Reciprocating Machine

In a reciprocating machine, pressure-waves are largely a response to accelerations.

From: The Air Engine, 2007

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Pipe expansion and flexibility

Maurice Stewart, in Surface Production Operations, 2016

10.8.2 Mechanical induced vibration Basic considerations

Unless reciprocating machine parts are balanced by parts of equal weight moving in the opposite direction, forces will be applied to the machine case through the bearings. These forces result in vibration, and even a perfectly balanced compressor will vibrate if connected to an internal combustion engine that is not balanced. An oscillating force is applied to the piping through connections to the machine. Pipe's natural frequency

Every object has a natural frequency at which it will vibrate. If excited at this frequency, the motion that results is amplified. Being excited, pipe vibrates much like a guitar string, and the bending moment applied to the pipe by motion may cause a stress that exceeds the pipe's cyclic endurance stress. In other words, the pipe stress is greater than the endurance limit of the pipe material, and the pipe will eventually fail from fatigue. Vibration analyzer

In analyzing a vibration to determine the source, a mechanically resonant motion can sometimes be identified by the fact that a relatively small force on the center of the pipe span will reduce the motion. This occurs because the force changes the natural frequency of the span. If the vibration is caused solely by pulsation or acoustic pressure waves, the forces necessary to restrain the motion would usually be great because the excitation force is located at coupling points in the pipe and is not externally controllable. A vibration analyzer is essential to determine forces, frequency, and displacements of vibrating equipment.

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Beyond the performance envelope

Allan J. Organ, in The Air Engine, 2007

13.1 Introduction

The underlying principle of Stirling engine operation amounts to biasing a mass of working fluid towards a cold space for a process of overall compression, and subsequently biasing it towards a hot space and allowing an overall expansion.

The biasing process is achieved largely by positive displacement between the two variable-volume spaces – ‘largely’ because flow resistance causes non-uniformity of pressure distribution, and so influences the distribution of density, and thus of mass.

There is an additional influence: pressure information propagates in the form of waves, and the speed at which it does so is limited. The consequences are minimal in engines charged with light gases such as hydrogen and helium, where acoustic speed is high. However, when the working fluid is air the phenomenon is readily provoked and recorded experimentally (see Organ 1992 text, p. 189 and Rix 1984).

In a reciprocating machine, pressure-waves are largely a response to accelerations. All other things being equal, raising rpm increases the accelerations of piston and displacer. This changes the phase of pressure disturbances relative to the angular position of the crankshaft and generally* increases their amplitude.

There are two implications for the performance potential of the air engine:


Power output is the product of work per cycle with cycle frequency. A modest value of cycle work can amount to high power output if rpm can be elevated.


Peak rpm of the Philips MP1002CA air-charged engine coincide (see Chapter 14) with the threshold of compressibility effects in the regenerator. The ‘obvious’ deduction is that work/cycle suffers by operating in the compressible region.

Before supersonic flight became a reality there appeared to exist a sound ‘barrier’. It is now appreciated that the barrier was imposed by lack of insight rather than by aerodynamic limitations. There is, to the writer's knowledge, no theorem prohibiting the design of closed-cycle, air-charged regenerative engines from exploiting compressibility effects rather than being limited by them.

No reason, that is, except:

that the computational tools for flow at elevated Mach numbers have not been much exercised in the present context

for the paucity of relevant flow friction and heat transfer data – a problem which is now duly recognized, but which these chapters have only just begun to address

The first point can be comprehensively tackled on the basis of arbitrary correlations while the definitive replacements are awaited. This chapter accordingly adapts the numerical modelling tools of classic, unsteady compressible flow to the context (boundary and operating conditions) of the Stirling engine. An air-charged, opposed-piston design is explored having a gas path 1 m long and operating at resonance at 12,500 rpm. On the basis of the provisional data, the numerical model predicts that a volume phase angle in the region of 180° is required for achievement of net positive indicated work. At this condition, the traditional contributions of expansion and compression spaces are reversed – compression space work is larger and positive, while expansion space work is smaller and negative. At the rpm called for by operation in this mode, a small value of work per cycle converts to significant indicated power.

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What Carnot efficiency?

Allan J. Organ, in The Air Engine, 2007

2.4.4 Unsteady flow – impedance (or admittance)

The cyclic flow in reciprocating machines is inherently unsteady. Unsteady flow proceeds by wave motion. At any point in a closed system, such as the gas path of the Stirling engine, the pressure–time history is in terms of two waves travelling in opposite directions. The interruptions in the regenerator flow passages are sites for wave reflections. Right- and left-travelling waves each comprise a near-infinity of reflected and re-reflected components. Finite time of traverse results in a phase shift between the pressure waveform at one piston face and that at the opposing face. The viscous effects of real flow modify the extent of the phase shift, and cause the pressure amplitude at one piston face to differ from that at the opposite piston face.

The phase shift is frequency-dependent, i.e., it is insignificant at low values of the parameter Lf/a: L is net gas path length, f is frequency (rpm/60) and a is acoustic speed. At high values of Lf/a, phase shift can assume the same order as volume phase angle α. This suggests characterizing the regenerator in terms of an ‘impedance’ (or ‘admittance’), and treating it as a reactive component in an a.c. circuit rather than as a series resistance of a dc circuit.

The author's 1997 text analyses the uniform-temperature case in terms of linear waves, and includes experimental pressure records in support. The approach is not readily modified to handle the severe temperature gradients of the regenerator under service conditions, although attempts to do so (Organ 2001) suggest that the effect of the gradient is to compound asymmetries (e.g. Rix 1984) inherent in the gas processes. Data to CfRe format do not convert to admittance form, so to date there is no link to the three sciences of steady flow.

Stirling engine technology draws heavily on Kays and London rather than on Pinker and Herbert, or on Forchheimer, or on any recognition of the capacity of unsteady flow for reactive behaviour. Had the start-point been, say, Pinker and Herbert, then performance predictions would be somewhat different – but not, as has been argued, necessarily more accurate or more relevant. The face-saver is that the regenerators of the ‘benchmark’ engines – GPU-3, V-160, P-40 etc. – have not, as far as can be ascertained from the literature or from reverse-engineering, been designed at all. To this extent, there is no wrong choice to get worked-up about.

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Electricity generation

I G Crow BEng, PhD, CEng, FIMechE, FIMarE, MemASME, K Shippen BSc, MBA, CEng, MIMechE, in Plant Engineer's Reference Book (Second Edition), 2002 Maintenance

The diesel engine, being a reciprocating machine, is mechanically complex, and in arduous environments its wear rate can be high. Major overhauls on high-speed engines are usually stipulated at 15 000 running hours, which extends to 20 000 and 30 000 on medium- and low-speed machines, respectively.

The major class of failure concerns the fuel supply and fuel-injection equipment followed by the water-cooling system, valve systems, bearings and governors. Collectively, these five categories account for some 70% of all engine stoppages. Thus the maintenance programme must take careful cognizance of these areas together with the manufacturer's recommendations. Under arduous conditions where fuel quality is questionable, where there are high dust levels or where the machine is subject to uneven and intermittent loading, enhanced maintenance at reduced intervals must be recommended.

Lubrication clearly plays a significant role in the reliable operation of the engine. In addition to the lubricant's primary task of reducing friction and minimizing wear it also acts as a cooling medium, a partial seal between the cylinders and piston rings, and a means of flushing combustion and other impurities out of the engine.

A pressurized lubrication system using an engine-mounted pump is the choice of most manufacturers. A sump in the crankcase or an external drain tank together with filters and coolers complete the system.

The choice of oil should be consistent with the manufacturer's recommendation, and should only be varied if the engine is intended to be operated in unusual or extreme conditions.

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Oil in Refrigerant Circuits

G.F. Hundy, ... T.C. Welch, in Refrigeration, Air Conditioning and Heat Pumps (Fifth Edition), 2016

5.4 Oil separators

During the compression stroke of a reciprocating machine, the gas becomes hotter and some of the oil on the cylinder wall will pass out with the discharge gas. Some oil carry-over will occur with all lubricated compressor types, and in small self-contained systems it quickly finds its way back to the compressor. Start-up after a long idle period can result in a large amount of oil carry-over for a short period due to foaming. To reduce the amount of oil carried over to the system, particularly where remote low temperature evaporators are in use, an oil separator (Fig. 5.5) can be used. It is located in the discharge line between the compressor and condenser.

Figure 5.5. Oil separator (Henry).

The hot entering gas is made to impinge on a spiral to lose much of the oil on the surface by centrifugal force. Some 95–98% of the entrained oil may be separated from the hot gas and fall to the bottom and can be returned to the crankcase. The oil return line is controlled by the float valve, or it may have a bleed orifice. In either case, this metering device must be backed up by a solenoid valve to give tight shut-off when the compressor stops, since the separator is at discharge pressure and the compressor oil sump at suction pressure.

On shutdown, high-pressure gas in the separator will cool and some will condense into liquid, to dilute the oil left in the bottom. When the compressor restarts, this diluted oil will pass to the sump. In order to limit this dilution, a heater is commonly fitted into the base of the separator on large installations.

Oil-injected screw compressors invariably have oil separators and these handle continuous oil carry-over from the injection process. They are frequently built-in to the compressor assembly, particularly with semi-hermetic air-conditioning types. Recirculation back to the injection ports and bearings is continuous. For low-temperature screw compressors the oil is normally cooled during the recirculation process. For installations, which might be very sensitive to accumulations of oil, a two-stage oil separator can be fitted and up to 99.7% of the entrained oil can be removed. However efficient the separation process, a small quantity of oil will be carried over, and the system design must accommodate oil circulation.

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J. Niemkiewicz, in Encyclopedia of Vibration, 2001

ISO/10816, Part 6: Reciprocating machines with power ratings above 100 kW

This establishes procedures and guidelines for the measurement and classification of mechanical vibrations of reciprocating machines. In general, this standard refers to vibration measurements made on the main structure of the machine, and the guide values are defined primarily to secure a reliable and safe operation of the machine, and to avoid problems with the auxiliary equipment mounted on the structure.

In the case of reciprocating machines, the vibrations measured on the machine main structure, and qualified according to this standard, may only give a rough idea of the stresses and vibratory states of the components within the machine itself. For example, torsional vibrations of rotating parts cannot generally be determined by measurements on the structural parts of the machine. Based on experience with similar machines, the damage that can occur when exceeding the guide values is sustained predominately by the machine-mounted components (e.g., turbo-chargers, heat exchangers, governors, pumps, filters, etc.), connecting elements of the machine with peripherals (e.g., pipelines), or monitoring instruments (e.g., pressure gauges, thermometers, etc.).

This standard generally applies to reciprocating piston machines mounted either rigidly or resiliently with power ratings above 100 kW. The vibration criteria for different classes of reciprocating machines are presented in Table 5. The class definitions are: (1) balanced opposed type rigidly mounted reciprocating gas compressors; (2) multithrow type rigidly mounted reciprocating gas compressors; (3) single-throw type rigidly mounted reciprocating gas compressors; (4) no example; (5) and (6) industrial and marine diesel engines (<2000 rpm); and, (6) and (7) industrial and marine diesel engines (>200 kW). The zone descriptions are the same as in 10816, Part 2.

Table 5. Reciprocating machinery class definitions

Vibration severity grade Maximum levels of overall vibration Measured levels of overall vibration Machine vibration classification number
Displacement(μm, RMS) Velocity (mms−1, RMS) Acceleration (ms−2, RMS) 1 2 3 4 5 6 7
1.8 17.8 1.12 1.76
2.8 28.3 1.78 2.79 A/B
4.5 44.8 2.82 4.42 A/B
7.1 71.0 4.46 7.01 C A/B
 11  113 7.07 11.1 D C A/B
 18  178 11.2 17.6 D C A/B
 28  283 17.8 27.9 D C A/B
 45  448 28.2 44.2 D C A/B
 71  710 44.6 70.1 D C
112 1125 70.7 111 D C
180 1784 112 176 D
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Vibration Fundamentals

R Keith Mobley, in Plant Engineer's Handbook, 2001

Machine descriptions

Reciprocating linear-motion machines incorporate components that move linearly in a reciprocating fashion to perform work. Such reciprocating machines are bi-directional in that the linear movement reverses, returning to the initial position with each completed cycle of operation. Non-reciprocating linear-motion machines incorporate components that also generate work in a straight line, but do not reverse direction within one complete cycle of operation.

Few machines involve linear reciprocating motion exclusively. Most incorporate a combination of rotating and reciprocating linear motions to produce work. One example of such a machine is a reciprocating compressor. This unit contains a rotating crankshaft that transmits power to one or more reciprocating pistons, which move linearly in performing the work required to compress the media.

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Overview of commonly used drivers

Maurice Stewart, in Surface Production Operations, 2019 General considerations

Rotating machines (gas turbines, steam turbines, motors, generators, and gear boxes) normally exert much smaller dynamic forces than reciprocating machines. In any case, these forces must be accounted for to avoid a potentially serious vibration problem during operation.

A fault in the design of a concrete foundation is difficult to correct after the concrete has been poured. There is no easy way to add mass, alter the stiffness, or adjust the damping to change the natural frequency of a concrete foundation in an effort to move the system away from a condition of resonance. In a few cases, it has been necessary to break out an existing foundation and pour a redesigned foundation to solve a serious vibration problem. Such instances are expensive and time consuming.

Guidelines have been developed through the years for the allowable vibration of the foundation; however, criteria for defining the forces to be used in foundation design have been lacking. A misunderstanding between the foundation designer and the machine manufacturer regarding the unbalanced forces to be allowed for in the design has contributed to many foundation vibration problems. These problems have been caused by not designing for the actual dynamic forces but rather for some lower value due to communication problems between the foundation designer and the machine manufacturer.

Depending on how the question concerning unbalanced force is asked, the manufacturer might respond with the rotor's residual unbalance from the dynamic balancing machine. The balancing machine tolerance is a very small number that might be only 1/20th of the actual force rated speed. At other times arbitrary values are assumed for foundation design, yet they are typically not representative of actual conditions.

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Machinery Component Maintenance and Repair

In Practical Machinery Management for Process Plants, 2005

Prealignment Requirements

The most important requirement is to have someone who knows what he is doing, and cares enough to do it right. Continuity is another important factor. Even with good people, frequent movement from location to location can cause neglect of things such as tooling completeness and prealignment requirements.

The saying that “you can't make a silk purse out of a sow's ear” also applies to machinery alignment. Before undertaking an alignment job, it is prudent to check for other deficiencies which would largely nullify the benefits or prevent the attainment and retention of good alignment. Here is a list of such items and questions to ask oneself:

Foundation Adequate size and good condition? A rule of thumb calls for concrete weight equal to three times machine weight for rotating machines, and five times for reciprocating machines.
Grout Suitable material, good condition, with no voids remaining beneath baseplate? Tapping with a small hammer can detect hollow spots, which can then be filled by epoxy injection or other means. This is a lot of trouble, though, and often is not necessary if the lack of grout is not causing vibration or alignment drift.
Baseplate Designed for adequate rigidity? Machine mounting pads level, flat, parallel, coplanar, clean? Check with straightedge and feeler gauge. Do this upon receipt of new pumps, to make shop correction possible—and maybe collect the cost from the pump manufacturer. Shims clean, of adequate thickness, and of corrosion- and crush-resistant material? If commercial pre-cut shims are used, check for actual versus marked thicknesses to avoid a soft foot condition. Machine hold-down bolts of adequate size, with clearance to permit alignment corrective movement? Pad height leaving at least 2 in. jacking clearance beneath center at each end of machine element to be adjusted for alignment? If jackscrews are required, are they mounted with legs sufficiently rigid to avoid deflection? Are they made of type 316 stainless steel, or other suitable material, to resist field corrosion? Water or oil cooled or heated pedestals are usually unnecessary, but can in some cases be used for onstream alignment thermal compensation.
Piping Is connecting piping well fitted and supported, and sufficiently flexible, so that no more than 0.003 in. vertical and horizontal (measured separately—not total) movement occurs at the flexible coupling when the last pipe flanges are tightened? Selective flange bolt tightening may be required, while watching indicators at the coupling. If pipe flange angular misalignment exists, a “dutchman” or tapered filler piece may be necessary. To determine filler piece dimensions, measure flange gap around circumference, then calculate as follows: in.+(MaxGap-MinGap)[Gasket O.D.Flange O.D]=Maximum Thickness of Tapered Filler Piece 1/8 in. = Dutchman Minimum Thickness (180° from Maximum Thickness). Dutchman OD and ID same as gasket OD and ID.
Spiral wound gaskets may be helpful, in addition to or instead of a tapered filler piece. Excessive parallel offset at the machine flange connection cannot be cured with a filler piece. It may be possible to absorb it by offsetting several successive joints slightly, taking advantage of clearance between flange bolts and their holes. If excessive offset remains, the piping should be bent to achieve better fit. For the “stationary” machine element, the piping may be connected either before or after the alignment is done—provided the foregoing precautions are taken, and final alignment remains within acceptable tolerances. In some cases, pipe expansion or movement may cause machine movement leading to misalignment and increased vibration. Better pipe supports or stabilizers may be needed in such situations. At times it may be necessary to adjust these components with the machine running, thus aligning the machine to get minimum vibration. Sometimes, changing to a more tolerant type of coupling, such as elastomeric, may help.
Coupling Installation Some authorities recommend installation on typical pumps and drivers with an interference fit, up to 0.0005 in. per in. of shaft diameter. In our experience, this can give problems in subsequent removal or axial adjustment. If an interference fit is to be used, we prefer a light one—say 0.0003 in. to 0.0005 in. overall, regardless of diameter. For the majority of machines operating at 3,600 rpm and below, you can install couplings with 0.0005 in. overall diametral clearance, using a setscrew over the keyway. For hydraulic dilation couplings and other nonpump or special categories, see manufacturers' recommendations or appropriate section of this text. Many times, high-performance couplings require interference fits as high as 0.0025 in. per in. of shaft diameter.
Coupling cleanliness, and for some types, lubrication, are important and should be considered. Sending a repaired machine to the field with its lubricated coupling-half unprotected, invites lubricant contamination, rusting, dirt accumulation, and premature failure. Lubricant should be chosen from among those recommended by the coupling manufacturer or a reputable oil company. Continuous running beyond two years is inadvisable without inspecting a grease lubricated coupling, since the centrifuging effects are likely to cause caking and loss of lubricity. Certain lubricants, e.g., Amoco and Koppers coupling greases, are reported to eliminate this problem, but visual external inspection is still advisable to detect leakage. Continuous lube couplings are subject to similar problems, although such remedies as anti-sludge holes can be used to allow longer runs at higher speeds. By far the best remedy is clean oil, because even small amounts of water will promote sludge formation. Spacer length can be important, since parallel misalignment accommodation is directly proportional to such length.

Alignment Tolerances

Before doing an alignment job, we must have tolerances to work toward. Otherwise, we will not know when to stop. One type of “tolerance” makes time the determining factor, especially on a machine that is critical to plant operation, perhaps the only one of its kind. The operations superintendent may only be interested in getting the machine back on the line, fast. If his influence is sufficient, the job may be hurried and done to rather loose alignment tolerances. This can be unfortunate, since it may cause excessive vibration, premature wear, and early failure. This gets us back to the need for having the tools and knowledge for doing a good alignment job efficiently. So much for the propaganda—now for the tolerances.

Tolerances must be established before alignment, in order to know when to stop. Various tolerance bases exist. One authority recommends 1/2-mil maximum centerline offset per in. of coupling length, for hot running misalignment. A number of manufacturers have graphs which recommend tolerances based on coupling span and speed. A common tolerance in terms of face-and-rim measurements is 0.003-in, allowable face gap difference and centerline offset. This ignores the resulting accuracy variation due to face diameter and spacer length differences, but works adequately for many machines.

Be cautious in using alignment tolerances given by coupling manufacturers. These are sometimes rather liberal and, while perhaps true for the coupling itself, may be excessive for the coupled machinery.

A better guideline is illustrated in Figure 5-2, which shows an upper, absolute misalignment limit, and a lower, “don't exceed for good long-term operation limit.” The real criterion is the running vibration. If excessive, particularly at twice running frequency and axially, further alignment improvement is probably required. Analysis of failed components such as bearings, couplings, and seals can also indicate the need for improved alignment.

Figure 5-2. Misalignment tolerances.

Figure 5-2 can be applied to determine allowable misalignment for machinery equipped with nonlubricated metal disc and diaphragm couplings, up to perhaps 10,000 rpm. If the machinery is furnished with gear-type couplings, Figure 5-2 should be used up to 3,600 rpm only. At speeds higher than 3,600 rpm, gear couplings will tolerate with impunity only those shaft misalignments which limit the sliding velocity of engaging gear teeth to less than perhaps 120 in. per minute. For gear couplings, this velocity can be approximated by V = (πDN) tan α, where

D = gear pitch diameter, in.

N = revolutions per minute

2 tan α = total indicator reading obtained at hub outside diameter, divided by distance between indicator planes on driver and driven equipment couplings.

Say, for example, we were dealing with a 3,560 rpm pump coupled to a motor driven via a 6-in. pitch diameter gear coupling. We observe a total indicator reading of 26 mils in the vertical plane and a total indicator reading of 12 mils in the horizontal plane. The distance between the flexing member of the coupling, i.e., flexing member on driver and flexing member on driven machine, is 10 in. The total net indicator reading is [(26)2 + (12)2]1/2 = 28.6 mils. Tan α (1/2)(28.6)/10) = 1.43 mils/in., or 0.00143 in./in. The sliding velocity is therefore [(π)(6)(3560)(0.00143)] = 96 in. per minute. Since this is below the maximum allowable sliding velocity of 120 in. per minute, the installation would be within allowable misalignment.

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R. Keith Mobley, in Fluid Power Dynamics, 2000

Reciprocating Positive-Displacement Compressors

Reciprocating compressors have a history of chronic failures that include valves, lubrication system, pulsation, and imbalance. Table 21-3 identifies common failure modes and causes for this type of compressor.

Table 21-3. Common Failure Modes of Reciprocating Compressor

Like all reciprocating machines, reciprocating compressors normally generate higher levels of vibration than centrifugal machines. In part, the increased level of vibration is due to the impact as each piston reaches top dead center and bottom dead center of its stroke. The energy levels also are influenced by the unbalanced forces generated by non-opposed pistons and looseness in the piston rods, wrist pins, and journals of the compressor. In most cases, the dominant vibration frequency is the second harmonic (2×) of the main crankshaft's rotating speed. Again, this results from the impact that occurs when each piston changes directions (i.e., two impacts occur during one complete crankshaft rotation).

Valves. Valve failure is the dominant failure mode for reciprocating compressors. Because of their high cyclic rate, which exceeds 80 million cycles per year, inlet and discharge valves tend to work-harden and crack.

Lubrication systems. Poor maintenance of lubrication-system components, such as filters and strainers, typically causes premature failure. Such maintenance is crucial to reciprocating compressors because they rely on the lubrication system to provide a uniform oil film between closely fitting parts (e.g., piston rings and the cylinder wall). Partial or complete failure of the lube system results in catastrophic failure of the compressor.

Pulsation. Reciprocating compressors generate pulses of compressed air or gas that are discharged into the piping that transports the air or gas to its point(s) of use. This pulsation often generates resonance in the piping system, and pulse impact (i.e., standing waves) can severely damage other machinery connected to the compressed-air system. Although this behavior does not cause the compressor to fail, it must be prevented to protect other plant equipment. Note, however, that most compressed-air systems do not use pulsation dampers.

Each time the compressor discharges compressed air, the air tends to act like a compression spring. Because it rapidly expands to fill the discharge piping's available volume, the pulse of high-pressure air can cause serious damage. The pulsation wavelength, λ, from a compressor having a double-acting piston design can be determined by


where λ = Wavelength, feet

a = Speed of sound = 1,135 feet/second

n = Compressor speed, revolutions/minute

For a double-acting piston design, a compressor running at 1,200 rpm will generate a standing wave of 28.4 feet. In other words, a shock load equivalent to the discharge pressure will be transmitted to any piping or machine connected to the discharge piping and located within twenty-eight feet of the compressor. Note that, for a single-acting cylinder, the wavelength will be twice as long.

Imbalance. Compressor inertial forces may have two effects on the operating dynamics of a reciprocating compressor, affecting its balance characteristics. The first is a force in the direction of the piston movement, which is displayed as impacts in a vibration profile as the piston reaches top and bottom dead center of its stroke. The second effect is a couple, or moment, caused by an offset between the axes of two or more pistons on a common crankshaft. The interrelationship and magnitude of these two effects depend upon such factors as (1) number of cranks; (2) longitudinal and angular arrangement; (3) cylinder arrangement; and (4) amount of counterbalancing possible. Two significant vibration periods result, the primary at the compressor's rotation speed (×) and the secondary at 2×.

Although the forces developed are sinusoidal, only the maximum (i.e., the amplitude) is considered in the analysis. Figure 21-1 shows relative values of the inertial forces for various compressor arrangements.

Figure 21-1. Unbalanced inertial forces and couples for various reciprocating compressors.

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