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Research Papers

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

[+] Author and Article Information
Vilmos V. Simon

Department for Machine Design,
Faculty of Mechanical Engineering,
Budapest University of Technology
and Economics,
H-1111 Budapest,
Műegyetem rkp. 3, Hungary
e-mail: simon.vilmos@gt3.bme.hu

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 19, 2013; final manuscript received May 1, 2014; published online June 2, 2014. Assoc. Editor: Zhang-Hua Fong.

J. Mech. Des 136(8), 081004 (Jun 02, 2014) (8 pages) Paper No: MD-13-1125; doi: 10.1115/1.4027635 History: Received March 19, 2013; Revised May 01, 2014

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

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References

Figures

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Fig. 1

Relative position of the head-cutter to the imaginary generating crown gear

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Fig. 2

Relative position of the pinion and the gear in mesh

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Fig. 3

Tooth contact pressure distributions along the potential contact lines when the pinion and gear tooth surfaces are fully conjugate

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Fig. 4

Tooth contact pressure distributions along the potential contact lines when the pinion tooth is manufactured by optimized head-cutter and machine-tool settings

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Fig. 5

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the transmitted torque is 20 Nm

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Fig. 6

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on torque 80 Nm, and the really transmitted torque is 20 Nm

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Fig. 7

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the transmitted torque is 200 Nm

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Fig. 8

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on torque 80 Nm, and the really transmitted torque is 200 Nm

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Fig. 9

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and no misalignments are in the gear pair

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Fig. 10

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the pinion offset is Δa = -0.5 mm

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Fig. 11

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and the actual pinion offset is Δa = -0.5 mm

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Fig. 12

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the horizontal angular misalignment of the pinion axis is ɛh = -0.5 deg

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Fig. 13

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and the actual horizontal angular misalignment of the pinion axis is ɛh = -0.5 deg

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