Foundations for Vibrating Machines
1.
Trial Sizing of Block Foundation:
The bottom of the block foundation should be above the water table,
wherever possible. In addition, block foundation should not rest on backfilled
soil or on soil sensitive to vibration.
Block foundation resting on soil should have a mass of 2 or 3 times
the supported mass for centrifugal machines, and 3 to 5 times for reciprocating
machines.
Top of the block foundation is usually kept 300 mm above the
finished floor to prevent damage from surface water runoff.
The thickness of the block foundation should not be less than 600
mm, or as dictated by the length of the anchor bolts. In any case, the
thickness of the block shall not be less than 1/5 of the least dimension and
1/10 of the largest dimension of the foundation in plan, whichever is greater.
The block foundation should be widened to increase damping in
rocking mode. The minimum width should be 1 to 1.5 times the vertical distance
from the machine base to the machine center line.
The plan dimensions shall be such that the block foundation extends
at least 300 mm beyond the edge of machine for maintenance purposes.
The length and width of the block foundations shall be such that
plan view eccentricities between the center of gravity of combined
machine-foundation system and the center of resistance (center of stiffness)
should be less than 5% of plan dimensions of the foundation
Should the dynamic analysis predict resonance with the machine
frequency, the mass of the block foundation shall be increased or decreased so
that the modified foundation is over-tuned or under-tuned for reciprocating and
centrifugal machines respectively.
The footing area shall be such that the soil bearing pressure under
the combined dead load of the machine and foundation shall not exceed 50% of
the allowable value.
Combined static and dynamic loads shall not create a bearing
pressure greater than 75% of the allowable soil pressure given in the
geotechnical report.
2. Equivalent static loading method: (for design of foundations for machines
weighing 10,000 lb (45 kN) or less
Static Loads:
Reciprocating Machines:
The weight of the machine and the self weight of foundation block,
the live load of platforms and any other loads on the foundation.
Unbalanced forces and couples supplied by machine manufacturer.
Centrifugal Machines:
Vertical pseudodynamic design force is applied at the shaft, it can
be taken as 50% of the machine assembly dead weight.
Lateral pseudodynamic forces representing 25% of the weight of each
machine, including its base plates, applied normal to its shaft at mid point
between end bearings.
Longitudinal pseudodynamic forces representing 25% of the weight of
each machine, including its base plates, applied along the longitudinal axis of
the machine shaft.
Vertical, lateral, and longitudinal forces are not considered to
act concurrently.
3. Dynamic Analysis:
Velocity = 6.28 f (cycles per second) x displacement amplitude.
Compare with limitation values for 'good' operating condition.
Magnification Factor (applicable for machines generating unbalanced
forces). The calculated value of M or Mr should be less than 1.5 at resonant
frequency.
Resonance: The acting frequencies of the machine should not be
within a 20% of the resonant frequency (damped or un-damped).
Transmissibility Factor: It is usually applied to high frequency,
spring-mounted machines. The value of transmissibility factor should be less
than 3%.
Resonance of individual components (supporting structure without
the footing) shall be avoided by maintaining the frequency ratio either less
than 0.5 or greater than 1.5.
For pile foundations, the effects of embedment are often neglected.
Floating piles have lower stiffness but higher damping than end-bearing piles
Unbalanced forced for centrifugal machines:
1). from balance quality by manufacturer:
e = Q / w (mm)
F_{0} = m_{r}.e.w^{2}.S_{f}
/ 1,000 (N)
F_{0} - dynamic force (N)
m_{r} - rotating mass (kg)
e - mass eccentricity (mm)
w - circular operating
frequency (rad/s)
S_{f} - service factor, = 2
Q - Balance quality, i.e. for G6.3, Q = 6.3
2). from empirical formula:
F_{0} = W_{r}.f_{0} / 6,000
f_{0} - operating speed (rpm)
W_{r} - weight of rotor (N)
For DYNA5, F^{*} = F_{0} / w^{2}
4. Drive torque:
NT = 5250 (P_{s}) / f_{0} (lb-ft)
NT = 9550 (P_{s}) / f_{0} (N.m)
NT - normal torque (m-N)
P_{s} - power being transmitted by the shaft at the
connection, horsepower(kilowatts)
f_{0} - operating speed, (rpm)
5. Misc. items
1 mil = 0.001 in. = 25.4 microns ( 1 micron = 10^{-6})
In foundation thicker than 4 ft (1.2m), the minimum reinforcing
steel is used (ACI207.2R), or a minimum reinforcing of 3.1 lb/ft^{3} (50
kg/m^{3} or 0.64%) for piers and 1.91 lb/ft^{3}(30 kg/m^{3}
or 0.38%) foundation slabs. For compressor blocks, 1% reinforcing by volume.
For dynamic foundation, epoxy grout should be used
Anchor bolts should be as long as possible so that the anchoring
forces are distributed lower in the foundation or ideally into concrete mat
below the foundation pier
For compressor foundation, post-tensionin anchor bolts are used to
prevent the generation of crack. the embeded end is anchored by a nut with a
diameter twice the rod diameter and a thickness 1.5 times the rod diameter,
minimum anchor bolt clamping force of 15% of the bolt yield strength is
required
6. Reference: ACI351.3R