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Effect of wire diameter compression ratio on drawing deformation of micro copper wire
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作者 Tao HUANG Han-jiang WU +3 位作者 Ke-xing SONG Yan-min ZHANG Yan-jun ZHOU Shao-lin LI 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2024年第8期2605-2618,共14页
A crystal plasticity finite element model was developed for the drawing deformation of pure copper micro wire,based on rate-dependent crystal plasticity theory.The impact of wire diameter compression ratio on the micr... A crystal plasticity finite element model was developed for the drawing deformation of pure copper micro wire,based on rate-dependent crystal plasticity theory.The impact of wire diameter compression ratio on the micro-mechanical deformation behavior during the wire drawing process was investigated.Results indicate that the internal deformation and slip of the drawn wire are unevenly distributed,forming distinct slip and non-slip zones.Additionally,horizontal strain concentration bands develop within the drawn wire.As the wire diameter compression ratio increases,the strength of the slip systems and the extent of slip zones inside the deformation zone also increase.However,the fluctuating stress state,induced by contact pressure and frictional stress,results in a rough and uneven wire surface and diminishes the stability of the drawing process. 展开更多
关键词 micro copper wire drawing deformation crystal plasticity finite element slip mode
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Modeling asymmetric fracture mechanics of Mg alloy wire in drawing process
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作者 Sunghoon Choi Jongwon Shin +1 位作者 Joung Sik Suh Dongchoul Kim 《Journal of Magnesium and Alloys》 SCIE EI CAS CSCD 2024年第5期2057-2069,共13页
In this study,a numerical analysis was conducted on the ductile fracture of a 2-mm diameter Mg-1Zn-0.5Mn-0.5Sr-0.1Ca alloy wire during drawing.The hexagonally close-packed crystal structure of Mg alloys causes asymmet... In this study,a numerical analysis was conducted on the ductile fracture of a 2-mm diameter Mg-1Zn-0.5Mn-0.5Sr-0.1Ca alloy wire during drawing.The hexagonally close-packed crystal structure of Mg alloys causes asymmetric fracture behavior,especially in the compression region.The aim of this study is to develop a comprehensive damage model for Mg alloy wire that accurately predicts ductile fracture,with a focus on the compression region.A novel experimental method was introduced to measure the ductile fracture of Mg alloy wires under different stress states.The wire drawing process was simulated using the Generalized Incremental Stress-State dependent damage(GISSMO)Model and the Semi-Analytical Model for Polymers(SAMP)model.The damage model's prediction and the experimental results were found to be in excellent agreement,especially in determining crack initiation.Computational analysis established a safe zone diagram for die angle and reduction ratio,and experimental validation confirmed the feasibility of this approach.The proposed damage model can provide a practical and reliable analysis for optimizing the drawing process of Mg alloy wire. 展开更多
关键词 Mg alloy Wire drawing Finite element method Damage model Safe zone diagram
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基于知识结构差异的CorelDRAW服装设计课程改革与实践
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作者 邓喜洪 《西部皮革》 2024年第17期68-70,共3页
文章分析了“新文科”建设内涵,基于海口经济学院南海美术学院2021级服装与服饰设计专业学生的知识结构差异,对Corel DRAW服装设计课程教学方法、教学思路、考核方式等进行改革,优化教学设计,将海南地域文化、时尚创意思维融入课程内容... 文章分析了“新文科”建设内涵,基于海口经济学院南海美术学院2021级服装与服饰设计专业学生的知识结构差异,对Corel DRAW服装设计课程教学方法、教学思路、考核方式等进行改革,优化教学设计,将海南地域文化、时尚创意思维融入课程内容,以项目伴随式、任务驱动式等方法开展教学,结课作业和服装设计大赛相结合,全面激发学生的思想内核和学习动力,取得了诸多教学成果,为设计类专业软件课程改革提供了新思路。 展开更多
关键词 新文科 知识结构差异 Corel draw服装设计 课程改革
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Flexible die drawing of magnesium alloy sheet by superimposing ultrasonic vibration 被引量:2
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作者 曹秒艳 李建超 +1 位作者 苑亚宁 赵长财 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2017年第1期163-171,共9页
Combining solid granule medium forming technology with ultrasonic vibration plastic forming technology, ultrasonic vibration granule medium forming (UGMF) technology was proposed. To reveal the effect of ultrasonic ... Combining solid granule medium forming technology with ultrasonic vibration plastic forming technology, ultrasonic vibration granule medium forming (UGMF) technology was proposed. To reveal the effect of ultrasonic vibration on flexible-die deep drawing, an ultrasonic vibration with a frequency of 20 kHz and a maximum output of 1.5 kW was on the solid granule medium deep drawing of AZ31B magnesium alloy sheet. The results revealed that ultrasonic vibration promotes the pressure transmission performance of the granule medium and the formability of the sheet. The forming load declines with the ultrasonic amplitude during the drawing process as a result of the combined influence of the "surface effect" and the "softening" of the "volume effect". 展开更多
关键词 ultrasonic vibration magnesium alloy sheet deep drawing solid granules
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Analysis of elliptical cup drawing process of stainless sheet metal 被引量:3
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作者 黄永明 陸嘯程 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2011年第2期371-377,共7页
Prandtl-Reuss flow rule and Hill’s yield criterion were adopted and combined with the concept of finite deformation theory, updated Lagrangian formulation, and a three-dimensional finite element analytical model was ... Prandtl-Reuss flow rule and Hill’s yield criterion were adopted and combined with the concept of finite deformation theory, updated Lagrangian formulation, and a three-dimensional finite element analytical model was established by application of quadrilateral four-node degenerated shell elements coupling into a rigid matrix to deal with the sheet metal forming problems. The fractured thickness of a specimen obtained from a simple tension test was used to be the fracture criterion for the numerical analysis to explore the relationship between punch load and stroke, the thickness distribution, the deformation history and the forming limit of work-piece in the elliptical cup drawing process. The numerical analysis and experiment results show that the punch load increases with the increase of punch stroke, and when the load reaches its maximum, the blank continues to deform with the increase of the punch stroke, resulting in a reduced load until the extension is completed. The minimum thickness of the work-piece concentrates in the contact region of the work-piece and long axis of the punch due to the smaller radius of the curvature of the long axis than the short axis. So the blanks bore the maximum tensile stress in the long axis. Through the limit drawing ratio defined by perimeter of the elliptical punch, the limit drawing ratio of this elliptical cup drawing is defined to be 2.136. 展开更多
关键词 yield criterion finite element elliptical cup drawing limit drawing ratio
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Process window diagram of conical cups in hydrodynamic deep drawing assisted by radial pressure 被引量:5
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作者 Abbas HASHEMI Mohammad HOSEINPOUR GOLLO S.M.Hossein SEYEDKASHI 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2015年第9期3064-3071,共8页
Major defects in forming of conical cups are wrinkles and rupture.Hydrodynamic deep drawing assisted by radial pressure(HDDRP) is a sheet hydroforming process for production of shell cups in one step.In this work,pr... Major defects in forming of conical cups are wrinkles and rupture.Hydrodynamic deep drawing assisted by radial pressure(HDDRP) is a sheet hydroforming process for production of shell cups in one step.In this work,process window diagrams(PWDs) for Al1050-O,pure copper and DIN 1623 St14 steel are obtained for HDDRP process.The PWD is determined to provide a quick assessment of part producibility for sheet hydroforming process.Finite element method is used for this purpose considering the process parameters including pressure path,and the blank material and its thickness.Numerical results are validated by experiments.It is shown that the sheets with less initial thickness and higher strength show better formability and uniformity of thickness distribution on final product.The results demonstrate that the obtained PWD can predict appropriate forming area and probability of rupture or wrinkling occurrence under different pressure loading paths. 展开更多
关键词 conical cups hydrodynamic deep drawing finite element simulation process window diagram
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High-Performance Solid-State Supercapacitors Fabricated by Pencil Drawing and Polypyrrole Depositing on Paper Substrate 被引量:4
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作者 Jiayou Tao Wenzhen Ma +4 位作者 Nishuang Liu Xiaoliang Ren Yuling Shi Jun Su Yihua Gao 《Nano-Micro Letters》 SCIE EI CAS 2015年第3期276-281,共6页
A solid-state powerful supercapacitor(SC) is fabricated with a substrate of Xerox paper. Its current collector based on a foldable electronic circuit is developed by simply pencil drawing. Thin graphite sheets on pape... A solid-state powerful supercapacitor(SC) is fabricated with a substrate of Xerox paper. Its current collector based on a foldable electronic circuit is developed by simply pencil drawing. Thin graphite sheets on paper provide effective channels for electron transmission with a low resistance of 95 X sq-1. The conductive organic material of polypyrrole coated on thin graphite sheets acts as the electrode material of the device. The as-fabricated SC exhibits a high specific capacitance of 52.9 F cm-3at a scan rate of 1 m V s-1. An energy storage unit fabricated by three full-charged series SCs can drive a commercial light-emitting diode robustly. This work demonstrated a simple, versatile and costeffective method for paper-based devices. 展开更多
关键词 SupERCAPACITOR PAPER Pencil drawing POLYPYRROLE
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Hydrodynamic deep drawing of double layered conical cups 被引量:4
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作者 Alireza JALIL Mohammad HOSEINPOUR GOLLO +1 位作者 M.Morad SHEIKHI S.M.Hossein SEYEDKASHI 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2016年第1期237-247,共11页
Hydrodynamic deep drawing assisted by radial pressure is an advanced sheet forming technology with great advantages such as higher drawing ratio, good surface quality and higher dimensional accuracy. In this process, ... Hydrodynamic deep drawing assisted by radial pressure is an advanced sheet forming technology with great advantages such as higher drawing ratio, good surface quality and higher dimensional accuracy. In this process, both the bottom surface and the peripheral edge of sheets are under hydrodynamic pressure, so that the forming procedure is more uniform with low failure probability. Multi-layered sheets with complex geometries could be formed more easily with this technique compared with other traditional methods. Rupture is the main irrecoverable failure form in sheet forming processes. Prediction of rupture occurrence is of great importance for determining and optimizing the proper process parameters. In this research, a theoretical model was proposed to calculate the critical rupture pressure in production of double layered conical parts with hydrodynamic deep drawing process assisted by radial pressure. The effects of other process parameters on critical rupture pressure, such as punch tip radius, drawing ratio, coefficient of friction, sheet thickness and material properties were also discussed. The proposed model was compared with finite element simulation and validated by experiments on Al1050/St13 double layered sheets, where a good agreement was found with analytical results. 展开更多
关键词 hydrodynamic deep drawing radial pressure double layered sheet conical cup critical pressure
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Formation of Aluminum-magnesium Alloy Cup by Hydrodynamic Deep Drawing with Twin-loading Paths 被引量:3
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作者 刘晓晶 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2009年第2期193-197,共5页
In order to overcome the limitation of hydro-rim deep drawing, a new process of hydrodynamic deep drawing (HDD) with independent radial hydraulic pressure was proposed. By employing the dynamic explicit analytical s... In order to overcome the limitation of hydro-rim deep drawing, a new process of hydrodynamic deep drawing (HDD) with independent radial hydraulic pressure was proposed. By employing the dynamic explicit analytical software ETA/DynaformS.5 which is based on LS-DYNA3D, the effects of independent radia! hydraulic pressure on the stress, strain and the sheet-thickness of aluminum-magnesium cylindrical cup with a hemispherical bottom were analyzed by numerical simulation. The feature of stress distribution is that there exists a stress-dividing circle in the flange, and the radius of dividing circle was determined by theoretical analysis and stimulation. The experimental results indicate that the reasonable match of independent radial hydraulic pressure and liquid chamber pressure can effectively reduce the thinning at the bottom of hemisphere, decrease the radial stress-strain, and improve the drawing limit of aiuminum-magnesium alloy cylindrical cup. 展开更多
关键词 hydrodynamic deep drawing numerical simulation independent radial hydraulic pressure 5A06 aluminum-magnesium alloy
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Integral as a Function of the Upper Limit to Solve Axial Symmetrical Rod Drawing and Extrusion 被引量:1
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作者 赵德文 赵志业 张强 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 1990年第4期282-288,共7页
A kinematically admissible velocity field which is different from Avitzur's has been proposed for axial symmetrical rod drawing and extrusion.An upper-bound analytical solution in cylindrical coordinates has been ... A kinematically admissible velocity field which is different from Avitzur's has been proposed for axial symmetrical rod drawing and extrusion.An upper-bound analytical solution in cylindrical coordinates has been obtained without any mathematical simplification in this paper. 展开更多
关键词 drawING EXTRUSION velocity field upper-bound power
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Key technologies of numerical simulation of cup hydrodynamic deep drawing 被引量:1
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作者 郎利辉 康达昌 +3 位作者 张士宏 戴 昆 王仲仁 苑世剑 《中国有色金属学会会刊:英文版》 CSCD 2000年第6期772-776,共5页
A math formula about the relation between fluid pressure after overflowing and punch stroke that can be applied in general FEM software was proposed. It is proved that theoretical results keep coincident to experiment... A math formula about the relation between fluid pressure after overflowing and punch stroke that can be applied in general FEM software was proposed. It is proved that theoretical results keep coincident to experimental results and the method to simulate hydrodynamic deep drawing process that integrates general FEM software with mathematical description is feasible. [ 展开更多
关键词 HYDRODYNAMIC DEEP drawING FLUID pressure F
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Numerical Analysis of Hydroforming Deep Drawing of Conical Cup 被引量:1
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作者 Yongming KONG Xianbin ZHOU and Min LI Research Center of Sheet Metal Forming, School of Mechanical Engineering & Automation, Beijing University of Aeronautics & Astronautics, Beijing 100083, China 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2001年第1期131-132,共2页
Aided by the FE-code. analysis is carried to find the proper hydroforming deep-drawing condition for the perfect forming of a conical cup that can not be drawn successfully by conventional deep drawing method. Hydraul... Aided by the FE-code. analysis is carried to find the proper hydroforming deep-drawing condition for the perfect forming of a conical cup that can not be drawn successfully by conventional deep drawing method. Hydraulic counter pressure must be reasonably controlled, otherwise defects such as fracture and wrinkling can not be avoided. Therefore, the forming procedure is divided into three stages, and the counter pressure is adjusted intentionally to make the blank clamped onto the punch at a suitable time, then deformation at dangerous area is resisted by the effect of the counter pressure and the conical cup can be formed without defects. 展开更多
关键词 Numerical Analysis of Hydroforming Deep drawing of Conical Cup FIGURE
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Prediction of mechanical properties for deep drawing steel by deep learning 被引量:2
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作者 Gang Xu Jinshan He +2 位作者 Zhimin Lü Min Li Jinwu Xu 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2023年第1期156-165,共10页
At present,iron and steel enterprises mainly use“after spot test ward”to control final product quality.However,it is impossible to realize on-line quality predetermining for all products by this traditional approach... At present,iron and steel enterprises mainly use“after spot test ward”to control final product quality.However,it is impossible to realize on-line quality predetermining for all products by this traditional approach,hence claims and returns often occur,resulting in major eco-nomic losses of enterprises.In order to realize the on-line quality predetermining for steel products during manufacturing process,the predic-tion models of mechanical properties based on deep learning have been proposed in this work.First,the mechanical properties of deep drawing steels were predicted by using LSTM(long short team memory),GRU(gated recurrent unit)network,and GPR(Gaussian process regression)model,and prediction accuracy and learning efficiency for different models were also discussed.Then,on-line re-learning methods for transfer learning models and model parameters were proposed.The experimental results show that not only the prediction accuracy of optimized trans-fer learning models has been improved,but also predetermining time was shortened to meet real time requirements of on-line property prede-termining.The industrial production data of interstitial-free(IF)steel was used to demonstrate that R2 value of GRU model in training stage reaches more than 0.99,and R2 value in testing stage is more than 0.96. 展开更多
关键词 machine learning recurrent natural network transfer learning on-line prediction deep drawing steel mechanical properties
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EMF CHANGES MADE BY COLD DRAWING AND HEATING TREATMENT IN TYPE K HEAVY-GAUGE SHEATHED THERMOCOUPLE CABLES
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作者 ZHAO Rong-bin(赵容斌) +2 位作者 LI Guan-jun (李冠军) 《Journal of Shanghai Jiaotong university(Science)》 EI 2002年第1期80-83,共4页
The electromotive force (EMF) changes in type K heavy gauge sheathed thermocouple cables was investigated. To cope with this discrepancy owing to EMF steep reduction and understand the difference between type K heavy ... The electromotive force (EMF) changes in type K heavy gauge sheathed thermocouple cables was investigated. To cope with this discrepancy owing to EMF steep reduction and understand the difference between type K heavy gauge sheathed thermocouple cables and small ones, the affects of EMF from sheath pipe, drawing times, annealing temperature, annealing time and annealing way were mainly studied and appropriately analyzed. The results show the change in the thermal EMF is related with the residual stress and crystal defects, which are imparted by cold work during manufacture. The affects of cold work can be removed by annealing. Finally, a feasible way of fabricating heavy gauge sheathed thermocouples was suggested according to practical situation. 展开更多
关键词 EMF CHANGES cold drawing HEATING TREATMENT TYPE K heavy-gauge THERMOCOupLE
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Numerical simulation of cup hydrodynamic deep drawing
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作者 郎利辉 康达昌 +3 位作者 张士宏 戴昆 王仲仁 苑世剑 《中国有色金属学会会刊:英文版》 CSCD 2000年第5期631-634,共4页
The simulation of hydrodynamic deep drawing by means of FEM is an efficient method that can relieve experimental burden and find the optimum process parameters. Some problems such as mathematical description of cavity... The simulation of hydrodynamic deep drawing by means of FEM is an efficient method that can relieve experimental burden and find the optimum process parameters. Some problems such as mathematical description of cavity liquid flow pressure must be solved firstly. A math formula about hydrodynamic flow pressure that can be applied in general FEM software was proposed, and good results were gained. It was proved that the theoretical results keep coincident with experimental results.[ 展开更多
关键词 HYDRODYNAMIC DEEP drawING overflowing pressure FEM
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Product Drawing Management System Based on Group Technology
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作者 REN Guang-sheng, YIN Xiao-qing (College of Mechanical Engineering, Chongqing University, Chongqing 40 0044, China) 《厦门大学学报(自然科学版)》 CAS CSCD 北大核心 2002年第S1期166-167,共2页
With the development and widely used of the compute r technology, the CAD has been more and more used in the process of designing prod uct. The number of the engineering drawings will greatly increase because of the c... With the development and widely used of the compute r technology, the CAD has been more and more used in the process of designing prod uct. The number of the engineering drawings will greatly increase because of the continually appearance of the new products. As a result, it has become a badly needed to be solved problem for us that how to rapidly and efficiently search an d appropriately preserve and manage the drawings. In this paper, a method of bui lding the product drawing management system for extrusion aluminum-type materia ls is discussed. This system is designed for the profile graphic of the aluminou s section material management by using Group Technology (GT) principle. Accordin g to the GT, we developed a classifying-coding system and drawing management sy stem about the extrusion aluminum-type materials through analyzing a large numb er of extrusion aluminum-type materials section drawings. The coding system has realized the flexible coding and hidden coding of the extrusion aluminum-type materials and then enhanced the flexibility and the expansible of the system. By supplying the designer with the human-computer interaction interface the drawi ng management system has been able to resolve many difficult problems such as se arch and manage the existed drawings about the extrusion aluminum-type material s very well. At the same time, it also helps the developing work enhance the abi lity of inheriting by applying this kind of variant method. In a word, with the help of this system we can not only shorten the designing time greatly and reduc e the cost of the product but also research the designing drawings rapidly. In o rder to output the data information related to the part drawing, the system uses the data-exchange standard to which the drawing support-software adapted as d ata-exchange interface. The system is advantageous to building a standard of dr awing design and increasing the efficiency of searching drawing and enhancing th e information management, which have had a base for building the best management system in the future. In addition, the paper has a detailed analysis about the principle of flexible classification code and data structure. 展开更多
关键词 group technology drawing management product des ign extrusion aluminum-type materials
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Deep drawing of cup shell by powder cavity flexible forming technology
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作者 XUE Ya-hong CHEN Ke +1 位作者 FAN Cun-jie LUO Jun-ting 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第4期766-772,共7页
A forming method named powder cavity flexible forming was proposed. It is a forming technology which uses powder medium instead of rigid punch or die to form sheet metals. Cup shells were successfully obtained by this... A forming method named powder cavity flexible forming was proposed. It is a forming technology which uses powder medium instead of rigid punch or die to form sheet metals. Cup shells were successfully obtained by this technology. The theoretical calculation equation of forming load was obtained through mechanical analysis and the stress state in cup shells was analyzed by finite element simulation. The results show that powder cavity flexible forming technology can improve the forming limit of sheet metal. Compared with rigid die forming process, the thickness reduction in the punch fillet area significantly decreases and the drawing ratio increases from 1.8 to 2.2. The thinning compressive stress in the bottom of cup shell emerges, which makes the bottom of the cup shell in three-dimensional stress state and the stress in punch fillet region decrease due to powder reaction force, which can effectively inhibit the sever thinning of the sheet and prevent the generation of fracture defects. 展开更多
关键词 cup shell POWDER cavity flexible forming drawing finite element simulation
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WORKING LIQUID PRESSURE AND ITS CONTROL IN HYDRAULIC DRAWING PROCESSES OF CUPS
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作者 Liu Yan,Bai Shujie,Kang Guosheng,Li Tianyou (Department of Mechanical Engineering, Taiyuan Heavy Machinery Institute) 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2001年第3期279-281,285,共4页
A method of setting up a pressure-stroke characteristic of the working liquid in hydraulic drawing is studied. A pressure-stroke characteristic and software for controlling its forming process are also developed. An... A method of setting up a pressure-stroke characteristic of the working liquid in hydraulic drawing is studied. A pressure-stroke characteristic and software for controlling its forming process are also developed. And a set of pressure controlling devices with PLC as a central processor are designed. It can be got from the relevant experiments that the pressure-stroke characteristic is correct and its control for forming process is available. 展开更多
关键词 Hydraulic drawing Working liquid pressure Pressure control
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Theoretical and Experimental Analysis of Deep Drawing Cylindrical Cup
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作者 Najmeddin Arab Abotaleb Javadimanesh 《Journal of Minerals and Materials Characterization and Engineering》 2013年第6期336-342,共7页
There are mainly two methods of deep drawing analysis: experimental and analytical/numerical. Experimental analysis can be useful in analyzing the process to determine the process parameters that produce a defect free... There are mainly two methods of deep drawing analysis: experimental and analytical/numerical. Experimental analysis can be useful in analyzing the process to determine the process parameters that produce a defect free product, and the analytical/numerical modeling can be used to model and analyze the process through all stages of deformation. This approach is less time consuming and more economical. Sheet metal forming often includes biaxial in-plane deformation with non-proportional strain paths. In deep drawing of cylindrical cup, the deformation in the flange is dominated by pure shear deformation, while it changes to plane strain when the material is drawn into the die. This paper deals with the analysis of deep drawing of circular blanks into axi-symmetric cylindrical cup using numerical modeling. The blank drawability has been related both theoretically and experimentally with the initial diameter of the blank and deep drawing parameters. The strains in the radial and circumferential directions have been measured. A correlation on the flange thickness variation by taking into account the work hardening with the analytical and experimental values also has been searched. 展开更多
关键词 Deep drawING CYLINDRICAL Cup Sheet Metal FORMING Analytical Analysis
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THE INTEGRAL AS A FUNCTlON OF THE UPPER LIMIT AND DEPENDING ON A PARAMETER TO SOLVE DRAWING THROUGH IDLING ROLLS
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作者 赵德文 赵志业 张强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第1期93-100,共8页
The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an... The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an analylical upper-bound solution todrawing stress through idling rolls has been obtained in this paper. 展开更多
关键词 drawing through idling rolls integral as a function of theupper limit. integration depending on a parameter analyticalsolution
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