Abstract
Energy modeling and efficiency analysis are considered the foundation of manufacturing process optimization to improve quality and efficiency and reduce energy consumption and carbon emissions during aluminum die-casting processes. This paper proposed an energy modeling method to connect gas and electric energy consumption with production rate of aluminum die-casting processes based on data collected at workshops with various combination of machines and products. The detailed modeling process involved the development of a data-acquiring system and the comparison of various kinds of nonlinear regression methods. The resulting models were validated with actual production data and were further used to improve production scheduling. It was found that if the modeling results are reasonably used and production is accordingly well-scheduled, 10 to 15% of energy savings could be realized without sacrificing profits.
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Abbreviations
- A P, B P, C P, D P :
-
Coefficients of polynomial cubic
- adjR 2 :
-
Adjusted coefficient of determination
- a E, b E, c E :
-
Coefficients of exponential functions
- a L, b L, c L :
-
Coefficients of logarithmic functions
- a R, b R :
-
Coefficients of reciprocal functions
- a P, b P :
-
Coefficients of power functions
- D :
-
Demanding amount of products of orders
- E c :
-
Calculation result of energy consumption of the overall processes for using electric energy [KW∙h]
- E real,:
-
The energy consumptions of the overall processes in real practice for using electric energy [KW∙h]
- F :
-
Coefficient of F test
- F(θ):
-
The function to get the aggregation of least relative error
- f SEC-P :
-
The alternative mathematical form to be used during the modeling process
- G c :
-
Calculation result of energy consumption of the overall processes for using gas [m3]
- G real :
-
The energy consumptions of the overall processes in real practice for using gas [m3]
- N :
-
The sample group number of observed SEC and P used for the modeling
- n :
-
The number of unknown coefficients of the regression model
- P :
-
Production rate
- P elec :
-
Production rate of die-casting machine producing finished products [piece/h]
- P gas :
-
Production rate of furnaces using gas [kg/h]
- R 2 :
-
Coefficient of determination
- R gas, R elec :
-
Relative energy efficiency evaluation indexes
- SEC :
-
Specific energy consumption. The amount of energy required for processing a certain amount of one kind of product
- SEC elec :
-
SEC of producing finished products from the machine using electric energy [KW∙h/piece]
- SEC gas :
-
SEC of melting raw materials using gas in furnace [m3/kg]
- SSE :
-
Sum of residual squares
- SST :
-
Sum of the total square
- s :
-
Residual standard deviation
- T :
-
Delivery time
- Tc :
-
Cycle of time of process
- T ca,G ca, E ca :
-
The real-time, gas consumption, and electric energy consumption of meeting the demand D operating casually
- T h ,G h ,E h :
-
The real-time, gas consumption, and electric energy consumption of meeting the demand D using high energy efficiency strategy
- t idle :
-
Stand-by idling time
- t p :
-
Production time
- x i :
-
One of the observed values of production rate P
- y i :
-
One of the observed values of SEC
- \( \widehat{y_i} \) :
-
One of the values of the model output
- δ elec, δ gas :
-
Relative error indexes to measure the accuracy of the prediction results
- θ :
-
The unknown coefficient vector of the regression model
- θ 1, θ 2, …, θ n :
-
The unknown coefficients of the regression model
- \( \widehat{\theta} \) :
-
Optimum solution vector of the unknown coefficients
- \( \widehat{\theta_1},\widehat{\theta_2},\dots, \widehat{\theta_n} \) :
-
Optimum solution group of the unknown coefficients
- ε :
-
The relative error between the calculation result by regression model and real value
- A P, B P, C P, D P :
-
Coefficients of polynomial cubic
- a E, b E, c E :
-
Coefficients of exponential functions
- a L, b L, c L :
-
Coefficients of logarithmic functions
- a R, b R :
-
Coefficients of reciprocal functions
- a P, b P :
-
Coefficients of power functions
- D :
-
Demanding amount of products of orders
- E c :
-
Calculation result of energy consumption of the overall processes for using electric energy [KW∙h]
- E real :
-
The energy consumptions of the overall processes in real practice for using electric energy [KW∙h]
- F :
-
Coefficient of F test
- F(θ):
-
The function to get the aggregation of least relative error
- f SEC-P :
-
The alternative mathematical form to be used during the modeling process
- G c :
-
Calculation result of energy consumption of the overall processes for using gas [m3]
- G real :
-
The energy consumptions of the overall processes in real practice for using gas [m3]
- N :
-
The sample group number of observed SEC and P used for the modeling
- n :
-
The number of unknown coefficients of the regression model
- P :
-
Production rate
- P elec :
-
Production rate of die-casting machine producing finished products [piece/h]
- P gas :
-
Production rate of furnaces using gas [kg/h]
- R 2 :
-
Coefficient of determination
- R gas , R elec :
-
Relative energy efficiency evaluation indexes
- SEC :
-
Specific energy consumption. The amount of energy required for processing a certain amount of one kind of product
- SEC elec :
-
SEC of producing finished products from the machine using electric energy [KW∙h/piece]
- SEC gas :
-
SEC of melting raw materials using gas in furnace [m3/kg]
- s :
-
Residual standard deviation
- T :
-
Delivery time
- Tc :
-
Cycle of time of process
- T ca, G ca, E ca :
-
The real time, gas consumption, and electric energy consumption of meeting the demand D operating casually
- T h, G h, E h :
-
The real time, gas consumption, and electric energy consumption of meeting the demand D using high-energy-efficiency strategy
- t idle :
-
Stand-by idling time
- t p :
-
Production time
- x i :
-
One of the observed value of production rate P
- y i :
-
One of the observed value of SEC
- δ elec, δ gas :
-
Relative error indexes to measure the accuracy of the prediction results
- θ :
-
The unknown coefficient vector of the regression model
- θ 1, θ 2, …, θ n :
-
The unknown coefficients of the regression model
- \( \widehat{\theta} \) :
-
Optimum solution vector of the unknown coefficients
- \( \widehat{\theta_1},\widehat{\theta_2},\dots, \widehat{\theta_n} \) :
-
Optimum solution group of the unknown coefficients
- ε :
-
The relative error between the calculation result by regression model and real value
References
Anderberg, S. E., Kara, S., & Beno, T. (2010). Impact of energy efficiency on computer numerically controlled machining. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 224(4), 531–541.
Bettoni, L., & Zanoni, S. (2011). Energy implications of production planning decisions. Berlin: Springer.
Børset, M. T., Wilhelmsen, Ø., Kjelstrup, S., & Burheim, O. S. (2016). Exploring the potential for waste heat recovery during metal casting with thermoelectric generators: on-site experiments and mathematical modeling. Energy, 118.
Brevick, J., Mountcampbell, C., & Mobley, C. (2004). Energy consumption of die casting operations. Office of Scientific & Technical Information Technical Reports.
Cao, H., Li, H., Cheng, H., Luo, Y., Yin, R., & Chen, Y. (2012). A carbon efficiency approach for life-cycle carbon emission characteristics of machine tools. Journal of Cleaner Production, 37(4), 19–28.
Das, S. K., & Yin, W. (2007). The worldwide aluminum economy: the current state of the industry. JOM, 59(11), 57–63.
Department Ofenvironment, T. (1997). Non-ferrous foundries.
Dunham, S. (2015). Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990–2013.
Eglins, F., & Röders, J. (2005). Method of measuring a tool of a machine tool. EP.
Gutowski, T., Dahmus, J., & Thiriez, A. (2006). Electrical energy requirements for manufacturing processes. Energy, 2.
He, K., Tang, R., & Jin, M. (2017). Pareto fronts of machining parameters for trade-off among energy consumption, cutting force and processing time. International Journal of Production Economics, 185, 113–127.
Heinemann, T. (2016). Energy and resource efficiency in aluminium die casting. Springer International Publishing.
Henninger, M., Schlüter, W., Jeckle, D., & Schmidt, J. (2016). Simulation based studies of energy saving measures in the aluminum tool and die casting industry. Applied Mechanics & Materials, 856.
Krause, M., Thiede, S., Herrmann, C., & Butz, F. F. (2012). A material and energy flow oriented method for enhancing energy and resource efficiency in aluminium foundries. Berlin: Springer.
Lazzarin, R. M., & Noro, M. (2015). Energy efficiency opportunities in the production process of cast Iron foundries: an experience in Italy. Applied Thermal Engineering, 90, 509–520.
Lazzarin, R. M., & Noro, M. (2016). Energy efficiency opportunities in the service plants of cast iron foundries in Italy. International Journal of Low-Carbon Technologies, 12(2).
Mishra, R. R., & Sharma, A. K. (2017). On melting characteristics of bulk Al-7039 alloy during in-situ microwave casting. Applied Thermal Engineering, 111, 660–675.
Mitterpach, J., Hroncová, E., Ladomerský, J., & Balco, K. (2017). Environmental evaluation of grey cast iron via life cycle assessment. Journal of Cleaner Production, 148, 324–335.
Mohr, S., Somers, K., Swartz, S., & Vanthournout, H. (2012). Manufacturing resource productivity. McKinsey Quarterly, June, 2012, 20–25.
Pagone, E., Jolly, M., & Salonitis, K. (2016). The development of a tool to promote sustainability in casting processes ☆. Procedia CIRP, 55, 53–58.
Rosen, M. A., & Lee, D. L. (2009). Exergy-based analysis and efficiency evaluation for an aluminum melting furnace in a die-casting plant. In Iasme/wseas international conference on energy & environment (pp. 160–165).
Salonitis, K., Jolly, M. R., Zeng, B., & Mehrabi, H. (2016a). Improvements in energy consumption and environmental impact by novel single shot melting process for casting. Journal of Cleaner Production, 137, 1532–1542.
Salonitis, K., Zeng, B., Mehrabi, H. A., & Jolly, M. (2016b). The challenges for energy efficient casting processes ☆. Procedia CIRP, 40, 24–29.
Salonitis, K., Jolly, M., & Zeng, B. (2017). Simulation based energy and resource efficient casting process chain selection: a case study ☆. Procedia Manufacturing, 8, 67–74.
Schwam, D. (2012). Energy saving melting and revert reduction technology: melting efficiency in die casting operations. Office of Scientific & Technical Information Technical Reports.
Selvaraj, J., Marimuthu, P., Devanathan, S., Ramachandran, K. I., Selvaraj, J., Marimuthu, P., et al. (2017). Mathematical modelling of raw material preheating by energy recycling method in metal casting process. In Intelligent systems technologies and applications (pp. 766–769).
Shao, Y. (2017). Analysis of energy savings potential of China’s nonferrous metals industry. Resources Conservation & Recycling, 117, 25–33.
Sharma, M., Singh, R., & Singh, R. (2017). Sustainable modeling of die-casting processes through Matlab.
Sieminski, A. (2016). International energy outlook 2016.
Singh, P., Madan, J., Singh, A., & Mani, M. (2012). Computer-aided system for sustainability analysis for the die-casting process. In ASME Manufacturing Science and Engineering ConferenceASME Manufacturing Science and Engineering Conference (pp. MSEC2012–7303).
Thiriez, A., & Gutowski, T. (2006). An environmental analysis of injection molding. In IEEE international symposium on electronics and the environment (pp. 195–200).
Trianni, A., & Cagno, E. (2012). Dealing with barriers to energy efficiency and SMEs: Some empirical evidences. Energy, 37(1), 494–504.
Trianni, A., Cagno, E., Thollander, P., & Backlund, S. (2013). Barriers to industrial energy efficiency in foundries: a European comparison. Journal of Cleaner Production, 40(3), 161–176.
Watkins, M. F., Mani, M., Lyons, K. W., & Gupta, S. K. (2013). Sustainability characterization for die casting process. In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (pp. V02AT02A006).
Yilmaz, O., Anctil, A., & Karanfil, T. (2015). LCA as a decision support tool for evaluation of best available techniques (BATs) for cleaner production of iron casting. Journal of Cleaner Production, 105, 337–347.
Zhong, Q., Tang, R., Lv, J., Jia, S., & Jin, M. (2016). Evaluation on models of calculating energy consumption in metal cutting processes: a case of external turning process. International Journal of Advanced Manufacturing Technology, 82(9–12), 2087–2099.
Funding
This work was partially supported by the National Natural Science Foundation of China (Grant No. U1501248) and Nantaihu Innovation Program of Huzhou Zhejiang China.
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He, K., Tang, R., Jin, M. et al. Energy modeling and efficiency analysis of aluminum die-casting processes. Energy Efficiency 12, 1167–1182 (2019). https://doi.org/10.1007/s12053-018-9730-9
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DOI: https://doi.org/10.1007/s12053-018-9730-9