非规则颗粒与滚筒球磨机相互作用的离散元–有限元耦合分析
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国家重点研发计划重点专项(2021YFA1500302);国家自然科学基金资助项目(42176241, 52192693, U20A20327, 12202095);大连市科技人才创新支持计划(2022RQ004)


A DEM-FEM coupled analysis for the interaction between the irregular granular materials and tumbling mill
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    摘要:

    非规则颗粒形态显著影响球磨机中颗粒材料的运动行为,同时对球磨机结构产生不同的力学响应。采用超二次曲面方程描述非规则颗粒材料,并发展了离散元(discrete element method, DEM)–有限元(finite element method, FEM)耦合算法以分析非规则颗粒材料与滚筒球磨机间的相互作用。在该算法中,滚筒球磨机被划分为一系列四边形单元,并且超二次曲面颗粒与球磨机间的接触判断可转化为超二次曲面颗粒与四边形单元间的接触判断。将计算得到的碰撞力向节点插值,该节点力作为载荷条件在有限元中进行隐式动力学求解,并通过求解颗粒运动方程和有限元动力方程实现颗粒运动更新和结构力学响应分析。进一步分析了滚筒球磨机中球体、圆柱体和立方体颗粒材料的运动行为以及滚筒球磨机的变形及应力分布规律。研究结果表明:颗粒形状显著影响球磨机研磨效果和球磨机结构位移;立方体颗粒具有最好的研磨效果,而圆柱体颗粒比球体颗粒具有更好的研磨效果;在结构位移上,立方体颗粒有最大的峰值位移,其次是圆柱体和球体颗粒;相比于规则的球体颗粒,超二次曲面颗粒有不规则的表面形状,这会导致更好的研磨效果和更大的结构位移。

    Abstract:

    The irregular granular morphology significantly affects the kinematic behavior of the granular materials in a tumbling mill, and simultaneously causes different mechanical responses of the tumbling mill. The superquadric functions were used to describe the irregular granular materials, and a discrete element method (DEM)-finite element method (FEM) coupled algorithm was developed to analyze the interaction between the irregular granular materials and tumbling mill. In this algorithm, the tumbling mill was divided into a series of quadrilateral elements, and the contact detection between the superquadric particles and the tumbling mill could be simplified as the contact detection between the superquadric particles and the quadrilateral elements. The calculated collision forces were interpolated in the nodes, which were used as the loading conditions in the finite elements for the solution of the implicit dynamics. The update of particle motion and the structural mechanical response were realized by solving the particle motion equation and the finite element dynamic equation. Furthermore, the motion behavior of spherical, cylindrical and cubic granular materials in a tumbling mill and the deformation and stress distribution of the tumbling mill were analyzed. The numerical results indicated that the particle shape significantly affected the grinding effect and structural displacement of the ball mill. The cube particles had the best grinding effect, while cylindrical particles had better grinding effect than spherical particles. In terms of structural displacement, cubic particles had the largest peak displacement, followed by the cylindrical and spherical particles. Compared to regular spherical particles, superquadric particles had irregular surface shapes, which lead to a better grinding effect and greater structural displacement.

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李天泽,王嗣强,杨冬宝,季顺迎.非规则颗粒与滚筒球磨机相互作用的离散元–有限元耦合分析[J].上海理工大学学报,2023,45(6):543-551,601.

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  • 收稿日期:2023-10-27
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  • 在线发布日期: 2023-12-28