49   A journal of the AMERICAN Journal of Engineering, Mechanics and Architecture                   www. grnjournal.us  

 
 

AMERICAN Journal of Engineering,  
Mechanics and Architecture 

Volume 01, Issue 07, 2023 ISSN (E): 2993-2637 

 
  

Theoretical Studies on the Justification of the Angle of Installation 

in Relation to the Direction of Movement of the Improved Harrow 

Leveller 
 

Tukhtakuziev Abdusalim
 

Doctor of Science, professor 

Rasuljonov Abdurakhmon Ravshanbek ugli
 

Philosophy of Doctor, s.s.e. 

Utepbergenov Bazarbay Kengesbayevich
 

Philosophy of Doctor, docent. 

Kengesbaev Rustem Bazarbayevich
 

Doctoral-student 

 

Abstract: The article presents the results of the theoretical studies on the justification of the 

angle of installation in relation to the direction of movement of the improved harrow leveller. 

According to it, in order to ensure free sliding of soil pieces along the working surface of the soil 

leveler, its installation angle of installation in relation to the direction of movement should be 

less than 55°.  

Keywords: leveler, installation angle of the leveler in relation to the direction of movement, 

leveler with full curved surface, the resistance of the field surface to the movement of the soil. 

 

INTRODUCTION. At the present time, the VP-8.0 pre-sowing leveler, MV-6.0, MV-6.5 and 

artificial harrow levellers are widely used in our country for the preparation of land for planting 

[1-5]. In this case, levelers level the surface of the fields, compact them as required and grind 

large lumps. But because they are trailers, they have low productivity, are inconvenient to use, 

and do not meet the requirements of minimum and economical tillage. Based on the above, a 

comprehensive suspension leveler was developed at SRIAM, which improved the work process 

[6-10]. The conducted tests showed that during the working process, the piled soil in front of the 

leveler of this harrow leveller is spilled to the side, and piles of soil are formed on both sides of 

it. To level these piles of soil, we have developed an improved harrow leveller (Fig. 1). 

This article presents the results of theoretical studies on the justification of the angle of 

installation in relation to the direction of movement of the improved harrow leveller. 



 

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1-a frame equipped with a suspension device; 2-full curved surface leveler; 3-soil leveler; 4-

compactor 

Figure 1. Construction scheme of a grinder-leveler equipped with a leveler with a full 

curved surface and a soil leveler 

Materials and methods. The pile of soil formed by the spilling of the soil piled in front of the 

leveler to its side is leveled by the soil leveler by leveling it to the side. Based on this, we 

determine the installation angle of the soil leveler in relation to the direction of movement on the 

condition that it scatters the soil pieces to the side to the maximum distance. For this purpose, we 

study the movement of soil particles under the influence of a soil leveler and after separation 

from it [11] (Fig. 2). During the movement of the soil leveler, the piece of soil that meets it at 

point 
1М  begins to move together with it at a speed 

1  in the direction deviating from the 

normal to its working surface by the angle of friction 

1

sin

cos

TYo
a

V
V




 , and after some time it 



 

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separates from it at point 
2М  and 

аV  continues its motion along the surface of the field with 

the initial velocity and stops at point 
3М . A piece of soil travels a distance L  after it is 

separated from the soil leveler until it stops moving. To determine this distance, the differential 

equation of the movement of a piece of soil on the field surface along the 
аV  direction, that is, 

along the X  axis, is created. It will look like this: 

2

2

d X
m F

dt
  ,                                                 (1) 

where m  – the mass of a piece of soil, kg; t  – time, s; F  – the resistance of the field surface to 

the movement of the soil, N. 

The movement of a piece of soil is caused by the force of its friction on the field surface 

TF f mg  (where Tf  – the soil-to-soil friction coefficient; g  – the acceleration of free fall, 

m/s
2
). Taking this into account, expression (1) becomes: 

2

2 T

d X
m f mg

dt
  .                                         (2) 

Reducing both sides of this equation to m  and integrating, we get: 

 

Figure 2. A scheme for studying the movement of a piece of soil under the influence of a soil 

leveler 



 

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1X TV f gt C                                                           (3) 

and  

2

1 2
2

T

t
X f g C t C    ,                                         (4) 

where 
1C , 

2C  – are integration constants. 

We determine the integration constants 
1C  and 

2C  using the following initial conditions: 

1

sin

cos

TYo
X a

V
V V




   and 0X   in 0t  . Substituting these into equations (3) and (4) 

we find that they are 1

1

sin

cos

TYoV
C




  and 2 0C  . Given these determined values of 

1C  

and 
2C , expressions (3) and (4) become: 

1

sin

cos

TYo
X TV V f gt




                                            (5) 

and 

2

1

sin

cos 2

TYo
T

t
X Vt f g




  .                                      (6) 

Taking into account that the final speed of the piece of soil is zero, from (6) we find the time of 

its movement after separation from the soil leveler: 

1

sin

cos

TYo

T

V
t

f g




 .                                                           (7) 

Putting this value of t  in (6), we determine the distance traveled by the piece of soil after 

separation from the soil leveler: 

2 2

2

1

sin

2 cos

TYo

T

V
L

f g




 .                                                    (8) 

This expression is the lateral spread distance of the soil 

 
2 2

12

1

sin
cos

2 cos

TYo
Yo TYo

T

V
L

f g


 


  .                    (9) 

As can be seen from this expression, the distance of the soil fragments to the side depends on the 

speed of movement, the installation angle of the soil leveler in relation to the direction of 

movement, and the friction coefficient of the soil on the soil and the angle of friction of the soil 

on the working surface of the soil leveler.  

According to expression (9), increasing the speed of movement and decreasing the coefficient of 

soil-to-soil friction leads to an increase in the distance of soil leveling to the side. 

But according to this expression, the angles of installation and friction of the soil to its working 



 

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surface in relation to the direction of movement of the soil leveler, that is, the effect of 
TYo  and 

1  on the lateral scattering distance of the soil cannot be directly estimated. 

In order to evaluate the effect of angles 
TYo  and 

1  on the lateral scattering distance of the 

soil, we plot the graphs of the change of 
YoL  depending on 

TYo  and 
1  according to the 

expression (9) (Fig. 3). 

The analysis of the graphical connections presented in Figure 3 shows that at all values of the 

friction angle, the distance of leveling the soil to the side changed according to the convex 

parabola law depending on the installation angle of the soil leveler in relation to the direction of 

movement, that is, it first increased and then decreased. As the angle of soil friction increases, 

the distance of soil leveling to the side decreases. 

We determine the values of the installation angle of the soil leveler in relation to the direction of 

movement, which ensure the maximum distance of the soil leveling to the side. For this, 

expression (9) is derived by TYo  and the obtained result is set to zero [12]: 

  
2

2

1

1

sin sin
2 cos

TYo TYo

T

V

f g
  


     

 12sin cos cos 0TYo TYo TYo      .                         (10) 

In this expression, only the expression in the middle parenthesis can be zero, that is: 

 

1 – φ1 = 25°; 2 – φ1 = 30°; 3 – φ1 = 35° 

Figure 3. Graphs of change of LYo depending on γTYo at different values of φ1 

    2

1 1sin sin 2sin cos cos 0TYo TYo TYo TYo TYo           .   (11) 

Let both sides of this equation be sin TYo , and write it in the following form: 

   1 12cos cos sin sin 0TYo TYo TYo TYo         .                              (12) 



 

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Using the rules known from trigonometry [13], we make  1cos cosTYo TYo    and 

 1sin sinTYo TYo    in expression (12) look like this: 

     1 1 1

1
cos cos cos cos

2
TYo TYo TYo TYo TYo TYo                   

 1 1

1
cos cos 2

2
TYo                                                                                   (13) 

     1 1 1

1
sin sin cos cos

2
TYo TYo TYo TYo TYo TYo                   

 1 1

1
cos cos 2

2
TYo                                                                                   (14) 

Taking into account these obtained results, the expression (12) will have the following form: 

   1 1 1 1

1
cos cos 2 cos cos 2 0

2
TYo TYo             ;                 (15) 

or 

 1 13cos 2 cos 0TYo     .                                                                             (16) 

From this  

1 1

1 1
arccos cos

2 3
TYo  

  
    

  
.                                                                  (17) 

it follows that. 

Results and discussion. By putting 1  in the expression (17) the values known from the 

literature (25-35°) [14, 15], we determine that the installation angle of the soil leveler should be 

in the range of 35-41° in relation to the direction of movement in order to maximize the leveling 

of the soil to the side. Comparing these data with the data presented in Figure 3, we see that they 

are in perfect agreement with each other. 

So, according to the conducted studies, the installation angle of the soil leveler should be in the 

range of 35-41° in relation to the direction of movement. 

During the working process of the soil leveler, it is necessary to ensure free sliding of soil pieces 

along its working surface so that the soil does not stick to its working surface and the soil does 

not accumulate in front of it. This is ensured when the following condition is met: 

190TYo   .                                                (18) 

Conclusion. Putting the above values of 1  in this expression, we determine that the angle of its 

installation in relation to the direction of movement should be less than 55° in order to ensure 

free sliding of soil pieces along the working surface of the leveler. Therefore, the soil leveler 

fully satisfies the condition that the soil leveler can freely slide along the working surface, 

provided that the distance of leveling the soil to the side is maximum. 

 



 

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