riooil2010 3298 201006290850rio_oil_3298_2010

______________________________ 1 Ger. Desenvolvimento, Engenheira Química – TEADIT 2 Ger. Eng.,Engenheiro Mecânico – TEADIT 3 Diretor Técnico, Engenheiro Mecânico – TEADIT 4 Engenheira de Equipamentos, Engenheira Mecânica – PETROBRAS 5 Consultor Sênior, Engenheiro Mecânico – PETROBRAS

IBP3298_10 DETERMINATION OF GIMBAL AND HINGED EXPANSION

JOINTS REACTION MOMENTS

Ana M. F. Sousa1, José C. Veiga2, Nelson Kavanagh3 Jordana L. Veiga4, Jorivaldo Medeiros5

Copyright 2010, Instituto Brasileiro de Petróleo, Gás e Biocombustíveis - IBP

Este Trabalho Técnico foi preparado para apresentação na Rio Oil & Gas Expo and Conference 2010, realizada no período de 13 a 16 de setembro de 2010, no Rio de Janeiro. Este Trabalho Técnico foi selecionado para apresentação pelo Comitê Técnico do evento, seguindo as informações contidas na sinopse submetida pelo(s) autor(es). O conteúdo do Trabalho Técnico, como apresentado, não foi revisado pelo IBP. Os organizadores não irão traduzir ou corrigir os textos recebidos. O material conforme, apresentado, não necessariamente reflete as opiniões do Instituto Brasileiro de Petróleo, Gás e Biocombustíveis, seus Associados e Representantes. É de conhecimento e aprovação do(s) autor(es) que este Trabalho Técnico seja publicado nos Anais da Rio Oil & Gas Expo and

Conference 2010.

Resumo Este trabalho propõe um método para estimar, mais próximo da realidade, as forças de reação em juntas de expansão metálicas do tipo cardânicas e dobradiças. Foram analisados os resultados de testes de movimento, sob pressão, desenvolvidos para realizar os ensaios de juntas de expansão de grandes diâmetros, a serem instaladas em uma unidade de craqueamento catalítico fluido (FCC), de uma refinaria. Foram analisados as várias componentes que influenciam nas forças de reação de uma junta de expansão: efeito mola do fole, atrito dos pinos das articulações, componente lateral de força de pressão, atrito de componentes estruturais diversos e propostos modelos teóricos, que pudessem melhor representar estas influências. Comparados os resultados reais dos ensaios com o modelo teórico, foram analisados estatisticamente e proposto uma equação final, para o cálculo de momentos de reação. Algumas componentes de forças de pressão e de atrito, que não são consideradas nos cálculos feitos pela norma de projeto do EJMA (“Expansion Joints Manufacturer Association”), são acrescentadas à constante de mola, para melhor estimar os momentos de reação devido ao movimento angular da junta de expansão.

Abstract This paper proposes a method to estimate, closer to actual situations, the reaction loads in gimbal and hinged metal expansion joints. It was analyzed the movement test results, under pressure, developed to test large diameter expansion joints, to be installed in a fluid catalytic cracking unit (FCC) from a refinery. It was analyzed the several components from the expansion joint reaction loads: bellows spring effect, hinges pin friction, lateral pressure component force, structural hardware friction and were proposed theoretical models, which could better represent those influences. Comparing the actual test results with the theoretical models, they were statistically analyzed and it was proposed the final equation for the reaction moment. Friction and some media pressure forces, which are not considered in the current EJMA standard (“Expansion Joints Manufacturer Association”), were added to the bellows spring rate to better estimate the expansion joint angular movement reaction moment.

1. Introduction

Expansion joints are used by the industry in process piping and ducts to compensate the thermal expansion and provide the proper pipe flexibility. A pipe line is considered flexible if the pipe stresses and the equipment connection loads are lower than an acceptable level.

Rio Oil & Gas Expo and Conference 2010

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The ASME Process Piping code B31.3 [1] establishes the rules and values for the maximum allowable stresses in a process piping system. In addition, rotating equipment like steam turbines , compressors, pumps and turbo-expanders, have the maximum allowable nozzle loads specified by the manufacturer or by an industry specific standard such as the NEMA SM23 [2] for steam turbines and turbo-expanders.

In a paper by the authors [3] metal bellows expansion joints actual reaction forces were compared with the theoretical values as per standards of the Expansion Joint Manufactures Association (EJMA) [4] equations. Since EJMA does not consider effects like friction and components interference there is a discrepancy in the calculations that can show an increase in the actual pipe stresses and equipment nozzle loads. This Paper presents a series of equations, based upon 13 large gimbal (Fig. 1) and hinged (Fig. 2) expansion joints pressure and movements tests, that take into account the loads not considered by the EJMA calculations. These equations can be used to estimate with higher precision the reaction forces in piping systems with metal bellows expansion joints.

Figure 1. Gimbal expansion joint

Figure 2. Hinged expansion joint

2. Expansion Joint Reaction Forces

The media pressure and the movement acting in a gimbal or hinged expansion joints causes reaction loads calculated according to EJMA equations. The source of these reaction loads may be attributed to the following effects:

- Bellows spring effect: a metal bellows acts like a spring when it is flexed by the piping movement (Fig. 3). - Pressure thrust: as a flexible element the media pressure creates a pressure thrust force (Fig. 4) that acts on

expansion joint hinges. In addition to these loads, other loads may be attributed to reactions as defined bellow: - Hinges pin friction: as the expansion joints move, there is friction force acting on the hinge pins (Fig. 5). This

force is due to the pressure thrust, joint weight and external forces. - Lateral pressure force: in a rotated bellows the difference between expanded and contracted sides generates a

lateral force - Hinges Arm friction: the rubbing effect of the arms (Fig. 5) creates a friction force that opposite to their

rotation. - Sleeve Seal friction: expansion joints with inner sleeves may have a seal to hold inside bellows insulation.

The seal creates a force which opposes the angular movement as shown in Fig. 6. The forces acting on the expansion joint create an angular moment which can be expressed as follows: Mav = Mb + Mpf + Mlpf + Marm + Ms (1) In the following paragraphs each reaction moment is analyzed.


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Figure 3. Spring effect

Figure 4. Thrust pressure

Figure 5. Hinged pin / arms friction

Figure 6. Inner sleeve seal friction 2.1. Moment Due to Bellows Spring Rate

The standard EJMA (Expansion Joint Manufacturers Association), state the spring rate calculation considering only the bellows spring effect.

Mb = α * kα (2)

2.2. Moment Due to Pin Friction

The pressure thrust force acting on an expansion joint hinge can reach very high values. For examples, in one of the joints tested, during the preparation of this paper, it reached 112 ton (248000 lbf) at its maximum test pressure. Consequently, it is necessary to account accurately and reduce the hinge pin friction.

An expansion joint, installed in a process piping to compensate thermal growth, is under a low frequency movement. A process which starts-up and stays for long periods at a steady-state, once the process temperature has been reached and hinges will not move.

In Fig. 7, see the sketch of the angular movement and the pin friction moment, due to the pin load. The hinges pin moment can be written as:

Mpf = Fp * µp * d/2 (3)


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Figure 7. Pin friction moment

The pin static friction coefficient value “µp” depends of several conditions, like materials, hardness, surface finishing, presence of dirty and others. The most part of expansion joints applications use some steel pin straight in contact with the arms steel or with a metal sleeve, not using any lubricant and usually, in this condition the “µp” value is from 0.25 to 0.9 and this values can change due to environmental conditions. The choice of the proper pin and arm or sleeve metal must be carefully studied during the expansion joint design.

It is not part of this paper to analyze pin and sleeve materials. Further studies are necessary to evaluate the best choices. The focus of this paper is to show the importance of pin/sleeve friction loads.

If the hinges pin and sleeves are not properly hardened, the pressure thrust force may create a galling effect at their contact surface, increasing the moment necessary to move the joint. To avoid galling the pins can be hardened or adopt some other solution. In the expansion joints tested, for this paper, the pins were hardened using stellite, with grinding surface finishing. In order to check the friction coefficient of stellite x stellite, it was developed a test using different contact pressures, considering that the media pressure would cause a pin contact pressure from 47 MPa to 73 MPa (6.8 ksi to 10.5 ksi). The test results for stellite friction coefficient were from 0.13 to 0.14. For this study we considered a friction coefficient of 0.14.

2.3. Moment Due to the Lateral Pressure Force

As shown in Fig. 8, as the expansion joint rotates, one side of the bellows expands and the opposite side contracts. The difference between the expanded and contracted areas (Fig.9) will generate a force in the opposite direction of the rotation. The moment due to the differential area can be written as follows:

Mlpf = Fb * H / 2 (4) Where: Fb = P * Ad (5) H = L / 2 (6) Figure 10 shows an angular sector equals to half of the total rotation angle α. A side view (X-X) of this sector is

shown in Fig. 11. The shaded portions are the differential areas between the expanded and contracted sides of the rotated bellows.


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Figure 8. Lateral pressure force

Figure 9. Bellows differencial areas

Figure 10. Bellows angular sector

Figure 11. Bellows angular view X-X

As shown in Fig. 12, it was considered a partial area, from the total differential area, to calculate in an easiest

way. So the equation is: Ad = 8* Ac (7)

Figure 12. Differential areas Considering the radius R in the view XX divided in “n” equal parts, the partial differential area can be

calculated as follows:


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( ( ) )ii

n

i

i AAHH

Ac −∗

−= +

−

=

∑ 1

1

0 2 (8)

Where:

∗=

−

4tan

2

αi

i BHH

(9)

( ) 5.022ii ARB −= (10)

So the equation becomes:

( ( ) ( ) )ii

n

i

i AAARAd −∗

∗−∗= +

−

=

∑ 1

5.01

0

22

4tan8

α (11)

In this study, it was adopted a division in 10 equal parts, so the equation becomes:

( ( ) ( ) )ii

i

i AAARAd −∗

∗−∗= +

=

∑ 1

5.09

0

22

4tan8

α (12)

Table 2 shows values of the differential areas Ad for the diameters and movements of this paper.

Table 2. Bellows sides area differences

ID mm

(in) 1650 (65)

1900 (75)

1930 (76)

α (°) Ad (cm²) 1 196,3 262,4 268,5

1,5 294,4 393,7 402,8 2 392,5 524,9 537,1

2,5 490,7 656,1 671,4 3 588,8 787,4 805,6

3,5 687,0 918,6 939,9 4 785,2 1049,9 1074,2

4,5 883,3 1181,2 1208,6 5 981,5 1312,4 1342,9

2.4. Moment Due to Hinges Friction

The friction between hinges will increase the moment required to move the expansion joint. This friction can not be accurately accounted for. Bending due to welding thermal stresses can reduce the gap between arms increasing their rubbing.

2.5. Moment Due to Inner Sleeve Seal

The expansion joints, with internal refractory insulation, may be fitted with a metal seal between sleeves as shown in Fig. 13. This seal usually is a steel wire braid with steel mesh filler.

If the seal is aligned with the hinge pin, it will slide between the internal sleeves when the expansion joint is subjected to an angular movement as shown in Fig. 13. If the seal is not aligned, it will slide as well as compress with


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the joint rotation as shown in Fig. 14. Both the sliding movement and the seal compression will generate a force, and consequently, a moment that can not be accurately calculated.

Figure 13. Sleeve seal centered

Figure 14. Sleeve seal not centered

3. Analysis of Large Expansion Joints Test Results

Pressure and movement tests were performed by the authors [3] with 13 large expansion joints. A summary of the test results are shown in Fig. 17 to 22. The actual moment values (black lines) are larger than the values calculated by the EJMA equations (green lines). Figure 15 shows a picture of a joint being tested and Fig. 16 shows a schematic drawing of the test device.

The force on hinges is affected by the weight of the test device and its value was excluded from calculations. The actual values can be as high as 3 times when compared with the EJMA equations results. Angles in the 1 to 2 degrees range increase the error. This difference can result large errors in the pipe flexibility analysis.

To minimize this error, at the piping design time, the actual values were compared with the theoretical values in order to define a correction factor (CR) to account for the uncertainties.

We have seen that is possible to calculate moment due to bellows spring rate (Mb), media pressure (Mlpf) and pin friction (Mpf), so the eq. (1) in theory can be calculated and becomes as eq. (13).

Mavt = Mb + Mlpf + Mpf (13) The value of CR can be used as a correction factor to adjust the Eq. (13) in order to have values closer to the

actual expanded joint.

Figure 15. Movement test

Figure 16. Movement test


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EJ ID1930mm P=3.6bar

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Figure 17. Test result 1 vs. theory



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Figure 22. Test result 6 vs. theory Thus, the ratio of actual value and Mavt is defined as moment Ratio (MR ) shown in Eq. (14). MR = Ma / Mavt (14) The moment ratios calculated using Eq.(14), for test pressures of 2.2 bar and 3.5 bar were feed into the

Statgraphics Centurion software [5] to determine the best probability distribution for the data. According to box-and-whisker plot for each pressure test, the variability is similar within each sample. The

mean comparison shows the same behavior of variability. It means that pressure does not have influence on MR; consequently all data can be used to determine the probability distribution.


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A distribution fitting procedure was performed to find a probability that provides a suitable model for the experimental data in order to determine MR tolerance limits. From this procedure, experimental data of MR can be adequately modeled by Weibull, as shown in Fig. 23, which compare frequency histogram to the estimated probability density according Weibull distribution.

Figure 23. MR histogram vs. Weibull distribution

Table 3 shows the calculated MR and its respective probability obtained from the fitted Weibull distribution.

Table 3. MR values probabilities

MR Probability, %

1.15 95.0 1.19 97.5 1.23 99.0 1.26 99,5 1.31 99.9

The values shown in Table 3 can be used as a correction factor (CR). The selection of the MR value, used as CR,

will depend upon how critical the application is. Thus the expansion joint estimated moment can be expressed as in Eq. (15) below.

Mejt=Mavt* CR (15) For example, the respective MR value of a probability of 99.5% is 1.26. Using this number as CR, the Mejt

calculated from Eq. (15) is plotted, in red lines, against the joint actual test results, as shown in Fig. 17 to 22.

4. Conclusion

Based upon test values it is possible to improve the EJMA reaction moment, represented by Eq. (2), which is considering just the bellows spring effect, by adding the friction and pressure forces effects with a correction factor. So, it is suggested to use Eq. (16), to calculate the angular moment for gimbal and hinged expansion joints, due to angular rotation.

Mejt=(Mb + Mlpf + Mpf )* CR (15) Using this equation at the design time will prevent an underestimation of the expansion joints reaction loads,

which are critical in rotating equipment like turbines and turbo-expanders. Additional studies are necessary to evaluate the CR variation according to the pin/sleeve different materials and

environment exposure.


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5. Nomenclature Ad = Differential area Aeff = Effective bellows area CR = Correction factor D = Bellows inside diameter Fb = Force due to the differential area Fe = External forces (weight, etc) Fp = Tf + Fe = Total transversal force in the pin L = Bellows length Ma = Actual moment calculated from expansion joint tests Marm = Moment due to hinges friction Mav = Total moment in a EJ with angular movement Mb = Bellows angular moment due to bellows spring rate Mejt = Theoretical moment in a expansion joint Mlpf = Moment due to the lateral pressure force Mpf = Moment due to pin friction Ms = Moment due to inner sleeve seal friction P = Pressure R = D / 2 Tf = Aeff . P = pressure thrust force calculated per EJMA equations d = Pin diameter kα = Bellows angular spring rate α = Movement angle µp = Pin friction coefficient

6. References

(1) ASME B31.3 – 2006 Process Piping, chapter II and appendix A, ASME Code for Pressure Piping, B31, New York, NY, USA.

(2) NEMA SM23 – 1991(R1997, R2002), Steam Turbines for Mechanical Drive Service, section 8.4, Steam Piping Systems, NEMA Standards, Rosslyn, VA, USA .

(3) Veiga J.C., Medeiros J., Veiga J.L.B.C., PVP2009-77828, “Analysis of FCC Expansion Joints Movement Test”, 2009 ASME Pressure Vessel and Piping Conference , Prague, Czech Republic.

(4) EJMA – 9th edition, section 4, Standards of the Expansion Joint Manufacturers Association, Inc., Terrytown, NY, USA.

(5) Statgraphics Centurion XV version 15.2.00 – Edition Profissional, StatPoint Technologies, Inc., Warrenton, VA, USA.

riooil2010 3298 201006290850rio_oil_3298_2010

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