Open Journal of Applied Sciences, 2013, 3, 56-60
doi:10.4236/ojapps.2013.32B011 Published Online June 2013 (
Stress-strain State and Vibration Frequencies of Blades of
the Main Mine Fan Impeller
N. V. Panova, E. A. Spiridonov
N.A. Chinakal Institute of Mining, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Novosibirsk state technical University
Received 2013
The paper discusses geometrical characteristics and strength parameters of fan blades equipped with replaceable active
part it end ended to improve the fan adjustability owing to replacement or removal of the active part, which allows the
fan to maintain a wide range of ventilation modes.
Keywords: Stress-strain State; Vibration Frequencies; Mine Fan Impeller
1. Introduction
The main ways to control air purity in a mine are dilution
and carryover of mining-induced toxic contaminants us-
ing main mine fans.
Main mine fans in existence are uneconomic and ac-
cident-sensitive; they take too much space to be located
on land surface and, among other shortcomings, are
poor-adaptable to mine ventilation mode changes when-
ever required.
Deficient adjustability results in low technical and
economic performance of a ventilation network unit or a
main mine fan for most of its running time; or else a
main mine fan, after several year of operation, becomes
incapable to service this particular ventilation network
and, consequently, modification of the ventilation net-
work or construction of new mine fans is required.
To study behavior of ventilation network parameters in
terms of actual mines in Russia, Ukraine and Kazakhstan
(e.g., Kuznetsk and Donetsk Coal Basins, and others), the
representative statistics over a period of 9 to 10 years
have been collected and processed. The basic index was
chosen the rate of change of the studied parameters, de-
termined as the ratio of the later time-interval value of a
parameter to its former time-interval value, the time
lengths being varied.
It was found that the rates of change of ventilation pa-
rameters in mines are not constant in time, are different
in different basins and vary in a wide range; at that, the
average capacities are VQ = 4.5 - 15.4% per year for a fan
and VA= -4.0 - 5.5% for an effective opening of a venti-
lation network. Accordingly, if the required fan capacity
has been increased by 0.9% per three months (Q
1.009), or by 3.8% per year, then the fan reserve (10%)
would be worked out less than in three years, and insuf-
ficient performance of the fan would retard development
of mining operations.
The analysis of different approaches to enhancement
of adaptability of main mine fans [1] showed the possi-
bility to provide the desired ranges for the fan capacity
(ten times and higher) and pressure (five times and
higher) by using modified axial fans with possible re-
placement or removal of a number of blades from the fan
The research into aerodynamics of axial fans, con-
ducted at N.A. Chinakal Institute of Mining, Siberian
Branch of the Russian Academy of Sciences [2], showed
that it is only possible to enlarge the area of reasonably
possible modes of fans in the coordinates Q—P by de-
signing of axial fans with replaceable, double, sheet
To reach the objectives, fans, series VO, were furnished
with replaceable (to be adaptable to different ventilations
network standards) and rotable-in-run blades, which al-
lowed continous control over their operation (see Figure
1: within b to b'; from а to а'; from с to с'). In this case,
the fan adjustment to changes in airing parameters is ac-
complished by replacement or removal of a number of
blades within the modes a—a`, b—b` or c—c`, upon
variation in air resistance of the ventilation network,
within R1, R2 and R3, respectively (refer to Figure 1).
The double, sheet blades designed for axial fans in-
clude a rotary base with a root fixing, two special-ge-
ometry blades and a connecting strap to maintain the
required stiffness of the blades. The double, sheet blades
as against profiled blades are advantageous for (1) total
elimination of bending and twisting moments of cen-
trifugal forces relative to the fan rotation axis; and (2)
Copyright © 2013 SciRes. OJAppS
greatly simplified manufacturing technology.
Figures 2 and 3 show the calculation schemes for cen-
trifugal forces and moments that influence the double,
sheet blades of axial fans.
The double, sheet blades are designed [1] for pre-set
parameters of a fan (pressure, capacity, etc.), additionally
considering the requirement of zero moment of centrifu-
gal forces on the blades [2], which is achieved by locat-
ing center of masses О1 and О2 of the blades so that the
center of masses of the entire blade couple is on the axis
Z: moment Mz is zero (see Figure 2).
Figure 1. Aerodynamic characteristics of fan, model VO-
21K, at rotation frequency 1000 (1500) rpm, with blades in
amount of Zimp= 8 and Zimp = 4, mounted on the fan impel-
ler according to aerodynamic schemes AM-17A (1 and 1',
high-pressure) and AM-19A (2 and 2', high-capacity), at
pitch θ = 15—50° and air resistances R1, R2 and R3.
Figure 2. Calculation scheme for moments on fan blades:
Мx, My, Mz—moments of forces affecting the blades relative
to the axes X, OY, OZ, respectively; ω—impeller rotation
frequency; О1 and О2—centers of masses of the blades;
θ—pitch of the blades.
Figure 3. Calculation scheme of forces affecting fan blades.
An illustration of the forces affecting a blade is given
in Figure 3, in the coordinates ОХ, ОУ, ОZ, where it is
assumed that the resultant of the forces is at the point М
[2]. It is taken that mine fans rotate counterclockwise if
watched from the direction of indraft, and the OX-way
projection dR is composed of the blade draft force dRа
and the blade rotational resistance dRu.
The components dRа and dRu of the force dR are
mainly of aerodynamic nature. The OM-way projection
dP of the force dR is conditioned by inertia (centrifugal)
forces influencing the blades.
The aerodynamic forces dRu and dRа generate the
twisting and bending moments, respectively, while the
centrifugal force dP creates tensile effect and twisting
moment on the blades.
Out of the forces dRu, dRа and dP, the centrifugal force
dP produces the highest load on the holder group of
blades, power of impeller and rotation mechanism of
The centrifugal component of mass of blades relative
to rotation axis of rotor shaft is calculated from the for-
mula [3]:
where: m—is mass of the unit of blades; r—distance
from center-of-gravity of the unit of blades to the rotation
—angular rotation frequency of impeller.
The total aerodynamic force is:
 
 
 
the blading section
area; D—impeller diameter measured between the tips of
the blades; P—maximal static pressure of fan (Pa).
To make the replacement of impeller blades simpler,
for instance, when the blades with other aerodynamic
characteristics are required to increase the main mine fan
pressure or capacity, the design of the unit of blades has
been modified: the base and replaceable part of the unit
of blades are fixed using a bolted-type connection (Fig-
ure 4).
The internal thread diameter of the bolted-type con-
Copyright © 2013 SciRes. OJAppS
nection is selected as follows:
where: N—external tension force on this particular
threaded joint; p
—admissible tension stress.
The area pressure exerted by circumference-unequal
flow on the surface of a blade, q(t), can be presented as
q(t) = qcons+
nkzt +
where: q(t)—time-variant load per unit length of blade;
qcons—constant load on blade;
qkz—amplitude of the time-variant load per unit length of
blade at frequency f = knz; 2
nt—angular coordinate of
blade rotation;
кz—phase angle.
Reliability of blades is assured through (1) their suffi-
cient structural strength and (2) absence of resonance
phenomena as a response to the nonstationary exposure,
e.g., rotor speed, ventilation network vibrations, etc. In
the first case it is required to sustain permissible stress in
a blade, considering strength limits and load factors of
the materials used; the second target is achieved owing to
safe tuning-out of the blade vibration frequencies under
the excitation forces and, thus, elimination of hazardous
dynamic stress under probable resonance effect.
The main way to solving the engineering tasks above
is the optimized selection of design variables of blades so
that to ensure required strength and frequency. Along
with classical approaches, such as material selection and
change of cross-sections in strained members of blades,
in case of the double, sheet blades, there is an additional
option of stress and frequency control by means of nu-
merical modeling of the parameters of connecting straps,
stiffening plates, etc.
Figure 4. Adaptable unit of blades for fans VO: a—re-
placeable part; b—rotary base with root fixing; 1—blades;
2—connecting strap; 3—stiffening plates; 4—opening for
the bolted-type connection; 5—the strap and blade fixture
point; 6—keyseat in the root fixing.
The mentioned above design of a blade unit, but with-
out the replaceable part, was analyzed earlier, though the
influence the bolted-type connection has on the strength
and resonance of the blade unit was left beyond the
analysis. The authors of the present paper have assessed
the stress-strain state and frequencies of the adaptable
blades, and the stress-strain state of the bolted-type con-
nection between the replaceable part and the base; the
principal condition here was the equal strengths of all
members of a blade unit and the tuning-out of excitation
force at the known frequency.
The strength calculations of different structures com-
monly use the finite element method that can be suc-
cessfully accustomed to the developed electronic and
computer technologies as well as allows computation of
complex objects, including their geometry, load distribu-
tion, boundary conditions and physical properties of the
materials the analyzed devices are made of.
The analysis of stress-strain state, frequencies and vi-
brations in the case in question used the ANSYS program,
three-dimensional modeling and finite-element modeling.
The blades were divided into 3D four-unit finite elements.
The bolting modeling involved imposition of zero dis-
placements and rotations; centrifugal forces were calcu-
lated automatically, via setting of a special option. As a
result, stress-strain state diagrams were obtained for the
given design blade unit and a fan with impeller diameters
of 2100 mm, 2400 mm, 3000 mm, 3600 mm, 4300 mm
and 5000 mm and rotation frequency range from 375 rpm
to 1500 rpm.
For every dimension-type of the fans, the authors have
determined the following characteristics:
1) Efficient geometrical characteristics and amount of
stiffening plates of the rotary base;
2) Permissible thickness of the material sheet to
manufacture the blades and connecting straps;
3)O Permissible width of the connecting straps;
4) Stress-strain state and frequencies of the blade unit:
individually for the replaceable part and the base;
5) The stress-strain state and frequencies of the blade
unit as an assembly.
Table 1 below presents the data of the analysis into
the influence of the connecting strap width, given the
equal width of the blade sheets, on the stress-strain state
and frequency of the blade unit mounted on the fan
model VO-43K with impeller diameter of 4300 mm and
speed ω = 600 rpm. The width of the connecting strap
was varied as a percentage of the blade chord length in
the calculation cross-section; the following strap width-
to-chord length percentage ratios were analyzed: 52%,
68%, 73%, 84%, 94%. It has been found that the maxi-
mal stresses arise either at the keyseat of the root fixing
(6 in Figure 4), or at the fixture point of the strap—2/3
of the blade length from the base (5 in Figure 4), de-
pending on the percentage.
Copyright © 2013 SciRes. OJAppS
Copyright © 2013 SciRes. OJAppS
Table 1. Influence of width of the connecting strap on the stress-strain state in the elements of the blade.
Percentage ratio of the strap width
to the blade chord length, %
strap weight, kg
Maximal displacements
at the tips of blade, mm
Maximum stresses in the
elements of the blade, MPa
Maximum stress location
in the elements of the blade
1 2 3 4 5
94 9 6.3 475 root fixing
84 8 6.2 472 root fixing
73 7 6.2 445 root fixing
68 6.5 6.5 466 connecting strap
52 5 6.5 490 connecting strap
Table 2. Vibration frequencies of blade units of the VO model fans.
Rotor speed, tip speed of blades
Fan model
rpm Hz m/s
Free vibration frequencies, blade
unit (1; 2; 3), Hz
Factor of safety (resonance tun-
ing-out), n
1 2 3 4 5 6
VO-30K 1000 16.7 157.3 69.97; 82.53; 198.01 4.2; 4.9; 11.8
VO-36K 750 12.5 141.3 50.63; 74.54; 155.44 4.0; 5.9; 12.4
VO-43K 600 10 135.0 26.62; 89.89; 114.58 2.6; 8.9; 11.4
VO-50K 500 8.3 130.3 39.03; 79.11;123.84 4.7; 9.5; 14.9
It follows from Table 1 that when the connecting strap
is reduced in width, the weight of the blade unit gets
lower, from 5 kg to 9 kg, and the centrifugal forces and
stresses at the keyseat of the root fixing decrease. After
the certain value of the percentage ratio between the strap
width and the blade chord length in the calculation
cross-section (namely, 68%), the maximum stresses are
observed at the strap fixture point; under further diminu-
tion of the connecting strap, the maximum stresses grow
and so do the maximum displacements at the tips of the
blades. The analysis of the free vibration frequencies of
the blade unit has shown that at the percentage ratio be-
tween the strap width and the blade chord length of 94%,
the first, second and third free frequencies were 26.6 Hz,
89.5 Hz and 115 Hz; the same for the percentage ratio of
52% made up 26.3 Hz, 91.8 Hz and 111.7 Hz, respec-
tively. It is seen that the frequencies differ insignificantly,
and the required tuning-out of resonance is achieved. The
strength assessment included calculation of the factor of
safety: n = abs/appl. For the analyzed blade units of the
fans VO, the factor of safety ranges from 1.4 to 4.5.
According to Russian Federation standards for the
mine fan designing, the deviation of the blade profile (by
tips), vane ring and directing vanes off the nominal pro-
file should be no more than 0.002 of the nominal diame-
ter of fan impeller. Accordingly, allowable deviation by
tips of blades for a fan impeller with the diameter of
4300 mm is 8.6 mm, and the maximum displacements
are within the limits (refer to Table 1).
It has been said above that the main reasons for vibra-
tions in a blade unit are the free vibration frequency of
the fan rotor and the variable aerodynamic flow distur-
bance in ventilation network. The aerodynamic flow dis-
turbance is conditioned by the unstable resistance in the
network. The flow disturbance behavior has sufficiently
been studied, and the ample experimental results give
evidence that the flow disturbance range lies at the sub-
low frequencies ( 10–3 - 10–2 Hz). Consequently, the
effect of the ventilation network vibrations is low as
compared with the influence of the rotor speed (Table 2)
and can be withdrawn from calculations.
The accomplished tests have shown that the blade
units with the replaceable part meet every demand of
strength and durability, namely, such blade units stand
permissible stress, displacements and resonance tuning-
out at the first three vibration frequencies.
2. Conclusions
The blade units of fans VO, equipped with replaceable
active part possess sufficient safety factor in terms of
permissible stress, displacement and resonance tun-
ing-out at the first three vibration frequencies.
Efficient adaptability of axial fans by replacement or
removal of active parts of the fan blades, designed ac-
cording to different aerodynamic schemes, favors wide
range of ventilation modes to be maintaned by fans.
3. Acknowledgements
Work is executed at financial support of the grant
14.В37.21.0333 of July 26, 2012.
[1] N. N. Petrov, “Main Axial-Flow Mine Fans with Higher
Adaptability, Maintainability and Reliability,” Proceed-
ings of the 22nd WMC&Expo, Istanbul, Turkey, 11-16
September, 2011.
[2] N. N. Petrov, N. A. Popov, E. A. Batyaev and V. A. No-
vikov, “Theory and Design of Reversible Axial fans with
Turn in Motion Blades of Impeller,” Journal of Mining
Science, Vol.35, No. 5, 1999, pp. 79-97.
[3] K. N. Borishansky, “Vibration of Turbine Blades,” Study
Guide, Saint-Petersburg: PIMash, 1995.
Copyright © 2013 SciRes. OJAppS