Forward And Inverse Problems Of Nonlinear Dynamics For Virtual Axis Machine Tool

In this dissertation, supported by the National 973 Program of China (Mathematic Mechanization and Automatic Deduction Platform-Mathematic Mechanization Method in Mechanics and Digital Control Technique) and the Mechanical Engineering School Foundation of Tsinghua University (Nonlinear Dynamic Characteristics of Parallel Mechanism and its Key Technique), dynamic analyses for a novel hybrid machine tool developed by Tsinghua University and the second machine tool factory in Qiqihaer are investigated and the dynamic modeling of 6-SPS Stewart platform is presented, the major contents are as follows:1. An iterative Newton-Euler dynamics algorithm is extended to general case. Two iterative Newton-Euler dynamics algorithms with movable base are given. The weight of each link is neglected in first case and considered in second case. The relationship between two algorithms, that is the latter can be derived by varying the initial value of the former, is derived and verified using a mathematical method. The algorithm varying the initial value of the former is applied to the dynamic analyses for the hybrid machine tool .The results show that the calculating efficiency is higher.2. Two kinds of milling force /moment models for end-milling cutter are derived respectively from two views. One of them does not need to be calibrated again. Choosing different milling parameters, milling force and moment are simulated.3. The inverse and forward kinematic analyses of the hybrid machine tool are given. The analytic solutions of displacement, velocity and acceleration for the machine tool are obtained.4. The hybrid machine tool is regarded as being composed of series and parallel structures. Using Newton-Euler approach, Newton-Euler dynamic equations for each isolated body of the parallel structure are established. The dynamic equations for the series structure are given using the extended iterative Newton-Euler dynamics algorithm. Then, a closed-form inverse dynamic formulation is derived through some elimination techniques. The simulation results show that the actuating forces required in one slider while the moving platform conducts one movement is equal to the actuating forces required in another slider while the moving platform conducts the symmetric movement about the symmetric plane of the machine tool. The inverse dynamic simulation considering milling process is carried out. The influence of milling parameters on the actuating forces is investigated.5. Based on the inverse dynamic formulation of the hybrid machine tool, the forward dynamic equations are developed. In two cases, one neglecting the milling process and the other considering it, simulations of the forward dynamics are investigated.6. The vibration model of the hybrid machine tool is established. The influence of milling parameters on vibration characteristics is investigated by simulation. Phase trajectory plots show that the vibration is chaotic.7. The dynamic equations for 6-SPS Stewart platform are established through graph theory. First,tree structure is constructed, and the oriented graph of the system is drawn. Second, the incidence matrix, entry matrix, rotation axis matrix, sliding axis matrix and so on are given. The dynamic equations of tree structure are obtained by calculating. Finally, the dynamic equations of 6-SPS Stewart platform are obtained by constraint equation.