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A novel approach to attain tooth flanks with variable pressure and helical angles utilizing the same cutter in the CNC gear skiving process

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Abstract

To save manufacturing costs and enhance design flexibility in gear skiving, a dual closed loop, including inner and outer closed loops, is proposed to generate skived gear tooth flanks with different pressure angles and helix angles using the same cutter. The skiving cutter is firstly generated based on the suitable form of the corrected rack, which is defined according to the target tooth surface. The additional motions considering the motion limits of an electronic gearbox for the machining axis are added in the form of polynomials. The inner closed loop based on the Levenberg–Marquardt algorithm is developed to attain the coefficients of polynomials in fitting the skived gear tooth flanks to the target surface. After completing a cycle of the inner closed loop, the skived gear’s pressure/helix angle is changed in the outer closed loop to renew the target surface, and then a new cycle of the inner closed loop is restarted. The suitable range of the skived gear’s pressure/helix angle is satisfied when the dual closed loop is fully ended. The effectiveness and practicality of the proposed method are verified by the presented numerical examples.

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Data availability

All data generated or analyzed during this study are included in the manuscript.

Code availability

Not applicable.

Abbreviations

\(a\) :

Polynomial coefficient

\(C\) :

Machine axes

\({\mathbf{k}}\) :

Unit normal vector in z-direction

\({\mathbf{L}}\) :

Upper-left 3 × 3 submatrix of \({\mathbf{M}}\)

\(m\) :

Gear module

\({\mathbf{M}}\) :

Transformation matrix

\({\mathbf{n}}\) :

Unit normal vector

\({\mathbf{r}}\) :

Position vector

\(s\) :

Grinding stock of work gear

\(S\) :

Coordinate system

\(t\) :

A half of gear pitch

\({\mathbf{t}}\) :

Tangent vector

\(u\) :

Profile parameter of normal rack

\(v\) :

Longitudinal parameter of inclined rack

\(\alpha\) :

Reference pressure angle

\(\beta\) :

Reference helix angle

\(\gamma\) :

Rake angle of skiving cutter

\(\eta\) :

Damping parameter

\(\lambda\) :

Relief angle of skiving cutter

\(\tau\) :

Side clearance angle

\(\varphi\) :

Rotation angle of cutter

\(b1\) :

Rotation axis of spindle assembly

\(c\) :

Skiving cutter

\(c1\) :

Rotation axis of cutter

\(c2\) :

Rotation axis of work gear

\(f\) :

Pitch point

\(n\) :

Normal section

\(oc\) :

Operation parameter of cutter

\(ow\) :

Operation parameter of work gear

\(p\) :

Reference pitch circle

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Acknowledgements

The authors are grateful to the Ministry of Science and Technology in Taiwan for its financial support under project number MOST 108-2628-E-008-007-MY3.

Funding

This research was supported by the Ministry of Science and Technology in Taiwan, project number MOST 108–2628-E-008–007-MY3.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, Taiwan, 320317, Republic of China

    Trong-Thuan Luu & Yu-Ren Wu

  2. School of Mechanical Engineering, Hanoi University of Science and Technology, 01 Dai Co Viet Rd., Hanoi City, Vietnam

    Trong-Thuan Luu

Authors
  1. Trong-Thuan Luu
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Contributions

TTL constructed the research design, accomplished the cutting simulation, and composed the manuscript, whereas YRW earned the funding and directed the research implementation. All authors worked concurrently to proofread and structure the submission.

Corresponding author

Correspondence to Yu-Ren Wu.

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Appendix

Appendix

In this paper, the corrected normal rack consists of seven segments, as shown in Fig. 29, proposed by Luu and Wu [15]. Each segment is presented in explicit equations in Table 8.

Fig. 29
figure 29

Definition of corrected rack (Rm1) [15]

Full size image
Table 8 Explicit equations of segments of the corrected normal rack [15]
Full size table

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Luu, TT., Wu, YR. A novel approach to attain tooth flanks with variable pressure and helical angles utilizing the same cutter in the CNC gear skiving process. Int J Adv Manuf Technol 123, 875–902 (2022). https://doi.org/10.1007/s00170-022-10220-4

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