Vibration Analysis Of Large-scale Complex Multibody Systems Based On Constraint Topology Transformation

As the increasement of requirements in dynamic performance of modern mechanical systems, the structural complexity of mechanical systems has significantly increased. Dynamic analysis and optimization has become the most critical issue in structural design. Since mechanical systems are usually modeled as large-scale complex multibody systems to acquire satisfied accuracy, it leads to two major problems for dynamic analysis of such kinds of large-scale complex multibody systems using conventional methods, i.e., accuracy and computational efficiency, which are one of the critical problems to be resolved in structural design at present. Particularly, vibration analysis is the core and basis of dynamic analysis of such kind of systems, and the computational efficiency becomes one of the bottlenecks for design, optimization and control. In order to fulfil the urgent requirements of state key scientific research and engineering projects, formulation and solution of vibrational equations for such kinds of systems are studied in this dissertation, by starting with investigation of constraint topologies for spatial multibody systems. A new method for vibration analysis of large-scale complex multibody systems with high accuracy and efficiency is finally presented.All the physical parameters are defined in matrix-vector form, including mass and inertia tensor of each body, coefficients of spatial spring-damper, mathematical representation of joint, and spatial motion status of rigid body, so as to get clear notation and provides clear insight into the system. Based on uniform transformation of vibrational displacements, a new method for formulating a minimal set of second-order linear ordinary differential equations (ODEs) in three steps is proposed. Firstly, a set of linearized ODEs are formulated in terms of absolute coordinates without considering any constraint in the system. Secondly, an open-loop constraint matrix is generated to formulate ODEs for open-loop mechanism system which is obtained by ignoring all cut-joints in the original system. Finally, a cut-joint constraint matrix is generated to formulate a minimal set of ODEs for the original closed-loop mechanism system. Since there is no need for derivation of matrices and linearization of equations, computational efficiency can be significantly improved by using the proposed method as compared with traditional approaches.Complex modal analysis is then performed to calculate the eigenvalues and eigenvectors, and then modal parameters are obtained. General formulation of transfer function between two arbitrary points with respect to different reference frames is derived. The presented physical-coordinates-based formula consists of explicit transformation between physical coordinates and modal coordinates, and hence is more practical than traditional general-coordinates-based formulation. Transfer function in the vicinity of each natural frequency is always computed to improve numerical accuracy near the resonance frequencies. Sensitivity of natural frequency with respect to design parameters, instead of conventional elements of mass (stiffness, or damping) matrix, is derived with a simple expression. A recursive algorithm is proposed to solve inverse equilibrium problems, which computes inner forces to keep the system with nearly zero deformation.Software named Simulith has been developed based on the proposed algorithm. Function such as normal mode analysis, transfer function analysis, sensitivity analysis, optimization and control are all included. The correctness and efficiency of the proposed method have been verified by numerical experiments on multibody systems with different kinds of constraint topologies. The results of performance test done by China Software Test Center (CSTC) show that, the computational efficiency of the presented approach has been significantly improved in compare with traditional methods such as ADAMS. Furthermore, the greater the number of bodies, joints, or spring-dampers is, the more the improvement in computational efficiency is obtained. The proposed method has been successfully applied in dynamic analysis and optimization of 100nm optical lithography equipment. The design period and the cost of development for the optical lithography equipment have been significantly reduced. Experimental results have further verified the correctness and effectiveness of the presented approach. The proposed method can also be used for vibration analysis of many other kinds of structures and mechanism systems.The study work is one of the major achievements in A Study of the Key Issues on Dynamics and Control in the Ultra Precision Mechanisms, which has won the First Prize of Ministry of Education Natural Science Award in 2007.