柔性电子卷到卷制造收卷内应力研究综述
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摘要
卷到卷制造是通过柔性基板成卷连续加工的制造技术,充分利用了柔性电子可变形特性,是实现柔性电子大面积、规模化制造的最有效技术途径之一.收卷单元是卷到卷连续制造系统的必要组成,其内应力控制是影响柔性电子成品质量与生产效率的关键因素.本文详细介绍了柔性基板卷绕收卷内应力研究概况,重点综述了基于叠加原理的弹性力学方法、开尔文模型的拉普拉斯变换方法、松弛半径概念的离散建模方法和有限元方法等建立的收卷内应力研究模型;讨论了收卷速度造成的惯性力变化、基板厚度不均及弹性变形、环境温度与卷绕基板各层间卷入空气夹层、以及收卷单元压辊与气胀轴结构因素对收卷内应力的影响;分析了常用锥张力、恒张力等收卷内应力控制方法,并介绍了柔性RFID标签、燃料电池膜电极和柔性OLED等代表性柔性电子卷到卷制造系统中收卷内应力控制工程应用;最后提出了柔性电子卷到卷制造系统中收卷内应力进一步研究的关键问题:非均匀非等厚基板引起周向应力分布变化和层间接触不连续,并展望了收卷内应力研究方向.
Flexible electronics has been widely used in many main-stream applications like flexible display, thin-film solar cell, RFID tags, flexible sensors, and so on. Roll-to-roll(R2R) is a kind of method by which flexible substrate can be processed in a continuous way. This kind of method saves time, cost, reduces delay time and increases efficiency, throughput, performance, etc. The typical R2 R system mainly consists of unwinding unit, feeding unit and winding unit, where deviation rectification control, tension control, vibration control and position control are needed. By taking full advantages of the deformation characteristics of flexible electronics, the R2R process has become one of the most effective ways in manufacturing flexible electronics. The winding unit is an essential part in the R2R system and the control of the wound roll stress in winding process is one of the main factors affecting the quality and productivity of flexible electronics. A tiny wound roll stress will cause difficulties in storage and transportation. The substrates or the electronic circuits mounted on it may be broken when the wound roll stress is too large. This paper begins with the discussion of common issues and the influence of wound roll stress in winding process. Currently, the web tension and its lateral position are two factors that mainly affect the wound roll stress. The wound roll stress will increase with the augment of the web tension. While a variation of lateral position can cause non-uniform wound roll stress in cross machine direction. Subsequently, the modelling methods and solution methods based on elastic mechanics, Laplace transformation, discrete modelling and finite element method are generalized. The four models are called elastic winding model, viscoelastic winding model, pseudo winding model and FEM winding model respectively. The elastic model is derived to predict wound roll stress of the elastic web. The viscoelastic model is developed to study how the wound roll stress changes with time after winding. In the pseudo model and the FEM model, the effect of thickness variation along the width direction is considered. Then this review analyses the effects of winding speed-induced inertia force, web deformation and its inhomogeneous thickness, temperature, air entrainment, structure of the nip roller and the core shaft on the wound roll stress. The taper tension control and constant tension control methods for wound roll stress and engineering applications in RFID tag packaging, seal lamination and flexible OLED manufacturing are also presented. Finally, this paper forecasts the key problems need to be further studied for the wound roll stress in winding process. The study of wound roll stress may focusing on the following aspects:(1) Conducting wound roll stress studies that considering the effect of thickness variation in machine direction;(2) usually we consider the wound roll as an axisymmetric cylinder, so it is necessary to develop a winding model to deal with the helical structure of the wound roll;(3) when deriving winding models, it's necessary to consider the discontinuous contact between layers.
Flexible electronics has been widely used in many main-stream applications like flexible display, thin-film solar cell, RFID tags, flexible sensors, and so on. Roll-to-roll(R2R) is a kind of method by which flexible substrate can be processed in a continuous way. This kind of method saves time, cost, reduces delay time and increases efficiency, throughput, performance, etc. The typical R2 R system mainly consists of unwinding unit, feeding unit and winding unit, where deviation rectification control, tension control, vibration control and position control are needed. By taking full advantages of the deformation characteristics of flexible electronics, the R2R process has become one of the most effective ways in manufacturing flexible electronics. The winding unit is an essential part in the R2R system and the control of the wound roll stress in winding process is one of the main factors affecting the quality and productivity of flexible electronics. A tiny wound roll stress will cause difficulties in storage and transportation. The substrates or the electronic circuits mounted on it may be broken when the wound roll stress is too large. This paper begins with the discussion of common issues and the influence of wound roll stress in winding process. Currently, the web tension and its lateral position are two factors that mainly affect the wound roll stress. The wound roll stress will increase with the augment of the web tension. While a variation of lateral position can cause non-uniform wound roll stress in cross machine direction. Subsequently, the modelling methods and solution methods based on elastic mechanics, Laplace transformation, discrete modelling and finite element method are generalized. The four models are called elastic winding model, viscoelastic winding model, pseudo winding model and FEM winding model respectively. The elastic model is derived to predict wound roll stress of the elastic web. The viscoelastic model is developed to study how the wound roll stress changes with time after winding. In the pseudo model and the FEM model, the effect of thickness variation along the width direction is considered. Then this review analyses the effects of winding speed-induced inertia force, web deformation and its inhomogeneous thickness, temperature, air entrainment, structure of the nip roller and the core shaft on the wound roll stress. The taper tension control and constant tension control methods for wound roll stress and engineering applications in RFID tag packaging, seal lamination and flexible OLED manufacturing are also presented. Finally, this paper forecasts the key problems need to be further studied for the wound roll stress in winding process. The study of wound roll stress may focusing on the following aspects:(1) Conducting wound roll stress studies that considering the effect of thickness variation in machine direction;(2) usually we consider the wound roll as an axisymmetric cylinder, so it is necessary to develop a winding model to deal with the helical structure of the wound roll;(3) when deriving winding models, it's necessary to consider the discontinuous contact between layers.
引文
1 Geller T.The promise of flexible displays.Association for Computing Machinery,2011,54:16-18
2 Yoon J,Baca A J,Park S I,et al.Ultrathin silicon solar microcells for semitransparent,mechanically flexible and microconcentrator module designs.Nat Mater,2008,7:907-915
3 Rogers J A,Someya T,Huang Y.Materials and mechanics for stretchable electronics.Science,2010,327:1603-1607
4 Park S,Vosguerichian M,Bao Z.A review of fabrication and applications of carbon nanotube film-based flexible electronics.Nanoscale,2013,5:1727
5 El-Kady M F,Strong V,Dubin S,et al.Laser scribing of high-performance and flexible graphene-based electrochemical capacitors.Science,2012,335:1326-1330
6 Nomura K,Ohta H,Takagi A,et al.Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors.Nature,2004,432:488-492
7 Kim D,Lu N.Epidermal electronics.Science,2011,333:838-843
8 Nathan A,Ahnood A,Hiralal P,et al.Flexible electronics:The next ubiquitous platform.Proc IEEE,2012,100:1486-1517
9 Allen K J.Reel to real:Prospects for flexible displays.Proc IEEE,2005,93:1394-1399
10 Huang M.Design and research on control system of lateral position of moving membrane web(in Chinese).Master Thesis.Wuhan:Wuhan University of Technology,2013[黄蒙.薄膜卷材纠偏控制系统设计与研究.硕士学位论文.武汉:武汉理工大学,2013]
11 Raul P R,Pagilla P R.Design and implementation of adaptive PI Control schemes for web tension control in roll-to-roll(R2R)manufacturing.ISA Trans,2015,56:276-287
12 Ma L,Chen J K,Tang W,et al.Vibration-based estimation of tension for an axially travelling web in roll-to-roll manufacturing.Meas Sci Technol,2017,133:752-758
13 Ye X B.Mechanism analysis and modeling of laminated position error for multi-layer flexible film(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2016[叶晓滨.多层柔性膜复合对位误差机理分析与建模.硕士学位论文.武汉:华中科技大学,2016]
14 Song X F.The research of tension control for high-accuracy winding vacuum film coating machine(in Chinese).Doctor Dissertation.Shanghai:Shanghai University,2007[宋晓峰.高精度卷绕真空镀膜设备张力控制技术研究.博士学位论文.上海:上海大学,2007]
15 Lin J H.Research on the rules of changing inner tension and the inertia force based on variable system(in Chinese).Master Thesis.Hangzhou:Zhejiang SCI-TECH University,2013[林佳辉.基于变质量系统的卷绕内张力变化规律研究.硕士学位论文.杭州:浙江理工大学,2013]
16 Yang Y J,Chen D C.The tension and its control upon rolling-up(in Chinese).Chin J Sci Instrum,2004,25:691-693[杨娅君,陈德传.收卷中的张力及其控制.仪器仪表学报,2004,25:691-693]
17 Li D.Research on tension control for winding system(in Chinese).Master Thesis.Xi’an:Xi’an University of Science and Technology,2007[李迪.卷绕系统中的张力控制研究.硕士学位论文.西安:西安科技大学,2007]
18 Catlow M G,Walls G W.A study of stress distribution in pirns.J Tex Inst Proc,1962,53:410-429
19 Altmann H C.Formulas for computing the stresses in center-wound rolls.Tappi J,1968,51:176-179
20 Pfeiffer J D.Internal pressures in a wound roll of paper.Tappi J,1966,49:342-347
21 Burns S J,Meehan R R,Lambropoulos J C.Strain-based formulas for stresses in profiled center-wound rolls.Tappi J,1999,82:159-167
22 Hakiel Z.Nonlinear model for wound roll stress,Tappi J,1987,70:113-117
23 Qualls W R,Good J K.An orthotropic viscoelastic winding model including a nonlinear radial stiffness.J Appl Mech,1997,64:201-208
24 Kokan D,Gramoll K.Development of a viscoelastic filament-winding process model.In:Structure,Structural Dynamics&Materials Conference,1996.1781-1787
25 Yu H W.Three-dimensional viscoelastic winding models for the analysis of baggy lanes formation.Doctor Dissertation.Oklahoma:Oklahoma State University,2007
26 Acton K,Weick B.Viscoelastic behavior of polymer tape in a wound roll.Mech Adv Mater Struct,2014,21:53-66
27 Cole A K,Hakiel Z.A nonlinear wound roll stress model accounting for widthwise web thickness nonuniformities.ASME,1992,149:13-14
28 Kedl D M.Using a two-dimensional winding model to predict wound roll stresses that occur due to circumferential steps in core diameter or to cross web caliper variation.In:Proceedings of the 2nd international Conference on Web Handling,1991.99-112
29 Hakiel Z.On the effect of width direction thickness variations in wound rolls.In:Proceedings of the 2nd international Conference on Web Handling,1991.79-98
30 Lee Y M,Wickert J A.Stress field in finite width axisymmetric wound rolls.J Appl Mech,2002,69:130-138
31 Murtaza K I.Verification of circumferential and axial strains in axisymmetric wound roll models.Doctor Dissertation.Oklahoma:Oklahoma State University,2009
32 Arola K,Hertzen R V.Two dimensional axisymmetric winding model for finite deformation.Comput Mech,2007,40:933-947
33 Timoshenko S P,Goodier J N.Theory of Elasticity.New York:McGraw-Hill,1970
34 Good J K,Mollamahmutoglu C,Markum R,et al.Residual winding stresses due to spatial web thickness variation.J Manuf Sci Eng,2017,139:031003
35 Sun H T.On survey of finite element method and analysis of its basic concepts(in Chinese).Shanxi Arch,2012,38:37-39[孙洪铁.有限单元法概述及其基本概念的分析.山西建筑,2012,38:37-39]
36 Hoffecker P.The analysis of a nip impinged three dimensional wound roll.Doctor Dissertation.Oklahoma:Oklahoma State University,2006
37 Mollamahmutoglu C,Good J K.Modeling the influence of web thickness and length imperfections resulting from manufacturing processes on wound roll stresses.CIRP Ann-Manuf Technol,2015,8:22-33
38 Yanabe S,Takahashi K,Yamashita T.Web winding simulation and wound roll stresses.J Adv Mech Des Syst Manuf,2010,4:281-289
39 Olsen J E.On the effect of centrifugal force on winding.Tappi J,1995,78:191-195
40 Yagoda H P.Centrifugally induced stresses within center wound rolls-part II.Mechanics Res Commun,1980,7:181-193
41 Benson R C.A nonlinear wound roll model allowing for large deformation.J Appl Mech,1995,62:853-859
42 Mollamahmutoglu C,Good J K.Analysis of large deformation wound roll models.J Appl Mech,2013,80:1016
43 Qualls W R,Good J K.Thermal analysis of a round roll.J Appl Mech,1997,64:871-876
44 Good J K,Holmberg M W.The effect of air entrainment in center wound rolls.In:Proceedings of the 2nd international Conference on Web Handling,1993.246-263
45 Tanimoto K,Kohno K,Takahashi S,et al.Wound stress of permeable papers with air-entrainment.Arch Appl Mech,2003,73:160-170
46 Good J K,Covell S M.Air entrainment and residual stresses in rolls wound with a rider roll.In:Proceedings of the 3rd International Conference on Web Handling,1995.95-112
47 Tanimoto K,Kohno K,Takahashi S.Numerical stress analysis of wound roll with air entrainment.Trans Jpn Soc Mech Eng Part A,2002,68:161-168
48 Mollamahmutoglu C.2D axis-symmetric wound roll model including nip effects.Doctor Dissertation.Oklahoma:Oklahoma State University,2009
49 Good J K,Wu Z.The mechanism of nip induced tension in wound rolls.J Appl Mech,1993,60:942-947
50 Deng N T,Zhang J Y,Xu J D.Analysis of web winding theory(in Chinese).Insul Mater,1986:8-13[邓乃绥,章兼源,徐景端.薄膜卷绕理论分析.绝缘材料,1986:8-13]
51 Rajannan D.The effect of web non homogeneity and core effects on wound roll stress.Doctor Dissertation.Oklahoma:Oklahoma State University,2011
52 Lee C W,Kang H,Shin K.Advanced taper tension method for the performance improvement of a roll-to-roll printing production line with a winding process.Int J Mech Sci,2012,59:61-72
53 Hashimoto H.Optimization of wind-up tension of webs preventing wrinkles and slippage.J Manuf Sci Eng,2009,131:054501
54 Yang Y J,Guo Y M.The stress distribution after the textile band rolled(in Chinese).J Tex Res,2003,24:56-58[杨娅君,郭乙木.纺织物带材收卷后的应力分布.纺织学报,2003,24:56-58]
55 Zhang H R,Wu D H,Nie J,et al.Optimal design of control tension in winding process for large wound roll(in Chinese).Meas Control Technol,2011,30:38-42[张海荣,吴德会,聂均,等.一种大卷装带材收卷过程中张力控制的优化设计方法.测控技术,2011,30:38-42]
56 Shao L.Study and application on tension control for flexible substrate transportation systems(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2012[邵琳.柔性薄膜卷绕输送系统中张力控制研究与应用.武汉:华中科技大学,2012]
57 Zhou C L.Modeling,simulation and experiment of tension control in flexible film discontinuous unwinding system(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2013[周春雷.柔性膜非连续放卷系统张力控制建模、仿真及实验.武汉:华中科技大学,2013]
58 Chen J K,Ying Z P,Xiong Y L.A conveyance method for discontinuous winding processes basedon synchronous position control(in Chinese).China Mech Eng,2010,14:1639-1642[陈建魁,尹周平,熊有伦.一种基于位置同步的非连续卷绕进给方法.中国机械工程,2010,14:1639-1642]
59 Zhang R.Study of lateral displacement control for flexible substrate(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2012[张锐.柔性基板横向偏移量控制方法研究.武汉:华中科技大学,2012]
60 Chen J K,Liu M H,Huang Y A,et al.High-rate roll-to-roll stack and lamination of multilayer structured membrane electrode assembly.J Manuf Process,2016,23:175-182
61 Mogck S,Wanski T,Lehmann C,et al.Present status of roll-to-roll OLED fabrication and encapsulation.J Jpn Soc Clr Mater,2013,86:461-465
2 Yoon J,Baca A J,Park S I,et al.Ultrathin silicon solar microcells for semitransparent,mechanically flexible and microconcentrator module designs.Nat Mater,2008,7:907-915
3 Rogers J A,Someya T,Huang Y.Materials and mechanics for stretchable electronics.Science,2010,327:1603-1607
4 Park S,Vosguerichian M,Bao Z.A review of fabrication and applications of carbon nanotube film-based flexible electronics.Nanoscale,2013,5:1727
5 El-Kady M F,Strong V,Dubin S,et al.Laser scribing of high-performance and flexible graphene-based electrochemical capacitors.Science,2012,335:1326-1330
6 Nomura K,Ohta H,Takagi A,et al.Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors.Nature,2004,432:488-492
7 Kim D,Lu N.Epidermal electronics.Science,2011,333:838-843
8 Nathan A,Ahnood A,Hiralal P,et al.Flexible electronics:The next ubiquitous platform.Proc IEEE,2012,100:1486-1517
9 Allen K J.Reel to real:Prospects for flexible displays.Proc IEEE,2005,93:1394-1399
10 Huang M.Design and research on control system of lateral position of moving membrane web(in Chinese).Master Thesis.Wuhan:Wuhan University of Technology,2013[黄蒙.薄膜卷材纠偏控制系统设计与研究.硕士学位论文.武汉:武汉理工大学,2013]
11 Raul P R,Pagilla P R.Design and implementation of adaptive PI Control schemes for web tension control in roll-to-roll(R2R)manufacturing.ISA Trans,2015,56:276-287
12 Ma L,Chen J K,Tang W,et al.Vibration-based estimation of tension for an axially travelling web in roll-to-roll manufacturing.Meas Sci Technol,2017,133:752-758
13 Ye X B.Mechanism analysis and modeling of laminated position error for multi-layer flexible film(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2016[叶晓滨.多层柔性膜复合对位误差机理分析与建模.硕士学位论文.武汉:华中科技大学,2016]
14 Song X F.The research of tension control for high-accuracy winding vacuum film coating machine(in Chinese).Doctor Dissertation.Shanghai:Shanghai University,2007[宋晓峰.高精度卷绕真空镀膜设备张力控制技术研究.博士学位论文.上海:上海大学,2007]
15 Lin J H.Research on the rules of changing inner tension and the inertia force based on variable system(in Chinese).Master Thesis.Hangzhou:Zhejiang SCI-TECH University,2013[林佳辉.基于变质量系统的卷绕内张力变化规律研究.硕士学位论文.杭州:浙江理工大学,2013]
16 Yang Y J,Chen D C.The tension and its control upon rolling-up(in Chinese).Chin J Sci Instrum,2004,25:691-693[杨娅君,陈德传.收卷中的张力及其控制.仪器仪表学报,2004,25:691-693]
17 Li D.Research on tension control for winding system(in Chinese).Master Thesis.Xi’an:Xi’an University of Science and Technology,2007[李迪.卷绕系统中的张力控制研究.硕士学位论文.西安:西安科技大学,2007]
18 Catlow M G,Walls G W.A study of stress distribution in pirns.J Tex Inst Proc,1962,53:410-429
19 Altmann H C.Formulas for computing the stresses in center-wound rolls.Tappi J,1968,51:176-179
20 Pfeiffer J D.Internal pressures in a wound roll of paper.Tappi J,1966,49:342-347
21 Burns S J,Meehan R R,Lambropoulos J C.Strain-based formulas for stresses in profiled center-wound rolls.Tappi J,1999,82:159-167
22 Hakiel Z.Nonlinear model for wound roll stress,Tappi J,1987,70:113-117
23 Qualls W R,Good J K.An orthotropic viscoelastic winding model including a nonlinear radial stiffness.J Appl Mech,1997,64:201-208
24 Kokan D,Gramoll K.Development of a viscoelastic filament-winding process model.In:Structure,Structural Dynamics&Materials Conference,1996.1781-1787
25 Yu H W.Three-dimensional viscoelastic winding models for the analysis of baggy lanes formation.Doctor Dissertation.Oklahoma:Oklahoma State University,2007
26 Acton K,Weick B.Viscoelastic behavior of polymer tape in a wound roll.Mech Adv Mater Struct,2014,21:53-66
27 Cole A K,Hakiel Z.A nonlinear wound roll stress model accounting for widthwise web thickness nonuniformities.ASME,1992,149:13-14
28 Kedl D M.Using a two-dimensional winding model to predict wound roll stresses that occur due to circumferential steps in core diameter or to cross web caliper variation.In:Proceedings of the 2nd international Conference on Web Handling,1991.99-112
29 Hakiel Z.On the effect of width direction thickness variations in wound rolls.In:Proceedings of the 2nd international Conference on Web Handling,1991.79-98
30 Lee Y M,Wickert J A.Stress field in finite width axisymmetric wound rolls.J Appl Mech,2002,69:130-138
31 Murtaza K I.Verification of circumferential and axial strains in axisymmetric wound roll models.Doctor Dissertation.Oklahoma:Oklahoma State University,2009
32 Arola K,Hertzen R V.Two dimensional axisymmetric winding model for finite deformation.Comput Mech,2007,40:933-947
33 Timoshenko S P,Goodier J N.Theory of Elasticity.New York:McGraw-Hill,1970
34 Good J K,Mollamahmutoglu C,Markum R,et al.Residual winding stresses due to spatial web thickness variation.J Manuf Sci Eng,2017,139:031003
35 Sun H T.On survey of finite element method and analysis of its basic concepts(in Chinese).Shanxi Arch,2012,38:37-39[孙洪铁.有限单元法概述及其基本概念的分析.山西建筑,2012,38:37-39]
36 Hoffecker P.The analysis of a nip impinged three dimensional wound roll.Doctor Dissertation.Oklahoma:Oklahoma State University,2006
37 Mollamahmutoglu C,Good J K.Modeling the influence of web thickness and length imperfections resulting from manufacturing processes on wound roll stresses.CIRP Ann-Manuf Technol,2015,8:22-33
38 Yanabe S,Takahashi K,Yamashita T.Web winding simulation and wound roll stresses.J Adv Mech Des Syst Manuf,2010,4:281-289
39 Olsen J E.On the effect of centrifugal force on winding.Tappi J,1995,78:191-195
40 Yagoda H P.Centrifugally induced stresses within center wound rolls-part II.Mechanics Res Commun,1980,7:181-193
41 Benson R C.A nonlinear wound roll model allowing for large deformation.J Appl Mech,1995,62:853-859
42 Mollamahmutoglu C,Good J K.Analysis of large deformation wound roll models.J Appl Mech,2013,80:1016
43 Qualls W R,Good J K.Thermal analysis of a round roll.J Appl Mech,1997,64:871-876
44 Good J K,Holmberg M W.The effect of air entrainment in center wound rolls.In:Proceedings of the 2nd international Conference on Web Handling,1993.246-263
45 Tanimoto K,Kohno K,Takahashi S,et al.Wound stress of permeable papers with air-entrainment.Arch Appl Mech,2003,73:160-170
46 Good J K,Covell S M.Air entrainment and residual stresses in rolls wound with a rider roll.In:Proceedings of the 3rd International Conference on Web Handling,1995.95-112
47 Tanimoto K,Kohno K,Takahashi S.Numerical stress analysis of wound roll with air entrainment.Trans Jpn Soc Mech Eng Part A,2002,68:161-168
48 Mollamahmutoglu C.2D axis-symmetric wound roll model including nip effects.Doctor Dissertation.Oklahoma:Oklahoma State University,2009
49 Good J K,Wu Z.The mechanism of nip induced tension in wound rolls.J Appl Mech,1993,60:942-947
50 Deng N T,Zhang J Y,Xu J D.Analysis of web winding theory(in Chinese).Insul Mater,1986:8-13[邓乃绥,章兼源,徐景端.薄膜卷绕理论分析.绝缘材料,1986:8-13]
51 Rajannan D.The effect of web non homogeneity and core effects on wound roll stress.Doctor Dissertation.Oklahoma:Oklahoma State University,2011
52 Lee C W,Kang H,Shin K.Advanced taper tension method for the performance improvement of a roll-to-roll printing production line with a winding process.Int J Mech Sci,2012,59:61-72
53 Hashimoto H.Optimization of wind-up tension of webs preventing wrinkles and slippage.J Manuf Sci Eng,2009,131:054501
54 Yang Y J,Guo Y M.The stress distribution after the textile band rolled(in Chinese).J Tex Res,2003,24:56-58[杨娅君,郭乙木.纺织物带材收卷后的应力分布.纺织学报,2003,24:56-58]
55 Zhang H R,Wu D H,Nie J,et al.Optimal design of control tension in winding process for large wound roll(in Chinese).Meas Control Technol,2011,30:38-42[张海荣,吴德会,聂均,等.一种大卷装带材收卷过程中张力控制的优化设计方法.测控技术,2011,30:38-42]
56 Shao L.Study and application on tension control for flexible substrate transportation systems(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2012[邵琳.柔性薄膜卷绕输送系统中张力控制研究与应用.武汉:华中科技大学,2012]
57 Zhou C L.Modeling,simulation and experiment of tension control in flexible film discontinuous unwinding system(in Chinese).Master Thesis.Wuhan:Huazhong University of Science and Technology,2013[周春雷.柔性膜非连续放卷系统张力控制建模、仿真及实验.武汉:华中科技大学,2013]
58 Chen J K,Ying Z P,Xiong Y L.A conveyance method for discontinuous winding processes basedon synchronous position control(in Chinese).China Mech Eng,2010,14:1639-1642[陈建魁,尹周平,熊有伦.一种基于位置同步的非连续卷绕进给方法.中国机械工程,2010,14:1639-1642]
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