基于颗粒缩放的小麦粉离散元参数标定

Parameter calibration of wheat flour for discrete element method simulation based on particle scaling

为获得小麦粉离散元仿真精确的接触参数,将不规则形状的小麦粉简化成软质球形颗粒,利用颗粒接触缩放原理和量纲分析进行颗粒缩放,将平均粒径0.212 mm的小麦粉放大至1.2 mm,选择"Hertz–Mindlin with JKR"接触模型,利用休止角对接触参数进行标定。首先通过Plackett-Burman试验筛选出对休止角影响显著的参数:表面能JKR(Johnson Kendall Roberts)、小麦粉-小麦粉滚动摩擦系数、小麦粉-不锈钢静摩擦系数;然后根据Box-Behnken试验建立并优化休止角与显著性参数的二阶回归模型,得到显著性参数的最佳组合为JKR为0.157、小麦粉-小麦粉滚动摩擦系数为0.25、小麦粉-不锈钢静摩擦系数为0.58;最后用标定参数仿真所得休止角大小与真实试验值进行对比,二者相对误差为0.61%。结果表明标定所得的接触参数可用于小麦粉放大颗粒的离散元仿真,为定量供送螺杆的设计提供参考。

In order to obtain the precise parameters for the wheat flour discrete element simulation, the actual repose angle of wheat flour was firstly measured by injection method. The experimental material was ordinary wheat flour, which average particle diameter is 0.212 mm and went through a 70-mesh standard sieve. Refer to GB 16913.5-1997, the inner diameter of the used funnel was 5 mm, the taper was 60°, and the cylindrical chassis was 80 mm in diameter. The result indicated the repose angle of the wheat flour was 52.37°, which was average value of five experiments. The irregular wheat flour was simplified into soft spherical particles, and then those particles with the size of 0.212 mm were enlarged to 1.2 mm for simulation thanks to the particle scaling and dimensional analysis, during those analyses, the 3D modeling and simulation were finished by SolidWorks and EDEM software respectively. Considering the bonding characteristics between wheat flour particles, the "Hertz-Mindlin with JKR" contact model was selected to calibrate the contact parameters of wheat flour for discrete element simulation with the repose angle as a reference. Then, through the design-expert software, the parameters that have significant influence on the repose angle of wheat flour by Plackett-Burman test design are surface energy JKR, the rolling friction coefficient for wheat flour-wheat flour, the static friction coefficient for wheat flour-stainless steel. According to the significance parameters designed and screened by the Plackett-Burman test, the steepest ascent test was carried out so that it could be quickly close to the optimal value. The steepest ascent test was stared at the center of the Plackett-Burman test and the step size was determined by the regression coefficients obtained from the test. The Box-Behnken test was then carried out by selecting the low, medium and high levels of the significant parameters according to the results of steepest ascent test and the design principle of response surface, and then the three mediate points were selected to evaluate the errors. At last, the quadratic polynomial model for the repose angle and the significant parameters was successfully established and optimized by the Box-Behnken test. The analysis of variance(ANOVA) of the quadratic polynomial model showed that this model was significant and the lack-of-fit term was non-significant, which means the model can be applied to determine whether the parameters combination is the best. However, some terms in the quadratic polynomial model were non-significant. Therefore, a modified regression model was established by deleting those non-significant terms. The ANOVA of the modified model showed all of the terms were desirable, and the first-order term of those 3 significant parameters, the interactive term of the wheat flour-wheat flour static friction coefficient and JKR surface energy, and the interactive term of the wheat flour-wheat flour rolling friction coefficient and JKR surface energy had a significant effect on the repose angle. The best combination of the significant parameters could be achieved when the JKR value was 0.157, the rolling friction coefficient of wheat flour-wheat flour was 0.25, and the static friction coefficient of wheat flour-stainless steel was 0.58. Finally, the rest simulation test was carried out with the optimal combination of parameters obtained from the experiments, which showed that the repose angle of the simulation test was 52.69°, the error of the repose angle measured by the test was 0.61%, and there was no significant difference between the simulation results and the actual test values. In conclusion, the contact parameters obtained based on the particle scaling calibration can be used for wheat flour discrete element simulation which was shown by the experimental results.