超声振动拉丝相关理论及其实验研究
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摘要
常规拉丝加工过程中,金属丝材在拉丝模的变形和成形区域内,由于变形剧烈、变形力和摩擦力大,容易出现断丝和表面及内部缺陷,而且在没有进行表面润滑处理的情况下无法进行钛和钛合金等难加工材料的加工。研究表明,超声振动拉拔的应用能够很好地解决这些问题。为此,开展超声振动拉丝的相关理论和实验研究,具有重要的意义。基于以上目的,本文对超声振动拉丝的数学模型、超声振动拉丝过程的模拟、正交复合超声振动拉丝以及难拉拔材料的超声振动拉丝等方面进行了深入的研究。
分别对常规拉丝和超声振动拉丝工作状态进行力学分析,在确立拉丝模及丝材在定径区和减径区的力学平衡微分方程的基础上,引入Oden提出的非局部摩擦理论代替经典的库仑摩擦模型,结合Taylor级数和Mises屈服准则,建立了定径区和减径区的摩擦应力分布、接触压力分布及拉拔力的数学模型,并通过MATLAB?编程进行了数值计算,该数学模型探讨并量化研究了超声振动拉丝的拉拔力及摩擦等影响因素。
利用有限元分析软件ANSYS?对超声振动拉丝及常规拉丝过程进行了模拟。在超声振动拉丝仿真过程中,将超声频率振动的简谐波变为同频率、同相位、同振幅的三角波,利用“同步加载,多步求解”的新方法解决了仿真中对拉丝模难于施加超声频率振动的问题,从而实现了超声振动拉丝过程的模拟仿真。对超声振动拉丝和常规拉丝的变形与应变、应力与拉拔力、接触面摩擦等仿真结果进行了重点分析,并与数学模型所得结果进行了比较。
分别采用经典动力学法和四端网络法设计并研制了超声振动系统,并对振子进行了动力学特性分析(包括模态分析、谐响应分析和瞬态分析)。对超声振动系统进行了电端匹配调试,并利用Polytec PSV-400-M2(德国)扫描式激光测振仪、HP4294A阻抗分析仪等仪器设备对振动装置进行了测试,获得了其振动性能参数。
为促进超声振动拉丝技术的实际应用,同哈尔滨电缆厂合作,以LH-200/17型拉丝机作为实验平台,进行了接近实际生产状态的超声振动拉拔铜丝(进线直径0.3mm,出线直径0.26mm,减缩率13.3%)实验。获得了拉丝速度对拉拔力的影响关系以及张力调节周期的变化规律。结果表明:施加超声振动可使拉拔力减小约7%;可有效延长张力调节周期3倍以上;超声振动可使拉拔力奇异尖峰的出现几率以及断丝现象明显减少,这些因素促使拉丝过程更加稳定。SEM扫描电镜照片表明,超声振动减少了金属丝材的表面划痕、凹坑等缺陷,提高了金属丝材的表面质量。通过金相观察和分析,表明超声振动能量能较好地传递到金属内部,缓和了晶粒的变形和晶格的畸变,减轻了加工硬化,改善了材料的使用性能和工艺性能。
最后,针对不同施振方式的作用效果、当前难拉拔材料的加工困难以及特种加工需求日益增长等问题,本文建立了一套正交复合超声振动拉丝实验系统,针对铜丝施加纵向振动、径向振动及正交复合振动三种形式的拉拔实验,通过测试和观察各种超声振动状态下的拉拔力和丝材表面形貌,结果表明:正交复合超声振动比其它两种振动形式更显著地降低了拉拔力和延长了张力调节周期,基本消除了断丝现象。采用正交复合超声振动系统对不锈钢丝和纯钛丝进行了拉拔实验,实现了不锈钢丝和纯钛丝不经过预处理的直接超声拉制,该结果表明正交复合超声振动能够更有效地解决难拉拔材料的加工问题,打破了国内行业纯钛丝不能直接拉制的局面。
本文的研究工作将在航空航天、装备制造、医疗器械、信息产业以及汽车工业等诸多领域具有广阔的应用前景,将在提高拉丝生产的效率、难拉拔材料加工以及超细丝的拉拔生产方面带来巨大的市场经济效益。
In the conventional wire drawing process, the deforming force and friction due to the acute deformation are great. Therefore, the broken wire and rough surface often come into being. The drawing of difficult-to-draw materials, such as the pure titanium, titanium alloys and the ultra fine-metal wire, can not been processed. In order to solve these problems, it is urgency to study the technology of ultrasonic-vibration drawing, and explore the effective technology and method. Hence, the mathematical model of the mechanism of ultrasonic drawing, the simulation of ultrasonic drawing, and composite ultrasonic-vibration wire drawing and the drawing of difficult-to-draw materials with ultrasonic were comprehensively studied in this dissertation.
Firstly, the mechanics analysis of the technology for the conventional and ultrasonic vibration drawing was performed. The force equilibrium equations in the calibrating strap and the reducing strap were built. The non-local friction theory presented by Oden was used in stead of the classical Column friction model. The Taylor series and the Mises yield criterion were used. The mathematical model on friction distribution, contact pressure distribution and the drawing force in the calibrating and reducing straps were built. A numerical method was developed in MATLAB?. This mathematical model provides method and theoretical support for the research on the drawing force and friction of the ultrasonic vibration drawing.
Secondly, simulation of the conventional and ultrasonic vibration drawing was carried out in ANSYS?. A new approach of same-step loading, multi-step solving was developed by reasonable simplification that the sine wave of ultrasonic vibration is transformed into the triangle wave, which has the same frequency, phase and amplitude of vibration as the sine wave. The difficulty on how to transferring ultrasonic vibration to the drawing dies is solved. The results of the drawing force, deformation, stress, strain and friction in the ultrasonic vibration drawing simulation were analyzed and compared with those in the conventional drawing simulation and the results obtained by the above mathematical model.
Then, the ultrasonic vibration system was designed and manufactured by using the classical dynamics method and the four-terminal network method. The dynamic characteristic of the transducer (including modal analysis, harmonic response analysis and transient analysis) was analyzed. The electricity matching of the ultrasonic vibration system was tested. The performance parameters of the system were measured on the Polytec PSV-400-M2 laser vibration meter and HP4294A resistance analyzer.
In order to promote the practical application of the technology, the wire drawing using ultrasonic vibration at the speed of practice was carried out firstly on the LH-200/17 drawing machine in Harbin Cable Factory. The affect of the speed on the drawing force was obtained and the changing regular of the periodic of the tension regulator. The results show that the drawing force reduced by 4%, and the ultrasound vibration effectively prolongs the period of tension regulation more than 3 times. And the regular tips of the drawing force and the broken wire were obviously reduced. These factors make the drawing process stable, and greatly improve the unevenness of the surface of the products. The results demonstrate that the drawing with ultrasound can increase the processing efficiency, reduce the power cost. The SEM pictures show that the ultrasonic vibration improves the contact status between the wire and the die, reduce the scratch marks and pits on the wire surface, and improve the surface quality. This demonstrates that the vibrating energy can be effectively transferred to the internal of the wire, which can gentle the deformation of the crystal and distortion of the crystal lattice and reduce processing hardening and improve the service performance and processing properties.
Finally, a composite ultrasonic-vibration system for the ultrasonic drawing was developed, by considering the different effects caused by different types of ultrasonic vibration, processing difficulties of the difficult-to-draw material and the expanding demand of non-conventional machining. The convenient, brief and reliable design method for the ultrasonic transducer was explored. In experiments, the three kinds of forms of ultrasonic vibration (longitudinal, radial and composite) were applied on the brass wire. The drawing force and the topography of the drawn wire were measured. The results show that the effect of the composite vibrating form is best. It can more effectively reduce the drawing force and prolong the periodicity of tension regulation. It almost eliminates the phenomena of broken wire. The stainless steel wire and the pure titanium wire were directly drawn in the composite ultrasonic vibrating system. Their success break the domestic deadlock of direct drawing for the pure titanium wire the, and demonstrates that the composite vibrating system can effective solve the processing problem of the difficult-to-draw material.
The present work will be widely used aerospace, equipment manufacturing, medical device, information industry and automobile industry. It will bring great market economic returns in the aspects of reducing drawing force, improving processing efficiency and processing difficult-to-draw material.
分别对常规拉丝和超声振动拉丝工作状态进行力学分析,在确立拉丝模及丝材在定径区和减径区的力学平衡微分方程的基础上,引入Oden提出的非局部摩擦理论代替经典的库仑摩擦模型,结合Taylor级数和Mises屈服准则,建立了定径区和减径区的摩擦应力分布、接触压力分布及拉拔力的数学模型,并通过MATLAB?编程进行了数值计算,该数学模型探讨并量化研究了超声振动拉丝的拉拔力及摩擦等影响因素。
利用有限元分析软件ANSYS?对超声振动拉丝及常规拉丝过程进行了模拟。在超声振动拉丝仿真过程中,将超声频率振动的简谐波变为同频率、同相位、同振幅的三角波,利用“同步加载,多步求解”的新方法解决了仿真中对拉丝模难于施加超声频率振动的问题,从而实现了超声振动拉丝过程的模拟仿真。对超声振动拉丝和常规拉丝的变形与应变、应力与拉拔力、接触面摩擦等仿真结果进行了重点分析,并与数学模型所得结果进行了比较。
分别采用经典动力学法和四端网络法设计并研制了超声振动系统,并对振子进行了动力学特性分析(包括模态分析、谐响应分析和瞬态分析)。对超声振动系统进行了电端匹配调试,并利用Polytec PSV-400-M2(德国)扫描式激光测振仪、HP4294A阻抗分析仪等仪器设备对振动装置进行了测试,获得了其振动性能参数。
为促进超声振动拉丝技术的实际应用,同哈尔滨电缆厂合作,以LH-200/17型拉丝机作为实验平台,进行了接近实际生产状态的超声振动拉拔铜丝(进线直径0.3mm,出线直径0.26mm,减缩率13.3%)实验。获得了拉丝速度对拉拔力的影响关系以及张力调节周期的变化规律。结果表明:施加超声振动可使拉拔力减小约7%;可有效延长张力调节周期3倍以上;超声振动可使拉拔力奇异尖峰的出现几率以及断丝现象明显减少,这些因素促使拉丝过程更加稳定。SEM扫描电镜照片表明,超声振动减少了金属丝材的表面划痕、凹坑等缺陷,提高了金属丝材的表面质量。通过金相观察和分析,表明超声振动能量能较好地传递到金属内部,缓和了晶粒的变形和晶格的畸变,减轻了加工硬化,改善了材料的使用性能和工艺性能。
最后,针对不同施振方式的作用效果、当前难拉拔材料的加工困难以及特种加工需求日益增长等问题,本文建立了一套正交复合超声振动拉丝实验系统,针对铜丝施加纵向振动、径向振动及正交复合振动三种形式的拉拔实验,通过测试和观察各种超声振动状态下的拉拔力和丝材表面形貌,结果表明:正交复合超声振动比其它两种振动形式更显著地降低了拉拔力和延长了张力调节周期,基本消除了断丝现象。采用正交复合超声振动系统对不锈钢丝和纯钛丝进行了拉拔实验,实现了不锈钢丝和纯钛丝不经过预处理的直接超声拉制,该结果表明正交复合超声振动能够更有效地解决难拉拔材料的加工问题,打破了国内行业纯钛丝不能直接拉制的局面。
本文的研究工作将在航空航天、装备制造、医疗器械、信息产业以及汽车工业等诸多领域具有广阔的应用前景,将在提高拉丝生产的效率、难拉拔材料加工以及超细丝的拉拔生产方面带来巨大的市场经济效益。
In the conventional wire drawing process, the deforming force and friction due to the acute deformation are great. Therefore, the broken wire and rough surface often come into being. The drawing of difficult-to-draw materials, such as the pure titanium, titanium alloys and the ultra fine-metal wire, can not been processed. In order to solve these problems, it is urgency to study the technology of ultrasonic-vibration drawing, and explore the effective technology and method. Hence, the mathematical model of the mechanism of ultrasonic drawing, the simulation of ultrasonic drawing, and composite ultrasonic-vibration wire drawing and the drawing of difficult-to-draw materials with ultrasonic were comprehensively studied in this dissertation.
Firstly, the mechanics analysis of the technology for the conventional and ultrasonic vibration drawing was performed. The force equilibrium equations in the calibrating strap and the reducing strap were built. The non-local friction theory presented by Oden was used in stead of the classical Column friction model. The Taylor series and the Mises yield criterion were used. The mathematical model on friction distribution, contact pressure distribution and the drawing force in the calibrating and reducing straps were built. A numerical method was developed in MATLAB?. This mathematical model provides method and theoretical support for the research on the drawing force and friction of the ultrasonic vibration drawing.
Secondly, simulation of the conventional and ultrasonic vibration drawing was carried out in ANSYS?. A new approach of same-step loading, multi-step solving was developed by reasonable simplification that the sine wave of ultrasonic vibration is transformed into the triangle wave, which has the same frequency, phase and amplitude of vibration as the sine wave. The difficulty on how to transferring ultrasonic vibration to the drawing dies is solved. The results of the drawing force, deformation, stress, strain and friction in the ultrasonic vibration drawing simulation were analyzed and compared with those in the conventional drawing simulation and the results obtained by the above mathematical model.
Then, the ultrasonic vibration system was designed and manufactured by using the classical dynamics method and the four-terminal network method. The dynamic characteristic of the transducer (including modal analysis, harmonic response analysis and transient analysis) was analyzed. The electricity matching of the ultrasonic vibration system was tested. The performance parameters of the system were measured on the Polytec PSV-400-M2 laser vibration meter and HP4294A resistance analyzer.
In order to promote the practical application of the technology, the wire drawing using ultrasonic vibration at the speed of practice was carried out firstly on the LH-200/17 drawing machine in Harbin Cable Factory. The affect of the speed on the drawing force was obtained and the changing regular of the periodic of the tension regulator. The results show that the drawing force reduced by 4%, and the ultrasound vibration effectively prolongs the period of tension regulation more than 3 times. And the regular tips of the drawing force and the broken wire were obviously reduced. These factors make the drawing process stable, and greatly improve the unevenness of the surface of the products. The results demonstrate that the drawing with ultrasound can increase the processing efficiency, reduce the power cost. The SEM pictures show that the ultrasonic vibration improves the contact status between the wire and the die, reduce the scratch marks and pits on the wire surface, and improve the surface quality. This demonstrates that the vibrating energy can be effectively transferred to the internal of the wire, which can gentle the deformation of the crystal and distortion of the crystal lattice and reduce processing hardening and improve the service performance and processing properties.
Finally, a composite ultrasonic-vibration system for the ultrasonic drawing was developed, by considering the different effects caused by different types of ultrasonic vibration, processing difficulties of the difficult-to-draw material and the expanding demand of non-conventional machining. The convenient, brief and reliable design method for the ultrasonic transducer was explored. In experiments, the three kinds of forms of ultrasonic vibration (longitudinal, radial and composite) were applied on the brass wire. The drawing force and the topography of the drawn wire were measured. The results show that the effect of the composite vibrating form is best. It can more effectively reduce the drawing force and prolong the periodicity of tension regulation. It almost eliminates the phenomena of broken wire. The stainless steel wire and the pure titanium wire were directly drawn in the composite ultrasonic vibrating system. Their success break the domestic deadlock of direct drawing for the pure titanium wire the, and demonstrates that the composite vibrating system can effective solve the processing problem of the difficult-to-draw material.
The present work will be widely used aerospace, equipment manufacturing, medical device, information industry and automobile industry. It will bring great market economic returns in the aspects of reducing drawing force, improving processing efficiency and processing difficult-to-draw material.
引文
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46刘新忠,孟永刚,苗金鱼.超声波在塑性加工中的应用研究.锻压技术.1998,(5):12~16
47曲建俊,姜开利,张凯,周铁英.超声驱动的超声波振动减摩作用研究.声学学报. 2001,26(6):497~502
48凌尔昌.功率超声在金属丝材加工中的应用.声学技术. 1982,(1):35~36
49 N. Maropis. Ultrasonic Energy Applied to Metal Drawing, Part I/Ⅱ/III. Wire Industry. 1991,58(5):251~256;58(6):327~333;58(7):371~373
50郑双.超声波拉丝机理及实验设备的研究.哈尔滨工业大学硕士学位论文. 2004
51 G. R. Dawson, C. E. Winsper, D. H. Sansome. Application of High and Low Frequency Oscillations to the Plastic Deformation of Metal. Metal Forming. 1970(8):234~238
52曹乃光.金属塑性加工原理.北京:冶金工业出版社. 1983
53 F. Blaha, B. Langenecker, D. Oelschlaegel. Zum Plastischen Verhalten von Metallen unter Schalleinwirkung. Z.Metallkde. 1960,51(11):636~638
54 K. F. Graff. Ultrasonics: History Aspects. 1977 Ultrasonics Symposium Proceedings, Phoenix. Oct 1977.
55 G. E. Nevill, F. R. Brotzen. The Effect of Vibration on the Static Yield Strength of Low-carbon Steel. Proc. Am. Soc. for testing materials. 1957,57:751~758
56 C. E. Winsper, D. H. Sansome. Fundamentals of“Ultrasonic”Wire Drawing. Journal of the Institute of Metals. 1969,97:274~280
57王仲仁,张旭.试论塑性加工的实质是“力处理”.塑性工程学报. 1997,4(3):9~13
58徐秉业,刘信声.应用弹塑性力学.北京:清华大学出版社. 1983
59孟永刚,刘新忠,陈军.超声波在拉丝中的减摩降载作用研究.清华大学学报(自然科学版). 1999,(38):28~32
60程光明,曾平,邱晓阳,铃木胜羲,广濑精二.超声振动减摩现象的研究.压电与声光. 1998,20(5):322~325
61吴博达,常颖,杨志刚,田丰君.超声振动减摩性能的实验研究及理论分析.中国机械工程. 2004,15(9):813~815
62 V. C. Kumar, I. M. Hutchings. Reduction of the Sliding Friction of Metals by the Application of Longitudinal or Transverse Ultrasonic Vibration. Tribology Internationaletal. 2004(37):833~840
63 M. Susan, L. G. Bujoreanu, D. G. G?lu?c?, C. Munteanu, M. Mantu. On theDrawing in Ultrasonic Field of Metallic Wires with High Mechanical Resistance. Journal of Optoelectronics and Advanced Materials. 2005,7(2): 637~645
64 M. Hayashi, M. Jin, S. Thipprakmas, M. Murakawa. Simulation of Ultrasonic-vibration Drawing Using the Finite Element Method (FEM). Journal of Materials Processing Technology. 2003,140:30~35
65 G. Gentsch. Anwendung von Ultraschallschwingungen bei Umformverfahren. Baeder Bleche Rohre. 1968,9(6):354~363
66 J. Gebhardt, P. Funke. Ziehen von Drahtenmi Tuber Lagerten Ultraschall Sch- wingungen-TeilI/II, Draht. 1983,34(5):199~204;34(6):297~301
67 N. Maropis. The Application of Ultrasonic Vibratory Energy to Metal Drawing. Wire Industry, PartI: 1991,58(689):251~256, Part II: (690):327~333, Part III: (691):371~373
68 T. Jimma, Y. Kasuga. An Application of Ultrasonics Vibration to Deep Drawing Process. Materials Processing Technology. 1998(80):406~412
69 K. Siegert, J. Ulmer. Superimposing Ultrasonic Waves on the Dies in Tube and Wire Drawing. Journal of Engineering Materials and Technology. 2001,(123):517~523
70 M. Murakawa, M. Jin, M. Hayashi. Study on Semidry/Dry Wire Drawing Using DLC Coated Dies. Surface and Coating Technology. 2004,(177):631~ 637
71李连诗,杨效平.超声波振动拔管换能器设计.钢管. 1994,(2):20~25
72 L. S. Li, X. P. Lang. Studies of Wire Drawing with Ultrasonic Vibration. Wire Industry. 1994,61:31~33,39
73 J. T. Oden, E. B. Pires. Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity. Journal of Applied Mechanics, Transactions of the ASME. 1983,50:67~76
74扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用.力学季刊. 2001,22(1):112~116
75蔡改贫,翁海珊.振动拉拔的非局部摩擦问题的近似求解及表面效应初探.机械工程学报. 2006,42(8):190~193
76 B. Avitzur.王学文,等译.金属成形工艺与分析.国防工业出版社. 1988
77商跃进.有限元原理与ANSYS应用指南.清华大学出版社. 2005
78 K. C. Rockey. The Finite Element Method. London: Granada Publishing. 1983
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80 A. Ahmed, A. Fahim, H. Naguib. A Study on the Design and MechanicalAdhesion of Polymer Foam-Metal Joints. Journal of Engineering Materials and Technology. 2008,130:031011-1~7
81 A. Saito, M. P. Castanier, C. Pierre, O. Poudou. Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades. Journal of Computational and Nonlinear Dynamics. 2009,4:011005-1~10
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44李连诗,张力行.超声波振动拔管拔丝的研究.钢铁. 1995,30(3):39~44
45赵学涛,陈维山,刘军考,石胜君.三种基于夹心式换能器驱动的球形超声马达设计.设计与研究. 2006,7:11~14
46刘新忠,孟永刚,苗金鱼.超声波在塑性加工中的应用研究.锻压技术.1998,(5):12~16
47曲建俊,姜开利,张凯,周铁英.超声驱动的超声波振动减摩作用研究.声学学报. 2001,26(6):497~502
48凌尔昌.功率超声在金属丝材加工中的应用.声学技术. 1982,(1):35~36
49 N. Maropis. Ultrasonic Energy Applied to Metal Drawing, Part I/Ⅱ/III. Wire Industry. 1991,58(5):251~256;58(6):327~333;58(7):371~373
50郑双.超声波拉丝机理及实验设备的研究.哈尔滨工业大学硕士学位论文. 2004
51 G. R. Dawson, C. E. Winsper, D. H. Sansome. Application of High and Low Frequency Oscillations to the Plastic Deformation of Metal. Metal Forming. 1970(8):234~238
52曹乃光.金属塑性加工原理.北京:冶金工业出版社. 1983
53 F. Blaha, B. Langenecker, D. Oelschlaegel. Zum Plastischen Verhalten von Metallen unter Schalleinwirkung. Z.Metallkde. 1960,51(11):636~638
54 K. F. Graff. Ultrasonics: History Aspects. 1977 Ultrasonics Symposium Proceedings, Phoenix. Oct 1977.
55 G. E. Nevill, F. R. Brotzen. The Effect of Vibration on the Static Yield Strength of Low-carbon Steel. Proc. Am. Soc. for testing materials. 1957,57:751~758
56 C. E. Winsper, D. H. Sansome. Fundamentals of“Ultrasonic”Wire Drawing. Journal of the Institute of Metals. 1969,97:274~280
57王仲仁,张旭.试论塑性加工的实质是“力处理”.塑性工程学报. 1997,4(3):9~13
58徐秉业,刘信声.应用弹塑性力学.北京:清华大学出版社. 1983
59孟永刚,刘新忠,陈军.超声波在拉丝中的减摩降载作用研究.清华大学学报(自然科学版). 1999,(38):28~32
60程光明,曾平,邱晓阳,铃木胜羲,广濑精二.超声振动减摩现象的研究.压电与声光. 1998,20(5):322~325
61吴博达,常颖,杨志刚,田丰君.超声振动减摩性能的实验研究及理论分析.中国机械工程. 2004,15(9):813~815
62 V. C. Kumar, I. M. Hutchings. Reduction of the Sliding Friction of Metals by the Application of Longitudinal or Transverse Ultrasonic Vibration. Tribology Internationaletal. 2004(37):833~840
63 M. Susan, L. G. Bujoreanu, D. G. G?lu?c?, C. Munteanu, M. Mantu. On theDrawing in Ultrasonic Field of Metallic Wires with High Mechanical Resistance. Journal of Optoelectronics and Advanced Materials. 2005,7(2): 637~645
64 M. Hayashi, M. Jin, S. Thipprakmas, M. Murakawa. Simulation of Ultrasonic-vibration Drawing Using the Finite Element Method (FEM). Journal of Materials Processing Technology. 2003,140:30~35
65 G. Gentsch. Anwendung von Ultraschallschwingungen bei Umformverfahren. Baeder Bleche Rohre. 1968,9(6):354~363
66 J. Gebhardt, P. Funke. Ziehen von Drahtenmi Tuber Lagerten Ultraschall Sch- wingungen-TeilI/II, Draht. 1983,34(5):199~204;34(6):297~301
67 N. Maropis. The Application of Ultrasonic Vibratory Energy to Metal Drawing. Wire Industry, PartI: 1991,58(689):251~256, Part II: (690):327~333, Part III: (691):371~373
68 T. Jimma, Y. Kasuga. An Application of Ultrasonics Vibration to Deep Drawing Process. Materials Processing Technology. 1998(80):406~412
69 K. Siegert, J. Ulmer. Superimposing Ultrasonic Waves on the Dies in Tube and Wire Drawing. Journal of Engineering Materials and Technology. 2001,(123):517~523
70 M. Murakawa, M. Jin, M. Hayashi. Study on Semidry/Dry Wire Drawing Using DLC Coated Dies. Surface and Coating Technology. 2004,(177):631~ 637
71李连诗,杨效平.超声波振动拔管换能器设计.钢管. 1994,(2):20~25
72 L. S. Li, X. P. Lang. Studies of Wire Drawing with Ultrasonic Vibration. Wire Industry. 1994,61:31~33,39
73 J. T. Oden, E. B. Pires. Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity. Journal of Applied Mechanics, Transactions of the ASME. 1983,50:67~76
74扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用.力学季刊. 2001,22(1):112~116
75蔡改贫,翁海珊.振动拉拔的非局部摩擦问题的近似求解及表面效应初探.机械工程学报. 2006,42(8):190~193
76 B. Avitzur.王学文,等译.金属成形工艺与分析.国防工业出版社. 1988
77商跃进.有限元原理与ANSYS应用指南.清华大学出版社. 2005
78 K. C. Rockey. The Finite Element Method. London: Granada Publishing. 1983
79张胜民.基于有限元软件ANSYS7.0的结构分析.清华大学出版社. 2003
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