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1、哈尔滨工业大学工学硕士学位论文 -I- 摘 要 目前精密/超精密加工产品在航空航天、生物医学、微型通信等领域中被广泛应用并扮演着日益关键性角色，同时这些领域迅猛发展也对产品精度提出了越来越苛刻的要求，如何提高产品的精度将是机械加工所面临的巨大挑战。机床作为加工产品的母机直接影响着产品的精度，故为保证产品精度首先需要采取合理措施以提高机床的精度等级。大量实践证实误差补偿法已是提高机床精度最为经济有效的方法，而实现误差补偿的首要条件则是辨识/预测出机床各项误差源。当前测量机床误差的方法虽然繁多，但是仍不能满足工业界的亟需，故本课题提出了基于特征样件的机床误差测量方法，以期提供一种新颖实用的误差测量
2、方式。因为样件是机床实际加工而得，故所识别出的机床各项误差更能反映出机床在加工过程中的动态特性，由于该方法的快速便捷性和高效多用性可预测出其在工业界具有广阔的潜在应用空间。为此本文针对基于特征样件的三轴数控铣床误差测量方法的关键性基础问题进行了研究。 由于机床众多误差源的存在，使得加工工件存有各种形位误差如直线度、位置度等。为了建立工件上形位误差与机床各项误差的解析关系，本文基于多体系统运动学理论对机床进行了数学解析。以 FXYZ 三轴铣床为研究对象，通过低序体阵列和自由度列表实现了对三轴铣床结构的数学描述，借助于理想特征矩阵、误差特征矩阵的叠乘建立了刀具成形点相对于工件的空间误差模型。同时基
3、于机床垂直度误差的数学定义，将三轴铣床的 21 项误差等效简化为 18 项独立的误差参数。这些数学表述为下述误差辨识奠定了数学分析基础。 在所建立的空间误差模型基础上反求出相关几何要素集及其之间位置参数关系。在由这些几何要素集构成的系列样件上选择合理成形点的位置参数，辨识出了三轴铣床的 18 项当量误差并给出了这些当量误差的解析式，基于这 18 项当量误差进一步获得三轴铣床的 21 项误差。针对样件测量过程中，三坐标测量机坐标系与工件坐标系不统一这一关键性问题，建立了坐标系间空间位姿模型，实现了工件上几何要素的坐标值在这两个坐标系内的互换。至此就完整地建立了基于特征样件的三轴铣床误差辨识/测量
4、方法的理论链。同时基于系列样件设计出了能够辨识出 FXYZ 三轴铣床 21 项误差的特征样件， 即 XY 平面特征样件和 Z 向特征样件。 文中采用 MATLAB 编程构建了基于特征样件的误差辨识方法的仿真系统。为了测试理论链中模型的鲁棒性及保证仿真系统运行的客观性，机床的各项误差、坐标系间变换角度等关键性参数均由随机函数产生，并引入了正态分布函数表征测量过程中存在的随机性误差。多次随机性的仿真结果显示刀具半径、成形点位哈尔滨工业大学工学硕士学位论文 -II- 置参数、几何要素的位置参数、测量过程的随机误差等对辨识精度均有影响，合理选择这些参数可使当量误差出色地逼近机床的实际误差，这就从模型仿
5、真角度说明了所建理论链是正确合理的。 本文最后在 XYFZ 三轴数控铣床上进行了实验研究来验证本文所提误差测量方法的可行性。基于样件建立了铣床 X 导轨广义直线度的数学解析，通过样件的实际加工与测量获得了基于样件的 X 导轨广义直线度误差；在实验中采用激光跟踪仪实时测量 X 导轨运行过程中的实际位姿并从中分离出基于激光跟踪仪的 X 导轨广义直线度。两个广义直线度的对比结果表明基于特征样件的三轴铣床误差测量方法是具有实际可行性。 关键词：特征样件；误差辨识；空间位姿模型；空间误差模型哈尔滨工业大学工学硕士学位论文 -III- Abstract At the present time, preci
6、sion / ultra-precision machining products are widely used in the field of aerospace, biomedical, micro communications, and play an increasingly critical role in these areas. At the same time, the rapid development of these fields raises increasingly demanding requirements for precision products, thu
7、s, how to improve the accuracy of the products will be the enormous challenges faced by the machining industry. As processing machines, Machine tools directly affect the accuracy of the processed components product, so in order to obtain the component and product accuracy, reasonable measures should
8、 be taken to improve the accuracy level of the machine tools. Numerous practices show that the error compensation is the most economical and effective method for the improvement of the machine tool precision, and the identification / prediction of various machine tool errors is the first condition f
9、or the realization of the error compensation. Despite the current many methods of measuring machine errors, the urgent need of the industrial sector still cannot be met. This subject proposes an error measuring methods based on a special artifact in order to provide a novel and unique machine tool e
10、rror measuring approach. Because of the actual machining of the special artifact, the measured machine tool error can better reflect the dynamic characteristics of the machine tool in processing. Also, for its convenience and efficiency, this method will obtain broad potential applications in the in
11、dustry. Consequently, based on the special artifact, this paper investigates the key fundamental problems aiming at 3-axis CNC milling machine error identification and measurement. Due to the presence of various machine tool errors, there are a variety of form and position errors such as straightnes
12、s and position accuracy on the work-piece. In order to establish the analytical relationship between the form and position errors on the work-piece and the 21 errors on the three-axis milling machine, the machine tool is modeled in this paper based on the kinetic theory of the multi-body system. Thr
13、ee-axis milling machine topology is described by means of multi-sequence body array and list of freedom degrees, and using the multiplication of ideal characteristic matrix and error characteristic matrix, spatial error model of tools forming point relative to the work-piece is established. Based on
14、 the definition of perpendicularity error of machine tools, the 21 motion errors of the three-axis milling machine are equivalently simplified to 18 independent error parameters. Take FXYZ 3-axis milling as an example, certain geometry elements sets and their relative relations of position parameter
15、s are solved on the basis of the spatial model. 18 equivalent errors of the three-axis milling machine are identified and analytic expression of the equivalent errors is given. Considering the non-unified coordinate 哈尔滨工业大学工学硕士学位论文 -IV- systems of the measuring machine and the work-piece, the spatia
16、l position and orientation model between the coordinate systems are established, and the conversion of the coordinate values in the two coordinate systems is realized. At this point, a complete error measurement theory chain is established based on the special artifact of the three-axis milling machine. At the same time, on the basis of the series special artifacts, an artifact, i.e. the XY plane special artifact and Z axis special artifact, which can i
