Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 863283, 12 pages http://dx.doi.org/10.1155/2013/863283 Research Article An Analysis Methodology for Stochastic Characteristic of Volumetric Error in Multiaxis CNC Machine Tool Qiang Cheng, 1 Can Wu, 1 Peihua Gu, 2 Wenfen Chang, 3 and Dongsheng Xuan 1 1 College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China 2 Department of Mechatronics Engineering, Shantou University, Shantou, Guangdong 515063, China 3 Beijing Precision Machinery & Eengineering Reserach Co., Ltd., Beijing 101312, China Correspondence should be addressed to Peihua Gu; phgu@yahoo.cn Received 20 March 2013; Accepted 26 August 2013 Academic Editor: Shihua Li Copyright © 2013 Qiang Cheng et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Traditional approaches about error modeling and analysis of machine tool few consider the probability characteristics of the geometric error and volumetric error systematically. However, the individual geometric error measured at diferent points is variational and stochastic, and therefore the resultant volumetric error is aslo stochastic and uncertain. In order to address the stochastic characteristic of the volumetric error for multiaxis machine tool, a new probability analysis mathematical model of volumetric error is proposed in this paper. According to multibody system theory, a mean value analysis model for volumetric error is established with consideration of geometric errors. Te probability characteristics of geometric errors are obtained by statistical analysis to the measured sample data. Based on probability statistics and stochastic process theory, the variance analysis model of volumetric error is established in matrix, which can avoid the complex mathematics operations during the direct diferential. A four- axis horizontal machining center is selected as an illustration example. Te analysis results can reveal the stochastic characteristic of volumetric error and are also helpful to make full use of the best workspace to reduce the random uncertainty of the volumetric error and improve the machining accuracy. 1. Introduction Along with rapid progress and development of science, tech- nology and social economy, the machining accuracy of CNC machine tools is increasingly demanding. How to improve the accuracy of CNC machine tools has been gotten great attention [1]. To enhance the machining accuracy of CNC machine tools, error modeling is crucial to maximize the performance of machine tools [2], and robust and accurate volumetric error modeling is also the frst step to correct and compensate these errors [3–5]. A volumetric error model, which is the relative error between the cutting tool and the work piece, is a system analysis implement, used when accu- racy is an important measure of performance to predict and control the total error of a system or to achieve compensation. However, machining accuracy of the multiaxis synchro- nized machine is mainly afected by the geometric errors of the guide system, structure stifness, thermal behavior and the dynamic response, and so forth. Te geometric errors are those errors that exist in a machine on account of its basic design and those resulting from the inaccuracies built in during assembly and from the components used in the machine [6]. Permanent and systematic geometric errors are the most common type found in CNC machine tools. In precision machining, geometric errors of machine tools have considerable efect on geometrical and dimensional accuracies of machined features [7] and make up the major part of the inaccuracy of a machine tool [5, 6, 8]. As for an important component of volumetric error, geometric error characterization and mapping is one of the most important steps to fnd a universal kinematic model [9]. Geometric error of the machine tool primarily comes from manufacturing or assembly defects misalignment of the machine’s axis and the position and straightness error of each axis. Because the errors of a drive or axis or the outcome of an assembly process are random at some level [10]; thus, the geo- metric errors vary at diferent locations instead of being con- stants and can be taken as a function of displacement [11]. Te