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Research Papers: Elastohydrodynamic Lubrication

A Transient Mixed Elastohydrodynamic Lubrication Model for Spur Gear Pairs

[+] Author and Article Information
S. Li

 Ohio State University, 201 West 19th Avenue, Columbus, OH 43210

A. Kahraman1

 Ohio State University, 201 West 19th Avenue, Columbus, OH 43210kahraman.1@osu.edu

1

Corresponding author.

J. Tribol 132(1), 011501 (Nov 09, 2009) (9 pages) doi:10.1115/1.4000270 History: Received September 16, 2008; Revised August 25, 2009; Published November 09, 2009; Online November 09, 2009

In this study, a transient, non-Newtonian, mixed elastohydrodynamic lubrication (EHL) model of involute spur gear tooth contacts is proposed. Unlike the contact between two cylindrical rollers, spur gear contacts experience a number of time-varying contact parameters including the normal load, radii of curvature, surface velocities, and slide-to-roll ratio. The proposed EHL model is designed to continuously follow the contact of a tooth pair from the root to the tip to capture the transient characteristics of lubricated spur gear contacts due to these parameter variations, instead of analyzing the contact at discrete positions assuming time-invariant parameters. The normal tooth force along the line of action is predicted by using a gear load distribution formulation and the contact radii and tangential surface velocities are computed from the kinematics and geometry of involute profiles. A unified numerical approach is adapted for handling asperity interaction in mixed EHL conditions. The differences between the transient and discrete EHL analyses are shown for a spur gear pair having smooth surfaces and different tooth profile modifications. The transient behavior predicted by the proposed model is found to be mainly due to the squeezing and pumping effects caused by sudden load changes. The lubrication behavior under rough conditions is also investigated at different operating conditions.

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Figures

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Figure 1

A lubricated spur gear contact showing various time-varying parameters

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Figure 2

Basic geometric parameters of an involute spur gear pair

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Figure 3

Variations in (a) radii of curvature, (b) velocities, and (c) normal load during a single tooth engagement cycle of the example gear pair with θ1. Input torque is 250 Nm and input speed is 2000 rpm.

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Figure 4

Comparison of hmin values of example unmodified spur gear pair with smooth surfaces predicted by the transient and discrete EHL models. Input torque is 250 Nm and input speed is 2000 rpm.

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Figure 5

Instantaneous p and h distributions of the example unmodified spur gear pair with smooth surfaces at the contact points (a) A, (b) B, (c) C, (d) D, (e) E, (f) F, and (g) G defined in Fig. 4. Input torque is 250 Nm and input speed is 2000 rpm.

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Figure 6

Instantaneous p and h distributions of the example unmodified spur gear pair with smooth surfaces at the contact points (a) H, (b) I, (c) J, (d) K, and (e) L defined in Fig. 4. Input torque is 250 Nm and input speed is 2000 rpm.

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Figure 7

(a) A linear tip relief modification, and (b) a profile crown modification

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Figure 8

Comparison of the variation in W for the unmodified gears with the gears modified using the tip relief and profile crown modifications in Fig. 7

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Figure 9

Comparison of hmin values of example spur gear pair with smooth surfaces and (a) the tip relief in Fig. 7 and (b) profile crown in Fig. 7 as predicted by the transient and discrete EHL models. Input torque is 250 Nm and input speed is 2000 rpm.

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Figure 10

Example measured surface roughness profiles of a pair of run-in ground gears: (a) gear 1 with Rq1=0.55 μm and (b) gear 2 with Rq2=0.32 μm

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Figure 11

Instantaneous p and h distributions of the example spur gear pair with profile crown modifications shown in Fig. 7 and rough profiles shown in Fig. 1: (a) θ1=16.6 deg, (b) θ1=19.3 deg (at the LPSTC), (c) θ1=20.9 deg (at the pitch point), (d) θ1=22.9 deg (at the HPSTC), and (e) θ1=26 deg. Input torque is 250 Nm and the input speed is 2000 rpm.

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Figure 12

Variation in the instantaneous area contact ratio Ca with θ1 at 250 Nm, and (a) 2000 rpm and (b) 10,000 rpm

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Figure 13

Variation in the instantaneous load contact ratio Cℓ with θ1 at 250 Nm, and (a) 2000 rpm and (b) 10,000 rpm

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