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附录一：提高数控机床几何精度使用生产过程分析技术文摘现代数控设备的精度要求越来越高,加工制造工艺和装配的结构组件是一个越来越重要的因素建立几何纠正机床。具体来说,平面度,垂直度、并行性和连接表面的平直度确定机床的基本精度。表现出更少的几何误差允许其他错误,如热增长,滚珠丝杆螺距误差和控制更容易被孤立和纠正错误。几何误差具有较高的机床加工和装配过程的一个因素。多个方向在夹具装配和加工导致显著的扭曲最终组装产品。这是由于切削力,夹具变形,重力变形,螺栓力变形。通过详细分析每个进程使用虚拟仿真技术,高保真模型相应的错误可以实现在每个生产步骤,不是身体上的可衡量的由于测量设备的约束。使用模拟数据作为抵消数据加工过程中以及在夹具及固定装置设计确保了几何准确的最终产品。关键词:仿真;加工精度;机床制造;有限元法1. 介绍实际上，精密机床制造业是在飞速发展的。增量经验基础的改进正在稳步实现机械本身精度的进步,机器的组件,这些组件构成了下一代也提高。再加上附加值由技术熟练的工匠导致机床精度不断增加。1然而,降低产品生命周期时间和机床行业竞争力的本质要求改进机床精度是不够的。此外,成本效益的实际限制机械与高精度生产零部件将物理限制的精度水平,可用于制造过程。2过程产生更严格的公差比传统加工和磨削往往是成本高昂,无法广泛采用到流程链。因此找到一种方法来改进过程是很重要的使用现有的设备。机器检查是 NHX4000,400 毫米托盘卧式数控加工中心由 DMG Mori 精在戴维斯,CA。1.1 在机床虚拟建模使用在过去的的五年里,计算能力已经足够成熟来处理完整的机床系统的复杂模型。作为一个例子,DMG Mori 精数字技术实验室(迪泰)购买了 32 节点 Linux 集群运行仿真,桌面 PC 的 30 天的时间来解决。集群计算机的时间缩短到一天! 今天,桌面可以击败,性能几乎任何级别的机床系统的计算机模拟现在是可能的。重要研究已经做了关于如何使用虚拟测试机床设计性能和造型是 Altintas CIRP 主题的一篇论文中总结,等人一个非常有前途的方法,可以用来分析制造过程有限元建模和其他形式的虚拟仿真。在过去在 2005 年。2研究成功完成从组件级别的完全模拟机床虚拟样机来证明传统的设计周期可以现实地缩短消除物理原型迭代。从简单的静态分析完成复杂的动态模型和热模型刚度模型。虽然仍有改进,这种方法的机床虚拟仿真已迅速成为成熟。已经被充分研究过的另一个方面是使用有限元法对微观的各个组件的性能复杂的内部行为(滚珠丝杆接触模型和阻尼运动组件的行为。健壮的组件模型可用于改善产品质量,也为开发更高的带宽控制算法。3详细接触模型被用来协助经验测试的组件发现阻尼值被回收用于整体机动态模型。4 另一个相当大的研究领域的仿真应用到模拟切削过程本身。这些类型的物理现象往往很难添加仪器,因此模拟的交互是非常可取的。是用来模拟切削过程的表面光洁度的决心,毛刺的形成,芯片形成温度分散,刀具磨损等等。56中使用喋喋不休和切削稳定性的预测也可以不去。7很明显,计算机模拟技术广泛用于机床和加工的好处。然而,这项技术还没有部署到研究机床本身的制造过程。这可能是由于精密机床的所有权性质。无论如何,有足够的机会,应用仿真技术以提高机床的精度。为了实现更大的精度,分析将显示改善的领域。这包括集成的切削力、夹具设计、组装顺序,等等。夹具和夹具一起把机器精度高和重复精度也非常重要,检查。这将是一个自然的结果上面的分析进行的。1.2 几何测量误差来源进行机床分析使用虚拟造型本身适用于只有某些错误。具体来说,可以纠正的错误本质上是几何和大量地重复。许多论文清晰地阐明几何错误。它们通常依赖。在旋转的轴的情况下,线性几何误差可以认为是比旋转式轴误差极小。然而,8的方法改善的准确性机床生产过程机器适用于任何配置的工具。此外,直线运动误差复合回转轴线的不确定性误差补偿9,建议尽可能降到最低。本研究将集中在错误的生产过程,可以纠正一次确认。2. 生产过程链的统计分析在制造精密数控设备,它是极其困难的,大大降低成本,同时保持产品质量。因此,分析生产周期中的变量系统和识别改进的重点领域有潜力提供最大限度的改善,在成本和精度/质量,同时保持最小中断生产。试图分析和优化每个测量和宽容将是理想的,但实际上是不可行的。也非常希望建立一个统计链接关键领域在生产过程的最终精度机床。为此,XY 平面的统计分析。机床是一个复杂的机器与数以百计的测量和检验点,只有最相关的常见的切割操作需要分析。大多数削减在 XY 平面二维轮廓线测量,直接影响到 XY 运动链的精度被用来调查统计关系。为了得到一个合理的样本量,30 台取样人口大约 150 台机器生产。为了进行统计分析,数据的形式。就是做出假设依赖于正态分布的数据,数据必须检查正常。使用 Z 分数正常的情节是一个可接受的方式建立一个正态分布。10的正常情节双球棒循环测量有线性回归与一个高度线性 R2 值为 0.96。其他数据集有类似的行为,所以是假设 30 机器的数据样本正态分布和基本假设可以应用正态分布。比较每个参数的方法是获取原始加工结果之间的相关系数和最终的精度测试。因此,发展关联矩阵的测量。这允许一个快速查看的参数可能有强壮的,温和,弱,或根本没有关系。系数超过 0.4 是强大而超过 0.3 是温和的。10是决定之间有很强的相关性的切圆和直线度测试组装机器单独的铸造精度。x 轴有强烈的相关性。y 轴的顶端安装轴和错误的轴通过这个运动链传播工具提示。此外,大型移动质量上的轴原因地方变形的初始精度轴直接增加了局部变形。此外,x 轴铸造(床)上加工大东芝龙门磨(MPC),y 轴(列)是一个紧凑的卧式加工中心上加工(NHX10000)。NHX10000 展品更高程度的精度和可重复性比东芝 MPC。统计分析的结论是,提高几何特性的 X,Y,Z 轴的铸造加工重点是X 轴将导致最终直接提高机床精度。3 .加工过程加工过程包括各种变量。摘要进行密切的两个变形由于夹具设计和变形由于切削力本身。重力是一组默认的加载,应用在整个制造过程。3.1 夹具的影响加工中使用的设备有四个标准,必须分析1. 铸件由于变形大的夹紧力2. 足够的支持在加工铸造的最小变形3. 中立的定位,以避免弹簧后切割和夹具释放。4. 足够的支持和取向的引力诱导变形降到最低。对于 NHX4000、夹具主要发现足够的设计方面的支持和夹紧的一个例外。图 3 所示的右下方夹从支持导致几乎抵消 2 点位移显示在图 4。由于机器的限制,铸造组件可能需要加工的方向不同的定向组装。这可能导致过度的重力变形的部分铸件。的列所示,水平夹具定位结果在 y 轴的直线度误差大于 4 点。床上铸有类似的结果,而是因为它是加工组装、定位 self-gravitational 效果取消,加工夹具是更健壮的床上。3.2. 贡献的力量切削力可以很容易地预测和仿真。Altintas 提出了一个广义切削力模型适用于各种刀具与给定的几何和切削条件。1112,值得注意的是,切削力的影响很小引力效应相比,决定研究中被认为可以忽略不计。4. 装配过程4.1. 夹具及固定装置设计部分机床组装在不同单位尽可能以最佳效率。X 和 Z rails 是直接安装在床上,但 y 轴 rails 安装到列在一个独立的车站。装配工人的有效的地方和测量 rails 在安装和调整,列必须放置在夹具上的水平方向与 rails 面临向上。稳定性和安全性,四点固定最初被设计为在图 7 中。分析显示严重灵敏度调整夹具。只有增加 4 点一个夹具的高度支持导致 Y-rails 平行度误差为 3.5 点。在这种情况下,夹具的腿没有微米级别的调整能力作为他们的高度调整是由普通 SAE 机线程。因此,装配调整并行的人为变形状态。释放后的变形状态列从夹具中移除并设置直立导致 y 轴失去并行性。由于并行性高依赖于夹具调整,变形也非可重复加工期间,不能得到补偿。找到的解决方案是使用三个点支持列在铁路修复。虽然列仍然变形由于重力,rails 近对称变形和没有灵敏度小夹具的高度变化。这是在 4.2 节详细讨论。结果是一个可重复的重力变形,可以补偿在加工步骤。4.2. 取向的结构当一个组件如列是聚集在一个取向有利于有效的装配工作正如上一节所讨论的,重力将发挥作用的测量步骤。这种引力效应可以有效地抵消了理解存在变形,随后装配调整过程中占了。当使用三个点支持,列会变形,但这将是可预测的,依赖于三个点的位置。因此,有必要总是使用相同的三个点位置每次测量列,以确保测量重复性。此外,因为它是可取的 Y Rails 准确测量并行性,指出应选择导致平衡 Rails 的 z 三个方向变形。同时,Y rails 变形在等量所以并行性是保存列时调整。下图显示了三个点位置选择基于有限元分析重力变形。关键是抵消略向电机支架的一面。这抵消抵消更大的质量。在质量控制和装配使用了相同的位置。4.3. 装配顺序和群众不移动组件的顺序获得机体创建大型机床结构的局部变形由于大质量的每个组件。当紧公差的轴运动系统已经在早期阶段获得,然后会产生大量添加二级精度设置,每个轴的保真度的准确性可以完全丢失。这可能并不总是会在最后的精度测试整机信封通常不是测试和局部变形可能只影响局部的信封。然而,详细检查整个机器的信封将揭示缺陷在不同工作信封的位置。因此,建议检查添加的效果通过有限元质量在每个装配步骤。减少这种影响的一个方法是解决运动组件安装后沉重的子单元的装配过程。然而, 在很多情况下这是不可行的,因为进入工作区域时抑制子单元连接,也因为铸件本身仍然看到了变形。一种更有效的解决方案是模拟装配顺序,并记录产生的变形。因为这是高度可重复的,可以直接做铸件加工补偿抵消变形,组装后获得一个中立的变形子单元。4.4. 影响移动组件最后分析执行检查装配机轴运动的影响下重力加载。轴,相对工具在中间冲程位置较高,由于不同的变形前后 X-rails 之间在床上。后方 X-rail 有积极弓虽然前面 Xrail 负弓沿着 Xstroke 随着列。的微分轨道高度传播到 2.3 点误差在 Y 的工具提示结束行程的中间!调整方法是一种积极的皇冠后方铁路。下图所示的数据。5. 最终的加工结果5.1. 加工计划每个组件有一个加工计划开发基于前面的分析结果。这个计划是累积的。的列,加冕应该相反的变形形状在 Y 中风。在质检过程中测量应仰卧位时重力变形直立时加上加冕变形减去重力变形。一个表面加工补偿目标的一个例子是提供在图 14。5.2。与其他工厂相比生产过程的分析是在戴维斯进行的,日本。在 Iga DMG Mori 精也有工厂,日本生产NHX4000 机相同。理解如果戴维斯的方法真的不同,戴维斯和Iga 的箱线图结果了。结果不仅显示出近似从戴维斯Iga 的平均提高20%,戴维斯数据变化少,一些极端的异常值,表明分析过程不仅增加了最终产品的精度,但一致性。重要的是要注意,所有最终机器测量改进是基于国际 ISO 标准。ISO 230 是用于最后的质量控制测量和 ISO 10791 用于最终的质量控制测试。循环的最大公差 5 微米和 8 微米直线度测量。6. 结论一个创新的使用现有的虚拟仿真技术已被提出和实施。一系列削减概要文件为每个部分是计算累计添加所有先前解释的影响。这些是有效的,一个特定的顺序和方向装配过程质量控制步骤和计划也交付。累积的结果完成机器是表明 20%的整体改进最后 NHX4000 产品。引用1 D. A. Dornfeld, 精密的道路:机床和他们创造的产品,First. Mori Seiki Co., Ltd., 2008.2 Y.Altintas,C.Brecher,M.Weck,and s.Witt,“虚拟机床”,CIRP Ann.-Manuf.technol,vol.54，no.2,pp.115-138,2005.3M.F.Zaeh,T.Oertli,and J.Milberg,“有限元建模的滚珠丝杆进给驱动系统,”CIRP Ann.-Manuf.technol,vol.53,no.1,pp.289-292,2004.4 C.Brecher,M.Fey,and S.Ba,“阻尼模型线性轴机床组件,” CIRP Ann.-Manuf.technol,vol.62,pp.399-402,2013.附录二：Improving CNC Machine Tool Geometric Precision Using Manufacturing Process Analysis TechniquesAbstractWith the ever increasing demands for higher and higher accuracy on modern CNC equipment, the manufacturing processes for machining and assembling the structural components are an increasingly important factor in establishing a geometrically correct machine tool. Specifically, flatness, perpendicularity, parallelism, and straightness of interfacing surfaces determine whether the machine tools basic accuracy. Exhibiting less geometric error allows other errors such as thermal growth, ballscrew pitch error, and control error to be isolated and more easily corrected.The geometric errors are predominately a factor of the machine tool machining and assembly process. Multiple orientations during fixturing in both assembly and machining result in significant distortions to the final assembled product. These are a result of cutting forces, fixturing deformations, gravity deformations, and bolt force deformation. By analyzing each process in detail using virtual simulation techniques, a high-fidelity model of the corresponding error at each manufacturing step can be achieved that is not physically measurable due to constraints ofmeasurement equipment. Using simulated data as offset data in the machining process as well as in the jig and fixture design ensures a geometrically accurate final product.Keywords: Simulation; machining accuracy; machine tool manufacturing; FEM1. IntroductionPrecision manufacturing of machine tools is very evolutionary in nature. Incremental experience based improvements are steadily achieved and as the machinery itself advances in precision, the components that make up the next generation of machines also improve. This, together with value added by skilled craftsman results in ever increasing accuracy of machine tools.1 However, decreasing product life cycle times and competitive nature of the machine tool industry dictate that incremental improvements to machine tool accuracy are not sufficient. Moreover, the practical limit of cost effective machinery to produce parts with high precision puts a physical limit on the level of precision that can be used in the manufacturing process.2 Processes that produce tighter tolerances than conventional machining and grinding tend to be cost prohibitive and are not able to be widelyadopted into the process chain. It therefore becomes important to find a way to improve the process using equipment that iscurrently available. The machine checked is the NHX4000, a 400 mm pallet horizontal CNC machining center produced by DMG Mori Seiki in Davis, CA.1.1. Virtual modeling uses in machine toolsA very promising method that could be used to analyse the manufacturing process is Finite Element Modelling and other forms of virtual simulation. In the last five years, computing power has become mature enough to handle full complex models of machine tool systems in a very short amount of time. As an example, DMG Mori Seikis Digital TechnologyLaboratory (DTL) purchased a 32 node Linux cluster for running simulations that took a desktop PC 30 days to solve. That cluster computer shortened the time to one day! Today, a desktop is able to beat that performance so virtually any level of computer simulation is now possible for machine tool systems.Significant research has been done on how to use virtual modelling to test machine tool designs performance and is well summarized in a CIRP keynote paper by Altintas, et al. in 2005.2 Research successfully accomplished has modelled machine tools from component level to full virtual prototype to prove that the traditional design cycle could be realistically shortened by eliminating physical prototype iterations.Analyses completed range from simple static rigidity models to complex dynamic models and thermal models. While there is still improvement to bemade, this method of machine tool virtual simulation has rapidly become mature.Another area that has been well studied is the use of FEM for the micro performance of individual components that have complex internal behaviour such contact models for ballscrews and damping behaviour of motion components. Robust component models are useful for improved product quality and also for developing higher bandwidth control algorithms. 3 Detailed contact models have been used to assist empirical testing of components to find damping values which are recycled for use in overall machine dynamic models.4Another considerable research area simulation is applied toward is simulation of the cutting process itself. These types of physical phenomena are often very difficult to add instrumentation and thus simulating the interaction is highly desirable. It is used to model cutting processes for surface finish determination, burr formation, chip formation, temperature dispersion, tool wear, and so on. 5 6 Use in the prediction of chatter and cutting stability can also not go unmentioned. 7It is clear that computer modelling techniques are widely used for the benefit of machine tools and machining. However, this technology has not been deployed to study the manufacturing process of the machine tool itself. This is perhaps due to the proprietary nature of precision machine tools.Regardless, there is ample opportunity to apply simulation technology in order to improve the accuracy of machine tools. To achieve greater accuracy, the analysis will show areas of improvement to be made. This includes integration of cutting forces, fixture design, assembly order, and so on. The fixtures and jigs to put the machine together for highaccuracy and repeatable accuracy are also very important and are examined. This will be a natural result of the analysis carried out above.1.2. Geometric measurable error sourcesCarrying out a machine tool analysis using virtual modelling applies itself to only certain errors. Specifically, the errors that can be corrected for are geometric in nature and measurably repeatable. Many papers articulate geometric errors clearly. They are generally position dependent. In the case of rotating axes, the linear geometric errors may be assumed to be negligibly small compared to rotary axes error. 8 However, the methods of improving the accuracy of the machine tool production process are applicable to machines tools of any configuration. Furthermore, linear motion errors compound the uncertainty of rotary axis error compensation9 and are advisable to minimize as much as possible. Thisresearch will focus on errors that are a result of the manufacturing process and can be corrected once identified.2. Manufacturing process chain statistical analysisIn manufacturing precision CNC equipment, it is extremely difficult to significantly reduce cost while maintaining product quality. Therefore, analysing the variables in the production cycle systematically and identifying key focus areas for improvement has potential to provide maximum improvement, both in cost and accuracy/quality, while maintaining minimal disruption to production. Attempting to analyse and optimize every measurement and tolerance would be ideal, but practically it is not feasible. It is also highly desirable to establish a statistical link to key areas in the manufacturing process to the final accuracy of the machine tool.To do so, a statistical analysis of the XY plane was carried out. A machine tool is a complex machine with hundreds of measurements and inspection points, only the most relevant for common cutting operations need be analysed. Most cutting is 2D contouring in the XY plane so the measurements that directly affect the XY accuracy in the kinematic chain were used to investigate a statistical relationship. In order to get a reasonable sample size, 30 machines were sampled out of a population of approximately 150 machines produced.In order to conduct a statistical analysis, the form of the data had to be established. That is, to make assumptions relying on the normal distribution of data, the data had to be checked for normalcy. A normal plot using the Zscore is an acceptable way to establish a normal distribution.10 The normal plot of the double ball bar circularity measurement has a linear regression line with an R 2 value of 0.96 which is highly linear. Other data sets had similar behaviour so it was assumed that the data sample of 30 machines had a normal distribution and basic assumptions regarding a normal distribution can be applied.The method used to compare each parameter was to obtain correlation coefficients between the initial machining results and the final accuracy tests. Thus, developing correlation matrices among the measurements was done. This allowed a quick view of what parameters may have strong, moderate, weak, or no relationship. Coefficients over 0.4 are strong while those over 0.3 are moderate. 10It was determined that there is a very strong correlation between the circularity and straightness in the cutting tests of the assembled machine to the individual casting accuracy. The X-axis had the strongest correlations. The Y-axis sits on top of the X-axis and errors of the X-axis are propagated through this kinematic chain to the tool tip. Additionally, the large moving mass on top of the X-axis causes local deformations so the initial accuracy of the X-axis directly adds to this local deformation. Furthermore, theX-axis casting (bed) is machined on a large Toshiba Gantry mill (MPC) while the Y-axis (column) is machined on a compacthorizontal machining center (NHX10000). The NHX10000 exhibits ahigher degree of accuracy and repeatability than the Toshiba MPC.The conclusion of the statistical analysis was that improving the geometric qualities of the X, Y, and Z axes of the casting machining with an emphasis on the X-axis would result in directly improved final machine tool accuracy.3. Machining ProcessThe machining process involves a variety of variables. The two that are examined closely in this paper are the deformations due to the fixture design and also the deformation due to the cutting force itself. Gravity is a default load set that is applied across the entire manufacturing process.3.1. Effect of fixturingThe fixtures used in machining have four criteria that must be analysed1. Deformation of casting due to large clamping force2. Sufficient support of the casting for minimal deformation during machining3. Neutral positioning to avoid spring back after cutting and fixture release.4. Adequate support and orientation to minimize gravitationally induced deformations.In the case of the NHX4000, the fixtures were largely found to be of sufficient design in terms of support and clamping with one exception. The lower right clamp shown in Fig. 3 is offset from the support which results in an almost 2m displacement indicated in Fig. 4.Due to machine constraints, casting components may need to be machined in orientations differing from the assembled orientation. This can result in excessive gravitational deformation for some sections of the casting. In the case of the column shown below, the horizontal fixture orientation results in a Y-axis straightness error of greater than 4m.The bed casting had similar results, but because it is machined in theorientation of assembly, the self-gravitational effect is cancelled and the machining fixture is more robust for the bed.3.2. Contribution of cutting forcesCutting forces can be fairly easily predicted and added to the simulation. Altintas proposed a generalized cutting force model suitable for a wide range of cutters with given geometry and cutting conditions. 11, 12 Notably, the cutting force effect was small in comparison to the gravitational effect and was decided to be assumed negligible in the study.4. Assembly Process4.1. Jig and fixture designParts of the machine tool are assembled in separate units as much as possible for optimal efficiency. X and Z rails are installed directly onto the bed, but the Y-axis rails are installed to the column in an independent station. For assembly workers to efficiently place and measure the rails during installation and adjustment, the column must be placed in the horizontal orientation on a jig with the rails facing upward. For stabilityand safety, a four point fixture was originally designed as in Fig. 7. Analysis showed a severe sensitivity to jig adjustment. Only a 4 ?m increase in the height of one jig support resulted in a parallelism error of3.5 ?m for the Y-rails. In this case, the jig legs do not have micron level adjustment capability as their height adjustment is determined by regular SAE machine threads. Therefore, assembly adjusts for parallelism in an artificially deformed state. The deformed state releases after the column is removed from the jig and set upright resulting in the Y-axis losing parallelism. Since parallelism is highly dependent on the fixture adjustment, the deformation is also non repeatable and cannot be compensated during machining.The solution found was to use a three point support for the column during rail fixing. Although the column still deforms due to gravity, both rails deform nearly symmetrically and there is no sensitivity to small height changes of the fixture. This is discussed in more detail in section 4.2. The result is a repeatable gravitational deformation that can be compensated in the machining step.4.2. Orientation of structureWhen a component such as the column is assembled in an orientation conducive to efficient assembly work as discussed in the previous section, gravity will play a role in the measurements of that step. This gravitational effect can be effectively cancelled out by understanding what deformationsare present and subsequently accounted for during the assembly adjustment process.When using three point support, the column will deform, but it will be predictable, dependent on the locations of the three points. Therefore, it is necessary to always use the same three point locations each time measuring the column to ensure measurement repeatability. In addition, since it is desirable to measure parallelism of the Y Rails accurately, points should be selected that cause a balanced Z-direction deformation of the rails. Also, both Y rails deform in equal amounts so parallelism is preserved when the column is reoriented. The diagram below shows the three point locations selected based on FE analysis gravity deformations. The point is offset slightly towards the motor bracket side. This offset counteracts the larger mass on that side. The same locations are used during QC and assembly.4.3. Assembly order and non-moving massesThe order in which components are secured to the machine body creates large local deformations in the machine tool structure due to the large mass of each component. When tight tolerances of the axis motion systems have been secured in early stages and then large masses are added secondary to the accuracy setting, the fidelity of each axis accuracy can be completely lost. This may not always be apparent in final accuracy testing as the whole machine envelope is not typically tested and local deformations may adversely affect only a localized section of the envelope. However, detailedinspection of the entire machine envelope will reveal deficiencies in various working envelope locations. Therefore, it is advisable to check the effect of adding mass ateach assembly step through FEM.One method of reducing this affect is to fix motion components after installing heavy subunits in the assembly process. However, in many cases this is not feasible because access to the work area is inhibited when subunits are attached and also because the casting itself still sees the deformation.A more robust and efficient solution is to simulate the assembly order piece by piece and record the resulting deformation. Since this is highly repeatable, machining compensation can be done directly to the castings to offset the deformation and obtain a neutral deformation after assemblyof subunits.4.4. Effect of moving componentsThe final analysis performed checked the effect of assembled machine axis movements under gravitational loading. For the X-axis, relative tool positions are higher at mid-stroke, due to disparate deformations between the front and rear X-rails on the bed. The rear X-rail has a positive bow while the front X-rail has a negative bow as the column moves along theX-stroke. The resulting differential in rail heights propagates to a 2.3 ?m error in Y at the tool tip from the end to the middle of the stroke! Theadjustment method is a positive crown on rear rail. The data is illustrated in the following figures.5. Final machining results5.1. Machining planEach component had a machining plan developed for it based on each of the previous analysis results. This plan is cumulative. In the case of the column, crowning should be opposite of deformed shape during Y stroke.Measurement during the QC process should be gravity deformation when supine plus crowning deformation minus gravity deformation when upright. An example of one surface machining compensation target is supplied in Fig. 14.5.2. Comparison with other plantThe analysis of the production process was conducted in Davis, Japan. DMG Mori Seiki also has a plant in Iga, Japan producing the same NHX4000 machine. To understand if the methods employed in Davis are really making a difference, a box plot of Davis and Iga results was constructed. Not only do the results show an approximate 20% improvement from Davis to Iga for the average, the Davis data has less variation and few extreme outliers as well which indicates the analysis process not only adds accuracy to the final product, but consistency as well. It is important to note that all final machine measurement improvement is based on international ISO standards. ISO 230 is used for final QCmeasurement and ISO 10791 is used for final QC