*Corr. Author’s Address: College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan, China, wxuew@163.com 501
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515 Received for review: 2021-06-24
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-09-05
DOI:10.5545/sv-jme.2021.7300 Original Scientific Paper Accepted for publication: 2021-09-21
Response Analysis of a Scraper Conveyor  
under Chain Faults Based on MBD-DEM-FEM
Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
Zisheng Wang
1,2
 – Bo Li
1,2
 – Chao Liang
1,2
 – Xuewen Wang
1,2,*
 – Jiahao Li
1,2
1 
Taiyuan University of Technology, College of Mechanical and Vehicle Engineering, China 
2 
Shanxi Key Laboratory of Fully Mechanized Coal Mining Equipment, China
To tackle the difficulty in obtaining the response data of chain and bulk coal under chain faults, this paper uses a new method for the fault 
simulation of scraper chains based on the coupling of multi-body dynamics (MBD), discrete element method (DEM), and finite element method 
(FEM). With the force and stacking angle as response values, the contact parameters of bulk coal were revised using a rotary transport test. 
The simplified DEM-MBD model was verified from the resistance using the point-by-point method. The static structure model of the chain was 
verified by the chain tensile experiment. The DEM-MBD coupling results show that when the chain is stuck or broken, the dynamic properties 
of the chain and bulk coal fluctuate sharply, and the wear of the medium plate increases. Based on the DEM-MBD coupling results and 
the DEM-FEM unidirectional coupling, the stress, strain and life were acquired, and were verified experimentally. Regarding the fracture, 
the Plackett-Burman test was used to determine that the crack depth, initial angle, and tensile load significantly affect the stress intensity 
factor (SIF). The quadratic model between significant factors and SIF was constructed using the response surface method, which provides a 
reference for the simulation of the scraper conveyor, the fault mechanism, and the optimization of the design of the chain.
Keywords: multi-body dynamics, discrete element method, finite element method, scraper chain fault, stress intensity factor, response 
surface method
Highlights
• 	 A method for the fault simulation of a scraper conveyor based on the MBD-DEM-FEM was proposed.
• 	 The contact parameters of bulk coal were revised from the force and stacking angle using the response surface method. 
• 	 The response data of the chain and bulk coal under chain faults were obtained.
• 	 The interactions between factors on stress intensity factor were analysed using the response surface method.
0  INTRODUCTION
As the core structure of the scraper conveyor, the 
scraper chain is subject to frequent faults, which 
seriously threatens the safety of workers and the 
mining efficiency of coal mines [1]. For satisfying the 
high requirements of intelligent coal mines for scraper 
chains, it is not feasible to perform fault tests on actual 
scraper conveyors or scaled models to obtain real-time 
data. This method is costly, and it is difficult to extract 
data. Consequently, safety cannot be guaranteed due 
to the uncertainty of fault. The simulation method 
based on computer aided design has low cost and 
high safety factor, and can reproduce the fault state 
realistically. The common simulation methods include 
finite element method (FEM), multi-body dynamics 
(MBD), and discrete element method (DEM).
FEM is based on the idea of discretization and 
numerical approximation to solve problems [2]. 
Based on the simplified chain transmission model, 
researchers have obtained the stress, strain, [3] and [4] 
and fatigue life [5] of chains under different conditions 
through transient dynamics or static structural 
analysis. However, the finite element analysis (FEA) 
based on the simplified model puts higher demands on 
the boundary conditions. The accuracy of boundary 
conditions set only by finite element software is not 
high but can be enhanced by coupling with DEM [6] 
and MBD.
MBD focuses on the kinematic and dynamic 
behaviour of multi-body systems and the mechanical 
interaction between parts. The velocity and vibration 
characteristics of the scraper chain under chain stuck 
and breaking faults were gained by Jiang et al. [7]. 
Xie et al. [8] discussed the torsional pendulum and 
vibration characteristics of the chain under chain 
stuck fault. With the maturity of flexible technology, 
scholars have made the chain flexible to obtain the 
stress and deformation [9] and [10]. Previous studies 
rarely considered the role of bulk coal or only replaced 
it with a constant load, ignoring the distribution and 
time-varying characteristics of bulk coal. However, 
the force and movement of bulk coal under fault 
conditions may worsen the fault and accelerate the 
failure of parts. 
Considering the discrete characteristics of bulk 
coal [11], DEM has been applied to research the 
transport state of scraper conveyors [6] and [12] and 
the failure of key parts [13] and [14]. Researchers have 
improved the reliability of simulation by modifying 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
502 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
parameters [15] and [16] and coupling simulation. The 
MBD-DEM bidirectional coupling model of scraper 
conveyor was established by Zhang et al. [17] to 
realize real-time sharing of information between bulk 
coal and rigid bodies.
The surface cracks caused by the synergy 
of complex factors such as wear, corrosion, and 
deformation are reasons for the fatigue fracture of the 
chain [18]. It is necessary to discuss the initiation and 
propagation of cracks. The stress intensity factor (SIF) 
is a fracture parameter that characterizes the stress 
field at the crack front, which is affected by the size 
and shape of the crack. Xue et al. [19] investigated 
the effects of crack depth and position on fracture 
parameters through the single factor test, which 
does not involve the interaction between the factors 
controlling the fracture of chains. The response 
surface method (RSM) is an optimization method 
combining mathematical statistics and modelling [20]. 
The effects of interaction on the response value can be 
investigated.
It can be seen that the advantages of each 
method can compensate for the deficiencies of other 
methods, so this study used a new method for the 
fault simulation of a scraper conveyor based on the 
coupling of MBD-DEM-FEM. First, the MBD-DEM 
coupling model was established and verified to gain 
the response characteristics of chain and bulk coal 
under chain stuck and breaking faults. Combining 
the above results and DEM-FEM coupling, this study 
obtained the stress, strain, and life of the chains. For 
the fracture failure, through single factor testing and 
response surface testing, the single and interactive 
effects of crack depth, initial angle, and tensile load on 
the SIF were investigated. This provides a reference 
for the simulation of scraper conveyors, and the fault 
mechanism and optimization design of the chain.
1  SIMULATION MODELS AND TEST
1.1  Dynamic Model
The coupling simulation with the complete length of 
the scraper conveyor (SGZ880/800) is not workable 
[17], so the dynamic model is simplified as necessary. 
When the chain is stuck or broken, the chain far 
from the fault point will not respond in a short 
time. Therefore, only three middle troughs, scraper 
chains, and drive sprockets are retained; the retarder, 
hydraulic coupler, and drive motor are removed, and 
the bottom chute for the return of the chains is added. 
The simplified model is 5 metres long, as shown in 
Fig. 1. In the pre simulation, the sprockets drove the 
scraper chains to run smoothly, which satisfied the 
desired motion characteristics. The kinematic pairs 
and contacts of components were set up in RecurDyn 
dynamic software. The stiffness and damping 
coefficients of contacts between parts were adjusted 
by pre-simulation to be 600000 N·mm
–1
 and 1000 
N·(mm/s)
–1
. 
1.2  Construction and Modification of Bulk Coal
1.2.1  Model of Coal Particle
The three typical shapes of coal particles were built 
by the spherical filling method [21], shown in Fig. 2. 
In order to obtain the contact characteristics of the 
bulk coal with the scraper chain and the medium plate 
more accurately, coal with large (50 mm to 100 mm), 
medium (25 mm to 50 mm), and small (13 mm to 25 
mm) sizes was generated by the particle factory fixed 
above the machine tail, and the mass proportions of 
three sizes are 0.25, 0.4, and 0.35.
Hertz-Mindlin (no slip) [22] and Hertz-Mindlin 
with Archard wear [14] were chosen for the contact 
models between particles and between particles and 
rigid bodies, respectively. The intrinsic parameters 
Fig. 1.  The mechanical relationship of simplified model; a) simplified model; and b) mechanical relationship

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
503 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
measured by the group members through the designed 
experiments are listed in Table 1 [16]. 
Fig. 2.  The shapes and mass proportions of particles
Table 1.  The intrinsic parameters
Parameters Steel Coal
Shear modulus [MPa] 800 470
Poisson’s ratio 0.3 0.3
Density [kg·m
–3
] 7850 1229
1.2.2  Modification of Contact Parameters
In current research, the calibration tests of coal 
particle parameters take the stacking angle at rest as 
the response variable. During the conveying process, 
the behaviour of bulk coal is not only macroscopic 
accumulation on the chutes, but also the mechanical 
interaction with the scraper conveyor. Therefore, it 
is necessary to modify the contact parameters of coal 
particles through the bulk coal transportation test with 
force and accumulation as the response variables. 
Using the actual scraper conveyor to carry 
out the transportation test is not feasible. Based on 
the transport principle, the rotary transport testing 
machine shown in Fig. 3a was designed. The upper 
sample has a wedge structure with the same slope as 
the scraper, as shown in Fig. 3e, and the material of 
the upper sample is 42CrMo (C: 0.38 % to 0.45 %), 
which is the same as the scraper. The lower samples 
are six fan-shaped plates with positioning holes, as 
shown in Fig. 3f, and the material of the lower samples 
is 16Mn (C: 0.13 % to 0.19 %), which is commonly 
used in the medium plate. The three-dimensional 
force sensor and the upper sample are fixed with the 
rack through the clamp, and the lower samples are 
fixed with the trough through the positioning holes. 
After the bulk coals with the required mass and size 
are paved in the trough, the motor drives the trough to 
rotate at a uniform angular velocity of 10 rad·s
–1
. The 
linear velocity of the position where the upper sample 
is located is the same as that of the scraper chain 
(1.1 m·s
–1
), as shown in Fig. 3c. The bulk coals are 
pushed by the upper sample and accumulate around 
the sample, which is consistent with the principle of 
scraper transportation in actual work, as shown in Fig. 
3c. The force on the upper sample when pushing the 
bulk coals was measured through the force sensor, as 
shown in Fig. 4. The stacking angle obtained using 
an image-processing program written in Matlab is 
38.59°.
Through Plackett-Burman and response 
surface tests, the quadratic polynomials between 
force, stacking angle and significant terms were 
established. The contact parameters obtained by 
solving the polynomials with the experimental force 
and stacking angle as the target values are shown in 
Table 2. Finally, the accuracy and applicability of the 
parameters were verified through tests under different 
transport conditions.
Fig. 3.  The test equipment and principle; a) test equipment; b) the rotary transport machine; c) test principle; d) three-dimensional force 
sensor; e) upper sample; f) lower sample; g) accumulation around the upper sample

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
504 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
Fig. 4.  The force on the upper sample
Table 2.  The corrected contact parameters
Parameters Coal-Steel Coal-Coal
Coefficient of restitution 0.65 0.64
Coefficient of static friction 0.401 0.333
Coefficient of rolling friction 0.032 0.041
1.3  DEM-MBD Coupling Simulation
1.3.1  Verification of DEM-MBD Coupling Model
Due to the short laying length, there is a gap in the 
speed and tension with the actual situation. The point-
by-point method is used to calculate the resistance 
of long-distance continuous conveying machinery; 
its main principle is shown in Eq. (1). This research 
focuses on the fault response of the scraper chain in 
the chutes, so it only verified the resistance of the 
loaded side (Points 3 and 4 in Fig. 1) and unloaded 
side (Points 1 and 2 in Fig. 1), which were calculated 
based on the parameters of the conveyor to be 348.9 
kN and 35.3 kN respectively [23].
 F F W
ijij
, (1)
where F
i
 [N] is the tension at the front point, F
j
 [N] 
is the tension at the back point, W
ij
 [N] is the running 
resistance. 
The engagement and separation points of 
the sprockets and the chains are often selected as 
measuring points, as shown in Fig. 1. The DEM-MBD 
simulation was carried out under normal conditions 
to extract the chain tension at four points. According 
to Eq. (1), the simulation values of the running 
resistance on the load side and the unloaded side were 
calculated, and the comparison with the theoretical 
resistance is listed in Table 3, the relative error under 
no-load and full-load is less than 8 %, which testifies 
that the simplified model can reflect the mechanical 
characteristics of scraper conveyor.
Table 3.  The comparison between theoretical resistance and 
tension difference
Items
No-load Full-load
i = 4
j = 3
i = 2
j = 1
i = 4
j = 3
i = 2
j = 1
W
ij
 [kN] 35.2 35.2 348.8 35.2
ΔF
ij
 [kN] 33.7 34.6 321.7 35.3
Relative error [%] 4.26 1.70 7.77 0.28
The chain tension at the middle section of 
the scraper conveyor provided by the cooperative 
enterprise (Yaxing Anchor Chain) is about 210 kN to 
223 kN; the simulation tension is about 200 kN, and 
the maximum relative error between them is 10.3 %.
The velocity curve of the chain under full-
load condition is shown in Fig. 5, which reveals the 
fluctuation of “decrease–increase” after the velocity is 
accelerated. It conforms to the polygon effect [24] and 
validates the kinematics characteristics of simplified 
model.
Fig. 5.  The velocity of scraper chain
1.3.2  Design of Fault Conditions
Chain breaking and chain stuck are the most frequent 
faults [25]. The small preload, rib spalling of coal 
wall, and coal blocks stuck at the connection of 
chutes can cause the chains to jam: we added irregular 
obstacles in the chute to simulate the chain stuck 
fault in dynamics software. The increased chain pitch 
caused by wear, the extreme impact load, the long-
term over-carrying and the fatigue crack generated by 
the synergy of corrosion and other factors can cause 
the chain to break; we did not deal with the stuck fault 
in time and set the simulation script for the contact 
between chain links to simulate chain breaking fault in 
dynamics software.

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
505 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
1.4  Experimental Verification of FEA Model
1.4.1  FEA Model of Chain 
The FEA model shown in Fig. 6 was employed to 
solve the non-linear contact between chain links. 
The size of the chain link made of 23MnNiCrMo54 
(C: 0.22 %) is Φ 34 mm × 126 mm; the properties of 
the material are listed in Table 4, and the S-N curve is 
NS 
2.49
 
= 1.30066×10
10
. The entire model was divided 
into tetrahedral mesh sized 6 mm, yielding 50,997 
elements with 76,070 nodes. The frictional contacts 
were set between the flat chains and the vertical 
chain, and the coefficient of friction is 0.2. The right 
surfaces of flat chain 2 were subjected to boundary 
loads based on the coupling results, while the left 
surfaces of flat chain 1 were fixed. The pressure of 
coal was distributed on vertical chain 1 according to 
the pressure file derived from EDEM software.
Fig. 6.  The FEA model of the chain
Table 4.  The mechanical properties of 23MnNiCrMo54
Properties Value
Density [kg·m
–3
] 7860
Young’s modulus [GPa] 210
Poisson’s ratio 0.3
Tangent modulus [MPa] 2444
Yield strength [MPa] 1166
Tensile yield strength [MPa] 1254
1.4.2  Experimental verification
The tensile testing machine (LAW-5000) was used 
to obtain the elongation rate of the chain under the 
test load (1160 kN to 1276 kN), as shown in Fig. 7, 
and the experiment was repeated three times. Based 
on the model in Fig. 6, the simulation value of the 
elongation rate is 1.33 %. The comparison between 
the experimental value and the simulated value is 
shown in Table 5. It can be seen from Table 5 that the 
relative error does not exceed 5 %.
Fig. 7.  The microcomputer controlled electro-hydraulic servo 
tensile testing machine (LAW-5000)
Table 5.  The comparison between experimental and simulation 
values of elongation
Number
Experimental 
value [%]
Simulation 
value [%]
Relative 
error [%]
Average 
relative 
error [%]
1 1.40
1.33
5.00
4.07 2 1.36 2.20
3 1.40 5.00
2  SIMULATION RESULTS
When the scraper chains are stuck or broken, the 
scraper de flects due to the uneven force on both 
ends, as illustrated in Fig. 8. The surrounding of the 
deflected scraper is divided into four areas, in which 
PQ is the stuck side and RS is the deflected side.
Fig. 8.  The areas around the deflected scraper
2.1  Dynamic Response  
2.1.1  Operating Tension
Fig. 9 is the tension diagrams of the measured chain 
links under faults. When the chain in areas PQ is stuck, 
the maximum tensions in areas Q and R reach 1139.9 
kN and 669.9 kN, respectively, and the stuck side is 

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506 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
larger than the deflected side; the tensions in areas P 
and S are reduced, and the minimums are both 0 kN. 
Furthermore, the tension on the stuck side changes 
earlier than the deflection side, but both sides return to 
stability concurrently. The dynamic responses of two 
chains are identical when both sides of the scraper are 
stuck, so only the curves on the side PQ are plotted. It 
can be seen from Fig. 9b that the maximum is 1155.9 
kN, and the growth rate of tension is faster. The reason 
is that when both sides of the scraper are stuck, the 
scraper cannot deflect, and the growth rate of chain 
tension cannot be alleviated by deflection. 
According to the tension response under chain 
stuck fault, the areas Q and R were set as the fracture 
points. When the area Q fails, the tension in area P 
decreases and stabilizes at 10 kN to 15 kN due to 
medium doubled chain; the tension in areas R and 
S increases due to the augment of load, and the 
maximum is 947.8 kN. When the chains in areas Q 
and R fracture, the middle scraper deflects instantly, 
the front and rear scrapers deflect in the opposite 
direction, and the chains in areas P and S are loose, as 
shown in Fig. 10. With the return of the front and rear 
scrapers and the deflection of the middle scraper, the 
chains finally break.
Fig. 10.  The deflection of the nearby scrapers
2.1.2  Velocity of Chains
Fig. 11 reveals the velocity curves of the measured 
chain links under faults. In Fig. 11a, compared with 
the deflected side, the velocity fluctuation of the 
stuck side is larger, and the two fluctuations in area 
P are earlier and later than those in area Q severally. 
In addition, the chain links on the stuck side have the 
opposite velocity. The reason is that the chains in areas 
            
             
Fig. 9.  The tension curves; a) unilateral jamming; b) bilateral jamming; c) unilateral breaking; d) bilateral breaking

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507 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
P and Q are piled up and tensioned, respectively, and 
this state is transmitted forward and backward with 
the stuck scraper as the centre. As a result, the tension 
at the rear of the tested link along the transportation 
direction is greater than that at the front in a short 
time. The velocity at the front and rear of the scraper 
are synchronous when two sides are stuck. The lowest 
velocity is almost 0 m·s
–1
, and there is a large positive 
mutation before recovery.
When the chain in area Q breaks, the velocity in 
area P is reduced by the deflection and impact of the 
scraper, and the velocities in areas R and S increase 
with different amplitudes. When the chains at areas 
Q and R both break, the velocity in area P fluctuates 
from decrease to increase, and the velocity in area S 
increases.
2.1.3  Acceleration in the Z-Direction
Fig. 12 shows the Z-direction acceleration curves of 
the measured chain links under faults. The scraper 
vibration can affect the chain vibration under normal 
conditions, and their vibrations are transmitted 
through the chain tension. From the chain tension 
curves under fault conditions (Fig. 9), it can be seen 
that when the PQ side of the scraper is stuck, the stuck 
scraper vibrates and deflects due to the external load. 
The scraper deflection loosens the chains in areas 
P and S, blocks the transmission of chain tension, 
causes the chain vibration in this area to weaken, and 
the minimum can reach 0. Additionally, the scraper 
deflection causes the chains in areas Q and R to be 
tightened, and the chain tension and its transmittance 
increases, resulting in the increase of chain vibration, 
up to 33 m·s
–2
. Since the chain vibrations in areas 
R and S are the same as those in areas Q and P, 
respectively, they are not repeated in the figure. The 
results of bilateral jamming and unilateral fracture of 
the chain are the same as above.
When the chains in areas Q and R break, the 
middle scraper deflects quickly, and then the front and 
rear scrapers deflect in opposite directions, as shown 
in Fig. 10. The remaining chains are piled up, the 
             
             
Fig. 11.  The velocity curves; a) unilateral jamming; b) bilateral jamming; c) unilateral breaking; d) bilateral breaking

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
508 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
angle, the velocity of the bulk coal in area Q instantly 
increases when the scraper returns to be steady, which 
can reach a maximum of 10.15 m·s
-1
. The flying bulk 
coal may injure the staff. The result when both sides 
are stuck is the same as the result on the stuck side in 
Fig. 13.
Fig. 14.  The velocity cloud diagram of bulk coal under unilateral 
breaking; a) before fault; and b) after fault
2.2.2  Wear of Medium Plate
A layer of coal with a smaller size is often covered 
between the medium plate and scraper chain. When 
the scraper chain moves, three-body abrasive wear 
is formed [13], as shown in Fig. 15. Due to the short 
simulation time, only the qualitative analysis and 
prediction of the wear area of the medium plate 
was carried out; the material of the medium plate is 
NM450 (C: ≤ 0.35 %). The wear depth in the EDEM 
software was calculated by Eq. (2).
 h QA WF dA
nt
= = , (2)
where Q [m
3
] is the volume of material removed, W 
[Pa
–1
] is the wear constant, the size is 1.2×10
–12
 Pa
–1
, 
F
n
 [N] is the normal force, d
t
 [m] is the tangential 
distance moved, and A [m
2
] is the area of material 
removed.
tension and its transmittance are reduced, resulting in 
reduced vibration of the chain and scraper.
2.2  Discrete Characteristics of Bulk Coal
2.2.1  Velocity of Bulk Coal
The velocity of bulk coal under unilateral jamming is 
shown in Fig. 13. 
Fig. 13. The velocity cloud diagram of bulk coal under unilateral 
jamming; a) before fault; b) initial stage of fault;  
c) middle stage of fault; d) after fault
The farther the bulk coal is away from the scraper 
and chains, the lower the velocity. When the scraper 
starts to deflect, the velocity of the bulk coal in area 
Q decreases first; the velocity of the bulk coal in area 
S increases briefly. During the continuous deflection 
of the scraper to the maximum, the bulk coal in areas 
P and Q continue to accumulate, and the bulk coal 
in area S gradually return to the normal velocity. As 
the stuck side lags behind the deflected side by an 
             
Fig. 12.  The curves of acceleration in the Z-direction; a) unilateral jamming; and b) bilateral breaking

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509 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
Fig. 15.  The three-body abrasive wear;  
a) furrow effect; b) micro-cutting effect
It can be seen from Fig. 16 that the wear area 
of the medium plate is concentrated near the chain 
paths, which is consistent with the wear area of the 
scrapped medium plate. The unilateral jamming 
condition deepens the wear at the chain paths. In 
addition to deepening the wear at the chain paths, the 
bilateral jamming condition also form new wear areas 
at the centre and both ends of scraper. When the chain 
fractures, curved wear marks are generated on the 
medium plate due to the severe deflection of scraper.
Fig. 16.  The wear areas of medium plate;  
a) normal; b) unilateral jamming; c) bilateral jamming;  
d) chain breaking; e) the actual wear area
2.3  Results of FEA
2.3.1  Static Structural Analysis
The results of static analysis under normal load and 
stuck fault load were obtained by applying tension 
of 180 kN and 1155.9 kN to the FEA model, shown 
in Figs. 17 and 18. The maximum equivalent stress 
occurs at the inner side of the connection between the 
curved section and the straight section. The equivalent 
stress and elastic strain under normal load are less than 
the yield strength. The maximum equivalent stress 
under fault load is 1238.2 MPa, which is higher than 
the yield strength, and the maximum plastic strain is 
0.10098. The above results explain that the chain has 
a high degree of damage when the chain is stuck. To 
prevent chain breaking accident, the damaged chain 
should be replaced in time.
Fig. 17.  The results of statics analysis under normal load;  
a) equivalent stress, b) equivalent elastic strain
   Fig. 18.  The results of static analysis under stuck fault load;  
a) equivalent stress, b) equivalent elastic strain

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510 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
Based on the equipment in Fig. 7, the deformation 
results of the chain were verified. The comparison of 
elongation is shown in Table 6. It can be seen that the 
relative error between simulation and experiment does 
not exceed 4 %.
Table 6.  The comparison between experimental and simulation 
values of elongation
Number
Experimental value  
[%]
Simulation 
value [%]
Average relative 
error [%]
Normal load 0.220 0.225 0.223 0.215 3.43
Fault load 1.27 1.25 1.28 1.22 3.68
2.3.2  Fatigue Life
According to the coupling results, the load history for 
one cycle under normal conditions was constructed, 
shown in Fig. 19. The fatigue life was calculated based 
on the results of static analysis and linear cumulative 
damage theory. The theory can be expressed as:
 D= n/N
ii
m
()
1
∑
, (3)
where D is the total damage, n
i
 is the number of cycles 
under stress level, N
i
 is the life under stress level, m is 
the number of stresses.
Fig. 19.  The load history under normal condition
Based on Fig. 19, the stuck fault load was added 
to obtain the fatigue life. The fatigue life is displayed 
in Fig. 20. The lowest parts of the life under the two 
conditions are the contact position and the inner side 
of the connection, and the lowest values are 20,070 
and 383.8 cycles respectively. The life under normal 
load is 52 times that under fault load. The chain near 
the stuck position should be overhauled and replaced 
in time to prevent the chain from breaking.
Fig. 20.  The fatigue life; a) normal load, b) fault load
3  ANALYSIS OF FACTORS AFFECTING CRACK GROWTH
3.1  Plackett-Burman Test
3.1.1  Design of Test
Defects in structure or material are inevitable, of 
which cracking is the most common. According to 
load and propagation form of the cracks, they can be 
divided into three types: open type, slip type, and tear 
type, as shown in Fig. 21.
Fig. 21.  The types of the crack 
Stress intensity factor (SIF) K is defined as the 
strength of the stress field around the crack front of 
linear elastic material. The main stresses in the chain 
link are tensile and compressive stresses. The fracture 
type of chain link is Type-I, which SIF K
1
 is expressed 
as:
 K= af aW
1
 (, ), (4)

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511 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
where σ [MPa] is the normal stress, a [mm] is crack 
size, W [mm] is the size of the component in the 
direction of crack depth, f (a, W) is the shape correction 
function.
The Plackett-Burman test determines the 
significance of the factor by comparing the response 
variables at different levels of each factor [26]. Based 
on the results of FEA, a semi-elliptical crack was 
set on the inner side of the connection. Through pre-
simulation, it is found that the positive or negative 
initial angle of the crack in Fig. 22 does not affect the 
result. Therefore, the crack depth, depth-length ratio, 
initial angle and tensile load were taken as factors, 
and the maximum K
1max
 of the type-I SIF at the crack 
front was used as the response variable to carry out 
the screening test. Each factor was set to high and 
low levels, as listed in Table 7, where the virtual 
parameters are used for error estimation.
Fig. 22.  The factors of crack
Table 7.  The factors and levels of Plackett-Burman test
Parameters Low (–1) High (+1)
Crack depth L [mm] 0.2 1
Depth to length ratio B 0.2 0.8
Initial angle A [°] 0 60
Tensile load F [kN] 90 270
Virtual parameters -1 +1
3.1.2 Results of Testing
Table 8 demonstrates the plan and results of test, 
and the significance ranking of factors on K
1max
 is 
listed in Fig. 23. From the pareto chart, the tensile 
load, initial angle, and crack depth are significant on 
K
1max
 (t > 2.36462), and the depth to length ratio is 
not significant. The tensile load and crack depth are 
positive effects, and the initial angle is negative. The 
order of significance is F > A > L. Therefore, the 
significant factors were selected for the following 
tests.
Table 8.  The plan and result of the Plackett-Burman test
Number L B A F K
1max
 [MPa·mm
–1/2
]
1 1 1 –1 1 682.48
2 –1 1 1 –1 31.16
3 1 –1 1 1 299.59
4 –1 1 –1 1 309.75
5 –1 –1 1 –1 43.38
6 –1 –1 –1 1 424.65
7 1 –1 –1 –1 293.58
8 1 1 –1 –1 226.25
9 1 1 1 –1 71.88
10 –1 1 1 1 94.07
11 1 –1 1 1 299.59
12 –1 –1 –1 –1 140.78
Fig. 23.  The pareto chart
3.2  Single Factor Test
The design of the single factor test is shown in Table 9, 
and the depth to length ratio is fixed at 0.5. The K
1
 on 
the crack front is plotted as Fig. 24, where the ratio of 
the arc length from a point to the end of crack front to 
the total arc length is the relative position of the point. 
In Fig. 24, K
1
 aggrandizes with the increase of crack 
depth, and the growth rate gradually slows down. K
1
 is 
negatively correlated with the initial angle; the larger 
the initial angle, the greater the decrease in K
1
, and the 
smoother the curve of K
1
. K
1
 is positively correlated 
with the tensile load, and the increase of K
1
 on the 
crack front is almost constant; the lower the load, the 
smoother the curve. In addition, as the initial angle 
increases, the maximum position of K
1
 moves to the 
end of crack front near the load side.

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
512 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
Table 9.  The design of the single factor test
Number L [mm] A [°] F [kN]
1 0.2 to 1.0 0 180
2 0.6 0 to 60 180
3 0.6 0 90 to 270
Fig. 24.  The effects on K
1
;  
a) crack depth; b) initial angle; c) tensile load
3.3  Box-Behnken Test
3.3.1  Design of Test
Based on the results of the Plackett-Burman test, 
the Box-Behnken test was designed with the K
1max
 
as the response value. Each factor was set to high 
(+1), medium (0), and low (-1) three levels, as listed 
in Table 10. The entire design includes 12 sets of 
factorial tests and three sets of central tests for error 
estimation.
Table 10.  The factors and levels of Box-Behnken test
Factors –1 0 +1
L [mm] 0.2 0.6 1
A [°] 0 30 60
F [kN] 90 180 270
3.3.2  Results of Test
Based on the results of the test in Table 11, the 
quadratic regression polynomial between factors and 
K
1max
 was constructed by Design-Expert software as:
KL AF LA
LF AF
max 1
124 6 245 42 54 91 53 82
14 60 026 126
  
 
.... .
.. .3 34 00 5
0 00017
22
2
LA
F


.
.. (5)
Table 11.  The results of the Box-Behnken test
Number L A F K
1max
 [MPa·mm
–1/2
]
1 -1 -1 0 239.98
2 1 -1 0 509.29
3 -1 1 0 72.71
4 1 1 0 158.86
5 -1 0 -1 92.02
6 1 0 -1 196.12
7 -1 0 1 277.36
8 1 0 1 591.39
9 0 -1 -1 201.01
10 0 1 -1 62.137
11 0 -1 1 605.63
12 0 1 1 187.59
13 0 0 0 310.23
14 0 0 0 305.57
15 0 0 0 316.51
The variance analysis of the regression 
polynomial is listed in Table 12. The model is 
extremely prominent (P < 0.0001), and the lack of fit 
is not prominent (P = 0.0839 > 0.05). The coefficient 
of variation (CV) is small (5.3 %), the R Square before 
(0.998) and after (0.993) correction is close to 1, and 
the accuracy is high (46 > 4). It can be concluded 
that the constructed quadratic model has high fitting 
accuracy and can characterize the relationship 
between K
1max
 and factors. The significance of term 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
513 Response Analysis of a Scraper Conveyor under Chain Faults Based on MBD-DEM-FEM 
was acquired by F-test. The larger the F value, the 
more prominent the impact. When the significance 
level is 0.05, the significances of terms are ranked as: 
F ＞ A ＞ L ＞ AF ＞ LF ＞ LA ＞ A
2
 ＞ L
2
.
Table 12.  The variance analysis of polynomial
Source Sum of Squares F-value P-value
Model 4.21E+05 220.05 < 0.0001
L 74805.19 351.97 < 0.0001
A 1.44E+05 679.18 < 0.0001
F 1.54E+05 725.54 < 0.0001
LA 8386.9 39.46 0.0015
LF 11017.65 51.84 0.0008
AF 19483.55 91.67 0.0002
L
2
1508.79 7.1 0.0446
A
2
7592.13 35.72 0.0019
F
2
6.56 0.0309 0.8674
Lack of Fit 1002.4 11.09 0.0839
R
2
 = 0.998;   R
a
2
 = 0.993;   CV = 5.3 %;   Precision = 46
3.3.3  The Effect of Interaction
Through the three-dimensional response surface 
graph, the relationship between the interaction and the 
response value can be understood intuitively. When 
a factor is at 0 level, the variation of K
1max
 with the 
interaction is shown in Fig. 25. It can be seen that the 
crack depth and tensile load are positively related to 
the rate of change of K
1max
 with other factors, while 
the initial angle has a negative effect on the rate of 
change of K
1max
 with other factors.
4  CONCLUSIONS
In this paper, a fault simulation method of scraper 
conveyor based on MBD-DEM-FEM coupling was 
used. The DEM-MBD-FEM models were established 
and verified by experiments and theory, the response 
data of the chain and bulk coal under chain stuck and 
chain-breaking faults were obtained, and some results 
were verified. For the fracture failure, the single factor 
test and response surface test were used to investigate 
the single and interactive effects of factors on the SIF.
1. With the force and stacking angle as response 
values, a rotary transport testing machine was 
designed to modify the contact parameters of 
coal. The DEM-MBD coupling model was 
verified, and the relative error between tension 
difference and resistance is less than 8 %. The 
static structure model of the chain was verified 
by the chain tensile experiment, and the relative 
error is less than 5 %.
2. In chain jamming and breaking faults, the 
deflection of scraper causes the uneven stress 
on chains. The tension of the tensioned chain 
increases rapidly, resulting in the torsion and 
vibration of chains. The tension, velocity, and 
Fig. 25.  Response surface of interaction to K
1max
;  
a) DA; b) DF; c) AF

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)10, 501-515
514 Wang, Z. – Li, B. – Liang, C. – Wang, X. – Li, J.
vibration of the loose chain decrease. The fault 
load leads to the plastic deformation of chain 
link and reduces its fatigue life. The wear of the 
medium plate is concentrated on the chain paths, 
which is consistent with the actual situation. In 
addition, the chain faults cause new wear on the 
centre and both sides of the medium plate surface.
3. The tensile load, initial angle and crack depth 
are significant on K
1
. Through response surface 
analysis, both the crack depth and tensile load are 
positively correlated with K
1
, and the initial angle 
is negatively correlated with K
1
. The initial angle 
has a negative effect on the change rate of K
1max
 
with other factors, while the crack depth and 
tensile load positively affect it.
5  ACKNOWLEDGEMENTS
This project was supported by National Natural 
Science Foundation of China (Grant Nos. 51875386 
and 51804207) and the Fund for Shanxi “1331” 
Project.
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