Machine Foundation
Machine Foundation
Machine Foundation
loads to soil in addition to static loads due to weight of foundation, machine and
accessories.
The dynamic load due to operation of the machine is generally small compared to the
static weight of machine and the supporting foundation.
In a machine foundation the dynamic load is applied repetitively over a very long
period of time but its magnitude is small and therefore the soil behaviour is essentially
elastic, or else deformation will increase with each cycle of loading and may become
unacceptable.
The amplitude of vibration of a machine at its operating frequency is the most important
parameter to be determined in designing a machine foundation, in addition to the
natural frequency of a machine foundation soil system.
There are many types of machines that generate different periodic forces. The most
important categories are:
2. Impact machines: These machines produce impact loads, for instance, forging
hammers. Their speeds of operation usually vary from 60 to 150 blows per minute.
Their dynamic loads attain a peak in a very short interval and then practically die out.
If two or more machines of similar type are to be installed in a shop, these can
profitably be mounted on one continuous mat.
A block foundation has a large mass and, therefore, a smaller natural frequency.
The block has large bending and torsional stiffness and easy to construct. To modify the
block foundation at a later time is extremely difficult.
However, if a relatively lighter foundation is desired, a box or a caisson type foundation
may be provided.
The mass of the foundation is reduced and its natural frequency increases.
It has high static stiffness just like a plate foundation and is not easily amenable to
alterations at a later date.
Steam turbines have complex foundations that may consist of a system of walls
columns, beams and slabs.
This type is usually adopted for very high-speed machines requiring large operational
space below for connecting pipes and additional equipment.
It can be made or either RCC or steel frames. Although the frame made of steel is easy
to alter at a later date, its behaviour under dynamic loading is not as good as that of an
RCC frame.
Plate foundation consists of a continuous plate made of concrete resting directly on soil
or supported on piles. The machine is placed on the plate.
The plate has high static stiffness and is easy to construct. Subsequent alterations to this
type of foundation are difficult to execute.
Spring foundation
Spring foundation consists of a concrete slab or a steel frame on which the machine
rests. The slab/frame is supported on a set of springs.
This type is used, if the subsoil is weak or we need to isolate the subsoil from the
transmitted vibrations.
Design Criteria for Machine Foundations
i. It should be safe from a bearing capacity failure under static and dynamic loads,
iii. The dynamic amplitudes of the machine-foundation-soil system must be within the
prescribed limits under service conditions.
iv. There should be no resonance, i.e. the natural frequency of the machine-
foundation-soil system should not coincide with the operating frequency of the
machine,
v. Preferably, the centre of gravity of the machine should lie in the same vertical line
as the centre of gravity of the foundation system.
the structure in which the machine is housed and adjacent structures do not suffer any
vibration induced damage,
employees working around the machine are not bothered by the vibrations.
One of the design criteria for machine foundations is that there should be no resonance.
Shifting the natural frequency of the machine-foundation-soil system well above the
operating frequency is called high tuning, or in the jargon of Mechanical Engineers sub-
critical run.
On the other hand shifting the natural frequency below the operating frequency is called
low tuning or supercritical run.
High tuning has the advantage that the machine does not have to go through resonance
either during start up or shut down of the machine.
Implementing high tuning for a very high-speed machine is difficult to achieve and can
be a costly proposition.
Under such situation have to opt for a low tuned system and yet are within the
prescribed level.
This is often accomplished by using a foundation system that allows alteration of the
natural frequency of the machine-foundation-soil system when necessary by changing
its mass or stiffness.
For example, by increasing the dimensions of the foundation which will change the
mass, providing cavities in the block where mass can be added, or using commercially
available mechanical springs which will change the stiffness.
Sometimes, avoiding resonance is not possible. In such a case, you will have to make
sure that the amplitude of vibration is in the acceptable limits by incorporating dampers
in the foundation system. Dampers are instruments that absorb vibrations.
The amplitudes of motion at operating frequencies should not exceed the limiting
amplitudes, which are generally specified by machine manufacturers. If the computed
amplitude is within tolerable limits, but the computed natural frequency is close to the
operating frequency, it is important that this situation be avoided.
The natural frequency of the foundation –soil system should not be whole number
multiple of the operating frequency of the machine to avoid resonance with the higher
harmonics.
The vibrations must not be annoying to the persons working in the shops or damaging
to the other precision machines. The nature of vibrations that are perceptible, annoying,
or harmful depends upon the frequency of the vibrations and the amplitude of motion.
METHODS OF ANALYSIS
Figure shows a schematic sketch of a rigid concrete block resting on the ground surface
and supporting a machine.
Let us assume that the operation of the machine produces a vertical unbalanced force
which passes through the combined centre of gravity of the machine-foundation system.
Under this condition, the foundation will vibrate only in the vertical direction about its
mean position of static equilibrium.
The vibration of the foundation results in transmission of waves through the soil.
These waves carry energy with them. This loss of energy is termed geometrical
damping‟. The soil below the footing experiences cyclic deformations and absorbs
some energy which is termed ,material damping‟.
The material damping is generally small compared to the geometrical damping and may
be neglected in most cases.
However, material damping may also become important in some cases of machine
foundation vibrations.
The problem of a rigid block foundation resting on the ground surface, (Fig. a) may
therefore be represented in a reasonable manner by a spring-mass-dashpot system
shown in Fig. b.
The spring in this figure is the equivalent soil spring which represents the elastic
resistance of the soil below the base of the foundation.
The dashpot represents the energy loss or the damping effect. The mass in Fig. b is the
mass of the foundation block and the machine.
Single degree of freedom models shown in Fig. b and c may in fact be used to represent
the problem of machine foundation vibration in any mode of vibration if appropriate
values of equivalent soil spring and damping constants are used. For coupled modes of
vibration, as for combined rocking and sliding, two degree-of-freedom model is used.
Vertical Vibrations of a Machine Foundation (a) Actual Case (b) Equivalent model with damping
( c) Model without damping
All foundations in practice are placed at a certain depth below the ground surface.
As a result of this embedment, the soil resistance to vibration develops not only below
the base of the foundation but also along the embedded portion of the sides of the
foundation.
Similarly the energy loss due to radiation damping will occur not only below the
foundation base but also along the sides of the foundation.
The type of models shown in Fig. b and c may be used to calculate the response of
embedded foundations if the equivalent soil spring and damping values are suitably
modified by taking into account the behavior of the soil below the base and on the sides
of the foundation.
For designing new foundations or retrofitting existing foundations for machines,
with reference to avoiding excessive settlement due to large number of cycles of load
applications- it means amplitude of displacement prescribed by the local codes
particularly for soil profiles consisting of loose sands and silts with high water table.
In order to calculate the natural frequency and amplitude of vibrations for a particular
machine-foundation-soil-system, you need to know the local soil profile and soil
characteristics as also the dynamic loads generated by the machine that are provided by
the manufacturer.
1. Empirical
2. Elastic half space method
3. Linear elastic weightless spring method, and
Empirical Method
On such design guideline, rather a rule of thumb was the weight of the foundation
should be at least three to five times the weight of machine being supported.
There are some empirical formulae available in literature for estimating the natural
frequency, mostly for the vertical mode of vibration.
In these formulae, it is assumed that a certain part of the soil, immediately below the
foundation, moves as a rigid body along with the foundation and is called apparent soil
mass or in-phase mass.
For example, D.D.Barken in 1962 suggested that the mass of the vibrating soil should
be between 2/3 to 3/2 times the weight of foundation and machine.
These guidelines/formulae do not take into account the nature of subsoil, type of
excitation force (harmonic/impact), contact area and mode of vibration.
In using the second and third methods, we use the concept of discrete system or lumped
parameter system,
In this system: the mass of the machine and the supporting foundation are lumped
together as one discrete rigid mass ‘m’- this is reasonable since the stiffness of
reinforced concrete and the machine is several times more than that of soil.
the soil resistance is represented by means of a spring with a constant ‘k’ ,and the
energy absorption characteristic of soil is represented by means of a dashpot with a
constant ‘c’.
Once we have these three quantities m, k, and c, using the theory of vibrations, the
natural frequency as well as the amplitude of vibration for any given type of load can be
calculated.
The formulae to calculate amplitude of vibration for either impact or cyclic type of
loading can be found in books dealing with structural dynamics.
The soil behaves essentially as a linear elastic material and the resistance to deformation
offered by it can be represented by a spring.
This is based on the fact that the magnitude of the dynamic force acting on the
foundation is very small compared to the static load, normally no more than 10%.
And, therefore, the amplitude of displacement is extremely small. Since the non-linear
behavior of the soil does not come into play, material dumping in the soil can be
neglected.
Every time a dynamically loaded foundation moves against soil, stress waves originate
at the contact surface in the form of surface waves and carry away some of the energy
transmitted to the soil.
This loss of energy is called radiation damping and in passing that it can be effectively
modeled by a dashpot.
Use of the elastic half space method or the linear elastic weightless spring method
enables us to calculate the value k and c.
This block foundation can deform in any one or all of six possible modes.
DEGREES OF FREEDOM OF A RIGID BLOCK FOUNDATION
A typical concrete block is regarded as rigid as compared to the soil over which it rests.
Under the action of unbalanced forces, the rigid block may thus undergo
displacements and oscillations as follows
1. translation along Z axis
2. translation along X axis
3. translation along Y axis
4. rotation about Z axis
5. rotation about X axis
6. rotation about Y axis
Any rigid-body displacement of the block can be resolved into these six independent
displacements. Hence, the rigid block has six degrees of freedom and six natural
frequencies.
Of six types of motion, translation along the Z axis and rotation about the Z axis
can occur independently of any other motion. However, translation about the X axis (or
Y axis) and rotation about the Y axis (or X axis) are coupled motions..
Therefore, in the analysis of a block, we have to concern ourselves with four types of
motions.
Two motions are independent and two are coupled. For determination of the natural
frequencies, in coupled modes, the natural frequencies of the system in pure translation
and pure rocking need to be determined.
Also, the states of stress below the block in all four modes of vibrations are quite
different.
This method is called the elastic half space method because the ground is assumed to be
an elastic, homogeneous, isotropic, semi-infinite body which in the Theory of Elasticity
is referred to as elastic half space.
The elastic half space theory can be used to determine the values of equivalent soil
springs and damping then make use of theory of vibrations to determine the response of
the foundation. These are known as the „the elastic half space analogs‟.
The Boussinesq’s solution for finding the stresses induced in soil due to a point load on
the ground surface.
In the elastic half space method, the point load is assumed to be dynamic. By
integrating the solution for a dynamic point load over a circular area, the stresses due to
a circular machine foundation is calculate.
It may be mentioned here that the equivalent soil spring and damping values depend
upon the ;
(i) type of soil and its properties,
(ii) geometry and layout of the foundation, and
(iii) nature of the foundation vibrations occasioned by unbalanced dynamic loads.
According to the theory with the vertical vibrations of a machine foundation of radius r₀
:
Linear Elastic Weightless Spring Method
The linear elastic weightless spring method differs from the elastic half space method in
two respects:
the soil below the foundation is considered weightless – this assumption is not valid
but it does not appreciably affect the computed response, and
damping in the soil below the foundation is neglected- this assumption is also not valid
since radiation damping exists in a machine foundation. The effect of damping is
incorporated in this method by independently estimating it using a field test.
There is no dashpot here since damping has been neglected. In this method, the spring
constant k for vertical vibrations is expressed as a function of the area of the foundation
Af and the coefficient of elastic uniform compression Cu is
Kz = Cu Af
INFORMATION NEEDED FOR DESIGN
Dynamic shear modulus of a soil is generally determined from laboratory or field tests.
Material damping can be determined from vibration tests on soil columns in the
laboratory.
The values of dynamic shear modulii and damping may be estimated from empirical
estimations for preliminary design purposes. Geometrical damping is estimated from
elastic half-space theory and appropriate analogs.
Design Procedure for a Block Foundation (Reciprocating Machine-Cyclic
Loading)
Obtain machine data: Operating speed of the machine; layout of the machine and a
detailed loading diagram; unbalanced forces from the machine; and permissible
amplitude of vibrations.
Obtain soil data: Soil properties to compute the allowable bearing capacity and spring
and damping constants of the soil.
Assume a trial size of the foundation: Usually the size of the machine dictates the
minimum plan size of the block. The minimum thickness of the block is dictated by the
depth of embedment required from bearing capacity considerations plus any ground
clearance required for operational purpose.
Evaluate the natural frequency and amplitude of vibration: First determine the natural
frequency of the block of size assumed in above placed on top of soil. Then determine
the amplitude of vibrations at this natural frequency subjected to unbalanced loads.
Check for resonance and whether amplitude is within acceptable limits:
If resonance is not likely to occur and the amplitude of vibrations is within the
permissible limits then the trial size of the block assumed at step (ii) is acceptable. If
not, change the dimensions assumed in (ii) and repeat steps (iii) and (iv) until the design
requirements are satisfied. Design is almost invariably an iterative process. Trial
dimensions are assumed based on experience.
Design Criteria for Foundation of Reciprocating Machine
The machine foundation should be isolated at all levels from the adjoining foundations
The natural frequency of the foundation –soil system should be higher then the highest
disturbing frequency and the frequency ratio should not be less then 0.4.
The amplitude of vibration should be within the permissible limits or any specified
permissible limits
For most soils, the another criterion, amplitude for low speed machines is usually taken
as 200 micron (=0.2 mm)
Concrete block foundations should be used. However, when the soil is not suitable to
support block foundation, cellular foundation may be used.
The size of the block in plan should be larger then the bed plate of the machine. There
should be a minimum all round clearance of 15 mm.
The total width of the foundation measured at right angles to the shaft should be at least
equal to the distance between the center of the shaft and bottom of the foundation.
The eccentricity of the foundation system along X-X and Y-Y axes should not exceed
not 5% of the length of the corresponding side of the contact area.
The combined center of gravity of machine and foundation should be as much below
the top of foundation.
The depth of foundation should be sufficient to provide the required bearing capacity
and to ensure stability against rotation in the vertical plane.
The stresses in the soil below the foundation should not excess 80% of the allowable
stresses under static loads. The base pressure is limited to half the normal allowable
pressure qna in extreme case.
The analysis for such machines can be made assuming that each foundation acts
independently up the raft into sections corresponding to separate machines.
Design Procedure for a Block Foundation (Hammer- Impact Loading)
The hammer system usually consists of a frame that guides a falling, weight, known as
the tup, that strikes down on the anvil that is supported on the foundation block.
Typical tup weights range between 2.5kN and 100kN and the drop height is in the range
of 0.3 m to 2 m or more.
The anvil gets repeated blows from the tup so that the piece of metal held by the anvil
gests forged to a desired shape or is broken.
High impact energy is transmitted to the anvil form the falling tup. A part of the energy
is used in forging and the rest gets transmitted to the soil below.
To avoid breakage of the concrete foundation due to impact stresses, an elastic pad
made of felt, cork or rubber is placed between anvil and foundation block.
We have to ensure that the compressive stresses induced in the pad do not exceed the
specified value. This is an additional design criteria for block foundations for a hammer.
You should note that unlike, the one degree freedom system with two springs and two
masses. One mass, M1, represents the mass of the anvil and spring. K1 , represents the
stiffness of the elastic pad and the other mass, M2 and spring k2 represents the mass of
the concrete foundation and the stiffness of soil.
In the design of these foundations, the damping in the soil is neglected since the period
of impact is very small compared to the period of natural frequency of vibration of
machine-foundation-soil system.
The rest of the design procedure is the same as that discussed for the block foundation
for reciprocating machines.
Steel reinforcement around all pits and opening shall be at least equal to 0.5 to 0.75 %
of the cross sectional area of the pit or opening.
If the height of the foundation block exceeds one metre, shrinkage reinforcement shall
be placed at suitable spacing in all the three directions.
The cover should be a minimum of 75 mm at the bottom and 50 mm on sides and the
top. The concrete shall be at least M-15 with a characteristic strength of 15 N/mm2.
The machine foundation should be located away from the adjoined structures. This is
known as geometric isolation.
Additional masses known as dampers are attached to the foundations of high frequency
machines to make it a multiple degree freedom system and to change the natural
frequency.
In reciprocating machines vibrations are considerably reduce by counter balancing the
exciting forces by attaching counterweight to the side of the crank.
Vibration are considerably reduce by placing absorbers such as rubber mounting, felts
and crock between the machine and the base .
If an auxiliary mass with a spring is attached to the machine foundation, the system
becomes a two degree freedom system. The method is especially effective when the
system is in resonance.
The propagation if wave can be reduced by providing sheet piles, screens or trenches.