蔡文源^1a，王利强¹，徐立敏²

1. 江南大学 a. 机械工程学院， b. 江苏省食品先进制造装备技术重点实验室，江苏 无锡 214122；2. 江苏创新包装科技有限公司，江苏 扬州 225600

引用格式：

蔡文源，王利强，徐立敏 . 基于静态和动态休止角的超细碳酸钙离散元参数标定［J］. 中国粉体技术，2024，30（4）：81-93.

CAI W Y， WANG L Q， XU L M. Discrete elemental parameter calibration of ultrafine calcium carbonate based on static and dynamic angle of repose［J］. China Powder Science and Technology，2024，30（4）：81−93.

摘要：【目的】 获得超细碳酸钙准确的仿真模型参数，实现超细碳酸钙的可靠仿真研究。【方法】 将超细碳酸钙精简为软质球形粒子，使用颗粒接触缩放原理与量纲分析进行颗粒缩放，采用Hertz-Mindlin with JKR 接触模型，结合物理实验和离散元软件EDEM仿真实验对超细碳酸钙的静态和动态休止角进行接触参数标定。首先利用单因素实验排除对静态和动态休止角影响不显著的参数。采用Box-Behnken实验搭建静态和动态的休止角和显著性参数之间的回归模型。将实际测定的静态和动态休止角作为响应值，进而对静态和动态休止角回归模型求解获得最佳的仿真参数组合，并对得到的仿真参数进行物理实验验证。【结果】 得到显著性参数的最佳组合为：超细碳酸钙-超细碳酸钙静摩擦系数和滚动摩擦系数为 0. 36、0. 31，超细碳酸钙-不锈钢静摩擦系数和滚动摩擦系数为 0. 38、0. 22，离散元仿真实验所得到的静态动态休止角分别为42. 5°和61. 3°，与实测值的误差分别为0. 96%和1. 32%，无明显差异。【结论】 参数标定后的接触参数能够应用于超细碳酸钙离散元仿真。

关键词：超细碳酸钙；休止角；粒径；参数标定；离散元

Abstract

Objective With the rapid development of material science and engineering technology， ultrafine calcium carbonate has shown broad application prospects in various fields owning to its excellent physiochemical properties. As an important inorganic powder material， it is widely used in industries such as paper， rubber， coatings， food， and pharmaceuticals to improve and enhance product performance. Ultrafine calcium carbonate requires a parameter calibration process before conducting discrete element simulation to obtain precise simulation parameters. However， most existing simulation parameter calibration methods use the static angle of repose as a response variable， which cannot fully represent the real characteristics of ultrafine calcium carbonate.Therefore， to improve the accuracy of discrete element simulation parameters for ultrafine calcium carbonate， obtain accurate simulation model parameters， and achieve reliable simulation results， the simulation parameters of the ultrafine calcium carbonate need to be calibrated.

Methods Basic parameters such as particle size distribution， surface morphology， static and dynamic angles of repose of ultrafine calcium carbonate were initially measured. Then， physical and simulation models of the static and dynamic angle of repose were developed for parameter calibration. Due to the extremely small size of ultrafine calcium carbonate， the number of particles can reach tens to hundreds of millions even in very small volumes， far exceeding the processing limit of ordinary computers.Therefore， particle scaling principle and dimensional analysis were used to scale the particles and reduce the ultrafine calcium carbonate to soft spherical particles. The Hertz-Mindlin with JKR contact model takes into account factors such as elastic deformation， friction， and adhesion， providing a comprehensive description of the contact behavior of solid surfaces at the microscopic scale. This allows for an accurate depiction of actual contact situations. The contact parameters for its static and dynamic angles of repose were calibrated using the Hertz-Mindlin with JKR contact model， combined with physical tests and discrete element software EDEM simulation experiments. Parameters which had no significant effect on static and dynamic angles of repose were excluded through single-factor tests. Box-Behnken test was used to establish regression models between the static and dynamic angles of repose and significant parameters. Using the measured static and dynamic angles of repose as the response values， the optimal simulation parameter combinations were obtained by solving the regression model and the then verified through physical experiments.

Results and Discussion The surface energy of JKR between ultrafine calcium carbonate was 0. 0321 J·m^-2， the shear modulus of ultrafine calcium carbonate was 5×10^-7 Pa， the restitution coefficient between ultrafine calcium carbonate particles was 0. 3，and the restitution coefficient between ultrafine calcium carbonate and stainless steel was also 0. 3. The optimal parameter combination for significant parameters was as follows： the static friction coefficient between ultrafine calcium carbonate was 0. 36，the rolling friction coefficient between them was 0. 31， the static friction coefficient between ultrafine calcium carbonate and stainless steel was 0. 38， and the rolling friction coefficient between them was 0. 22. The static and dynamic angles of repose obtained by the discrete element simulation test were 42. 5 ° and 61. 3 °， respectively. The static and dynamic angles of repose measured in actual experiments were 41. 8 ° and 60. 5 °， respectively. The error between the physical experiment and the simulation experiment for the static angle of repose was 0. 96%， and for the dynamic angle of repose， the error was 1. 32%. There was no significant difference between the experiment and the simulation results for both the static and dynamic angles of repose.

Conclusion The calculation speed of the discrete element simulation is greatly improved by reducing the stiffness and scaling down dimensions of the ultrafine calcium carbonate. The contact parameters of the ultrafine calcium carbonate are calibrated using the JKR model of the discrete element method. Based on the dual response indices of the static and dynamic repose angles of ultrafine calcium carbonate， the Box-Behnken response surface test method can be used to obtain the parameters of simulated particles more accurately， bringing them closer to the real state. According to the results of variance analysis of the model， the significant parameters for the static repose angle are the static friction coefficient between ultrafine calcium carbonate particles，the rolling friction coefficient between ultrafine calcium carbonate particles， and the static friction coefficient between ultrafine calcium carbonate particles and stainless steel. The significant parameters for dynamic repose angle are rolling friction coefficient between ultrafine calcium carbonate particles， static friction coefficient between ultrafine calcium carbonate and stainless steel， and rolling friction coefficient between ultrafine calcium carbonate particles and stainless steel. The results verify the effectiveness of the parameter calibration method， which can be used to conduct simulation experiments on ultrafine calcium carbonate. This has significant engineering application value for the design and optimization of ultrafine calcium carbonate conveying equipment.

Keywords：ultrafine calcium carbonate； angle of repose； particle size； parameter calibration； discrete element

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