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Mutually different tooth surface contact characteristics of a noncircular face gear with intersecting axes

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Abstract

The noncircular face gear (NFG) with intersecting axes is composed of a spur gear and a NFG, which can realize the reduced and variable-speed integrated transmission between any intersecting axes. To study the contact characteristics of NFG with intersecting axes, the mutually different tooth surface mathematical model of the NFG with intersecting axes was established, and a tooth surface analysis method based on rotational projection was innovatively proposed. By using this method, the distribution characteristics of contact traces on different tooth profiles can be accurately compared through establishing the comparison reference of the middle plane on gear teeth. At the same time, the effects of installation errors and eccentricity on the contact characteristics of tooth surface were analyzed in detail. Results demonstrate that the change in the same kind of installation error has the same effect on the offset direction of the contact traces on each gear tooth. Under the same installation error, changing the eccentricity of the NFG will cause different changes in the offset of the contact traces on each gear tooth. Finally, a gear transmission device of NFG with intersecting axes was designed and manufactured. The correctness of the contact model and the analysis results were proven by the gear pair rolling experiment, which provides a theoretical basis for the design and installation of NFG with intersecting axes.

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Abbreviations

c a*:

Tip clearance coefficient

h a*:

Addendum coefficient

i js :

Ratio of the tooth numbers for the NFG to the cutter

i s2 :

Transmission ratio

m s :

Module of the gear

n d1 :

Normal vector of the spur gear

n d2 :

Normal vector of the NFG

r as :

Radius of the top circle of the slotting cutter

r b1 :

Radius of the base circle of the spur gear

r bs :

Radius of the base circle of the slotting cutter

r d1 :

Position vector of the spur gear

r d2 :

Position vector of the NFG

r(φ 2):

Radius vector of the pitch curve of the NFG

Z 1 :

Tooth numbers of the spur gear

Z 2 :

Tooth numbers of the NFG

Z s :

Tooth numbers of the slotting cutter

α :

Pressure angle

ϕ :

Eccentricity of the NFG

κ :

Angle between gears

φ 2 :

Rotation angle of the NFG

φ s :

Rotation angle of the slotting cutter

π :

Pitch radius of the slotting cutter

ρ 1 :

Pitch radius of the spur gear

ψ 1 :

Rotation angles of the spur gear

ψ 2 :

Rotation angles of the NFG

Δκ :

Axis intersection angle error

ΔE :

Offset error

Δq :

Axial error

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Acknowledgments

This work was supported by Hebei Natural Science Foundation (Grant No. E2022203006) and the University Science and Technology Research Project of Hebei Province (Grant No. QN2020266).

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Authors and Affiliations

  1. College of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Dawei Liu, Heng Li, Zhenzhen Lv & Yuetong Cao

Authors
  1. Dawei Liu
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  2. Heng Li
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  3. Zhenzhen Lv
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  4. Yuetong Cao
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Corresponding author

Correspondence to Dawei Liu.

Additional information

Dawei Liu is an Associate Professor of the College of Mechanical Engineering, Yanshan University, Qinhuangdao, China. He received his Ph.D. in Mechanical Design and Theory from Yanshan University. His research interests include new mechanical transmission, new energy vehicle and tactile sensor.

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Liu, D., Li, H., Lv, Z. et al. Mutually different tooth surface contact characteristics of a noncircular face gear with intersecting axes. J Mech Sci Technol 37, 1903–1912 (2023). https://doi.org/10.1007/s12206-023-0327-7

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  • DOI: https://doi.org/10.1007/s12206-023-0327-7

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