Abstract
A calculation method for the friction coefficient and meshing efficiency of plastic line gear (LG) pair under dry friction conditions was studied theoretically and experimentally, taking a polyoxymethylene parallel line gear pair (POM PLGP) as an example. Firstly, the geometric and mechanical models of PLGP were built by considering the effects of misalignment and loaded deformation under the actual operating condition. Then, the friction coefficient of POM specimens was obtained via the ball-on-disk experiment, of which the value varies between 0.35 and 0.45 under the experimental conditions. The calculation formula for the friction coefficient of POM LG pair was obtained by fitting the friction coefficient of the POM specimens, and the meshing efficiency of POM LG pair was calculated based on the calculation formula for friction coefficient and the meshing efficiency calculation approach. Finally, the meshing efficiency of POM PLGP specimens was measured using a homemade gear meshing efficiency test rig. The experimental results validated the feasibility of the proposed calculation method for the friction coefficient and meshing efficiency of the plastic LG pair. This study provides a method for the calculation of the friction coefficient and meshing efficiency of plastic gear pairs under dry friction conditions. It also provides the basis for the wear calculation of plastic LG pair under dry friction conditions.
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Abbreviations
- o i − x i y i z i :
-
Coordinate system fixed with driving and driven LG
- o − xyz, o f − x f y f z f :
-
Fixed coordinate system for
- M f1, M f2, L f1, L f2 :
-
Transformation matrix
- r i :
-
Contact curve
- m i, n i :
-
Helix radius and pitch parameter of ri
- Σi :
-
Tooth surface
- n i0 :
-
Unit normal vector of Σi
- P i :
-
Section of tooth profile
- R i, φ zi :
-
Radius and modification angle of Pi
- t i, θ i :
-
Scope parameter of ri and pi
- ϕ i :
-
Rotation angle
- z i :
-
Number of teeth
- i 12 :
-
Transmission ratio
- δa, δb, γ h, γ v :
-
Misalignment of PLGP
- Δθ 2kl :
-
Additional angular displacement along the circumferential direction
- ϕ′ 2kj (ϕ 1kj):
-
Rotation angle of the driven LG considering misalignment and loaded deformation
- F n2(ϕ 1k):
-
Normal force
- F t2(ϕ 1k):
-
Peripheral force
- F r2(ϕ 1k):
-
Radial force
- F a2(ϕ 1k):
-
Axial force
- T 1, T 2 :
-
Calculated input and output torques
- K akj :
-
Load distribution coefficient among the loaded tooth pairs
- α k :
-
Pressure angle
- m 2c(ϕ 1k):
-
Meshing radius of the driven LG
- ω ?(ϕ 1k):
-
Angular velocity
- v i(ϕ 1k):
-
Line velocity
- v 12(ϕ 1k):
-
Relative sliding velocity
- R ixk, R iyk :
-
Radii of principal curvatures of Σi
- e iIk, e iIIk :
-
Principal direction of Σi
- γ k Angle between e 1Ik :
-
and e2Ik
- p kj(g, h):
-
Contact pressure distribution
- p akj :
-
Average contact pressure on tooth surfaces
- δ kj :
-
Mutual approach
- K g-e,h-f :
-
Influence coefficient
- F ns :
-
Normal force applied on the POM ball and disk specimens
- p as :
-
Average contact pressure of the POM specimens
- v s :
-
Relative sliding velocity of the POM ball and disk specimens
- μ s :
-
Friction coefficient of the POM specimens
- μ(ϕ 1k):
-
Friction coefficient of the POM LG pair
- P ins :
-
Calculated instantaneous frictional power losses
- η ins :
-
Calculated instantaneous meshing efficiency
- η cal :
-
Calculated average meshing efficiency
- P total :
-
Measured total power losses
- P spin, P load :
-
Measured load-independent and load-dependent power losses
- P bearing, P coupling :
-
Power losses of bearings and couplings
- P mesh :
-
Power losses of gear meshing
- η mesh :
-
Measured average meshing efficiency
- T in, T out :
-
Measured input and out torque data
- ω in, ω out :
-
Measured input and output angular velocity data
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Acknowledgements
The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No. 51575191) and 2019 Guangzhou Technology Project (No. 201904010368).
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Yangzhi CHEN. He received his bachelor degree from Tianjin University, China, in 1986. He received his master and Ph.D. degrees from Zhejiang University, China, in 1992 and 1995, respectively.
Currently, he is a professor and doctoral supervisor at the School of Mechanical and Automotive Engineering, South China University of Technology, China. His research areas cover line gear, tribology, and micro/nanotransmission.
Yifan LIN. He received his bachelor degree from South China University of Technology, China, in 2014. Currently, he is a Ph.D. candidate in South China University of Technology, China. His research interests include line gear, friction, and wear of polymer gears.
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Chen, Y., Lin, Y. A calculation method for friction coefficient and meshing efficiency of plastic line gear pair under dry friction conditions. Friction 9, 1420–1435 (2021). https://doi.org/10.1007/s40544-020-0424-x
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DOI: https://doi.org/10.1007/s40544-020-0424-x