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This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.

The relationship between significant wave height and period, the variability of significant wave period, the spectral peak enhancement factor, and the directional spreading parameter of large deepwater waves around the Korean Peninsula have been investigated using various sources of wave measurement and hindcasting data. For very large waves comparable to design waves, it is recommended to use the average value of the empirical formulas proposed by Shore Protection Manual in 1977 and by Goda in 2003 for the relationship between significant wave height and period. The standard deviation of significant wave periods non-dimensionalized with respect to the mean value for a certain significant wave height varies between 0.04 and 0.21 with a typical value of 0.1 depending upon different regions and different ranges of significant wave heights. The probability density function of the peak enhancement factor is expressed as a lognormal distribution, with its mean value of 2.03, which is somewhat smaller than the value in the North Sea. For relatively large waves, the probability density function of the directional spreading parameter at peak frequency is also expressed as a lognormal distribution.

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Thermally induced errors have been significant factors affecting machine tool accuracy. In this paper, the spindle thermal error is examined, where thermal error components with five degrees of freedom (DOFs) are considered. An effective measurement system has been devised for five-DOF thermal errors, consisting of gap sensors and thermocouples around the microcomputer-interfaced environment. Several thermal error modelling techniques are also implemented for the thermal error prediction: multiple linear regression, neural network, system identification methods, etc. The performance of the thermal error modelling techniques is evaluated and compared, giving the system identification method as the optimum model having the least deviation. The developed system for the thermal error measurement and modelling has been practically applied to a computer numerically controlled machining centre, and the spindle thermal errors are effectively compensated using the microcomputer-machine tool interfaced networks. The machine tool accuracy has been improved about four to five times typically.