foundations for dynamic and sensitive equipment · foundations for dynamic and sensitive equipment...

Foundations for Dynamic and Sensitive Equipment

University of Minnesota - Structures Seminar October 30, 2015

Carl Nelson, Ph.D., P.E.

Tony Baxter, P.E.

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ESI’s History Our roots go back to a

group of professors and graduate students at the

U of M in the 1960’s

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Who We Are Today!

Minnesota based consulting engineering firm since 1970

Provide specialized engineering services

Specialists in high force/shock, vibration and noise control

From small medical devices and consumer products to sensitive buildings and large industrial facilities, ESI helps clients with advanced analysis and design. Our professional

engineering services are focused in the areas of structural dynamics and design, vibration control, noise and acoustics, and monitoring.

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FEA and Structural Analysis

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High Force Structures and Foundations

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Vibration Measurements and Monitoring

Vibration Analysis for Healthcare, Manufacturing and Research

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Recent Projects at U of M

Rec Center Expansion Cancer and Cardio Research Building

Physics and Nanotechnology Cleanroom Northrop Balconies

SE corner of clean

room floor

soil

drilled piers

(soil not shown)

N

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What we will talk about today

1. Types of Foundations for Equipment • Foundations for Sources • Foundations for Receivers

2. Vibration Control Methods for Foundations • In ground – Viper Example (Source), Physics & Nanotechnology

Cleanroom Floor Example (Receiver)

• Isolated – Toyota Example

3. Technical Discussion of Dynamic Foundation in Soil • Model, Equations • Example Calculations and Recommendations

4. References – ACI Committee 351, Books

5. Closing & Questions

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Types of Foundations For Equipment

1. Not Dynamic (Inertial Forces are Not Significant)

2. Foundations for Dynamic Sources a) Isolated b) On ground

3. Foundations for Sensitive Receivers a) Isolated b) On ground

Sources

Receiver

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?

Foundation Types - not dynamic -

Not Dynamic (Inertial Forces are Not Significant)

Multi-Axial Subassembly Testing (MAST) Laboratory

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React forces, provide a stable base and maintain alignment

Foundations For Dynamic Sources

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• React forces • Provide a stable base and maintain alignment • Minimize motion, on and off foundation

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Sensitive Receiver

K1 C1

M1

X1

Xg

Foundation

Soil

Foundation in Soil

2 MW

Generator

K1 C1

M1

X1

Xg

Foundation

Soil

K1 C1

M1

X1

Xg

Foundation

Soil

K2

M2

C2

X2

K1

K2

M2

C2

C1

M1X1

X2

F2(t)

M3

Press

Tub and Soil

Press and

foundation

Tub and soil

Foundation

Dynamic Source

Fou

nd

atio

n in

Gro

un

d

Iso

late

d F

ou

nd

atio

n

The Concept of Transmissibility

0.00001

0.0001

0.001

0.01

0.1

1

10

100

0 1 10 100

Fo

rce O

ut/

Fo

rce In

f/fn

Force Transmissibility

0

0.01

0.05

0.1

0.2

0.5

1

2

Fraction of Critical Damping

F

Fground

xground

/groundT F F

/ groundT x x

Transmissibility applies (exactly the same equation!) to both source force transmissibility and receiver displacement transmissibility

Receiver

Source

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Foundations for Dynamic Sources

actuators

Test item

Soil Supported Viper Test Rig at Virginia International Speedway

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Foundations for Dynamic Sources

Soil Supported Viper Test Rig at Virginia International Speedway

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Foundations for Dynamic Sources Air Mount Isolated with Foundation

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High force

Mass

Air Springs

- Attenuated force transmitted to foundation - Minimize motion at actuator base

Foundation Isolation with Air Mounts

Soil Supported Foundations for Sensitive Receiver Overview of Concepts

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Engineered Fill

Slab

1. Simple Thick Slab on Ground – Wavelength Effect

2. Isolated Slab for Electron Microscopy Center - Shepherd Laboratories

Bedrock

Sand

Thick Slab

Criteria 125 u"/s --- Measured > 300 u"/s

Tall

“Isolated” Caissons

Slab-on-Grade

Typical Wavelength = 50 - 100 ft

Bedrock

Sand Auger

Cast Piles

3. Physics and Nanotechnology Cleanroom – U of M

Air Space

Floor Structure Criteria 125 u"/s --- Measured ~ 100 u"/s

Foundations for Sensitive Equipment Isolated with Various Types of Isolators

Sensitive Equipment Isolation Techniques

Air Mounts (<2 Hz) Steel Springs (2-5 Hz) Resilient Pad or Sheets (>6 Hz)

Entire Building Isolation Drachen-Center Basel Switzerland

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22

Rigid Foundation on Elastic Halfspace

under harmonic loading

, ,G

,or m

( ) i t

oP t P e

What do all these foundations have in common?

Two Minutes on Elastic Wave Propagation

P Waves – Compression (fastest) S Waves – Shear Rayleigh Waves – Speed close to that of S waves

Amplitude decreases with

Accounts for 2/3 of the energy

(See Figure 3-16 on p. 91 in Richart, Hall, and Woods)

s

G

V

2

P

G

V

1

r

(1 )(1 2 )

E

23

24

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Predicting Vibration Versus Distance

0 15 30 45 60 75 90 105 1200

0.02

0.04

0.06

0.08

0.1

0.12

LRT Vibration Amplitude vs. Distance

Dista nce - Fe et

Vib

ration

Am

pli

tude

- Inch

es/s

econ

d

.12

0.002

.z( )r 12

.z g( )r 12

.z lim 12

1205 r

Geometric Damping Only: z g( )r .z 1

r 1

r

Geometric & Material Damping: z( )r ..z 1

r 1

rexp . r r 1

Early Boussinesq (1885), Lamb (1904) – static, dynamic load on the surface of elastic halfspace Riessner (1936) – Dynamically loaded, rigid circular foundation on elastic halfspace Lysmer and Richart – “Dynamic Response of Footings to Vertical Loading,” ASCE Journal of the Soil Mechanics and Foundations Division, January 1966. “Lysmer’s Analog” Numerical Methods Many Contributors – FEA, Boundary Element Method Beskos and Co-Workers and the University of Minnesota (1970s-80s)

Some History Development of Techniques

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Winkler Foundation Plate on Elastic Halfspace Rigid Plate on Elastic Halfspace

Lysmer’s Analogue (1966)

Complicated! Still Complicated!

But…

Approaches to the Dynamic Foundation Problem

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Lysmer’s Analog

( )i tP

F ek

1 2( ) ( ) ( )iF F F

F is a dimensionless displacement function with real and imaginary parts

2

2 2 2 2

1( )

(1 )

(1 ) (1 )

o o

o o o o

i

i

Ba aF

Ba a Ba a

2 2 2

1

(1 )o o

M FBa a

Textbook so far, but with slightly unfamiliar notation

( ) i t

oP t P e

Magnification Factor

2n

o

ca

k

2

k mB

c

Introducing the dimensionless ratios

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Model

Static vertical stiffness

Dimensionless frequency

Dimensionless mass

Equation of motion

Lysmer’s Analog

Simple Damped Oscillator

2n

o

ca

k

2 2 2

1

(1 )o o

FBa a

2

k mB

c

4

1

oG rk

, ,G

,or m

Rigid Circular Foundation on Elastic Halfspace

oo o

sG

ra r

V

2

24

1s

o o

Vm mB

k r r

k

( ) i t

oP t P e ( ) i t

oP t P e

1 1s

i too

V

k rm c k k P e

i t

om c k P e

o

s

rck V

o

s

rkc

V

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Lysmer’s Analog

, ,G

,or m

( ) i t

oP t P e

1 1s

i too

V

k rm c k k P e

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Magnification Factor vs. Frequency and Mass Ratio

2 2 2(

1

(1 ) 0.85 )o o

M FBa a

oo

s

ra

V

24

1

o

mB

r

0.5B

0B

1B

5B

2B

See Fig. 11 of Lysmer (1966) to see how well this compares to the elastic halfspace solution

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Sample Calculations Reciprocating Compressor

oo

s

ra

V

2 2 2(

1

(1 ) 0.85 )o o

M FBa a

0.5B

0B

Note that B will generally be in

this range

Soil properties, medium dense silty sand

Vs 750ft

s 115

lbm

ft3

G Vs2

13962psi

Sallowable 2000psf 0.35

Foundation pad properties

L 25 ft b 15 ft rob L

10.925ft t 4.5 ft

Wf ro2

t 150 pcf 2.531 105

lbf

k4 G ro

1 11.26 10

6

lbf

in

Vertical stiffness

Compressor Weight

Wequip 50000lbfWf

Wequip

5.062 >5

Wf Wequip

b L808psf < 0.5Sallowable 1000psf

mWf Wequip

g Total mass of foundation plus equipment

B1

4

m

ro3

0.328Mass ratio

fn1

2

k

m 19.06

1

s Vertical natural frequency

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Sample Calculations More Plots

20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1

0.036

M i

1001 f i

Hz

1 10 1000.01

0.1

1

M i

f i

Hz

Mi

1

1

fi

fn

2

2

0.85aoi

2

fn 19.06Hz

In terms of actual frequency…

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Sample Calculations

o

PM

k

Let’s get down to some real numbers. Suppose that the compressor exerts a vertical force of 4500 lb at a frequency of 600 rpm (10 Hz).

P 4500lbfP

k3.99 10

4 in in 10

6in g 10

6g

20 40 60 80 1000

1 104

2 104

3 104

4 104

Displacement vs frequency

Frequency (Hz)

Dis

pla

cem

ent (i

n)

P

kM i

in

f i

Hz

20 40 60 80 1000

10000

20000

30000

40000

Velocity in micro in/sec vs frequency

Vel

oci

ty (

mic

ro in

/sec

)

2 f iP

k M i

in

s

f i

Hz

20 40 60 80 1000

5000

10000

15000

Acceleration in micro g's vs frequency

Acc

eler

atio

n (

mic

ro g

's)

2 f i 2 P

k M i

g

f i

Hz

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Sample Calculations

Let’s see how this compares to some vibration criteria

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Sample Calculations

Forces exerted by seismic tables with heavy specimens can be large

The system shown above has a 4m x 4m table with 8 actuators. The four vertical actuators are capable of generating a total of 343 kN (77 kips) at frequencies

from 1 to 30 Hz.

Note the size of the foundation mass reacting the actuator forces..

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Case Study Foundations for Sensitive Equipment- Soil Supported

Physics and Nanotechnology Clean Floor Design at U of M

Project / Location: P1721- U of M Physics & Nanotech Building Measurement ID: File: TEST004.AE2 Record Date and Time :12/20/2010 1:35:53 PM

Date: 20-Dec-10 Channel 3: Sidewalk NW corner

Conditions: Delivery truck leaving by CH 4 Channel 4: Asphalt SW corner

Setup: 90% overlap, hanning window, delta f = 0.125 Hz Vibration Criteria VC-C (green), VC-D, VC-E

Channel 3 Trigger Channel 4 Trigger

Channel 3 Peakhold Spectrum Channel 4 Peakhold Spectrum

-0.20

-0.10

0.00

0.10

0.20

0 1 2 3 4 5 6 7 8

Acce

lera

tio

n (in

/s2)

Time (s)

-0.2

-0.1

0.0

0.1

0.2

0 1 2 3 4 5 6 7 8

Acce

lera

tio

n (in

/s2)

Time (s)

12.5, 289

10

100

1000

1 10 100

Ve

locit

y (m

icro

-in

/s r

ms)

Freq (Hz)

12.5, 460

10

100

1000

1 10 100

Ve

locit

y (m

icro

-in

/s r

ms)

Freq (Hz)

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Measurement Locations

Sample of Ground Vibration Measurements Prior to Construction

N

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Auger Cast Pile Placement

Pile Top and Floor Detail

Foundation Plan

1/3 Octave Velocity vs. Frequency

Floor Response at Vistec-E-Beam

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35 40

Frequency (Hz)

Ve

loc

ity -

(in

/se

c)

Predicted Response at 75





VC-E

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SE corner of clean

room floor

soil

drilled piers

(soil not shown)

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Predicted Velocity on Cleanroom Floor

FEA Model (COSMOS)

ACI Committee 351 – Foundations for Equipment and Machinery

Active Committee Documents: • 351.1R-12: Report on Grouting between Foundations and Bases for Support of Equipment and Machinery • 351.2R-10: Report on Foundations for Static Equipment • 351.3R-04: Foundations for Dynamic Equipment • 351.4-14: Specification for Installation of Cementitious Grouting between Foundations and Equipment Bases • 351.5-15 Specification for Installation of Epoxy Grout between Foundations and Equipment Bases Documents Under Development: • 351.3R: Foundations for Dynamic Equipment • 351.4M-14: Specification for Installation of Cementitious Grouting between Foundations and Equipment Bases • 351.5M-15: Specification for Installation of Epoxy Grouting between Foundations and Equipment Bases

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Wrap Up

Important Topics We Have Not Talked About Today Rotational and Horizontal Modes Embedment Effects Strength Requirements Anchorage Numerical Methods/Software Questions? Thank you for inviting us!

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