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During the working process of high-speed multiaxis machine tools, inertial forces can cause vibration and deformation of mechanical structure, which lead to the dynamic error of tool center point (TCP) relative to worktable and can adversely affect the machining performance. Considering the varying feed positions and accelerations during machining, a parameter-varying multi-rigid-body dynamic model of a 3-axis gantry machine tool is proposed. This model represents the position dependent structural dynamics and inertial forces, which can simulate the dynamic error of TCP relative to worktable within the entire workspace. The results show that the dynamic error in one direction is affected by the feed motions of multiple feed axes. The magnitudes of the dynamic error significantly vary with the position of Z-axis. And the dynamic errors in Y- and Z-direction show different varying trends. Then the theoretical model is used to discuss the dynamic error and position dependency. The expressions of TCP dynamic response and inertial forces reveal the reason why the dynamic errors in Y- and Z-direction show different varying trends.

In the working process of high-speed multiaxis machine tools, inertial loads due to high feed acceleration and time-varying gravity loads due to changing configuration of multiaxis structure result in time-varying complex loads applied to linear rolling guideway. Existing models cannot efficiently represent the effect of complex loads on multidirectional stiffness variation of linear rolling guideway. In this paper, a hybrid model of multidirectional stiffness of linear rolling guideway and the solving algorithm are proposed. The complex loading conditions of linear rolling guideway in high-speed multiaxis machine tool structure are considered. And contact flexibilities between rolling balls and grooves are modeled with the effect of elastic deformations of runner block and rail. The proposed model can calculate the multidirectional stiffness with high accuracy. Meanwhile the differences between the stiffness characteristics in different directions are represented correctly. The variations of multidirectional stiffness of linear rolling guideway under time-varying combined loads are analyzed. This study provides an effective way to comprehensively evaluate the stiffness characteristics of linear rolling guideway which can contribute to the dynamic analysis and active design of high-speed machine tool structure.

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The geometric configurations, vibration frequencies and thermodynamics properties of Al2O3X2 (X= H, D, T) molecular clusters with lower energy are optimized using the B3LYP/6-311++g (d, p) method. The changes of entropy, enthalpy and Gibbs free energy of the reactions between Al2O3 and hydrogen (deuterium or tritium) gas are calculated by the solid electron-vibration approximate method and thermodynamic formulae at temperatures of 298, 398, 498, 598, 698, 798, 898, 998 and 1098 K, and then the relationships between the equilibrium pressure of hydrogen (deuterium or tritium) gas and temperature in these reactions are obtained. The results show that the ground state of the gaseous Al2O3H2 is Al2O3X2 (X= H, D, T) (1A') Cs. Hydrogen can be displaced by deuterium; deuterium can be displaced by tritium in the reactions between Al2O3 and X2 with the productions of solid Al2O3X2 which relates to ground gaseous Al2O3X2 with Cs symmetry. This displacement sequence is opposite to that in the reactions between titanium and X2. These displacement effects are very weak, and they are weaker and weaker as the temperature increases.