Papers by Keyword: Dynamics of Flexible Multibody Systems

Abstract: A new type of dynamic equations of flexible multibody systems is derived via virtual work principle together with floating frame approach. The absolute Cartesian coordinates are used to describe positions of floating frames’ origins of deformable bodies; The orientation transform matrices as special orthogonal groups are used to describe rotation motions; The modal coordinates are used to express small deflections of deformable bodies with respect to the corresponding floating frames. The resulting equations are mixed classic Euler-Lagrange equations of translational motion of bodies and deformation and Euler-Poinaré equations of rotation in Lie groups and Lie algebras, the Lie-Poisson equations as reconstruction equations obtaining Lie Groups from Lie algebras, constraint equations Lie groups and Lie algebras. In order to simplify the implementation, we separate the constant coefficient matrices in generalized mass matrices and generalized forces in detail. The results can be easily used to design geometric integrators of Lie group structure preserving.

Abstract: This paper develops a novel five DOF hybrid polishing kinematics machine tool in order to obtain more stable machining result in the elastic polishing on the free-form surfaces. Because the machine tool is a complex multi-body system that comprises many close-loop structures, jointing clearance becomes the important influence factor to its moving stability. The unified rigid multi-body and flexible multi-body dynamics equation of for the parallel mechanism of hybrid polishing kinematics machine tool is respectively built, which considers the influence of joint with clearance and applies the kinematics model of Newton second state. The result of analysis shows that the moving stability of the hybrid polishing kinematics machine tool is reduced due to the existing jointing clearance. However, the interior flexibility of the mechanism can reduce the shock effect of collision in the part of motion pair. It can improve the working stability of mechanism.

Abstract: The hybrid polishing kinematics machine tool (HPKMT) which is made up of “3 axes parallel + 2 axes series” is developed with the specially designed elastic polishing tool system for the polishing operation on the free-form surfaces by using the characteristic of the elastic polishing adequately by the authors. In order to control the HPKMT effectively, its characteristic of the kinematics and dynamics need be known deeply. Moreover, the problem of inverse dynamics is the theory foundation to apply dynamic control of the HPKMT. The analysis of the inverse of mechanism is the important part in the research of dynamics. On the basis of the differential equations of flexible multi-body dynamics, this paper discusses on the condition of knowing the trace, posture and velocity for the end of bodies how to solve the constraint force and constraint moment of each joint on the 3- PTT parallel mechanism and two-joint series mechanism.

Abstract: The virtual axis hybrid polishing machine tool (VAHMPT) is the novel equipment developed by the authors that is aimed at the precision machining on the free-form curved surfaces. This paper establishes the dynamic equations of the spatial rigid-flexible coupling multibody systems considering the coupling for the rigid movement of the whole VAHMPT with the elastic deformation of each leg by means of the theory of dynamics of flexible multibodysystems. Meanwhile the dynamic characteristics of the hybrid machine tool is studied in detail by the dynamics simulation analysis. The dynamic simulation of the machine shows that the elastic deformation of each leg is very small during the movement of the machine and the influence of the flexibility of each leg on the trace of moving platform is not obvious due to the characteristics of joints. The dynamic characteristics of the VAHPMT is verified combining with the experiments. It is shown that the experiments result is almost accorded with the simulation analysis. The satisfied polishing effect on the curved surfaces can be obtained and the demand of the polishing can be achieved by the VAHPMT.