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 Academic Journal of Science, Engineering and Technology 

Vol.7, Issue 5; September - October 2022; 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

  

 

 

1 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

A COMPARATIVE STUDY OF LOADER SHOVELLING MECHANISMS WITH 

DISCRETE UNIT MODELING 

 

Mei Ying Wang, Jian Hong Liu and Xin Wei Zhao  

School of Intelligent Engineering, Jinzhong College of Information, Jinzhong, 030800, China 

 

Abstract: Loader shovelling mechanisms are used in various industrial applications, and the resistance 

encountered during the shovel loading process greatly affects the loading efficiency. Shovel loading resistance is 

the reaction force of the material on the bucket during the shovel loading process and contains two parts: the 

resistance of the bucket insertion stage and the resistance of the lifting stage. Therefore, it is essential to conduct 

research on shovel loading resistance to improve the performance of the loader shovelling mechanism. This paper 

presents a simulation analysis of the loader shovelling mechanism using the discrete element theory and EDEM 

software. A simulation model of the loading process is established, and the forward and reverse shovel loading 

processes are simulated. The mechanical characteristics of the shovelling operation are analysed visually, and the 

obstructing effect of the material on the bucket is clarified. The shovelling resistance of the key parts of the bucket 

at different stages of the shovelling process is specifically analysed, and the parts where the peak shovelling 

resistance is located and the stages where it is located are identified. The influence of the shovel angle on the 

resistance is also analysed. The results of the simulation analysis provide insight into the shovel loading resistance 

and the performance of the loader shovelling mechanism. The study demonstrates that the discrete element 

method can be effectively used in the simulation analysis of loader shovelling mechanisms, providing a useful 

tool for the design and optimisation of the loader shovelling mechanism. 

In conclusion, this research sheds light on the important mechanical characteristics of the shovel loading process 

and provides a comprehensive analysis of the shovelling resistance encountered by the loader shovelling 

mechanism. The results of this study can be applied to improve the design and performance of the loader 

shovelling mechanism, which can have a positive impact on various industrial applications that rely on this 

technology. 

Keywords: Shovel loading resistance, discrete element theory, EDEM software, simulation model, loading 

efficiency, mechanical characteristics, obstructing effect, peak shovelling resistance, shovel angle. 

 

 

1. Introduction  

The discrete unit method is to view the medium as a set of discrete independent moving units and to build a 

mathematical model through the properties of the discrete body, treating the object of analysis as a discrete 

particle, which corresponds to the properties of the discrete body itself. EDEM software is based on the discrete 

unit method and is widely used in many fields to calculate simulation processes quickly and efficiently. The 

software allows detailed analysis of the simulation results, such as graph types, particle tracking, transient 

analysis, etc. Yang study loader shovelling mechanisms. Includes the shovelling operation process and the 

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 Academic Journal of Science, Engineering and Technology 

Vol.7, Issue 5; September - October 2022; 

1252 Columbia Rd NW, Washington DC, United States 

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2 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

theoretical basis[1]. Based on the discrete element principle, Pang Lizhi studied the bucket wheel pick-up process. 

Taking the pick-up machine of a power plant as the research object, he applied EDEM software to simulate the 

horizontal pick-up process[2]. Wang proposed the use of RecurDyn to construct the loader model, and the use of 

EDEM to construct the material model, and carried out the coupling simulation analysis of RecurDyn-EDEM to 

study the coupling effect between the loader working device and the material under different trajectories[3]. 

Zheng according to the collapsed material working conditions occurring in the actual operation of the material 

extractor, the bucket wheel excavation EDEM simulation model was established by studying the bucket wheel 

three-dimensional model, combined with the discrete unit method; the time course curves of the excavation 

resistance of multiple buckets in the material collapse process, under different deep burial conditions and in 

different directions were calculated, and the calculated values of the bucket wheel excavation resistance in the 

design specification were compared to assess the hazards of the maximum excavation resistance under different 

deep burial conditions[4]. Li through data processing and setting of simulation parameters, a shovel loading model 

was established in EDEM software for shovel excavation conditions, and the accuracy of the model was verified 

by experimental and simulation methods; afterwards, the shovel loading process was simulated, and the resistance 

of different parts of the bucket at different stages of shovel loading was analysed to find out where the peak of 

shovel loading resistance was located[5].The characteristics of the bulk material and the loading conditions of the 

loader were analyzed by Yu, the characteristics of the rock material were introduced, the calculation methods for 

calculating the operating resistance were summarized, and the factors influencing the size of the loading resistance 

were classified in the shovelling process, and the main factors were grasped for analysis [6].  

2. Bucket model  

The bucket is an important actuator for loading, transporting and discharging materials in the loader's working 

equipment. It is usually made of the front edge (sometimes equipped with bucket teeth), the bottom of the bucket, 

the circular bucket wall, the side edge, the side wall and the rear baffle welded together, and the shape in the 

transverse direction of the body remains basically unchanged, so the geometry of the bucket is determined by the 

longitudinal section size. At present, the bucket radius of gyration R is usually used as the basic parameter for the 

calculation of other parameters in the design, with the following formula.  

R=              (1)  

R: bucket radius of rotation/m; Vs : bucket flat capacity/m3 ; B0 : bucket internal measured width/m; λg : bucket 

bottom length coefficient; λz : back wall length coefficient; λk : baffle height coefficient; λr : radius of circle 

coefficient; γ: opening angle; γ1 : angle between baffle and back wall  

Bulk materials consist of dispersed particles with a bulk substance that is not normally found in solids, liquids 

and gases, and whose garments of motion follow Newton's second law [7]. Under the action of internal forces, 

the particles of an object device undergo some kind of flow and take on the characteristics of a liquid, eventually 

forming a particle flow. In our daily life there are mainly gravel, sand, coal and grains, of which gravel, sand and 

[ ] 
 
 
 

 
 
 

 
 

 
 
 

 
− − − + ) 

180 
0.5(1 

2 
cos 0.5 cos 

2 
1 k 0 

γ 
π 

γ 
λλγλ r Z 

S 

B 

V 

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 Academic Journal of Science, Engineering and Technology 

Vol.7, Issue 5; September - October 2022; 

1252 Columbia Rd NW, Washington DC, United States 

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3 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

coal are of most interest. The general rock materials are granite, limestone, sandstone, shale, etc. The characteristic 

features are different and Table 1 shows the relevant physical properties of crushed rock [8].  

Table 1: Physical properties of aggregates  

Properties  Numerical 

values  

Properties  Numerical 

values  

Modulus of 

elasticity E  

1.5 x 108 

N/m2  

Resistance 

factor  

0.20  

Density  1.9 x 103 

kg/m3  

Coefficient 

ostatic friction  

0.90  

Friction 

angle  

32.5°  Rolling 

friction 

coefficient  

0.66  

Poisson's 

ratio  

0.35      

3. Non-adhesive spherical particle contact forces (Hertz theory)  

The contact model is an important basis for modelling the discrete element method, its description of the contact 

behaviour between elements and the analytical calculations directly determine the magnitude of the forces and 

moments applied to the particles. Therefore when using the discrete element method for different objects, the 

contact models differ and the results vary, but all simulation models must include at least one basic particle-to-

particle and particle-to-geometry boundary contact model [9-12]. In this paper, in order to simplify the simulation, 

the default contact model Hertz theory model set in the EDEM software is used uniformly, which has an efficient 

and accurate computational performance.  

Hertz contact theory assumes that the surfaces of particles in contact with each other are smooth and 

homogeneous, that the contact surface is small compared to the particle surface, that only elastic deformation 

occurs at the contact surface, and that the contact force is perpendicular to the contact surface [13-14]. The Hertz 

contact theory is the theoretical basis of the problem and is applicable to the elastic contact of curved bodies such 

as spheres, columns and ellipsoids, and even to the contact of micro-convex bodies between contact surfaces. As 

shown in Fig.1, two spherical particles of radii R1 and R2 are in elastic contact, and the normal overlap α is  

α = R1 + R2 -|r1 -r2 |>0                                (2)  

The radii of particle 1 and particle 2 are R1 , R2; r1 and r2 are the spherical position vectors of the two particles 

respectively.  

The dotted line in Figure 1 shows the location of the particle surface when no deformation is considered, and the 

contact surface between the particles is circular, then the contact surface radius a is:  

a= aR*                                  (3)  

The inter-particle normal forces N are:  

 1 3 

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N=E R*( *) 2α 2                               (4)  

R* and E* are the effective particle radius and effective modulus of elasticity respectively.  

 1 1 1 

 = +                             (5)  

 R* R R1 2 

 1 1−ν12 1−ν22 

 = +                          (6)  

 E* E1 E2 

E1,v1,E2,v2 are the modulus of elasticity and Poisson's ratio of particle 1 and particle 2, respectively.  

When the increment of overlap between two contacting particles is Δα, the increment of normal force ΔN is 

calculated from (4) or (5).  

∆ =N 2 αR E* *∆ =α 2a *E ∆α                    (7)  

4. Analysis of forward shovelling resistance  

4.1 Forces on the bucket in the X, Y and Z directions  

The forces on the bucket in the X, Y and Z directions are first analysed. In the simulation, a certain number of 

gravel particles are loaded into the bucket. The bucket is first shovelled into the rubble pile and then the bucket 

filled with rubble leaves the pile. The software offers linear translational rotation, sinusoidal translational rotation 

and convey or translational rotation. Therefore, here we use linear translation and rotation. First, the bucket is 

shovelled parallel into the pile to a certain depth, then the bucket is turned over and lifted up. Figures 2, 3, 4 and 

5 show the variation of forces in the X,Y and Z directions versus time. Where the full shovelling process is 15s. 

The horizontal axis represents the time of shovelling and the vertical axis represents the amount of shovelling 

resistance applied in each direction.  

  
Figure 1: Particle contact deformation diagram   Figure 2: Shovel loading simulation  

Analysis of Figure 3 shows that the resistance of the bucket in the X-axis direction exceeds 9KN when the bucket 

is just shovelling into the rubble pile, there are small fluctuations in the resistance during the process of shovelling 

into the rubble, but when the bucket is filled with rubble the resistance rises rapidly to 12KN when the bucket is 

turned over and lifted off the pile, then the maximum partial force falls rapidly to the lowest resistance 

corresponding to the bucket shovelling out of the rubble pile. The X-directional force then does not change much. 

The peak force is generated in approximately 1.5s.  

   

2 a  

a  

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 Academic Journal of Science, Engineering and Technology 

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5 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 
   

Figure 3: X-directional component of shovel loading resistance  

The peak force is approximately 1.5 s. The corresponding force in the Z-axis in Figure 5 is not very large 

compared to the X and Y-axis. Y-axis is not very large. The rest of the time is very smooth. The z-directional 

force is much smaller than the x- and y-directions.  

 
   

2                 5              8  

Time/s  

12   

  

  

11   

  

  

10   

  

  

9   

2                 5               8  

Time/s  

-8   

  

  

-9   

  

  

-10   

  

  

-11   

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6 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

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Figure 4: Y-direction of the shovel load resistance  

  
Figure 5: Z-directional component of shovel loading resistance  

4.2 Force analysis of the bucket base plate  

As the forces exerted on the base plate are the greatest during the shovelling process, the next discussion will 

focus on the base plate and the left and right plates of the bucket will not be analysed for the time being. 

Simplifying the actual shovelling process of the loader, the shovel-in phase lasts 7 seconds and the bucket speed 

is 0.2 m/s; the effective working phase lasts 4 seconds and the angular speed of the bucket is 0.15 arc/s. The forces 

exerted by the material on the bucket floor during the horizontal shovel-in phase are shown in Figure 6. The forces 

exerted by the material on the bucket during the bucket reversal lift are shown in Figure 7.  

 
   

3                  5                 7   

Time/s  

3.5   

  

3   

  

2.5   

  

2   

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Figure 6: Bucket forces in the horizontal shovel-in phase  

 
   

Figure 7: Bucket stress diagram in lifting phase  

The analysis of the shovel loading resistance during the horizontal insertion phase showed that during the 

horizontal insertion phase the total force at the bottom first increased, then decreased and finally stabilised, with 

local fluctuations during which it showed a secondary peak. The maximum force was 3.5 KN. In the subsequent 

stages, the force gradually stabilised when the amount of material loaded reached a threshold. As the bucket 

rotates upwards, the forces previously concentrated at the bottom of the bucket are gradually transferred to the 

circular wall of the bucket during this phase, so that the forces acting on the bottom of the bucket are significantly 

reduced during this phase.  

5. Results of reverse shovel analysis  

5.1 Forces on the bucket in the X, Y and Z directions  

Figures 8, 9 and 10 show the relationship between the total force applied to the bucket during excavation in the 

X, Y and Z directions as a function of time. Where the full shovelling process is 14s. where the horizontal axis 

indicates the digging time and the vertical axis indicates the magnitude of the digging resistance applied in each 

direction.  

 
   

7                9              11  

Time/s  

2   

  

1.5   

  

1   

  

0.5   

3                 9               6   

Time/s  

10   
  
  

9   
  
  

8   
  
  

7   

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Figure 8: X-directional component of the digging resistance  

The relationship between the X-directional force and time can be seen in Figure 8. The resistance of the bucket 

in the X-direction was just over 7KN when the bucket was just shovelling into the rubble pile, and its X-directional 

force reached its maximum value of 9.8KN around the 8th s. Between 5.5s and 8s, the bucket force had a more 

obvious fluctuation. As the time increases, its digging resistance gradually decreases, and after 9s its resistance 

drops significantly.  

 
   

Figure 9: The Y-directional component of the digging resistance  

 
   

Figure 10: Z-directional component of the digging resistance  

From the results of the Y-axis force splitting simulated in Figure 9, it can be seen that the bucket's force splitting 

decreases gradually from 3 to 7.5s, reaching a minimum of -25KN, and gradually increases after 7.5s. After 6s, 

the force varies considerably, especially between 7 and 7.5s, when the trend of force decrease is extremely 

obvious.  

3                6             9  

Time/s  

-10   

  

20   

  

15   

  

-25   

3               6             9  

Time/s  

32   

  

  

24   

  

  

16   

  

  

8   

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The results of the Z-directional forces simulated in Figure 10 show that the bucket's digging resistance gradually 

tends to increase from 3s onwards, reaching a peak of 32KN at around 5s, and then showing a decline to a 

minimum of 8KN at the initial resistance.  

5.2 Force analysis of the bucket base plate  

The following analysis of the horizontal insertion phase of the excavation resistance analysis, in edem derived 

from the bucket bottom part in the horizontal insertion phase of the force diagram as Figure 11, horizontal 

insertion phase, the bucket bottom overall force first increase and then decrease, local fluctuations. In the later 

stages, the forces are gradually stabilised as the amount of excavated material has reached its limit. As the bucket 

is turned upwards, the bucket floor, which previously bore the main part, is gradually shifted to the circular wall 

at this stage, so that the forces on the floor at this stage are on a decreasing trend, as shown in Figure 12.  

 
  

Figure 11: Bucket forces in the horizontal insertion phase  

 
  

Figure 12: Bucket forces during the pick-up phase  

6. Effect of shovel entry angle on resistance  

When shovelling horizontally, the bucket is shovelled into the rubble pile at a natural horizontal ground level, but 

due to the influence of the front teeth of the bucket, the bottom plate of the bucket is tilted at a certain angle to 

10               12              14   

Time/ 

12   
  
  

11   
  
  

10   
  
  

9   

3               6             9  

Time/ 

24   

  

  
18   

  

  
12   

  

  
6   

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the horizontal surface and cannot achieve true horizontal; while shovelling into the rubble pile at a certain angle, 

the bottom plate of the bucket must be at a certain angle to the horizontal surface. When the shovel entry angle is 

less than 11°, the simulation result is close to the calculated value. In particular, when the shovel entry angle is 

between 5° and 10°, the two almost coincide. Therefore, we analytically derived the process of shovelling the 

bucket into the rubble pile, where 7° and 9° were targeted, in order to obtain the best insertion angle. As shown 

in Figure 13, it is concluded that the shovel entry resistance increases with increasing shovel entry depth, and 

with increasing shovel entry angle. When the shovel penetration depth is 0.3 m, the effect of the shovel penetration 

angle on the shovel penetration resistance is relatively small; when the shovel penetration depth exceeds 0.5 m, 

there is a significant increase in the shovel penetration resistance.  

 
Figure 13: Resistance variation curve  

7. Conclusion  

Based on the discrete element theory, this paper applies EDEM software to establish a simulation model of the 

loading process and realise the simulation of the forward and reverse shovelling operation process. Through the 

simulation, the shovel resistance of different parts of the bucket at different stages of the shovel loading process 

is analysed, and the parts where the peak shovel resistance is located and the stages where it is located are 

identified. The resistance of the bucket in the X, Y and Z directions was analysed in the forward and reverse 

shovelling process. According to the force analysis of the bucket, the force on the bucket floor is the largest, after 

which the force analysis of the bucket floor during forward and reverse shovelling was carried out to obtain the 

trend of force changes. Finally, the influence of the shovel entry angle on the resistance was analysed. It can be 

seen that when the shovel entry angle is 9°, the resistance increases with the depth of shovel entry.  

Acknowledgements  

This paper was supported by①“2022 Science and Technology Innovation Project for Higher Education 

Institutions in Shanxi Province (2022L659)”②“2022 Innovation and Entrepreneurship  

Project for Students in Shanxi Province(20221640)”  

References  

Yang Zikang. Research on resistance reduction shoveling strategy of loader based on EDEM [D]. Jilin 

University, 2022.  

  

2   

  

1.5   

  

1   

  

0.5   

Bucket  penetration  

0.2               0.4             0.6  

Shovel-in angle 7°  
Shovel-in angle 9°  

  

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Pang, L. C.. Research on the bucket-material interaction mechanism of bucket wheel stacker bucket based on 

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Zheng Pei, Song Wenxi, Hu Xiong. EDEM simulation of excavation resistance of bucket wheel stacker reclaimer 

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Yang Xu. Research on discrete unit method for bucket shovel resistance of loader [J]. Journal of Guangxi 

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Yu, Xuebang. Simulation study of loader bucket operation resistance based on EDEM [D]. Guangxi University 

of Science and Technology, 2018.  

Seife C. Can the laws of physics be unified? Science,2005,309(5731): 82-82.  

Yan Bo, Zhan Kai, Guo Xin, Li Hengtong, Shi Xiaojie. Simulation study of underground scraper shoveling process 

based on EDEM [J]. Nonferrous Metals (Mining part),2019, 71(06):74-77. [9] Sun QC, Wang GQ. 

Introduction to the Mechanics of Particulate Matter. Beijing:Science Press, 2009.  

Sun Qicheng, Hou Meiying, Jin Feng. Physics and Mechanics of Particulate Matter. Beijing: Science Press, 2011.  

Jaeger HM, Nagel SR, Behringer RP. Granular solids, liquids, and gases. Reu Modern Phgs, 1996, 68(4): 1259-

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De Gennes PG. Granular matter: a tentative view.RevModern Phys, 1999, 71(2): S374-S382. [14] Forterre Y, 

Pouliquen O. Flows of dense granular media.Annual Review Flauid Mechanics, 2008, 40: 1-26.   

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