VERTICAL FORCES CAUSE VIBRATION IN A RECIPROCATING COMPRESSOR

Brian C. Howes, M.Sc., P.Eng. Valerie A. Zacharias, M.A.

ABSTRACT of the forces from all of the crossheads is zero.

Such an analysis can be misleading.
It is well known that forces that cause vibrations in This paper describes the origin of these forces,
reciprocating compressors arise from a number of discusses their practical implications, and presents
sources. These include unbalanced reciprocating examples.
forces and moments, piping system pulsations, and
cylinder stretch. Reliable and efficient reciprocating INTRODUCTION
compressor installations will result from including the
effects of all forces in the design calculations. Recent field trouble-shooting experiences have
shown severe vertical vibration problems in certain
Evidence from field trouble-shooting indicates that reciprocating compressor installations. The severity
force mechanisms operating in the vertical direction of these vibration problems was made worse by the
in horizontal cylinder assemblies can cause presence of mechanical resonance.
significant vibration. Therefore, a design that
ignores these potential sources of vibration In the first case, lack of attention by the designers to
problems (as is common) may be inadequate. the potential for large vertical shaking forces
between cylinders and pulsation dampener bottles
One such vertical force is caused by pressure aggravated the problem.
pulsations acting on the suction and discharge
cylinder nozzle areas and bottles. While the nozzle In the second case, vertical forces acting through
areas are generally equal, the differing pulsation the crosshead guides appear to have contributed to
amplitudes and phases result in net vertical forces high vibrations.
on the cylinder. This paper presents a proposal for
enhancing the API 618 guideline for pulsation PRESSURE PULSATION GUIDELINES
control in reciprocating compressors. Currently, the
compressor side guideline is higher than the line The shaded areas on each graph (Fig. 2 – 7)
side guideline and disregards frequency. The indicate acceptable pulsations based on the
proposed guideline incorporates frequency and adds American Petroleum Institute standard (API 618).
a limit based on vertical shaking forces that could be
generated in a cylinder. Compressor Side

A second vertical force in a horizontal cylinder The time domain curves show the compressor side
assembly arises because the connecting rod motion pulsation limit (CPL), which shall be the lesser of
is not purely horizontal. The slider-crank mechanism
generates a time-varying force perpendicular to the  7% of average absolute line pressure, OR
motion of the piston through the crosshead guide.
Which varies with the crankshaft angle, the l/r  3R% of average absolute line pressure, where R
(connecting rod to crankshaft pin radius) ratio, the is stage compression ratio.
gas forces, and the reciprocating inertia. These
vertical crosshead forces are sometimes contained The purpose of the CPL is to avoid pressure-volume
by the foundation, but in some applications the curve distortion. It does not address concerns about
stiffness under the crosshead guide is too low, and vibration or compressor valve life.
high vibrations result. In many cases, a rigid body
analysis of these forces shows that the vector sum

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Lineside  high vibrations were observed on the

concrete pedestal under the outboard
The frequency domain curves show the API lineside cylinder support.
design pulsation limit (DPL):
Measurements
P Excessive rod loads were ruled out as a cause of the
DPL = 3● breakage, because rod loads during the tests were
ID  f within or at the manufacturer’s guidelines.

Where DPL = maximum allowable peak to peak level Pulsations were measured in the time domain at the
of pulsation at discrete frequencies, suction and discharge valve caps (Fig. 2 & 3).
P = average absolute line pressure,
ID = inside pipe diameter (inches), Suction side pulsations were within the compressor
f = pulsation frequency (Hertz). side guideline (CPL), while discharge side pulsations
The purpose of the DPL is to avoid high unbalanced were about 120% of the guideline.
forces due to pressure pulsations.

CASE 1 – SINGLE STAGE FOUR THROW

COMPRESSOR

The Problem

Two four throw compressors had been experiencing

failures of pistons and rods over some years. On a
visit to the site in February, 1994, the following
problems were found:
 cylinder supports were loose or broken

 discharge bottle wedge supports were

broken

 joints had fretted, shown by red dust (iron

oxide) present at most of the joints in the Figure 2 Suction side overall pulsation was within
cylinder supports guideline.

 anchor bolts and grout under the crosshead

guide had broken

Figure 1 Rod and piston failures over many years Figure 3 Discharge side overall pulsation was
made this unit uneconomic to run. about 120% of guideline.

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Figure 6 The orifice plate significantly reduced

Figure 4 As-found spectrum on the suction side pulsation levels.
shows high pulsation at 7X shaft speed.

Modifications to the System

A spectrum of the as-found suction valve cap
pulsation is shown in Fig. 4, and of the discharge As-left readings (Fig. 6 & 7) were taken after orifice
valve cap pulsation in Fig.5. plates were installed in both the suction and
discharge nozzles. As shown in Fig. 7, the as-left
The DPL is included as a reference in each plot, pulsation at the seventh order on the discharge side
since there is currently no recognized pulsation limit still exceeded the line side guideline by about 3X,
based on discrete frequencies for the compressor even though it was only about 20% of the as-found
side piping. In both cases, the DPL has been greatly reading.
exceeded at seven times crankshaft speed (7X).
Three years later, the compressor is still working
well.

Figure 5 As-found spectrum on the discharge side

shows pulsation at 7X shaft speed is Figure 7 The orifice reduced pulsation at 7X to
about 15 X DPL. about 20% of as-found; still three times
DPL.

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Figure 9 The maximum unbalanced force occurs

when pipe length equals half wave length.

Figure 8 Vertical forces due to pulsation can Note that over the short length between the cylinder
develop between the cylinder and the and the bottle, there is very little change in pressure
bottle. amplitude at low frequencies (Fig. 9). The
unbalanced force generated in short pipe runs by
Vertical Forces Between Bottle and Cylinder pressure pulsations at low orders of run speed (long
wave lengths) will be much lower than at higher
Figure 8 shows a cross-section of the suction and orders, all other things being equal.
discharge bottles and cylinder on one side of the
machine. The standing wave pattern of the pressure Proposal for Additional API 618 Guideline
pulsation carries from the valves through the cylinder
gas passages and the cylinder nozzle into the bottle, That proposed guideline prevents design conflicts
on each side of the cylinder. There is no direct that arise between the CPL and the DPL in the piping
connection between the two standing waves, between the bottles and the cylinder.
because the suction and discharge valves are never
open at the same time. In Beta’s experience, the DPL is too restrictive to be
applied to the piping between the bottles and the
There is a difference between the amplitude and cylinders. It is generally acceptable to have low
phase of the pulsation at different points on the frequency (long wave length) cylinder side pressure
standing wave. pulsations that meet CPL but exceed DPL. If the
DPL were applied, unnecessary and uneconomic
Varying pressure acting on an area produces a design changes would be required in many cases.
varying force. In the vertical direction, the areas of
concern are the projected areas of the inside Pressure pulsations by themselves do not shake the
diameters of the suction and discharge nozzles (Fig. compressor. It is the forces generated because of
8) on the bottle and the cylinder passages. pulsations that cause vibration problems. For this
reason, we propose that compressor designs should
A computer model was used to predict pulsations, limit potential transverse (vertical in horizontal
and the model was verified with field measurements cylinders, horizontal in vertical cylinders) unbalanced
(Figs. 5 – 7). The worst vertical forces in the forces, not just pulsations. This force guideline is a
discharge nozzles were calculated to be about 7000 compromise between ignoring the transverse forces
pounds peak to peak (pk – pk) and in the suction on the compressor side of the pulsation bottle and
nozzles about 1100 pounds pk – pk) and in the using the more restrictive (and likely uneconomic)
suction nozzles about 1100 pounds pk – pk, both at DPL guideline. It should be used with the CPL.
the seventh order. It is clear that these forces are
sufficient to cause the problems found.

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Unbalanced Force Guideline

CASE 2 – SINGLE STAGE, SIX THROW
Unbalanced forces are calculated according to the COMPRESSORS
equation below, (where the pressures are vectors).
The three units (Fig. 11) are large variable speed
Force = (area 1 x pressure 1) – (area 2 x pressure 2) horizontal compressors, mounted on skids bolted to
3 ft. thick concrete foundation blocks. The
On the basis of empirical studies, the following foundation blocks are embedded into the sandy soil.
staged unbalanced force guidelines are proposed: No piles were used.

 Avoid coincidence between the vertical

mechanical natural frequency of the cylinder
bottle system and any peaks in the vertical
unbalanced force spectra.

 Limit unbalanced forces in the cylinder nozzles at

any discrete frequency as follows:

1) the lesser of 500 lbs. Or 50 X nominal

diameter (inches) maximum pk – pk on either the
suction or the discharge side.

2) if 1) is exceeded, the arithmetic sum of the

suction and discharge forces should be less than
1000 lbs. Or 100 X nominal diameter pk pk.

3) If 2) is exceeded, the vector sum of suction Figure 11 Elevation view, with operating deflected
and discharge forces should be less than 1000 shapes (ODS) at resonance.
lbs or 100 X nominal diameter pk – pk.

 If 3) is exceeded, the forces must be reduced. The Problem

To illustrate, one can calculate from the equation in The units are equipped with vibration sensors, which
Fig. 9 the allowable pulsations for a particular indicated excessive vibration. Supporting the exciter
system, as shown in Fig. 10. The CPL is too high to to the foundation had not helped.
control vibration; the DPL is too stringent.
Measurements

The highest vibration occurs near the top of the

speed range at twice shaft speed in the vertical
direction outboard on the exciter.

The foundation exhibits a resonance near the top of

the runspeed range. The modal damping of the
foundation was estimated from vibration
measurements to be about 3% of critical damping.
The foundation vertical vibrations had node points
located at the mid points of the motor and the
compressor.

Operating deflections (Fig. 11) showed that the

exciter was amplifying the motion of the motor-
Figure 10 The proposed frequency-based
compressor-foundation system due to geometry
compressor side pulsation limit is a
effects.
compromise.

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Vibrations were not significantly different between

loaded and bypass conditions. Therefore, pulsations
were ruled out as a cause of the problem.

The shaft alignment of the unit was checked and

found to be acceptable. A small improvement in
alignment had no effect on vibration levels.

Modelling of the System

The motor-compressor-skid system had been

modelled in the design stage. The foundations had
been assumed to be rigid, an assumption which
proved to be incorrect.

A new finite element model of the system was Figure 12 Slider-crank mechanism generates
created following start-up, and after the problem had vertical force.
been identified. Using the model to test the effect of
changes showed that the skid-foundation resonance
is very hard to change without major modifications.

Modelling proved to be very valuable in the sense

that it indicated that doing a major change that made
intuitive sense would not have worked. The skid has
a weak shear connection to the concrete. It seemed
obvious that a continuous grout connection between
skid and concrete would stiffen the system, raise the
natural frequency, and solve the problem.

The model quickly showed that the stiffening effect of

the grout would be counteracted by moving the mass
of the motor and compressor farther away from the
neutral axis of motion. The rotational inertia of the
motor and compressor would be made more
influential on the mode, lowering the natural
Figure 13 Substantial vertical forces are generated
frequency and counteracting the stiffening effect.
by the motion of the crosshead
Analysis
torsional mode about the centreline of the crankshaft
It was unclear what force could be present in the
with a node in the middle of the compressor, the
system at 2X shaft speed that could cause such
couple shown in Fig. 14 would have caused high
vibrations, even with the foundation resonance since
vibration.
it was reasonably well damped.
Upon reflection, it was realized that the offset
Figure 12 illustrates the source of vertical force at the
between cylinders (Fig. 15) causes the forces in the
crosshead. Figure 13 shows the vertical force versus
opposed pairs (e.g. throws 1 & 2 or 5 & 6) to produce
crank angle for this compressor at the cylinder 1
another couple, this one about an axis parallel to
crosshead. These vertical forces were considered
piston motion. If the foundation behaved as a rigid
and initially rejected as a source of the problem,
body, the three couples from the three pairs of
since they are all equal in magnitude and vectorially
throws would cancel.
cancel due to the phasing of the 6-throw crankshaft
(120 degrees between throws).
In this case, the out-of-phase motion of the
foundation at twice crankshaft speed allows the
Figure 14 shows how the crosshead forces can
couples to excite the mode.
cause the compressor to rock. Had there been a

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SUMMARY

Vertical forces in compressor cylinder-to-bottle

nozzles need to be considered in the design stage.
Since there is no suitable design guideline currently
available for these forces, one is proposed.

Slider crank mechanisms produce forces transverse

to the crosshead guide or cylinder. These forces
should be considered in the design of reciprocating
machinery systems.

FURTHER WORK
Figure 14 Crosshead forces produce a couple
about the centreline of the crankshaft. Consideration should be given to enhancing the DPL
guideline to include unbalanced forces, or even to
replacing the DPL guideline with an unbalanced
force guideline. In many instances, the DPL by itself
is too strict or too lenient, depending on how the
pulsations couple with the pipe lengths.

REFERENCES

Reciprocating Compressors for General Refinery

Services. API Standard 618. Third Edition.
American Petroleum Institute, Washington, 1986.

Reciprocating Compressors for Petroleum, Chemical,

& Gas Industry Services. API Standard 618. Fourth
Edition. American Petroleum Institute, Washington,
Figure 15 Side view of compressor – offset 1995.
cylinders generate moments.
Reports 1440, 1453, 1510, 5167, Beta Machinery
Analysis Ltd. Various dates.
Modification
THE AUTHORS
The amplitude of the vibrations was reduced by 30%
The two authors are employed by Beta Machinery Analysis Ltd.
by stiffening the connection of the motor end bells to Brian Howes obtained his M.Sc. in Mechanical Engineering in
the skid, using jacking bolts. This modification did 1972. His experience includes trouble-shooting on a wide variety
not change the frequency of the peak response. It of high end equipment, research and development in pulsation
appears that no complete solution is possible except and vibration of piping systems, and analysis of mechanical and
structural systems so as to ensure acceptable static strength and
by changing the foundation natural frequency. dynamic response. He is Beta’s Chief Engineer.

Conclusions – Case 2 Valerie Zacharias obtained her M.A. in Communications in 1978,

and did a postgraduate year in Computer Science in 1979. Her
experience includes acoustical modelling of reciprocating
The forces and moments in a reciprocating compressors, and ten years in the predictive maintenance
compressor do not necessarily cancel. In particular, business, primarily in customer service, training, and
when the unit is not mounted on a rigid body, modal communications. Mrs. Zacharias handles Customer Service.
excitation may result. Care must be taken when
designing compressor foundations to avoid natural
frequencies at one and two times crankshaft speed.

It is also clear that vertical forces at crossheads

should be considered when trouble-shooting
vibration problems in the field.

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