**1. Introduction**

In the cost structure of feed production, grinding represents a very labor- and energy-intensive process, constituting, according to various datasets, at least half of the total costs associated with the conservation, storage, and preparation of feed mixtures. Hence, implementing a sustainable design of tools and processes is becoming increasingly important for manufacturers [1]. There is an increasing use of concentrated feed in the composition of mixed fodder [2–4]. An important factor for improving the digestibility and ensuring the most complete extraction of the potential energy of the feed is the method of its grinding. To date, the most common method in agricultural production is grinding with hammer mills (disintegrators) [5–7]. However, modern requirements for the quality of the feed obtained in the grinding process require the minimization of metal and energy intensity.

The main approach for solving the problems discussed above is to improve existing machines and devices (units) by optimizing structural elements and the subsequent control of technological operating modes. Furthermore, one can develop and implement technical solutions based on new physical principles or by combining several previously known approaches. Thus, recently, the design of grinders has become of great practical interest in the field of grinding grain. It is possible to significantly reduce the specific energy consumption for the production of concentrated feed and obtain a product with a high uniformity of particle size by combining the grinding process with shearing and chipping [5,8–15].

Pushkarev A.S. and Fomin V.V. [3,16], in their research on the parameters of the work tools (units) of a centrifugal–rotary grain grinder, found that by modifying the curvilinear shape of the cutting pair, the specific energy intensity of the grinding process of grain is reduced; increasing the grinder's performance without changing its energy consumption. Further they found, the moisture content of the material being crushed has a significant effect on the specific energy intensity of the grinding process; an increase in the moisture content of grain, increases the energy consumption. However, the trend towards a decrease in energy intensity remains when curvilinear work tools are used. Finally, by taking into account the change in the optimal cutting angle of the material being processed as it moves in the channel of the work tool of a small-size centrifugal–rotary grinder, the grain size distribution (granulometric composition) is equalized, the dust fraction decreases, and there are no whole grains in the finished product [3,16].

Based on the analysis of Druzhynin R.A. and Ivanov V.V. [2,4] on the research of theorists and practitioners, it is recommended to use two-stage grinding for the manufacture of coarse and medium grinding products. Additionally, multi-stage crushers and grinders are more effective to obtain a fine grinding product. At the same time, the disadvantages of knife-type grinders compared to impact crushers are also noted [17]: intensive wear of the working parts (knives), a sharp decline in the quality of grinding as a result of wear of the working bodies (knives), and a higher specific energy consumption than crushers, with greater productivity.

Considering the existing industrial designs of grinders that have knives (blades) as work tools, it can be seen that they are used mainly in personal subsidiary farms, where high performance and drive power are not required, but a low price and simplicity of design are needed. Such crushers are widely represented on the market by the following manufacturers: Electromash, Greentechs, Bison, Kolos, Yarmash, Cyclone, Niva, Fermer, ZDN, etc. [17].The analysis of existing models of grinders on the market and scientific research on grinding and crushing suggests that the search continues for a method of grinding feed which improves the economic efficiency of the process, while simultaneously ensuring a high quality of the resulting product of concentrated feed.

The purpose of this study is to assess the structural elements and various operating modes of a rotary–centrifugal grinder according to key performance indicators. The task of the study is to determine the significance of factors (*x*1–*x*7) according to certain optimization criteria (*y*1–*y*3), allowing for more specific implementation in further research of rotary–centrifugal grain grinders.

#### **2. Materials and Methods**

#### *2.1. Design of a Rotary–Centrifugal Device for Grinding Grain*

Based on the analysis of the designs of crushers and grinders, we have developed and proposed the design of a rotary–centrifugal device for grinding grain [18]. The proposed device (Figure 1) consists of a stationary case or housing (1) with loading (input, 2) and output (3) nozzles. Two adjacent

disks are coaxially mounted inside the housing (1): the upper (4) (Figure 2a) and the lower movable disks (5) (Figure 2b). On the work surface of the lower disk (5) there are annular protrusions (6), and on the work surface of the upper disk (4) there are installed knives (7), which are diamond-shaped with small cutting angles with respect to the large diagonals. The outer row of knives (8) forms a separating surface; thus, changing the angle of the knives makes it possible to continuously adjust the degree of grinding for the material. The lower disk (5) has grooves (9) in the radial direction which are made opposite in terms of angle to the direction of rotation of this disk. The lower disk (5) is mounted on the flange of the drive shaft (10) and is rotated by means of a pulley (11) mounted on it. The upper disk (4) is rigidly fixed to the stationary case (1). In the upper part of the stationary case, a receiving chamber (12) is installed, which is formed by vertical walls. The receiving chamber (12) communicates in its upper part with the loading nozzle (2) and is connected with the working chamber (14), which is the space between disks (4) and (5), through the radial windows (13).

**Figure 1.** Design overview of a rotary–centrifugal device for grinding bulk materials. Parts include: 1—case; 2—loading (input); 3—output nozzles; 4—upper disk; 5—lower movable disk; 6—annular protrusions; 7—knives; 8—outer row of knives; 9—groove; 10—drive shaft; 11—pulley; 12—receiving chamber; 13—radial windows; and 14—working chamber.

**Figure 2.** Photographs of the (**a**) upper disk and (**b**) lower disk.

The working process of grinding grain in the rotary–centrifugal device is carried out as follows (Figure 1). The incoming grain is subjected to the mechanical action of the first cutting pair; then, under the action of centrifugal forces, the pre-ground material moves along the grooves to the next pair. Then, the ground grains (groats or stock feed), having reached the outer row of the knives (8) which form the separating surface, pass into the gap between the knives (8) and, under the influence of the air flow created by the rotating lower disk (5), leave the housing (1) through the outlet nozzle (3).

The studies were carried out on an experimental installation of a rotary–centrifugal grinder (Figure 3) made on-site at the Federal State Budgetary Educational Institution of Higher Professional Education Vologda State Dairy Farming Academy (DSFA) named after N.V. Vereshchagin.

**Figure 3.** Overview of the experimental installation.
