本文導入變異數觀念先建立與驗證工具機空間誤差變異模式以及藉放電加工建立與確認一套有效判認製程變異的方法，進一步結合工具機誤差模式與加工製程變異估測不同加工條件銑削後之工件幾何尺寸誤差。
研究先以向量法完成XYFZ構型之三軸工具機誤差模式，再導入變異數分析法建立工具機幾何誤差變異影響空間誤差變異之模式。經由雷射對角線量測實驗，此模式成功模擬出路徑誤差範圍於兩個標準差準確包含實際量測之循圓路徑，意即具信心指出路徑95%之範圍。為建立判認製程變異方法，本研究則藉放電加工製程為研究載具。先以標準件法量測出各製程變異數據，再利用變異數分析方法考慮交互作用已可成功判認製程變異與估測機台誤差。
最後，統合工具機空間誤差變異模式與製程變異分析方法，銑削工件的幾何尺寸誤差可有被估測並已經由實驗驗證。因此，對一現有機台，本研究方法可設計適當的製程參數以達到最適工件品質要求。

By analysis of variance, variance model of spatial error of machine tool and a method for identification of process variance both have been developed and verified. Further, the geometrical dimensional error of a milling product can be estimated by combining spatial error of machine tool and processing variance under different cutting conditions.
The kinematical spatial error model for XYFZ machine configuration was first investigated using vector method. Based on analysis of variance, the spatial error model considering stochastic nature then has been developed. This model was validated through experiments conducted on a milling machine with laser diagonal method as measurement. The two standard-deviation estimated is shown to excellent agreement with measured. For identification of process variance by analysis of variance, a series of EDMed experiments were performed and their results discussed to validate this method. Through considering coupling effect, the results shown that process variance and machine error can be estimated accurately by proposed.
With spatial error model of machine tool and the analysis method of process variance, the investigation of milling process shown that the geometrical dimensional error of a milling product can been evaluated. For a given machine tool, the appropriate process parameters can be designed to achieve the best work quality.

[1] Dorndorf, U., Kiridena, V., S., B., and Ferreira, P., M., Optimal budgeting of quasistatic machine tool errors, ASME Journal of Engineering for Industry, Vol. 116, pp. 42-53,1994.
[2] Alexander, H., Slocum, Precision machine design, Prentice-Hall, Englewood Cliffs, New Jersey, 1992.
[3] Zhang, G., Ouyang, R., Lu, B., and Hocken, R., A displacement method for machine geometry calibration, Annals of the CIRP, Vol. 37/1, pp. 515-518, 1988.
[4] Zhang, G., Veale, R., Charlton, T., Borchardt, B., and Hocken, R., Error compensation of coordinate measuring machine, Annals of CIRP, Vol. 34/1, pp. 445-448, 1985.
[5] Schultschik, R., The components of the volumetric accuracy, Annals of the CIRP, Vol. 25/1, pp. 223-228, 1977.
[6] Tong, K., Amine Lehtihet, E., and Joshi, S., Parametric error modeling and software error compensation for rapid prototyping, Rapid Prototyping Journal, Vol. 9, pp. 301-313, 2003.
[7] Zhang, G. X., and Fu, J. Y., A method for optical calibration using a grid plate, Annals of the CIRP, Vol. 49/1, pp. 339-402, 2000.
[8] Jung, J. H., Choi, J. P., Lee, S. J., Machine accuracy enhancement by compensating for volumetric errors of a machine tool and on machine measurement, Journal of Materials Processing Technology 174, pp.54-66, 2004.
[9] Okafor, A. C., and Ertekin, Y. M., Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics, International Journal of Machine Tools & Manufacture, Vol. 40, pp. 1199-1213, 2000.
[10] Heui, J. P., Young, S. K., and Joon, H. M., A new technique for volumetric error assessment of CNC machine tools incorporating ball bar measurement and 3D volumetric error model, International Journal of Machine Tools & Manufacture, Vol. 37, pp.1583-1596, 1997.
[11] Lee, J. H., Liu, Y., and Yang, S. H., Accuracy improvement of miniaturized machine tool: Geometric error modeling and compensation, International Journal of Machine Tools & Manufacture, Vol. 46, pp. 1508-1516, 2006.
[12] Hsieh, J. F., and Lin, P. D., Application of homogeneous transformation matrix to measurement of cam profiles on coordinate measuring machines, International Journal of Machine Tools & Manufacture, Vol. 47, pp. 1593-1606, 2007.
[13] Ferreira, P. M., and Liu, C. R., A contribution to the analysis and compensation of the geometric error of a machining center, Annals of CIRP, Vol. 35/1, pp. 259-262, 1986.
[14] Mou, J., and Liu, C. R., An adaptive methodology for machine tool error correction, Journal of Engineering for Industry, Vol. 117, pp. 389-399, 1995.
[15] Lin., Y., and Shen, Y., Modeling of five-axis machine tool metrology models using the matrix summation approach, The International Journal of Advanced Manufacturing Technology, Vol. 21, pp. 243-248,2003.
[16] Qian, G. Z., and Kazerounian, K., Statistical error analysis and calibration of industrial robots for precision manufacturing, The International Journal of Advanced Manufacturing Technology, Vol. 11, pp. 300-308, 1996.
[17] Shen, Y., and Duffie, N. A., An uncertainty analysis method for coordinate referencing in manufacturing systems, ASME Journal of Engineering for Industry, Vol. 117, pp.42-48, 1995.
[18] Wilhelm, R. G., Hocken, R., and Schwenke, H., Task specific uncertainty in coordinate measurement.
[19] Lira, I., and Cargill, G., Uncertainty analysis of positional deviations of CNC machine tools, Precision Engineering, Vol. 28, pp. 232-239, 2003.
[20] Menq, C. H., and Borm, J. H., Statistical characterization of position errors of an ensemble of robots and its applications, ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111, pp. 215-222, 1989.
[21] Ahn, K. G., and Cho, D. W., An analysis of the volumetric error uncertainty of a three axis machine tool by beta distribution, International Journal of Machine Tools & Manufacture, Vol. 40, pp. 2235-2248, 2000.
[22] Yau, H. T., Evaluation and uncertainty analysis of vectorial tolerances, Precision Engineering, Vol. 20, pp. 123-137, 1997.
[23] Kiridena, V., and Ferreira, P. M., Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools, International Journal of Machine Tools & Manufacture, Vol. 33, pp. 417-437, 1993.
[24] Castro, H. F. F., Uncertain analysis of a laser calibration system for evaluating the positioning accuracy of a numerically controlled axis of coordinate measuring machine and machine tools, Precision Engineering, Vol. 32, pp. 106-113, 2008.
[25] Abbe, M., Takamasu, K., and Ozono, S., Reliability on calibration of CMM, Measurement, Vol. 33, pp. 359-368, 2003.
[26] Wang, S. M., and Ehmann, K. F., Measurement methods for the position errors of a multi-axis machine. Part 1: principles and sensitivity analysis, International Journal of Machine Tools & Manufacture, Vol. 39, pp. 951-964, 1999.
[27] Wang, C., Laser vector measurement technique for the determination and compensation of volumetric positioning errors. Part 1: Basic theory, American Institute of Physics, 2000.
[28] Chapman, M. A. V., Limitations of laser diagonal measurements, Precision Engineering, Vol. 27, pp. 401-406,2003.
[29] Castro, H. F. H., and Burdekin, M., Evaluation of the measurement uncertainty of a positional error calibrator based on a laser interferometer, International Journal of Machine Tools & Manufacture, Vol.45, pp. 285-291, 2005.
[30] Schwenke, H., Franke, M., and Hannaford, J., Error mapping of CMMs and machine tools by a single tracking interferometer, Annals of the CIRP, Vol. 54, pp. 475-478, 2005.
[31] Elman, C. J., Electrical Discharge Machining, SME Publication, 2001.
[32] Guitrau, E. B., The EDM Handbook, Hanser Gardner Publications, 1997.
[33] Ho, K. H., and Newman, S. T., State of the art electrical discharge machining(EDM), International Journal of Machine Tools & Manufacture, Vol.43, pp. 1287-1300, 2003.
[34] Sachez, J. A., Lopez de Lacalle, L. N., Lamikiz, A., and Bravo, U., Dimensional accuracy optimization of multi-stage planetary EDM , International Journal of Machine Tools & Manufacture, Vol.42, pp. 1643-1648, 2002.