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Research Papers: Design of Direct Contact Systems

Global Synthesis for Face Milled Spiral Bevel Gears With Zero Transmission Errors

[+] Author and Article Information
Peng Wang

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: wangpeng@buaa.edu.cn

Yidu Zhang

State Key Laboratory of Virtual Reality Technology and Systems,
Beihang University,
Beijing 100191, China
e-mail: ydzhang@buaa.edu.cn

Min Wan

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: mwan@buaa.edu.cn

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 16, 2015; final manuscript received December 22, 2015; published online January 27, 2016. Assoc. Editor: Hai Xu.

J. Mech. Des 138(3), 033302 (Jan 27, 2016) (9 pages) Paper No: MD-15-1709; doi: 10.1115/1.4032471 History: Received October 16, 2015; Revised December 22, 2015

Local synthesis establishes a relationship between the relative motion and the local geometry properties of gear and pinion surfaces at one single (mean) point. Theoretically, local synthesis design of spiral bevel and hypoid gears cannot ensure the contact performance along the entire contact point path (CPP) resulting in uncontrolled contact ellipses with different sizes and unavoidable transmission errors (TEs). Based on local synthesis, tooth contact analysis (TCA) and third-order contact analysis provide supplementary methods for improvement but still cannot directly control the entire CPP. A global synthesis approach is proposed to directly design the entire CPP by which it is possible to design each instantaneous contact ellipse (ICE) for load capacity and to achieve any function of TEs. A detailed implementation based on a free-form five-axis machine is presented in which the machine settings are obtained by definite relative position and motion between the tool and the workpiece at every instant. An example and the results obtained from the authors’ implementation are also provided for illustration and validation and show better control of contact ellipses and remarkable reduction of TEs to near zero.

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References

Figures

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Fig. 1

Contact paths of the gear (a) and the pinion (b)

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Fig. 2

Position relation between the generating tool surface and the generated pinion surface

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Fig. 4

Contact ellipses of local synthesis (a) and global synthesis (b) for the gear convex (1) and the pinion concave (2)

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Fig. 5

TEs of local synthesis (left) and global synthesis (right) for the gear convex and the pinion concave

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Fig. 6

Contact ellipses of local synthesis (a) and global synthesis (b) for the gear concave (1) and the pinion convex (2)

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Fig. 7

TEs of local synthesis (left) and global synthesis (right) for the gear concave and the pinion convex

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Fig. 3

Sketch and coordinate systems for the applied CNC machine

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Fig. 8

Normal deviations of the global synthesis pinion concave (a) and convex (b) surfaces with respect to local synthesis (unit: μm)

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Fig. 9

Ease-off of the global synthesis pinion convex (a) and concave (b) surfaces (unit: μm)

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Fig. 10

TEs of local synthesis (left) and global synthesis (right) with the assembly error of gear axial displacement ΔG = −0.04 mm

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Fig. 11

TEs of local synthesis (left) and global synthesis (right) with the assembly error of shortest distance ΔE = 0.04 mm

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Fig. 12

TEs of local synthesis (left) and global synthesis (right) with the assembly error of pinion axial displacement ΔP = −0.04 mm

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Fig. 13

TEs of local synthesis (left) and global synthesis (right) with the assembly error of shaft angle ΔΣ = −10 arcmin (−0.0029 rad)

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