Table of Content

25 October 2017, Volume 45 Issue 10

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Chemistry & Chemical Engineering

Corrosion Behaviors of Austenitic Stainless Steel in NaCl-CaCl₂ -MgCl₂ Molten Salt

WEI Xiao-lan LIU Bo SONG Ming WANG Wei-long DING Jing

2017, 45(10):  1-7.  doi:10.3969/j.issn.1000-565X.2017.10.001

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In order to understand the corrosion of the austenitic stainless steel in the molten salt of the ternary mag- nesium-based chloride NaCl-CaCl₂ -MgCl₂ during a thermal storage,the corrosion behaviors of five kinds of stainless steels (201,304,310S,316L and 321) after being corroded in the molten salt in a short term were investigated by means of the mass loss measurement.Then,a long-term corrosion test on 316L stainless steel which had shown a better corrosion resistance in the short-term corrosion test was conducted.Finally,the changes of the corrosion phase and morphology with the corrosion time were analyzed by means of XRD and SEM.The results show that (1) when the five kinds of stainless steels are immersed in an open crucible full of the molten salt,they suffer more ob- vious corrosion mass loss than those with a capped crucible do; (2) 316L stainless steel which contains Mo shows a better corrosion resistance at any one of 500,600 and 700 ℃,furthermore,the annual corrosion rate of 316L stainless steel at 600℃ is 0. 347mm per year; (3) the diffraction peak of 316L stainless steel substrate still ap- pears in the pattern after a five-day corrosion,but after a ten-day immersion,the diffraction peak of MgO appears; and (4) the surface of 316L stainless steel is porous after a five-day corrosion,and then,after a ten-day immer- sion,the corrosion pores are gradually filled by MgO,which is formed by means of the hydrolysis of MgCl₂2 at high temperatures.

Application and Exergy Analysis of Heat Pumps in Co-generation Central Heating System

LI Ya-jun TAN Rong-shuai LIANG Wen-hao

2017, 45(10):  8-15.  doi:10.3969/j.issn.1000-565X.2017.10.002

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In order to improve the heating capacity and efficiency of the existing central heating system and thus re- lieve the growing pressure on the heating system in winter,two schemes of adding new heating and adopting heat pumps are designed based on an existing co-generation central heating system.Then,the COP,the exergy efficien- cy and the payback period are used to evaluate the two schemes.The results show that,when the new heating is added,the central heating system achieves a COP of 0. 98,which is almost equal to that of the existing system,and an exergy efficiency of 28. 39%,which is decreased by 39. 15%,as well as a dynamic payback period of 7. 98 years,and that,when the heat pumps are adopted,the COP and the exergy efficiency of the central heating system are respectively 1. 34 and 62. 69%,which are respectively 35. 4% and 34. 36% higher than those of the existing system,and the dynamic payback period is 5. 73 years.In addition,the system adopting the heat pumps is of a good economic adaptability.

Optimal Operation Strategy of Parallel-Connection Solar Air-Source Heat-Pump Hot-Water System

ZHOU Xuan LIU Guo-qiang YAN Jun-wei

2017, 45(10):  16-25.  doi:10.3969/j.issn.1000-565X.2017.10.003

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At a university in a hot summer and warm winter region,there exist some problems in the parallel-connection solar air-source heat-pump hot-water system at 26 student apartments.For example,the hot water supply is not enough during the abrupt changes of outside meteorological parameters,the solar energy efficiency is low,and the power frequency running of the water pump may cause an energy waste.In this paper,the running mode of the system is divided into the water replenishment mode,the heat storage mode and the water supply mode,and according to the characteristics of different modes,a strategy of streamline management and optimal operation is proposed based on the daily water upper limit control,the hourly water lower limit control,the heating capacity forecast of the solar collector system,the heating capacity forecast of the air-source heat-pump and the water supply at different pressure difference hourly.Then,the proposed strategy and the parameters obtained through experiments are applied to the real-time control of the system.The running results show that the proposed strategy can meet the requirements of the hot water supply,and it achieves a power consumption decrease of 17. 49% and a system COP increase of 19. 98% in 2016 in comparison with those in 2015.

Cold Transmitting Control and Terminal Cold Adjusting of District Cooling System

ZHANG Yan CHU Xiao-li LIU Yong-qiang

2017, 45(10):  26-33.  doi:10.3969/j.issn.1000-565X.2017.10.004

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In order to realize the cold transmitting and terminal temperature adjusting of district cooling systems,a transitive theoretical model of the cold from a water system to an air system by a two-stage cooling exchange station is constructed,and by combining a dynamic change model of indoor temperature,a transfer function from the volume of the water-system primary side to the indoor temperature of the air conditioning terminal is derived.Then,the technology integrating the variable water volume (VWV) of the water-system primary side with the variable air volume (VAV) of the air conditioning terminal is applied,and according to the change of cold load,the PI and PID controllers are respectively employed to adjust the speed of pumps and fans in real-time.Moreover,the energyconsumption modeling and energy-saving analysis of the fans and the pumps are performed,so as to control the indoor temperature and save the electric quantity.Finally,by using the Simulink software,the schematic diagrams of the variation of such parameters as the indoor temperature,the pump speed,the water volume,and the energy-saving quantity are put forward,and the effectiveness of the above energy-saving control method is exhibited.

Determination and Correlation of Liquid-Liquid Equilibrium Data of Methyl Isobutyl Ketone-Phenol-Catechol-Water

CHEN Yun WANG Hui-min XIONG Kang-ning LI Li-bo

2017, 45(10):  34-38,45.  doi:10.3969/j.issn.1000-565X.2017.10.005

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In order to obtain the basic data of the process simulation and design of both the extraction of the phenolic compounds from the highly-concentrated phenolic wastewater in coal chemical industry by using methyl isobutyl ke- tone (MIBK) and the corresponding solvent recycling at an industrial operating temperature,the liquid-liquid equilibrium (LLE) data of a MIBK-phenol-catechol-water quaternary system were measured at 70 ℃ under the atmospheric pressure,and the reliability of the LLE data was ascertained by using the Hand and Othmer-Tobias equations.Moreover,the experimental data were thermodynamically correlated by adopting the NRTL and UNIQUAC models,and binary interaction parameters were calculated by using simulation software.The results show that the calculated data based on the NRTL and UNIQUAC models accord well with the measured data,and the root-mean-square-deviations (RMSD) of the two models are less than 0. 02,which means that the binary inte- raction parameters obtained through the two models can be used to precisely predict the LLE data.Therefore,it can be concluded that the MIBK extraction at high temperatures is of good practical value in industry from the per- spectives of anti-blockage and extraction efficiency.

Modification of Li[Li_0.2 Ni_0.2 Mn_0.6 ]O₂ Cathode Materials by Means of Nano-TiO₂ Doping

WANG Wei-gang HU Guo-rong ZHOU Xing-hua PENG Zhong-dong DU Ke

2017, 45(10):  39-45.  doi:10.3969/j.issn.1000-565X.2017.10.006

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The Li[Li_0.2 Ni_0.2 Mn_0.6-X Ti_X]O₂(x =0. 00，0. 01,0. 02,0. 05 and 0. 10) cathode materials were pre- pared by uniformly mixing the carbonate precursor Mn_0.75 Ni_0.25CO₃ obtained by means of the co-precipitation meth- od,Li₂ CO₃ and different amounts of nano-TiO₂ and then sintering them under 900℃ for 10h.The ICP (Inductively Coupled Plasma) analysis indicates that the components of the prepared materials accord well with the initial de- sign.By means of XRD and SEM,it is found that,when the doping amount of Ti 4 + reaches up to a certain degree,the structure of the pristine material is changed and the micro particles are refined.The results of electrochemical tests show that,when the doping amount of Ti is 0. 02,the doped material exhibits an optimal electrochemical per- formance: specifically,the capacity still keeps constant and the mean voltage fading decreases to 0. 08 mV after 30 cycles at 0. 1C rate.In addition,the discharge capacities of the doped material at various rates increase by 7 ～ 13mAh/g in comparison with that of the material before the doping． EIS (Electrochemical Impedance Spectroscopy) tests demonstrate that the electrochemical performance improvement of the Li[Li_0.2 Ni_0.2 Mn_0.58 Ti_0.02 ]O₂ may be at- tributed to the improvement of the material structure stability by means of the Ti doping.

Transient Overvoltage Simulation of Medium-Voltage Cable Collector System in Offshore Wind Farm

LIU Gang JIANG Xiao-feng GUO Ya-xun XIN Yan-li LIANG Jia-hao ZHOU Lu ZHNEG Ming

2017, 45(10):  46-52,61.  doi:10.3969/j.issn.1000-565X.2017.10.007

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In order to reveal the mechanism of how the re-ignition of a vacuum circuit breaker in an offshore wind farm causes the damage of the insulation of the generators with step-up transformers,the high-frequency modeling and the analysis of the vacuum circuit breaker are performed in this paper.First,a simplified simulation model of the medium-voltage cable collector system PSCAD/EMTDC for the offshore wind farms is constructed by using a self-defined vacuum circuit breaker model.Then,the effects of the re-ignition characteristics of the circuit breaker,the initial phase angle of switching and the cable length on the transient overvoltage on the high voltage (HV) side of the generators with the step-up transformers and the re-ignition number are investigated.Simulation results show that the dielectric recovery strength of the three characteristic parameters of the circuit breaker has the greatest in- fluence on the transient overvoltage and the re-ignition number,and that,when the initial phase angle of switching is 45° and the re-ignition phenomenon caused by the interruption of an inductive load circuit breaker occurs,the overvoltage reaches the maximum and its amplitude and steepness are up to 3. 26p. u.and 12. 46p. u.respective- ly.Finally,the scheme of installing the series of choking coils,the parallel small capacitor and the overvoltage pro- tection device of zinc oxide arrester on the HV side of the generators with the step-up transformers at the same time is proposed.Simulation results show that，after the overvoltage protection device is installed,the overvoltage ampli- tude and steepness as well as the re-ignition number are effectively suppressed.

Power & Electrical Engineering

Maloperation Analysis and Optimizing Strategy of Travelling Wave Protection for UHVDC Transmission Lines Under Lightning Strike

CAI Ze-xiang TIAN De-liang LIANG Yi LI Xiao-hua LI Shu-yong

2017, 45(10):  53-61.  doi:10.3969/j.issn.1000-565X.2017.10.008

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In the practical running of UHVDC,if a lightning current attacks one polar of a transmission line,the maloperation of the non-lightning traveling wave protection may occur，which is likely to result in a bipolar locking in the DC system.In this paper,based on a practical UHVDC model in EMTDC,a correct lightning strike model is constructed,and the dynamic response of the three protection criteria (namely,dU/dt,ΔU,ΔI) under lightning strikes is investigated.Moreover,the logical coordination of the three criteria is also discussed.The analysis shows that an important reason for the traveling wave maloperation of non-lightning lines is that,when one polar of a line is hit by the lightning strike,the electromagnetic coupling between circuits leads to a drastic fluctuation in the elec- trical quantities of the non-lightning lines,and this fluctuation will cause the response of the protection criteria in the recovery from distraction to satisfy a set time series exactly.Therefore,an optimizing strategy of adding a sub- sidiary locking logic on the basis of the original voltage criterion of the traveling wave protection is proposed,so as to improve the selectivity without sacrificing the sensitivity.Simulation results show that the proposed strategy is effective.

Precise Modeling and Coordinate Control of Unified Power Quality Conditioner

XU Xiao-gang XIE Yun-xiang WANG Ying-pin LI Lan-fang ZENG Zhi-wu ZHANG Xiao-yu

2017, 45(10):  62-70.  doi:10.3969/j.issn.1000-565X.2017.10.009

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In the modeling process of a unified power quality conditioner (UPQC),a series unit model and a pa- rallel unit model are separately constructed in general,and an idealized series transformer is applied.In addition,the interaction between the series unit and the parallel unit has been rarely analyzed.In this paper,a precise mathematical model of the UPQC is constructed by using an equivalent transformer model,which integrates the se- ries unit with the parallel unit.Then,the interaction between a series inverter and a parallel inverter is analyzed,and the corresponding interaction mechanism is obtained.Furthermore,a coordinate control method of the UPQC is proposed based on the unity power factor (UPF) detection method.Simulation and experimental results prove that the proposed method can help the UPQC achieve a better compensation effect,thus verifying the correctness of the constructed mathematical model and the obtained interaction mechanism.

Improved Thermal-Electrical Analogy Model for Evaluating Loading Capability of Transformer

TANG Wen-hu QIAN Tong HUANG Jing-jing LU Guo-jun WANG Yong LUAN Le

2017, 45(10):  71-77,86.  doi:10.3969/j.issn.1000-565X.2017.10.010

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The loading capability of an oil-immersed power transformer is closely related to oil temperatures and hot-spot temperatures (HST). In order to accurately calculate top-oil temperatures (TOT) and HSTs and thus help evaluate the loading capability of the oil-immersed transformer,a thermal-electrical analogy model for the trans- former is improved based on the principle of heat transfer and the circuit laws.In the improved model,first,the oil viscosity is introduced to redefine the nonlinear thermal conductance of the relative parts of the transformer,and the heat transfer between the transformer and the ambient environment is taken into account.Then,a hot-spot temperature node is introduced into the improved model,so that this model can really reflect the general process of the heat transfer in the transformer.Finally,a genetic algorithm (GA) is employed to globally optimize thermal parameters.By taking a 180000kVA oil-immersed power transformer as an example,the calculated results of the HSTs,TOTs and bottom-oil temperatures of the original and improved models are compared with the on-line data and the results calculated by the recommended empirical formulas in the transformer loading guide.It is found that the improved model is more accurate.Then,the improved model is used to calculate the relative daily loss of life,the maximum TOT and the maximum HST of a large oil-immersed power transformer in given working conditions,so as to evaluate the loading capability of the tested transformer and thus provide a reference for the load rating in- crease of the tested transformer.

Security-Constrained Unit Commitment Model with Wind Power and Electric Vehicles

ZHAO Qiang LIU Hai-yong WANG Jin-kuan HAN Ying-hua

2017, 45(10):  78-86.  doi:10.3969/j.issn.1000-565X.2017.10.011

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In view of the impact of the large-scale access of wind power and electric vehicles on power grids,a multi-objective security-constrained unit commitment model based on the co-scheduling of the wind power and the electric vehicles (EVs) is constructed by taking the lowest operating cost and the lowest pollution emission as the objectives.In the model,by regarding a charging and discharging electric vehicle as an optimal scheduling unit,a virtual electricity pricing strategy is established to make a reasonable charge and discharge plan with the goal of minimizing the charge cost.Then,a fuzzy chance-constrained program is used to describe the intermittency and uncertainty of the wind power,and the vehicle-to-gird (V2G) method is adopted to stabilize the wind power fluc- tuation and reduce the adjusting frequency of the unit,thus improving the economy of the power grids in a safe ope- ration.Simulation results demonstrate that the constructed model can utilize the complementarity between various factors to promote the utilization of the wind power and thus achieve better economic and environmental benefits.

Design of EKNN Algorithm for Regional WiFi Localization

FU Yu-li YANG Shuai CHEN Pei-lin HUANG Zhi-jian TANG Jie

2017, 45(10):  87-92,99.  doi:10.3969/j.issn.1000-565X.2017.10.012

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Since WiFi is widely used,it is selected as one of the popular technologies for indoor positioning.The positioning accuracy and speed have always been hot research issues.In this paper,an evidence K-nearest neigh- bor(EKNN) algorithm is proposed for the localization of the region of interest(ROI).In the algorithm,first,by taking a received signal strength indicator as the fingerprint,a wireless fingerprint database is established as a recognition class in each region.Then,based on the evidence theory,the neighbor evidences within each class are combined and the combined results among the classes are fused.Finally,the ROI class of the target is deter- mined,and a precise positioning is performed within this class.As compared with other algorithms,the EKNN al- gorithm can achieve a recognition rate of 97% at best and a maximum positioning error of about 2. 2 meters as well as a great positioning efficiency improvement.

Electronics, Communication & Automation Technology

Sorting Route Optimization of Parallel Robot Based on Improved Genetic Algorithm

ZHANG Hao-jian SU Ting-ting WU Shao-hong ZHENG Jun WANG Yun-kuan

2017, 45(10):  93-99.  doi:10.3969/j.issn.1000-565X.2017.10.013

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By analyzing the production process of packaging lines and aiming at the multiple-target problem of the Delta parallel robot sorting with dynamically changing positions under complex multi-constraint conditions,a me- thod to optimize the sorting trajectories of the parallel robot is proposed based on an improved genetic algorithm and the thought of beats.By analyzing the sorting strategy,the practical problem is transformed into a similar traveling salesman problem (TSP),and an improved genetic algorithm is put forward according to the particularity of the sorting process.Moreover,the thought of beats is introduced,and the sorting trajectories in every beat are opti- mized by transforming the constraint conditions into a genetic operator combining the fission and merge operations of chromosomes.The test results show that,as compared with the traditional methods,the proposed method can ef- fectively shorten the average sorting stroke,with an average efficiency increase of 14. 76%.

Monitoring Range Offset Detection Method of Highway Camera Based on Corner Set Feature

ZHAO Min MEI Deng SUN Di-hua

2017, 45(10):  100-107.  doi:10.3969/j.issn.1000-565X.2017.10.014

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For the automatic detection of abnormal accidents on highways and the analysis of other video contents,the monitoring range offset detection is the precondition and basis.Due to the interference of moving objects,light and noises in the highway scenes,the existing detection methods show poor real-time performance and robustness.In order to solve these problems,an offset detection method based on corner set features is proposed.In this meth- od,first,false corners are removed according to the characteristics of the Taylor series,such as great extremism and few clusters of random noisy points.Then,the trained corner set features are used to accurately represent the image.On this basis,a matching is conducted by employing the corner set information rejecting the light interfer- ence,and both the cross correlation method and the dynamic threshold are adopted to realize the matching of the corner position and the number respectively,so as to avoid such interferences as light.Thus,the accurate detec- tion of deviation events is accomplished.The results of comparative experiments show that the proposed method im- proves the real-time performance and still maintains an average detection rate of 92%,which can better meet the requirement of highway monitoring.

Blind Image De-blurring Based on Sparse Prior and Relative Total Variation

YAO Ruo-he RAO Jing-song LIU Wei-jian

2017, 45(10):  108-113.  doi:10.3969/j.issn.1000-565X.2017.10.015

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In a blind image de-blurring,estimating a blur kernel from a single blurred image is a severely ill-posed problem.In this paper,a blind image de-blurring method based on sparse prior and relative total variation is pro- posed.In this method,a smoothing algorithm based on weighted L0 is employed to adaptively extract the main structure of an image and remove such factors adverse to a kernel estimation as the noise,the details and the edges of a small object,and a relative total variation method is adopted to overcome the inaccuracy of estimating a com- plex blur kernel by means of the regularization method of the sparse prior.Moreover,the regularization method of the Super-Laplacian prior is used to estimate the latent image.Experimental results show that，as compared with the existing image de-blurring method,the proposed method helps achieve the latent image of better structure and less artifacts,and it can better recover the latent image.

Image Matching Algorithm Based on Mahalanobis-Distance Spectral Features

BAO Wen-xia YU Guo-fen HU Gen-sheng ZHU Ming

2017, 45(10):  114-120,128.  doi:10.3969/j.issn.1000-565X.2017.10.016

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In the traditional image matching algorithms based on spectral features,the Euclidean distance metric can not fairly reflect the underlying relationship between the dimensions of sample data,and large deformation and outliers will lead to poor matching accuracy and stability.In order to solve these problems existing in the structure of spectral features,an image matching algorithm based on Mahalanobis-distance spectral features is proposed.In the algorithm,first,a local undirected weighted graph is constructed in sub feature point sets by using the Maha- lanobis distance.Next,the singular value decomposition of the adjacent matrixes of the graph is performed,and the Mahalanobis-distance spectral features describing the attributes of the point sets are constructed by using spec- tral value vectors.Then,a matching matrix is constructed based on the Mahalanobis-distance spectral features,and the matching relationships among the feature points of the image are obtained by using the greedy algorithm.Finally,in order to further improve the matching accuracy,the false matching points are eliminated by means of the SVM method.A large number of experimental results show that the proposed algorithm improves the matching accuracy,and it is robust to outliers.

Mechanical Engineering

A Ｒeal-time Look-ahead Interpolation Algorithm for NURBS Curves Based on Runge-Kutta

WU Yu-xiang WANG Peng

2017, 45(10):  121-128.  doi:10.3969/j.issn.1000-565X.2017.10.017

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During the traditional NURBS machining,the calculation precision of the interpolation parameters of the interpolation algorithm is low,the real-time performance is poor,and too high acceleration causes a dramatic im- pact on machine tools.In order to solve these problems,a real-time look-ahead interpolation algorithm for NURBS curves based on Runge-Kutta is proposed.In the algorithm,first,the interpolation parameters are calculated by using the four-order Runge-Kutta method,and the feedrate is adjusted automatically according to the constraints of the chord error and the normal acceleration.Next,the parameters are revised according to the deviation between the theoretical feed step and the actual one.Then,based on the offline data from a rough interpolation,the extreme points of the feedrate are calculated and the parametric curves are divided into several look-ahead sections,thus finding the first and last sensitive feedrate points in each look-ahead section.Finally,the feedrate is re-planned ac- cording to the relationship between the sensitive feedrate and the interpolation distance,so as to avoid the dramatic variation of the feedrate.Thus,the demand of the machine tool in the acceleration and deceleration performance is satisfied.The proposed algorithm is proved to be effective by a Matlab simulation.

Dynamic Parameter Identification of SCARA Robots Based on Newton-Euler Method

ZHANG Tie LIANG Xiao-hong QIN Bin-bin LIU Xiao-gang

2017, 45(10):  129-136,143.  doi:10.3969/j.issn.1000-565X.2017.10.018

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SCARA robots have been widely used in industrial production.In order to meet the requirements of high speed and high precision,it is necessary to conduct a dynamics analysis of SCARA robots.In this paper,a dynamic model of a SCARA robot is constructed by means of the Newton-Euler method.Then,the effects of friction and mo- tor rotors on joint torques are taken into account in the dynamic model,and a linear expression of the joint torque with respect to a set of identifiable parameters is established.Finally,the excitation trajectories generated by means of the Fourier series formulation are used in an excitation experiment,and the least squares method is employed to identify the identifiable parameters.Experimental results show that the variation trend of the joint torque obtained through the established linear expression is consistent with that of the actual value.When the dynamic parameters obtained through the identification method proposed in this paper are applied to a dynamic modeling,the joint torque of a running SCARA robot can be achieved.The proposed method can provide basic equations for the future work on a dynamic control.

Synthesis of Belt Mechanism for Rigid-Body Guidance Based on Similarity Transformation

LIU Jing-shuai LIN Song WANG Han-chao ZHANG Yu

2017, 45(10):  137-143.  doi:10.3969/j.issn.1000-565X.2017.10.019

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In order to overcome the defects of the traditional synthesis methods for rigid-body guidance mecha- nisms,such as the limitation of mechanism structure types and the uncertainty of functions,a generalized synthesis method based on the similarity transformation of mechanism function modules is proposed.In the method,first,by taking a belt mechanism as the objective,a kinematic analysis model is constructed and the output motion charac- teristic parameters are extracted.Next,the corresponding function module with full topology information is built.Then,by analyzing the intrinsic relationship between the mechanism parameters and the coupler rotation-angle function as well as that between the mechanism parameters and the guidance trajectory,the mapping rules between the guidance functions and the dimension parameters are revealed,and a method to preselect the reasonable dimen- sions of function modules is put forward.Finally,a fuzzy guidance motion design is introduced,and the geometric positioning of the mechanism function modules is accomplished through the center projective similarity transforma- tion,thus obtaining the actual dimensions and installation parameters of the mechanism.By a numerical example,it is proved that the proposed method is effective and applicable.

A Combined Hardening Model for Multi-Stage Sheet Metal Forming

CHEN Jiang CHEN Wen-liang

2017, 45(10):  144-150.  doi:10.3969/j.issn.1000-565X.2017.10.020

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The accurate prediction of the multi-stage sheet metal forming including springback is of great signifi- cance for stamping industries,and the Bauschinger effect is a key factor influencing the accuracy.In this paper,an improved multi-stage combined hardening model is constructed.In the model,based on the two-yield-surface model of the Yoshida-Uemori hardening model,the equivalent back stress of the boundary surface between stages is calcu- lated for each stage by using the nonlinear isotropic hardening equations with different factors influencing strain paths.In a real tension and compression test of DP600,in comparison with other hardening models,both the Yo- shida-Uemori model and the constructed model can better reflect the Bauschinger effect and calculate the stress- strain curve more accurately.In a multi-axial tension and compression test,the constructed model is more accurate than the Yoshida-Uemori model.By the experiment and numerical simulation of the multi-stage manufacturing process of an A-pillar,it is proved that，in comparison with other constitutive models,the constructed model can achieve a higher accuracy in predicting springback in the numerical simulation of the multi-stage sheet metal for- ming.