轴承圆柱滚子直径接触式动态测量动力学研究
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摘要
针对轴承圆柱滚子直径快速测量时,传感器触头与滚子接触产生的作用力导致其变形影响精度这一问题,提出了一种考虑微观变形的接触动力学模型的研究方法。该方法基于Hertz接触理论、非线性阻尼理论和Coulomb摩擦理论,根据动态测量过程中传感器触头的变形,建立了触头与滚子之间的运动学微分方程,并分析了接触点处法向力与变形量之间关系,得到不同测量速度、位置角与变形量之间的变化规律;利用虚拟仿真技术分析,结合搭建的物理样机进行试验。实验结果表明,滚子直径测量误差不超过1μm。本研究成果量化了测量速度与精度之间的关系,为实际工程应用中圆柱体零件的直径进行高效、精确的接触式测量提供了理论依据。
During the fast measurement process of measuring the bearing cylindrical roller diameter,the sensor contact deforms due to the applied force produced when the sensor contact approaches the roller,which may reduce the measurement accuracy. Therefore,this workproposesa contact dynamics research methodology considering the microscopic deformation. Based on Hertz contact theory,nonlinear damping theory and Coulomb friction theory,a kinematic differential equation between the contact and the roller isestablished based on the sensor contact deformation during dynamic measurement. Different measurement speed,position angle and deformation amount areobtained by analyzing the relationship between the normal force and the deformation at the contact point. In addition,the test results from the virtual simulation and the physical prototype experiment show that the roller diameter measurement error is no more than 1 μm.By quantifying the relationship between measurement speed and measurement accuracy,this workcontributes to the bearing cylindrical roller diameter measurement studies,and provides a theoretical basis for efficient and accurate contact measurement of the diameter of cylindrical parts in practical engineering applications.
During the fast measurement process of measuring the bearing cylindrical roller diameter,the sensor contact deforms due to the applied force produced when the sensor contact approaches the roller,which may reduce the measurement accuracy. Therefore,this workproposesa contact dynamics research methodology considering the microscopic deformation. Based on Hertz contact theory,nonlinear damping theory and Coulomb friction theory,a kinematic differential equation between the contact and the roller isestablished based on the sensor contact deformation during dynamic measurement. Different measurement speed,position angle and deformation amount areobtained by analyzing the relationship between the normal force and the deformation at the contact point. In addition,the test results from the virtual simulation and the physical prototype experiment show that the roller diameter measurement error is no more than 1 μm.By quantifying the relationship between measurement speed and measurement accuracy,this workcontributes to the bearing cylindrical roller diameter measurement studies,and provides a theoretical basis for efficient and accurate contact measurement of the diameter of cylindrical parts in practical engineering applications.
引文
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[12] WOZ'NIAK A,DOBOSZ M. Metrological feasibilities of CMM touch trigger probes. Part I:3D theoretical model of probe pretravel[J]. Measurement,2003,34(4):273-286.
[13]罗哉,刘晖,田焜,等.关节臂式坐标测量机测量力误差分析及补偿[J].仪器仪表学报,2017,38(5):1159-1167.LUO Z, LIU H, TIAN K, et al. Analysis and compensation of measuring force error of articulated arm coordinate measuring machine[J]. Chinese Journal of Scientific Instrument,2017,38(5):1159-1167.
[14]李海龙.轴承圆柱滚子尺寸综合测量方法及测量系统研究[D].哈尔滨:哈尔滨理工大学,2018.LI H L. Research on comprehensive measurement method and measurement system of bearing cylindrical roller size[D]. Harbin:Harbin University of Science and Technology,2018.
[15] ZHAO Y L,XIA CH T,WANG H B,et al. Analysis and numerical simulation of rolling contact between sphere and Cone[J]. Chinese Journal of Mechanical Engineering,2015,28(3):521-529.
[16] HUNT K H,CROSSLEY F R E. Coefficient of restitution interpreted as damping in vibroimpact[J]. Journal of Applied Mechanics,1975,42(2):440-445.
[17] DONG X,SHEN Y H,WEI Y ZH,et al. A comparative study of the dissipative contact force Models for collision under external spring forces[J]. Journal of Computational and Nonlinear Dynamics,2018,13(10):101009.
[18] FLORES P,MACHADO M,SILVA M T,et al. On the continuous contact force models for soft materials in multibody dynamics[J]. Multibody System Dynamics,2011,25(3):357-375.
[19]韩维.斜碰撞振动系统动力学研究[D].南京:南京航空航天大学,2003.HAN W. Dynamics study of oblique impact vibration system[D]. Nanjing:Nanjing University of Aeronautics and Astronautics,2003.
[2]赵燕,毕明龙,石东丹.基于抑制滚子歪斜的高速圆柱滚子轴承设计[J].轴承,2018(12):14-16.ZHAO Y,BI M L,SHI D D. Design of high speed cylindrical roller bearing based on suppression of roller skew[J]. Bearing,2018(12):14-16.
[3]王红军. 2008. GB/T 4661-2002《滚动轴承圆柱滚子》滚动轴承测试技术[S].北京:机械工业出版社,2008:158-166.WANG H J. GB/T 4661-2002 “Rolling bearing cylindrical roller”rolling bearing testing technology[S].Beijing:Mechanical Industry Press,2008,158-166.
[4]张学昌,梁涛,张旭,等.基于误差转换的汽车曲轴圆度及圆柱度误差评价数学模型构建研究[J].机械工程学报,2016,52(2):91-98.ZHANG X CH, LIANG T, ZHANG X, et al.Mathematical model construction of automobile crankshaft roundness and cylindricity error evaluation based on error transformation[J]. Journal of Mechanical Engineering,2016,52(2):91-98.
[5]贲春雨,郑宇,郭蕴纹,等.大尺寸直径非接触光电检测系统研究[J].仪器仪表学报,2006,27(1):72-74.QI CH Y,ZHENG Y,GUO Y W,et al.Study on largediameter non-contact photoelectric detection system[J].Chinese Journal of Scientific Instrument,2006(1):72-74.
[6] LIU S Y,TAN Q CH,ZHANG Y CH. Shaft diameter measurement using structured light vision[J]. Sensors,2015,15(8):19750-19767.
[7]孙秋成,谭庆昌,唐武生,等.基于CCD的轴径检测方法[J].吉林大学学报(工学版),2010,40(5):1273-1277.SUN Q CH,TAN Q CH,TANG W SH,et al. Shaft diameter measuring method based on CCD[J]. Journal of Jilin University(Engineering and Technology Edition),2010,40(5):1273-1277.
[8] DEMEYER M,DEREINE E,EUGENE C, et al.Measurement of cylindrical objects through laser telemetry:Application to a new forest caliper[J].Instrumentation and Measurement, 2002, 51(4):645-649.
[9] CHEN Y D, LIU CH X. Radius and orientation measurement for cylindrical objects by a light section sensor[J].Sensors,2016,16(11):1981.
[10] THAMRIN N M,ARSHAD N H M,ADNAN R,et al.Enhanced technique for cylindrical object diameter measurement via low-cost and innovated rotational nonintrusive sensor[C]. IEEE 10th International Colloquium on Signal Processing&its Applications. 2014:251-256.
[11] THAMRIN N M,ARSHAD N H M,ADNAN R,et al. A low-cost rotational infrared scanner for cylindrical object diameter measurement[C].IEEE International Conference on Control System,Computing and Engineering,2013:616-620.
[12] WOZ'NIAK A,DOBOSZ M. Metrological feasibilities of CMM touch trigger probes. Part I:3D theoretical model of probe pretravel[J]. Measurement,2003,34(4):273-286.
[13]罗哉,刘晖,田焜,等.关节臂式坐标测量机测量力误差分析及补偿[J].仪器仪表学报,2017,38(5):1159-1167.LUO Z, LIU H, TIAN K, et al. Analysis and compensation of measuring force error of articulated arm coordinate measuring machine[J]. Chinese Journal of Scientific Instrument,2017,38(5):1159-1167.
[14]李海龙.轴承圆柱滚子尺寸综合测量方法及测量系统研究[D].哈尔滨:哈尔滨理工大学,2018.LI H L. Research on comprehensive measurement method and measurement system of bearing cylindrical roller size[D]. Harbin:Harbin University of Science and Technology,2018.
[15] ZHAO Y L,XIA CH T,WANG H B,et al. Analysis and numerical simulation of rolling contact between sphere and Cone[J]. Chinese Journal of Mechanical Engineering,2015,28(3):521-529.
[16] HUNT K H,CROSSLEY F R E. Coefficient of restitution interpreted as damping in vibroimpact[J]. Journal of Applied Mechanics,1975,42(2):440-445.
[17] DONG X,SHEN Y H,WEI Y ZH,et al. A comparative study of the dissipative contact force Models for collision under external spring forces[J]. Journal of Computational and Nonlinear Dynamics,2018,13(10):101009.
[18] FLORES P,MACHADO M,SILVA M T,et al. On the continuous contact force models for soft materials in multibody dynamics[J]. Multibody System Dynamics,2011,25(3):357-375.
[19]韩维.斜碰撞振动系统动力学研究[D].南京:南京航空航天大学,2003.HAN W. Dynamics study of oblique impact vibration system[D]. Nanjing:Nanjing University of Aeronautics and Astronautics,2003.