Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function.

Accepted:

Published online:

Oussama Graja ^{1};
Bacem Zghal ^{1};
Kajetan Dziedziech ^{2};
Fakher Chaari ^{1};
Adam Jablonski ^{2};
Tomasz Barszcz ^{2};
Mohamed Haddar ^{1}

@article{CRMECA_2019__347_1_49_0, author = {Oussama Graja and Bacem Zghal and Kajetan Dziedziech and Fakher Chaari and Adam Jablonski and Tomasz Barszcz and Mohamed Haddar}, title = {Simulating the dynamic behavior of planetary gearbox based on improved {Hanning} function}, journal = {Comptes Rendus. M\'ecanique}, pages = {49--61}, publisher = {Elsevier}, volume = {347}, number = {1}, year = {2019}, doi = {10.1016/j.crme.2018.09.006}, language = {en}, }

TY - JOUR AU - Oussama Graja AU - Bacem Zghal AU - Kajetan Dziedziech AU - Fakher Chaari AU - Adam Jablonski AU - Tomasz Barszcz AU - Mohamed Haddar TI - Simulating the dynamic behavior of planetary gearbox based on improved Hanning function JO - Comptes Rendus. Mécanique PY - 2019 SP - 49 EP - 61 VL - 347 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2018.09.006 LA - en ID - CRMECA_2019__347_1_49_0 ER -

%0 Journal Article %A Oussama Graja %A Bacem Zghal %A Kajetan Dziedziech %A Fakher Chaari %A Adam Jablonski %A Tomasz Barszcz %A Mohamed Haddar %T Simulating the dynamic behavior of planetary gearbox based on improved Hanning function %J Comptes Rendus. Mécanique %D 2019 %P 49-61 %V 347 %N 1 %I Elsevier %R 10.1016/j.crme.2018.09.006 %G en %F CRMECA_2019__347_1_49_0

Oussama Graja; Bacem Zghal; Kajetan Dziedziech; Fakher Chaari; Adam Jablonski; Tomasz Barszcz; Mohamed Haddar. Simulating the dynamic behavior of planetary gearbox based on improved Hanning function. Comptes Rendus. Mécanique, Volume 347 (2019) no. 1, pp. 49-61. doi : 10.1016/j.crme.2018.09.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.09.006/

[1] Vibration signal modeling of a planetary gear set for tooth crack detection, Eng. Fail. Anal., Volume 48 (2015), pp. 185-200

[2] Vibration signal modeling of a planetary gear set with transmission path effect analysis, Measurement, Volume 85 (2016), pp. 20-31

[3] Frequency analysis of a two-stage planetary gearbox using two different methodologies, C. R. Mecanique, Volume 345 (2017), pp. 832-843

[4] Dynamic modeling and vibration characteristics of a two-stage closed-form planetary gear train, Mech. Mach. Theory, Volume 97 (2016), pp. 12-28

[5] A theoretical and experimental investigation of modulation sidebands of planetary gear sets, J. Sound Vib., Volume 323 (2009), pp. 677-696

[6] A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors, J. Sound Vib., Volume 329 (2010), pp. 371-393

[7] Vibration signal models for fault diagnosis of planetary gearboxes, J. Sound Vib., Volume 331 (2012), pp. 4919-4939

[8] Assessment of sideband energy ratio technique in detection of wind turbine gear defects, Case Stud. Mech. Syst. Signal Process., Volume 2 (2015), pp. 1-11

[9] Modelling of gearbox dynamics under time-varying nonstationary load for distributed fault detection and diagnosis, Eur. J. Mech. A, Solids, Volume 29 (2010), pp. 637-646

[10] A dynamic model of a double-helical planetary gear set, Mech. Mach. Theory, Volume 70 (2013), pp. 157-174

[11] Three-dimensional modeling and structured vibration modes of two-stage helical planetary gears used in cranes, Hindawi: Shock Vib., Volume 2017 (2017)

[12] Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity, Eur. J. Mech. A, Solids, Volume 29 (2010), pp. 1022-1033

[13] Nonlinear dynamics of planetary gears using analytical and finite element models, J. Sound Vib., Volume 302 (2007)

[14] Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects, Mech. Mach. Theory, Volume 109 (2017), pp. 231-249

[15] Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack, Mech. Mach. Theory, Volume 62 (2013), pp. 63-74

[16] The influence of tooth pitting on the mesh stiffness of a pair of external spur gears, Mech. Mach. Theory, Volume 106 (2016), pp. 1-15

[17] Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects, Eng. Fail. Anal., Volume 70 (2016), pp. 200-211

[18] Time-varying mesh stiffness calculation of spur gears with spalling defect, Eng. Fail. Anal., Volume 66 (2016), pp. 166-176

[19] Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission, Eur. J. Mech. A, Solids, Volume 27 (2008), pp. 691-705

[20] Natural modes of planetary gear trains, J. Sound Vib., Volume 173 (1994) no. 1, pp. 125-130

[21] Contribution à l'étude du comportement dynamique des trains épicycloïdaux à denture droite en présence de défauts, ENI, Sfax, Tunisia, 2005 (PhD thesis)

[22] Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness, Eur. J. Mech. A, Solids, Volume 28 (2009), pp. 461-468

[23] A novel vibration-based fault diagnostic algorithm for gearboxes under speed fluctuations without rotational speed measurement, Mech. Syst. Signal Process., Volume 94 (2017), pp. 14-32

[24] Mesh stiffness variation instabilities in two-stage gear systems, J. Vib. Acoust., Volume 124 (2002), pp. 68-76

[25] A comparison of gear mesh stiffness modeling strategies, Jacksonville, FL, USA, 1–4 February 2010 (2010), pp. 255-263

[26] Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations, Mech. Syst. Signal Process., Volume 20 (2006) no. 2, pp. 332-349

[27] A CAD-FEM-QSA integration technique for determining the time-varying meshing stiffness of gear pairs, Measurement, Volume 100 (2017), pp. 139-149

[28] Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons, J. Sound Vib., Volume 237 (2000) no. 3, pp. 435-455

[29] Analytical load sharing and mesh stiffness model for spur/helical and internal/external gears towards constant mesh stiffness gear design, Mech. Mach. Theory, Volume 113 (2017), pp. 126-140

[30] Effect of load and meshing stiffness variation on modal properties of planetary gear, Appl. Acoust. (2017) (in press) | DOI

[31] Non-stationary dynamic analysis of a wind turbine power drivetrain: offshore considerations, Appl. Acoust., Volume 77 (2014)

[32] Gear transmission dynamic: effects of tooth profile deviations and support flexibility, Appl. Acoust., Volume 77 (2014)

[33] Gear transmission dynamics: effects of index and run out errors, Appl. Acoust. (2015) (in press) | DOI

[34] A hybrid 3D finite element/lumped parameter model for quasi-static and dynamic analyses of planetary/epicyclic gear sets, Mech. Mach. Theory, Volume 41 (2006)

[35] Gear tooth mesh stiffness: a comparison of calculation approaches, Mech. Mach. Theory, Volume 105 (2016)

[36] Modelling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears, NASA, 2001 (NASA/CR–2001-210939, ARL-CR-462)

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