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Energy Efficiency

, Volume 12, Issue 5, pp 1167–1182 | Cite as

Energy modeling and efficiency analysis of aluminum die-casting processes

  • Keyan He
  • Renzhong TangEmail author
  • Mingzhou JinEmail author
  • Yanlong Cao
  • Sachin U. Nimbalkar
Original Article
  • 169 Downloads

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.

Keywords

Aluminum die-casting process Energy consumption modeling Data acquisition Energy efficiency analysis 

Nomenclature

AP, BP, CP, DP

Coefficients of polynomial cubic

adjR2

Adjusted coefficient of determination

aE, bE, cE

Coefficients of exponential functions

aL, bL, cL

Coefficients of logarithmic functions

aR, bR

Coefficients of reciprocal functions

aP, bP

Coefficients of power functions

D

Demanding amount of products of orders

Ec

Calculation result of energy consumption of the overall processes for using electric energy [KW∙h]

Ereal,

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

fSEC-P

The alternative mathematical form to be used during the modeling process

Gc

Calculation result of energy consumption of the overall processes for using gas [m3]

Greal

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

Pelec

Production rate of die-casting machine producing finished products [piece/h]

Pgas

Production rate of furnaces using gas [kg/h]

R2

Coefficient of determination

Rgas, Relec

Relative energy efficiency evaluation indexes

SEC

Specific energy consumption. The amount of energy required for processing a certain amount of one kind of product

SECelec

SEC of producing finished products from the machine using electric energy [KW∙h/piece]

SECgas

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

Tca,Gca, Eca

The real-time, gas consumption, and electric energy consumption of meeting the demand D operating casually

Th ,Gh ,Eh

The real-time, gas consumption, and electric energy consumption of meeting the demand D using high energy efficiency strategy

tidle

Stand-by idling time

tp

Production time

xi

One of the observed values of production rate P

yi

One of the observed values of SEC

\( \widehat{y_i} \)

One of the values of the model output

δelec, δgas

Relative error indexes to measure the accuracy of the prediction results

θ

The unknown coefficient vector of the regression model

θ1, θ2, …, θn

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

AP, BP, CP, DP

Coefficients of polynomial cubic

aE, bE, cE

Coefficients of exponential functions

aL, bL, cL

Coefficients of logarithmic functions

aR, bR

Coefficients of reciprocal functions

aP, bP

Coefficients of power functions

D

Demanding amount of products of orders

Ec

Calculation result of energy consumption of the overall processes for using electric energy [KW∙h]

Ereal

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

fSEC-P

The alternative mathematical form to be used during the modeling process

Gc

Calculation result of energy consumption of the overall processes for using gas [m3]

Greal

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

Pelec

Production rate of die-casting machine producing finished products [piece/h]

Pgas

Production rate of furnaces using gas [kg/h]

R2

Coefficient of determination

Rgas , Relec

Relative energy efficiency evaluation indexes

SEC

Specific energy consumption. The amount of energy required for processing a certain amount of one kind of product

SECelec

SEC of producing finished products from the machine using electric energy [KW∙h/piece]

SECgas

SEC of melting raw materials using gas in furnace [m3/kg]

s

Residual standard deviation

T

Delivery time

Tc

Cycle of time of process

Tca, Gca, Eca

The real time, gas consumption, and electric energy consumption of meeting the demand D operating casually

Th, Gh, Eh

The real time, gas consumption, and electric energy consumption of meeting the demand D using high-energy-efficiency strategy

tidle

Stand-by idling time

tp

Production time

xi

One of the observed value of production rate P

yi

One of the observed value of SEC

δelec, δgas

Relative error indexes to measure the accuracy of the prediction results

θ

The unknown coefficient vector of the regression model

θ1, θ2, …, θn

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

Notes

Funding information

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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Fluid Power and Mechatronic Systems, School of Mechanical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Department of Industrial and Systems EngineeringThe University of TennesseeKnoxvilleUSA
  3. 3.Energy and Transportation Science DivisionOak Ridge National LaboratoryOak RidgeUSA

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