Study On Modal Analysis & Optimization Of Measuring Points & Modeling Technique For Thermal Errors Of CNC Machine Tools

Based on the analysis and summarization of the study status on thermal errors compensation field, this dissertation carries on deeper studies on the following key techniques in this field: the relationships between modal analysis and thermal errors of machine tools, optimization of thermal key points and thermal errors modeling method. Conclusions from this dissertation are all verified by simulation and experiment application. The main study contents are outlined as follow:Modal analysis has big significance for discovering the thermal errors formation mechanism of machine tools. Here take a turning center for an example, simulate and calculate its two kinds of modes: vibration modes and thermal modes. The modal results show: the outside distance constraints only have effects on the vibration modes and not on thermal modes; the eigenvalues for vibration modes are far greater than that for thermal modes; the outer loads are usually not taken into account in doing vibration modal analysis while the heat transfer by convection must be considered in doing thermal modal analysis; vibration mode is a vector quantity while thermal mode is a scalar quantity. According to the evolution of modal theory, a mode is only an eigenvector corresponding to a specific eigenvalue and embodies the relative displacements of all points within a system. Furthermore, the negative value of an eigenvector is still the mode of the same eigenvalue. Thus what a mode shape reflects is not the real deformation but the intrinsic property of the system. The real deformation can be got by superposition of all modes.Derive a new method for computing the coefficient of convection heat transfer of the spindle surface on revolving. The theory on computing the transient thermal response and thermal deformation is introduced and the simulation is implemented on the spindle and spindle box of the CNC turning center. The relations between thermal errors and cutting tool position are discussed and give the limitation solution of the radial thermal error changing with cutting tool positions.By use of the thermal error sensitivity, according to the principle of maximizing the sum of absolute value of the differences among thermal key points'thermal error sensitivities, provide a simple arithmetic to select the thermal key points in the case of less number of candidate points which is verified on the spindle.As for a large number of candidate points, develop a combined optimizing method using the wavelet analysis and genetic algorithm. The optimization verifications with 10, 6 and 2 key points are done respectively on the spindle box. The optimization results show that: when there are enough number of thermal key points, the optimization effects are not evident; when there are less key points to be selected, the optimization effects are very evident; in addition, the thermal key points for the radial and axial thermal errors are usually not the same group of points.The performances of several common-used modeling methods are studied. Compared with multivariable regression analysis, the thermal errors models established by genetic algorithm are also closely related to the number of thermal key points, but their accuracy is poorer than that by multivariable regression analysis, which can be attributed to the different solution mechanism between these two modeling methods.Neural network models are less affected by the number of thermal key points. Network structure and weight coefficients determine the accuracy of network models. It can be seen that when there are a lot of key points, the thermal errors models by multivariable regression analysis have a better accuracy than net work models; while there are less key points, the former has a poorer accuracy than the latter.A new modeling method, that is, Stepped Coefficients-modifying Modeling method is developed and applied to building the thermal errors models. By modeling instances, this modeling method has the following benefits:1) The models computed thermal errors are exactly fitted to the real thermal errors at the sampling data points.2) The models have better interpolating capacity at the non-sampling data points, which show that the model's robustness is good.3) The number of sensors used is largely reduced while keeping the high accuracy. At last, using the real-time thermal errors compensation controller developed by ourselves, the real-time compensation experiment is implemented on a turning center to verify the study methods and its conclusions from this article. The experimental results show: after compensation, thermal erros are largely reduced and the machine tool accuracy is significantly improved.