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The approach to multi-objective optimization for process parameters of dry hobbing under carbon quota policy

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Abstract

For process parameter optimization in high-speed dry hobbing, an optimization decision method is proposed in this study based on the multi-objective whale optimization algorithm (MOWOA). Firstly, according to the characteristics of high-speed dry hobbing, the processing time and processing error models are constructed; considering the carbon quota energy conservation and environmental protection policy, the processing cost model is established. Founded on the above models, the fitness function of the multi-objective optimization model is proposed. Afterward, on the basis of the traditional single-objective whale algorithm, the non-dominant set and crowding calculation method is introduced to establish a multi-objective optimization whale algorithm model. On this basis, the Pareto solution set is obtained. Finally, the actual decision case is compared to verify the effectiveness of the proposed method. Furthermore, the optimization data of MOWOA and several commonly multi-objective algorithms are compared to analyze the characteristics of the optimization solution set, thus verifying the superiority of the process parameter optimization method based on MOWOA.

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Availability of data and materials

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Code availability

Not applicable.

Abbreviations

m (mm):

Workpiece modulus

z :

Number of teeth

β (rad):

The helix angle of workpiece

α n (rad):

The pressure angle of workpiece

n (r/min):

Spindle rotation speed

f (mm/r):

Feed rate (axial direction)

q :

Hob threads

v a (mm/min):

Axial feed speed

D (mm):

Hob diameter

v r (mm/min):

Radial feed speed

B (mm):

Tooth width

B 1 (mm):

Cutting length

L 1 (mm):

Cutting-in route

L 2 (mm):

Cutting-out margin

L 3 (mm):

Cutting-in margin

A (rad):

Installation angle

h a (mm):

Addendum

T total (min):

Processing time

T a (min):

Air cutting time

T m (min):

Cutting time

T w (min):

Tool withdrawal time

T e (min):

Tool changing time

T au (min):

Assistance time

T ex (min):

Time of tool change

N tg :

Grinding times

T l (min):

Tool life (once)

T cw (min):

Assistance time of workpiece movement

T sz (min):

Assistance time of loading and unloading parts

T oa (min):

Operating assistance time

P c (CNY):

Processing cost

B c (CNY):

Ground billet cost

L c (CNY):

Labor cost

E cost (CNY):

Electric power cost

M c (CNY):

Depreciation cost of machine tool

T cost (CNY):

Tool cost

Q c (CNY):

Carbon quota purchase cost

R i (CNY):

Scrap returns income

B v (cm3):

Gear blank volume

G v (cm3):

Volume of post-hobbing

ρ (kg/cm3):

Material density

P br (CNY/kg):

Recycling unit price of round billet

P b (CNY/kg):

The unit price of round billet

m f :

Margin coefficient

d a (mm):

Addendum circle

c* :

Tip clearance coefficient

x n :

Modification coefficient

h r (CNY/min):

Hourly pay

W m (kwh):

Energy consumption by the processing of each workpiece

e p (CNY/kwh):

Electricity price

m c (CNY/min):

Depreciation cost of machine tool

T p (CNY):

Hob price

s c (kgCO2):

Carbon emission per single piece processing

c p (CNY/kg):

Carbon emission index per unit price

C t (kg):

Total carbon emissions for the year

q f (kg):

Free carbon quota

F e (kgCO2/kwh):

Carbon Emission Factor

e w :

Weight

e x (μm):

Tooth direction error

e y (μm):

Tooth profile error

Q e (μm):

Processing error

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Funding

This work was supported by the Key Projects of Strategic Scientific and Technological Innovation Cooperation of National Key Research and Development Program of China (Grant No. 2020YFE0201000).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China

    Yifan Liu, Chunping Yan & Hengxin Ni

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  1. Yifan Liu
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  2. Chunping Yan
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  3. Hengxin Ni
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Contributions

Yifan Liu analyzed the data; Chunping Yan and Hengxin Ni contributed experimental equipment and analysis tools; Yifan Liu wrote the paper.

Corresponding author

Correspondence to Chunping Yan.

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Liu, Y., Yan, C. & Ni, H. The approach to multi-objective optimization for process parameters of dry hobbing under carbon quota policy. Int J Adv Manuf Technol 121, 6073–6094 (2022). https://doi.org/10.1007/s00170-022-09669-0

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