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Integrated optimization of cutting parameters and hob parameters for energy-conscious gear hobbing

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Abstract

Optimum process parameters play an important role in improving manufacturing process which have a vital influence on the energy consumption and production cost. Considering the fact that hobbing process is sensitive to process parameters, an integrated multi-objective process parameters optimization method for gear hobbing is proposed to reduce energy consumption and production cost. Thus, this paper firstly analyzes the hobbing process parameters and establishes a description of hobbing process parameters problem. Then a multi-objective optimization model of hobbing process parameters is introduced, with energy consumption and production cost to be optimized. An improved multi-objective ant lion optimizer (IMOALO) is designed to solve multi-objective optimization problem. Finally, a case study is presented in detail to verify the optimization model. The results show that energy consumption and production cost can be optimized simultaneously by determining appropriate process parameters based on proposed method. It has potential in providing favorable support and assistance for technical operators in the practical parametric decision.

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Data availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The code for current study is available from the corresponding author on reasonable request.

Abbreviations

a p :

Cutting depth (mm)

A :

Surpass stroke of hob (mm)

B :

Gear width (mm)

cpi :

Cutting parameters

C f, K 1, K 2, K 3, x f, y f, z f, u f, v f :

Hobbing force coefficients

C energy :

Energy consumption cost (yuan)

C gear :

Gear blank cost (yuan)

C labor :

Labor cost (yuan)

C machine :

Machine tool wear cost (yuan)

C tool :

Tool cost (yuan)

C total :

Production cost (yuan)

C T, ω :

Tool life coefficients

d a0 :

Diameter of hob tip (mm)

d 0 :

Diameter of hob (mm)

E :

Approach stroke of hob (mm)

E a :

Energy consumption in air-cutting state (J)

E c :

Energy consumption of cutting state (J)

E s :

Energy consumption in standby state (J)

E total :

Hobbing energy consumption (J)

f a :

Axial feed (mm/r)

F a :

Axial feed speed (mm/min)

F amax :

Maximum axial feed speed (mm/min)

F amin :

Minimum axial feed speed (mm/min)

F c :

Hobbing force (N)

F cmax :

Maximum hobbing force (N)

F r :

Radial feed speed (mm/min)

hpi :

Hob parameters

j :

Total passes of hob

L a :

Axial air-cutting length (mm)

L r :

Radial air-cutting length (mm)

m n :

Normal module of gear (mm)

n 0 :

Spindle speed (r/min)

n max :

Maximum spindle speed (r/min)

n min :

Minimum spindle speed (r/min)

P a :

Power consumption in air-cutting state (W)

P ap :

Additional power consumption (W)

P c :

Power consumption of cutting state (W)

P e :

Rated motor power (W)

P n :

Power consumption under non-loaded machine running (W)

P r :

Power consumption in removing process (W)

P s :

Power consumption in standby state (W)

P sc :

Power consumption of the activated auxiliary systems (W)

r :

Radius of hob tip (mm)

R a :

Finished surface roughness (μm)

s :

Number of slots

s e :

Unit cost of electricity energy (yuan/kWh)

s l :

Unit cost of labor (yuan/min)

s m :

Unit cost of machine wear (yuan/min)

s t :

Unit cost of tool (yuan/min)

t a :

Air-cutting time (s)

t c :

Cutting time (s)

t s :

Standby time (s)

t total :

Total processing time (s)

\( {T}_{\mathrm{hob}}^i \) :

Service life of tool (min)

\( {T}_{\mathrm{hob}}^{\mathrm{min}} \) :

Minimum tool life (min)

T m :

Service life of machine tool (year)

U :

Safety allowance (mm)

v :

Cutting velocity (m/min)

wpi :

Gear workpiece parameters

X i :

Parameters set

z 0 :

Number of hob heads

z 2 :

Number of gear teeth

α n :

Profile angle (°)

β 0 :

Helix angle (°)

ε i :

Additional power coefficients

κ i :

Non-loaded machining power coefficients

η :

Motor power factor

ABC:

Artificial bee colony

AMGA:

Archive-based micro-genetic algorithm

COA:

Cuckoo optimization algorithm

GA:

Genetic algorithm

HH:

Hoopoe heuristic

IMOALO:

Improved multi-objective ant lion optimizer

MOGWO:

Multi-objective grey wolf optimizer

MOPSO:

Multi-objective particle swarm optimization

MOSA:

Multi-objective simulated annealing

MRR:

Material remove rate

NSGA-II:

Non-dominated sorting genetic algorithm-II

NSTLBO:

Non-dominated sorting teaching-learning-based optimization

SEC:

Specific energy consumption

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Funding

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

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, China

    Hengxin Ni, Chunping Yan, Weiwei Ge, Han Sun & Teng Xu

  2. Hefei Meiya Photoelectric Technology Co., Ltd, Hefei, 230088, China

    Shenfu Ni

Authors
  1. Hengxin Ni
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  2. Chunping Yan
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  3. Weiwei Ge
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  4. Shenfu Ni
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  5. Han Sun
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Contributions

Hengxin Ni: Conceptualization, Methodology, Data curation, Writing—original draft, Investigation, Writing - review and editing, Software, Visualization. Chunping Yan: Conceptualization, Writing—review and editing, Investigation, Supervision, Project administration. Weiwei Ge: Writing—review and editing, Data curation, Visualization. Shenfu Ni: Writing—review and editing, Methodology, Formal analysis. Han Sun: Writing—review and editing, Validation, Formal analysis. Teng Xu: Writing—review and editing, Validation, Formal analysis

Corresponding author

Correspondence to Chunping Yan.

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Ni, H., Yan, C., Ge, W. et al. Integrated optimization of cutting parameters and hob parameters for energy-conscious gear hobbing. Int J Adv Manuf Technol 118, 1609–1626 (2022). https://doi.org/10.1007/s00170-021-07804-x

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