Dynamic modeling and selection of rational parameters for a millstone mill mechanism to reduce energy consumption

Introduction. Millstone mills hold a special place among the grinding equipment used in the food industry, as they produce flour with a high content of biologically valuable grain components through the repeated action of working surfaces on the processed material. However, existing industrial designs of millstone units are characterized by significant energy consumption caused by the high moments of inertia of the rotating millstones. In the context of the ongoing drive toward import substitution and modernization of grain processing enterprises, there is a need to develop new energy-efficient equipment that meets modern requirements for productivity and specific energy consumption. Despite the long history of millstone mill application, the issues of selecting rational inertial-mass characteristics and design parameters of the rotating millstone and their influence on the dynamic parameters of the drive and support forces remain insufficiently studied. The purpose of this study is to reduce the power consumption of a millstone mill by developing a dynamic model of the mechanism and determining rational design and kinematic parameters of the unit. Methods. Based on D'Alembert's principle, a system of differential equations of motion was formulated for a shaft with a disk (millstone), taking into account the eccentricity of the rotation axis relative to the geometric axis of the millstone. The law of motion was determined by numerical integration using the fourth-order Runge–Kutta method with variation of the moments of inertia of the rotating millstone (25.185–40.388 kg•m²) and driving torques (250–500 N•m). Support forces were then calculated by solving matrix equations of static equilibrium , using the previously obtained kinematic characteristics. Finally, a parametric analysis of the influence of inter-supports distances and manufacturing accuracy on the magnitude of support forces was carried out. Results and Discussion. It was found that reducing the moment of inertia of the rotating millstone from 40.388 to 25.185 kg•m² leads to a decrease in shaft acceleration time to steady-state rotational speed from 12.2–15.7 s to 7.2–10.0 s and to a reduction in maximum support forces at the most loaded support from 1,000–1,700 N to 600–1,000 N over the driving torque range of 300–500 N•m. It was shown that the rational inter-support distance is 0.58 m, and the permissible displacement of the rotation axis relative to the geometric axis of the millstone should not exceed 0.5–1.0 mm, at which the maximum support force does not exceed 360–700 N. For the proposed design with a millstone moment of inertia of 25.185 kg•m² and a driving torque of 280–300 N•m, the power consumption at the drive shaft was 10.5 kW, which is 50% lower than that of the industrial mill AVR 6-890 (21 kW) at a comparable capacity of 490 kg/h. The obtained results demonstrate the feasibility of structural lightening of the rotating millstone as an effective strategy for improving the energy efficiency of millstone mills.