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Reliability analysis of thin-walled ring gear based on tooth surface fatigue and wear

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Abstract

Based on the Hertz contact theory, the criterion of local yield strength value and the Archard wear theory, reliability analysis models of two failures are established and validated by the Monte Carlo simulation method to assess the tooth surface fatigue and wear reliability of thin-walled ring gears. Sensitivity analysis is carried out near the design point and assessed for the influence of operational torque, manufacturing parameters and assembly accuracy on reliability. The results show that the difference between the reliability of the two failures calculated by the first-order second-moment method and Monte Carlo simulation method is less than 1.1 %, and the reliability calculated by the first-order second-moment method is persuasive. The influence of operational torque on tooth surface fatigue reliability and wear reliability is similar, and tooth surface fatigue reliability is more sensitive to core hardness and carburized layer thickness, while tooth surface wear reliability is more sensitive to center distance and parallelism.

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Abbreviations

α 0 :

Theoretical engagement angle

α :

Actual engagement angle

r 1b :

Base circle radii of transmission gear

r 2b :

Base circle radii of thin-walled ring gear

T :

Parallelism

M :

Transmission gear torque

r 1 :

Radius of the gear pitch circle

B :

Gear teeth width

α′ :

Pressure angle of tip circle of the transmission gear

α″ :

Pressure angle of tip circle of the ring gear

r 1a :

Radius of the tooth-top circle of the gear

r 2a :

Radius of the tooth-top circle of the ring gear

θ :

Pressure angle of limit engagement point

R 1 :

Radii of curvature of gear

R 2 :

Radii of curvature of ring gear

\(R_1^\prime \) :

Curvature radius of limit meshing point of gear

\(R_2^\prime \) :

Curvature radius of limit meshing point of ring gear

b :

Half-width of the contact area of the pitch circle

b′ :

Half-width of the contact area of the limit meshing point

E i :

Elastic modulus

v i :

Poisson’s ratio

f :

Friction coefficient

σ zz :

Z normal stress

σ yy :

Y normal stress

σ xx :

X normal stress

τ zy :

YZ plane shear stress

τ max :

Maximum shear stress in the yz plane

\(p_{max}^\prime \) :

Surface maximum stress the limit meshing point

H :

Hardness at one point below the tooth surface

H b :

Hardness at the critical part of the hardened layer

H 0 :

Surface hardness

H k :

Hardness of the tooth ring gear core

h t :

Thickness of the hardened layer

σ b :

Yield strength under the tooth surface

τ :

Shear strength under the tooth surface

[τ]:

Allowable shear stress without fatigue

G f :

State function of fatigue failure reliability

V :

Wear volume

K :

Wear coefficient

F :

Normal load on the contact surface

L :

Relative sliding distance

P :

Contact pressure

h :

Wear depth

S :

Contact area of the tooth surface meshing

Δh :

Wear increment

ξ :

Ratio of the relative sliding distance

ω i :

Gear and ring gear angular speed

ΔL :

Relative sliding distance

n :

Bending fatigue safety factor

m :

Modulus

x :

Displacement coefficient

β :

Tooth shape angle

[h]:

Allowable wear depth

G w :

State function of the wear failure reliability

\({\beta _{{G_i}}}\) :

Reliability index

R f :

Fatigue reliability of the thin-walled ring gear

R w :

Wear reliability of the thin-walled ring gear

S μ :

Mean sensitivity matrix

S σ :

Standard deviation sensitivity matrix

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Acknowledgments

This work is supported by National Natural Science Foundation of China (U20A20281 and 52372424).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100091, China

    Boyuan Pang, Xianming Wang & Tianxiao Zhang

Authors
  1. Boyuan Pang
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  2. Xianming Wang
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  3. Tianxiao Zhang
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Corresponding author

Correspondence to Tianxiao Zhang.

Additional information

Boyuan Pang is currently a master student at the School of Mechanical Engineering and Automation, Beihang University, Beijing, China. His main research interests include failure analysis of gears and mechanical reliability design.

Xianming Wang is currently a Ph.D. student at the School of Mechanical Engineering and Automation, Beihang University, Beijing, China. He is doing research in the areas of reliability design and sensitivity analysis of mechanical structure, failure analysis of mechanical components.

Tianxiao Zhang is a Professor and Director of the Department of Mechanical Design, at the School of Mechanical Engineering and Automation, Beihang University, Beijing, China. His research areas include: uncertainty analysis and reliability design, failure prediction and health management, quality engineering and manufacturing systems.

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Pang, B., Wang, X. & Zhang, T. Reliability analysis of thin-walled ring gear based on tooth surface fatigue and wear. J Mech Sci Technol 38, 1985–1997 (2024). https://doi.org/10.1007/s12206-024-0330-7

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  • DOI: https://doi.org/10.1007/s12206-024-0330-7

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