This thesis addresses a comprehensive approach to understanding the time-varyingthermal errors in machine tools. Errors in machine tools are generally classified as beingtime or spatial dependent. Thermal errors are strongly dependent on the continuouslychanging operating conditions of a machine and its surrounding environment. Uniformtemperature rises or stable temperature gradients, which produce time-invariant thermalerrors, are considered to be rare in ordinary shop floor environments. Difficulties inanalysing time-varying thermal errors are that, first of all, the temperature distributionwithin the components of a machine should be evaluated, and secondly, the distributionis continuously changing with time. These difficulties can be overcome by introducing apoint-wise description method with three thermal parameters. From the theoreticalanalysis of simple machine elements such as bars, beams and cylinders, and extensivefinite-element simulation data for a straightedge subject to room temperature variations,three thermal parameters, i. e. time-delay, time-constant and gain, were identified toobtain a precise description of the thermal deformation of a point of a machine body.Time-delay is dependent largely on thermal diffusivity, and the heat transfer mechanism.The time-constant is governed by heat capacity, heat transfer mechanism and body size.Gain, on the other hand, is determined by the thermal expansion coefficient, heattransfer mechanism and mechanical constraint. The three thermal parameters, in turn,imply that thermal deformation of a point in a body can be described by a simple first-order differential equation. Regarding their dependence on the heat transfer mechanism,a more refined description requires a time-varying linear first-order differentialequation. Such an equation can be applied to each point of interest of a machine body.The final form of modelling, using the parameters, is a state-space equation gatheringthe governing equations for the points of interest. By adopting the point-wise discretemodelling method, we can overcome the difficulty of the spatial distribution of thetemperature. Indeed, the calibration of a machine tool is usually performed at discretepoints.The completion of this approach was made by presenting the methods by which thethree thermal parameters can be evaluated. The first method employs analytical toolsbased on simplifying assumptions about the shape and boundary conditions of machinecomponents. The second method was to apply numerical techniques to complexmachine components. Because there are many drawbacks in theoretical approaches,experimental techniques are essential to complement them. The three thermalparameters can be easily identified using popular parameter identification techniqueswhich can be applied to time-varying cases by their recursive forms. The techniquesdescribed were applied to modelling the thermal errors in a single-point diamondturning research machine. It was found that the dominant error component was spindleaxial growth. The predictive model for the time-constant was shown to be in agreementwith both the machine and with the scaled physical model rig.
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