## 1 _Problem Formulation_  
Earthworksh are one of the most important stages of any transport construction project. The overall cost of earthmoving activity during construction projects can account for more than 30% of the total cost [1]. The construction of pipe communications for various purposes, communication lines, irrigation canals, and other similar facilities, first of all, requires fast and high-quality earthworks with minimal financial costs [2]. One scientific article [3] described the energy intensity of the soil digging process and the nature of changes in the values that make up the cutting forces acting on the actuator, which are necessary for effective interaction with soil. Earthworks can be done in the shortest possible time by using continuous earthmoving machinery able to provide earthworks with a productivity of 5-10 times higher than the operation of single-bucket excavators. However, continuous excavators are ad hoc machinery and can construct only long excavations in the ground of specified dimensions, which limits the scope of their use. Recently, there has been an acute necessity to increase the pace of earthworks in transport construction. As a result, the researchers' efforts in the field of excavation engineering are increasingly aimed at creating the universal continuous earthmoving machinery (UEM) able to dig long excavations of variable width and depth [4] with the same actuator without realignment of machinery equipment. Technological capabilities of the machinery are expanded by combining the variations of three speeds that move the soil-developing actuator in the face, namely: cutting the soil with the rotor revolution speed \(V_{c}\), supplying the actuator to the face due to translational movement of the machinery with the speed \(V_{s}\), and cyclic lateral reciprocating movement of the actuator relative to the longitudinal axis of the machinery at a certain angle \(\alpha\) with a speed \(V_{Lm}\), see Figure 1.  
The combination of translational movement of the machinery with simultaneous lateral reciprocating movement of the soil-developing actuator characterizes the mode of translational and rotational supply of the actuator to the face. The peculiarity of such movement of the UEM actuator in the face is its cyclicity. The full cycle of movement is carried out when the actuator moves from one extreme point (the side wall of the excavation in the soil) to the second one and vice versa, to the starting point. The actuator movement from one side wall of the excavation in the soil to another (opposite) one is a half-cycle of movement (Figure 1). When digging excavations of the minimum width (trench), the actuator remains stationary relative to the longitudinal axis of the machinery, and the width of the excavation is determined by the width of the actuator. The PZM-2 machinery with a chain actuator and its modification PZM-3 are widely known continuous UEM with the specified mounting [5; 6]. If the above-mentioned structural scheme of the mounting (Figure 1) of soil-developing equipment on the base chassis is used, in the mode of translational and rotational supply of the actuator to the face, the excavation is determined by the speed ratio \(V_{s}\) and \(V_{Lm}\) and is developed by uneven wedge-shaped shavings. Their thickness \(c\) varies from zero to a definite maximum for each half cycle of movement. It causes fluctuations in the value of external loads on the actuator when digging the soil and reduces the reliability and durability of the machinery. In addition, the potential productivity of the rotor actuator in this case is 50%. The analysis of the UEM operating processes shows that the reduction, stabilization, and minimization of external loads of the UEM actuator, the machinery productivity improvement can be achieved by aligning the thickness of the shavings cut by the actuator buckets during each half-cycle of the actuator motion in the face.