ORIGINAL ARTICLE Modeling, measurement, and evaluation of spindle radial errors in a miniaturized machine tool S. Denis Ashok & G. L. Samuel Received: 5 July 2010 / Accepted: 4 July 2011 / Published online: 22 July 2011 # Springer-Verlag London Limited 2011 Abstract Miniaturized machine tools have been established as a promising technology for machining the miniature components in wider range of materials. Spindle of a miniaturized machine tool needs to provide extremely high rotational speed, while maintaining the accuracy. In this work, a capacitive sensor-based measurement technique is followed for assessing radial errors of a miniaturized machine tool spindle. Accuracy of spindle error measurement is affected by inherent error sources such as sensor offset, thermal drift of spindle, centering error, and form error of the target surface installed in the spindle. In the present work, a model-based curve-fitting method is proposed for accurate interpretation and analysis of spindle error measurement data in time domain. Experimental results of the proposed method are presented and compared with the commonly followed discrete Fourier transform-based frequency domain-filtering method. Proposed method provides higher resolution for the estima- tion of fundamental frequency of spindle error data. Synchro- nous and asynchronous radial error values are evaluated in accordance with ANSI/ASME B89.3.4M [9] standard at various spindle speeds and number of spindle revolutions. It is found that the spindle speed and number of spindle revolutions does not have much influence on synchronous radial error of the spindle. On the other hand, asynchronous radial error motion exhibits a significant speed-dependant behavior with respect to the number of spindle revolutions. Keywords Spindle radial errors . Modeling . Curve fitting . Analysis Nomenclature Symbol Description C h Magnitude of harmonic components of spindle error measurement data D Basis matrix containing the mathematical functions of the proposed model Ej Sum of squared residual value for the given discrete frequency f j f 0 Fundamental frequency of spindle error measurement data f j Discrete frequency value around the rotation frequency of spindle H Harmonic cutoff value for spindle radial error measurement X Unknown model parameters for the given discrete frequency f j a h ,b h Fourier coefficients of the spindle error measurement data m i Estimated value using the mathematical model m i ' Radial error measurement data at the given sampling time m ci Contribution of centering error of artifact at the given sampling time m si Contribution of synchronous components at the given sampling time m ti Contribution of sensor offset and thermal drift at the given sampling time p 0 Contribution of sensor offset p 1 , p 2 Coefficients of second order polynomial function t i Sampling time for the spindle error measurement data e i Residual of the estimated values or asynchronous radial error S. D. Ashok : G. L. Samuel (*) Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600-036, India e-mail: samuelgl@iitm.ac.in Int J Adv Manuf Technol (2012) 59:445–461 DOI 10.1007/s00170-011-3519-8