A. Eijk Flow and Structural Dynamics (PULSIM) TNO Institute of ...

COST-EFFECTIVE AND DETAILED MODELLING OF COMPRESSOR MANIFOLD 

VIBRATIONS 

A. Eijk 

Flow and Structural Dynamics (PULSIM) 

TNO Institute of Applied Physics (T PD) 

Delft, The Netherlands 

ABSTRACT 

In systems with large reciprocating compressors, so-calIed compressor manif\)ld 

vibrations can contribute to fatigue failure of the pipe system. These vibrations are 

excited by pulsation-induced forces and by forces generated by the compressor. 

This paper describes an advanced and accurate method for predic- ting vibration levels 

and cyclic stresses in critical parts of the piping, based on detailed modelling of the 

pulsations and compressor parts. Although detailed finite element modelling is applied. 

the method can compete in ease of use with analytical methods and is far more accurate. 

The effectiveness of this approach will be demonstrated by a case study in which a 

detailed compressor manifold vibration analysis has been carried out. 

INTRODUCTION 

Reciprocating compressors are used in gas transportation. gas storage and in the 

process industry. The compressor, including the pulsation dampers and connected pipe 

work. is often the heart of an installation and should therefore operate reliably. Pulsations 

and vibrations may disturb safe and reliable operation. To avoid vibration problems and 

to optimize the dynamic behaviour, it is common practice to carry out a so-calIed 

pulsation and mechanical response study during the design of an installation. Such studies 

include investigation of compressor manifold vibrations. which are the vibrations of 

compressor cylinders. di stance pieces, crosshead guides, pulsation dampers and piping 

near the compressor. Especially for larger compressors, compressor manifold vibrations 

are important as the mass of compressor parts and pulsation dampers increases. 

which leads to low-resonance frequencies which may be excited by pulsation forces. by 

gas forces in the compressor cylinder, and by unbalanced forces and moments of the 

compressor (Palazzolo, Smalley and Lifshits, 1985, Lifson and Dube 1987). We have 

encountered several actual cases in which pulsation forces have excited compressor 

manifold vibrations and caused fatigue failure. 

The importance of calculations of compressor manifold vibrations is also retlected in the 

fourth edition of the API Standard 61 R 

J.P .M. Smeulers 

Flow and Structural Dynamics (PULSIM) 



415 

PVP-Vol. 328. Flow-lnduced Vibration 

ASME 1996 

G. Egas 

Flowand Structural Dynamics (PULSIM) 



(11). 

In this paper, a method for the prediction of compressor manifold vibrations 

is discussed, which is based on rigorous finite element modelling of the 

compressor parts. Despite rigorous modelling, the method is efficient and 

easy to" use and more accurate than the usual analytical methods. 

Before going into detail about the method, a short overview of the pulsation 

and mechanical response study will be given. fol- lowed by a description of 

the kind of compressor manifold vibrations which may occur. 

The paper concludes with a description of a case study, in which the accuracy 

of FEM roodels of compressor parts has been asses- sed by means of modal 

analysis measurements. 

PULSATION AND MECHANICAL RESPONSE STUDY 

Pulsation and mechanical response studies have become ac- cepted as part of the 

process of designing a reliable instalIation free of vibration problems. Such studies are 

carried out by the Flow and Structural Dynamics Department of the TNO Institute of 

Applied Physics T PD, also known by the name PULSIM. The Flow and Structural 

Dynamics Department is specialized in thé dynamics of pipe systems and has carried out 

some 600 studjes over a period of 25 years. 

In the study, a two-step approach is folIowed. In the first step, the pulsations, e.g. 

pressure and tlow velocity waves in the pipe system and tluid machinery are calculated, 

including pulsation- induced vibration forces. The layout of the pipe system and the 

design of pulsation dampers are harmonized to minimize pulsation levels and forces. 

In the pulsation study, worst-case situations are calculated, which means that aII resonant 

conditions in a certain range around the nominal condition are investigated. Calculated 

amplitudes and phases of the forces which act on the system at elbows, T -joints, 

reducers, pulsation dampers etc., are stored so that they can be used later in the 

mechanjcal response study of the pipe system. 

The pulsatjon study js carried out using the djgjtal sjmulation environment PULSIM 

(pJ.!L.sation SIMulatjon), whjch has been developed by the Flow and Structural 

Dynamics Department of the T PD. In general, PULSIM is a simulation envjronment for 

one-

dimensional non-stationary flow. Besides the functionality for pulsation 

studies, other non-stationary flow phenomena, such as tran- sients, can also 

be modelled in the PULSIM environment (Smeulers, 1988. Egas, 1988, Van 

Bokhorst and Korst, 1993, Van Bokhorst, 1995). 

In the second step. the mechanjcaJ response study. vjbratjonal response of the pjpe 

system. jncludjng pulsatjon dampers. js calculated on the basjs of predjcted pulsation 

forces. 

In the mechanjcal response studjes. a finjte element model js made of the pjpe system 

and the supportjng structure. The finjte element program ANSYS (14) js used for thjs 

purpose. 

In the mechanjcal response studjes. the pu1satjon forces used have been calculated wjth 

the PULSIM program. A Ijnk js made between the PULSIM and ANSYS programs. so 

that the ampljtude and phase of the calculated pulsatjon forces can be transferred to the 

ANSYS program for a11 the jmportant acoustjc resonance 

condjtjons (worst-case condjtjons). 

COMPRESSOR MANIFOLD VIBRATIONS 

Compressor manifold vibrations are a specialized and com- plicated form 

of vibration of part of the piping, pulsation dampers and compressor parts 

such as cylinders, distance pieces and crosshead guides. If not proper I y 

controlled, these vibrations can cause fatigue failure of the system. Figure l 

shows an example of a compressor manifold. Some of the common 

compressor manifold vibrations have special narnes and are summarized as 

follows: 

Low mode 

This mode is shown in figure 2 and is generally the lowest mode of the compressor 

system. This mode is a rigid body motion and the cylinders and dampers vibrate inphase 

horizontally to the combined flexibility of the distance piece and the crosshead 

guide. As the nozzles must twist to accommodate this motion, high torsional stresses in 

the cylinder nozzles can occur. 

Rotary mode 

This mode is shown in tigure 3. The suction and discharge 

dampers move out-of-phase in a horizontal direction. In this mode, high bending 

stresses can occur, and the highest stress points are at the cylinder flanges and in the 

joints between bottIes and nozzles (named branch connections). 

Cylinder resonance mode 

This mode is shown in tigure 4. The cylinders move out-of- phase relative to each 

other. With more than two cylinders, various combinations of one cylinder moving 

out-of-phase in relation to the others will occur. In this mode, high bending stresses can 

occur and the highest stress points are at the cylinder flanges and branch connections. 

Suction damper cantilever mode 

This mode is shown in tigure 5. In this case, the suction damper moves out-ofplane 

and the cylinder nozzles will bend. There may be a component of cylinder 

"diving" associated with this mode. This mode will cause high bending stresses and can 

cause fatigue failure of the system. 

If the discharge damper is not supported, it is also possible for a discharge damper 

cantilever mode to occur. The highest stress points are at the cylinder flanges and at the 

branch connections. 

416 

Suction damper angular mode 

This mode is shown in tigure 6. The two ends of the dampers move out-of-phase in 

the horizontal direction. In this case, high torsional stresses can occur. If the discharge 

damper is not sup- poned, a discharge damper angular mode may also occur. The 

highest stress points are at the cylinder flanges and at the branch connections. 

The compressor manifold vibration modes as mentioned above, occur only 

in systems without connecting piping. In most practi- cal cases, a part of the 

connected pipe system will also contribute to the compressor manifold 

vibrations. 

SIMUL.ATIONS 

Calculation of the Dulsation forces 

The pulsation forces which act on the pulsation dampers are the most 

important cause of compressor manifold vibrations. Por example, standing 

wave type resonances in the pulsation dampers will generate large pulsation 

forces. 

With PULSIM, the pulsation forces which act on pulsation dampers, bends, 

reducers, T -joints, orifice plates etc., and the gas force in the cylinders, 

which cause stretching of the cylinders, are calculated in detail. 

The amplitude and phase of the calculated forces are stored for worst-case 

conditions so that they can be used later in the mechanical response study. 

Finite element model (FEM) of the nine svstem with comol"es- SOl" ual"ts 

Pipe system 

The pipe system as weIl as the structure on which the supports are 

mounted are modelled with Timoshenko beam-type elements (ANSYS 

elements: PIPEI6, PIPEI8 and BEAM4). lnasmuch as numerous mechanical 

response studies are carried out each year at the Flow and Structural 

Dynamics Department, special piping pre- and postprocessors have been 

developed to carry out mechanical response studies in an easy and cost-effec- 

tive way. Pre- and postprocessors have been written with the ANSYS 

Parametric Design Language (APDL) and use ANSYS piping commands. 

Preprocessor databases include standardized pipes, ASA and DlN flanges, 

and DlN beams. With the postpro- cessor, vibration velocities, support 

reactions and cyclic stresses in the pipe system are calculated and compared 

with permissible levels. 

Some components of the pipe system, such as fianged connections and 

branch connections, always require special attention because the fiexibility of 

these parts can have a distinct influence on the natural frequencies of some 

compressor manifold vibration modes, such as suction bottIe cantilever 

modes, suction bottIe angular modes and cylinder resonance modes (Lifson 

and Smal- ley, 1989, Tjeng and Wickert, 1994). 

Branch connections can be modelled by means of 3 translation and 3 rotation springs, 

and for the calculation of spring constants and stress intensification factors (SIFs), a 

finite element modelof the branch connection is made which is built up with shell elementso 

For this purpose, the finite element program FE-PIPE ( 13) is used. which is a specialpurpose 

program developed for detailed

stress analysis of piping coroponents such as elbows, T -joints, etc. Calculated 

spring constants and SIFs are used in ANSYS bearo type roodels of the pipe 

systeros. 

Compressor parts 

The flexibility and mass distribution of compressor parts such as cylinders. 

di stance pieces and crosshead guides are very important. because these 

parameters determine some of the possible compressor manifold vibration 

modes described previously. It strongly depends on the construction of the 

machine what parts have to be included in the calculations. In most cases. the 

di stance piece is the most flexible part of the compressor. Most of the 

cylinders can be modelled by means of concentric pipe elements. Field 

measurements have also shown that the flexibility of the connection of the di 

stance piece with the crosshead guide can have an important effect on the 

natural frequencies of some compressor manifold vibration modes (see also 

the case study in this paper). 

Compressor parts such as the di stance piece and crosshead guide can often be 

modelled with shell elements (ANSYS elements: SHELLA3 and SHELL63), 

but this depends largely upon the compressor type. 

In compressor manifold vibration studies. cyclic stresses in the compressor 

parts are not calculated and models can therefore be kept relatively simple. 

Nevertheless, the number of degrees of freedom of compressor parts is very 

large ( 10.000-20,000) in comparison with the number of degrees of freedom 

of the pipe system. The number of responses to be calculated in the mechanical 

response study can also be considerable (1,500 responses is no 

exception). This leads to unacceptable computer times. which is why it is not 

feasible to include the shell element models in the pipe system model. One 

solution is the use of so-calIed substructures. Substructuring is a technique 

that simp I y condenses a group of elements into a single element represented 

as a matrix (ANSYS element: MA TRIX50). This single matrix element is 

called a substructure or superelement. The number of degrees of freedom of 

the superelement (called master degrees of freedom: MDOF) will be only a 

few hundred. However. accuracy of stiffness and mass is preserved. As the 

ANSYS program uses Guyan (or static) reduction in the substructure 

technique. this is only applicable for linear systems. Substructures can be 

easily included in the beam type modelof the pipe system using a procedure 

that has been developed especially for this purpose. 

Each substructure of the di stance piece and crosshead guide is stored in a 

central database and can be employed by several users in various projects. 

Mechanical reSDOnSe studv 

The fust step in the mechanical response study is the calcu!a- tion of !ower 

mechanica! natura! frequencies of the system (moda! ana!ysis). The maximum number 

of natura! frequencies which are of interest depend on the maximum frequency of 

pu!sation forces. The second step is the harrnonic response ca!cu!ation of the system. 

In the harrnonic response ca!cu!ation, the system is excited sepa- rately by pressure 

pulsation forces originating from the piston action (this force wil! cause stretching of the 

compressor cy!inder, di stance piece and crosshead guide), by pu!sation forces and by 

unbalanced forces and unbalanced moments of the compressor. 

The amplitude and phase of pu!sation forces for acoustic resonance conditions. which 

have been ca!culated by PULSIM. are rcad 

417 

into the ANSYS program. Due to the fact that boundary conditions, for 

instance. are not weIl defined, calculated resonance frequencies will be 

established with a cenain inaccuracy. In harmonic response calculations, it 

is therefore assumed that the frequency of pulsation forces. or equivalently, 

mechanical natural frequencies can shift to such an extent as to coincide. 

This may seen very conservative but, panicularly for compressors with a 

variabIe speed, it is possible that this wiII occur in practice. 

The amplitude of the response at resonance is direct I y dependent on the 

damping in the system. and in the harmonic response calculations a damping 

ratio of 4% is taken into account. 

The last step is postprocessing of harmonic response calculation results. At 

the postprocessing stage, vibration velocities of the pipe system and 

compressor pans, pipe suppon reactions and cyclic stresses in the pipe system 

are calculated and presented in easy-to-read tables, which provide a quick 

overview of how the system responds in several acoustic resonance 

conditions (worst- case conditions). Cyclic stresses in the compressor pans 

are not calculated because. in most cases, this is not a pan of a compressor 

manifold vibration study and therefore. as mentioned previously, sheII 

element models of the compressor pans can be kept relatively simple. When a 

stress analysis of compressor pans has to be made. more accurate models of 

the compressor pans must be generated. The required computer time wiII also 

increase considerably because so-calIed ex pansion passes of the 

substructures have to be carried out to calculate stresses in the sheII models. 

Evaluatian af the results 

When the vibration levels and/or cyclic stresses exceed permissible values. design 

modifications are investigated to reduce system responses. In most cases extra pipe 

supports or modifications of the supporting structures are advised. 

The calculated cyclic stresses include stress intensification factors for T -joints, flanges, 

elbows and reducers and are taken according the piping code ASME B31.3 ( 12 ). If the 

peak value of cyclic stresses exceeds the endurance limit of the material, fatigue 

problems will occur. Unless the client specifies another crite- rion, a pennissible cyclic 

stress value according to the API Standard 618 of 179 N/mm2 peak-to-peak (pp) will be 

used. This value has been based on the endurance limit and is only valid for carbon steel 

pipe with an operating temperature below 371° C. AII other stresses must be within the 

applicable code limits (API Standard 618, paragraph 3.9.2.2.1.). 

Ta ensure that small-diameter side branches and equipment such as temperature 

transmitters, pressure gauges, valves, etc. will nat fail due ta high vibratians, vibratian 

levels are alsa calculated and shauld be belaw a velacity level af 80 m mis pp. 

Static effects 

To determine static effects on the pipe system such as pressure, weight and therm al 

expansion, it is advisable to carryout a static analysis of the pipe system as part of the 

total study. Por the static stress calculation we use the pipe stress program CAESAR-II. 

The calculated static stresses in the pipe system can be compared with permissible values 

as stated in several piping codes, but we will apply the ASME 831.3 code in most cases.

CASE STUDY OF A COMPRESSOR MANIFOLD VIBRA- T!ON 

ANAL YS!S 

The following is a summary of the results of a compressor manifold 

vibration analysis of a 1485 kW compressor system used for underground 

storage of natura! gas in a salt dome in Germany. The compressor is a onestage 

compressor with 4 cylinders. Gas is pumped into the dome mainly in 

summer at a discharge pressure of 152 bar. The stored gas is used for peak 

shaving times in the winter when demand is high. 

The two cylinders at each side of the crankcase have one common suction 

pu!sation damper, while each cylinder has a discharge pulsation damper. 

Pulsation study and mechanica! response studies have been carried out for the 

complete pipe system from the compressor up to a few hundred metres from 

the compressor. However, only the resu!ts of 

the compressor manifold vibration ana!ysis will be discussed here. For this 

system, the compressor cylinders have been modelled by means of concentric 

pipe elements. The di stance piece and the crosshead guide have been 

modelled by means of shell-type elements and the plots of the FEM models 

are shown in figure 7 through 9. The FEM model consists of 5,046 shell 

elements with 27 ,660 degrees of freedom. The crankcase, the concrete 

foundation on which the compressor has been insta!led and the connection 

of the compressor with the foundation have been assumed to be infinitely stiff 

for this project. For this study, the crankcase has therefore been modelled as 

an anchor point. 

From this model, several substructures have been made with different master 

degrees of freedom (MDOF). Tab!e I gives an overview of natural 

frequencies of the substructures with different MDOF, and the differences 

between natural frequencies of the substructures and the shell model. 

The two lowest natural frequencies are bending modes of the distance piece, 

while the next three are natural frequencies of the stiffening parts of the 

crosshead guide. The substructure with 300 MDOF has been included in the 

piping models because the two lowest natura! frequencies, which are the 

most important natura! frequencies for the compressor manifo!d vibrations, 

differ by less than I. 1% from the natura! frequencies of the shell model. 

Summarv or the results 

A so-calied solid model representation of the compressor manifold system is shown 

in tigure 10. 

The pulsation study revealed that pipe system pulsation levels were within permissible 

levels by installing oritice plates at the line connection of the suction aod discharge 

dampers. Pulsation forces acting on the suction and discharge dampers were extre- mely 

high, however, which was caused by standing wave-type resonances in the dampers. The 

maximum amplitude of the forces on the suction damper was 80 KN peak-to-peak (pp) 

and 40 KN pp on the discharge damper, both with frequen

Figures 18 and 19 (mode shape numbers 7 and 8) show that relative 

displacement exists between the distance piece and crosshead guide at the 

location where these parts are bolted to each other. The differences of -25.0% 

and -28.7% between measured and calculated natural frequencies can be 

explained by the fact that the prestressed bolted connection of the crosshead 

guide to the distance piece and cylinder has been modelled with too great a 

stiffness in FEM calculations. To calculate these natural frequencies more 

accurately. it is necessary to model the prestressed bolted connections with 

greater precision. 

CONCLUSIONS 

A cost-effective and accurate tooi has been developed to calculate compressor 

manifold vibrations, so that fatigue failure of the pipe system can be predicted at the 

design stage, avoiding unsafe situations, high maintenance costs and production losses. 

With this tool, vibration velocities, suppon reactions and cyclic stresses in 

critical pans of the pipe system can be calculated easi- I y and costeffectively, 

and can be presented in easy-to-read tables for the most imponant 

resonance conditions (worst-case situations). Special piping pre- and postprocessors 

have been developed for this purpose. 

Important compressor parts, such as distance pieces, crosshead guides and 

crankcases, which determine the mechanica! characte- ristics of a compressor, 

are modelled with shell elements, which are used as a basis for model 

substructures, so that with a relatively small number of (master) degrees of 

freedom, the stiffness and mass of compressor parts can be included in the 

beam-type analysis of the pipe system. This technique will cut computer time 

quite considerably. 

Each substructure is stored in a central database, so that the substructures can all be 

easily incorporated into a piping analysis without the need for tedious finite element 

modelling. 

Pulsation forces have been calculated with the PULSIM digital program. An 

easy-to-use interface has been developed to transfer the amplitude and phase 

of the pulsation forces from the PULSIM program to the ANSYS program, so 

that a whole range of response calculations can be carried out in an easy and 

cost-effective way. 

Modal analysis measurements have been carried out to verify the accuracy of 

FEM models of the compressor pms. Measurements have been carried out on 

a compressor configuration consisting of a cylinder, distance piece, crosshead 

guide and crankcase. These measurements showed that there is only a minor 

deviation between measured and calculated natural frequencies for the most 

important (lower) natural frequencies. The measurements also showed that. 

for the higher modes, the prestressed bolted connections of the compressor 

parts and stiffness of the crankcase play an important role. To calculate 

natural frequencies of the higher compressor manifold vibration modes more 

accurately, the prestressed bolted connections and stiffness of the crankcase 

should also be incorporated into the FEM models in greater detail. 

419 

REFERENCES 

[1] Smeulers, J.P.M., "Simulation of flow dynamics in pipe systems," 

Proceedings ImechE Seminar "Gas and liquid pulsations in piping 

systems-prediction and control, London, 1988, pp.97-105. 

[2] Egas, G., "Gas pulsations in pipe systems-a case history and solutions," 

Proceedings ImechE Seminar "Gas and liquid pulsations in piping 

systems-prediction and control, London, 1988, pp.107-116. 

[3] Van Bokh~rst, E., and Korst, H., "The centrifugal pump as a source of 

pu1sations in pipe systems-a comparison of measurements and 

simulation results," Proceedings of the fifth European Congress on 

Fluid Machinery for the Oil, Petro- chemical and Related Industries, 

1993, pp. 83-91. 

[4] Van Bokhorst, E., Korst, H., Smeulers, J.P.M., and Brug- geman, J.C., 

"The simulation of pulsating flow generated by centrifugal pumps by 

means of the simulation program PULSIM," Proceedings of the lst. 

International Symposium organized by SHF, 1993, Clamart (France). 

[5] Van Bokhorst, E., Korst, H. and Smeulers, J.P.M., "PUL- SIM3, a 

program for the design and optimization of pulsation dampers and 

pipe systems," Proceedings of the Euro- Noise, 1995, pp. 751-756. 

[6] Lifson, A. and Smalley, A.J., "Bending Flexibility of Bolted Flanges and 

lts Effects on Dynamical Behaviour of Struc- tures," Volume III, 

Joumal of Vibration, Stress and Relia- bility in Design, October 1989, 

pp. 392-398. 

[7] Palazzolo, A.B., Smalley, A.J., and Lifshits, A. "Recent Developments in 

Simulating Reciprocating Compressor Manifolds for Vibration 

Control," ASME 85-DET-179, presented at the ASME Design 

Engineering Division Con- ference and Exhibit on Mechanical 

Vibration and Noise, Cincinnati, Ohio, September 10-13, 1985. 

[8] Lifson, A. , and Dube, J.C., "Specifying Reciprocation Ma- chinery 

Pulsation and Vibration Requirements Per API- 618," DT-66, American 

Gas Association Operating Section Proceedings, 1987, pp. 50-58. 

[9] Tseng, J.G., and Wickert, J.A., "On the vibration of bolted plate and 

flange assemblies," Joumal of Vibration and Acoustics," Volume 116, 

1994, pp.468-473. 

[10] API Standard 618, third edition, February 1986, "Recipro- cating 

Compressors for General Refinery Services. 

[11] API Standard 618, fourth edition, June 1995, "Reciprocating 

Compressors for Petroleum, Chemical, and Gas Industry Services. 

[12] ASME B31.3-1993, "Chemical Plant and Petroleum Refi- nery Piping." 

[13] FE-PIPE Manual, version 2.8. 

[14] ANSYS Users' Manual Volume I, II, III and IV (DN- R301:50A).

Freq. 

no. 

2 

3 

4 

5 

100 

195.391'2.36 

206.591'2.81 

313.16/3.40 

316.58/3.12 

320.93fJ.72 

200 

194.17/1.72 

204.08/1.56 

307.75/1.61 

310.93/1.28 

319.79/3.35 

Master degraes of treeOOm (MDOF) 

300 

192.99/1.10 

202.79/0.92 

307.47/1.52 

310.24/1.06 

318.93/3.08 

400 

192.42/0.81 

202.4~.74 

308.39/1.16 

309.81/0.92 

311.96/0.82 

1000 

191.29/0.21 

201.40/0.22 

304.~.40 

307.61/0.20 

309.7~.11 

Table 1 Table with the natural frequencies of the substructure with different master degrees of freedom (MDOF) and the natural 

frequencies of the shell rnodel. The figure af1er the slash (/) Indicates the difference in % between the natural frequency of the 

substruCture and the natural frequency of the shell model. 

Mode 

shape 

nunj)er 

Measured 

frequentie 

Hz 

CaJculaled 

frequentie 

Hz 

Difference . 

% 

40.6 

43.6 

-7.4 

2 

62.1 

51.2 

17.6 

3 

82.0 

74.6 

9.0 

4 

90.6 

75.0 

17.2 

5 

128.0 

190.7 - 

6 

170.6 

219.3 49.0 

7 

182.6 

228.0 - 

8 

186.8 

240.4 28.6 

- 

25.0 

Table 2 Measured and calculated natural frequencies 

- 

.((measured-calculated)/measured))x100% 28.7 

suction 

damper 

cyltnders 

dlsd1arge 

damper 

Fig. 2 Low mode 

Fig. 3 Rotary mode 

420 

Fig.1 Example of a compressor manifold 

Fig. 4 Cylinder resonance mode 

Shell model 

190.88 

200.95 

302.87 

306.99 

~.41

Fig. 5 Suction damper cantilever mode 

Fig. 7 FEM modelof the distance piece 

Fig. 6 Suction damper angular mode 

Fig. 8 FEM modelof the crosshead guide 

Fig. 9 FEM modelof the distance piece with crosshead guide 

421

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