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Influencing factors of effective tooth depth in the cylindrical gear rolling process with axial infeed

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Abstract

Working tooth depth is the key factor of affecting the transmission of motion and power for gear pair, which is closely related to the tooth depth of gear. To reveal the growth law of the formed teeth in the cylindrical gear rolling process with axial infeed, a sliding ratio model and contact stress model between tooth profiles of rolling die and workpiece were firstly derived based on the characteristics of the gear pair and rolling process with axial infeed. Rolling of cylindrical gears with module of 1.75 mm and pressure angle of 20° was then taken as an example to verify the above-mentioned models, and the influence of the working pressure angle, number of teeth of workpiece, and rotational speed of rolling dies on the effective tooth depth of the workpiece were analyzed by using finite element simulations (FES) and experiments. The results show that the effective tooth depth of the formed workpiece increases with the increases of the addendum modification coefficient of the rolling dies, number of teeth of the workpiece, and rotational speed of the rolling dies. The sliding ratio and contact stress decrease with the increases of the addendum modification coefficient of the rolling dies and number of teeth of the workpiece. Moreover, the effective tooth depth of the workpiece formed by the rolling dies with addendum modification coefficient of 1 is increased by 7.41% compared to that formed by the rolling dies with addendum modification coefficient of the 0.

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Data availability

The authors declared that the data and material are available.

Abbreviations

v t1 :

Tangential velocity of the rolling dies

v t2 :

Tangential velocity of the workpiece

v 21 :

Relative sliding velocity of the rolling dies and workpiece

w 1 :

Angular velocity of the rolling dies

w 2 :

Angular velocity of the workpiece

r Q1 :

Distance between point Q and o1

r Q2 :

Distance between point Q and o2

α Q1 :

Pressure angle of the circle where point Q is located on the rolling dies

α Q2 :

Pressure angle of the circle where point Q is located on the workpiece

η 2 :

Sliding ratio of the formed tooth profile

η 2t :

Sliding ratio of the formed tooth top

r b2 :

Base radius of the workpiece

r 0 :

Initial radius of the workpiece

α :

Pressure angle of the pitch circle

α′ :

Working pressure angle

α B2 :

Pressure angle of the circle where point B2 is located

z 1 :

Number of teeth of the rolling dies

z 2 :

Number of teeth of the workpiece

E :

Equivalent modulus of elasticity

E 1 :

Elasticity modulus of material of the rolling dies

E 2 :

Elasticity modulus of material of the workpiece

ρ :

Equivalent radius of curvature

ρ 1 :

Curvature radius of teeth of the rolling dies at contact point Q

ρ 2 :

Curvature radius of teeth of the workpiece at contact point Q

h i :

Height increment of the formed teeth

H i :

Effective tooth depth of the workpiece

F n :

Normal force at contact point Q

F t :

Circumferential force at the contact point Q

s :

Standard center distance between the rolling dies and workpiece

s′ :

Actual center distance between the rolling dies and workpiece

b :

Tooth width

λ :

Gear ratio between the rolling dies and workpiece

x 0 :

Abscissa of point o2

y 0 :

Ordinate of point o2

x ti :

Abscissa of point at

y ti :

Ordinate of point at

φ′:

Similar geometric pressure coefficient

μ :

Effective tooth depth coefficient

m :

Module of the workpiece

n :

Number of measurement

x :

Addendum modification coefficient

h * :

Addendum coefficient

c * :

Clearance coefficient

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Acknowledgements

The authors extend sincere gratitude to Xiaogao Yang, College of Mechanical Engineering, Hunan University of Arts and Science, China, for his editing and technical advice.

Funding

This project is supported by the National Natural Science Foundation of China (No. 51775062), Shanxi Province Science Foundation for Youths (No. 201901D211292), Award Grants for Outstanding Doctors Working in Shanxi Province (No. 20202036), and Taiyuan University of Science and Technology Scientific Research Initial Founding (TYUST SRIF) (No. 20192022).

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Authors and Affiliations

  1. College of Mechanical Engineering, Hunan University of Arts and Science, Changde, 415000, China

    Youxin Luo

  2. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Ziyong Ma, Xueyang Fang & Fuquan Zhang

  3. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Yuanxin Luo

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  1. Youxin Luo
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Contributions

Yuanxin Luo and Ziyong Ma contributed to the conception of the research; Youxin Luo and Ziyong Ma performed the experiment; Youxin Luo, Fuquan Zhang, and Ziyong Ma contributed significantly to analysis and manuscript preparation; Xueyang Fang performed the data analyses and wrote the manuscript; Yuanxin Luo helped perform the analysis with constructive discussions.

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Correspondence to Ziyong Ma.

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Luo, Y., Ma, Z., Fang, X. et al. Influencing factors of effective tooth depth in the cylindrical gear rolling process with axial infeed. Int J Adv Manuf Technol 118, 497–510 (2022). https://doi.org/10.1007/s00170-021-07965-9

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  • DOI: https://doi.org/10.1007/s00170-021-07965-9

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