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Digital twin-based dynamic prediction of thermomechanical coupling for skiving process

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Abstract

Skiving has potential for gear machining, but its cutting force fluctuates greatly, its cutting temperature is high during processing, and it has the characteristics of thermomechanical coupling. It is difficult for traditional methods to dynamically predict the thermomechanical coupling during the skiving process, whose efficiency and stability cannot be guaranteed. Aiming to solve these problems, a digital twin (DT)-based dynamic method is proposed to predict thermomechanical coupling in the skiving process. Considering the time-varying characteristics and coupling of the cutting force and temperature, a multi-physical modeling method dual-driven by mechanism and data is proposed to establish a thermomechanical coupling DT (TMDT) model of the skiving process. The dynamic consistency of the skiving process between the digital and physical spaces is realized. Principal component analysis (PCA) and an extreme learning machine (ELM) are used to reduce the order of the TMDT, the reduced-order model is trained using the skiving big data, and a relationship mapping model of the cutting parameters and the cutting force and temperature is established to realize the dynamic prediction of the cutting force and temperature. The effectiveness of the proposed method is verified through gear skiving experiments. This research has important theoretical guiding significance to realize efficient and stable skiving processing.

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Availability of data and material

All data generated or analyzed during this study are included in this published article [and its supplementary information files].

Abbreviations

P s :

Cutting plane

P r :

Base plane

P e :

Equivalent section plane

t p :

Tangential vector of cutting edge

n p :

Normal vector of rake face

l p :

Vector in the direction of the intersection of plane Pe and the rake face

l r :

Vector in the direction of the intersection of planes Pe and Pr

γ e :

Rake angle on plane Pe

v x :

Cutting speed of the cutting edge

C O :

A local coordinate system

v ch :

Flow velocity of chips

v s :

Shear velocity

F Os :

Cutting force of the MSCE

F x /F y /F z :

Cutting force of the MSCE in x, y, and z directions

a kc :

Cutting thickness

a kw :

Cutting width

σ s :

Yield strength of the workpiece material

ϕ e :

Shear angle on plane Pe

γ e :

Rake angle on plane Pe

ψ λ :

Chip flow angle

β e :

Friction angle on the tool-chip contact surface

λ s :

Edge inclination angle

c :

Specific heat capacity of the workpiece material

l :

Tool-chip contact length

ξ :

Distribution index of compressive stress on the rake face

T t :

Initial temperature of the skiving tool

n(t):

Number of MSCEs or MSTs

S g :

Tooth surface model of the gear workpiece

C :

Cutting-edge curve of the cutter

t :

Skiving time

F 1 :

Mapping relationship between n(t) and related parameters

γ(n) :

Rake angle of all MSCEs participating in cutting at any time

F 2 :

Mapping relationship betweenγ(n) and related parameters

m :

Mean

k :

Covariance

\(\overline{n}_{*}\) :

Mean of n*

γ n :

Rake angle in normal section plane

ω 1 :

Vector of the rotation speed of the gear workpiece

ω 1 :

Scalar of the rotation speed of the gear workpiece

ω 2 :

Vector of the rotation speed of the skiving tool

ω 2 :

Scalar of the rotation speed of the skiving tool

f :

Vector of the feed speed

f :

Scalar of the feed speed

r 1 :

Workpiece tooth surface in workpiece coordinate system

r 2 :

Conjugate surface in tool coordinate system

i 1 :

Unit vector of the x-axis in the workpiece coordinate system

j 1 :

Unit vector of the y-axis in the workpiece coordinate system

k 1 :

Unit vector of the z-axis in the workpiece coordinate system

k 2 :

Unit vector of the z-axis in the tool coordinate system

a :

Center distance between the skiving tool and the gear workpiece

v n :

Velocity component perpendicular to the shear zone

v s1/v s2 :

Shear slip speeds in the shear deformation zone

T ins :

Cutting temperature of the MST

R chf :

Proportion of friction heat flowing into the chip

μ :

Friction coefficient of the tool-chip contact surface

σ ro :

Maximum compressive stress on the rake face

λ w :

Thermal conductivity of the workpiece material

ρ :

Density of the workpiece material

\(DT_{F \oplus T}\) :

TMTD of the skiving process

\({\mathbf{F}}_{{{\text{ws}}}}^{k}\) :

Cutting force of the kth MSCE on a certain tooth in the global coordinate system

M wO :

Transformation matrix

\(T_{{{\text{ins}}}}^{k}\) :

Cutting temperature of the kth MST on a certain tooth

Q j :

Contribution rate of principal component

Q ( p ) :

Cumulative contribution rate of the first p principal components

\(\lambda_{j/k}\) :

Different eigenvalues

L :

Number of hidden layer neurons

M :

Numbers of input layers

N :

Numbers of output layers

\({\hat{\mathbf{\beta }}}\) :

Weight matrix of the hidden layer and the node of the output layer

H :

Output matrix of the hidden layer

H + :

Moore–Penrose generalized inverse of H

Q :

Output matrix of the ELM network

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Acknowledgements

We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Funding

This research was financially supported by the National Natural Science Foundation of China (52,165,060), and in part by the Science and Technology Projects of Inner Mongolia Autonomous Region (2021GG0432), and in part by the Beijing Institute of Technology Research Fund Program for Young Scholars.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University of Commerce, Tianjin, 300134, China

    Lei Zhang

  2. Laboratory of Digital Manufacturing, School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Lei Zhang, Jianhua Liu & Cunbo Zhuang

  3. Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, 314000, China

    Jianhua Liu & Cunbo Zhuang

  4. School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China

    Xiaoqiang Wu

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  1. Lei Zhang
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Correspondence to Cunbo Zhuang.

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Zhang, L., Liu, J., Wu, X. et al. Digital twin-based dynamic prediction of thermomechanical coupling for skiving process. Int J Adv Manuf Technol 131, 5471–5488 (2024). https://doi.org/10.1007/s00170-022-08908-8

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  • DOI: https://doi.org/10.1007/s00170-022-08908-8

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