摘要(英) |
The purpose of this study is to analyze the transmission error and meshing frequency energy of spur gear with different linear tip reliefs. Experiments and simulation of spur gear pairs with different linear tip reliefs are carried out in this thesis.
Three pairs of spur gear with different linear tip reliefs are used in the transmission error experiments. The torque applied were 0 N, 2 N, 4 N, 6 N, 8 N, and 10 N, and the speed was fixed at 10 RPM on the single-flank test. Empirical mode decomposition method and Fourier Transform were applied to analyze the transmission error signal. Finally, the corresponding IMF signals were used to calculate the tooth profile error, runout error, and pitch error.
For the energy of meshing frequency experiments, the torque was fixed at 10 N and the rotation speed were 500 RPM, 600 RPM, 700 RPM and 800 RPM. Fast ensemble empirical mode decomposition method and the Fourier Transform were used to find the IMF of the meshing frequency, and the energy value of meshing frequency was calculated.
In this study, it was found that tip relief may avoid the abnormal vibration caused by tip interference, but improper modification will lead to an increase of the transmission error. In addition, the design of linear tip-relief should also consider the load conditions to achieve on optimal tip relief. |
參考文獻 |
[1] R. E. Smith, “Single Flank Testing of Gears,” Gear Technology, 2004.
[2] R. E. Smith, “Identification of Gear Noise with Single Flank Composite Measurement,” Gear Technology, 1986.
[3] R. E. Smith, “Quality Gear Inspection-Part1,” Gear Technology, 1994.
[4] R. E. Smith, “Quality Gear Inspection-Part2,” Gear Technology, 1994.
[5] R. E. Smith, “Redliner Charts and Gear Inspection,” Gear Technology, 1999.
[6] 陳義仁, “受負載之正齒輪對的傳動誤差探討,” 國立交通大學, 碩士論文, 2005。
[7] ISO 6336, Part 1, Organization for International Standardizations, 2007.
[8] ISO 6336, Part 2, Organization for International Standardizations, 2006.
[9] ISO 6336, Part 3, Organization for International Standardizations, 2008.
[10] ISO 6336, Part 5, Organization for International Standardizations, 2003.
[11] ISO 6336, Part 6, Organization for International Standardizations, 2006.
[12] BS 436-2, “Specification for Spur and Helical Gears. Part2. Basic Rack Form Modules and Accuracy,” British Standards Institution, 1970.
[13] H. Sigg, “Profile and Longitudinal Corrections on Involute Gears,” AGMA 109.16, 1965.
[14] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis,” Proceedings: Mathematical, Physical and Engineering Sciences, Vol.454, No.1971, pp. 903-995, 1998.
[15] Z. Wu and N. E. Huang, “Ensemble Empirical Mode Decomposition: A Noise Assisted Data Analysis Method,” Advances in Adaptive Data Analysis, Vol.1, No.1, 1-41, 2009.
[16] G. Jager, “Fast Empirical Mode Decompositions of Multivariate Data Based on Adaptive Spline-Wavelets and a Generalization of the Hilbert-Huang-Transformation (HHT) to Arbitrary Space Dimensions,” World Scientic Publishing, 2010.
[17] X. W. Zeng, et al., “The Study of Single Channel Blind Separation Based on Fast EEMD,” Journal of China of Electronic Design Engineering, Vol.23, No.14, 2015.
[18] 梅澤清彦,松村茂樹,北条春夫など,“誤差を考慮したはすば歯車の軽負荷における回転方向振動解析,”(第一報、誤差をもつ歯面の接触による近寄りの解析法),日本機械学会論文集(C編)60卷575号,論文No.94-0048, 1994。
[19] 梅澤清彦,松村茂樹,北条春夫,“誤差を考慮したはすば歯車の軽負荷における回転方向振動解析,”(第二報、回転方向振動シミュレーションの開発),日本機械学会論文集(C編)60卷575号,論文No.94-0049, 1994。
[20] 梅澤清彦,松村茂樹,北条春夫,“誤差を考慮したはすば歯車の軽負荷における回転方向振動解析,”(第三報、歯すじ方向誤差と振動性能曲線),日本機械学会論文集(C編)62卷603号,論文No.95-1849, 1996。
[21] 梅澤清彦,松村茂樹,北条春夫,“誤差を考慮したはすば歯車の軽負荷における回転方向振動解析,”(第四報、歯形方向誤差と振動性能曲線),日本機械学会論文集(C編)62卷603号,論文No.96-0073, 1996。
[22] 井上彰哲など,“歯車を含む動力伝達軸のねじり振動,”日本機械学会論文集No.00-6, 2000。
[23] 馮芳,“歯車装置の異常時の動特性と状態診断法に関する基礎研究,”九州工業大学,博士論文, 2001。
[24] 北条春夫,“歯車装置の騒音と振動,”J-STAGE, Vol.17, No.1, 1993。
[25] H. Houjoh, C. Ratanasumawong and S. Matsumura, “Utilization of Synchronous Averaging for Inspection of Tooth Surface Undulations on Gears (localization of nonmesh harmonic components to individual gear),” ASME, Journal of Applied Mechanics, Vol.74, 2007.
[26] V. K. Tamminana, A. Kahraman and S. Vijayakar, “A Study of the Relationship between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs,” ASME, Journal of Mechanical Design, Vol. 129, 2007.
[27] C. Ratanasumawong, S. Matsumura and H. Houjoh, “An Alternative Method for Evaluating Gear Tooth Surface Geometry Based on Synchronous Average of Vibration of a Gear Pair,” ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC1007-34051, 2007.
[28] C. Ratanasumawong, S. Matsumura, T. Tatsuno and H. Houjoh, “Estimating Gear Tooth Surface Geometry by Means of The Vibration Measurement: Distinction of The Vibration Characteristics of Gears with Tooth Surface form Error,” ASME, Journal of Mechanical Design, Vol.131, 101003-1, 2009.
[29] S. Matsumura, T. Nagumo and H. Houjoh, “Estimation Method of Mesh Excitation Waveform of a Gear System (hybrid estimation with vibration measurement and simulation),” ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2011-48130, 2011.
[30] 張銘弘, “應用經驗模態分解法於正齒輪對之傳動誤差分析,” 國立中央大學, 碩士論文, 2013。
[31] 鄭凱鴻,“修整型正齒輪對動態模擬與實驗,” 國立中央大學, 碩士論文, 2014。
[32] 王志根,“正齒輪之齒輪精度對傳動誤差及動態特性影響之研究(II),” 科技部專題研究計畫結案報告, MOST 104-2221-E-008-020, 2016。
[33] 笹倉実, 近藤稔,“モーター‧歯車装置からの音と振動を減らす,”鉄道総合技術研究所 RRR Vol.71 No.11, 2014。
[34] 北条春夫,“歯車装置の静粛化技術の動向,”精密工学誌, Vol.69, No.3, 2003。 |