An energy consumption prediction approach of die casting machines driven by product parameters
Erheng CHEN, Hongcheng LI, Huajun CAO, Xuanhao WEN
An energy consumption prediction approach of die casting machines driven by product parameters
Die casting machines, which are the core equipment of the machinery manufacturing industry, consume great amounts of energy. The energy consumption prediction of die casting machines can support energy consumption quota, process parameter energysaving optimization, energysaving design, and energy efficiency evaluation; thus, it is of great significance for Industry 4.0 and green manufacturing. Nevertheless, due to the uncertainty and complexity of the energy consumption in die casting machines, there is still a lack of an approach for energy consumption prediction that can provide support for process parameter optimization and product design taking energy efficiency into consideration. To fill this gap, this paper proposes an energy consumption prediction approach for die casting machines driven by product parameters. Firstly, the system boundary of energy consumption prediction is defined, and subsequently, based on the energy consumption characteristics analysis, a theoretical energy consumption model is established. Consequently, a systematic energy consumption prediction approach for die casting machines, involving product, die, equipment, and process parameters, is proposed. Finally, the feasibility and reliability of the proposed energy consumption prediction approach are verified with the help of three die casting machines and six types of products. The results show that the prediction accuracy of production time and energy consumption reached 91.64% and 85.55%, respectively. Overall, the proposed approach can be used for the energy consumption prediction of different die casting machines with different products.
die casting machine / energy consumption prediction / product parameters
[1] 
Fu M W, Yong M S. Simulationenabled casting product defect prediction in die casting process. International Journal of Production Research, 2009, 47( 18): 5203– 5216
CrossRef
Google scholar

[2] 
Accessed at The North American Die Casting Association (NADCA) website, 2012

[3] 
Brevick J R, MountCampbell A F, MountCampbell C A. Modeling alloy and energy utilization in high volume die casting. Clean Technologies and Environmental Policy, 2014, 16( 1): 201– 209
CrossRef
Google scholar

[4] 
Brevick J, MountCampbell C, Mobley C. Energy Consumption of Die Casting Operations. Scientific and Technical Information Technical Reports DEFC0700ID13843, 2004

[5] 
Schwam D. Energy Saving Melting and Revert Reduction Technology: Melting Efficiency in Die Casting Operations. Office of Scientific and Technical Information Technical Reports DEFC3604GO14230, 2012

[6] 
Liu W, Tang R, Peng T. An IoTenabled approach for energy monitoring and analysis of die casting machines. In: Proceedings of the 25th CIRP Life Cycle Engineering (LCE) Conference. Copenhagen: CIRP, 2018, 69

[7] 
Chen E, Cao H, He Q. An IoT based framework for energy monitoring and analysis of die casting workshop. In: Proceedings of the 26th CIRP Life Cycle Engineering (LCE) Conference. West Lafayette: CIRP, 2019, 80

[8] 
Watkins M F, Mani M, Lyons K W. Sustainability characterization for die casting process. In: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE). Portland: ASME, 2013, 2A

[9] 
Bettoni L, Zanoni S. Energy implications of production planning decisions. In: Frick J, Laugen B T, eds. Advances in Production Management Systems. Value Networks: Innovation, Technologies, and Management. APMS 2011. IFIP Advances in Information and Communication Technology. Berlin: Springer, 2012, 384

[10] 
He K, Tang R, Jin M. Energy modeling and efficiency analysis of aluminum diecasting processes. Energy Efficiency, 2019, 12( 5): 1167– 1182
CrossRef
Google scholar

[11] 
Gutowski T, Dahmus J, Thiriez A. Electrical energy requirements for manufacturing processes. In: Proceedings of the 13th CIRP Life Cycle Engineering (LCE) Conference. Leuven: CIRP, 2006,

[12] 
Li B J, Cao H J, Hon B. Exergybased energy efficiency evaluation model for machine tools considering thermal stability. International Journal of Precision Engineering and ManufacturingGreen Technology, 2021, 8( 2): 423– 434
CrossRef
Google scholar

[13] 
Imani Asrai R, Newman S T, Nassehi A. A mechanistic model of energy consumption in milling. International Journal of Production Research, 2018, 56(1‒2): 642– 659

[14] 
Ribeiro I, Peas P, Henriques E. Assessment of energy consumption in injection moulding process. In: Proceedings of the 19th CIRP Conference on Life Cycle Engineering. Berkeley: CIRP, 2012,

[15] 
Pawanr S, Garg G K, Routroy S. Development of a transient energy prediction model for machine tools. Procedia CIRP, 2021, 98
CrossRef
Google scholar

[16] 
Deng Z, Zhang H, Fu Y. Optimization of process parameters for minimum energy consumption based on cutting specific energy consumption. Journal of Cleaner Production, 2017, 166
CrossRef
Google scholar

[17] 
Sealy M P, Liu Z Y, Zhang D. Energy consumption and modeling in precision hard milling. Journal of Cleaner Production, 2016, 135
CrossRef
Google scholar

[18] 
Meekers I, Refalo P, Rochman A. Analysis of process parameters affecting energy consumption in plastic injection moulding. In: Proceedings of the 25th CIRP Life Cycle Engineering (LCE) Conference. Copenhagen: CIRP, 2018, 69

[19] 
Vishnu V S, Varghese K G, Gurumoorthy B. Energy prediction in process planning of fiveaxis machining by datadriven modelling. Procedia CIRP, 2020, 93
CrossRef
Google scholar

[20] 
Pawar S S, Bera T C, Sangwan K S. Modelling of energy consumption for milling of circular geometry. Procedia CIRP, 2021, 98( 22): 470– 475
CrossRef
Google scholar

[21] 
He Y, Wu P, Li Y. A generic energy prediction model of machine tools using deep learning algorithms. Applied Energy, 2020, 275
CrossRef
Google scholar

[22] 
Pan J, Li C B, Tang Y. Energy consumption prediction of a CNC machining process with incomplete data. IEEE/CAA Journal of Automatica Sinica, 2021, 8( 5): 987– 1000
CrossRef
Google scholar

[23] 
Liu Z, Guo Y. A hybrid approach to integrate machine learning and process mechanics for the prediction of specific cutting energy. CIRP AnnalsManufacturing Technology, 2018, 67( 1): 57– 60
CrossRef
Google scholar

[24] 
Peng T, Xu X, Wang L. A novel energy demand modelling approach for CNC machining based on function blocks. Journal of Manufacturing Systems, 2014, 33( 1): 196– 208
CrossRef
Google scholar

[25] 
Kolar M, Vyroubal J, Smolik J. Analytical approach to establishment of predictive models of power consumption of machine tools’ auxiliary units. Journal of Cleaner Production, 2016, 137
CrossRef
Google scholar

[26] 
Li W, Kara S. An empirical model for predicting energy consumption of manufacturing processes: a case of turning process. Proceedings of the Institution of Mechanical Engineers. Part B, Journal of Engineering Manufacture, 2011, 225( 9): 1636– 1646
CrossRef
Google scholar

[27] 
Madan J, Mani M, Lee J H. Energy performance evaluation and improvement of unitmanufacturing processes: injection molding case study. Journal of Cleaner Production, 2015, 105
CrossRef
Google scholar

[28] 
Andresen B. Die Casting Engineering: A Hydraulic, Thermal, and Mechanical Process. Boca Raton: CRC Press, 2004

[29] 
Boothroyd G. Product design for manufacture and assembly. ComputerAided Design, 1994, 26( 7): 505– 520
CrossRef
Google scholar

[30] 
Ostwald P F. American Machinist Cost Estimator. New York: McgrawHill, 1986

[31] 
Blum C. Early cost estimation of die cast components. Thesis for the Master’s Degree. Kingston: University of Rhode Island, 1989

[32] 
Pokorny H H, Thukkaram P. Gating Die Casting Dies. River Grove: Society of Die Casting Engineers, 1981

[33] 
Herman E A. Die Casting Dies: Designing. River Grove: Society of Die Casting Engineers, 1985

[34] 
Johannaber F. Injection Molding Machines. 4th ed. Munich: Hanser Publications, 2007

[35] 
Ke J, Price L, McNeil M. Analysis and practices of energy benchmarking for industry from the perspective of systems engineering. Energy, 2013, 54
CrossRef
Google scholar

[36] 
Yang F, Liu Y, Liu G. A process simulation based benchmarking approach for evaluating energy consumption of a chemical process system. Journal of Cleaner Production, 2016, 112
CrossRef
Google scholar

[37] 
Zhan S, Liu Z, Chong A. Building categorization revisited: a clusteringbased approach to using smart meter data for building energy benchmarking. Applied Energy, 2020, 269
CrossRef
Google scholar

[38] 
Veloso A, Souza R, Santos F. Energy benchmarking for office building towers in mild temperate climate. Energy and Buildings, 2020, 222
CrossRef
Google scholar

[39] 
Cai W, Li L, Jia S. Taskoriented energy benchmark of machining systems for energyefficient production. International Journal Precision Engineering ManufacturingGreen Technology, 2020, 7( 1): 205– 218
CrossRef
Google scholar

[40] 
Chen D, Cao L, Si H. Benchmark value determination of energy efficiency indexes for coalfired power units based on data mining methods. Advanced Engineering Informatics, 2020, 43
CrossRef
Google scholar

[41] 
Spiering T, Kohlitz S, Sundmaeker H. Energy efficiency benchmarking for injection moulding processes. Robotics and ComputerIntegrated Manufacturing, 2015, 36( C): 45– 59
CrossRef
Google scholar

[42] 
Bunse K, Vodicka M, Schönsleben P. Integrating energy efficiency performance in production management–gap analysis between industrial needs and scientific literature. Journal of Cleaner Production, 2011, 19(6‒7): 667– 679

Abbreviations  
CNC  Computer numerical control 
DC  Die closing 
DCO  Die closing and opening 
DO  Dosing 
DP  Die opening 
ECPA  Energy consumption prediction accuracy 
EO  Ejector out 
EX  Extracting 
IoT  Internet of Things 
PB  Plunger backward 
PF  Plunger forward 
PFB  Plunger forward and backward 
SO  Solidification 
SP  Spraying 
Variables  
A_{ap}  Shot piston area 
A_{ar}  Shot piston area minus the rod area 
A_{DC}  Crosssectional area of the hydraulic cylinder 
A_{EO}  Crosssectional area of the piston 
A_{pa}  Cavity projected area 
A_{PB}  Area of plunger tip 
A_{PF}  Area of the plunger tip 
A_{pt}  Area of the plunger tip 
A_{sa}  Cavity surface area 
A_{SO}  Area of the gate 
d_{DC}  Diameter of the hydraulic cylinder 
d_{eo}  Displacement of EO 
d_{EO}  Diameter of the piston 
d_{PB}  Diameter of plunger tip 
d_{PF}  Diameter of the plunger tip 
d_{PFB}  Displacement of PFB 
d_{SP}  Diameter of hydraulic cylinder for a certain subprocess 
E_{basic}  Basic energy consumption 
E_{DC}  Energy consumption of DC 
E_{DO}  Energy consumption of DO 
E_{DP}  Energy consumption of DP 
E_{EO}  Energy consumption of EO 
E_{EX}  Energy consumption of EX 
E_{ideal}  Sum of the ideal energy consumption 
${E}_{\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}}^{i}$  Ideal energy consumption of the ith subprocess 
E_{PB}  Energy consumption of PB 
E_{PF}  Energy consumption of PF 
E_{predict}  Predicted energy consumption per part 
E_{SO}  Energy consumption of SO 
E_{SP}  Energy consumption of SP 
E_{theoretical}  Theoretical energy consumption 
F_{PBA}  Average force of PB 
h  Average wall thickness of product 
h_{max}  Maximum wall thickness 
K  Magnification times of toggle clamps 
L  Product length 
L_{DC}  Displacement of DC 
L_{EO}  Displacement of EO 
L_{PB}  Displacement of PB 
L_{PF}  Displacement of PF 
L_{SO}  Theoretical length of the metal liquid 
L_{SP}  Displacement during a certain subprocess 
n_{c}  Number of die cavities 
n_{l}  Number of machine cycles per lubrication 
n_{s}  Total number of sidepulls 
P  Injection pressure of PF or SO 
P_{ap}  Accumulator pressure 
P_{basic}  Basic power of die casting machine 
P_{DC}  Instantaneous hydraulic pressure of DC 
P_{DCA}  Average hydraulic pressure during DC 
P_{EO}  Instantaneous hydraulic pressure of EO 
P_{EOA}  Average hydraulic pressure of EO 
P_{ep}  Exhaust pressure 
P_{PB}  Instantaneous hydraulic pressure of PB 
P_{PBA}  Average hydraulic pressure of PB 
P_{PDCA}  Preset hydraulic pressures of DC 
P_{PDP}  Preset hydraulic pressures of DP 
P_{PEO}  Preset hydraulic pressures of EO 
P_{PF}  Instantaneous hydraulic pressure of PF 
P_{PFA}  Average hydraulic pressure of PF 
P_{PPBA}  Preset hydraulic pressures of PB 
P_{PPFA}  Preset hydraulic pressures of PF 
P_{PSOA}  Preset hydraulic pressures of SO 
P_{SO}  Instantaneous hydraulic pressure of SO 
P_{SOA}  Average hydraulic pressure of SO 
P_{SP}  Instantaneous hydraulic pressure 
t_{cycle}  Production cycle 
t_{DC}  Duration of DC 
t_{DCO}  Duration of DCO 
t_{DCT}  Machine dry cycle time 
t_{DO}  Duration of DO 
t_{DP}  Duration of DP 
t_{EO}  Duration of EO 
t_{EX}  Duration of EX 
t_{PB}  Duration PB 
t_{PF}  Duration of PF 
t_{SO}  Duration of SO 
t_{SP}  Duration for a certain subprocess 
t_{SPR}  Duration of SP 
T_{i}  Recommended melt injection temperature 
T_{l}  Die casting alloy liquid temperature 
T_{m}  Die temperature before the shot 
v_{eo}  Average velocity of EO 
v_{PFB}  Average velocity of PFB 
V_{cavities}  Volume of cavities 
V_{feed}  Volume of feed system 
V_{inject}  Shot volume 
V_{overflow}  Volume of overflow wells 
V_{SO}  Volume of the metal liquid 
W  Product width 
W_{SP}  Power value of a certain subprocess 
${y}_{\mathrm{a}\mathrm{c}\mathrm{t}}^{i}$  Actual time or energy consumption 
${y}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{i}$  Predicted time or energy consumption 
β  Cooling factor 
${\eta}_{\mathrm{D}\mathrm{C}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of DC 
${\eta}_{\mathrm{D}\mathrm{C}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of DC 
η_{DCA}  Hydraulic system average efficiency of DC 
${\eta}_{\mathrm{D}\mathrm{P}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of DP 
${\eta}_{\mathrm{D}\mathrm{P}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of DP 
η_{DPA}  Hydraulic system average efficiency of DP 
${\eta}_{\mathrm{E}\mathrm{O}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of EO 
${\eta}_{\mathrm{E}\mathrm{O}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of EO 
η_{EOA}  Hydraulic system average efficiency of EO 
η_{machine}  Efficiency of die casting machines 
${\eta}_{\mathrm{P}\mathrm{B}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of PB 
${\eta}_{\mathrm{P}\mathrm{B}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of PB 
η_{PBA}  Hydraulic system average efficiency of PB 
${\eta}_{\mathrm{P}\mathrm{F}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of PF 
${\eta}_{\mathrm{P}\mathrm{F}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of PF 
η_{PFA}  Hydraulic system average efficiency of PF 
${\eta}_{\mathrm{S}\mathrm{O}}^{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$  Pump efficiency of SO 
${\eta}_{\mathrm{S}\mathrm{O}}^{\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}}$  Servo efficiency of SO 
η_{SOA}  Hydraulic system average efficiency of SO 
η_{SP}  Average efficiency of hydraulic system 
/
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