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Research Papers

Estimation of Bending Fatigue Life of Hypoid Gears Using a Multiaxial Fatigue Criterion

[+] Author and Article Information
M. A. Hotait

Department of Mechanical Engineering,
American University of Sharjah,
PO Box 2666, Sharjah, UAE
e-mail: mhotait@aus.edu

A. Kahraman

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 3, 2013; final manuscript received June 16, 2013; published online August 21, 2013. Assoc. Editor: Qi Fan.

J. Mech. Des 135(10), 101005 (Aug 21, 2013) (10 pages) Paper No: MD-13-1062; doi: 10.1115/1.4025024 History: Received February 03, 2013; Revised June 16, 2013

In this study, a crack initiation life prediction methodology for the tooth bending fatigue of hypoid gears is proposed. This methodology employs a previously developed finite-element based hypoid gear root stress model (Hotait et al. 2011, “An Investigation of Root Stresses of Hypoid Gears with Misalignments,” ASME J. Mech. Des., 133, p. 071006) of face-milled and face-hobbed hypoid gears to establish the multiaxial stress time histories within the root fillet regions. These stress time histories are combined with a multiaxial crack initiation fatigue criterion to predict life distributions along roots of the pinion and the gear. The predictions of the multiaxial fatigue model are compared to those from a conventional uniaxial fatigue model to establish the necessity for a multiaxial approach. The model is exercised with an example face-milled hypoid gear set from an automotive application to demonstrate the impact of various misalignments well as the key cutting tool parameters on the resultant tooth bending lives.

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Figures

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Fig. 1

(a) Blade geometry parameters, (b) definition of the gear blank, and (c) pinion concave side surface (top) and gear convex side surface (bottom)

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Fig. 2

(a) FE mesh template, and (b) example of FE gear segment

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Fig. 3

(a) Contact stress distribution on the tooth flank, (b) maximum principal stress distribution of the example gear pair at T = 1000 Nm, and time histories of stress components (c) at point B with (R,Z) = (72.9,28.9) mm, and (d) at point C with (R,Z) = (94.9,37.7). T = 1000 Nm, where R.C. is the root center curve and S.A.P. represents the start of active profile

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Fig. 4

(a) Definition of the Euler transformations, and (b) definition of the fracture plane and the characteristic plane

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Fig, 5

Computational methodology of the proposed multiaxial tooth bending fatigue model

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Fig. 6

(a) The maximum principal root stress distribution, (b) the uniaxial fatigue life distribution, and (c) the multiaxial fatigue life distribution of the example FM gear at T=1000 Nm with no misalignment

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Fig. 7

Comparison of the crack initiation lives from the uniaxial and multiaxial models (a) along the root profile in the middle of the face width and (b) along the face width in the middle of the root profile. T = 1000 Nm with no misalignment

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Fig. 8

Definition of four types of misalignments

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Fig. 9

Contact pattern, predicted maximum principal the root stress distribution, and the tooth bending fatigue life distribution of the example FM gear at T = 1000 Nm for (a) V = 0,H = G = 0.1 mm, and γ = 0 (b) V = -0.1 mm,H = 0,G = 0.15 mm, and γ = 0, (c) V = -0.1 mm,H = -0.05 mm,G = 0, and γ = -0.1 deg, and (d) V = -0.1 mm,H = -0.05 mm, G = 0, and γ = -0.1 deg

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Fig. 10

Combined influence of (a) V and H errors, (b) V and G errors, (c) V and γ errors, (d) H and G errors, (e) H and γ errors, and (f) G and γ errors on the predicted tooth bending fatigue lives log(Nf/Nf_noerror) of the example FM gear set at T = 800 Nm

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Fig. 11

The maximum principal root stress and tooth bending fatigue life distributions of the example hypoid gear pair cut with a blade having (a) ρt = 0.5 mm and (b) ρt = 1.7 mm. T = 1000 Nm

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Fig. 12

Normalized life versus ρt of the example FM gear at T = 1000 Nm

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