## 2 Materials and Methods
### Experimental Setup  
Calculations of external forces affecting the UEM operating equipment when digging the soil according to the obtained dependences are possible if the values of correction factors \(\psi_{1}\), \(\psi_{2}\), \(\psi_{3}\) in the formulas of external forces calculation are experimentally determined. The values of the coefficients are conditioned by the peculiarities of digging the soil in the mode of translational and rotational supply of the actuator, which have not been sufficiently studied so far. They include: the complexity of the actuator trajectory when digging the soil and the formation of a drawing prism in the lateral motion of the rotor, pressing this prism to the side wall of the excavation at the end of each half-cycle. Experimental studies were performed to determine the absolute values of the coefficients by conducting planned experimental studies of the physical model (M1:5) of the UEM operating equipment. The experiments were carried out on a test bench for the physical and mathematical modeling of the continuous earthmoving machinery operating processes (Figure 9). The test bench is mounted on the ground channel by a tensometric cart made in the form of a spatial truss. It consists of the main frame (1) and a frame (2) moving in the vertical direction of the carriage (3). The actuator under investigation (5) is mounted with a special strain gauge (4) [23] on the carriage. The parameters of the spatial load are fixed simultaneously using the strain gauge (4) during the experimental research. These parameters are the forces on the actuator (traction force \(T\) (\(P_{x}\)), vertical force \(P_{v}\) (\(P_{z}\)), lateral force \(P_{l}\) (\(P_{y}\))) and moments of the specified forces \(M_{xyz}\), \(M_{xyz}\), and \(M_{yzz}\) relative to the center of the strain gauge (4) (the hinge to secure the operating equipment on the tractor atft). The directions of the actuator in the up and down motion are provided by a special drive of the carriage. It includes a reversible motor (6), a worm gearbox (7), and a lead screw (8) with a nut fixed in the upper ball bearing (9) of the carriage. To transfer the vertical loading from the carriage to the worm gearbox, the lower end of the lead screw rests on the lower ball bearing (10), rigidly fixed to the frame. The lead screw is connected to the worm gearbox via an elastic finger coupling. In addition to the carriage, the main frame includes: a roller (11) for compacting the model soil with a separate profiling device (12), a pump station of the test bench (13), a station hydraulic panel (14), a starter panel (15), automatic control system units for the actuator tested, and the control panel of the test bench. To ensure the supply of hydraulic fluid to the actuators of the model, a pump station is used. It includes five pumps (Figure 10). On the control panel of the test bench (Figure 11), there are buttons to turn on the pump station units, mechanisms for raising the carriage, and control and measuring devices to provide the necessary operating mode of the actuators tested. Figure 10: A pump station (1—adjustable pump NAR-40/200; 2—gear pump NCH-6; 3—gear pump NCH-10; 4—electric motor; 5—tank; 6—flow regulator; 7—station hydraulic panel). Figure 9: General view of the test bench with a model of the actuator (1—main frame; 2—frame; 3—carriage; 4—strain gauge; 5—actuator; 6—reversible motor; 7—worm gearbox; 8—lead screw; 9—upper ball bearing; 10—lower ball bearing; 11—roller; 12—profiling device; 13—pump station; 14—station hydraulic panel; 15—starter panel). The automatic control system for the operating process of the operating equipment model provides its automatic work when digging trenches of various width under the conditions of translational and rotational supply of the actuator to the face. The automatic control system consists of two units--the operating unit and the control unit. It is connected to the hydraulic valves to control the drive mechanisms of the actuator.