Fractal analysis of friction torque performance evolution of rolling bearing
-
摘要:
以轴承全周期摩擦力矩时间序列为分析对象，以分形理论为主要分析方法，通过互信息法确定最佳延迟时间，通过观察法确定最佳嵌入维数，最终得到关联维数。结果表明：轴承摩擦力矩性能具有混沌特性；嵌入维数与系统非线性及混沌程度呈正相关，而关联维数则呈负相关；关联维数可以作为轴承性能衡量指标，A、B轴承可分别提前120、160 min预报轴承失效；基于最大熵原理验证A轴承与分形理论预测的失效时间相差12 min，仅占预报时间120 min的10%，偏离误差处于较低水平，充分验证了分形理论表征轴承性能演变的有效性和可靠性。
Abstract:The time series of the full-cycle friction torque of the bearing were taken as the analysis object, the fractal theory was used as the main analysis method, the optimal delay time was determined through the mutual information method, and the optimal embedding dimension was determined through the observation method, finally the correlation dimension was obtained. The results showed that the friction torque performance of the bearing had chaotic characteristics; the embedding dimension was positively correlated with the nonlinearity and chaos degree of the system, while the correlation dimension was negatively correlated. The correlation dimension can be used as an indicator for measuring the performance of bearings. Bearings A and B can predict bearing failure 120 min and 160 min in advance respectively. Based on the principle of maximum entropy, it was verified that the failure time of bearing A differed from that predicted by the fractal theory by 12 min, accounting for only 10% of the predicted time of 120 min. The deviation error was at a relatively small level, fully verifying the effectiveness and reliability of the fractal theory in characterizing the performance evolution of bearings.
-
图 1 轴承摩擦力矩试验机结构示意图及原理图
Figure 1. Schematic diagram and principle diagram of bearing friction torque testing machine
图 2 A轴承全周期摩擦力矩时间变化曲线
Figure 2. Full cycle friction torque time change curve of bearing A
图 6 各子序列最佳嵌入维数（A轴承）
Figure 6. Optimal embedding dimension of each subsequence （bearing A）
图 9 关联维数演变（A轴承，原第8组子序列）
Figure 9. Evolution of correlation dimension （bearing A, original group 8 subsequence）
图 10 各子序列关联维数（A轴承，原第8组子序列）
Figure 10. Correlation dimension of each subsequence （bearing A, original group 8 subsequence）
图 12 B轴承全周期摩擦力矩时间变化曲线
Figure 12. Full cycle friction torque time change curve of bearing B
图 15 各子序列最佳嵌入维数（B轴承）
Figure 15. Optimal embedding dimension of each subsequence （bearing B）
图 18 关联维数演变（B轴承，原第8组子序列）
Figure 18. Evolution of correlation dimension （bearing B, original group 8 subsequence）
图 19 各子序列关联维数（B轴承，原第8组子序列）
Figure 19. Correlation dimension of each subsequence （bearing B, original group 8 subsequence）
表 1 试验机主要技术指标
Table 1. Main technical indexes of testing machine
参数 数值 试验轴承内径/mm 20～60 径向载荷/kN ±30 径向载荷精度/% 设定值的±1 试验轴承数量/套 2 电动机功率/kW 7.5 最高转速/（r/min） 1440 转速精度/% 设定值的±2 扭矩传感器测量量程/（N·m） 0～100 扭矩传感器测量精度/% ±0.5 径向位移传感器量程/mm 0～100 
下载: 导出CSV
表 2 试验轴承的主要参数
Table 2. Main parameters of test bearings
参数 数值 3208A-2RS1TN9/
MT333209A-2RS1TN9/
MT33内径/mm 40 45 外径/mm 80 85 宽度/mm 30.2 30.2 接触角/（°） 30 30 额定动载荷/kN 48 52 额定静载荷/kN 36.5 41.5 极限转速/（r/min） 5600 5300
下载: 导出CSV
-
[1] 拜国圣. 数据驱动的滚动轴承性能退化分析与剩余寿命预测研究[D]. 成都: 电子科技大学, 2024. Bai Guosheng. Research of data-driven based analysis of rolling bearing performance degradation and remaining life prediction[D]. Chengdu: University of Electronic Science and Technology of China, 2024. (in ChineseBai Guosheng. Research of data-driven based analysis of rolling bearing performance degradation and remaining life prediction[D]. Chengdu: University of Electronic Science and Technology of China, 2024. (in Chinese) [2] 孟凡念, 杜文辽, 李浩, 等. 基于混沌理论的滚动轴承振动信号融合模型预测[J]. 航空动力学报, 2020, 35(8): 1664-1675. Meng Fannian, Du Wenliao, Li Hao, et al. Fusion model prediction of rolling bearing vibration signal based on chaos theory[J]. Journal of Aerospace Power, 2020, 35(8): 1664-1675. (in Chinese doi: 10.13224/j.cnki.jasp.2020.08.011Meng Fannian, Du Wenliao, Li Hao, et al. Fusion model prediction of rolling bearing vibration signal based on chaos theory[J]. Journal of Aerospace Power, 2020, 35(8): 1664-1675. (in Chinese) doi: 10.13224/j.cnki.jasp.2020.08.011 [3] 张若愚, 余永健, 李济顺, 等. 加速工况角接触球轴承摩擦力矩仿真分析[J]. 机械与电子, 2024, 42(10): 8-14, 21. Zhang Ruoyu, Yu Yongjian, Li Jishun, et al. Simulation analysis of friction torque of angular contact ball bearings under accelerated working conditions[J]. Machinery & Electronics, 2024, 42(10): 8-14, 21. (in Chinese doi: 10.3969/j.issn.1001-2257.2024.10.002Zhang Ruoyu, Yu Yongjian, Li Jishun, et al. Simulation analysis of friction torque of angular contact ball bearings under accelerated working conditions[J]. Machinery & Electronics, 2024, 42(10): 8-14, 21. (in Chinese) doi: 10.3969/j.issn.1001-2257.2024.10.002 [4] 时保吉, 栗永非. 基于灰自助GBM(1, 1)的滚动轴承摩擦力矩不确定性的动态预报方法[J]. 轴承, 2015(11): 35-38. Shi Baoji, Li Yongfei. Dynamic forecasting method for uncertainty of friction torque for rolling bearings based on grey bootstrap GBM(1, 1)[J]. Bearing, 2015(11): 35-38. (in Chinese doi: 10.3969/j.issn.1000-3762.2015.11.011Shi Baoji, Li Yongfei. Dynamic forecasting method for uncertainty of friction torque for rolling bearings based on grey bootstrap GBM(1, 1)[J]. Bearing, 2015(11): 35-38. (in Chinese) doi: 10.3969/j.issn.1000-3762.2015.11.011 [5] 铁晓艳, 张振潮, 李文超, 等. 成对角接触球轴承摩擦力矩测量装置的设计[J]. 机械制造, 2022, 60(4): 50-53, 58. Tie Xiaoyan, Zhang Zhenchao, Li Wenchao, et al. Design of friction torque measuring device for paired angular contact ball bearings[J]. Machinery, 2022, 60(4): 50-53, 58. (in Chinese doi: 10.3969/j.issn.1000-4998.2022.04.017Tie Xiaoyan, Zhang Zhenchao, Li Wenchao, et al. Design of friction torque measuring device for paired angular contact ball bearings[J]. Machinery, 2022, 60(4): 50-53, 58. (in Chinese) doi: 10.3969/j.issn.1000-4998.2022.04.017 [6] 林兴武. 圆锥滚子轴承摩擦力矩在线自动检测技术研究[D]. 武汉: 华中科技大学, 2009. Lin Xingwu. Research on online automatic measurement technology for the friction torque of tapered roller bearings[D]. Wuhan: Huazhong University of Science and Technology, 2009. (in ChineseLin Xingwu. Research on online automatic measurement technology for the friction torque of tapered roller bearings[D]. Wuhan: Huazhong University of Science and Technology, 2009. (in Chinese) [7] 刘雷. 滚子轴承摩擦力矩特性分析与测试装置设计[D]. 济南: 济南大学, 2022. Liu Lei. Friction torque characteristic analysis and test device design of roller bearing[D]. Jinan: University of Jinan, 2022. (in ChineseLiu Lei. Friction torque characteristic analysis and test device design of roller bearing[D]. Jinan: University of Jinan, 2022. (in Chinese) [8] 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, 40(4): 202-205. Xia Xintao, Jia Chenhui, Wang Zhongyu. Nonlinear characteristic of rolling element bearing friction torque[J]. Transactions of the Chinese Society for Agricultural Machinery, 2009, 40(4): 202-205. (in ChineseXia Xintao, Jia Chenhui, Wang Zhongyu. Nonlinear characteristic of rolling element bearing friction torque[J]. Transactions of the Chinese Society for Agricultural Machinery, 2009, 40(4): 202-205. (in Chinese) [9] Chen Long, Xia Xintao, Zheng Haotian, et al. Chaotic dynamics of cage behavior in a high-speed cylindrical roller bearing[J]. Shock and Vibration, 2016, 2016: 9120505. [10] 常振. 滚动轴承性能时间序列演变历程的评估[D]. 洛阳: 河南科技大学, 2018. Chang Zhen. Evaluation of the evolution history of rolling bearing performance time series [D]. Luoyang: Henan University of Science and Technology, 2018. (in ChineseChang Zhen. Evaluation of the evolution history of rolling bearing performance time series [D]. Luoyang: Henan University of Science and Technology, 2018. (in Chinese) [11] 郎诗慧. 摩擦副磨合过程的分形与混沌表征及预测模型研究[D]. 徐州: 中国矿业大学, 2023. Lang Shihui. Study on fractal and chaotic characterization and prediction models of friction pair in running-in process[D]. Xuzhou: China University of Mining and Technology, 2023. (in ChineseLang Shihui. Study on fractal and chaotic characterization and prediction models of friction pair in running-in process[D]. Xuzhou: China University of Mining and Technology, 2023. (in Chinese) [12] 邵茁凯, 孙志, 刘坤, 等. 基于分形理论的亚毫米间隙正负极性流注放电特性[J]. 物理学报, 2023, 72(19): 125-135. Shao Zhuokai, Sun Zhi, Liu Kun, et al. Discharge characteristics of positive and negative polarity streamers with submillimeter gap based on fractal theory[J]. Acta Physica Sinica, 2023, 72(19): 125-135. (in Chinese doi: 10.7498/aps.72.20230937Shao Zhuokai, Sun Zhi, Liu Kun, et al. Discharge characteristics of positive and negative polarity streamers with submillimeter gap based on fractal theory[J]. Acta Physica Sinica, 2023, 72(19): 125-135. (in Chinese) doi: 10.7498/aps.72.20230937 [13] 孟凡念. 滚动轴承摩擦力矩的试验数据分析[D]. 洛阳: 河南科技大学, 2010. Meng Fannian. Experimental data analysis of rolling bearing friction torque[D]. Luoyang: Henan University of Science and Technology, 2010. (in ChineseMeng Fannian. Experimental data analysis of rolling bearing friction torque[D]. Luoyang: Henan University of Science and Technology, 2010. (in Chinese) [14] 姬翠翠. 基于混沌与分形理论的缸套—活塞环磨损过程动力学行为研究[D]. 徐州: 中国矿业大学, 2012. Ji Cuicui. Study on the dynamic properties during the wear process of cylinder liner-piston ring based on chaos and fractal theories[D]. Xuzhou: China University of Mining and Technology, 2012. (in ChineseJi Cuicui. Study on the dynamic properties during the wear process of cylinder liner-piston ring based on chaos and fractal theories[D]. Xuzhou: China University of Mining and Technology, 2012. (in Chinese) [15] 李国宾, 王素芳, 黄福权. 磨合磨损过程摩擦力矩分形行为研究[C]//中国造船工程学会学术论文集. 大连: 中国造船工程学会, 2005: 143-145. Li Guobin, Wang Sufang, Huang fuquan. Research on fractal behavior of friction torque in running-in wear process[C]//Proceedings of Chinese Society of Naval Architecture and Engineering. Dalian: Chinese Society of Naval Architecture and Engineering, 2005: 143-145. (in ChineseLi Guobin, Wang Sufang, Huang fuquan. Research on fractal behavior of friction torque in running-in wear process[C]//Proceedings of Chinese Society of Naval Architecture and Engineering. Dalian: Chinese Society of Naval Architecture and Engineering, 2005: 143-145. (in Chinese) [16] Yang Xiaomin, Xiang Yongbing, Jiang Bingzhen. On multi-fault detection of rolling bearing through probabilistic principal component analysis denoising and Higuchi fractal dimension transformation[J]. Journal of Vibration and Control, 2022, 28(9/10): 1214-1226. doi: 10.1177/1077546321989527 [17] 苏晶晶, 许志红. 基于混沌分形理论的故障电弧诊断方法研究[J]. 电机与控制学报, 2021, 25(3): 125-133. Su Jingjing, Xu Zhihong. Arc fault diagnosis method based on chaos and fractal theories[J]. Electric Machines and Control, 2021, 25(3): 125-133. (in Chinese doi: 10.15938/j.emc.2021.03.014Su Jingjing, Xu Zhihong. Arc fault diagnosis method based on chaos and fractal theories[J]. Electric Machines and Control, 2021, 25(3): 125-133. (in Chinese) doi: 10.15938/j.emc.2021.03.014 [18] Mischaikow K, Mrozek M, Reiss J, et al. Construction of symbolic dynamics from experimental time series[J]. Physical Review Letters, 1999, 82(6): 1144-1147. doi: 10.1103/PhysRevLett.82.1144 [19] Grassberger P, Procaccia I. Characterization of strange attractors[J]. Physical Review Letters, 1983, 50(5): 346-349. doi: 10.1103/PhysRevLett.50.346 [20] 史丽晨, 段志善. 基于混沌-分形理论的往复式活塞隔膜泵磨损故障分析[J]. 农业机械学报, 2010, 41(4): 222-226. Shi Lichen, Duan Zhishan. Wearing fault diagnosis of reciprocating membrane pump based on chaos and fractal theory[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(4): 222-226. (in Chinese doi: 10.3969/j.issn.1000-1298.2010.04.045Shi Lichen, Duan Zhishan. Wearing fault diagnosis of reciprocating membrane pump based on chaos and fractal theory[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(4): 222-226. (in Chinese) doi: 10.3969/j.issn.1000-1298.2010.04.045 [21] 吕小青, 曹彪, 曾敏, 等. 确定延迟时间互信息法的一种算法[J]. 计算物理, 2006, 23(2): 184-188. Lyn Xiaoqing, Cao Biao, Zeng Min, et al. An algorithm of selecting delay time in the mutual information method[J]. Chinese Journal of Computational Physics, 2006, 23(2): 184-188. (in Chinese doi: 10.3969/j.issn.1001-246X.2006.02.010Lyn Xiaoqing, Cao Biao, Zeng Min, et al. An algorithm of selecting delay time in the mutual information method[J]. Chinese Journal of Computational Physics, 2006, 23(2): 184-188. (in Chinese) doi: 10.3969/j.issn.1001-246X.2006.02.010 [22] 孔庆鸽. 基于关联维数和K熵的PIM充模过程中混沌特性的研究[D]. 长沙: 中南大学, 2013. Kong Qingge. The research of chaos in the PIM filling process based[D]. Changsha: Central South University, 2013. (in ChineseKong Qingge. The research of chaos in the PIM filling process based[D]. Changsha: Central South University, 2013. (in Chinese) [23] 高磊磊. 滚动轴承性能的乏信息过程实验评估[D]. 洛阳: 河南科技大学, 2012. Gao Leilei. Experimental assessment of rolling bearing performance based on poor information process[D]. Luoyang: Henan University of Science and Technology, 2012. (in ChineseGao Leilei. Experimental assessment of rolling bearing performance based on poor information process[D]. Luoyang: Henan University of Science and Technology, 2012. (in Chinese) [24] 徐志栋. 航天轴承摩擦力矩特性的试验研究[D]. 洛阳: 河南科技大学, 2008. Xu Zhidong. Experimental study on friction torque characteristics of aerospace bearing[D]. Luoyang: Henan University of Science and Technology, 2008. (in ChineseXu Zhidong. Experimental study on friction torque characteristics of aerospace bearing[D]. Luoyang: Henan University of Science and Technology, 2008. (in Chinese) [25] Yano J I, Heymsfield A J, Phillips V T J. Size distributions of hydrometeors: analysis with the maximum entropy principle[J]. Journal of the Atmospheric Sciences, 2016, 73(1): 95-108. doi: 10.1175/JAS-D-15-0097.1 [26] 夏新涛, 陈向峰, 叶亮. 卫星动量轮轴承摩擦力矩性能可靠性动态预测[J]. 中国机械工程, 2019, 30(11): 1268-1275. Xia Xintao, Chen Xiangfeng, Ye Liang. Dynamic prediction of friction torque performance reliability for satellite momentum wheel bearings[J]. China Mechanical Engineering, 2019, 30(11): 1268-1275. (in ChineseXia Xintao, Chen Xiangfeng, Ye Liang. Dynamic prediction of friction torque performance reliability for satellite momentum wheel bearings[J]. China Mechanical Engineering, 2019, 30(11): 1268-1275. (in Chinese) -
点击查看大图
计量
- 文章访问数: 176
- HTML浏览量: 138
- PDF量: 22
- 被引次数: 0