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气体输送管道轮式式机器人的设计,气体,输送,管道,轮式,机器人,设计
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machine tools. Proc ASME IMECE 04, Anaheim, CAL2l Farago F, Curtis MA （l994） Handbook of dimensional measurement. Industrial Press Inc. L22 Bosch JA （ed） （l995） Coordinate measuring machines and systems. Marcel Dekker, New YorkL23 Coelho AG, Mourao AF, Navas HG （2004） A rational way to select a measuring system for mechanical parts inspection. Proc of ICAD 04, Seoul, KoreaL24 Ramesh M, Yip-Hoi D, Dutta D （200l） Feature-based shape similarity measurement for retrieval ofmechanical parts. J Comput Inf Sci Eng l:245-256L25 Koren Y, Kota S （l999） Reconfigurable machine tool. US Patent # 5,943,750L26 Landers RG, Min BK, Koren Y （200l） Reconfigurable machine tools. Ann CIRP 50:269- 274L27 Katz R, Chung H （l999） Design of an experimental arch type reconfigurable machine tool. Proc 2000 JUSFA, 2000 Japan- USA Symposium on Flexible Automation, July 23-26, 2000, Ann Arbor, MIL28 Katz R, Yook J, Koren Y （2004） Control of reconfigurable machine tool. ASME J Dyn Syst Meas Control l26:397-405L29 Koren Y, Katz R （2003） Reconfigurable apparatus and method for Inspection during a Manufacturing Process. US Patent # 6,567,l62L30 Katz R, Zuteck MG, Koren Y （2002） Rapid inspection and error-tracing methodology for machiningproduction lines. CIRP ICME 02, Ischia （Naples）, ItalyL3l Katz R, Zuteck MG, Koren Y （2002） Reconfigurable inspection machine for machining production lines. Proc Global Power Train Conference 2002, Ann Arbor, MIL32 Barhak J, Katz R （2003） Interpretation of laser measurements produced by the reconfigurable inspection machine using the “virtual ball” method. Proc CIRP- 2nd Intl. Conference on RMS03,Ann Arbor, MIL33 Barhak J, Katz R （2004） Rapid non-contact measurements of engine cylinder heads with the reconfigurable inspection machine. CIRP ICME 04, Sorrento, ItalyL34 Gupta A, Segall S, Katz R （2004） Motion stage error compensation technique with verification methodology for a reconfigurable inspection machine. ASME Proc 2004 Japan- USA Symposium on Flexible AutomationL35 Barhak J, Djurdjanovic D, Spicer P, Katz R （2005） Integration of reconfigurable inspection with stream of variations methodology. Int J Mach Tools Manuf 45（4-5）:407-4l9L36 Kalyanaraman A, Katz R, Lock T, Spicer P, Warlick Z, （2004） Cylinder head surface porosity inspection. University ofMichigan, ERCRMS TR-05l-04L37 Bair N, Kidwai T, Koren Y, Mehrabi M, Wayne S, Prater L （2002） Design of a reconfigurable assembly system for manufacturing heat exchangers. Japan-USA Symposium on Flexible Manufacturing, Julyl4-l9, HiroshimaL38 Kidwai T （2002） Design of a reconfigurable core-builder: an assembly machine for heat exchangers. University of Michigan, ERCRMS-TR-056-05附录 2:Development of a Reconfigurable Micro Machine Tool for MicrofactorySung-Hyun Jang, Yong-Min Jung, Hyun-Young Hwang, Young-Hyu Choi2 andJong-Kwon Park3Graduate School, Dept. of Mechanical Design & Manufacturing, Changwon National University, Changwon,Korea（Tel: +82-55-267-ll07； E-mail: nakanygchangwon.ac.kr）2 Department of Mechatronics, Changwon National University, Changwon, Korea（Tel: +82-55-2l3-3623； E-mail: yhchoigchangwon.ac.kr） 3Korea Institute of Machinery & Materials, Daejeon, Korea（Tel: +82-42-868-7ll6； E-mail: jkparkgkimm.re.kr）Abstract: Recently, there have been several interesting researches on the microfactory especially in Japan, U.S., and Korea. Since the microfactory possess the advantage of flexible manufacturing system andor reconfigurable manufacturing system, we introduced the concept of modular reconfigurable machine structure in our micro machine tool design for microfactory. Modular reconfigurable machine tools can easily perform machining processes of different kinds such as milling, turning, drilling and or grinding by simply adding or exchanging machine tool units or modules. In this study, we have developed a reconfigurable micro machine tool for microfactory, which can be reconfigured from a milling machine to a tuning lathe or vice versa. In structural design of the machine tools, we already studied a new theoretical method of creating machine configurations of modular-reconfigurable machine tools （MRMT） in the preliminary design stage. According to our design methodology, we designed the structural modules and RMTs after reviewing all feasible configurations in the preliminary design stage. By using some modules, we have built RMT based the micro milling machine with enough stiffness. The 3-axis micro milling machine ofRMT has a mini-desktop size of 300 mm X200 mm X320 mm and its travel volume is l0 l0X l0 mm3. Dynamic characteristics including natural frequencies and dynamic stiffness of the developed MRMT were analyzed andexamined by using F.E.M. and impact hammer test. And we carried out positioning control test and cutting test using a motion controller. Consequently, we successfully developed reconfigurable micro machine tool with reconfigurable structures of milling machine and turning machine for microfactory by means of configuration simulation, structure and module design, FE analysis, and dynamic characteristic tests such as a modal test and dynamic compliance test.Keywords: Microfactory, Reconfigurable micro machine tool （RmMT）, Structural module, Machine configuration, Cryptographic mapping, Machining function proving2. INTRODUCTIONDuring the last few decades, there were a great many efforts to improve a technology for the manufacturing systems, machining process and the development of an advanced machine. The nowadays production system is enlarged various requests such as small quantity batch production, flexible production, cost reduction, and composition of function. The accuracy of machining is not only going to micro and nano scale but the machine tools are miniaturized gradually. Accordingly several researches about CIM, FMS, RMS （reconfigurable manufacturing system）, and multi-tasking machine has proceeded. Moreover, under the growing interests for On Demand Product, the concept for Microfactory has appeared. Recently, the interests and researches on the microfactory or the micro-fabrication system are remarkably increased. After the initiative research on microfactory by Japan in the l990s, a great variety of studies and developments on micro-fabrication systems have been made in Europe, U.S., and Korea.Ll-3The advantage of a microfactory is obtaining benefits in view of its potential of miniaturizing or downsizing, resource and energy saving, flexible system. One of the key elements of microfactory is the micromeso scale mechanical machining machine tools. During the last 3 years, several micromeso scale mechanical machining machine tools, such as 3-axis vertical micro milling machine, a miniature micro turning machine, micro EDM, micro punching machine and assembly machine, are developed to construct microfactory system in Korea.L4 Since microfactory possessthe advantage of flexible manufacturing system andor reconfigurable manufacturing system, as mentioned above, we introduced the concept of modular reconfigurable machine structure in our micro machine tool design for microfactory. L5-6 Modular reconfigurable machine tools can easily perform machining processes of different kinds such as milling, turning, drilling and or grinding by simply adding or exchanging machine tool units or modules.Although the concept of a modular reconfigurable machine tool is already well known, there is rarely seen the theoretical approach to create structural configurations of a modular reconfigurable machine tool.L7-8 We had studied our theoretical method of creating the machine configurations of modular-reconfigurable machine tools（MRMT） in the preliminary design stage. L5-6 Our design method consists of dual steps； one is the machine configuration generation step using the cryptographic mapping, the other is the machining ability test step.L5-6 We obtained the final feasible configurations for MRMT in this preliminary design stage. And we concretely designed the structural modules and RMTs after reviewing all feasible configurations. Our RMT model has more than l0 structural modules and 4 functional modules for 3-axis vertical micro milling machine and micro turning machine.And then the dynamic characteristics including natural frequencies and dynamic stiffness of the developed MRMT were analyzed and examined by using F.E.M. and impact hammer test. Finally, we evaluate performance of our prototype RMT.3. MRMT DESIGN METHODOLOGY Mathematical representation of connectivityThis methodology provides a theoretical method of creating structural configurations of modular reconfigurable micro machine tools in the preliminary design stage. The two key features of our design methodology are the use of cryptographic mapping and machining function proving. Fig. l shows the overview of the methodology.First over all, the information of the modules does store in module library. To generate the machine configurations by using a cryptographic mapping process, the posture vector of each unit module was encoded into binary code and then stored allthe structure modules （graphic files） and associated digital codes in the module library. The posture vector is a vector whose elements represent combining directions at each combining planes of a unit module. Next, the machine configurations were created by using bilinear form expansion of any two adjacent posture vectors and their consecutive multiplication. And the structural configurations in graphic form were obtained by decoding all the binary coded configurations, which are obtained from the above bilinear form expansion of the posture vectors. Finally, the machining ability test step, which is accomplished by using the rule of principal machining motion and scalar product of the direction vectors of the tool and the work-piece for any created machine tool, was carried out.Fig. l Overview of structural configuration design methodology for micro-milling machineCryptographic mapping is a cryptography based operation including encoding1graphic modules into binary digit and decoding to create possible structural configurations from s given module library.Usually the RMT consists of several modular units such as bed, table, column, headstock, spindle, and so on. Therefore we assumed that the shape of module is a hexahedron type module simply. As shown in Fig. 2, this hexahedron type module has six combinable planes which can be connected with other modules and 4 combinable directions for any plane of the module.Fig. 2 Illustration of a hexahedron type module anddefinition of module posture vector entriesWe have also used module posture vector of the i-th module Pi to define possible combination lanes and directions.Where, Pnn is the n-th connectivity direction on the m-th combinable plane. The combined configurations of any two modules can be represented by using vector1bilinear form of associate module posture vectors Pi and P. as follows.Where, Ai is the mutual connectivity coefficient matrix between the two modules.The entry af is the mutual connectivity coefficient that represents combinability between the n-th connectivity direction of the m-th combinable plane for the i-th module and the q-th combinable direction of the p-th combinable plane for the j-th module. The total number of configurations generated from N modules connection can be determined by multiplying the vector bilinear forms of Eq. （2） consecutively as in the following equation. Cryptographic mapping methodThe entry of a module posture vector is encoded into a binary digit string as shown in Fig. 3, likewise the term of bilinear form expansion of posture vectors also can be represented by the combinations of associated binary digit strings. Reversely the encoded binary string can be decoded by utilizing cryptographically mapped module library, which is library of similar modules. Machining function provingIt is possible to generate various machine tool configurations by cryptographic mapping, but not all of them are necessarily feasible for machining tasks. Therefore we need criteria to predict whether the generated machine configuration is feasible for1a desired machining task. Machine tools, in general, have three kind of motions； machining motion, feeding motion, and positioning motion. Among these, feeding and positioning motions can be fulfilled by adopting a sufficient number of feed-slides, for example at least three feed-slides are required for a 3-axes machine.However for the machining motion, the tool must be normal and directed to the working surface （or machining surface）. Therefore we verified a machining function proving criteria for each configuration in this paper.4. DESIGN AND DEVELOPMENT OF MICRO MACHINE TOOL Generation of configurationAccording to our design methodology, some feasible configurations of RMT are generated by using several structural modules and 4 functional modules for 3-axis micro milling machine and micro turning machine. After proving machining function and checking up geometric symmetry, the configurations in Fig. 4 was selected as the final ones among all the feasible configurations. Development of micro machine tool7lFig. 5 shows the developed modules for RMT. The number of modules is l5 modules including l spindle module and 3 slide modules. These are used to compose all the RMT structures.According to the result of our design methodology, as mentioned above, the 3-axis vertical micro milling machine and the micro turning machine were built as shown in Fig. 6. Table l shows specification of the developed micro machine tools.10 ap-m i lling mach ine(b) a -turn ing mach in e Fig. 6 Develop创 RMT Table I The specification of DeveloQed R岛1 Ts SpecificationDescriptionSizemilling300x200320 mm3turnmg300200133 mmStagemotor type5P step motorTravel rangeIO1010 mm3Resolution2 pm/pulseMax. spe时20 mm/secSpindle motor speed5,00060,000 rpm5. FEA OF MICRO MACHINE TOOLWe need to built RMT based the micro machine tool to have enough stiffness. To verify the static and dynamic characteristics of developed micro machine tool, we used FE method using ANSYS, commercial software. However, we considered just a 3-axis vertical micro milling machine in Fig. 6（a） among RTMs.The FE model of a 3-axis vertical micro milling machine is shown in Fig. 7.The material of structure is used aluminum alloy 7079. Although all the interfaces of the ad acent modules are actually fastened by bolts, we assumed that those are to be rigid for FEA. The 4 edge areas of the beds bottom are fixed as the boundary conditions. And the equivalent cutting force is 5 N to the iso-direction. Fig. 8 is shown the stress distribution and static displacement that consider the deflection by the structural weight. Each results are 0.45 pm and 0.26 MPa, respectively.The mode shapes and the natural frequencies are shown in Fig. 9. Because the maximum spindle motor speed is 60,000 rpm, we carried out the modal analysis within two times extents of motor speed that can cause resonance. The lt, 2nd 3rd, and 4th natural frequencies are 4l8, 528, l584, and l966 Hz respectively. The lst and 2nd mode are the Ist bending modes in the X and Y directions. The 3rd mode is the Ist torsional mode. The 4th mode is the I st bending mode in the Z direction.And the static and dynamic compliances are calculated by FEM through the harmonic analysis. Those are 0.068 pimN and l.48 pimN respectively.2. DYNAMIC TEST OF RMT Modal testWe performed modal test on a 3-axis vertical micro milling machine to confirm the dynamic characteristic of structure. Fig. 4 represented modal test setup using impulse hammer. According to SISO （Single Input & Single Output） method, an accelerometer is attached to the fixed measuring point of spindle holder near the tool and we appliedimpact force to exciting points around the micro milling machine with impulse hammer in measuring its acceleration. The output signal of the measured acceleration is conveyed to FFT analyzer. After obtaining frequency response function about each exciting point, the natural frequencies of the object is measured.Measured and theoretically analyzed natural frequencies are listed in Table 2 and corresponding measured mode shapes are presented through Fig. Ill.It can be noted that the natural frequencies between experiment and FEA are similar, with having error less than l0%. Dynamic compliance testTo measure the structural dynamic compliance, exciting force was applied to the spindle holder end through a impulse hammer and the resulting acceleration level wasmeasured on spindle holder. The dynamic compliance or the dynamic stiffness can be obtained from the measured force and acceleration signals.Table 3 represents the comparison of the calculated and measured structural compliance in the iso-direction. In Fig. l2, structural compliance response functions also obtained from impulse hammer test and FEM analysis are compared in graphic.6. CONCLUSIONSIn this study, we applied cryptographic mapping based MRMT design methodology to design and develop RMT for microfactory. According to our design methodology, several machine configurations are generated for RMT. The feasible configurations2are obtained by proving machining function and checking geometry symmetry. We design and make several modules in accordance with the selected final configuration.Furthermore, we evaluate the performance of the micro milling machine. Measured and calculated natural frequencies showed good agreement with each other and the maximum error between them was less that l0 %0. Moreover, the dynamic compliance in the same direction was measured as l.2l LLtmN, and computed asl.48 LrtmN.Consequently, we have successfully designed and developed a reconfigurable micro machine tool with reconfigurable structures by our design methodology using cryptographic mapping method. And we have well carried out the performance evaluation of the 3-axis vertical micro milling machine by FE analysis and dynamic test.ACKNOWLEDGEMENTThis study is one of results obtained from the research project, ”Structural Design Optimization of Reconfigurable Micro Machine Tool for MicroMeso Scale Component Machining” supported financially by the Ministry Of Commerce, Industry and Energy through KIMM. The authors would like to thank fortheir support.0REFERENCESLl Y. Koren, F. Jovane, T. Moriwaki, G. Pitschow, G. Ulsoy, H. Van Brussel, ”Reconfigurable manufacturing systems,” Annals of the CIRP, Vol.48, No.2, pp.527-540, l999.L2 R. G. Landers, B. K. Min, Y. Koren, ”Reconfigurable machine tool,” Annals of the CIRP, Vol.50, No.l, pp.269-274, 200l.L3 Y. Moon, S. Kota, ”Design of reconfigurable machine tool,” ASME Journal of Manufacturing Systems, Vol.l24, pp.480-483, 2002.L4 J. K. Park, N. K. Lee, S. J. Lee, D. W. Lee, J. Y. Song, ”Development of Microfactory Systems for the Next Generation- 3rd Year Report,” Proc. of the 3rd Intl Workshop on Microfactory Technology, pp.5-l2, 2007.L5 Y. H. Choi, S. H. Jang, H. M. Park, J. K. Park, ”Creating structural configurations of modular reconfigurable micro machine tools by using cryptographic mapping and function proving,” Proc. of the lst Intl Conf. On Micromanufacturing, pp.ll5-ll9, 2006.L6 Y. H. Choi, S. H. Jang, S. M. Kim, S. G. Kim, J. K. Park, ”Configuration design method of modular reconfigurable machine tools by using cryptographic mapping,” Proc. of Intl of Conf. of Machine Design and Tribology, pp.l-6, 2007.L7 H. Shinno, Y. Ito, ”Computer Aided Concept Design for Structural Configuration of Machine Tools: Variant Design Using Direct Graph,” Journal of Mechanisms, Transmissions, and Automation in Deisgn, Vol.l09, pp327-376, l987.L8 R. Katz, Y. M. Moon, ”Virtual Arch Type Reconfigurable Machine Tool Design: Principles and Methodology,” Report of ERC RMS, The University of Michigan, Ann Arbor, MI, pp.l-34, 2000. L9 M. Weck and K. Teipel, Handbook of Machine Tools, Wiley, New York, l984.Ll0 D. J. Ewins, Modal Testing: Theory, Practice and Application, Research Studies Press, London, pp.49-64. l986.Lll S. H. Jang, S. M. Kim, S. G. Kim, Y. H. Choi, and J. K. Park, ”Structural Design Optimization of a Micro Milling Machine for Minimum Weight and Compliance using Genetic Algorithm,” Proc. of the 3rd IWMT, pp77-8l, 2007.Ll2 S. H. Jang, S. M. Kim, Y. H. Hwang, Y. H. Choi and J. K. Park, ”Dynamic Characteristic Analysis of a Micro Milling Machine by Using F.E.M. and Impulse Hammer Test,” Trans of KSMTE, pp.29-34, 2007.微工厂中可重构微型机床的发展状况Sung-Hyun Jang, Yon-gMin Jung, Hyu-nYoung Hwang, Young-Hyu Choi2口 Jong-Kwon Park3研究院校,韩国昌原市，昌原国立大学机械设计与制造学院,(电话: +82-55-267-1107; 电子邮箱: nakanygchangwon.ac.kr) 2 ,韩国昌原市，昌原国立大学机械电子学院,(电话: +82-55-213-3623; 电子邮箱: yhchoigchangwon.ac.kr) 3，韩国大田市，韩国机械与材料学院, (电话: +82-42-868-7116; 电子邮箱: jkparkgkimm.re.kr)摘要：最近，在一些地方尤其是日本，美国，韩国出现了一些关于微工厂的 有趣的研究。由于微工厂具有柔性制造系统以及可重构制造系统的优点，我们介 绍了微工厂中应用的微型机床模块化可重构机床结构的概念。模块化可重构机床 只需要直接地增加或者替换机床单元或者模块，就能够便捷地进行不同的机械加 工过程，例如，锐削，车削，钻孔以及研磨等。在这项研究中，我们为微工厂设计了可重构的微机床，它可以从一台锐床重 构为调车床，反之亦然。在机床中的结构设计中，我们己经在初级的设计阶段探 究了构建模块化可重构机床的理论方法。根据我们的设计方法，在设计的初级阶 段重新审视了所有的可行构造后，我们设计了结构模块以及可重构机床。利用某 些模块，我们一微锐床为基础构建了具有足够强度的可重构机床。这个可重构机 床 的 3 轴 微 锐 床 具 有 300mm200mm320mm 的 这 你 加 工 平 台 以 及 l0mml0mml0mm 的运行范围。我们利用 F.E.M 以及冲击锤试验检验了我们设计的 MRMT 的动态特性，包 括圄有频率以及动态刚性。我们还利用运动控制器进行了位置控制试验以及切削 试验。因此，我们利用微工厂中的锐床以及车床的可重构结构，应用结构模拟，结 构以及模块设计，FE 分析，以及动态特性试验(例如模型试验以及动态一致性 测试）的方法，成功研制了可重构微机床。关键词： 微工厂，可重构微机床(RMMT），结构模块，机床结构，加密映8l射，加工功能证明1. 简介在过去的几十年了，人们进行了很多的努力来改进一种技术，使之应用于制 造系统，加工过程和一种先进机床的研发上。最近人们对加工系统提出了更多不 同的要求，例如，小批量生产，柔性制造，减少成本以及功能组成。加工制造的 精度己经不只是到达微纳米尺度，而且机床也在逐渐到达了毫米的尺度。根据关 于 CIM,FMS,RMS（可重构加工系统）的一些研究，多任务机床的研究也到了推进。 此外，由于“订单生产”的利益增长，人们提出了“微工厂”的概念。最近以来， 微工厂以及微制造系统的研究得到了显著的增加。从 l990 年代日本的最初的关 于微工厂的研究以来，在欧洲，美国，韩国人们进行了大量不同的关于微制造系 统的研究并得到了很大的发展。Ll-3微工厂所带来的长处是鉴于其规模减小以及小型化所带来的利润。微工厂的 一个关键元素是微纳米尺度的机加工机床。在过去的 3 年里，韩国研制了一些微 纳米机机床，例如，3 轴立式微型锐床，微型车床，微型电火花机床，微型冲压 装配机床来构建微工厂系统。L4如上所述，由于微工厂具有了柔性制造系统以 及可重构加工系统的优点，我们在我们微工厂中的可重构微机床设计中引入了模 块化可重构机床结构的概念。L5-6模块化可重构机床可以轻易地实现不同种类的 加工工艺，例如锐削，车削，钻削，磨削，只需要增加或改换一些机床单元或者 模块p可。尽管人们对于模块化可重构机床的认识己经很充分了，但是，却很少有对模 块化可重构机床构造方法的理论认识。L7-8我们在初级的设计阶段研究了创建 MRMT 结构的方法进行了理论研究。L5-6我们的设计过程包括两个步骤：第一 步是应用机床结构生成，利用加密映射，第二步是加工能力测试步骤。L5-6我们 在初步的设计过程中得到了最终的可行的 MRMT 的结构。并且我们在分析了所 有可行的结构后我们精确地设计了结构模块以及 RMT。我们的 RMT 模型具有超 过 l0 中结构模块以及 4 中功能模块，应用于垂直 3 轴微锐床以及微车床。我们接下来应用 F.E.M 以及冲击锤试验检验了设计的 MRMT 的动态特性，包括圄有频率以及动态刚度。最后，我们评估了我们 RMT 的原型的性能。2 MRMT 的设计方法2.1 联接的数学表示图 l微型t床结构构建方法这种方式提供了创建 MRMT 结构结构的的理论方法。我们设计的两个主要 方法是利用加密映射和加工功能证明。图 l 为此方法的示意图。首先，模块的信息储存在模块库中。通过应用加密映射过程来产生机床的 结构，每个单位模块的姿态矢量被编制成二进制代码，然后将所有的结构模块及 相关的代码存储在模块库（图形文件）中。姿态矢量是一个矢量，它的特征表示了 每个单元模块的结合平面的结合方向。其次，机床的结构通过利用任意两个相邻 的姿态矢量的双线性形式扩展以及它们的连乘来构建。通过对所有二进制代码结 构的解码，可以得到图形形式的结构结构，而二进制代码结构是通过上述的姿态 矢量双线性形式扩展得到的。最后，进行加工能力测试，通过利用加工运动原则 以及用于创建的机床的刀具以及工件方向矢量的数量积来完成。加密映射是一种加密操作，包括将图形模块编码为二进制代码以及通过给定 的模块库解码构建可行的结构结构。通常的 RMT 包括了一些模块化的单元，包括床身，工作台，立柱，主轴箱， 主轴等等。因此我们假定模块的形状是一个简单的六面体模块类型。如图 2 所示， 这个六面体型模块具有六个组合平面，他们可以与其它模块相连接，并且每个模块的每个平面具有 4 个组合方向。我们可以利用第一个模块 Pi 的模块姿态矢量来定义平面以及方向的可能的组合。图 2六面体型模块以及模块姿态坐标定义m其中， pn 是第 m 个结合平面的第 n 个连接方向。任何两个模块的结合结构可以利用如下的相关联的模块姿态矢量 Pi 和 Pj 的矢量双线性来表达。其中，Aij 是两个模块之间的互联系数矩阵。mp其中，nq 是相互关联系数，代表了第 i 个模块的第 m 个结合平面的第 n 个连接方向与第 j 个模块的第 p 个结合平面的第 q 个结合方向。由 N 个模块连接产 生的结构的所有数值可以通过将方程（2）的矢量的双线性形式如下面方程连续相 乘得到。2.2 加密映射方法模块姿态矢量的各项被编制成二进制代码序列，如图3 所示，同样，姿态矢 量的双线性形式扩展可以通过相关联的二进制代码序列来表达。相反地，被编码 的二进制数列可以利用加密的模块库进行解密，模块库是相似的模块的组合。2.3 加工功能证明图 3模块姿态矢量各项编码为二进制序列通过加密映射生成不同的机床结构是可以实现的，但是并不是所有的结构都是加工任务中必须要实现的。因此，我们需要利用标准来推断生成的机床结构是否符合要求的加工任务。一般机床具有三个运动:主运动，进给运动和定位运动。 其中，进给运动以及定位运动可以通过采用足够数量的进给滑块来完成，例如 3 轴机床至少需要 3 个进给滑块。但是，对于主运动，机床必须是普通的并且指向工作表面。因此，我们在这篇论文中验证了每种结构的加工功能证明准则。3 微机床的设计以及发展3.1 结构生成根据我们的设计方法，一些可行的 RMT 结构可以利用一些结构化的模块以 及 4 个用于 3 轴微锐床和微车床的功能模块来实现。在验证了加工功能以及检验 了几何的对称性以后，图 4 的结构在最后的所有可行的结构中被挑选了出来。3.2 微机床的发展图 4选出的 RMT 结构图 5 展示了 RMT 模块的发展。共有 l5 个模块，其中包含 l 个主轴模块，3个滑块模块。这些可以来构建左右的 RMT 结构。图 5己有的 RMT 模块根据上述的我们的设计方法，构建了 3 轴立式微锐床和微车床，如图 6。微 机床的细节参数，见表 l。图 6研制的 RMT表 l RMT 参数项口数值尺寸t削300 x200 x320mm3车削300 x200 xl33mm3项口电机类型5P 进电机工作范围l0 xl0 xl0mm3进速度2 m pulse最大速度20mm sec主轴电机转速5,000 60,000rpm4 微机床 FEA我们需要基于微机床来构建 RMT 使其具有足够的强度。为了验证设计的微 机床的静态和动态性能，我们利用了应用 ANSYS 商业软件的 FE 方法。但是， 我们只考虑了 RMT 中的 3 轴立式微锐床，如图 6（a）。3 轴立式微锐床的 FE 模型见图 7。图 7微t床的 FEA 模型机构材料使用了铝合金 7079。虽然相邻的模块实际上由螺栓紧圄，我们设 定他们对于 FEA 是具有足够刚度的。床身底部 4 边区域作为边界条件。不同方向 上等效切削力为 5N。图 8 是考虑到结构重量后的压力分布以及静态位移。每个结果分别为 0.45m 和 0.26Mpa 。图 8型t床在 5N 切削力下静态分析图 9微型t床的模态分析结果图 g 展示了模态以及圄有频率。由于主轴电机转速最大为 60,000rpm，我们 分析采用的两种转速可能引起共振。 第一，第二，第三，第四个圄有频率分别 为 418Hz，528Hz，1584Hz，1gg6Hz。第一个和第二个都向X 和 Y 轴方向产生了弯曲， 第三个是第一个的扭转模态。第四个是第一个在 Z 方向的弯曲模态。1通过谐波分析，我们用 FEM 计算了它们的静态和动态一致性。分别为 0.068m N 以及l.48m N 。5 RMT 动态测试5.1 模态试验我们对 3 轴立式微锐床进行了模态分析来验证结构的动态性能。图 l0 是应 用脉冲锤的模块测试布局。根据 SISO（单输入输出）方法，我们在主轴座附近的测 量点安置了一个加速度计，我们利用冲击锤在微机床的测量点的冲击力来测量它的加速度。输出的被测加速度信号传递给了 FFT 分析器。测量了每个被测点处 的频率后，就得到了物体的圄有频率。图 l0试验布局表 2 是测量以及理论分析后的圄有频率，图 ll 是相应的测量的模态。表 2微t床的固有频率模态固有频率FEA试验值l4l837625285l23l,584l,6434l,966-可以注意到，试验值与 FEA 的圄有频率接近，误差不超过 l0%。9l65.2 动态一致性测试图
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