Basic Theories And Research Of Algorithms For DEM Based On Ellipsoidal Particles Model

There are lots of granular materials in the nature, and the traditional continuum mechanics method (CMM), which is applied to research the interaction between granular materials and related mechanical parts, can only consider the granular colony as a whole, and it is unable to analyze the movement course of each granular particle and the interaction among the colony. As a result, it cannot resolve the problem very well. Recently when designing the related mechanical parts, the experience and experimentation methods are depended on mostly, and it takes both time and stamina a lot and cannot achieve the expected designing purpose, and the demand of optimized design and energy saving is far away from satisfaction.In 1970s, Cundall et al. put forward the DEM primarily. The basic thought is to simplify granular materials as a set of particles with a certain kind of shape and mass, and endue the particle-particle and particle-boundary relationship with a certain kind of contact mechanics model and some parameters. The DEM is applied to research the contact effects, which influence the particle-particle and particle-boundary relationship, and the different physical and mechanical characteristics between particle and contacted boundary. The dynamic laxity method, the Newton's Second Law and time step iteration are introduced into DEM to calculate the movement and displacement of each particle, and thus it is especially compatible to resolve the nonlinear problem. It can analyze not only the interaction between various granular materials and different border but also the influence on the motion of granular materials, according to changing the model of particle, the model of border, dynamics equations and parameters in Discrete Element Method. Because of these advantages, the DEM has been widely used.With the extensive application of DEM, it becomes an emphasis and difficulty in the research of boundary modeling of DEM and the development of the software of DEM that how to build up an analysis of boundary model of DEM with the complicated structure and the style of movement. At present, there is not too much research about boundary modelings. And the research about boundary modeling which reported doesn't has the function that combine the boundary design and the analysis of DEM. In this situation, new boundary modeling is needed to satisfy more requests. Besides, during the simulate computation of the DEM, we also need more models which are more complicated about granular materials, only the spheroid particles can not satisfy the need of the users. It needs more complicated models to simulate the natural things. Based on the present status of the research of DEM and the summary of the current boundary modeling of DEM, and related the characteristics and design requirements of working parts of machinery, this paper presents a novel method to establish a three-dimension Discrete Element Method (DEM) to analyze model of machine's parts based on their three-dimension CAD model. And with the environment, which developed by the former people in the lab, I realize the function that can do some computation of simulation based on the granular models which are ellipsoid models. All of these not only combine the two parts of the software-the boundary modeling part and the simulation parts, but also strength the software and make it satisfy more requests.The modeling of 3D entity in Pro/E should be decomposed according to the topology, until it make them to be basic primitive that can be recognized by the boundary modeling parts of the software. Now, we can recognize the primitive atomics contains plane, circle, sphere, ellipse, cylinder, conical surface and so on. In order to recognize more complicated boundaries, it need to man-machine communication, during the boundary modeling process the program gives instructions, and the user follow the instructions, until the end of the modeling. Then we need combine the type of movement, and set the information of movement and material up to the 3D mechanical, and then we transfer the information of topology, geometry, movement and material to external database. The software of 3D DEM simulation obtain the primitive record, including the geometric information of boundary (type of primitive topology, feature parameter of boundary), the information of movement (movement attribute parameter of primitive), the information of material (material parameter of primitive). It need build up the instance of the class of primitive of DEM.With the DEM simulation software, takes ellipsoidal particles for example, presents the thought of modeling DEM computing courses, such as the force between the particles and the force betweem particles and simple boundary, also do some work on the transform of coordinate system, the force between particles and boundaries, in order to distinguish whether two particles contact and get the contact-overlaps between them, do some work on the solution of algebraic equation, do some work on establishing the theory of DEM computing based on the ellipsoidal particles.Based on the methodology and theory above, the code of Discrete Element Method is developed with WINDOWS platform. Pro/E graphics library is introduced to draw graphics. It introduces the framework, function of the software and the key techniques to realize the software, and introduce key technology and the way to realize it about the determinant of contact of ellipsoids, and the overlaps between two particles. And also do some simple experiments, they confirm the software's validity accuracy and advantage. The virtues of this competitive design-analysis software are:①It can establish the DEM based on the CAD model of related mechanism directly, and then can implement the integration between CAD software and the DEM analysis software, thereby can integrate the CAD design and DEM performance analysis of related mechanism.②It can carry through a dynamic simulation for the working process of mechanical parts based on the CAD model, therefore can analyze the working mechanism and invent the mechanical parts with new mechanism. These cannot be implemented by current design methods and technique of mechanical parts that are relative to granular materials.③It can build the particle's model by ellipsoid equations. This extends the particle models, and makes it possible that can do simulations of DEM with more kinds of particles. also do some prepare works for the more complicated models of particles.