Plough calculation peculiarities for walking tractors

. The influence of forces and moments on a plowing walking tractor is considered. The main regularities in calculating the component forces of resistance to the tool in the mode of digging and changing the treatment depth are determined. It is established that physical efforts of the operator, aimed at regulating the depth of soil treatment, significantly exceed the permissible.


Results of work
The forces acting on the plough arise as a result of the soil resistance against the share's blade and its working surfaces during the operation of the plough-body. In each plane of projections, the total effect of elementary soil resistance forces on the body can be represented by a single resultant force ( Figure 1) of a certain quantity and direction [3]. In the horizontal plane of projections ( Fig. 1, a), the force Rxy acts on the plough-body, forming the angle η=(15-25°) with the axis x. The force Rху crosses the share's blade at a distance equal to 0.4 of the plough width and 0.5 of the soil treatment depth. The components of the forces Rxy on the x and y axes are determined by the correlations (1) and (2) where ηpl is the plough efficiency, ηpl = 0.7; k is the soil resistivity obtained by linear dynamometry of the plough; а, bк -the plough depth and width, respectively. According to agrotechnical requirements, the minimum depth of soil treatment should be a = 15 cm, hence the plough width bк = 18 cm.
The soil resistivity k depends on the soil type and structure, humidity and density. The average values of the soil resistivity after harvesting of the crops are: for heavy soils -90 kPa, medium soils -60 kPa, light soils -30 kPa.
In the vertical projection plane, the force Rzx, forming an angle ψ with the x-axis, acts on the plough-body (Fig. 1, б). On dense soils , the angle ψ can have a negative value when a plough operates with a dull plough-share [3]. Considering modern technologies of self-sharpening of plough-shares, we assume that in the calculations the angle ψ will be equal to + 12°and on the overgrown sections + 8°. The vertical component of the force Rzx is determined from the dependence (3). In the transverse plane, the projection of the force Rzx, which is equal to the vector sum of the forces Rz and Ry (4), acts on the body (Fig. 1, c). The direction of the force Rzy is characterized by the value of the angle ξ, the tangent of which is determined by the ratio (5). The distance ρzy from the nose of the share to the straight line, which is the continuation of the force Rzy, is approximately 0.5 of the arable layer depth for positive and 0.75 of the depth for negative values of the angle ξ.
The forces acting on the walking tractor ( Figure 2): Gм is the motoblock weight force; Gор is the tool weight; Pоп is the effort operator applies on the control bars in the vertical plane; Rxz is the reaction of the soil to the tool in the longitudinal plane; Rx is the horizontal component of Rxz; Rz is the vertical component of the force Rxz; S is the resultant force on the working parts of the tool.
To ensure self-digging of the plough-body, it is necessary for the resultant force S to pass above the rotation axis of the wheels. Herewith, the moment S⋅ρzx is formed. The working parts of the tool are deepened until the plank reaches the furrow bottom, which leads to an increase of the soil reaction in the vertical direction up to leveling with the vertical load, thereby limiting further digging.
To determine the vertical component of the tool's weight force acting on the working parts, we will compose the equation for determining the tool's gravity center. Depending on the weight and location of the tool, ballast weights, the coordinates of the gravity center will change. where Gi is the weight of the i tool, device rigidly connected to the motor block; xi is a longitudinal coordinate of the weight center of i tool, device relative to the rotation axis of the wheels; хоп is the longitudinal distance from the rotation axis of the wheels to the arms of the control bars.
During the movement the rotating torque develops on the wheels' axes of the walking tractor and it is equal to the moment resistance of the external forces. Accordingly, the reactive torque will act on the motor block frame and it will be numerically equal and opposite to the rotating torque. The action of this torque will increase the digging depth.
The rotating torque on the wheel axis will increase as the plough digs into the soil. When the nominal depth is reached, the plough resistance torque is not a constant value, as specific soil resistivity varies depending on soil structure and it is random. Consequently, the operator's efforts in the vertical plane on the motoblock's bars vary in proportion to the changes of rotating torque on the wheel drive axis.
To determine the values of the reactive torque, we consider the process of plough-body digging (Fig. 3). The soil reaction in the longitudinal plane will increase as the plough digs into the soil (8). The value of the vertical load is determined from the moment equation (9). The resultant force at the initial moment of digging is determined by the dependence (10). Herewith, a digging moment is formed (11) if it is directed clockwise relative to the wheel rotation axis, otherwise it is a shallowing moment. While digging, the direction of the soil reaction vector Rzx deviates from the horizontal direction by an angle ψ, at the nominal position the angle is ψ = 12° [3]. Then the resultant force S is determined from the relation (12). (9) (10) (11) (12) where z is the plough depth, 0 <z <a. In the process of digging, the angle α of the vector tilt of the resultant force S changes. We determine the angle value using the formula (13), applying the sine theorem. The direction of the digging moment rotation is determined from the condition (14). The arm of the digging moment is determined by the formula (16).
where ξ1 is the angle of tilting of the motor block in proportion to the plough digging: As an example, the plowing walking tractor calculations were conducted on basis of Motor-Sich motoblock. As a result of calculations it was established that on medium and heavy soils with a treatment depth of more than 10 cm, the operator is forced to limit the digging depth of the plough, moreover, the efforts on the control bars are much higher than it is permissible (more than 200 N). In order to reduce the operator's force load, it is necessary to install support wheels on the plough.

Conclusions
The received mathematical model allows to define the basic parameters of a plough and a plowing walking tractor in general. As a result of calculations based on the obtained mathematical model, it is established that when working on plowing walking tractors, the operator has to apply considerable physical efforts to regulate the depth of plowing, and these efforts are twice or three times as high as the permissible ones.