Applied Mechanics and Materials
ISSN: 1662-7482, Vol. 389, pp 1058-1061
doi:10.4028/www.scientific.net/AMM.389.1058
© 2013 Trans Tech Publications, Switzerland
Online: 2013-08-30
Rock Floor Pressure Analysis of Hydraulic Support
Wang Zhi*,1,2,a, Ni Heping1,b
1
Zhengzhou Coal Mining Machinery(Group) Co., Ltd., Zhengzhou 450013, China
2
School of Mechanics & Engineering Science, Zhengzhou University, Zhengzhou 450001, China
a
[email protected], [email protected]
Keywords: Hydraulic support, Rock floor, Elastic foundation beam, Floor pressure.
Abstract. According to the plastic floor assumptions, the floor pressure distribution law was obtained
based on plane force analysis of hydraulic support. In order to compare the floor pressure on the
elastic floor and plastic floor, Elastic foundation beam theory was introduced to the calculation of the
floor pressure. The results show that the pressure distribution is changed with the changing of the
subgrade coefficient. The pressure is trapezoidal distributed when the floor is relatively soft and the
plastic floor assumptions is reasonable. In a relatively hard rock floor, the maximum pressure appear
near the column nest which is very different from the calculation results based on the plastic base
plate assumptions. It is suggested that the soft and the hard rock floor should be treated differently
during the design and selection of hydraulic support. .
Introduction
With the continuous improvement of the requirements of the coal mining mechanization, the coal
mining equipment have been developed again. It is important to study the interaction between the
hydraulic support and surrounding rock. There are more references about coupling between the top
beam and surrounding rock[1-3]. The coupling calculation results of roof subsidence was obtained.
But the reference about the coupling calculation of the floor and the pedestal is rarely mentioned[7-8].
The role of the floor to the hydraulic support is an important aspect of the relationship between the
hydraulic support and the surrounding rock and should be taken seriously. Under normal
circumstances, the floor is assumed to plastic foundation and the pedestal is assumed to rigid. Elastic
floor assumption is also introduced to more precise calculation[9]. It is essential to simulate the
coupling between the surrounding rock and the pedestal reasonably for the mechanical properties of
the pedestal analysis.
Plane force analysis of the hydraulic support
As shown in Fig.1, the plane force analysis of the two-column hydraulic support can be calculated by
the knowledge of structural mechanics[10].Take the top beam and Gob Shield as separator, the
equilibrium equation of moment of point O1 can be described as:
r1P + ( H 0 + bc tan ϕ ) fQ − ( x + bc )Q = 0
(1)
Force balance equation in the horizontal direction and the vertical direction can be described
respectively as:
Qf + F1 sin α1 + F2 sin α 2 − P sin β = 0
(2)
− Q + F1 cos α1 + F2 cos α 2 + P cos β = 0
(3)
Then take the top beam as separator, the equilibrium equation of moment of point O can be
described as:
tPE + QfH 0 + r2 P − xQ = 0
(4)
The simultaneous solution can be obtained from the above formula (1) to (4):
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Applied Mechanics and Materials Vol. 389
1059
r P + PE t
P(r1 − r2 ) − PE t
；x= 2
+ fH 0 ;
bc(1 − f tan ϕ )
Q
Q( f + tan α 2 ) − P (sin β + cos β tan α 2 )
Q − P cos β − F1cos α1
F1 =
; F2 =
cos α1 tan α 2 − sin α1
cos α 2
Where f is the friction coefficient between the top beam and roof, and P is the total working
resistance of column, PE is the total force of the balance jack.
Q=
Fig.1 Plane force diagrams of Hydraulic support
A hydraulic support produced by Zhengzhou Coal Mining Machinery Group Co., Ltd. was taken
for plane force analysis. The plane force analysis calculation results of different height and different
balance jack force were listed in Table 1.
Table 1 Plane force analysis results of hydraulic support
H
m
（）
6
7
P
(kN)
18000
18000
18000
18000
18000
18000
PE
(kN)
-1561
2771
0
-1561
2771
0
α1
α2
β
()
48.82
48.82
48.82
29.53
29.53
29.53
()
33.52
33.52
33.52
14.04
14.04
14.04
()
11.28
11.28
11.28
9.44
9.44
9.44
°
°
°
Q
(kN)
17924.38
17379.72
17728.12
18744.59
17811.90
18408.51
x
（mm）
1422.19
1607.83
1487.77
1369.51
1576.44
1441.66
F1
(kN)
-6431.79
-4775.84
-5835.08
-10593.81
-8730.69
-9922.45
F2
(kN)
5405.92
3444.85
4699.27
10520.38
7887.99
9571.82
According to the plastic foundation assumption and the rigid pedestal to and the pedestal is
assumed to rigid. The floor pressure is approximate linear distribution( as shown in Fig.2). The
position of the resultant force of the pedestal can be calculated as follows:
xD = xQ − H ⋅ f
When
x2
2x
≤ xD + L17 ≤ 2 , the floor pressure can be calculated as:
2
3

Q  6 x1
2Q
Pb1 =
− 2 Pb 2 =
− Pb1

x2 Bw  x2
x2 Bw
;
Fig. 2 The simplification of base pressure
(5)
1060
Materials Technologies, Automation Systems and Information Technologies
in Industry
The pressure calculation results are listed in Table 2.
Table2 Pressure results of rock floor
H
（m）
PE
xD
Pb1
Pb2
(kN)
(mm)
(MPa)
(MPa)
-1561
1874.874
4.144921
2.1736
6
2771
2060.514
4.884957
1.241566
0
1940.454
4.411591
1.837746
-1561
1622.194
3.063305
3.544348
7
2771
1829.124
3.900186
2.378685
0
1694.344
3.364874
3.124307
It can be seen that the floor pressure were 1.24MPa-4.88MPa and changed with the push-pull force
alter of balanced jack. The maximum pressure occur when the balanced jack force was pushing force.
The floor pressure decreases as the height increases. The pedestal will plunge into the floor when the
floor pressure is greater than the yield stress.
Pedestal force analysis based on Elastic foundation theory
BEAM54 is a uniaxial element with tension, compression, and bending capabilities and a 2-D Elastic
Tapered Unsymmetric Beam of ANSYS software. It can be used to simulate the general stress
analysis of the beam and analyze the elastic foundation beam after entering the foundation coefficient.
Local deformation theory (E.Winkler model) was adopted and the foundation settlement is
proportional to the pressure on and inversely proportional to the foundation coefficient. For the
Winkle elastic foundation beam:
d 4w
EI 4 + kbw = bq
dx
Where E is elastic modulus of the pedestal, I is section moment of inertia of the pedestal, q is floor
pressure, b is width of the pedestal, w is settlement.
Fig. 3 is the floor pressure distribution law under different subgrade coefficients. It can be seen that
floor with different subgrade coefficients may induced different pressure distribution. The pressure is
trapezoidal distributed when the floor is relatively soft and the plastic floor assumptions is reasonable.
In a relatively hard rock floor, the maximum pressure appear near the column nest which is very
different from the calculation results based on the plastic base plate assumptions. It is suggested that
the soft and the hard rock floor should be treated differently during the design and selection of
hydraulic support.
Fig.3 The floor pressure under different subgrade coefficients
Applied Mechanics and Materials Vol. 389
1061
Conclusion
The floor pressure distribution is changed with the changing of the subgrade coefficient. The pressure
is trapezoidal distributed when the floor is relatively soft and the plastic floor assumptions is
reasonable. In a relatively hard rock floor, the maximum pressure appear near the column nest which
is very different from the calculation results based on the plastic base plate assumptions. It is
suggested that the soft and the hard rock floor should be treated differently during the design and
selection of hydraulic support.
Corresponding Author
Wang Zhi, Email: [email protected], Tel: +86-0371-67783367.
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