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Multi-objective parameter optimization to support energy-efficient peck deep-hole drilling processes with twist drills

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Abstract

Reducing energy consumption (EC) is an essential strategy for improving the sustainability of manufacturing industry. Machining processes have been widely applied in manufacturing industry, and current research has demonstrated that the machining parameter optimization is an effective energy-saving measure under the given processing conditions. Drilling is a typical machining process, and it is convenient to make deep holes through peck drilling with twist drills in practice. However, owing to the inefficiency of peck drilling with twist drills, many efforts have been devoted to improving the performance of peck deep-hole drilling process (PDDP). Correspondingly, the parameter optimization considering traditional performance indicators, such as processing time, tool wear, and drilling force, has been fully investigated. Nevertheless, the existing research rarely touches on the EC optimization or the improvement of EC-related environmental impacts. To bridge this gap, an approach based on the operating parameter optimization is proposed to fulfill the energy saving of PDDP, and the corresponding mathematical model considering EC and processing time simultaneously is established. To evaluate the EC of PDDP reliably, the Therblig-based energy supply models of machines are utilized. Further, a particle swarm optimization algorithm-based solution method is adopted, which can make a trade-off between two optimization objectives objectively and acquire the most suitable operating parameters. Moreover, experiments have been made to evaluate the energy-saving potential and the performance of the algorithm. Experimental results show that there could be significant potential for improving optimization objectives simultaneously through the operating parameter optimization, and the solution method is feasible.

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Abbreviations

A :

Coded variable corresponding to helix angle

Acc :

Acceleration of drill vibration velocity [m/s2]

Aj, Bj :

Constant coefficients related to the calculation of PSR when the spindle speed belongs to the jth speed interval

B :

Coded variable corresponding to the feed rate of Z-axis

C :

Coded variable corresponding to the rotation speed of the drill

C G :

Social acceleration coefficient

C L :

Cognitive acceleration coefficient

CM, zM, yM, kM :

Coefficients related to the calculation of drilling torque

CZ1, CZ2 :

Constant coefficients related to the calculation of PZF

d :

The distance between the initial point of cutting feed motion and the starting point of material removal in each peck drilling cycle after the first cycle [mm]

d 0 :

Drill diameter [mm]

f c :

Cutting feed rate of the drill/Z-axis [mm/r]

fmin, fmax :

Cutting feed rate bounds of the drill/Z-axis [mm/r]

f r :

Rapid feed rate of the drill/Z-axis [mm/min]

f z :

Feed rate of Z-axis [mm/min]

\( {G}_q^k \) :

Value of the position of global best particle on dimension q until the kth iteration

H :

The distance between the retract point and final point [mm]

h 1 :

The distance between the retract plane and the upper blank surface [mm]

h 2 :

Overcutting [mm]

HA :

Helix angle of the drill [degree]

h c :

Hole depth [mm]

H w :

Blank thickness [mm]

i :

Peck drilling cycle index

I max :

Maximum iteration number of PSO

j :

The index of spindle speed interval under the given power transmission route of spindle system

k :

PSO iteration index

L cf :

Total distance of cutting feed motion [mm]

L rd :

Total distance of rapid downward feed motion [mm]

L rf :

Total distance of rapid feed motion [mm]

L ru :

Total distance of rapid upward feed motion [mm]

L uc :

Total distance of cutting feed motion without material removal [mm]

\( {L}_{pq}^k \) :

Value of the individual best position of particle p on dimension q until the kth iteration

M :

The number of speed intervals when evaluating PSR under the given power transmission route of spindle system

M D :

Drilling torque [N ⋅ m]

M max :

Maximum output torque of spindle [N ⋅ m]

N :

The number of peck drilling cycles

N * :

The number of particles in the swarm

N D :

Dimensions of search space

n :

Rotation speed of the drill[r/min]

nmax, nmin :

Rotation speed bounds of the drill/spindle [r/min]

\( {n}_j^{\mathrm{L}} \) :

Lower bound of the jth spindle speed interval [r/min]

\( {n}_j^{\mathrm{U}} \) :

Upper bound of the jth spindle speed interval [r/min]

p :

Particle index

P C :

Therblig-cutting(C) power [W]

P CFS :

Therblig-cutting fluid spraying (CFS) power [W]

P R :

Rated power of spindle motor [kW]

P SO :

Therblig-standby operation (SO) power [W]

P SR :

Therblig-spindle rotation (SR) power [W]

P ZF :

Therblig-Z-axis Feeding (ZF) power [W]

\( {P}_{\mathrm{ZF}}^{\mathrm{U}} \) :

Therblig-ZF power when Z-axis moves upward [W]

\( {P}_{\mathrm{ZF}}^{\mathrm{D}} \) :

Therblig-ZF power when Z-axis moves downward [W]

Q :

Pecking depth [mm]

q :

Particle position dimension index

Qmin, Qmax :

Pecking depth bounds of the drill [mm]

Ra :

Surface roughness [μm]

T c :

Material removal time [s]

T cf :

Total time of cutting feed motion [s]

T nc :

Non-cutting time [s]

T total :

Total processing time of peck deep-hole drilling process [s]

VB :

Flank wear of the drill [mm]

V c :

Cutting speed [m/min]

V pq :

Velocity on the qth dimension of particle p

\( {V}_{pq}^k \) :

Velocity of dimension q for particle p in the kth iteration

Vqmin, Vqmax :

Velocity bounds on the qth dimension

X pq :

Value of the qth dimension of the position of particle p

\( {X}_{pq}^k \) :

Value of the position of particle p on dimension q in the kth iteration

η :

Machine efficiency

α, β, λ :

Constant coefficients depending on specific processing conditions for calculating PC

ε , ξ :

Separately generated random uniformly distributed numbers in [0, 1]

ω :

Inertia weight

ωmin, ωmax :

Inertial weight bounds

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Acknowledgments

The authors sincerely thank all the editors and anonymous reviewers for their beneficial suggestions on the improvement of this paper.

Funding

The authors would like to acknowledge the support provided by the National Natural Science Foundation of China (Grant No. U1704156), the Key Science and Technology Program of Henan Province (Grant No. 182102210391), the Foundation of the Education Department of Henan Province (Grant No. 18A460013), the Fundamental Research Funds for the Henan Provincial Colleges and Universities in Henan University of Technology (Grant No. 2016QNJH09), and the Foundation of Henan University of Technology (Grant No. 2017BS014).

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Authors and Affiliations

  1. School of Mechanical & Electrical Engineering, Henan University of Technology, Zhengzhou, 450001, China

    Zhongwei Zhang & Lihui Wu

  2. State Key Laboratory of Fluid Power and Mechatronic Systems, School of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China

    Zhongwei Zhang & Tao Peng

  3. Department of Industrial Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Shun Jia

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  1. Zhongwei Zhang
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Correspondence to Lihui Wu or Tao Peng.

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Zhang, Z., Wu, L., Jia, S. et al. Multi-objective parameter optimization to support energy-efficient peck deep-hole drilling processes with twist drills. Int J Adv Manuf Technol 106, 4913–4932 (2020). https://doi.org/10.1007/s00170-020-04967-x

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