FIELD OF THE INVENTION
This invention relates generally to foundations of axial fans in thermal power
plants. More particularly, the invention relates to a partially cantilevered block
foundation for axial fans adaptable to thermal power plants.
BACKGROUND OF THE INVENTION
Presently, all the axial fan foundations in Thermal Power Plants are constructed
out of reinforced concrete. The basic reasons for selecting concreted structure
for fan-foundations are, that the concrete is inexpensive, has good strength
properties including relatively high damping coefficient. The centerline of the fan
shaft is located at above ground level to give enough ground clearance for the
impeller blades of the fan to freely rotate. The fan shaft along with the bearings,
the motor and the diffuser are supported on reinforced concrete pedestals from
the shaft bearing level to the ground level. Below ground level the fan
foundation essentially is a block of reinforced concrete, which connects all the
pedestals and embedded in soil.

The fans used in thermal power plants have an operating speed of about
1000rpm and classified as low frequency machines as per IS 2974 Part IV 1979
(Up to 1500 rpm) and the foundation has to be designed not only for the static
and dynamic forces imposed by the fan but also the dynamic behavior of the
foundation itself.
Dynamic analysis is used to predict the natural frequencies of the system and
compared with the operating frequency of the machine and resonance is avoided
by keeping the natural frequency of the system ± 20% away from the operating
frequency of the fan.
Resonance and its effect:
Any physical system has a characteristic frequency of its own known as 'natural
frequency'. This is defined as the frequency at which the system would vibrate
when subjected to free vibration. As the operating frequency of a machine
approaches the natural frequency of its foundation, the amplitudes tend to
become large. The system is said to be in 'resonance' when the two frequencies
become equal. At resonance, it is found that in addition to excessive amplitudes,
large settlements also occur.

Importance of Design Parameters
The various parameters influencing the design of a machine foundation are :
a. Centre of Gravity
b. Moment of inertia of the base
c. Mass moment of inertia
d. Effective stiffness of the base support
e. Damping
The parameters mentioned in (a),(b),(c) are known as 'geometrical properties of
the machine foundation system', and the parameters (d) and (e) are generally as
physical properties of the elastic base of the foundation.
The features like center of gravity, moment of inertia and mass moment of
inertia hardly need any elucidation. The eccentricity of the center of the gravity
of a machine foundation with reference to the vertical axis passing through the
center of elasticity of the base support induces coupling of vibratory modes and
this complicates the design procedure. It is, therefore, desirable in design
practice to ensure that the eccentricities in the two horizontal directions (x and y)
are within permissible limits.
The moment of inertia of the base of the foundation and mass moment of inertia
influence the dynamic calculations for the rocking (or twisting) mode of vibration.
The moment of inertia and the mass moment of inertia are direction dependent
in the sense that their expressions differ with the chosen reference axis.

The effective stiffness and damping offered by the base support depend on the
type of the flexible base provided under the foundation for example, soil springs,
elastic-pads, etc.
The theory based on the undamped linear spring analog for soil, as proposed by
D.D.Barkan requires the evaluation of certain soil parameters, which are listed
below.
Coefficient of elastic uniform compression (Cz)
Coefficient of elastic uniform shear (G)
Coefficient of elastic non-uniform compression (Cθ)
Coefficient of elastic non-uniform shear (Cφ)
The soil parameters mentioned above are used for the evaluation of the spring
stiffness of soil in various modes of vibration.
The coefficient of elastic uniform compression (Cz) is defined as the ratio of
compressive stress applied to a rigid foundation block to the 'elastic' part of the
settlement induced consequently. It has been found that within a certain range
of loading, there is a proportional relationship between the elastic settlement and
the external uniform pressure on soil, the constant of proportionally being
designated as the coefficient of elastic uniform compression.

The coefficient of elastic uniform shear (C) may likewise be defined as the ratio
of average stress at the foundation contact area to the 'elastic' part of the sliding
movement of the foundation.
The coefficients described above are functions of soil-type and of size and shape
of the foundation. However, for practical purposes they are often assumed to be
functions of soil-type only.
Damping is a measure of energy dissipation in a given system. Being a physical
property of a system, damping can be evaluated only by tests.
The practice prevalent for the design of machinery foundation is mainly based on
the method proposed by D.D.Barken. D.D.Barken ignores the effects of
'damping' and considers the soil as a linear weightless spring. According to the
theory, damping has only a slight effect upon calculated natural frequency, and if
the operating and natural frequencies are well apart, the effect of damping on
amplitudes can be neglected. In respect of the effect of soil inertia, D.D. Barken
had shown that the apparent mass of soil participating in foundation vibrations
does not normally exceed 23% of total mass of machine and foundation. Thus,
according to Barken, the calculated natural frequency should not be in error by
more than 10 percent.
For foundations resting directly on soil, D.D.Barken has introduced the following
soil parameters, which yield the spring stiffness of soil in various modes. These
parameters are already defined.

Coefficient of elastic uniform compression for vertical
translatory mode Cz
Coefficient of elastic non-uniform compression for
rocking mode Cθ
Coefficient of elastic uniform shear for horizontal
translatory mode C
Coefficient of elastic non-uniform shear for twisting
(or yawing) mode Gφ
If the common center of gravity of the machine and foundation and the centroid
of the base area lie on the same vertical line in one of the principal planes of the
foundation, it can be shown that the translatory motion of the foundation along
the vertical axis (or the 'Z' axis) and the rotary motion about the same axis
(yawing) are independent (or uncoupled). Therefore, the motion in these two
modes can be represented by two separate single-degree systems. On the other
hand, the sliding motion in the horizontal x (or y) axis and the rocking (rotary)
motions of the foundation in xz and yz planes are, therefore, represented by two
'two-degree freedom systems' separately.
The foregoing discussion leads to the conclusion that the dynamic analysis of a
block foundation should be carried out for the following cases:

a. Uncoupled translatory motion along (z) axis (Vertical).
b. Coupled sliding and rocking motion of the foundation in x-z and y-z
(vertical) planes passing through the common center of gravity of
machine and foundation.
c. Uncoupled twisting motion about z axis.
Dynamic analysis proposed by D.D.Barkan is used for the design of fan
foundation i.e. low frequency machines. The basic theory of the analysis is
essentially that of a block foundation. (Ref. Dynamics of bases and foundation by
D.D.Barkan, Publisher McGraw Hill - New York, 1962)
The natural frequencies are calculated in three modes (vertical and coupled) as
per IS 2974 - Part 1 1969 (Based on D.D. Barkan method).
The amplitude of vibration is also to be limited to acceptable standard and three
modes of amplitudes are calculated in the dynamic analysis as per IS - 2974 -
Part 1 1969.
The foundation is dimensioned in such a way that the resultant force due to
weight of the machine and foundation as far as possible passes through the C.G.
of the base contract area, as per IS 2974 - Part IV 1979.
The eccentricity of the common center of gravity of machine and foundation
referred to the centroid of base contact area should not exceed 5% (ref. Hand
Book of machine foundations by P.Srinivasulu, Structural Engineering Research
Centre, Madras - Publisher Tata McGraw - Hill 1976, New Delhi).

The total mass of foundation is kept more than 2.5 times the weight of the
machine as recommended by IS 2974 Part IV 1979.
The low frequency rotary type machines (less than 1500 rpm) and specially the
fans like induced draft fans in thermal power stations have a common problem
and that is the speed of the fans are around 1000 rpm and the natural frequency
of the block foundation calculated based on the Dynamic Analysis also ends up in
the same range. So design of fans having speed of round 1000 rpm is always
posing problems to designers.
The general arrangement drawings are made by fans designers, which give
details of foundation above ground level i.e. motor pedestal, fan pedestal,
diffuser pedestal giving also the sizes of the pedestals, (length, breadth and
width). So what is left out for the civil design engineering is to play with below
ground level sizes only in terms of length, breadth and depth of the foundation.
To cite an example the foundation for the axial fan of 980 rpm in a Thermal
Power Station used as indicated draft fan, several alternatives designed after
altering the size of the foundation in terms of length, width and depth below
ground level could not provide a satisfactory design with respect to natural
frequencies.

OBJECTS OF THE INVENTION
It is therefore an object of the invention to propose a partially cantilevered block
foundation for axial fans adapted to thermal power plants, which is cheaper and
requires less volume of concrete.
Another object of the invention to propose a partially cantilevered block
foundation for axial fans adapted to thermal power plants, which has a reduced
aspect ratio of the foundation.
Yet another object of the invention to propose a partially cantilevered block
foundation for axial fans adapted to thermal power plants, which ensures a low
vibration amplitude.
A further object of the invention to propose a partially cantilevered block
foundation for axial fans adapted to thermal power plants, which maintains
center of gravity of the machine and the foundation closer to that of the base
contact area.
A still further object of the invention to propose a partially cantilevered block
foundation for axial fans adapted to thermal power plants, which ensures that
the above-ground-level cantilever slab supports the diffuser-end pedestal to
match the required frequency, amplitude and center gravity.

SUMMARY OF THE INVENTION
According to the invention, the partially cantilevered block foundation for axial
fan will have a cantilever slab, supporting the end pedestals of the diffuser.
The cantilever will be above ground level leaving a 100mm gap between ground
level and bottom of the cantilever. The cantilever slab will be taken from the
main pedestal for the impeller bearing.
The thickness of the slab will be proportioned in such way to avoid independent
vibration of the cantilever by keeping the depth/length ratio not less than 0.6.
The new configuration will improve the aspect ratio making the foundation closer
to the block, since the axial fan the foundation length/breadth ratio is very large
taking the aspect ratio closer to a beam.
Because of the cantilever, the Centre of Gravity of the machine and foundation is
brought closer to the C.G. of the base contact area.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWING
Fig. 1 shows an elevational view of the partially cantilevered block foundation for
axial fans according to the invention.

Fig.2 shows an elevational view of the rectangular block foundation for axial fans
according to the prior art.
Fig.3 shows an elevational view of the block foundation with cantilever for axial fans
according to the invention.
DETAILED DESCRIPTION OF THE INVENTION
An axial fan diffuser is only a static part, which exerts only a small load on the support
pedestal as compared to the impeller and motor. According to the invention, the
diffuser end pedestal (03) is supported on a cantilever slab (02) rather than extending
the whole foundation up to the end of the diffuser and pedestal (03). The fan pedestal
(04) and the motor pedestal (05) are supported directly on the block foundation (01).
Partial cantilever is adapted in the block foundation, which reduces the foundation
concrete volume considerably.
The dynamic analysis of the fan foundation is done as per IS 2974 Part IV 1979 which
assumes the foundation as a block. But because of the length of the axial fans are
larger, the aspect ratio of the foundation is in the threshold of a beam.
Because of the cantilever slab (02), the aspect ratio of the base contact area is reduced
which brings the foundation closer to a block and thus the actual dynamic performance
of the foundation will be closer to that of the Dynamic Analysis.
The cantilever slab supporting the diffuser end pedestal is proportioned in such a way
to avoid independent vibration of its own.

The cantilever slab brings the C.G. of the machine and foundation closer to the
C.G. of the base area since the weight of the diffuser is very small when
compared to the weight of fan and motor.
The eccentricity of the center of gravity of a machine foundation with reference
to the vertical axis passing through the center of gravity of the base contact area
induces coupling of vibratory modes and this complicates the design procedure.
It is therefore, desirable in design practice to ensure that eccentricities in two
horizontal directions are within 5%.
The partially cantilevered block foundation for axial fans can be used in steel
plant, cement plant and in refineries for axial fans.
The partially cantilevered block foundation can be used in any rotary machine,
which will have a static part in one end in first time installation in new plants or
in retrofit installation in existing plants.

WE CLAIM
1. A partially cantilevered block foundation for axial fans in Thermal Power Plants
comprising:
a concrete block (01) which supports a motor pedestal (05) and a fan pedestal
(04);
characterized in that,
a cantilever slab (02) supports the diffuser end pedestal (03) rather than
extending the whole foundation up to the end of the diffuser end pedestal, and
the thickness of the slab is so proportioned to avoid independent vibration of the
cantilever by keeping the depth/length ratio not less than 0.6, wherein aspect
ratio of the base contact area is reduced bringing the foundation closer to the
block wherein the center of gravity (C.G.) of the machine and foundation is
brought closer to the C.G. of the base contact area and length of the foundation
base is reduced leading to reduction of the amplitude of vibration.
2. The partially cantilevered block foundation for axial fans as claimed in claim 1,
wherein the cantilever base (02) is provided in the form of a slab interconnecting
both the pedestals (03) and supporting the diffuser end pedestals (03) which
have only a static load.
3. The partially cantilevered block foundation for axial fans as claimed in claim 1 or
2, wherein the cross section of the cantilevered slab (02) is rectangular.
4. The partially cantilevered block foundation for axial fans as claimed in claim 2,
wherein the cantilever slab (02) is made of concrete

5. The partially cantilevered block foundation for axial fans as claimed in claim 3,
wherein the cantilever slab (02) is raised above the ground level to avoid support
in soil and to reduce the contact area of the foundation base.
6. The partially cantilevered block foundation for axial fans as claimed in claim 6,
wherein the aspect ratio length/breadth is reduced bringing the proportioning of
the foundation base closer to a block rather than a beam and thus the actual
dynamic performance of the foundation is brought closer to that of the Dynamic
Analysis.

A partially cantilevered block foundation for axial fans in thermal power plants consists
of a concrete block (01) which supports a motor pedestal (05) and a fan pedestal (04).
A cantilever slab (02) supports the diffuser end pedestal (03) rather than extending the
whole foundation up to the end of the diffuser end pedestal and the thickness of the
slab is so proportioned to avoid independent vibration of the cantilever by keeping the
depth/length ratio not less than 0.6. The aspect ratio of the base contact area is
reduced bringing the foundation closer to the block wherein the centre of gravity (C.G.)
of the machine and foundation is brought closer to the centre of gravity
of the base contact area and length of the foundation base is reduced leading to
reduction of the amplitude of vibration.