Foundation Design Philosophy for Rotating Equipment

References has been taken from,

Design of structures and foundations for vibrating machines by S. Arya, M. O'Neill and G. Pincus
Foundation analysis and design by J. E. Bowels
Dynamics of bases and foundations by D. Barkan
Design of Machine Foundations - Lecture Notes of Professor M.H. El Naggar, Department of Civil Engineering, The University of Western Ontario, London, Ontario, Canada, N6A 5B9

In this page I will talk about the rigid block foundation for Centrifugal (Pump) and Reciprocating machines (Compressor). We are considering the concrete block is infinitely rigid and thus a lump mass model can be considered in computer 3D modelling. To start the design of a block foundation, we need to follow the following steps to collect the design data:

Step-1 : Review of pump / compressor drawing (Vendor Equipment Drawing)

The machine data pertinent to the dynamic analysis and design of the block foundation should be obtained from vendors.

Plan dimension of pump / compressor base frame
Height of rotor / shaft center line from the bottom of skid
Anchor bolt location, size and embedment depth
Weight of machine parts and the rotor parts (pump / compressor rotor and motor rotor)
Location of center of gravity both vertically and horizontally
Operating speed of machines and power rating of motor (RPM)
Magnitude and direction of unbalanced forces.
For reciprocating machines both primary and secondary unbalanced forces and couples and respective CG locations needs to be checked.
Limit of deflection and vibration amplitudes at center line of rotor.

Step-2 : Collection of Geotechnical / soil data (Pl discuss with soil consultant and look into project design criteria)

The Geotechnical data are used for evaluating the soil / pile stiffness and damping coefficients, and are required for both static and dynamic design and analysis of of block foundations. Following soil parameters are required:

Soil weight density
Poisson's ratio
Dynamic shear modulus (G)
Shear wave velocity (v_s)
Dynamic modulus of sub-grade reaction (k_s)
Allowable soil bearing pressure or pile load carrying capacity for design of foundation

Step-3 : Categorization of rotating machines based on machine speed:

The rotating machines are categorized based on machine speed. Following are different categories of machines:

Low Speed machine: The low speed machines operate at a speed range of less than 500 RPM. High tuned foundations, having first natural frequency more than machine's operating speed, should be designed for this type of machines. In this case machine do not pass the resonance during machine start up and coast down condition.
Intermediate speed machine: The intermediate speed machines operate at a speed range 500 RPM to 1000 RPM. Foundations should be designed for this type of machines high tuned or low tuned side whchever more practical. If the foundation is low tuned, dynamic amplitude shall be checked during start up and coast down condition.
High Speed machine: The high speed machines operate at a speed range of more than 1000 RPM. Low tuned foundations, having first natural frequency less than machine's operating speed, should be designed for this type of machines. In this case machine will pass the resonance during machine start up and coast down condition. Dynamic amplitude shall be checked during start up and coast down condition. You need to ensure that there is no adverse effect to machine operation during the resonant conditions.
Variable Speed machine: The variable speed machines operate at a speed range as prescribed by vendor. Foundations should be designed for this type of machines high tuned or low tuned side whchever more practical. A detail dynamic analysis of foundation is required for a range of machine operating speeds to ensure that the dynamic design criteria are met.

Step-4 : Preliminary sizing of foundations:

A block foundation consists of massive concrete blocks, piers and mat foundation. The preliminary sizinng of block should be based on the following:

Weight of the block foundation should be at least 4 times the weight of reciprocating machines and 3 times the weight of centrifugal machines.
The width of foundation should be at least 1.5 times the vertical distance from the bottom of foundation to the center line of the shaft / rotor.
The center of mass of machine foundation (machine+foundation system) should coincide with the centroid of the soil foundation or pile group resistance. Horizontal eccentricity should be limited to 5% of the corresponding foundation dimension.
For a rigid mat, following criteria to be followed:

Minimum thickness of the mat will be 600 mm or 1/5 th of least foundation dimensions or 1/10 th of largest foundation dimensions, whichever is greater .
Maximum thickness of the mat will be 1500 mm
Minimum thickness of mat, t = 0.0012 x (k_s x (a)⁴)^1/3 ft, k_s = soil dynamic modulus of subgrade reaction, lbs/in³, from soil report, a = maximum cantilever projection (inches), measured from face of block (Refer: Foundation analysis and design by J E Bowles)

Step-5 : Requirement for dynamic analysis of foundations:

Dynamic analysis of concrete foundations are not required for all the foundations supporting rotating equipment. You need to refer your project design criteria for the conditions for dynamic analysis. Following are the general criteria for not performing any dynamic analysis of foundation supporting rotating equipment:

Dynamic analysis is not required if the weight of machine is less than 25kN.
Dynamic analysis is not required if the power rating of motor is less than 200hp.

If you are not doing any dynamic analysis of concrete block foundation, then follow Step-4 for foundation sizing and put it into 3D model for any interference check.

If you are doing the dynamic analysis of concrete block, then follow the following steps.

Step-6 : Calculation of un-balanced forces for dynamic analysis of foundations:

If unbalance force is not mentioned in the Vendor equipment drawing, then you will calculate the force as follows:

Un-balance force for pump: F_pump = m_p-rotor x e x w²

Un-balance force for motor: F_motor = m_m-rotor x e x w²

Where, m_p-rotor = weight of pump rotor, m_m-rotor = weight of motor rotor

w = circular frequency = 2 x pi x (f / 60), f = speed of machine from vendor drawing (RPM).

e = rotor eccentricity, depends on machine speed

Eccentricity Table ( Refer reference -1)


Machine	Operating Speed (f in RPM)	Eccentricity e (mils)
Pump / compressor	f < 3000	(1.8-10⁷) / (f)²
Pump / compressor	f > 3000	(12000/f)^1/2
Motor	f < 1500	1.5
Motor	1500< f < 3000	1
Motor	f > 3000	0.5

Now you are having all the information to start the foundation analysis and design. You can put all the above data in any computer software program (say - Dyna5) or use any text books to calculated the natural frequencies of foundation. You can also use the different tables that I have attached here (click for the table).

Natural frequency analysis of foundation:

This rigid block has six degree of freedom. So, you will calculate all the following uncouple natural frequencies:

Sliding Frequency along horizontal X-direction
Sliding Frequency along horizontal Y-direction
Sliding Frequency along vertical Z-direction
Rocking Frequency about X, rotational mode
Rocking Frequency about Y, rotational mode
Rocking Frequency about Z, rotational mode

When the CG of foundation system is far above the foundation base, coupling effect needs to be considered to calculate the foundation natural frequency. In this case sliding mode and rocking mode frequencies overlap each other and as a result foundation dynamic analysis may be more critical. You can calculate the coupled natural frequency using the formula mentioned in the table.

Coupled condition: 1. Sliding along X & Rocking about-Y and 2. Sliding along Y & Rocking about X

Once, analysis is completed, please check the foundation for the following conditions:

Resonance Frequency Check:

Calculate resonanace frequency and check that the ratio of machine frequency vs resonance frequency (f / f_d) is either less than 0.8 or greater than 1.2 in all six degrees of freedom.

Resonance frequency can be calculated as follows: f_d = f_n / (1-2 x D²)^½

where, f_n= foundation natural frequency, D = Damping ration (see table 5 and 12)

Soil Bearing Pressure / Pile Capacity Check

Soil bearing pressure or pile load should not exceed 75% of the allowable. Please avoid any foundation upliftment in seismic / wind condition.

Maximum Velocity check:

Maximum velocity should fall in "Good Condition" per table-1 of attached table

Environmental condition

Maximum displacement amplitude of vibration at foundation level should lie within or below "Zone-B" of figure -1 and it should fall below the Zone "Troublesome to persons" of figure -2 in the attached table.

Reinforcement:

Reinforcement shall be provided per project approved design code. However, you can use minimum reinforcement as follows:

0.2% rebar on all face of concrete block and mat.

1% rebar for all concrete pedestal.

Rebar spacing should not be more than 300 mm.

Anchor Bolt:

Anchor bolt shall be checked for start-up and coast down contion.

For a typical pump foundation drawing click here

I hope this page will be very helpful to you to understand the basic design of a Pump foundation.

Please donate generously for more development of this site:

Copyright 2009. All rights reserved. Please do not print or copy of this page or any part of this page without written permission from Subhro Roy.
Disclaimer: This page is prepared based on experience on Civil Engineering Design. All definitions and most of the explanations are taken from different text books and international design codes, which are referenced in the contents. Any similarity of the content or part of with any company document is simply a coincidence. Subhro Roy is not responsible for that.