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Research Papers

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

[+] Author and Article Information
M. Gabiccini1

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italym.gabiccini@ing.unipi.it

A. Bracci

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italya.bracci@ing.unipi.it

M. Guiggiani

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italym.guiggiani@ing.unipi.it

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1

Corresponding author.

J. Mech. Des 132(4), 041010 (Apr 22, 2010) (8 pages) doi:10.1115/1.4001485 History: Received May 29, 2009; Revised November 16, 2009; Published April 22, 2010; Online April 22, 2010

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth microtopography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here, the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Outside blade of the grinding wheel

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Figure 2

Schematic layout of the cradle-style machine

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Figure 3

System setup and misalignments definition

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Figure 4

Approximation of the instantaneous contact area

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Figure 5

Nominal contact pattern estimated as the convex hull of the instantaneous contact zones

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Figure 6

Perturbed contact patterns and their convex hull

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Figure 7

Current and target contact patterns

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Figure 8

Definition of the residual ease-off

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Figure 9

Basic loaded patterns (filled areas: HFM patterns; black dashed curves: estimated by SLTCA)

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Figure 10

Target and final ease-off topographies

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Figure 11

Milestone CPs in the nominal optimization process (dashed: basic CPs (Table 2, Basic column); filled: target CPs; dash-dotted: CPs of the basic design with overlaid target ease-off topography; black solid: CPs with modified settings (Table 2, CUSTOM column)

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Figure 12

Optimized contact patterns with machine-tool settings from Table 2, CUSTOM set (filled areas: HFM patterns; black dashed curves: estimated by SLTCA)

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Figure 13

Perturbed contact patterns for different (E,P,G) with nominal optimal ease-off topography (filled areas: HFM patterns; black dashed curves: estimated by SLTCA)

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Figure 14

Milestone CPs in the robust optimization process (dashed: basic CPs (Table 4, Basic column); filled: robust target CPs; dash-dotted: CPs of the basic design with overlaid robust target ease-off topography; black solid: CPs with modified settings (Table 4, CUSTOM column)

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Figure 15

Robust target and final ease-off topographies

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Figure 16

Perturbed contact patterns for different (E,P,G) with robust optimal ease-off topography (filled areas: HFM patterns; black dashed curves: estimated by SLTCA)

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Figure 17

Transmission error: basic configuration (dashed); robustly optimized configuration (solid)

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