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Energy consumption investigation of a three-axis machine tool and ball-end milling process

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Abstract

The manufacturing industry consumes a considerable amount of energy every year, which poses a major challenge to resource consumption and environment problem. To overcome these difficulties, it is necessary to understand the machine tools’ power characteristics. The current research aims to investigate the energy consumption of the machine tool and to establish a cutting power model for ball-end milling process. First, a cutting power theoretical model for a ball-end milling cutter was established based on the infinitesimal cutting force. Secondly, a series of experiments were conducted to reveal and validate the mathematical function of spindle power and feed power. Finally, slotting milling experiments were conducted, and a cutting power empirical model was proposed by analyzing the correlation between cutting forces and cutting power. The results showed that the spindle power, feed power, and cutting power could be exactly predicted by the proposed method. Furthermore, the Z-axis’s feed power characteristic was revealed that the gravity made the Z-axis’s motor transform to the generator when Z-axis moved in the downward direction. For cutting power model, the theoretical model and empirical model had the same predictive accuracy, while the empirical model had a simpler form and could be easier applied. The proposed power investigation method provided technical support for the research of the machine tools’ energy consumption characteristics.

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Availability of data and material

The authors declare that the data and material used or analyzed in the present study can be obtained from the corresponding author at reasonable request.

Code availability

Custom code.

Abbreviations

dF t, dF r, dF a :

Differential cutting forces in tangential, radial, and axial direction (N)

K te, K re, K ae :

Edge-specific coefficients (N/mm)

K ts, K rs, K as :

Shear-specific coefficients (N/mm2)

dS :

Differential length of cutting-edge (mm)

t n :

Instantaneous undeformed chip thickness (mm)

db :

Differential width of chip (mm)

R :

Radius of the ball-end milling cutter (mm)

f z :

Feed per tooth (mm)

k :

Axial position angle (rad)

α :

Helix angle of the ball-end milling cutter (rad)

θ :

Angular position of the elemental cutter edge (rad)

ψ :

Angular position of the reference cutting edge (rad)

φ :

Lag angle of the elemental edge (rad)

O c-X c Y c Z c :

Cutting tool coordinate system

O-XYZ :

Machine tool coordinate system

P :

A point on the cutting edge

dF Xc, dF Yc, dF Zc :

Differential cutting forces in Xc, Yc, and Zc direction (N)

\({\overline F}_{{\mathrm X}_{\mathrm c}({\mathrm Y}_{\mathrm c},{\mathrm Z}_{\mathrm c})}\) :

Mean cutting forces in Xc, Yc, and Zc direction (N)

N :

Total number of cutting edges

θ st, θ ex :

Cut-in and cut-out angular position of the elemental cutting edge (rad)

k up, k low :

Upper and lower bounds of the axial position angle (rad)

P c :

Cutting power (kW)

dF f :

Differential cutting force in feed direction (N)

n :

Spindle speed (r/min)

v f :

Feed rate (mm/min)

η :

Coefficient considering the power loss of spindle transmission

a p :

Axial cutting depth (mm)

P SR :

Spindle power (kW)

P X, P Y :

Feed power of X-axis and Y-axis (kW)

P Z-up, P Z-down :

Feed power of the Z-axis in the upward direction and downward direction (kW)

R 2 :

Coefficient of determination

P 1 :

Cutting power calculated by theoretical model (kW)

P 2 :

Cutting power calculated by empirical model (kW)

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 51975333), The National New Material Production and Application Demonstration Platform Construction Program (Grant No. 2020–370104-34–03-043952), and Taishan Scholar Project of Shandong Province (No. ts201712002).

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Authors and Affiliations

  1. Key Laboratory for High Efficiency and Clean Mechanical Manufacture of Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan, 250061, People’s Republic of China

    Renjie Ge, Song Zhang, Renwei Wang, Xiaona Luan & Irfan Ullah

  2. Key National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan, 250061, People’s Republic of China

    Renjie Ge, Song Zhang, Renwei Wang, Xiaona Luan & Irfan Ullah

Authors
  1. Renjie Ge
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  2. Song Zhang
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  3. Renwei Wang
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  4. Xiaona Luan
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Contributions

Renjie Ge provided the methodology, wrote the program code, investigated the experiments, and wrote the original manuscript. Song Zhang also provided the methodology, reviewed the manuscript, and provided the funding. Renwei Wang investigated the experiments and reviewed the manuscript. Xiaona Luan provided the methodology and reviewed the manuscripts. Irfan Ullah reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Song Zhang.

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Ge, R., Zhang, S., Wang, R. et al. Energy consumption investigation of a three-axis machine tool and ball-end milling process. Int J Adv Manuf Technol 121, 5223–5233 (2022). https://doi.org/10.1007/s00170-022-09627-w

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  • DOI: https://doi.org/10.1007/s00170-022-09627-w

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