軟球顆粒離散元素法碰撞模型之研究

A Study of the Soft-Sphere Discrete Element Method Contact Model Parameters

賴建丞(Chien-Cheng Lai)

指導教授 ： 郭修伯

國立臺灣大學/工學院/化學工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101851

摘要

離散元素法(DEM)利用計算粉粒體系統中所有粒子對之間的相互作用力來描述系統運動狀態等整體性質。粒子碰撞模型的選擇會大幅影響DEM模擬的表現，因此選擇適合的碰撞模型為DEM模擬的重要課題。本研究主要討論兩個最常使用的粒子碰撞模型，線性/非線性彈簧—阻尼模型。首先對此兩模型的參數進行完整推導，並推導出一項原本需查表的非線性彈簧—阻尼模型中的阻尼項係數。本研究對線性與非線性彈簧—阻尼模型進行碰撞過程中的速度、形變量及受力變化與文獻實驗值作分析與比較，也比較兩模型對恢復係數與碰撞時間的預測能力。本研究發現無論線性/非線性彈簧—阻尼模型，恢復係數的預測結果均與碰撞初速度無關。但經實驗證實恢復係數會隨著碰撞速度上升而下降，因此本研究比較三種不同粒子碰撞恢復係數的模型，分析其適用範圍。並將恢復係數表示式代入線性/非線性彈簧—阻尼模型中，使其成為碰撞速度的函數。比較三種以恢復係數模型修正的線性/非線性彈簧—阻尼模型之速度、形變量、受力變化、回彈速度與碰撞時間，結果顯示回彈速度預測值誤差大幅下降。

關鍵字

離散元素法 ； 碰撞模型 ； 彈簧 —阻尼模型 ； 恢復係數 ； 碰撞時間

並列摘要

Discrete Element Method (DEM) is a numerical simulation method that has been widely used to describe the motion and mechanical behavior of assemblies of particles by calculating the interaction forces between all particle pairs. The selection of the contact model between particles will affect the DEM simulations performance. In this study, we discuss the two most frequently used contact models, the linear/non-linear spring-damping models. This work gives a complete derivation of the parameters used in the spring-damper models, including a new derivation of a damp coefficient for the non-linear spring-damping model, which was previously empirical. The particle velocity, deformation and contact force during the contact calculated by the contact models are described and compared. The predictions of the coefficient of restitution and contact duration by the two spring-damping models are also compared. Previous spring-damping models predict the coefficient of restitution being irrelevant to the contact velocity, which does not agree with experimental data. We incorporate three contact velocity-related coefficients of restitution into the spring-damping contact models. The velocity, deformation, contact force, rebound velocity, and contact duration predicted by the modified spring-damping models are compared with those determined by the original spring-damping model. The modified models can predict a more accurate rebound velocity.

並列關鍵字

Discrete element method (DEM) ； Contact mechanic ； Spring-damping model ； Coefficient of restitution ； Contact duration

參考文獻

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