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Con.guration analysis of .ve-axis machine tools using a generic kinematic modelO. Remus Tutunea-Fatan, Hsi-Yung Feng _Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ont., Canada N6A 5B9Received 13 November 2003; received in revised form 4 February 2004AbstractFive-axis machine tools are designed in a large variety of kinematic con.gurations and structures. Regardless of the type of the intended analysis, a kinematic model of the machine tool has to be developed in order to determine the translational and rotational joint movements required to achieve a speci.ed position and orientation of the cutting tool relative to the workpiece. Ageneric and uni.ed model is developed in this study as a viable alternative to the particular solutions that are only applicable to individual machine con.gurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of .ve-axis machine tools: the spindle rotating, rotary table, and hybrid type. A numerical measure of total translational joint movement is proposed to evaluate the kinematic performance of a .ve-axis machine tool. The corresponding kinematic analyses have con.rmed the advantages of the popular machine design that employs intersecting rotational axes and the common industrial practice during setup that minimizes the characteristic rotating arm length of the cutting tool and/or workpiece.# 2004 Elsevier Ltd. All rights reserved.Keywords: Con.guration analysis; Kinematic model; Machine design; Machine setup; Five-axis machine tool1. IntroductionFive-axis machining o.ers de.nite advantages over the more common three-axis machining process. Fiveaxis machine tools are often quoted for their increased productivity, accuracy and .exibility in contrast to the three-axis ones 1,2. Notable e.orts have been takingplace in recent years to overcome some of the inherent drawbacks of .ve-axis machines like more complex programming and post-processing, greater possibility of gouging and collision during cutting, and higher machine costs. Despite these known shortcomings, more and more of these machines are being used in practice. The balance between positioning-only andcontinuous .ve-axis machining work has become more equilibrated lately than it was a few years ago 3. Most research studies on .ve-axis machining have commonly identi.ed the need to develop a model to analyze the kinematic structure of the machine. There are several approaches proposed for this purpose, with some of them transferred from robotics research. One such approach, which is well known and extensively used, was introduced by Denavit and Hartenberg 4 and later modi.ed by Paul 5. The concept of form shaping functions was also proposed for machine tool kinematic analyses 6. Some research studies only containedlimited development on this subject, as their focuses were more on other aspects of .ve-axis machining. Suh and Lee 7 used the DenavitHartenberg representation to develop a versatile path planning method by which .ve-axis machining can be done by a three-axis machine and rotary table combination. Similar applications have resulted in an adaptive algorithm for tool path optimization 8 and a combined 3D linear and circular interpolation technique for the .ve-axis machining of complex surfaces 9.The machining accuracy is a resultant of both internal and external factors acting on the cutting process. Evidently, the accuracy of the whole kinematic chain will have a direct in.uence on the overall machining precision. As a result, a number of studies attempted to establish relationships between the inaccuracy in the components of the kinematic chain and the resulting position and orientation error of the cutting tool. Oneof the early studies in this area was reported by Kiridena and Ferreira 10. They suggested a method to outline the e.ects of positioning errors of machine axes on the cutting tool position and orientation in its workspace. Later, Mahbubur et al. 11 showed that the perpendicularity between the rotational axes of a .ve-axis machine signi.cantly a.ected the positioning error at the tool tip. Bohez 12 proposed a new general approach to compensate for systematic errors in a horizontal .ve-axis machine based on the closed loop volumetric error relations.The common point of almost all of the above-mentioned studies is the fact that a kinematic model of the machine is essential, as the position and orientation of the cutting tool, represented by the cutter location (CL) data and the tool axis vector, have to be converted into machine control coordinates (MCC) for inputting to the CNC machine controller. This conversion is commonly referred to as post-processing. Post-processing for .ve-axis machining is more complex than that for three-axis machining and many parameters requireattention when a full portable post-processor is desired 13. One of the .rst attempts in post-processor development for .ve-axis machining belonged to Takeuchi and Watanabe 14. Lee and She 15 developed individual post-processors for three main types of .ve-axismachines. A post-processing algorithm able to correct erroneous operations for a particular con.guration of the machine tool was proposed by Jung et al. 16. The concept of form shaping functions was used by Cheng and She 17 to develop forward and reverse postprocessors. 利用一般的运动学模式对五轴机床的结构进行分析摘要:五轴机床的设计常用于许多种类的运动学配置和结构中。先不管将要分析的这种类型,为了确定实现切削刀具相对工件的的具体位置和方向所必须的平移和旋转合成运动,一种机床的运动学模型将得到阐述。在本次研究中,一种通用和统一的模型作为可变选择的特殊的仅运用于单独机器配置的解决方案将得到阐述。这种通用的模型可用于检验两旋转连接件在三种主要的五轴机床运动链中的可行性:旋转轴,旋转工作台以及混合类型。一种完整的平移合成运动数字测量已经提出用于估计五轴机床的运动性能。相对应的运动分析已经证实了利用交叉旋转轴和在设置中最小化典型的切削刀具和工件旋转臂长度共同的工业实践的普及的机械设计的效益。绪论:五轴加工相对更普遍的三轴加工来说提供有限的优点,五轴机床由于它相对三轴机床有不断上升的生产效率、准确性、灵活性而得到利用。为了克服五轴机床存在一些潜在缺点,如复杂的编程以及后处理,在切削过程中更大的刨销和冲突的可能性,以及更高的加工费用,已经付出了很大的努力。尽管这些已知的缺点,但是在实际生产过程中越来越多的这种机床得到广泛的运用。目前平衡的定位以及连续五轴加工之间的平衡已经比以前变得更加相称3.。大多数对五轴加工的研究已普遍认识到建立一个模型来分析机器运动学结构的必要性。为此可以提出几种方法,其中一些方法是从机器人研究中转移过来的。有这样一种方法是众所周知和广泛使用的,它是由Denavit和Hartenberg 引进的4,并且后来由保罗修改5而成的。这种成型功能的概念也是为机床运动学分析而提出的。有些研究只包含这个主题的有限发展,正如它们更加关注五轴加工的其它方面。Suh和Lee 7利用Denavithartenberg表达方法来阐述一个通用的路径规划方法,通过这种方法,五轴加工能够通过三轴加工和转盘的组合来实现。 类似的应用可为复杂表面的五轴加工产生自适应刀具轨迹优化8并结合三维直线和圆弧插补技术。加工精度是作用在切削过程中内部和外部因素共同作用的结果。由此可见,整个运动链的精度都将对整体加工精度有直接的影响。因此, 多项研究试图在运动链构件的误差及由此产生的方向和位置误差之间建立关系。在这个领域的研究最早由kiridena和费雷拉10报道。 他们提议一种概述机床主轴定位误差对刀具在工件上的位置以及方向影响的方法。后来,mahbuburetal11表明五轴机床相互垂直的转轴对刀尖的定位误差有很大的影响,bohez12提出了一种新的常规的做法以补偿基于闭环容积误差的关系横向五轴机床的系统误差。几乎上述的所有研究都有这样一个共同点:机器的运动学模型是至关重要的,刀具的方向和位置是通过切刀位置(CL)的数据和刀具轴矢量来表示的, 必须转换成机器控制座标(mcc)输入到数控机床控制器。 这种转换是通常所说的后处理。五轴加工的后处理比三轴加工的后处理更加复杂及当需要一个完全便携式后处理器时多种参数需要注意。五轴机床后处理器开发其中的一个尝试属于Takeuchi和 Watanabe 14。Lee 和 She 15 为三大类五轴机床开发了个别后处理器。 由Jung et al. 16提出的后处理算法能为特别配置的机床纠正错误的操作。Cheng和She使用成型功能的概念去开发前向和反向后处理器。然而,这些研究的问题没有一个能够阐述一种通用和统一的应用于五轴机床结构的运动学模型。后处理器实际上是带有五轴功能的商业计算机辅助制造软件的必须单元。在主要的软件系统之间的差异是由裴etal合成的18。虽然这些商业产品中有些可能包括一种通用的机器运动学模型这种情况是可能的,但是没有现有相关文献资料提交正式回应. 除了先前提到的误差分析和后处理,另一种五轴机床通用运动学模型的应用是与一种满足加工中特别要求的最优机器配置的

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