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A novel method for longitudinal modification and tooth contact analysis of non-circular cylindrical gears

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Abstract

The traditional geometry of non-circular cylindrical gears provides a contact line between tooth surfaces. In a misaligned non-circular cylindrical gear drive, causing edge contacts that result in noise and vibration. The point contact of the tooth surface is achieved by modification of the driving gear in the longitudinal direction, in order to reduce the sensitivity of tooth surface contact to installation errors. The proposed longitudinal modification method is based on the application of a grinding worm by controlling the center distance of non-circular cylindrical gear and worm. Based on the gear meshing principle, a mathematical model of the tooth surfaces of non-circular cylindrical gears is established, and a parametric tooth surface equation with a unified expression is obtained. Tooth contact analysis (TCA) of non-circular cylindrical gears shows that the contact path and contact area on the tooth surface are shifted with the change of installation error, but still distributed in the middle of the tooth surface without creating edge contact. The transmission error is increased with the growth of installation error. Tooth modification in a longitudinal direction has an obvious improvement effect on the bad tooth contact condition, but too large a tooth modification parameter will make the tooth surface load distribution concentrated in a smaller area, which results in the decrease of gear load capacity.

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Abbreviations

φ 1 :

The polar angle of the driving gear

φ 2 :

The polar angle of the driven gear

a :

Center distance of non-circular gear pair

μ :

The angle between the tangent line and the radius vector

r b :

Base circle radius of generating gear

r g :

Pitch circle radius of generating gear

u s :

The involute variation parameter

v s :

The tooth width parameter

δ 0 :

The starting angle of the involute

θ i :

The rotation angle of non-circular gear

φ i :

The polar angle of non-circular gear

ϕ i :

The rotation angle of generating gear

L i :

Non-circular gear pitch curve arc length

E wp :

Center distance of non-circular gear and worm

λw :

The lead angle of worm grinding wheel

λwp :

The worm installation angle

Δsw :

The distance that the worm moves along the non-circular gear axis

TE :

Transmission error

i 12 :

Transmission ratio of non-circular gear pair

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Acknowledgments

This research gained sponsorship from The National Natural Science Foundation of China (Grant No. 52105058), Gansu Provincial Natural Science Foundation of China (Grant No.21JR7RA235), and The Open Fund of Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering at Wuhan University of Science and Technology (Grant No. MTMEOF2020B03).

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Authors and Affiliations

  1. School of Mechanical & Electronical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Dawei Li, Yongping Liu, Jun Gong & Yongqiao Wei

  2. Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan, 430000, China

    Gang Zhao

Authors
  1. Dawei Li
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  2. Yongping Liu
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  3. Jun Gong
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  4. Yongqiao Wei
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  5. Gang Zhao
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Corresponding author

Correspondence to Dawei Li.

Additional information

Dawei Li is a Ph.D. candidate in the Lanzhou University of Technology. His research interests include theoretical research and application design of non-circular gears and digital design and manufacturing technology of complex shaped gears.

Yongping Liu is a Professor in the School of Mechanical and Electrical Engineering of Lanzhou University of Technology. His research interests include meshing theory of non-circular gears and special equipment and its control.

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Li, D., Liu, Y., Gong, J. et al. A novel method for longitudinal modification and tooth contact analysis of non-circular cylindrical gears. J Mech Sci Technol 36, 6157–6170 (2022). https://doi.org/10.1007/s12206-022-1130-6

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  • DOI: https://doi.org/10.1007/s12206-022-1130-6

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