高转速化,乃至为工程实际中广泛存在的重载低速滚子轴承系统工作性能的提高奠定了坚实基础,同时也值得标准或通用滚子轴承、铁路机车、冶金轧机等行业的研究人员借鉴。
In order to speed up the rate of oil & gas exploration and development, and improve the international competition of drilling engineering technology, improving the working performance and working life of bit especially the rock bit is very important. Currently the knowledge of contact mechanics, lubrication theory and other disciplines should be utilized to carry out in-depth research on some critical problems such as roller crowned design, hollow cylindrical roller and its lubrication status, thus researching and developing roller bearing rock bit with long life and high speed.
Fist of all, by studying the solution method of Hertzian point contact problem, the accurate and efficient full numerical method was obtained. Through comparative study of calculation speed, calculation accuracy, and calculation convenience of some typical algorithms, the applicable condition of each algorithm under different conditions was obtained. And then full numerical method was applied to single-arc crowned roller in rock-bit roller bearing, to analyze the change of contact parameters under different conditions. Secondly, taking advantage of Finite Element software MSC. Marc, the stress distribution of common representative types of crowned roller so far were analyzed. It is put forward that the Lundberg theoretical logarithmic crowned type can be replaced approximately by multiple-variable-curvature arcs, and according to the theoretical research, the appropriate number of variable-curvature-arc segments were presented. And then the stress distribution of hollow as well as concave-ended hollow cylindrical roller was analyzed. It is shown that, the reasonable hollow ratio can reduce the contact stress concentration in the roller end, But it can not avoid the sharp edge equivalent stress, under the same hollow ratio, the change of equivalent stress and contact stress is different with the change of loads. The optimal hollow ratio is also different under different extrnal loads. The equivalent stress on the inner wall can exceed the corresponding value on the outer wall, thus making the inner wall be the dangerous area under large hollow ratio. The bending stress should be considered in the mean time to avoid the bending fatigue failure occurred on the inner wall of roller. Compared with ordinary hollow roller, concave-ended hollow cylindrical roller can effectively overcome the stress concentration at the end of roller. Finally, the multilevel method was utilized to analyze the elastohydrodynamic lubrication (EHL) condition of solid as well as hollow cylindrical roller in rock bit. The analysis of EHL for infinite line contact illustrated that the change of film pressure and thickness under different load parameters, velocity parameters, and material parameters. The change of hollow ratio for hollow cylindrical roller can cause the change of velocity parameter and load parameter, but will not cause the obvious change of film thickness and minimum film thickness at central contact area. The increase of hollow ratio can reduce the film pressure, but the stress distribution on inner wall should be considered when selecting a reasonable hollow ratio. The analysis of EHL for finite line contact showed that, the maximum film pressure and minimum film thickness were both at the end of roller, therfore the end of roller is the easily damaged area. The lubrication condition at middle part of the roller can be treated as infinite, due to its similarity to the infinite one. At the end part and middle part of roller, the influence of hollow ratio on lubrication condition was the same. Because the film pressure at the end was larger than that at the middle, the second peak and minimum film thickness were both closer to inlet-zone.
The research results established a solid foundation for accomplishing the long-life and high-speed of rock bit with roller bearing, furthemore it can be used to improve the working performance of heavy-load and low-speed roller bearing system widely existed in engineering practice. It is also worth to be learne by the researchers in standard or universal roller bearing, railway locomotive, metallurgical mill and so on.
本文首先针对Hertz点接触问题的求解方法进行了研究,得到了关于点接触问题精确高效的完全数值算法；从计算速度、计算精度和计算方便性等方面对几种典型算法进行了对比研究,得出了各算法在不同条件下的适用情况；并将完全数值算法应用于牙轮钻头滚动轴承中的全圆弧凸型滚子,分析了其接触参数在不同条件下的变化。然后,采用MSC.Marc有限元软件对迄今常见代表性凸型滚子的应力分布规律和特点进行了分析,提出采用多段变曲率圆弧组合替代Lundberg理论对数凸型的工程化模拟技术,给出了较为合理的圆弧组合数目；分析了空心圆柱滚子及其进行凹端处理后的应力分布规律。结果表明,合理的空心度可减小接触应力的边缘效应,但等效应力在滚子两端的应力集中始终存在；在相同空心度下,等效应力和接触应力随载荷的变化规律不同；且不同载荷作用下,最佳空心度的理论值不同；空心度较大时,滚子内壁等效应力会超过外壁成为危险区域,同时应考虑弯曲应力的影响,避免滚子内壁发生弯曲疲劳断裂；较之普通空心滚子,凹端空心圆柱滚子有效克服了滚子端部的应力集中现象。最后,采用多重网格法对牙轮钻头实心圆柱滚子和空心圆柱滚子的弹流润滑情况进行了分析,通过对无限长滚子线接触弹流润滑问题的研究,揭示了实心圆柱滚子油膜压力和膜厚随载荷参数、速度参数和材料参数的变化规律；空心圆柱滚子空心度的变化会引起速度参数和载荷参数的变化,但并没有引起接触区域中部油膜厚度以及最小膜厚的明显变化；空心度的增加可以降低油膜压力,但合理空心度的选取应考虑其对滚子内壁应力分布的影响。有限长线接触弹流润滑中最大油膜压力和最小膜厚都位于滚子端部,故滚子端部为易破坏部位；滚子中部润滑状况与无限长滚子几乎一致,可按无限长处理；空心度对滚子端部润滑情况的影响与中部相同,由于端部油膜压力大于中部,故二次峰值和最小油膜厚度较之中部都更靠近出口区。
本文的研究成果为国内自主实现滚动轴承牙轮钻头的长寿命和高转速化,乃至为工程实际中广泛存在的重载低速滚子轴承系统工作性能的提高奠定了坚实基础,同时也值得标准或通用滚子轴承、铁路机车、冶金轧机等行业的研究人员借鉴。
In order to speed up the rate of oil & gas exploration and development, and improve the international competition of drilling engineering technology, improving the working performance and working life of bit especially the rock bit is very important. Currently the knowledge of contact mechanics, lubrication theory and other disciplines should be utilized to carry out in-depth research on some critical problems such as roller crowned design, hollow cylindrical roller and its lubrication status, thus researching and developing roller bearing rock bit with long life and high speed.
Fist of all, by studying the solution method of Hertzian point contact problem, the accurate and efficient full numerical method was obtained. Through comparative study of calculation speed, calculation accuracy, and calculation convenience of some typical algorithms, the applicable condition of each algorithm under different conditions was obtained. And then full numerical method was applied to single-arc crowned roller in rock-bit roller bearing, to analyze the change of contact parameters under different conditions. Secondly, taking advantage of Finite Element software MSC. Marc, the stress distribution of common representative types of crowned roller so far were analyzed. It is put forward that the Lundberg theoretical logarithmic crowned type can be replaced approximately by multiple-variable-curvature arcs, and according to the theoretical research, the appropriate number of variable-curvature-arc segments were presented. And then the stress distribution of hollow as well as concave-ended hollow cylindrical roller was analyzed. It is shown that, the reasonable hollow ratio can reduce the contact stress concentration in the roller end, But it can not avoid the sharp edge equivalent stress, under the same hollow ratio, the change of equivalent stress and contact stress is different with the change of loads. The optimal hollow ratio is also different under different extrnal loads. The equivalent stress on the inner wall can exceed the corresponding value on the outer wall, thus making the inner wall be the dangerous area under large hollow ratio. The bending stress should be considered in the mean time to avoid the bending fatigue failure occurred on the inner wall of roller. Compared with ordinary hollow roller, concave-ended hollow cylindrical roller can effectively overcome the stress concentration at the end of roller. Finally, the multilevel method was utilized to analyze the elastohydrodynamic lubrication (EHL) condition of solid as well as hollow cylindrical roller in rock bit. The analysis of EHL for infinite line contact illustrated that the change of film pressure and thickness under different load parameters, velocity parameters, and material parameters. The change of hollow ratio for hollow cylindrical roller can cause the change of velocity parameter and load parameter, but will not cause the obvious change of film thickness and minimum film thickness at central contact area. The increase of hollow ratio can reduce the film pressure, but the stress distribution on inner wall should be considered when selecting a reasonable hollow ratio. The analysis of EHL for finite line contact showed that, the maximum film pressure and minimum film thickness were both at the end of roller, therfore the end of roller is the easily damaged area. The lubrication condition at middle part of the roller can be treated as infinite, due to its similarity to the infinite one. At the end part and middle part of roller, the influence of hollow ratio on lubrication condition was the same. Because the film pressure at the end was larger than that at the middle, the second peak and minimum film thickness were both closer to inlet-zone.
The research results established a solid foundation for accomplishing the long-life and high-speed of rock bit with roller bearing, furthemore it can be used to improve the working performance of heavy-load and low-speed roller bearing system widely existed in engineering practice. It is also worth to be learne by the researchers in standard or universal roller bearing, railway locomotive, metallurgical mill and so on.
引文
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