Energy consumption model for milling processes considering auxiliary load loss and its applications

  • Qi Wang
  • Dinghua Zhang
  • Kai TangEmail author
  • Ying Zhang


With the modern manufacturing industry evolving and advancing and amid a more energy conscious society, high energy demand in manufacturing—particularly in machining—has drawn more and more attention. Accurate energy consumption modelling is critical to the improvement of energy efficiency in machining. In the existing energy models of machining processes, typically the so-called auxiliary load loss (which is whatever the difference between the total energy consumption and the amount of energy consumed due to the physical cutting of material and the idle running of the machine tool) is not considered. However, the auxiliary load loss could account for as much as 15–20% of the total energy consumption; simply ignoring it or making crude assumption on it would obviously lead to a less accurate energy consumption model. In this paper, a new energy consumption model for milling that takes full account of the auxiliary load loss is proposed. The proposed energy consumption model is crucially based on an empirical validation work that correctly characterizes the auxiliary power loss as a quadratic function of the cutting power. Cutting experiments are then carried out that convincingly confirm the correctness of the proposed energy consumption model. Moreover, as an application of the proposed energy consumption model, we perform two deep slot cutting experiments and show how our new energy model can help find the best process parameter—the number of intermediate layers to cut—that will consume the minimum amount of energy, which is as much as more than 52% less than that without considering the auxiliary load loss. It is expected that the proposed energy consumption model will have its application in minimization of energy consumption to a wider range of machining tasks, not limited to only the simplest deep slot cutting operation.


Energy consumption modelling Energy efficiency Auxiliary load losses Cutting power Energy saving 


Funding information

This study is co-supported by the Major National Science and Technology Projects (No. 2017ZX04011430), the Shanxi Provincial Key Research and Development Program (No. 2018ZDXM-GY-063).


  1. 1.
    Liu N, Zhang YF, Lu WF (2019) Improving energy efficiency in discrete parts manufacturing system using an ultra-flexible job shop scheduling algorithm. Int J Precis Eng Manuf Green Technol 6(2):349–365. CrossRefGoogle Scholar
  2. 2.
    Cai W, Liu F, Zhou XN, Xie X (2016) Fine energy consumption allowance of workpieces in the mechanical manufacturing industry. Energy 114:623–633. CrossRefGoogle Scholar
  3. 3.
    Li L, Li C, Tang Y, Yi Q (2017) Influence factors and operational strategies for energy efficiency improvement of CNC machining[J]. J Clean Prod 161:220–238. CrossRefGoogle Scholar
  4. 4.
    Hu S, Liu F, He Y, Hu T (2012) An on-line approach for energy efficiency monitoring of machine tools. J Clean Prod 27:133–140. CrossRefGoogle Scholar
  5. 5.
    Gutowski TG, Branham MS, Dahmus JB, Jones AJ, Thiriez A, Sekulic DP (2009) Thermodynamic analysis of resources used in manufacturing processes. Environ Sci Technol 43(5):1584–1590. CrossRefGoogle Scholar
  6. 6.
    Kara S, Li W (2011) Unit process energy consumption models for material removal processes. CIRP Ann 60(1):37–40. CrossRefGoogle Scholar
  7. 7.
    Li L, Yan J, Xing Z. Energy requirements evaluation of milling machines based on thermal equilibrium and empirical modelling[J]. Journal of Cleaner Production, 2013, 52: 113-121. CrossRefGoogle Scholar
  8. 8.
    Costa DMD, Brito TG, de Paiva AP, Leme RC, Balestrassi PP (2016) A normal boundary intersection with multivariate mean square error approach for dry end milling process optimization of the AISI 1045 steel. J Clean Prod 135:1658–1672. CrossRefGoogle Scholar
  9. 9.
    Camposeco-Negrete C, Nájera JDC, Miranda-Valenzuela JC (2016) Optimization of cutting parameters to minimize energy consumption during turning of AISI 1018 steel at constant material removal rate using robust design. Int J Adv Manuf Technol 83(5-8):1341–1347. CrossRefGoogle Scholar
  10. 10.
    Warsi SS, Jaffery SHI, Ahmad R, Khan M, Agha MH, Ali L (2018) Development and analysis of energy consumption map for high-speed machining of Al 6061-T6 alloy. Int J Adv Manuf Technol 96(1-4):91–102. CrossRefGoogle Scholar
  11. 11.
    Yoon HS, Lee JY, Kim MS, Ahn SH (2014) Empirical power-consumption model for material removal in three-axis milling. J Clean Prod 78:54–62. CrossRefGoogle Scholar
  12. 12.
    Zhong Q, Tang R, Peng T (2017) Decision rules for energy consumption minimization during material removal process in turning. J Clean Prod 140:1819–1827. CrossRefGoogle Scholar
  13. 13.
    Shi KN, Zhang DH, Liu N, Wang SB, Ren JX, Wang SL (2018) A novel energy consumption model for milling process considering tool wear progression. J Clean Prod 184:152–159. CrossRefGoogle Scholar
  14. 14.
    Wang Q, Zhang DH, Tang K, Zhang Y (2019) A mechanics based prediction model for tool wear and power consumption in drilling operations and its applications. J Clean Prod. CrossRefGoogle Scholar
  15. 15.
    Shi KN, Liu N, Wang SB, Ren JX, Yuan Y (2019) Experimental and theoretical investigation of milling tool selection towards energy-efficient process planning in discrete parts manufacturing. Int J Adv Manuf Technol 104:1–9. CrossRefGoogle Scholar
  16. 16.
    Diaz N, Choi S, Helu M, Chen Y, Jayanathan S, Yasui Y, Kong D, Pavanaskar S, Dornfeld D (2010) Machine tool design and operation strategies for green manufacturing.
  17. 17.
    Guo Y, Loenders J, Duflou J, Lauwers B (2012) Optimization of energy consumption and surface quality in finish turning. Procedia CIRP 1:512–517. CrossRefGoogle Scholar
  18. 18.
    Wang Z (2017) Optimization calculation of reverse energy consumption based on feature parameter of NC code. Int J Adv Manuf Technol 93(9-12):3437–3448. CrossRefGoogle Scholar
  19. 19.
    Chen X, Li C, Jin Y, Li L (2018) Optimization of cutting parameters with a sustainable consideration of electrical energy and embodied energy of materials. Int J Adv Manuf Technol 96(1-4):775–788. CrossRefGoogle Scholar
  20. 20.
    Draganescu F, Gheorghe M, Doicin CV (2003) Models of machine tool efficiency and specific consumed energy. J Mater Process Technol 141(1):9–15. CrossRefGoogle Scholar
  21. 21.
    Rodrigues AR, Coelho RT (2007) Influence of the tool edge geometry on specific cutting energy at high-speed cutting. J Braz Soc Mech Sci Eng 29(3):279–283. CrossRefGoogle Scholar
  22. 22.
    Wang YC, Kim DW, Katayama H, Hsueh WC (2018) Optimization of machining economics and energy consumption in face milling operations. Int J Adv Manuf Technol 99(9-12):2093–2100. CrossRefGoogle Scholar
  23. 23.
    Li W, Kara S (2011) An empirical model for predicting energy consumption of manufacturing processes: a case of turning process. Proc Inst Mech Eng B J Eng Manuf 225(9):1636–1646. CrossRefGoogle Scholar
  24. 24.
    Liu N, Zhang YF, Lu WF (2015) A hybrid approach to energy consumption modelling based on cutting power: a milling case. J Clean Prod 104:264–272. CrossRefGoogle Scholar
  25. 25.
    Shi KN, Ren JX, Wang SB, Liu N, Liu ZM, Zhang DH, Lu WF (2019) An improved cutting power-based model for evaluating total energy consumption in general end milling process. J Clean Prod 231:1330–1341. CrossRefGoogle Scholar
  26. 26.
    Shi J, Liu F, Xu D, Xie D (2010) Power balance equation about the numerical control machine tool’s main driver system driven by variable voltage variable frequency. J Mech Eng 46(3):118–124. CrossRefGoogle Scholar
  27. 27.
    Hu S, Liu F, He Y, Peng B (2010) Characteristics of additional load losses of spindle system of machine tools. J Adv Mech Des Syst Manuf 4(7):1221–1233. CrossRefGoogle Scholar
  28. 28.
    Ma F, Zhang H, Cao H, Hon K K B. An energy consumption optimization strategy for CNC milling[J]. The International Journal of Advanced Manufacturing Technology, 2017, 90(5-8): 1715-1726. CrossRefGoogle Scholar
  29. 29.
    Lee P, Altintaş Y. Prediction of ball-end milling forces from orthogonal cutting data[J]. International Journal of Machine Tools and Manufacture, 1996, 36(9): 1059-1072. CrossRefGoogle Scholar
  30. 30.
    Budak E, Altintas Y, Armarego E J A. Prediction of milling force coefficients from orthogonal cutting data[J]. Journal of Manufacturing Science and Engineering, 1996, 118(2): 216-224. CrossRefGoogle Scholar
  31. 31.
    Liu N, Wang S B, Zhang Y F, Lu W F. A novel approach to predicting surface roughness based on specific cutting energy consumption when slot milling Al-7075[J]. International Journal of Mechanical Sciences, 2016, 118: 13-20. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.The Key Laboratory of High Performance Manufacturing for Aero Engine (Northwestern Polytechnical University)Ministry of Industry and Information TechnologyXi’anChina
  2. 2.The Hong Kong University of Science and TechnologyClear Water BayHong Kong

Personalised recommendations