Reversing Behavior of Planetary Gear Train Influenced by Support Stiffness of Driving Shaft
Seiya Hamada*,, Kazutoshi Otokodani*, Masao Nakagawa**, Toshiki Hirogaki*, and Eiichi Aoyama*
1-3 Tataramiyakodani, Kyotanabe-shi, Kyoto 610-0394, Japan
**National Traffic Safety and Environment Laboratory, Tokyo, Japan
Planetary gear trains (PGTs) are widely used in many machines and are one of the most important mechanisms in hybrid and electric vehicles. Previous research, based on empirical knowledge gained from the automobile industry, indicates that high carrier-support stiffness and low ring-gear support stiffness are required to reduce ring-gear errors. Therefore, here, we evaluate the vibration characteristics of a PGT as a function of the support stiffness, which is varied by inserting urethane rubber into the driving shaft. We conducted experiments using a 2K-HV-type tester, which contains a coaxially rotating and revolving planet gear shaft based on a universal joint. This mechanism allows the observation of the inner workings of the mechanism with the use of a transparent acrylic carrier. We were able to detect the so-called “bounce” phenomenon consisting of a swaying motion when the rotation of the ring gear is reversed, and this result was confirmed by our internal observations of the mechanism. It is evident that the index of vibration increases due to the bounce phenomenon because the reversal of the ring gear causes a larger vibration than that of the carrier because the ring gear can vibrate without restraint, unlike the planet gear that is sandwiched between the sun and ring gears. Furthermore, the influence of the radial support stiffness of the driving shaft, load torque to the output shaft, and acceleration time of the reversing gear on the “bounce” phenomenon were evaluated. We found that a larger load torque corresponds to a greater difference depending on the acceleration conditions of the sun gear. During reversal, at the moment when the rotation speed is zero and rotation recommences, the ring gear exerts the maximum force, and the larger is the load torque, the greater is the effect of the difference in acceleration.
-  S. Cho, K. Ahn, and J. M. Lee, “Efficiency of the planetary gear hybrid powertrain,” J. of Automobile Engineering, pp. 1445-1454, 2006.
-  X. Zhang, S. E. Li, H. Peng, and J. Sun, “Efficient exhaustive search of power-split hybrid powertrain with multiple planetary gears and clutches,” J. of Dynamic Systems, Measurement, and Control, Vol.137, 121006-1, 2005.
-  L. Birglen and C. M. Gosselin, “Force analysis of connected differential mechanisms: Application of grasping,” The Int. J. of Robotics Research, pp. 1033-1046, 2006.
-  T. Endo, H. Kawasaki, T. Mouri, Y. Doi, T. Yoshida, Y. Ishigure, H. Shimomura, M. Matsumura, and K. Koketsu, “Five-fingered haptic interface robot: HIRO3,” Proc. of 3rd Joint Eurohaptics Conf. and Symp. on Haptic Interfaces for Virtual Environment and Teleoperator Systems, pp. 14-27, doi: 10.1109/whc.2009.4810812, 2009.
-  D. J. Williams, H. I. Krebs, and N. Hogan, “A robot for wrist rehabilitation,” Proc. of the 23rd Annual EMBS Int. Conf., pp. 1336-1339, doi: 10.1109/IEMBS.2001.1020443, 2001.
-  D. Surdilovic, R. Bernhardt, and L. Zhang, “New intelligent power-assist systems based on differential transmission,” Robotica, Vol.21, pp. 295-302, 2003.
-  M. Higuchi, “Development of a Human Symbiotic Assist Arm “PAS-Arm” (Basic Concept and Mechanism),” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.73, No.730, pp. 1762-1768, 2007 (in Japanese).
-  M. Higuchi, “Development of a Human Symbiotic Assist Arm ‘PAS-Arm’ (Design of Mechanism: CVT and Experimental System),” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.75, No.749, pp. 104-112, 2009 (in Japanese).
-  K. Morikawa and R. Nishihara, “Dynamic Vibration Analysis of Planetary Gear Train,” The Japan Society of Mechanical Engineers, Vol.2004, pp. 213-216, doi: 10.1299/jsmempt.2004.213, 2004 (in Japanese).
-  K. Kumagai, K. Morikawa, R. Nishihara, J. Nemoto, and Y. Tomita, “Vibration Behavior of Stepped Pinion Type Planetary Gears,” The Japan Society of Mechanical Engineers, pp. 59-62, 2006 (in Japanese).
-  K. Morikawa, K. Kumagai, and R. Nishihara, “A study on the sideband phenomenon of planetary gears,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.80, No.815, 14-00158, 2014 (in Japanese).
-  M. Nakagawa, D. Nishida, T. Hirogaki, and E. Aoyama, “Investigation of Dynamic Characteristic of Instantaneous Center of Rotation Planet Gear based on the Sun Gear Speed Contour Map in Continuously Varying Transmission under Three-axis Driving of Planetary Gear Train,” J. of the Japan Society of Precision Engineering, Vol.83, No.6, pp. 572-578, 2017 (in Japanese).
-  M. Nakagawa, D. Nishida, T. Hirogaki, and E. Aoyama, “Designing on Original Three-axis Driving Planetary Gear Train Test Stand and Its Estimation Based on Trials,” J. of Japan Society for Design Engineering, Vol.53, No.2, pp. 161-176, 2018 (in Japanese).
-  M. Nakagawa, D. Nishida, T. Fukuda, S. Matsui, T. Hirogaki, and E. Aoyama, “Investigation of Tooth Precision on Meshing Noise of Planetary Gear Train: Combinations of Different Tooth Precisions and Sound Intensity,” J. of the Japan Society of Precision Engineering, Vol.84, No.8, pp. 724-730, 2018 (in Japanese).
-  T. Chiang and R. H. Badgley, “Reduction of vibration and noise generated by planetary ring gears in helicopter aircraft transmissions,” Power Transmission Gearing Papers, Vol.95, No.4, 1149, 1973.
-  M. Nakagawa, Ph.D. thesis, Doshisha University, p. 105, 2019 (in Japanese).
-  J. Lin and R. G. Parker, “Sensitivity of planetary gear natural frequencies and vibration modes to model parameters,” J. of Sound and Vibration, No.228, pp. 109-128, 1999.
-  K. Suzuki and T. Morita, “From the basics of mechanism,” pp. 36-49, 2010 (in Japanese).
-  K. Ikebuchi, T. Takahashi, K. Abe, T. Yanome, M. Miyazawa, and K. Tsurumoto, Science and Engineering Reports of Tohoku Gakuin University, Vol.49, pp. 1-8, 2015 (in Japanese).
-  A. Ishibashi, M. A. Haidar, and K. Sonoda, “Theoretical efficiency of planetary gear drives with two degrees-of-freedom,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.63, No.611, pp. 2518-2525, 1997 (in Japanese).
-  M. Nakagawa, D. Nishida, T. Hirogaki, and E. Aoyama, “Investigation of reducing noise and wide geared for a planetary gear train using universal joint (Basic investigation of novel component and its evaluation under driving tests),” J. of the Japan Society for Precision Engineering, Vol.84, No.1, pp. 89-96, 2017 (in Japanese).
-  K. Yada, “Design of advanced gear mechanism,” Association of Mechanical Technology, 2011 (in Japanese).
-  M. Yoshino, “The influence of the parts error on torsional resonance of star-type planetary gear train,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.78, No.789, pp. 1779-1791, 2012 (in Japanese).
-  Japanese Industrial Standards, JIS K 6253, 1997 (in Japanese).
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