## 3 Results and Discussion
The very soft, small-sized particles of the suspension, in the form of protein flakes, easily break apart under low forces. Therefore, the resulting equations of motion do not include terms describing the whipping effect. These equations are easily solved numerically using the Runge-Kutta method quartic with a moderate integration step that ensures the required accuracy. Therefore, the equations of motion (25) and (26) are non-stiff. No signs related to stiffness were observed while solving Equation (25). The phase trajectories of the vibrational motion of the driving member are represented as twisted spirals [8; 50; 51]. These spirals become more pronounced with increasing crank length, number and radius of piston holes, and piston mass, and decrease with higher fluid density. As the system transitions to rotational motion [7; 8; 9; 10; 41; 42], the spirals straighten out and transform into curves with periodically varying amplitude \(\dot{\varphi}=\dot{\varphi}(\varphi)\) around lines defined by the driven angular velocity of the engine shaft [7; 8; 9; 10; 50]. Principles of Operation and Creation of a Mixing and Churning Device Based on a Crank-Slider Mechanism  
The device based on the slide-crank mechanism of the second class operates as follows (Figure 28). From the engine 1 through the drive (gearbox and clutch) rotating crank 2, the motion is transmitted through the connecting rod 3 to the slide 4 and then to the piston 5. The piston is made in the form of a cylindrical disk with round holes for technological processes. The piston with oscillating motion mixes, whips and agitates the primary products fed into the cylinder 6 through the nozzle 7. The periodic movement of the piston contributes to the uniform distribution of ferment in the cylinder, the breakdown of protein flakes into fine particles, and the strengthening of enzymatic processes, as a result of which the quality of fermented milk products and aroma are achieved. The whipping process occurs at the moment when the maximum force of mixing and whipping of the piston or its power is reached. The shaking process can be enhanced by means of a communicating tube 8 to the cylinder. The finished products of the technological process are discharged through the nozzle 9 (Figure 28). The mixing and whipping force or its power can be adjusted by varying the torque of the engine, the length of the crank, the number of piston holes and their radius. The mixing-whipping and stirring device is designed for the production of fermented milk products with healing properties: kumys (fermented milk drink made from mare's milk) [see Wikipedia] and shubat (fermented milk drink made from camel's milk) [see Wikipedia]. A mare is milked at hourly intervals, yielding approximately 5 L of milk per day. A small amount of previously prepared kumys (used as a fermentation starter) in the device is added with fresh mare's milk, etc. The mixture is then regularly mixed, whipped, and stirred over a period of one to two days, for several hours per day. The longer the whipping process continues, the greater its healing effect, i.e., enhancing the flavor, aroma, and overall quality of the kumys. Camel milk (shubat) is left in the device for fermentation for 24 h. Unlike kumys, shubat is well stirred before consumption (at low motor shaft speeds). If the power of the engine is equal to or slightly greater than the power of the resulting pressure force, the buoyancy force and gravity, and the friction forces between the piston and the liquid in the round holes and in the gap between the cylinder, then the crank performs the rotational mode of movement; if the torque \(a\) of the engine is less than the torque caused by the action of the total forces of pressure and gravity, buoyancy force, friction forces between the piston and the liquid, i.e., not enough for the rotational movement of the crank, then the crank will perform the damping oscillatory process.