DEVELOPMENT OF A PARAMETRIC MODEL OF THE SPATIALLY ORIENTED KNIFE ON THE BULLDOZER BLADE

The paper considers the results of the study of resistances arising during the operation of a bulldozer in the soil environment and processes in the drawing prism. What affects the stability and productivity of the bulldozer during excavation works. The geological map of the "Ukrainian crystalline shield" was studied, where the most common soils on the territory of Ukraine were found. Using the proposed hypothesis of the movement of spatially oriented knives on a bulldozer blade, it was shown that when excavating soil at different speed ratios, there is a deviation of the cutting force application vector by an angle (α), which in turn affects the geometric interaction of the spatially oriented knife with the working environment. Changing the geometric interaction of the spatially oriented knife with the soil affects the cutting force, which led to the creation of a parametric model of the interaction of spatially oriented knives with the working environment. The model was developed for different knife configurations and different ratios of the bulldozer speed to the spatially oriented knife movement speed. The total, normal, and orthogonal cutting forces for the working, subcritical, and critical depths of soil cutting were calculated, according to changes in the parametric model of the spatially oriented knife. A comparative calculation of the cutting force by a bulldozer without and with spatially oriented knives was carried out.


Introduction
During the operation of the earthmoving machine, its executive mechanism interacts with the soil, destroying and separating it from the massif.
The main characteristics of the digging process are geometric, kinematic, force and energy parameters, as well as indicators that determine the physical features of soil destruction, and the properties of the soil as an object of interaction, the design of the working body and the conditions of interaction of the working body with the soil.
The peculiarity of the digging process is that its power and energy indicators depend on kinematic conditions and on geometric parameters -thickness, width and area of the section, as well as on the angles of orientation of the working body in space.
Most calculations of knives and teeth of earthmoving equipment are based on the fact that its parameters do not change during the interaction of the working body with the soil.
Changes in parameters during the multi-vector action of parts of the working body have not been studied much.Therefore, the issue of creating a methodology for determining the parameters of a spatially oriented knife of dynamic action is particularly relevant.

Research analysis
The Ukrainian shield is covered with a small layer of Paleogene-Neogene sedimentary rocks, represented by limestones, sands, clays, siltstones, ferruginous quartzites, etc. Indigenous igneous rocks of the Archaean -Proterozoic -gneisses, granites, quartzites, diorites, etc. are exposed in river valleys.
On the slope of the shield, there is a stronger layering of sedimentary rocks, but Neogene Miocene and Pliocene deposits -clays, siltstones, sands -come to the surface.
Anthropogenic deposits are represented by Pleistocene deluvial loams and loess.Therefore, the main soils with which the bulldozer works are soils located in the Ukrainian Crystalline Shield.
Cutting is the main method of mechanical soil development.The main geometric conditions are proposed to be the position of the edge of the cutting wedge relative to the direction of cutting and the surface of the massif, the contours of the cutting edge, the contours and number of working surfaces of the cutting edge, the number of the so-called side cut surface and the socalled blocked cut surfaces.
Based on these characteristics, the varieties of the process are distinguished and a classification of types of cutting is created [1].
Nominal traction force of the bulldozer , where U fr -coefficient of grafting of the base machine (Table 1) with bulldozer and ripper equipment, corresponding to permissible skidding and traction efficiency; G fr -towing weight of the bulldozer in working condition.
where G B -is the operating weight of the machine; L sup -is the length of the track bearing surface, taking into account the ground clamps; b -is the width of the tracks.
The total resistance on the bulldozer blade W (kN) when digging and moving soil on a horizontal surface is determined by the sum of the resistance to cutting W 1 ; movement of the dragging prism W 2 ; movement of soil up the blade W 3 ; movement of the bulldozer horizontally or on a slope (rise) W 4 and friction of the bulldozer blade on the soil W 5 and is calculated from the ratio: cutting resistance of the working environment, (kN): the specific cutting resistance (K 1 = 0,06; 0,09; 0,12; 0,15 -for sand, sandy loam, loam and clay, respectively) (MPa); B o -the length of the blade, (m); h -the thickness of the layer to be cut (m), W 2 -resistance to soil prism dragging ahead of the blade, (kN):
Resistance to movement of the bulldozer W 5 , (kN):
Volume of the dragging prism: 2 0,5 .When working with a dozer with a pivoting blade and setting it at an angle, the total resistance will be less than when working with a fixed blade.
The coefficient of friction between soil and steel μ 1 depends on the type and condition of the soil, as well as the condition of the steel surface, and is 0,25…1,0 decreasing with increasing humidity and the degree of soil structure disruption.There is a connection between the coefficients μ 1 and μ 2 which is determined by the attitude μ 1 ≈ 0,75 μ 2 , where μ 2 -is the coefficient of internal friction of the soil, μ 2 = 0,58…1,1.
The coefficient of digging resistance K 1 for soft and dense soil, the relative density of which can be characterised by the number of blows С of the density meter, is recommended to be determined from the ratio: 1 0,16 0,1 .K C   All soil groups are divided into eight categories, including non-frozen (categories I -IV) and frozen (categories V -VIII) soils.Soils of categories I -IV are developed with conventional earthmoving equipment.Soils of categories V -VIII are more durable and, in case of a large frost depth, are excavated after preliminary mechanical or explosive loosening.
For dense and semi-rocky soils, as well as for hard coal and hard frozen rocks, the digging resistance coefficient K 1 should be determined taking into account the specific structural and strength characteristics of the soil in the massif.The position of the centre of pressure, the point at which all soil reactions on the bulldozer track are applied, is determined for the various cases that may occur in the operating conditions.The offset of the centre of pressure must not result in the front or rear edge of the track or wheels of the machine coming off the bearing surface.
The bulldozer is acted upon by a system of external forces: vertical rock reaction at the dump R o ; soil cutting resistance W 1 ; vertical reactions R A and R B at the tipping edges; grafting force with the surface F fr = Q fr U; weight of the base machine G B .Internal forces also act in the system: S -force on the hydraulic cylinder; N R and P R -vertical and horizontal reactions in the pins О 1 of the pushing frame, respectively.Ψ -is the stability coefficient of edges A and B, respectively , . During the operation of the earthmoving machine with oblique cutting, the interaction of the knife with the soil has a spatial character, which is manifested in the formation of a nonsymmetric slot of a trapezoidal cross section.In order to quantify the influence of the spatial process, it is proposed to consider the force P as a component of parts corresponding to the nature of soil resistance in different parts of the area of destruction in front of the knife.Thus, the force P of oblique cutting of soil is defined as the sum of three components P f -the force of overcoming the resistance of the soil by the front edge of the knife, P s -the force to overcome the resistance of the soil to destruction in the lateral expansions of the slot, and P s.c -the force of overcoming the resistance of the soil cut by the side edges of the knife.
The difference between P f with a rectangular cut and P f with an oblique cut is proposed to be taken into account by the coefficient φ f , which depends on the ratio h/b and the angle γ pl of the rotation of the knife in the plan The forces P s and P s.c depend, in addition to the properties of the soil, only on the thickness of the section and the angle of rotation of the knife in the plan.The influence of the angle of rotation of the knife in the plane on the change of these forces is taken into account by the coefficients φ s and φ s.c [2].
The ratio h/b between the thickness and the width of the section, when the thickness of the section increases, the dimensions of the side extensions increase proportionally, while when the width changes, they remain constant.After the thickness of the section reaches the so-called critical depth of cutting, the increase in the lateral expansion of the slot stops and the intensive growth of the zones of the lateral section of the soil by the edges of the knife begins.The soil in front of the knife beyond the critical cutting depth is pressed into the massif on the sides of the knife and is not separated from the massif.Therefore, the critical cutting depth corresponds to the minimum energy intensity [4].
The peculiarity of the digging process is that its power and energy indicators depend on kinematic conditions and on geometric parameters -thickness, width and area of the section, as well as on the angles of orientation of the working body in space [3].

The aim of the research
Creation of a methodology for calculating the parameterization of soil cutting with a spatially oriented knife of dynamic action depending on the application of the cutting force α.

Research results
The working hypothesis is based on the fact that the movement of a spatially oriented knife will be carried out longitudinally -a translational movement, perpendicular to the trajectory of the movement of the working body.What is schematically depicted in (Fig. 2), which should ensure undercutting of the soil and its easy removal from the development zone.Thereby reducing the supports that arise during the operation of the bulldozer and increasing its productivity, as well as expanding the area of use.When the blade is fed into the spatially oriented knife, the vector 1 V appears, depending on the ratio, it has its coordinates on the Y axis, when the knife is moved, the vector 2 V appears, which in turn has its coordinates on the X axis.To determine the displacement vector, we sum the vectors according to the parallelogram rule, since the vectors have a common origin (Fig. 3).
Using the data obtained during the vector calculation, we apply the vector indicating the direction of the cutting force to the spatially oriented knife of dynamic action, taking into account the angle α, the indicator of the direction of application of the cutting force, we can find the change in the angle γ pl of the rotation of the knife in the plan and the wide b change [4].The angle of deviation of the total cutting force a was determined at the ratio of the bulldozer speed to the speed of movement of the spatially oriented knife in the range from 10:1 to 1:10 (Fig. 4).V to the speed of movement of the spatially oriented knife 2 V Due to the use of a dihedral knife, we get two angles γ pl.y and γ pl.x of rotation in the plan, which correspond to each of the faces, and a change in the cutting width b.These parameters affect the cutting width b therefore, the definition of the cutting width is derived according to the movement vector and is calculated according to the equations (b com ), which are given below.The critical cutting depth for most soils at normal knife cutting angles, the ratio h/b of the cutting depth h to the knife width b is in the range from 1 to 3.
Nine main dependences of the parameterization of the knife on the angle α were deduced: 1.When γ pl.у > α < γ pl.х is presented in (Fig. 5) then the turning angles in the plan will be: . .1 .
Vector notch width: .Having determined the parameters of the interaction of the knife with the working environment, the change in the cutting width b com and the change in the angle of rotation in the γ pl.v.1 we can calculate the full cutting force.
Calculation of the total cutting force: Normal cutting force:  Where b will be equal to b com , h -is the width of the knife and the depth (thickness) of the cut; m fthe strength coefficient characterizing the specific resistances in the frontal part of the notch (МPа); m sstrength factor characterizing specific resistances in lateral extensions (МPа); m s.cthe strength coefficient characterizing the specific resistance along the lines of the side section (кN/м); φ (δ) -coefficient that takes into account the influence of the cutting angle δ; φ f -the coefficient that takes into account the effect of the angle γ pl.v.1 of the blade turning in the plane, according to the force Р f ; φ s -the coefficient that takes into account the effect of the angle γ pl.v.1 of the blade turning in the plane, according to the force Р s ; φ s.c -the coefficient that takes into account the effect of the angle γ pl.v.1 of the blade turning in the plane, according to the force Р s.c ; μ -angle of soil friction on steel.
The calculation for clay loam was carried out and three main cutting forces were determined, namely, the total cutting force, the normal cutting force and the orthogonal cutting force, the calculation results are presented in the form (Tabl. 3) and graphs on (Fig. 15, Fig. 16, Fig. 17).P B -soil cutting forces with a bulldozer without knives, and three cutting forces P, at different angles α, which show how much easier soil digging is when using spatially oriented knives.
Soil cutting was calculated for a bulldozer with a blade size of B o = 4m.The graph shows: 1) Soil cutting with the blade without spatially orientated blades, at a depth of 5 to 35 cm.
2) Soil cutting with a blade with spatially orientated blades, at a cutting depth of 5 to 35 cm and a cutting force angle of α = 0 o .
3) Soil cutting with a blade with spatially orientated knives, at a cutting depth of 5 to 35 cm and a cutting angle of α = 45°.
4) Cutting soil with a blade with spatially oriented knives, at a cutting depth of 5 to 35 cm and a cutting force angle of α = 90°.
The graph (Fig. 18) clearly shows the effect of spatially oriented knives on the cutting force of soils, namely its decrease with an increase in the angle of application of the cutting force α.

Conclusions
Knowing that the cutting supports of the bulldozer strongly influence its stability and productivity, we used our working hypothesis when the spatially oriented knife moves perpendicular to the movement of the working machine, and depending on the speed ratio, its interaction with the working environment changes.Further affects the calculation of the cutting force.
Based on the ratio of the speeds of the bulldozer and the spatially oriented knife, a vector representation of the cutting forces and a general vector of the direction of the cutting force, which has a deviation from the axis of the bulldozer's motion by an angle, is created α.
Applying the obtained vectors to a spatially oriented knife of dynamic action, nine main correlations were found with respect to the angles of rotation in the plan and a method of their calculation was created.
With the help of the method, we find that the deviation to the angle α will affect the geometric interaction of the knife with the soil, namely, the angles of rotation change in plan γ pl.v.1 and γ pl.v.2 , and the total width b com .
The geological map of Ukraine was studied, with the help of which the most common soils were determined.
A calculation was made for the cutting forces for clay loam, which is shown in the graphs, where it can be seen that when using the theory of oblique cutting of dynamic action, the cutting forces decrease, which accordingly reduces the resistance of the bulldozer, increases its directional stability and productivity.
The calculation of the digging resistance for the bulldozer blade was carried out, comparing the cutting force without spatially oriented knives and with them.
The calculation of the cutting force of the bulldozer blade without and with spatially orientated blades showed us the effect of increasing the cutting angle α on the cutting force.
The graph (Fig. 18) clearly shows the effect of spatially oriented knives on the cutting force of soils, namely its decrease with an increase in the angle of application of the cutting force α.

3 -
resistance to soil movement up the blade, (kN): Friction resistance of the bulldozer blade against the soil W 4 (kN):

Fig. 1 .
Fig. 1.Diagram of the forces acting on a bulldozer when calculating for overturning

Fig. 2 .
Fig. 2. Schematic representation of the trajectories of the working body: 1) Bulldozer blade; 2) spatially oriented knife of dynamic action; 1 V -the trajectory of the bulldozer movement; 2 V -the trajectory of the spatially oriented knife of dynamic action; Bo -blade wight; Ho -blade hight; h -the thickness of the layer to be cut; Qv -volume of the dragging prism; β -cutting angle of the blade; A -centre of mass of the dragging prism

Fig. 3 .
Determination of the vector of the direction of the cutting forces and the angle α: (a) -deviation of the angle α in the vector display of the ratio of the speeds of movement of the bulldozer blade faster than the movement of the spatially oriented knife; (b) -the deviation of the angle α in the vector mapping of the ratio of the speeds of movement of the bulldozer blade is the same as the movement of the spatially oriented knife; (c) -the deviation of the angle α in the vector display of the ratio of the speeds of movement of the bulldozer blade is less than the movement of the spatially oriented knife

Fig. 4 .
Fig. 4. The graph of the dependence of the angle α on the ratio of the traction speed of the working machine 1V to the speed of movement of the spatially oriented knife 2 V

Table 1
The value of the coefficient U fr friction between the wheels and the road surface values of the dragging prism coefficient Kv depending on the ratio of the blade height H o to its length B o and the type of soil are shown in table 2:

Table 3
Cutting forces of clay loam at a depth of 10, 20, 35 cm