Energy saving design of the machining unit of hobbing machine tool with integrated optimization

Abstract

The machining unit of hobbing machine tool accounts for a large portion of the energy consumption during the operating phase. The optimization design is a practical means of energy saving and can reduce energy consumption essentially. However, this issue has rarely been discussed in depth in previous research. A comprehensive function of energy consumption of the machining unit is built to address this problem. Surrogate models are established by using effective fitting methods. An integrated optimization model for reducing tool displacement and energy consumption is developed on the basis of the energy consumption function and surrogate models, and the parameters of the motor and structure are considered simultaneously. Results show that the energy consumption and tool displacement of the machining unit are reduced, indicating that energy saving is achieved and the machining accuracy is guaranteed. The influence of optimization variables on the objectives is analyzed to inform the design.

Key words： energy saving design; energy consumption; machining unit; integrated optimization; machine tool

Nomenclature

a	Distance between the two sliders
ap	Cut depth
A	Surface area of the motor core
B	Equivalent viscous friction damping coefficient
Bsm	Servo motor damping coefficient
c1, c2	Learning factors
dh	Hob outer diameter
Dim	Particle dimension
E	Energy consumption of the machining unit
Ek	Kinetic energy of mechanical transmission components
fBA	Basic frequency of the inverter
fc	Coulomb friction force
fi	ith order natural frequency of the machine tool after optimization
[fi]	ith order natural frequency before optimization
fv	Viscous friction force
fz	Axial feed of the hob
Fc	Cutting force
Fcz	Cutting force on the slide plate
Ff	Friction force between the sliding plate and the vertical guide rail
FN	Normal force on the guide rail
Ft	Slide plate load force
g	Gravitational acceleration
h	Heat dissipation coefficient
Jl, Js, Jsm	Moments of inertia of the coupling, ball screw, and servo motor, respectively
Js*	Moment of inertia equivalent to the motor shaft of the transmission system
K1, K2, K3	Coefficients associated with the materials, hardness, and helical angle of the gear, respectively
l1	Distance between the barycenters of the slide plate and the axis of the ball screw
l2	Distance between the barycenters of the tool post and the axis of the ball screw
l3	Distance between the barycenters of the main gearbox and the axis of the ball screw
l4	Distance between the barycenters of the additional component and the axis of the ball screw
l5	Distance between the barycenters of the hob and the axis of the ball screw
Lb	Ball screw lead
m	Normal modulus of the hob
M, Ma, Mc, Mh, Mk, Mt	Masses of the machining unit, additional components, main gearbox, slide plate, tool post shell, and tool post support plate, respectively
M0	Equivalent nonload Coulomb friction moment
Mit	Maximum iteration number
n*	Initial speed before the motor is accelerated
ngm	Hob speed
nN	Rated speed of the motor
nN1, nN2	Rated speeds of the main and servo motors, respectively
nsm	Servo motor speed
Ni	Motor speed under working condition i
Nip	Initial population number
Ns	Number of samples
p	Number of pole pairs of the motor
P	Power of the machining unit
Pad-i	Additional loss power under working condition i
Pc	Cutting power
PCu	Peak copper loss power
PCu-i	Copper loss power under working condition i
Pe	Peak eddy current loss power
Pe-i	Eddy current loss power under working condition i
Ph	Peak hysteresis loss power
Ph-i	Hysteresis loss power under working condition i
Ploss	Peak loss power of the motor
Ploss-i	Motor loss power under working condition i
Pm-i	Mechanical loss power under working condition i
Pmax	Peak power of the motor
Pmax1, Pmax2	Peak powers of the main and servo motors, respectively
Pmec	Mechanical loss power
Pmo	Main motor output power
Pn-i	Motor input power under working condition i
PN	Rated power
PN1	Rated power of the main motor
PN2	Rated power of the servo motor
Psm	Servo motor output power
Po-i	Motor output power under working condition i.
PSA	Motor acceleration power
PSR	Motor shaft rotation power
sgn(·)	Symbolic function
t	Operation time of the machine tool.
t*	Duration of the rotation acceleration
tA	Acceleration time of the inverter
tr	Limit value of temperature rise
Tb	Frictional moment generated by the bearing preload
Ti	Motor output torque under working condition i
Tl	Coupling output torque
Tsm	Servo motor output torque
Tt	Output torque of the ball screw
Tz	Input torque of the ball screw
Τ	Output threshold vector
vc	Cutting speed
Vz	Axial feed speed of the moving components along the Z axis
x	Sample data set
xi, xj	Sample points
x1, x2, x3, x4, x5	Structure parameters of the tool post support plate
\hat{y}	Fitting expression of y
Z	Tooth number of the workpiece
α	Load factor of the mechanical transmission system
α*	Motor angular acceleration
γi	ith observed value
{\gamma }_i^{\ast }	ith predicted value
{\overline{\gamma }}_i	Mean value of the ith observed value
δ	Tool displacement
ϛ(·)	Global prediction polynomial
Θ(·)	Random error
κ(·)	Radial basis function
ηb	Bearing transmission efficiency
ηm, ηsm	Motor efficiencies of the main and servo motors, respectively
ηz	Ball screw transmission efficiency
η(i)	Motor efficiency under working condition i
μc	Coulomb friction coefficient
μv	Viscous friction coefficient
χ	Center of κ(·)
\omega*	Angular velocity of the motor
{\omega }_{\mathrm{e}\mathrm{n}\mathrm{d}}, {\omega }_{\mathrm{i}\mathrm{n}\mathrm{i}}	Final and initial values of the inertia weight, respectively
{\omega }_{\mathrm{m}}	Angular velocity of the spindle motor shaft
{\omega }_{\mathrm{s}\mathrm{m}}	Servo motor output angular velocity
ξ0, ξi, ξij	Undetermined coefficients of the RSM model
ℓ(·)	Linear polynomial function
ћ2	Variance of Θ(·)
Ξ(·)	Correlation function
ϑk	Related parameter determined by the maximum likelihood estimation
ϖi	Adaptability weight coefficient
ϖ50×1	Synaptic weight matrix
||·||	Euclidean norm

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 51975075 and 52105506) and the Chongqing Technology Innovation and Application Program, China (Grant No. cstc2020jscx-msxmX0221).

References

1 Triebe M J , Zhao F , Sutherland J W . Genetic optimization for the design of a machine tool slide table for reduced energy consumption. Journal of Manufacturing Science and Engineering, 2021, 143(10): 101003

2 Zhong Q Q , Tang R Z , Peng T . Decision rules for energy consumption minimization during material removal process in turning. Journal of Cleaner Production, 2017, 140(3): 1819–1827

3 Papetti A , Menghi R , Di Domizio G , Germani M , Marconi M . Resources value mapping: a method to assess the resource efficiency of manufacturing systems. Applied Energy, 2019, 249: 326–342

4 Zhao J H , Li L , Wang Y , Sutherland J W . Impact of surface machining complexity on energy consumption and efficiency in CNC milling. The International Journal of Advanced Manufacturing Technology, 2019, 102(9): 2891–2905

5 Apostolos F , Alexios P , Georgios P , Panagiotis S , George C . Energy efficiency of manufacturing processes: a critical review. Procedia CIRP, 2013, 628–633

6 Kara S , Li W . Unit process energy consumption models for material removal processes. CIRP Annals, 2011, 60(1): 37–40

7 Xiao Y M , Jiang Z G , Gu Q , Yan W , Wang R P . A novel approach to CNC machining center processing parameters optimization considering energy-saving and low-cost. Journal of Manufacturing Systems, 2021, 59: 535–548

8 Zhang T , Liu Z Q , Shi Z Y , Xu C H . Investigation on size effect of specific cutting energy in mechanical micro-cutting. The International Journal of Advanced Manufacturing Technology, 2017, 91(5): 2621–2633

9 Xiao Q G , Li C B , Tang Y , Pan J , Yu J , Chen X Z . Multi-component energy modeling and optimization for sustainable dry gear hobbing. Energy, 2019, 187: 115911

10 Li C B , Xiao Q G , Tang Y , Li L . A method integrating Taguchi, RSM and MOPSO to CNC machining parameters optimization for energy saving. Journal of Cleaner Production, 2016, 135: 263–275

11 Vu N C, Dang X P, Huang S C. Multi-objective optimization of hard milling process of AISI H13 in terms of productivity, quality, and cutting energy under nanofluid minimum quantity lubrication condition. Measurement and Control, 2021, 54(5–6): 820–834

12 Nguyen T T , Nguyen T A , Trinh Q H . Optimization of milling parameters for energy savings and surface quality. Arabian Journal for Science and Engineering, 2020, 45(11): 9111–9125

13 Arriaza O V , Kim D W , Lee D Y , Suhaimi M A . Trade-off analysis between machining time and energy consumption in impeller NC machining. Robotics and Computer-Integrated Manufacturing, 2017, 43: 164–170

14 Sihag N , Sangwan K S . A systematic literature review on machine tool energy consumption. Journal of Cleaner Production, 2020, 275: 123125

15 Li B , Tian X T , Zhang M . Modeling and multi-objective optimization method of machine tool energy consumption considering tool wear. International Journal of Precision Engineering and Manufacturing-Green Technology, 2022, 9(1): 127–141

16 Zhang X W , Yu T B , Dai Y X , Qu S , Zhao J . Energy consumption considering tool wear and optimization of cutting parameters in micro milling process. International Journal of Mechanical Sciences, 2020, 178: 105628

17 He K Y , Tang R Z , Jin M Z . Pareto fronts of machining parameters for trade-off among energy consumption, cutting force and processing time. International Journal of Production Economics, 2017, 185: 113–127

18 Kumar R , Bilga P S , Singh S . Multi objective optimization using different methods of assigning weights to energy consumption responses, surface roughness and material removal rate during rough turning operation. Journal of Cleaner Production, 2017, 164: 45–57

19 Yoon H S , Kim E S , Kim M S , Lee J Y , Lee G B , Ahn S H . Towards greener machine tools—a review on energy saving strategies and technologies. Renewable and Sustainable Energy Reviews, 2015, 48: 870–891

20 Triebe M J , Zhao F , Sutherland J W . Achieving energy efficient machine tools by mass reduction through multi-objective optimization. Procedia CIRP, 2019, 80: 73–78

21 Ji Q Q , Li C B , Zhu D G , Jin Y , Lv Y , He J X . Structural design optimization of moving component in CNC machine tool for energy saving. Journal of Cleaner Production, 2020, 246: 118976

22 Lv J X , Tang R Z , Tang W C J , Liu Y , Zhang Y F , Jia S . An investigation into reducing the spindle acceleration energy consumption of machine tools. Journal of Cleaner Production, 2017, 143: 794–803

23 Wójcicki J , Bianchi G . Electric load management in spindle run-up and run-down for multi-spindle machine tools via optimal power-torque trajectories and peak load synchronization. The International Journal of Advanced Manufacturing Technology, 2018, 95(5): 1819–1835

24 Denkena B , Abele E , Brecher C , Dittrich M A , Kara S , Mori M . Energy efficient machine tools. CIRP Annals, 2020, 69(2): 646–667

25 Liu S , Liu F , Hu S H , Yin Z B . Energy survey of machine tools: separating power information of the main transmission system during machining process. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2012, 6(4): 445–455

26 Liu X , Zhao F , Mei X S . A fuzzy adaptive controller for constant cutting torque in high-performance gear hobbing process. In: Proceedings of 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM). Munich: IEEE, 2017, 1725–1730

27 Hall E , Ramamurthy S S , Balda J C . Optimum speed ratio of induction motor drives for electrical vehicle propulsion. In: Proceedings of APEC 2001 the 16th Annual IEEE Applied Power Electronics Conference and Exposition (Cat. NO.01CH37181). Anaheim: IEEE, 2001, 371–377

28 Afzal A , Kim K Y , Seo J W . Effects of Latin hypercube sampling on surrogate modeling and optimization. International Journal of Fluid Machinery and Systems, 2017, 10(3): 240–253

29 Li C B , Li Y S , Gao L , Garg A , Li W . Surrogate model-based heat dissipation optimization of air-cooling battery packs involving herringbone fins. International Journal of Energy Research, 2021, 45(6): 8508–8523

30 Amouzgar K , Strömberg N . Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias. Structural and Multidisciplinary Optimization, 2017, 55(4): 1453–1469

31 Kleijnen J P C . Regression and Kriging metamodels with their experimental designs in simulation: a review. European Journal of Operational Research, 2017, 256(1): 1–16

32 Ni H X , Yan C P , Ni S F , Shu H , Zhang Y . Multi-verse optimizer based parameters decision with considering tool life in dry hobbing process. Advances in Manufacturing, 2021, 9(2): 216–234

33 Paul D , Jain A , Saha S , Mathew J . Multi-objective PSO based online feature selection for multi-label classification. Knowledge-Based Systems, 2021, 222: 106966

34 Oliveira B , Ballio F , Maia R . Numerical modelling-based sensitivity analysis of fluvial morphodynamics. Environmental Modelling & Software, 2021, 135: 104903

35 Xu C , Zhu P , Liu Z , Tao W . Mapping-based hierarchical sensitivity analysis for multilevel systems with multidimensional correlations. Journal of Mechanical Design, 2021, 143(1): 011707