彈塑性球體衝擊碰撞之解析力學與計算模擬研究

本論文研究彈塑球體衝擊之碰撞力學問題，由精密控制與能量循環等工程技術開發考量，研究旨在球體碰撞的過程中，系統於何控制條件中，能夠有最小的動能損失，將以理論探討與模擬計算進行研究與驗證。理想狀況下的碰撞是彈性碰撞，即無動能損失。然而在現實生活中，碰撞球前後難免會有動能損失，損失的部分會轉換成熱能、旋轉動能等。動能損失大多被認為與碰撞體的材料有關，因此分析方式將以有限元素軟體ABAQUS (ABAQUS, Inc.)模擬球體碰撞，研究在不同材料與幾何下碰撞的動能損失，搭以理論碰撞模型驗證模擬的準確性。從模擬結果觀察以及論文中的無因次化分析，得到只須給定材料條件，代入楊氏模數、降伏強度、密度可以計算出極限撞擊速度(critical impact velocity)。只要碰撞速度不超過極限撞擊速度，球體碰撞的動能損失將為零。論文內容安排為：第二章為介紹本論文所使用到的理論碰撞模型，驗證ABAQUS模擬結果。第三章為模擬半徑相同之兩球的碰撞，其中包含了無因次化分析，為了方便分析模擬結果數據以及探討動能損失與材料參數之關係。第四章為結果討論，分析並提出一個合理的關係描述動能損失與材料參數之關係。第五章為在本研究中如何使用ABAQUS，包括數學模型建置、材料參數設定、接觸性質設定、網格劃分以及後處理。第六章為研究之結論以及未來展望。

關鍵字

碰撞；降伏強度；接觸力學；恢復係數

並列摘要

This thesis investigates the collision mechanics of elasto-plastic spherical collisions with a view to developing engineering technologies for precision control and energy recycling. The study aims at minimizing the kinetic energy loss of the system during the collision of spheres under controlled conditions. Ideally, the collision is elastic, i.e., no kinetic energy is lost. However, in real life, there is inevitable loss of kinetic energy, and the loss will be converted into thermal energy or rotational kinetic energy. The loss of kinetic energy is mostly considered to be related to the material of the colliding body. Therefore, the analysis will be performed by simulating the collision of a sphere with finite element software ABAQUS (ABAQUS, Inc.) to study the loss of kinetic energy under different materials and geometries condition. To verify the accuracy of the simulation, we adopted theoretical collision models. From the simulation results and the dimensionless analysis in the research, we can calculate the critical impact velocity by substituting Young's modulus, yielding strength, and density of the colliding body. As long as the collision velocity does not exceed the critical impact velocity, the kinetic energy loss of the sphere collision will be zero. The paper is organized as follows: In Chapter 2, we introduce the theoretical collision model used in this research to verify the ABAQUS simulation results. In Chapter 3, we simulate the collision of two spheres with the same radius, which includes the dimensionless analysis to facilitate the analysis of the simulation results and to investigate the relationship between kinetic energy loss and material parameters. In Chapter 4, we discuss the results in Chapter 3, and analyzes and proposes a reasonable relationship to describe the relationship between kinetic energy loss and material parameters. In Chapter 5, showing how we use ABAQUS to study, including building mathematical model, setting material parameter, setting contact property, grid delineation, and post-processing. In Chapter 6, we presents the conclusion of the study and prospects.