Research Papers

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

[+] Author and Article Information
R. Fargère

DCNS Research
Centre d'Expertise des Structures &
Matériaux Navals,
Département Dynamique des Structures,
La Montagne 44 620, France

P. Velex

Université de Lyon INSA Lyon,
LaMCoS, UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cédex 69 621, France
e-mail: Philippe.Velex@insa-lyon.fr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 27, 2012; final manuscript received July 9, 2013; published online August 9, 2013. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 135(6), 061014 (Aug 09, 2013) (16 pages) Paper No: VIB-12-1083; doi: 10.1115/1.4025018 History: Received March 27, 2012; Revised July 09, 2013

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

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Fig. 1

Wide-faced gear model with tooth shape deviation em, tooth elasticity kij, and deformable gear bodies [18]

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Fig. 2

Journal bearing and its planar expansion with useful areas, (I) pressurized zone, (II) cavitated zone, (III) possibly pressurized zone, and (IV) oil injection zone

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Fig. 3

Single stage geared system on four journal bearings with the initial global frame and some modeling elements

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Fig. 4

Gauge locations and parameters for the calculation of tooth root stresses

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Fig. 5

Comparisons between the simulated and measured local dynamic coefficient with Cr = 1540 N m: (a) maximum bearing spacing and (b) minimum bearing spacing

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Fig. 6

Comparisons between the simulated and measured dimensionless tooth root stress (helical gear case), with Cr = 1540 N m and maximum bearing spacing: (a) on gauge PA2 and (b) on gauge PA4

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Fig. 7

Comparison of the shaft center positions at equilibrium over a range of input speed Ω1 0 [80; 900 rad/s] and various bearing models. Keys: SBA (blue dot-dashed line); 1DA (red dashed line); 1DAT (solid black line); and bearing clearance circle (thick black line).

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Fig. 8

Evolutions of (a) the tooth load distribution coefficient KHβ* and (b) the dynamic tooth load ratio R, with speed for several bearing models

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Fig. 10

Angular position γi of the oil injection zone for bearing i with respect to the initial global frame

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Fig. 11

Influence of the oil injection area on the static equilibrium position of shaft centers and on the pressure field in bearings (particular case of the oil injection zone interfering with the active zone in bearing 1 with fluid reformation and no recirculation)

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Fig. 12

Influence of the input speed Ω1 on the lubricant injection temperature Tinj, running temperature Tr, and viscosity μ for an ill-located oil injection zone in bearing 1 only (γ1 = π/2; γ2 = 0) inducing Tinj = Tinj0∀ Ω1 on bearing 1

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Fig. 13

Influence of the position of the lubricant injection zone: (a) tooth load distribution coefficient KHβ*, (b) shaft misalignment coefficient κ, and (c) dynamic tooth load ratio R

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Fig. 14

Influence of the position of the lubricant injection area on tooth load distribution for Ω1 = 250 rad/s, Cm = 1000 N m: (a) γ1 = 0; γ2 = 0, (b) γ1 = π/2; γ2 = 0, (c) γ1 =0; γ2 = π/2, and (d) rigid supports

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Fig. 15

Influence of the coupling stiffness kr (motor) on the reference position and static deformed shape (Ω1 = 450 rad/s, Cm = 1000 N m). 3D representations and projections (magnified displacements ×1000): (a) kr = 1 × 107 N/m and (b) kr = 3 × 108 N/m.

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Fig. 16

Influence of the coupling stiffness kr (motor) on: (a) the tooth load distribution coefficient KHβ* and (b) dynamic tooth load ratio R (Cm = 1000 N m)

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Fig. 17

Influence of the coupling stiffness kr (motor) on the reactions at bearings 1 and 2 (Cm = 1000 N m): (a) static solution and (b) rms of the dynamic reaction over the last five mesh periods

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Fig. 18

Influence of the coupling stiffness kr (motor) on the reaction at bearings 1 and 2: (a) kr = 107 N/m, (b) kr = 3 × 108 N/m (Ω1 = 450 rad/s, Cm = 1000 N m)




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