Planet position errors in planetary transmission: Effect on load sharing and transmission error

Abstract

In this paper an advanced model of spur gear transmissions developed by the authors is used to study the influence of carrier planet pin hole position errors on the behaviour of the transmission. The model, initially conceived for external gear modeling, has been extended with internal meshing features, and thus increasing its capabilities to include planetary transmission modeling. The new features are presented, along with the summary of the model general approach. The parameters and characteristics of the planetary transmission used in the paper are introduced. The influence of carrier planet pin hole position errors on the planet load sharing is studied, and several static cases are given as examples in order to show the ability of the model. Tangential and radial planet pin hole position errors are considered independently, and the effect of the load level is also taken into account. It is also given attention to the effect on the transmission error of the transmission. Two different configurations for the planetary transmission are used, attending to the fixed or floating condition of the sun, and the differences in terms of load sharing ratio are shown.

Key words： gear; planetary; epicyclic; transmission; load sharing; transmission error

References

1 Heng A, Zhang S, Tan A C C, Mathew J. Rotating machinery prognostics: State of the art, challenges and opportunities. Mechanical Systems and Signal Processing, 2009, 23(3): 724–739

2 Bartelmus W. Mathematical modelling and computer simulations as an aid to gearbox diagnostics. Mechanical Systems and Signal Processing, 2001, 15(5): 855–871

3 Smith J D. Gear Noise and Vibration. New York: Marcel Dekker Inc., 1999

4 Hayashi T, Li X Y, Hayashi I, Endo K, Watanabe W. Measurement and some discussions on dynamic load sharing in planetary gears. Bulletin of the JSME, 1986, 29(253): 2290–2297

5 Hidaka T, Terauchi Y. Dynamic behavior of planetary gear—1st report, load distributions in planetary gear. Bulletin of the JSME, 1976, 19(132): 690–698

6 Singh A. Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation. Mechanism and Machine Theory, 2010, 45(3): 511–530

7 Bodas A, Kahraman A. Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets. JSME International Journal. Series C, Mechanical Systems, Machine Elements and Manufacturing, 2004, 47(3): 908–915

8 Kahraman A.Non-linear dynamics of a spur gear pair. Journal of sound and vibration, 1990, 142 (1): 49

9 Viadero F, del Rincon A F, Sancibrian R, Fernandez P G, Juan A D. A model of spur gears supported by ball bearings. In Proceedings of 13th International Conference on Computational Methods and Experimental Measurements CMEM, 2007, 711–722

10 del Rincon A F, Viadero F, Iglesias M, de Juan A, Garcia P, Sancibrian R. Effect of cracks and pitting defects on gear meshing. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012

11 Litvin F, Fuentes A.Gear Geometry and Applied Theory. Cambridge: Cambridge University Press, 2004

12 Vedmar L, Andersson A. A method to determine dynamic loads on spur gear teeth and on bearings. Journal of Sound and Vibration, 2003, 267(5): 1065–1084

13 Welbourn D B.Fundamental knowledge of gear noise—A survey. In: Proceedings of Noise & Vibration of Engine and Transmission, Cranfield, UK, 1979, 9-14