Dynamic Modeling And Contact Impact Analysis Of Flexible Systems Based On NURBS

With the development of domestic aerospace and robotics in the direction of lighter weight and precision,the large deformation characteristics of multi-body systems are becoming more and more impossible to be ignored.The traditional floating coordinate method is based on the assumption of small deformation and cannot accurately describe the multi-body system with large flexibility.However,the absolute node coordinate method replaces the rotation with the gradient vector,and the node coordinates are defined in the global coordinate system.The element mass matrix is a constant matrix and does not contain Coriolis force and centrifugal force.The incompatibility of the configuration between the NURBS method in the computer-aided design system and the finite element method in the computer-aided analysis results in that the conversion of the CAD model to the CAA model needs to spend a lot of time on meshing.And because the traditional finite element method uses polynomials to describe the elements,it is not accurate to describe the complex configurations.Therefore,the integration of CAD and CAA systems can not only save time in meshing,but also construct CAA analysis models that are more accurate.The NURBS description method and the absolute node coordinate method are compatible with each other and can be converted to each other,which provides the possibility for the "seamless connection" of CAD and CAA systems.By deriving the conversion relationship between the NURBS surface and the ANCF element,the modeling process based on the NURBS rational finite element is completed,and the information of the CAA model can be obtained only according to the knot vector,the basis functions of degree,the control points and the weights of the CAD model.The element mass matrix,elastic force matrix and generalized external force matrix for dynamic analysis are deduced,and the dynamic equations of flexible multi-body systems based on NURBS rational high-order thin plate elements are established by Lagrange method and least unknown method.A simulation example verifies the convergence and accuracy of this method,and at the same time proves that the model based on the NURBS rational finite element method is more accurate when describing the configuration with features such as conic section.Then this rational element is used in the contact collision problem of the multi-body system.By embedding the normal contact force model and the tangential contact force model into the multi-body system,the multi-body system contact collision dynamic model is established.And the simulation example of the ball-plate contact verifies the accuracy of the contact collision model and the feasibility of handling the contact collision problem of multi-body systems based on the NURBS rational finite element method.The contact and collision problems of flexible multi-body systems with clearance joints are further studied.The NURBS rational shear beam element model is constructed through conversion relations.The clearance joints’ mathematical model is established according to the kinematic relationship and then embedded in the flexible multi-body system in order to establish the contact collision dynamics equation of flexible multi-body system with clearance joints.Taking the flexible double pendulum as a simulation example,the influence of the different clearance hinge models,elastic modulus of different materials and the number of elements on the dynamic response of the system is analyzed.