Визначення фізико-механічних параметрів зерна пшениці для чисельного моделювання процесу його руйнування

Abstract

UA: У статті розглянуто метод визначення фізико-механічних параметрів зерна пшениці сорту «Патрас» для коректного налаштування DEM-моделі. На основі вимірювання геометричних параметрів 150 зернин у середовищі Simcenter STAR-CCM+ методом агрегації сфер побудовано модель дискретних елементів. Проведено повнофакторний чисельний експеримент зі змінними факторами: коефіцієнтом Пуассона (ν), модулем Юнга (Ep) та граничною напругою розтягу і зсуву (Wp). За результатами оброблення даних у Wolfram Cloud отримано рівняння регресії для трьох просторових положень зернини. Лабораторні випробування на власному стенді з тензометричним датчиком підтвердили достовірність результатів моделювання. Встановлено уточнені параметри моделі: Ep = 21,2 МПа, μp = 0,50, Wp = 2,2 МПа. /// EN: The study addresses the problem of determining verified physical and mechanical parameters for the discrete element method (DEM) model of wheat grain, which is essential for reliable numerical simulation of grain destruction processes in feed grinding equipment. The research object is wheat grain of the ‘Patras’ variety. Geometric parameters – length (L), width (W), and thickness (H) – were measured for 150 grains using an indicator thickness gauge with an accuracy of 0.01 mm. Statistical processing yielded mean values of L = 6.70 mm, W = 3.19 mm, and H = 2.89 mm, with a sphericity of approximately 0.57. Based on these measurements, a three-dimensional DEM model of the grain was constructed in Simcenter STAR-CCM+ using the multi-sphere aggregation method. Contact interactions between particles and the steel punch were described using the Hertz–Mindlin contact model. A full factorial numerical experiment was conducted with three variable factors: Poisson’s ratio (ν), Young’s modulus (Ep), and tensile and shear bond strength (Wp), each varied at three levels. Destruction forces were evaluated in three spatial orientations of the grain relative to the loading axis: vertical (Fz along length L), lateral (Fy along width W ), and horizontal (Fx along thickness H). The experimental data were processed in Wolfram Cloud, yielding regression equations for each orientation. Analysis of the equations showed that tensile and shear bond strength Wp has the greatest influence on destruction force across all rientations, while Poisson’s ratio ν has the least effect. The highest destruction force was recorded in the horizontal orientation due to the larger contact area between the punch and the grain. Laboratory experiments were performed on a custom-built test bench equipped with a strain gauge load cell, an HX711 analog-to-digital converter, and an Arduino Uno microcontroller. Three groups of 50 grains each were tested at a moisture content of 11.31 %. Mean experimental destruction forces were: Fz = 147.73 N, Fy = 155.09 N, and Fx = 267.33 N. Comparison of numerical and experimental results using regression equations allowed calibration of the DEM model parameters. The following physical and mechanical properties of ‘Patras’ wheat grain were established: Young’s modulus Ep = 21.2 ± 3.1 MPa, Poisson’s ratio ν = 0.50 ± 0.03, and tensile and shear bond strength Wp = 2.2 ± 0.1 MPa. The obtained parameters can be applied in numerical simulations of wheat grinding processes in disc mills and other types of grinding equipment.