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A thermomechanical model for mesh deflection calculation of crown spur gear pair

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Abstract

An analytical model of evaluating tooth pair deflection along the line of contact is proposed in this paper to preliminarily determine the load distribution between tooth pairs contacting instantaneously for crown spur gears. Further, a three-dimensional thermomechanical point contact method is introduced for modeling the normal approach of two contacting teeth. Combined with tooth and fillet-foundation deflections, a coupled thermoelastic mesh deformation model for crown gears is developed. The influence of load, angular velocity and friction coefficient on the normal approach of the contact, load sharing ratio and transmission error during meshing are respectively investigated. It is suggested that without considering thermal influence, the vibration excitation of gears can be underestimated. Considering the coupled thermoelastic deformation of meshing gears may result in a better evaluation of transmission error and facilitate the subsequent tooth modification design and dynamic study.

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Abbreviations

a :

Semi-major axis of the contact ellipse, mm

b :

Semi-minor axis of the contact ellipse, mm

B :

Face width, mm

C 0 :

The amount of axial modification, mm

C p :

The crowning value of the section where the distance to the tooth center is zp, mm

E :

Elastic modulus, GPa

F :

Meshing force, N

G :

Shear modulus, GPa

h f :

The dedendum of gear tooth, mm

m :

Module, mm

n 1 :

Rotational speed, r/min

p h :

The maximum Hertzian contact pressure, MPa

p b :

Base pitch of pinion, mm

r :

Reference radius, mm

r b :

Base radius, mm

r f :

Root radius, mm

q :

Heat flux, mJ/(s mm2)

Q :

Heat flow, mJ/s

R :

Radius of circular arc crowning, mm

T:

Torque applied to gear, N m

t p :

Parameter of rack-cutter flank profile equations

u :

Tooth surface displacement, mm

v :

Poisson’s ratio

V s :

Relative sliding speed between the two meshing tooth surfaces, mm/s

z p :

The distance of gear section to tooth center, mm

Z:

Number of teeth

α :

Profile angle of the rack cutter, rad

ρ :

Tool tip radius, mm

μ :

Friction coefficient

Δ:

Distance between tool tip fillet arc center and tool symmetric line, mm

ΔT :

Flash temperature rise, K

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Funding

This study was funded by National Natural Science Foundation of China (No. 51875373) and the Science and Technology Foundation of Sichuan (2019YJ0093). Q. Zhou would also like to acknowledge the supports from China Postdoctoral Science Foundation (Nos. 2018M643469, 2019T120836).

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Authors and Affiliations

  1. Wuhan Second Ship Design and Research Institute, Wuhan, 430064, China

    Yong Yang & Gang Zhu

  2. School of Aeronautics and Astronautics, Sichuan University, Chengdu, 610065, China

    Yong Yang, Jiaxu Wang, Wanyou Yang & Qinghua Zhou

  3. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400030, China

    Jiaxu Wang

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  1. Yong Yang
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  2. Jiaxu Wang
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  3. Gang Zhu
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  5. Qinghua Zhou
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Correspondence to Qinghua Zhou.

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Yang, Y., Wang, J., Zhu, G. et al. A thermomechanical model for mesh deflection calculation of crown spur gear pair. Meccanica 55, 1393–1411 (2020). https://doi.org/10.1007/s11012-020-01160-y

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