Design of shallow foundations for vibrating machines

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Design of Shallow Foundations

for Vibrating Machines

By : Le Chi Hung, Ph.D

Civil Engineering Team

Manager, Civil Engineering teamGlobal Engineering Technology, Seoul, South KoreaWebsite: www.getech.com.sg

Email: chlee@getech.com.sg

lchhung@gmail.com

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 Machine and foundation types

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 Machine types

Machine and Foundation types

 Common foundation types

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 Produces periodic unbalanced force

 Unbalanced for can be approximately considered as sinusoidal in analysis

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 Impact machine

 Produces Impact load

 Example: Forge hammer

 Operating frequency: 60 -150 blows/min

 Dynamic loads reach in a very short time

Machine and Foundation types

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 Design: based on the theory of harmonic motion.

 Assume: (1) Soil-foundation system as an idealized lumped

parameter system (single mass, single spring, single damping for

each vibration mode), or (2) a circular rigid plate resting on an

elastic-half-space media.

Design basic

A lumped parameter system

An harmonic motion A Rigid plate on an elastic media

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 Vibrating machine foundation system: resist static, dynamic

 The basic goal in the design is to limit the dynamic motion, which

neither danger the machine nor disturbing working people.

Design basic

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 Basic design criteria

 For static loads

 No shear/bearing capacity criteria

 No excessive deformation/Serviceability

 For dynamic loads:

 No resonance (operating frequency and nature frequency should not similar).

 Dynamic displacement amplitude must be below the permissible value (given by machine manufacturer).

 Minimized unbalance forces and moments (mechanical engineers).

 The amplitudes : within the permissible limit (provided by manufacturer).

 Vibrating must not be annoying working people and no damage to adjoined structures.

 Other requirements:

 Water table should be below the foundation base [minimum below 0.5B (CP 2012-1), otherwise, use piled

foundation].

 Separated from other structures, component or other machine foundations.

 Foundation level should be below the level of adjoining structures.

 Acid-resisting coating needed for foundation

Design criteria

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 General considerations

 Site condition (soil characteristics, ground water level, topography, seismicity, climate condition….etc)

 Machine types (rotating, reciprocating, impact… etc)

 Machine configuration (machine size, machine type, operating configuration,…etc)

 Loading (static weight, dynamic force, testing, operating, shutdown…etc)

 Operational requirements (settlement, vibration amplitude and resonance criteria…etc)

 Frequency categories (after Bhatia, 2008):

 Very low frequencies: 0-100 rpm

 Low frequencies: 100 -1500 rpm

 Medium frequencies: 1500-3000 rpm

 High frequencies : greater than 3000 rpm

Design criteria

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Soil data (static, dynamic) Trial FND dimension

Static loads

Load combination

Vibration analysis Dynamic loads

Stability check Strength check

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 General flow chart for vibration analysis for foundation

Design criteria

Machine data

Soil data (static, dynamic)

Gravity calculation

Spring constant calculation

Trial FND dimension

Mass/ Moment of Inertia Cal.

Frequency Cal.

Resonance Check Machine speed

Vibration force FND Amplitude Cal Allowable amplitude Check

NG

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 Method of analysis model

 There are many methods that can be applied

 Most recent methods are:

 Elastic-half-space model: Based on linear elastic theory.

 Lumped Mass-Spring-Dashpot model: Based on Elastic-half-space theory (Richart and Whitman, 1970;.

 Linear elastic weightless spring model: based on subgrade reaction theory.

Design criteria

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 Degree of freedom of machine foundation

Design criteria

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 Minimum required machine data to be provided by Machine Manufacturer

Design criteria

Description of driving and driven

machinery

Detailed loading diagram including plan, elevation, magnitudes and direction of all loads acting on foundation

Details of all balance forces (external, couples, torques) with associated frequencies of vibration

Operating speed or speed ranges Detailed drawing showing the plate size, bolt

position or size of holding feet

Mass of Moment of inertia for X, Y Z direction

Number and arrangement of cylinders Minimum foundation size, foundation shape… Center of gravity position

Distance between main shaft and FND

Maximum rate out put Hydraulic force during operating Permissible natural frequency of the

system (machine + soil-foundation)

 Note: Machine data items listed above are minimum requirement Any further data requested by civil engineer for

foundation design should be provided by Machine Manufacturer.

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Design criteria

 Example of machine data and layout for a pump

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Design criteria

 Example of machine data and layout of a compressor

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 Dimensional criteria

 If done by foundation designer: must satisfy the general requirements (presented above)

 The foundation designer must evaluate the natural frequency of soil-foundation system as

well as the amplitude of the dynamic motion (vibration) under the service condition

Design criteria

 Foundation eccentricity

 Eccentricity: as the horizontal distance from the gravity center of the machine and foundation to

the center of foundation base area

 If very long foundation is used, eccentricity should be ≤ 2%

 Center of gravity of machine + foundation should be close to the foundation base

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Design criteria

 Soil bearing capacity (static load + dynamic load)

 For low speed machine: Applied 100 % allowable bearing capacity

 For medium speed machine: Applied 90 % allowable bearing capacity

 For high speed machine: Applied 80 % allowable bearing capacity

 For impact machine (crusher and hammer): Applied 50% to 70 % allowable bearing capacity

 For elevated foundation: Applied 70% allowable bearing capacity

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 Foundation material

Design criteria

• Concrete grade (28 days)

• Strength fck (MPa)

• Mass density (kN/m 3 )

• Poison ratio (for dynamic analysis

• Elastic modulus (typical values) (kPa)

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Design criteria

 Foundation mass ratio

• Total pedestal mass

• Ratio should not lesser than that of machine.

• Close to the mass of the machine

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Design criteria

 Minimum reinforcement requirement

 For block foundation: minimum steel quantity of 25 kg/m3 -50 kg/m3 of concrete

 For elevated foundation:

 Reinforcement for top-desk: 100 kg/m 3 – 120 kg/m 3 of concrete.

 For base : 70 kg/m 3 – 80 kg/m 3 of concrete.

 Minimum strength of re-bar shall be followed from standards (local codes, ASTM, BS standards…etc)

 Longitudinal bars : Rsn = 390 MPa (Grade A–III)

 Shear bars : Rsn = 235 MPa (Grade A-I)

 Steel welded wire mesh : Rsn = 490 MPa (Class Bp-I)

 Fatigue factors should be applied to consider the effect of dynamic loads

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 Vibration amplitude criteria (after Sulu and Nathan, 1976; Bhatia, 2008)

 Permissible amplitude by manufacturer is considered at machine level, whereas computed one is at

foundation based level

 Even calculated amplitude is acceptable for machine, it would be unacceptable for adjoin

structures/machines

 Similar machine might have different amplitude criteria

 If done by foundation designer: must satisfy the general requirements (presented above)

 Computed amplitude are always half amplitude, whereas given one are invariably double

 Following criteria off vibration amplitude must be applied:

Design criteria

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 Vibration amplitude criteria (after Richart et al., 1970; Blake, 1964, ACI 351)

Design criteria

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 Vibration amplitude criteria (after Baxter and Berhard, 1967, ACI 351)

Design criteria

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 Vibration amplitude criteria (Bhatia, 2008)

Design criteria

Foundation for rotary machine Permissible vertical amplitude (mm)

Low speed rotary machines (100 -100 rpm)

• Operating speed 100 -500rpm

• Operating speed 500 to 1500rpm

• 0.2 to 0.08

• 0.08 to 0.04 Medium speed machine (1500 -3000 rpm) • 0.02 to 0.04 High speed machine ( >3000 rpm) • 0.02 to 0.005

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 Vibration amplitude criteria (after Richart, 1970; Bhatia, 2008)

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 Vibration amplitude criteria (after Barkan, 1962)

Design criteria

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Design criteria

± 20%

 Resonance criteria

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Design criteria

 Resonance criteria

 Low for high speed machine and high for low speed machine

 Frequency of Soil-FND: minimum ± 20 % far away from the machine frequency

 Consideration to avoid possible resonance in practical (Das and Ramana, 2010):

 System frequency ≤ 0.5 × machine frequency ( speed ≥ 1000 cpm)

 System frequency ≥ 1.5 – 2.0 × machine frequency ( speed < 350-400 cpm)

 Increase FND weight  decrease possible resonant frequency

 Increase FND area  Increase possible resonant frequency

 Increase G of soil (soil improvement)  Increase resonant frequency

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Analysis tools

 Calculating by commercial software

(STAAD Foundation) (DYNA N)

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Analysis tools

 Example of calculation using STAAD FND

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Conclusions

 Based on the machine data given by machine manufacturers and Geotechnical investigation report

The foundations for vibrating machines can be designed

 Foundations for vibrating machines are subjected to static and dynamic loads

 Dynamic forces are much smaller than the static forces, but they are applied repeatedly

 Therefore, dynamic (vibration) analysis must be performed to ensure that the soil-foundation system

behaves as an elastic material during the life time of the machine Otherwise, the soil-foundationsystem will be deformed excessively under the dynamic force from the machine

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Question?

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Thank you for your attention

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