Dynamic Model Of Fiber Motion And Its Numerical Simulation

In textile engineering program, many spinning processes are completed by employing the airflow to drive the fiber. During the design and improvement process of the spinning technology and spinning machines, it is urgent to understand the law of fiber motion in different conditions by means of numerical simulation methods in advance.The main research work of this paper is to explore an efficient and effective numerical calculation method, which can be used to calculate the nonlinear geometric large deformation problems of statics and dynamics when the fiber is under any one of general applied forces. So it will be used to simulate the behavior of the fiber under various process conditions in the textile engineering and then the results can be used as the basis for the design and improvement of the spinning technology or the spinning machinery.In this paper, the fiber is considered as an elastic thin rod model. Although there have been a complete set of theoretical methods for nonlinear geometric large deformation of the elastic thin rods. These methods are expressed by partial differential equations of multiple parameters, which are very difficult to be used in the numerical solution of the behavior of the fiber at any arbitrary state in the space.In view of the characteristic of the super large length-diameter ratio of the fiber, the paper decomposes a complete fiber into a number of finite elements, and it uses the finite element method to solve the static and dynamic problems of the nonlinear geometric large deformation of the elastic thin rod. At present, the finite element method is usually used in the structural mechanics to solve the problem of the linear statics of the rod structure, but it can not be used to solve the mechanical problem of nonlinear geometric large deformation. So the work of this paper is creative in a certain sense.The work in this paper can be divided into two parts, which are the statics of the elastic thin rod and the dynamics of the elastic thin rod. Main work in the static part can be seen in the following:1. The space bar element stiffness matrix is deduced which is considered the influence of tension, torsion and bending, and also the axial force on the bending;2. The body-fixed coordinate system is established for the cross section of each node, which spatial position is described by the Euler angles of the rigid body dynamics, which is relative to the general coordinate system. The transformation relations between the small angular displacement components and the Euler Angle coordinate increment is deduced which expresses as a rectangular cross section in the cross section;3. For the nonlinear geometric large deformation problem, this paper dose the calculation in the way of loading step by step,the load increment of each step is tiny and the system displacement is tiny too, so that the stiffness matrix of each step is efficiency and accuracy;4. The total displacement increment equation of the static equilibrium analysis of the system is deduced, which corresponds to each load increment step.The main work in the dynamic part can be seen in the following:1. In dynamics, the elasticity and the quality of the elastic thin rod are divided into two parts to process respectively, and the processing method of the elastic part is same to the static method;2. Regarding the quality of each tiny element as a rigid body which is fixed at the node section. The dynamic equation of the general motion of the rigid is deduced in the spatial related the global coordinate, based on the Euler dynamic equation, which is related to the rigid body in rotation round a fixed point, and the mass center motion theorem;3. The differential equations of motion of the finite element analysis of the elastic thin rod are derived, and the numerical calculation method of the differential equation is presented;4. In terms of the contact problem of fiber, this paper refers to the penalty function method, which is used in the treatment of boundary in mathematics. This method constructs a repulsive force between the two contacts. The force increases rapidly when the distance between the two is close, while it is quickly attenuated to zero when there exists a certain distance.The feasibility and accuracy of this method are verified by several numerical examples in the paper.