渐开线齿廓偏差测量不确定度的计算与分析
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摘要
为了研究渐开线齿廓测量方法对其测量不确定度的影响,建立了渐开线齿廓偏差测量方法的数学模型.对展成法、斜向展成法、极坐标法和直角坐标法测量齿廓偏差过程中存在的误差因素进行了分析与比较.通过实例计算出测量不确定度值.研究结果表明:测量仪器的示值误差通过测量模型的误差传递函数影响测量结果;不同测量方法的运动几何误差对测量结果不确定度的影响由阿贝误差决定.在测量温度和被测工件相同的情况下,展成法的测量结果稳定性优于其他测量方法.
In order to study the influence of the involute tooth profile measurement method on the measurement uncertainty,the mathematical models of measurement of involute tooth profile deviation are established.The error factors of measurement methods,which include generating method,normal direction generate method,polar generating method and rectangular coordinate method in measuring the tooth profile deviation,are analyzed and compared.The measurement uncertainty value is calculated by an example.The results show that the error of the measuring instrument is influenced by the error transfer function of the measuring model,and the effect of the geometric errors of different measurement methods on measurement uncertainty is determined by the Abbe error.For the same workpiece measured in same temperature,the measurement result of generating method is more stable than other methods.
In order to study the influence of the involute tooth profile measurement method on the measurement uncertainty,the mathematical models of measurement of involute tooth profile deviation are established.The error factors of measurement methods,which include generating method,normal direction generate method,polar generating method and rectangular coordinate method in measuring the tooth profile deviation,are analyzed and compared.The measurement uncertainty value is calculated by an example.The results show that the error of the measuring instrument is influenced by the error transfer function of the measuring model,and the effect of the geometric errors of different measurement methods on measurement uncertainty is determined by the Abbe error.For the same workpiece measured in same temperature,the measurement result of generating method is more stable than other methods.
引文
[1]费业泰.误差理论与数据处理[M].6版.北京:机械工业出版社,2010.FEI Yetai.Error Theory and Data Processing[M].6th ed.Beijing:China Machine Press,2010.(in Chinese)
[2]王阔,马勇.超精密齿轮齿廓偏差测量系统测量不确定度的评定[J].计量技术,2008(9):63.WANG Kuo,MA Yong.Evaluation of Measurement Uncertainty in the Measurement System of Tooth Profile Deviation of Ultra Precision Gear[J].Measurement Technique,2008(9):63.(in Chinese)
[3]YUZAKI M.Gear Measuring Machine by“NDG Method”for Gears Ranging from Miniature to Super-large[J].Gear Technology,2011,28(2):55.
[4]王建华,劳奇成.极坐标法测量渐开线齿形的数据处理与精度分析[J].西安工业学院学报,1996,16(3):189.WANG Jianhua,LAO Qicheng.The Data Processing and the Accuracy Analyzing of the Involute Profile Measurement on a Polar Coordinate[J].Journal of Xi’an Institute of Technology,1996,16(3):189.(in Chinese)
[5]石照耀,张宇,张白.三坐标机测量齿轮齿廓的不确定度评价[J].光学精密工程,2012,20(4):766.SHI Zhaoyao,ZHANG Yu,ZHANG Bai.Uncertainty Evaluation of CMM Measurement for Gear Profile[J].Optics and Precision Engineering,2012,20(4):766.(in Chinese)
[6]石照耀,费业泰,谢华锟.齿轮测量技术100年——回顾与展望[J].中国工程科学,2003,5(9):13.SHI Zhaoyao,FEI Yetai,XIE Huakun.Review&Prospect of 100Years of Gear Measurement Technology[J].Engineering Science,2003,5(9):13.(in Chinese)
[7]吕季轩.虚拟齿轮测量中心的几何与运动误差的建模[D].西安:西安工业大学,2014.LYU Jixuan.Geometric Error and Motion Error Modeling of Virtual Gear Measuring Center[D].Xi’an:Xi’an Technological University,2014.(in Chinese)
[8]British Standards Institution.Cylindrical Gears-Code of Inspection Practice-Part5:Recommendations Relative to Evaluation of Gear Measurement Instruments:BS PD ISO/TR 10064-5-2005[S].London:British Standards Institution,2005:2.
[9]FANG S P,LIU Y S,WANG H Y,et al.Compensation Method for the Alignment Angle Error of a Gear Axis in Profile Deviation Measurement[J].Measurement Science&Technology,2013,24(5):509.
[10]庄葆华,李真.齿轮近代测量技术与仪器[M].北京:机械工业出版社,1986.ZHUANG Baohua,LI Zhen.Modern Gear Measurement Technology and Instrument[M].Beijing:China Machine Press,1986.(in Chinese)
[11]张大厦.极坐标法测量渐开线齿轮的研究[D].天津:天津大学,2010.ZHANG Dasha.Study on Measuring Involute Profile Gear in a Polar Coordinate Method[D].Tianjin:Tianjin University,2010.(in Chinese)
[12]全国滚动轴承标准化技术委员会.滚动轴承硬质合金球:JB/T 9145-2010[S].北京:中国标准出版社,2010:3.National Rolling Bearing Standardization Technical Committee.Rolling Bearings-Cemented Carbide Balls:JB/T 9145-2010[S].Beijing:China Standard Press,2010:3.(in Chinese)
[2]王阔,马勇.超精密齿轮齿廓偏差测量系统测量不确定度的评定[J].计量技术,2008(9):63.WANG Kuo,MA Yong.Evaluation of Measurement Uncertainty in the Measurement System of Tooth Profile Deviation of Ultra Precision Gear[J].Measurement Technique,2008(9):63.(in Chinese)
[3]YUZAKI M.Gear Measuring Machine by“NDG Method”for Gears Ranging from Miniature to Super-large[J].Gear Technology,2011,28(2):55.
[4]王建华,劳奇成.极坐标法测量渐开线齿形的数据处理与精度分析[J].西安工业学院学报,1996,16(3):189.WANG Jianhua,LAO Qicheng.The Data Processing and the Accuracy Analyzing of the Involute Profile Measurement on a Polar Coordinate[J].Journal of Xi’an Institute of Technology,1996,16(3):189.(in Chinese)
[5]石照耀,张宇,张白.三坐标机测量齿轮齿廓的不确定度评价[J].光学精密工程,2012,20(4):766.SHI Zhaoyao,ZHANG Yu,ZHANG Bai.Uncertainty Evaluation of CMM Measurement for Gear Profile[J].Optics and Precision Engineering,2012,20(4):766.(in Chinese)
[6]石照耀,费业泰,谢华锟.齿轮测量技术100年——回顾与展望[J].中国工程科学,2003,5(9):13.SHI Zhaoyao,FEI Yetai,XIE Huakun.Review&Prospect of 100Years of Gear Measurement Technology[J].Engineering Science,2003,5(9):13.(in Chinese)
[7]吕季轩.虚拟齿轮测量中心的几何与运动误差的建模[D].西安:西安工业大学,2014.LYU Jixuan.Geometric Error and Motion Error Modeling of Virtual Gear Measuring Center[D].Xi’an:Xi’an Technological University,2014.(in Chinese)
[8]British Standards Institution.Cylindrical Gears-Code of Inspection Practice-Part5:Recommendations Relative to Evaluation of Gear Measurement Instruments:BS PD ISO/TR 10064-5-2005[S].London:British Standards Institution,2005:2.
[9]FANG S P,LIU Y S,WANG H Y,et al.Compensation Method for the Alignment Angle Error of a Gear Axis in Profile Deviation Measurement[J].Measurement Science&Technology,2013,24(5):509.
[10]庄葆华,李真.齿轮近代测量技术与仪器[M].北京:机械工业出版社,1986.ZHUANG Baohua,LI Zhen.Modern Gear Measurement Technology and Instrument[M].Beijing:China Machine Press,1986.(in Chinese)
[11]张大厦.极坐标法测量渐开线齿轮的研究[D].天津:天津大学,2010.ZHANG Dasha.Study on Measuring Involute Profile Gear in a Polar Coordinate Method[D].Tianjin:Tianjin University,2010.(in Chinese)
[12]全国滚动轴承标准化技术委员会.滚动轴承硬质合金球:JB/T 9145-2010[S].北京:中国标准出版社,2010:3.National Rolling Bearing Standardization Technical Committee.Rolling Bearings-Cemented Carbide Balls:JB/T 9145-2010[S].Beijing:China Standard Press,2010:3.(in Chinese)