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基于误差预测机床精度的设计摘要目前，数字化精度分析是保证机床的设计精度的一个重要的工具。而相关的精确建模与分析的研究主要集中在对机床的几何精度和运动精度，和成工件表面的运动精度的研究。机床复杂的成形运动，还没有准确的精度设计和加工精度的工件现有标准之间的对应关系。因此，提出了一种对机床精度的基于误差预测的设计方案，它是分为两级数字化精度分析的关键。第一阶段的目标是在指定的加工精度的情况下由技术系统来完成工件的各种精度的分布和检验组成部分的技术体系和实现机床总输出精度；第二阶段是针对机床系统完成从输出精度分布来检验机床的零部件。这篇文章是以 YK3610 滚齿机为例，描述了两个系统和基本应用方法的误差模型，并对该机床的实际加工精度达到 5-4-4等级。所提出的方法以复杂的成形运动机床的精度设计来提供可靠的指导。关键词：复杂的成形运动，机床，精密设计，位置误差，误差敏感性1.介绍错误的预设和误差补偿是两种为了提高加工精度的方法，它们的有效的实现是基于掌握调节误差源均匀的影响。误差建模和分析是实现这一目的的主要技术手段。早在 20 世纪 60 年代，McClure 开始执行并对机床热作用的实验研究工具；1992，陈等人，建立了系统的运动模型适用于非刚性条件，分析了几何误差和机床热误差以及综合效率的工具。1993，林等人，提出了一种误差分析方法来评估多轴机床直接的空间位置和方向误差。目前，误差建模及分析机床，多体理论结合齐次坐标方法变换的原理得到了广泛的应用。诸如天津大学，上海交通大学，华中理工大学，浙江大学应用技术和误差方法并取得了系列的建模与分析对机床精度控制研究的进展。本文旨在研究和开发高精度滚齿机YK3610 为例来描述机床的精度设计系统误差预测技术中的应用方法。在本文中，实施的基本内容和整体在错误的预测方案进行了阐述。以滚齿机 YK3610为例详细描述建模基本分析方法和机床系统技术。最后，本文对机床精度的控制效果作出预测。2.误差预测与实现方案机床的设计和制造是系统工程，讨论仅针对其精度的设计如下。在传统的模式下，确定机床的精度设计的直接依据主要是指相应的国家标准，如定位精度，重复定位精度和几何精度组件以及主轴跳动。这些精度指标可以保证通过诸如公差设计，控制系统的设计和机床调整。对于这样的复杂机床成形运动的齿轮滚齿机，插齿机和铣床锥齿轮，不同的设计精度指标之间的规定，国家标准和加工工件的精度是没有准确的对应关系。例如，对于传动技术的介绍，本次设计的对象是一台具有明显的高精度和高效率特性数控滚齿机。其唯一的要求是不低于齿轮精度 5-6-6 水平，精度设计是只取决于由现行国家标准规定的设计标准是具有巨大的风险。在这种情况下的考虑，本工作组对机床的各个步骤精密的设计以及提出并实现了一个基于误差对机床精度设计方案预测。2.1 基于精确分布的误差检验预测一个系统的错误结果的输出是通过本系统各误差元素的综合作用。错误预测的目的在于掌握系统误差元素之间的精确关系和最终输出误差系统的设计提前。数字化分析中的应用技术提供了错误预测的条件。具体来说，错误预测工作应包括以下两部分。（1）对单因素作用的纪律预测误差。主要功能是为精度提供分布依据和随后的精密调整。（2）所有预测元素误差累积效应。功能检查的结果的精度分布。如果精度分配结果不符合要求或不满意，以前的工作可以采用执行精度调整和复核。2.2 阶梯误差的预测方案机床的服务对象是工件。更复杂的机床成形运动采用基于精确的设计模式工件的加工精度是必要的。对滚齿机 YK3610 精度分析工作是由两个阶段完成。图 1 是实施的素描方案。2.2.1 基于工件的加工精度确定机床输出精度工件的加工精度取决于由工件的夹具,机床和刀具工艺系统，因此，建模在第一阶段的分析对象是技术系统。其分析内容是加工齿轮和其他零件在技术系统精度之间的关系。目标是完成从工件精度分布检验技术系统的其他组成部分。通过在这一阶段的工作，所需要的输出精度机床在指定的加工精度得到可靠的依据，同时，也可以提供刀具的选择和夹具设计在未来的加工调整。毫无疑问，这里强调的是最后两个执行元件的输出精度机床、齿轮加工精度预测之间的关系，机床的输出精度是工作在下一阶段的目标。2.2.2 合理控制机床输出精度机床的输出精度，必须经过在第二阶段的工作保证有效地解决了对机床的输出精度合理的分配和控制问题。机床输出误差综合作用的结果在机床各部件，在建模与分析这个阶段，如果每个组件命名为机床细胞，对象是机床系统，该分析内容涉及各机床单元和机床输出精度之间的关系，目标是完成从机床输出精度检验机床精度的细胞分布。因此， 图 1.实施方案草图各种机床精度设计指标的确定是合理的。 在上述分析工作中的两个阶段可以提供机器的精度设计一个准确的设计依据。由于对 YK3610 系统的巨大工作量的精度分析，只有系统误差模型和基本应用方法在两个阶段是对重点描述如下。3.滚齿工艺系统误差模型和分析方法3.1工艺系统误差模型滚齿加工成形运动应保证空间啮合关系；这是一个困难的工作，使用齿轮啮合方程求解空间加工齿表面是为了简要介绍分析的目的并对模型的应用方法，简化模型参考方便代替空间滚齿模型的研究。如图2所示，而滚齿直齿圆柱齿轮，滚齿模型可以转换为齿轮齿条的形式。其中，运动坐标系 1（t）= O1（T） ；I1，J1，K1 与齿条连接牢固，I1，J1，K1是与时间无关的活动协调系统 1（t） = O2（T） ；2，J2，K2 坚决与工件原点，O2（T）是与时间无关。它是假定的节圆半径工件为 R 点 O1向量时，T = 0 m， （0）= I1，I2 = J1，J2 （0） （0） = K1，K2；T0，工件包围 K2轴顺时针旋转角度，现在机架运行 R 向右，因此，参数方程加工齿面可以推断：图 2. 滚齿加工啮合的关系的二维草图方程（1）反映了滚刀和加工齿形参数的变化（包括误差）之间的真实关系对方程右端可直接反映在加工齿廓，如总的输出参数和机床误差，形状和误差滚刀本身，滚刀的安装位置和在滚刀主轴的错误，工件尺寸及误差和作为工件的安装尺寸及误差。这模型可以分析误差源单个错误动作和分析的多误差源综合效应。滚齿加工工艺系统模型加工精度之间的严格的对应关系的实现对技术系统各部分的齿轮精度是通过合理的精度分配的，准确的机床的输出精度可得到检查。此外，应用程序模型可以提供作为设计精密可靠的价值基础，这样的工作控制卡，加工参数的调整，刀选择，误差源的判断以及误差补偿。由于模型的简化，将相关的参数和误差的技术服务于模型相应的参数的系统是必需的。3.2 演示应用程序的方法MATLAB 是仿真工具。它是 假定加工齿轮是直齿圆柱齿轮，模块 M = 2.5 毫 米，齿数 z 40，标 准的压力 20角滚刀。加工误差预测两种条件下进行：（1）的滚刀齿形角有 1误差 滚刀的安装角误差和滚刀主轴姿态误差可以转换成这样的参数。（2）滚刀与中心之间的距离工件有 0.1 毫米的误差，这可以代表机床或加工调整定位误差错误。分析步骤如下。（1）转换和误差分析的参数是模型参数；（2）计算的离散齿面坐标,当这个参数是错误；（3）计算的离散齿面坐标,当这个参数存在误差；（4）输出的两种以上的齿廓说案例；（5）计算两个齿面微分值坐标集和输出图；（6）分析和结论。图 3 显示了理想和实际加工齿廓齿形；图 4 显示偏差值和实际齿廓偏差特性理想的齿形在误差源的不同。上述结果只显示基本分析方法单一误差因素影响齿型的错误简介。指定的滚齿过程的分析精度，工作等一系列的误差特性单因素分析，综合效应分析多因素影响，精度分布以及对分配的影响检查和精心的策划和实施要求都包括在内。结果分析是指定机床的整体输出精度相应的滚齿精度，这是制定精密准确的目标在下一阶段的指标。由于受长度限制一篇完整的分析过程，这里省略了。4.机床系统的误差模型和分析方法机床系统误差模型可以准确地描述机床误差之间的细胞关系和机床的最终输出误差，包括位置，运动误差的关系。这模型主要用于分析的传递规律在这一错误的细胞和积累影响研究。分析结果提供准确的依据当 公差分配和检查这样的工作整个机床的刚度，控制全机和组件以及装配调整机床精度。样机的服务为实例，介绍了一种基于分析的基本内容该系统模型：对机床细胞误差的敏感性分析下的工具。 4.1 机床部件敏感性误差由于每个几何结构和尺寸在机床组件和它们的位置工具是不同的，对机床精度后输出转移误差的来源有不同的影响。对机床误差的敏感性分析工具是预测误差的影响程度每个工具机的输出精度影响的细胞机床，它是合理控制的一项基础工作机床的输出精度。由于存在对加工误差敏感方向，误差机床细胞敏感性应覆盖变化在传输误差的大小和方向。4.2 分析的原理和基本公式图 5（a）是原型机 YK3610 的照片，和图 5（ b）是它的结构示意图。它是假定，在刻加工，一个固定的点 QT =（XT ，YT， ZT）在滚刀主轴坐标系可以转化为坐标系中对应的点工件主轴的一系列的齐次坐标后从中间部分到另一个转换。如果两个主轴坐标系和坐标中间部件的系统不产生位置误差，这对应点位于理论位置 Qw =（XW，YW，ZW） 。相反，这对应点应偏离理想位置定位在实际位置的 QW =（XW，YW，ZW ） 。两偏差值和偏差方向体现综合结果由各机床部件误差引起的。如果机床部件建立误差为相同的值之一，提供了它们的效果具有可比性。基本公式如下:（1）计算 QW 的理想位置。QW 理想的位置坐标可以从下面的公式计算：在 t17 是总的特征变换矩阵滚刀主轴和工件主轴 1 7 之间，可通过将达到不断根据之间的特征变换矩阵序列每个相邻系统。t67 代表特色滚刀主轴 7 和滚刀之间的变换矩阵头 6，包括 3 组矩阵几何位置，两者之间的运动和误差。误差矩阵是在理想状态的单元矩阵为特征的意义和表达方式在相邻的其他机构的变 换矩阵方程可以类推。从式（3） ，不同的转换矩阵 Tij 之间在等式右端相邻体（5）是实际 位置变换矩阵，包括转换矩阵 Tij 为两位置误差相邻的体。它 TIJ 和 TIJ 的关系可以表示为：其中，T IJ 包括的误差矩阵，即三线性位移误差矩阵和 3 角误差相邻的体坐标系之 间的矩阵 j 和 i，表示为：（3）的位置偏差值。采用 除 可以获得的差异 和 之间实际位置与理想位置；它们不仅反映了尺寸的变化，部件在迁移过程中，但错误也反映了方向的变化。4.3 分析方法每个组件的目标的坐标系统机床是建立如图 6 所示。一点 Q（0，0，150）在坐标系的选择滚刀主轴系统，它是假定坐标每个工具机的电池系统已经产生了一个单元错误 6 自由度分别为。他们是翻译错误方向和沿 x 方向Z 方向；周围的 X 轴角误差，Y 轴Z 轴与和 表示，在本文中。最后位置的差异 造成上述公式可以计算。在这项工作中，均匀光源角度误差为 1100 ；源的线性误差为 1 / 100 毫米。为了减少工作量示范适当，部分 3（滑台） ，4（柱）为一体，方程（3）可以表示为在这个演示：公式中的转换矩阵是指是从滚齿机 YK3610 经常使用平移和旋转矩阵的一致每个组件的几何位置的数据。每个部件产生作用的结果在最后的执行元件误差是指表 1。表 1 角误差项的结果表示为直方图（如图 7 所示） ，其误差敏感性显得更直观。它可以被称为拱原理，从齿轮齿轮负误差敏感方向是指 XW和 YW方向在工件轴坐标系，ZW 垂直方向的敏感性，因此，归属最不敏感的方向。图 7 显示了从角误差每个机床误差存在明显差异的细胞。例如，从和 导致的结果，不仅反映在加工敏感方向但也有一个明显的误差放大效应。掌握机床的误差敏感性的细胞可以用于精度分配提供准确的依据（包括刚度公差）和调整并提供误差补偿的指导未来，如热误差的合理选择监测点。表 1. 最终执行元件误差传递的结果5.加工精度的控制影响对于 YK3610 经过研究与开发原型已经完成，两个精密切削试验进行第二次；试验条件为如下。图 8 显示试样切割后。代码是 yk3610-sq0104，和总数量是 8。模块标本 M = 1.25，N = 62 齿数，压力角= 20和螺旋角 = 20。小笠原公司在日本选择了硬质合金 AA 级滚刀这试验。主要的切削参数如下滚刀转速为 900 转/分钟，和轴向进给 0.15 毫米/ R.径向进给深度达到两倍，T1 = 2.6 毫米和 T2 = 0.2 毫米预热后的机床，试样加工连续。加工的试样是本周节累积误差，齿距误差和接触加工的试样的线误差控制 5-4-4 级，这是比 5-6-6 级高。此外，样机的高效切割精度也比预定的精度高。6.结论（1）对机床的复杂成形运动，两步精度分析方法更为有利对机床的设计精度控制。第一步：建立技术系统的误差模型和执行系统误差的预测；用指定的零件的加工精度来制定的机床总产量精度检验；第二步：建立机床的误差模型系统合理地控制总的输出精度基于机床误差敏感性机床部件。控制精度的实际结果表明用这种方法可以达到预期的目的。（2）灵敏度的错误分析不仅是适用于机床系统也是适用于技术系统。对于复杂的成形运动，在技术系统的误差敏感性应包括结果误差的大小和特点。参考【1】杨建国，误差综合补偿技术及数控机床中的应用研究 D 。上海：上海交 通大学，1998。 （中文）【2】McClure E R，热效应在制造计量方法的意义J. 。CIRP ，1967，15（5）：6166。【3】陈劲松，袁锦芳，Ni J.一种补偿非刚体加工中心运动的影响 J.。1992， 20（9）：325329。【4】林 P D，K埃曼，体积误差直接评价，国际 J.马赫，机床制造，1993，33 （5）：675693。【5】李圣怡，戴一帆，精密准确的建模技术和超精密机床 M 。长沙：国立大 学国防科技出版社，2007。 （中文）【6】张勤，刘又午，赵晓松，多体机床系统热误差补偿技术J.。中国机械 工程学报，2002，38（1）：127130。 （中文）【7】金华申，在误差补偿的关键技术及应用数控机床的研究 D 。上海上海交 通大学。2008。 （中文）【8】夏勇，胡友民，吴波。在热弹性和热动态特性建模机床的进给系统分析多 米诺效应J.。中国机械工程学报，2010，46（15）：191198。 （中文）【9】林卫青，傅建中，陈子辰。数控加工机床建模的热误差的基于自适应最佳 拟合 WLS-SVM J 。中国机械工程学报，2009，45（3）：178182。 （中文）【10】 特温。齿轮啮合理论M.上海上海科学技术出版社，1984。 （中文）【11】曾涛。螺旋锥齿轮的加工设计M.哈尔滨：哈尔滨工业大学出版社，1989。【12】黄强，张根保，任先林。公差设计和机床的几何误差源的互相补偿应用J. 中国机械工程，2010，21（5）：580584。 （中文）【13】黄强，张根保。机床刚度识别的敏感性分析畸变的关键理论和方法J.。 中国机械工程，2009，20（24）：2 8992 902。 （中文）【14】华楚胜，王钟馗，谢黎明。机械制造技术M.重庆大学出版社，2003。 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 26, No. 1, 2013 151DOI: 10.3901/CJME.2013.01.151, available online at ; ; Precision Design for Machine Tool Based on Error Prediction HUANG Qiang1, *and ZHANG Genbao21 College of Automobile, Chongqing University of Technology, Chongqing 400054, China 2 College of Mechanical Engineering, Chongqing University, Chongqing 400044, China Received April 1, 2012; revised September 27, 2012; accepted October 12, 2012 Abstract: Digitization precision analysis is an important tool to ensure the design precision of machine tool currently. The correlative research about precision modeling and analysis mainly focuses on the geometry precision and motion precision of machine tool, and the forming motion precision of workpiece surface. For the machine tool with complex forming motion, there is not accurate corresponding relationship between the existing criterion on precision design and the machining precision of workpiece. Therefore, a design scheme on machine tool precision based on error prediction is proposed, which is divided into two-stage digitization precision analysis crucially. The first stage aims at the technology system to complete the precision distribution and inspection from the workpiece to various component parts of technology system and achieve the total output precision of machine tool under the specified machining precision; the second stage aims at the machine tool system to complete the precision distribution and inspection from the output precision of machine tool to the machine tool components. This article serves YK3610 gear hobber as the example to describe the error model of two systems and basic application method, and the practical cutting precision of this machine tool achieves to 5-4-4 grade. The proposed method can provide reliable guidance to the precision design of machine tool with complex forming motion. Key words: complex forming motion, machine tool, precision design, position-pose error, error sensibility 1 IntroductionThe error prevention and error compensation are two ways to improve the machining precision, and their effective implementation is based on mastering the effect regulation of error source uniformly1. Error modeling and analysis is the main technical means to realize this purpose. As early as 1960s, MCCLURE2began to perform the modeling and experimental study on heat effect of machine tool; in 1992, CHEN, et al3, established the system movement model applicable for the non-rigidity condition to analyze the geometrical error and heat error of machine tool as well as the comprehensive efficiency. LIN, et al4, put forward a kind of error analysis method for direct space to evaluate the location and direction error of workpiece and multi-axis machine tool in 1993. Currently, the error modeling and analysis method for machine tool that the multi-body theory combines the homogeneous coordinate transform principle has been applied widely5. Such universities as Tianjin University, Shanghai Jiaotong University, Huazhong University of Science and Technology and Zhejiang University have applied the error modeling and analysis method and achieved series of progress on machine tool precision control69. This article * Corresponding author. E-mail: This project is supported by National Natural Science Foundation of China (Grant No. 51075419), and Chongqing Municipal Natural Science Foundation of China (Grant No. CSTC, 2009BB3234 ) Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2013 serves the research and development for highprecise gear hobber YK3610 as an example to describe the systemic application method of error prediction technology in the machine tool precision design. In this paper, the basic content and whole implementation scheme on error prediction are expounded firstly. Serving YK3610 gear hobber as the example, modeling method and basic analysis method for the technology system and machine tool system are described in detail. Finally, the control effect on machine tool precision is presented. 2 Error Prediction and Implementation Scheme The design and manufacturing of machine tool is a systematic engineering. The discussion is performed only aiming at its precision design below. Under the conventional mode, the direct basis to determine the design precision of machine tool mainly refers to the corresponding national standard, such as locating precision, repeated locating precision and geometrical precision of components as well as the spindle bounce. These precision indexes can be ensured by such means as tolerance design, control system design and machine tool adjusting. For such machine tools with complex forming motion as the gear hobber, gear-slotting machine and the milling machine for bevel gear, there is not accurate corresponding relationship between various design precision indexes specified in national standard and the precision of machined workpiece. YHUANG Qiang, et al: Precision Design for Machine Tool Based on Error PredictionY 152 For example, the design object for this time is the first CNC gear hobber to introduce the zero transmission technology that is provided with evident high precision and high efficiency characteristics. Only for the requirement not lower than the gear precision with 5-6-6 level, that the precision design is performed only depending on the design standard specified by existing national standard is provided with tremendous risk. In consideration of this condition, the work group analyzes various steps on machine tool precision design as well as proposes and implements a design scheme on machine tool precision based on error prediction. 2.1 Precision distribution and inspection based on error prediction The output error for a system is the result of comprehensive action by each error element in this system. The purpose of error prediction lies in mastering the accurate relationship between the error element of system and the final output error of system in the design in advance. The application of digitization analysis technology provides the condition for error prediction. Specifically, the error prediction work should cover the following two parts. (1) Prediction on action discipline of single error element. The function is to provide the basis for the precision distribution and subsequent precision adjustment. (2) Prediction on accumulated effect for all error elements. The function is to inspect the result on precision distribution. If the result on precision distribution does not conform to the requirement or is unsatisfied, the result for previous work can be employed to perform the accuracy adjustment and rechecking. 2.2 Stepped-type error prediction scheme The service object of machine tool are of workpieces. It is more necessary that the machine tool with complex forming motion adopts a precision design mode based on the machining precision of workpiece. The precision analysis work on YK3610 gear hobber is performed by two stages entirely. Fig. 1 is the sketch of implementation scheme. 2.2.1 Determine the output precision of machine tool based on the machining precision of workpiece The machining precision of workpiece depends on the technology system composed of workpiece, clamp, machine tool and cutter, therefore, the modeling and analysis object on the first stage is technology system. The analysis content is the relationship between the precision of machined gear and the precision of other component parts in the technology system. The target is to complete the precision distribution and inspection from the workpiece to other component parts of technology system. Through the work on this stage, the required output precision of machine tool under the specified machining precision can be obtained, meanwhile, the reliable basis can also be provided for the cutter selection, clamp design and the machining adjustment in future. Undoubtedly, the work emphasis here is to predict the relationship between the output precisions of two final executive components on machine tool and the machining precision of gear. The concluded output precision of machine tool is the work target on next stage. Fig. 1. Sketch of implementation scheme 2.2.2 Reasonable control on output precision of machine tool After the output precision of machine tool that must be guaranteed is obtained, the work on the second stage is to effectively solve the reasonable distribution and control problems on output precision of machine tool. The output error of machine tool is the result of comprehensive action by each component in machine tool. If each component is named as the machine tool cell, the modeling and analysis object on this stage is of the machine tool system, the analysis content refers to the relationship between the precision of each machine tool cell and output precision of machine tool, and the target is to complete the distribution and inspection from the output precision of machine tool to the precision of machine tool cell. Thus, various precision design indexes of machine tool can be determined reasonably. The analysis work on above-said two stages can provide an accurate design basis for precision design of machine tool. Since there is tremendous workload on systematic precision analysis of YK3610, only the system error model and the basic application method employed on two stages are described on emphasis below. 3 Error Model and Analysis Method on Hobbing Technology System 3.1 Error model on technology system The hobbing forming motion should guarantee the space CHINESE JOURNAL OF MECHANICAL ENGINEERING 153meshing relationship; it is a difficult work to employ the gear space meshing equation to solve the machined tooth surface10. In order to briefly introduce the analysis purpose and the application method of model, the simplified model11convenient for reference is employed to replace the space hobbing model in this paper. As shown in Fig. 2, while hobbing the straight-tooth column gear, the hobbing model can be converted to be gear-rack form. Therein, the movement coordinate system 1(t)=O1(t); i1, j1, k1 is firmly connected with the rack, i1, j1, k1is irrelevant with the time; the movement coordination system 1(t) =O2(t); i2, j2, k2 is firmly connected with the workpieces, the original point O2(t) is irrelevant with the time. It is assumed that the pitch radius of workpiece is r and vector of point O1 is m. When t=0, i2(0)=i1, j2(0)=j1, k2(0)=k1; t0, the workpiece surrounds k2axle to rotate angle in clockwise, right now, the rack moves r toward right accordingly, the parameter equation of machined tooth surface can be deduced: 221 12cos (1 sin cos )sincos cos( ) ( )cosrr ir jrit =+- =-+ - +2cossin( ) ( ) .cosjt-(1) Fig. 2. Two dimension sketch of meshing relationship for Hobbing Eq. (1) reflects the true relationship between the hob and machined tooth profile; the parameter variation (including the error) on the right end of equation can be directly reflected on the machined tooth profile uniformly, such as the total output parameters and error of machine tool, shape and error of hob itself, installation location and error of hob on the hob spindle, workpiece dimension and error as well as installation dimension and error of workpieces. This model can analyze the action discipline of single error source and also analyze the comprehensive effect of multiple error sources. The technology system model of hobbing realizes the strict correspondence between the machining precision of gear and the precision for each part of technology system. Through reasonable precision distribution, the accurate output precision of machine tool can be obtained and inspected. In addition, the application model can provide such work as reliable value basis for design precision control of clamp, machining parameter adjustment, cutter selection, judgment of error source as well as the error compensation. Since the model is simplified, it is required to convert the relevant parameters and error of technology system into corresponding parameters of model in service. 3.2 Demonstration of application method The simulation tool is of MATLAB. It is assumed that the machined gear is of straight tooth column gear, module m=2.5 mm, number of teeth Z=40, the standard pressure angle of hob is of 20. The machining error prediction under two kinds of condition is performed respectively: (1) The tooth profile angle of hob is provided with -1 error (=19). The error of installation angle for hob and the pose error of hob spindle can be converted into this parameter. (2) The central distance between the hob and the workpiece exists 0.1 mm error, this can represent the locating error of machine tool or the machining adjustment error. The analysis step is as follows. (1) Convert the analyzed parameters and its error to be model parameters; (2) Compute the coordinate set of dispersed tooth surface when this parameter is free of error; (3) Compute the coordinate set of dispersed tooth surface when this parameter exist error; (4) Output the tooth profile for two kinds of above-said case; (5) Compute the differential value of two tooth surface coordinate set and output the diagram; (6) Analysis and conclusion. Fig. 3 shows the ideal machining tooth profile and actual tooth profile; Fig. 4 shows the deviation value and the deviation characteristics between the actual tooth profile and ideal tooth profile under the different error source. Above demonstrations only show the basic analysis method how the single error factor affects the error of tooth profile. The analysis process for specified hobbing precision, such series of work as error characteristic analysis on single factor, comprehensive effect analysis on multiple factors, precision distribution as well as the inspection for distribution effect are included, and the elaborate planning and implementation are required. The result on analysis is to specify the overall output precision of machine tool corresponding to the hobbing precision, which is an accurate target to formulate the precision indexes in next-stage. Due to being confined by the length of an article, the complete analysis process is omitted here. YHUANG Qiang, et al: Precision Design for Machine Tool Based on Error PredictionY 154 Fig. 3. Simulation diagram of tooth profile Fig. 4. Deviation value and its characteristics 4 Error Model and Analysis Method for Machine tool System The error model of machine tool system should accurately describe the relationship between the error of machine tool cells and the final output error of machine tool, including the position-pose, movement and error relationship. This model is mainly used for analyzing the transfer discipline of each error cell and their accumulated effect in this research. The analysis result provides the accurate basis for such work as tolerance distribution and inspection12of whole machine tool, rigidity control13for whole machine and components as well as the adjustment on assembly precision of machine tool. The prototype machine is served as the sample to introduce a basic analysis content based on this system model: sensitivity analysis on error of machine tool cell below. 4.1 Error sensibility of machine tool cell Since the geometric structure and dimension of each machine tool component and their location in the machine tool are different, the source error has different influence degree on output precision of machine tool after being transferred. The sensibility analysis on error of machine tool cell is to predict the influence degree that the error of each machine tool cell affects the output precision of machine tool, which is a basic work to reasonably control the output precision of machine tool. Due to the existence of sensibility direction for machining error14, the error sensibility of machine tool cell should cover the variation of error size and direction during transferring. 4.2 Analysis principle and basic formula Fig. 5(a) is a photo of YK3610 prototype machine, and Fig. 5(b) is its structure sketch. It is assumed that, at the moment of machining, a fixed point (, , )ttttQxyz= in the coordinate system of hob spindle can be transformed to a corresponding point in the coordinate system of workpiece spindle after a series of homogenous coordinate conversion from a middle component to another. If two spindle coordinate systems as well as the coordinate systems of middle components do not produce the position-pose error, this corresponding point is located in the theoretical location (, , )wwwwQxyz= . Conversely, this corresponding point shall deviate the ideal location and locate in the actual location (, , )wwwwQxyz= . Both deviation value and deviation direction embody the comprehensive result caused by error of each machine tool cell. If the error of machine tool cell is established as the identical value one by one, their effect results are provided with the comparability. The basic formulas are show as follows. (1) Compute the id
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