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2nd Reading
October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623
1850013
International Journal of Modeling, Simulation,
and Scientific Computing
Vol. 9, No. 2 (2018) 1850013 (17 pages)
c World Scientific Publishing Company
DOI: 10.1142/S1793962318500137
Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com
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The structural optimization of roadheader conical picks
based on fatigue life
Zhenguo Lu, Lirong Wan∗ , Qingliang Zeng, Xin Zhang
and Kuidong Gao
College of Mechanical and Electronic Engineering
Shandong University of Science and Technology
266590 Qingdao, Shandong, P. R. China
∗[email protected]
Received 16 March 2017
Accepted 28 September 2017
Published 27 October 2017
Conical picks are the key cutting components used on roadheaders, and they are replaced
frequently because of the bad working conditions. Picks did not meet the fatigue life when
they were damaged by abrasion, so the pick fatigue life and strength are excessive. In the
paper, in order to reduce the abrasion and save the materials, structure optimization was
carried out. For static analysis and fatigue life prediction, the simulation program was
proposed based on mathematical models to obtain the cutting resistance. Furthermore,
the finite element models for static analysis and fatigue life analysis were proposed.
The results indicated that fatigue life damage and strength failure of the cutting pick
would never happen. Subsequently, the initial optimization model and the finite element
model of picks were developed. According to the optimized results, a new type of pick
was developed based on the working and installing conditions of the traditional pick.
Finally, the previous analysis methods used for traditional methods were carried out
again for the new type picks. The results show that new type of pick can satisfy the
strength and fatigue life requirements.
Keywords: Structure optimization; static analysis; fatigue life prediction; the new type
of pick.
1. Introduction
Picks have been widely used, e.g., in roadheader, coal mining machine and continuous mining machine. As the store conditions of coal/rock are complex, picks are
subject to random load and wear, loss, tipping, crack, alloy head fall-off, which often
occur in the process of coal/rock cutting. This situation would affect the working
stability and reliability of roadheader. Therefore, it is necessary to improve the pick
structure that can reduce occurrence of the pick damage and save materials.
∗ Corresponding
author.
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Z. Lu et al.
In the past decades, many scholars have done a lot of theoretical and laboratorial researches on the cutting force and the technique methods in the progress of
coal/rock cutting. Evans1–5 was the first to put forward the pick cutting theory.
Evans pointed out that the main characteristics influencing the cutting process are
tensile and compressive strengths, and these basic criteria have been widely used
in guiding the design of roadheader picks and coal mining machines. Roxborough6
verified the Evans theory through experimental method and concluded that experimental and theoretical data have a strong correlation. Goktan7 corrected the Evans’
cutting theory and applied to point attack tools, the theory that he proposed is
closer to experimental data and has better practical value. Roxborough and Liu8
also put forward point attack tool-modified cutting theory based on the Evans’
cutting theory, and the average peak forces they got through the modified cutting
theory were consistent with experiments. Nishimatsu9 found that shear failure is
the main damage form of the coal with high tensile strength, and the equations
of cutting force were discussed. Bilgin10 carried out 22 groups of experiments with
different rock properties, and concluded that the major factors affecting the pick
cutting performance are uniaxial tensile strength, uniaxial compressive strength,
dynamic and static elasticity modulus. Liu11 measured cutting force by experimental method and investigated the relationship between the cutting parameters and
the geometry of pick. Li12,13 considered the load of the pick as stationary random
process, and established random load model of the pick in simple structure coal
seam and complex coal seam by Rayleigh distribution and χ2 distribution, and
established the mathematical model of cutting head load based on the force of a
single pick in hard rock condition. Sun14 presented quantitative analysis methods
for the cutting force interaction between the picks. Hurt15 measured service life and
cutting efficiency of the pick under controlled experimental conditions. Parameters
investigated included pick type and quality, depth and speed of cutting and the
cobalt content of the tungsten carbide pick tips. Hkimoglu16 described the underground and laboratory trails with radial type picks and examined the optimal pick
position with respect to the radial line. Chen17 designed and fabricated Fe-based
alloy coating with high toughness and high wear resistance on the positon of heavy
wear by suing plasma jet surface metallurgy. Huang18 simulated the rock cutting
progress in deep mining condition used LS-DYNA software, and compared the
simulation results with the theoretical and experimental results. Su19 attempted
to model rock cutting tests and the mean peak cutting force was obtained and
discussed. He pointed out that there is a strong correlation between simulation,
theoretical and experimental results. Dai20 proposed a new type cutter and established the DEM model for excavation progress. Menezes21 used the LS-DYNA to
predict the fragmentation process during rock cutting and obtained a valuable result
that the chip morphology as significantly influenced by cutting depths and velocities. Jaime22 developed an FEM procedure that was able to obtain the cutting
forces and fragments. In his research, an element erosion critical was applied where
the elements were removed when the element energy equalled fracture energy.
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The structural optimization of roadheader conical picks based on fatigue life
Fig. 1.
Topology optimization process of the pick.
Although until now considerable cutting theories and experimental studies have
been done by researchers, and all these researches have improved our understanding
of rock cutting, however, fatigue life analysis and structure optimization of the
pick have never been mentioned. In other fields, fatigue life analysis and structure
optimization are important research contents. Holmberg23 researched the structure
strength under the variable load, proposed a topology optimization method that
was constrained by the structure fatigue life. Domazet24 took roller as the research
object and developed the fatigue life optimization program. Shim25 finished the
optimal design of the pulley based on the response surface method.
In this paper, fatigue life prediction and topology optimization of the pick were
carried out. The prediction of fatigue life can evaluate the production quality of
the pick effectively, and the structure optimization can reduce materials in the
premise of the pick reaching the strength requirement. The cutting pick optimization method (Fig. 1) is established in this paper. In the considered method, the
cutting head dynamic model was established for simulating the cutting force of the
pick in each position, a load spectrum and maximum cutting force can be got from
this simulation for fatigue life analysis and static analysis, respectively. On this
basis, the topological optimization of the pick was carried out.
2. Prediction of the Cutting Forces and Results Discussion
The pick’s performance and service life are affected by the situation of cutting forces
directly, and this is the main fundamental index to evaluate pick performances.
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However, the forces on cutting head and picks have no unified and accepted calculation method due to nonlinear contact, inhomogeneous coal and rock material.
The former Soviet Union, Germany, France and other countries have their own
calculation theory and methods.
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2.1. Mathematical modeling
A number of researchers have formulated a mathematical model for coal and rock
cutting progress. The pioneering work on pure coal cutting mechanics was performed by a Former Soviet Union scholar. The theory has been widely used to
calculate the average loads of cutting picks by the following empirical equation26 :

1
0.35bp + 0.3


htkz kφ ky kc kot
,
Z0 = 10A
0.5 B

b
+
h
cos
β

p


Y0 = Yn Z0 ,
(1)



C1
h



X0 = Z0 C + h + C3 t ,
2
where X0 , Y0 , and Z0 are the three-axis force, side resistance, tractive resistance,
cutting resistance; A is average value of cutting intensity; bp is the working part
width of pick shaped cutter equivalent to the cutting flat pick; h is the average
value of cutting thickness; B is the brittleness degree of coal; t is the average line
spacing of pick arrangement; kz is the coal bared coefficient; kφ is the front cutter
face shape influence coefficient of pick-shaped cutter equivalent to the cutting flat
pick; ky is the influence factor of cutting angle to energy consumption of cutting
ratio; kc is the influence factor of the cutting method; kot is the coal pressure coefficient; β is the installation angle of the pick axial direction and feed direction;
Yn is a ratio of cutting resistance and tractive resistance; C1 , C2 , C3 are influence
coefficients of pick arrangement on the cutting head. In this paper, the meaning
of coefficients is emblematic of influence extent generated by the relevant parameters in the equations. The values of the coefficients are determined by empirical
data.
The pick suffered the random load because the coal/rock as the anisotropic
material and heterogeneous. The cutting resistance and tractive resistance are usually according with the Gamma distribution, and the modified Rayleigh distribution
can fit the Gamma distribution better. Rayleigh random processes can be determined by two normal random processes which have same independent variance.
The random coefficient can be determined by the following equation:
(2)
k = ξ12 (t) + ξ22 (t) − 1.25,
where ξ1 (t), ξ2 (t) are two independent and standard normal random processes with
the mean value as 0, the variance value as 1.
According to superposition principle, random load of cutting resistance can be
determined by a combination of the average load and random components as the
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The structural optimization of roadheader conical picks based on fatigue life
following equations:


Z[n] = σz kz [n] + Z0 ,

Y [n] = σy ky [n] + Y0 ,


X[n] = σ k [n] + X ,
x x
(3)
0
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where n are the simulation points of cutting resistances n = 1, 2, 3, . . . , X[n], Y [n],
Z[n] random cutting resistance sequence; σx , σy , σz are standard deviations of random cut resistance under Rayleigh distribution; kx [n], ky [n], kz [n] are random
sequences of pick cutting resistance coefficient.
2.2. Numerical simulations of the cutting force
The main purpose of the cutting force simulation was to determine the parameters
for static analysis and fatigue life analysis. In this paper, MATLAB program was
written to simulate the random cutting force of the pick. There are 51 cutting picks
(Fig. 2) distributed on the cutting head (Fig. 3) forming a helical line, picks in
different installing positions have different work conditions and suffered different
cutting forces.
In the MATLAB simulation, the rotational speed and transverse speed of the
cutting head took 50 r/min and 2 m/min, the cutting head rotated 10 circles, the
resistance of the coal/rock took 30 MPa. The histories of the tool forces were
recorded at frequent intervals such as 18,000 data per minute. According to the
histories of the force, the random forces of pick were estimated. The variations of
cutting force are depicted in Fig. 4, we took pick 23 as an example. It is apparent
Fig. 2.
Pick shape and size.
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Fig. 3.
Picks distribution on the cutting head.
(a)
Fig. 4.
force.
(b)
The cutting force history of the pick 23: (a) Random cutting force, and (b) theory cutting
that the theory cutting force follows the sine, and random cutting force has no
regularity.
Since the picks in different positions suffered different three-axis force, it is
necessary to find out the biggest force for static analysis. The three-axis force of
each pick has been compared. Pick 1 bore the smallest cutting force and pick 51
bore the biggest cutting force, along with the serial number increase in and cutting
force, so the three-axis cutting force of pick 51 will be applied for static analysis.
Table 1 shows the theoretical forces and random forces of pick 1, pick 7 and pick 51.
It indicated that the minimum value of the side cutting forces is negative because in
the MATLAB program, the positive direction for cutting force must be specified.
In the progress of calculation, if the cutting forces are in opposite direction, the
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The structural optimization of roadheader conical picks based on fatigue life
Table 1.
Cutting pick 1
Cutting pick 7
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Cutting pick 51
Results of the three-axis force.
Theory force (KN)
Random force (KN)
Z
X
Z
Y
X
Y
Max
Min
Mean
10.197
0
8.134
7.564
0
5.137
3.256
0
1.766
24.784
0
8.180
15.179
0
5.431
6.387
−0.403
1.880
Max
Min
Mean
Max
Min
Mean
12.864
0
9.015
21.868
0
13.964
8.562
0
6.012
13.889
0
9.584
4.012
0
1.875
5.979
0
3.087
25.497
0
9.164
45.301
0
14.035
15.134
0
6.132
25.011
0
9.621
7.178
−1.397
1.895
11.032
−0.009
3.112
Z = Cutting resistance; Y = Tractive resistance; X = Side resistance; Max =
Maximum value; Min = Minimum value; Mean = Mean value.
value of the cutting forces should be shown as a negative number. The theoretical
model of the random cutting force is complex, the negative value indicated that the
cutting pick bore the side cutting forces both in the positive direction and in the
negative direction.
The load spectrum also can be obtained from the MATLAB program. In consideration of each pick bearing the different forces, pick 51 random spectrum was
adopted. In the software for fatigue analysis, the three-axis force coefficient and
maximum force should be input, so the random load spectrum had to transform
to three-axis force coefficient (Fig. 5), the reason why simulated rotation angle is
1800◦, not 3600◦ is because the pick taking part is cutting only in half cycle, and
the load spectrum with no cutting force had been removed. The coefficient can be
defined as follows:
C = F/Fmax ,
(4)
(a)
Fig. 5. The coefficients of three-axis force: (a) The coefficient of X, (b) the coefficient of Y , and
(c) the coefficient of Z.
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(b)
(c)
Fig. 5.
(Continued)
where C is cutting force coefficient, F is the three-axis force, Fmax is Maximum
value of the three-axis force.
3. Prediction of the Fatigue Life and Results
The pick’s strength and fatigue life requirement must be modified firstly, so it is
important to perform static analysis. This would provide the basis for topological
optimization if the fatigue life is excessive. The process of the fatigue life analysis
is shown in Fig. 6. Finite software was used for static analysis and fatigue life
prediction.
3.1. The finite element model
The pick is composed of the pick head and the pick bar. There are different materials
with these two parts, the pick head is tungsten carbide–cobalt, and the pick bar is
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The structural optimization of roadheader conical picks based on fatigue life
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Fig. 6.
Fig. 7.
Process of the fatigue life.
Numerical model of rock cutting.
42CrMo, so they must be divided with the mesh alone. The mesh size took 1.5 mm,
and tetrahedron mesh was taken. Three-axis constant force of pick 51 was exerted
on the pick head. The bottom of the pick bar was fixed, and the cylindrical surface
of the pick bar was constrained (Fig. 7).
3.2. Static analysis results and discussion
The displacement and the von Mises stress results are shown in Fig. 8. The maximum displacement of the pick occurred at the head with 0.14 mm. It was negligible
because the deformation was far less than the overall size, and had no influence on
rigidity. The maximum von Mises stress also occurs at head with 747 MPa, and it
is less than permissible stress of 950 MPa of the tungsten carbide–cobalt. For the
pick bar, the maximum von Mises stress occurred at connection between bar and
head with 249 MPa at less than permissible stress 310 MPa of the 42CrMo. As can
be seen, the strength requirement of the pick can be satisfied, however, the pick
head and the connection are damaged easily.
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(a)
(b)
(c)
(d)
Fig. 8. Static analysis results of the pick: (a) Displacement of the pick, (b) Von Mises stress of
the pick, (c) Von Mises stress of the pick bar, and (d) Von Mises stress of the pick bar.
3.3. Fatigue life analysis and discussion
The finite model built for static analysis was also applicable to fatigue life analysis,
but some parameters were replaced. In the cutting progress, the cutting pick only
bore the cutting force of the load spectrum. Therefore, load spectrum is the only
factor that lead to the fatigue failure of cutting pick, and it can be seen as fatigue
load. In Fig. 7, the three-axis forces loaded on the cutting pick were the biggest cutting force that the pick 51 bore, and they should be replaced by the load spectrum
as shown in Fig. 5. The 50% survival material S–N curve was took. The material
properties are as same as before. Nominal stress method was taken because the pick
had no plastic deformation in the cutting progress, and rain flow counting method
was set to deal with the stress history data. In order to reduce the computational
burden of the computer, one cyclic load contains 12 load spectra.
The fatigue life results are shown in Fig. 9, both the pick head and the connection
between the bar and the head have the tendency of fatigue failure, besides, there is
no fatigue damage tendency. The minimum fatigue life of the connection between
the bar and the head is 1.00e19 cyclic loads, less than 1.25e19 cyclic loads of the
pick head, reflecting that the head has the risk of being detached from the pick.
That is agreed with static analysis results. But the pick fatigue failure has not been
considered in theory because 1.00e19 cyclic load is very high. The static analysis
and fatigue life analysis results indicated that both the strength and the life of
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The structural optimization of roadheader conical picks based on fatigue life
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(a)
(b)
Fig. 9. Results of the fatigue life analysis: (a) Fatigue life cloud of the pick, and (b) fatigue life
cloud of the pick bar.
pick designed are excessive. The topological optimization will be carried out for
material saving and reduce wear under the premise of satisfying strength and life
requirement.
4. Topological Optimization Based on Fatigue Life
4.1. Topological optimization
The volume of the pick bar is far greater than the pick head, the paper took the
pick bar as the main optimized objective. In order to better optimize, the initial
structure of the pick as shown in Fig. 10 was chosen. This structure is an improved
version of the pick as shown in Fig. 7. The pick head was retained and used for
Fig. 10.
The initial structure of topology optimization model.
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Fig. 11.
The volume iterative curve of the pick.
applying load. It did not involve optimization. The load spectrum applied on the
pick head was same with the fatigue life analysis. Assuming that picks work 24 h
a day with the speed of 50 r/min, in these working conditions, its fatigue life must
be met in 30 days.27 Volume minimization was taken as the optimization objective
based on variable density method.
Results for volume decreases are shown in Fig. 11. As can be seen, the convergence occurs many times in the iterative process, e.g., the 13th, 14th, 23th, 26th,
27th, 42th, 43th results satisfied the convergence criterion. The first five of them
have smaller volume fraction fluctuation with the average value of 45.18%, when the
42th, 43rd steps are reached, the average value is 33.1%. The 43rd step result was
taken as the optimum result. The initial volume of pick is 2.69191e5 mm3 , after the
topological optimization the volume is 1.01149e5 mm3 . Based on this, the volume
decreased 64.42%.
Specific iterative processes are shown in Fig. 12. Figure 12(d) presents the final
optimization results, compared with the traditional pick structure as shown in
Fig. 7. There are some similarities, but also differences. All of the pick heads have
the taper and the taper measures are very similar. After optimization, the bottom
half of the pick disappeared, instead of a cavity. The pick bar also emerged as the
symmetric groove because of the influence in the force direction.
4.2. Structure improvement
Optimized model is shown in Fig. 13(a), with no pick head and fixed structure,
and cannot be applied directly. Based on the pick actual working conditions and
characteristics, the improvement is carried out according to the installation method
of traditional pick. As shown in Fig. 13(b), the pick with new structure is composed
of three sections which are pick head, pick head seat and pick bar. The volume of the
new type of pick is 2.1455e5 mm3 , compared with the traditional pick, its volume
decreases 23.83%.
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The structural optimization of roadheader conical picks based on fatigue life
(a)
(b)
(c)
(d)
Fig. 12. The results of topological optimization: (a) The 10th optimization result, (b) the 20th
optimization result, (c) the 30th optimization result, and (d) the 43rd optimization result.
(a)
(b)
Fig. 13. The improvement of the pick: (a) The optimized result model of the pick, and (b) the
new structure of the pick.
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Fig. 14.
The rotation of the new type of pick.
To avoid the wear at the same position, the traditional pick rotation relies on
frictional contact, but because the rotational torques are small, the pick is difficult
to rotate. This caused the pick one side wear and led to the pick failure. With the
new type of picks, the groove can increase the rotational torques, reduce the wear
and improve the service life is shown in Fig. 14.
4.3. Static analysis results and discussion of the new pick
The new pick must also satisfy the strength and fatigue life requirement, so the
static analysis and fatigue life analysis are carried out. The static analysis method
and parameters of the new pick were the same as in Sec. 3.1, and the analysis results
shown in Fig. 15. The biggest displacement of the pick still occurred at pick head
with 0.0612 mm. Compared with the 0.140 mm of the traditional pick, the strength
of pick obviously is reinforced. The biggest von Mises stress occurred at the pick
head with 883 MPa. Compared with 747 MPa of the traditional pick, the maximum
stress increased, but still less than the pick head material allowable stress with
950 MPa, so the pick head satisfied strength requirement. The biggest von Mises
stress of the pick head seat occurred at the connection between pick head and the
pick head seat with 301 MPa, also bigger than traditional connection stress with
(a)
(b)
Fig. 15. Static analysis of the new type pick: (a) The displacement of the pick, and (b) the von
Mises stress of the pick.
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The structural optimization of roadheader conical picks based on fatigue life
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(a)
(b)
Fig. 16. Static analysis of the new type pick: (a) The fatigue life analysis result of the pick, and
(b) the fatigue life analysis result of the pick bar.
249 MPa, less than the allowable stress 310 MPa of the material 42CrMo. The pick
bar and pick head seat bore the small stress relative to the connection position. On
the whole, the new pick satisfies application requirements.
4.4. Fatigue life analysis results and discussion of the pick
By the previous approach, fatigue life analysis of the new pick was finished. The
results shown in Fig. 16. All of the pick head, pick bar and pick head seat have the
tendency of fatigue life, the minimum fatigue life occurred at the connection with
1.92e4 cyclic loads. The working days can be calculated as the following equations:
n ∗ n1 ∗ n2
,
(5)
D=
24 ∗ 60 ∗ r
where n is the number of cyclic loads, n1 is the number of load spectrum in one
cyclic load, n2 is the number of cutting head rotate circle, r is the speed of cutting
head. As mentioned above, n = 1.92e4, n1 = 12, n2 = 10, r = 50 r/min, D can be
calculated as 32 days, meet the working requirement 30 days. The static analysis
and fatigue analysis of the new pick have shown that topological optimization and
structure results are feasible.
5. Conclusions
The picks are the important cutting tools used on excavators, especially used on
roadheaders, replaced frequently due to bad damage, so it is important to analyze
their fatigue life and topological optimization in order to save material and estimate on time. This paper presented the simulation process based on finite element
method.
The cutting force of the pick was simulated based on the theory model. Results
show that the pick 51 which was installed at the front of the head that bore the
maximum three-axis resistance. Additionally, the static analysis of the pick 51 shows
that all of the picks’ strength requirements were satisfied. The fatigue life analysis
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of the traditional pick showed that fatigue damage is impossible and concluded
that material waste always exist. Finally, a new pick initial structure for topological
optimization is proposed. The optimized result of the cutting pick cannot be applied
directly, so with the improved measures the new type of pick was proposed. The new
type of pick can save 23.83% materials compared with the traditional pick and can
meet the strength and fatigue life requirement with the pick working for 32 days.
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Acknowledgments
The study is financially supported by National Natural Science Foundation of China
(Grant No. 51674155), China Postdoctoral Science Foundation Funded Project
(Project No. 2016M592214) and Natural Science Foundation of Shandong Province
(Grant No. ZR2014EEM021).
References
1. Evans I., A theory of the basic mechanics of coal ploughing, Mining Research 2:761–
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