滚动轴承摩擦力矩预报方法研究
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摘要
滚动轴承摩擦力矩是评价轴承运转灵活性及寿命的重要指标。目前关于滚动轴承摩擦力矩预测的研究还不多,由于摩擦力矩值呈现一种随机的、非稳定的周期性变化,用传统的统计理论预测与控制常常不能取得预期的效果,本文将混沌理论引入到滚动轴承摩擦力矩预测领域,着重讨论了滚动轴承摩擦力矩时间序列的混沌特性和滚动轴承摩擦力矩时间序列局域预测问题,并结合乏信息系统理论,讨论了混沌局域区间预测问题。
研究了滚动轴承摩擦力矩的混沌特性及其识别方法。提出了一种新的求解相空间重构参数的方法-灰关系法,可以同时求解最优延迟时间和嵌入维数;并采用小数据量法计算最大Lyapunov指数。通过对四种型号轴承的摩擦力矩试验所得时间序列的应用研究表明,所研究的时间序列具有混沌特性,存在着低维的奇异吸引子。
在对滚动轴承摩擦力矩混沌识别的基础上,研究了滚动轴承摩擦力矩的灰混沌评估与预报模型(GCEM)。在乏信息系统理论和加权一阶局域预测模型的基础上,首先采用灰关系法同时求取相空间重构参数,然后,在不同的重构参数下,结合滚动灰自助融合理论,提出了一种新的预测模型-灰混沌评估与预报模型,该预测模型可以同时实现点预测和区间预测,以深沟球轴承HKTB的摩擦力矩试验数据作为实例进行计算分析,结果验证了GCEM模型的有效性。
研究了滚动轴承摩擦力矩时间序列的多种混沌预测模型。针对既有混沌时间序列单一预测方法的局限性,选取了五种混沌预测方法,建立了混沌动态融合预测模型(CGBM),该模型有很高的预测精度和可靠度。实例分析表明该模型是有效的。
本论文所研究的基本理论和方法具有通用性和可行性。研究表明本文所建立的两种模型对滚动轴承摩擦力矩的预测分析是正确可靠的,预测精度能够达到实际工程的需要,在不同的置信水平下,可靠度也很高。
The bearing friction torque is an important index of evaluating the operational sensitivity and life of rolling bearing. Presently, there are few researches on the prediction of rolling bearing friction torque. Because the friction torque values show random and unstable periodic change, using the traditional statistical theory to predict and control often can not achieve the desired results. So chaotic theory is introduced in the prediction field of rolling bearing friction torque. In the paper, chaos characteristics and local-region prediction problem of rolling bearing friction torque time series are discussed, and based on the poor information system theory, the problem of chaotic local interval prediction is discussed.
Firstly, rolling bearing friction torque chaotic characteristics and identification methods are discussed. A novel method for solving phase space reconstruction parameters - the grey relation method, which synchronously calculate the optimal delay time and embedding dimension is proposed. The small data sets method is adopted to calculate the maximum of Lyapunov exponents. The results of application study on the four types of bearing have shown that the studied time series have chaotic characteristics, and there are low-dimensional strange attractors.
Secondly, based on chaos identification of bearing friction torque, the grey chaos evaluation model (GCEM) is proposed. On the basis of poor information system theory and add-weighted one-rank local-region model , first, the optimum embedding dimension and optimum delay time for the phase space reconstruction are synchronously calculated with the grey relation method, and then, at different reconstruction parameters, based on the grey bootstrap fusion method, a novel model called the grey chaos evaluation model is presented . It can effectively predict the value and its fluctuation interval. The test data of HKTB bearing friction torque as an example is analyzed, the calculated results validate the availability.
Rolling friction torque studies a variety of chaotic time series forecasting models. Considering the limitations of a single chaotic time series prediction, selecting the five kinds of chaotic forecasting methods, a chaotic dynamical fusion prediction models (CGBM) is established, selected the five kinds of chaotic forecasting methods. The model has high prediction accuracy and reliability. Case analysis shows that the model is effective.
Elementary theories and methods studied in this paper are of the versatility and feasibility. Studies show that the two models established in this paper using rolling bearing friction torque analysis are correct and reliable, the prediction accuracy can reach the requirements of the actual engineering; On the different confidence levels, its reliability is also high.
研究了滚动轴承摩擦力矩的混沌特性及其识别方法。提出了一种新的求解相空间重构参数的方法-灰关系法,可以同时求解最优延迟时间和嵌入维数;并采用小数据量法计算最大Lyapunov指数。通过对四种型号轴承的摩擦力矩试验所得时间序列的应用研究表明,所研究的时间序列具有混沌特性,存在着低维的奇异吸引子。
在对滚动轴承摩擦力矩混沌识别的基础上,研究了滚动轴承摩擦力矩的灰混沌评估与预报模型(GCEM)。在乏信息系统理论和加权一阶局域预测模型的基础上,首先采用灰关系法同时求取相空间重构参数,然后,在不同的重构参数下,结合滚动灰自助融合理论,提出了一种新的预测模型-灰混沌评估与预报模型,该预测模型可以同时实现点预测和区间预测,以深沟球轴承HKTB的摩擦力矩试验数据作为实例进行计算分析,结果验证了GCEM模型的有效性。
研究了滚动轴承摩擦力矩时间序列的多种混沌预测模型。针对既有混沌时间序列单一预测方法的局限性,选取了五种混沌预测方法,建立了混沌动态融合预测模型(CGBM),该模型有很高的预测精度和可靠度。实例分析表明该模型是有效的。
本论文所研究的基本理论和方法具有通用性和可行性。研究表明本文所建立的两种模型对滚动轴承摩擦力矩的预测分析是正确可靠的,预测精度能够达到实际工程的需要,在不同的置信水平下,可靠度也很高。
The bearing friction torque is an important index of evaluating the operational sensitivity and life of rolling bearing. Presently, there are few researches on the prediction of rolling bearing friction torque. Because the friction torque values show random and unstable periodic change, using the traditional statistical theory to predict and control often can not achieve the desired results. So chaotic theory is introduced in the prediction field of rolling bearing friction torque. In the paper, chaos characteristics and local-region prediction problem of rolling bearing friction torque time series are discussed, and based on the poor information system theory, the problem of chaotic local interval prediction is discussed.
Firstly, rolling bearing friction torque chaotic characteristics and identification methods are discussed. A novel method for solving phase space reconstruction parameters - the grey relation method, which synchronously calculate the optimal delay time and embedding dimension is proposed. The small data sets method is adopted to calculate the maximum of Lyapunov exponents. The results of application study on the four types of bearing have shown that the studied time series have chaotic characteristics, and there are low-dimensional strange attractors.
Secondly, based on chaos identification of bearing friction torque, the grey chaos evaluation model (GCEM) is proposed. On the basis of poor information system theory and add-weighted one-rank local-region model , first, the optimum embedding dimension and optimum delay time for the phase space reconstruction are synchronously calculated with the grey relation method, and then, at different reconstruction parameters, based on the grey bootstrap fusion method, a novel model called the grey chaos evaluation model is presented . It can effectively predict the value and its fluctuation interval. The test data of HKTB bearing friction torque as an example is analyzed, the calculated results validate the availability.
Rolling friction torque studies a variety of chaotic time series forecasting models. Considering the limitations of a single chaotic time series prediction, selecting the five kinds of chaotic forecasting methods, a chaotic dynamical fusion prediction models (CGBM) is established, selected the five kinds of chaotic forecasting methods. The model has high prediction accuracy and reliability. Case analysis shows that the model is effective.
Elementary theories and methods studied in this paper are of the versatility and feasibility. Studies show that the two models established in this paper using rolling bearing friction torque analysis are correct and reliable, the prediction accuracy can reach the requirements of the actual engineering; On the different confidence levels, its reliability is also high.
引文
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[2] Gan K G, Zaitov L M. Investigation into the dependence of the friction moment of high-speed self-lubrication ball bearings on the duration of work, rotational speed and load[J]. Soviet Engineering Research, 1990, 10(2): 41-46.
[3] Zheng Dezhi, Wang Liqin, Gu Le, Wei Yongqiang. Study of friction moment measurement system of small rolling bearing[J]. Journal of Harbin Institute of Technology, 2005, 37(SUPPL. 1): 161-163.
[4]夏新涛,陈晓阳,张永振等.航天轴承摩擦力矩的最大熵概率分布与bootstrap推断[J].宇航学报,2007,5(28):1395-1400.
[5]徐跃进.高速脂润滑滚动轴承的摩擦力矩的计算[J].株洲师范高等专科学校学报,2007,12(5):18-21.
[6]朱江红.低速球轴承摩擦力矩的分析研究[J].导弹与航天运载技术,2000,(6):20-25.
[7] Xia Xintao, Chen Xiaoyang, Zhang Yongzhen, etal. The dynamic evaluation and diagnose of the friction torque of the bearing for space using[J]. Journal of Airspace Power, 2007, 22(1), 156-162.
[8] Fidel Ernesto Hernandez Montero, Oscar Caveda Medina. The application of bispectrum on diagnosis of rolling element bearings: A theoretical approach [J]. Mechanical Systems and Signal Processing. 2008 (22):588-596.
[9] Townsend D P,Allen C W,Zaratsky E V.Study of ball bearing torque under elastohydrodynamic lubrication[R].National Aeronautics and Space Administration,Lewis Research Center ,Cleveland,Ohio,NASA-TM-X-68271,1973.
[10] Kitahara Tokio, Okamoto Junzo.Friction Torque of Instrument Ball Bearings Under Comined Radial and Thrust Load[J] . Japan Society of Lubrication Engineers , 1984,(5 ) :131-136.
[11]李智慧.弹流润滑高速滚动轴承性能分析[J].北京:北京工业大学,2007.
[12]张葵,李建华.球轴承摩擦力矩的分析计算[J].轴承,2001,(1):8-11.
[13]朱爱华,朱成九,张卫华.滚动轴承摩擦力矩的计算分析[J].轴承,2008,(7)::1-3.
[14]高晓康,万德安.微型轴承的摩擦力矩及其测量[J].上海计量学报,2003,30(6):13-
[15]张永,夏新涛,王中宇等.滚动轴承摩擦力矩的预测方法研究[J].轴承,2006,(10):22-24.
[16]王长兴.大型滚动轴承摩擦力矩试验研究[D].洛阳:河南科技大学,2008.
[17]夏新涛,贾晨辉,王中宇.滚动轴承摩擦力矩的非线性特征[J].农业机械学报, 2009,4(40):202-205.
[18]彭涛.滚动轴承的技术动向[J].轴承,2005,(7):45-46.
[19]刘泽九,贺士荃,刘晖.滚动轴承应用[M].北京:机械工业出版社,2007.
[20]贾群义.滚动轴承设计原理与应用技术[M].西安:西北工业大学出社,1988.
[21]李建华,邓四二,马纯民.陀螺仪框架灵敏轴承摩擦力矩影响因素分析[J].轴承,2006,(7):4-7.
[22]朱孔敏.成对角接触球轴承摩擦力矩测量仪研制[D].合肥:合肥工业大学,2004.
[23]马小梅,邓四二,梁波等.航天轴承摩擦力矩的实验分析[J].轴承,2005,(10):22-24.
[24]王振华.实用轴承手册[M].上海:上海科学技术文献出版社,1990.
[25] Harris T A. Rolling Bearing Analysis[M]. New York: John Wiley and Sons, 1984.
[26]任海东,杨伯原,李建华等.航天高速轴承动态摩擦力矩的预测[J].润滑与密封2008,(2):1-4.
[27] Harris T A, Kotzalas Michael N. Advanced concepts of bearing technology[M]. USA: CRC press, 2007.
[28] Harris T A, Kotzalas Michael N. Essential concepts of bearing technology[M]. USA: CRC press, 2007.
[29] Harris, T A.滚动轴承分析[M].第三版(罗继伟译等).洛阳:洛阳轴承研究所,1997.
[30] SKF. General Catalogue 4000E[C]. Swedish: SKF, 1989.
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