Machine foundation notes for civil engineering students

Machine foundation short notes for engineering students

1. Machine foundation Notes
Types of machine foundation
1. Block Type Machine Foundation
 Consists of a solid concrete block.
 Provides high mass and low natural frequency.
 Suitable for heavy machines with low dynamic forces.

2. Box Type Machine Foundation
 Made of a hollow concrete block.
 Lower mass compared to block type, higher natural frequency.
 Used for machines with moderate dynamic forces.

3. Wall Type Machine Foundation
 Consists of two vertical walls with a top slab.
 Economical for smaller machines.
 Provides moderate mass and frequency.

2. 4. Framed Type Machine Foundation
 Composed of vertical columns and a horizontal frame.
 Suitable for large machines with high dynamic forces.
 Provides flexibility and high natural frequency.

5. Non-Rigid or Flexible Type Machine Foundation
 Uses flexible materials like rubber or springs.
 Absorbs vibrations effectively.
 Suitable for machines with high dynamic forces and vibrations.


Basic terminologies in machine foundation and its definitions
 Dynamic Load: The load that varies with time due to the operation of the machine.
 Static Load: The constant load exerted by the weight of the machine and its components.
 Natural Frequency: The frequency at which a system tends to oscillate in the absence of any
driving or damping force.
 Resonance: The condition when the frequency of dynamic loads matches the natural frequency
of the foundation, causing excessive vibrations.
 Damping: The process of reducing the amplitude of vibrations.
 Amplitude: The maximum displacement of a vibrating system from its equilibrium position.

3.  Frequency: The number of oscillations per unit time.
 Vibration Isolation: Techniques used to reduce the transmission of vibrations from the machine
to the foundation.
 Foundation Mass: The total mass of the foundation structure.
 Soil Bearing Capacity: The ability of the soil to support the loads applied to the ground.
 Settlement: The downward movement of the foundation due to the load applied.
 Dynamic Analysis: The study of the behavior of structures subjected to dynamic loads.
 Static Analysis: The study of the behavior of structures under constant loads.
 Base Isolation: A technique to decouple the foundation from ground motion.
 Machine Foundation: The structure that supports and anchors a machine, designed to absorb
and mitigate vibrations and dynamic forces.
 Vibration :The oscillatory motion of a body or system about its equilibrium position.
 Periodic Motion: Motion that repeats itself at regular intervals of time.
 Period : The time taken to complete one cycle of periodic motion.
 Cycle: One complete sequence of motion in a periodic system.
 Damping: The process of reducing the amplitude of oscillations in a vibrating system.
 Degree of Freedom: The number of independent ways in which a system can move.

Requirements of good machine foundation
 Adequate Load-Bearing Capacity
The foundation must support the static and dynamic loads of the machine without excessive
settlement or failure.
 Vibration Isolation
It should effectively isolate and absorb vibrations produced by the machine to prevent
transmission to adjacent structures or the ground.
 Resonance Avoidance
The natural frequency of the foundation–soil system should not match the operating frequency
of the machine to avoid resonance.
 Rigidity and Stability
The foundation must be rigid and stable enough to prevent tilting, sliding, or overturning under
machine operation.

4.  Proper Alignment
It should maintain accurate alignment of the machine parts during operation for effective
performance and safety.
 Durability
The foundation material must resist weathering, chemical attack, wear, and fatigue caused by
dynamic loads over time.
 Minimum Settlements
The total and differential settlements should be within permissible limits to maintain machine
accuracy and safety.
 Efficient Load Distribution
Loads should be evenly distributed to the soil to avoid localized stress concentrations and
uneven settlement.
 Ease of Maintenance and Inspection
The foundation should allow easy access for machine maintenance, repair, and visual inspection.
 Compliance with Safety and Design Codes
It must satisfy relevant building codes, standards, and safety requirements related to dynamic
loading and environmental conditions.
Barkan’s Method
Barkan’s Method is a classical analytical approach used for the design and analysis of
machine foundations. It helps determine the response of a foundation to dynamic loads by
modeling the soil as a system of elastic springs. The method is especially useful in evaluating
vibrations of block-type machine foundations under dynamic forces.
Assumptions of Barkan’s Method
 Soil is homogeneous and isotropic.
 Foundation behaves as a rigid body.
 Linear elastic response of soil.
 Soil–foundation contact is continuous and uniform.
Additionally following points are considered in method;
1. Elastic Soil Behavior:
Soil is assumed to behave like an elastic medium, with the foundation supported by
vertical and horizontal springs (spring constants represent soil stiffness).

5. 2. Degrees of Freedom:
A rigid block (foundation) on soil has 6 degrees of freedom:
o 3 translational (vertical, longitudinal, lateral)
o 3 rotational (pitching, rolling, yawing)
3. Modes of Vibration Considered:
o Vertical vibration
o Horizontal vibration (longitudinal and lateral)
o Rocking, pitching, and yawing (rotational modes)
These modes are analyzed independently or in coupled form.
4. Stiffness Coefficients:
Barkan proposed values for stiffness coefficients (spring constants) for each type of
motion based on the contact area of foundation and soil type.
5. Natural Frequency Calculation:
For each mode, the natural frequency (fn) of vibration is given by:
??????
?=
1
2 ??????
?
??????
??????


o k: stiffness of soil for that mode
o m: mass of the foundation + machine
2. Resonance Avoidance:
The design ensures that the natural frequency of the foundation–soil system does not
coincide with the machine operating frequency (to avoid resonance).
Steps in Barkan’s Method (Simplified)
1. Determine Machine Loads and Operating Frequency
Identify the dynamic forces and the frequency of operation.
2. Model the Foundation as a Rigid Block
Consider soil reaction via equivalent springs (vertical and horizontal).
3. Calculate Soil Stiffness Coefficients
Use Barkan's charts or empirical formulae for different modes.

6. 4. Compute Natural Frequencies
Use the above formula for each mode of vibration.
5. Check for Resonance
??????
?≠ ??????
?
(natural frequency ≠ machine frequency)
6. Design the Foundation Dimensions
Adjust mass and contact area until the criteria are met.

Applications
 Design of machine foundations for turbines, compressors, pumps, etc.
 Preliminary design stage to estimate dynamic response.
 Verification of vibration criteria for sensitive equipment.

7. Problems on Barkan’s method
Q: Determine the natural frequency of a machine foundation having a base area of 1mx1m and mass
of 10kg excluding mass of machine. Mass of machine is 5kg. Take Cu 40000kn/cum
Solution:-
??????
?= ?
??????
? ??????
??????

m = mass of foundation + mass of amchine = 10+5 = 15kg
??????
?= ?
40000 × (1 × 1)
15 × 10
7

??????
?= 1.63 ?????????????????? /??????????????????
??????=
??????
?
2 ??????
=
1.63
2 ??????
= 0.259 ????????????


Q: Determine cioeffficient of uniform compression if a vibration test on block (1m x 1m x 1m) gave
resonance frequency of 50Hz in the vertical direction. Mass of oscillators used was 50kg
Solution:-
Mass of foundation = (1 x 1 x 1) x 2500 = 2500
Total Mass = m = 2500 +50 = 2550kg
??????=
??????
?
2 ??????
= ?
??????
? ??????
??????

50 × 2 ?????? = ?
??????
? (1 × 1)
2550

Cu = 251674912.2 = 2.51 x 10
8
N/cum = 2.51 x 10
5
kN/cum