Evaluation of Tube-to-Tubesheet Junctions - CiteSeerX

M. H. Jawad Manager,

Engineering Design.

E. J. Clarkin Vice President, Plant Manager.

R. E. Schuessler Director,

Research Development and Quality Assurance.

Nooter Corporation, St. Louis, Mo. 63166

Evaluation of Tube-to-Tubesheet Junctions The strength of tube-to-tubesheet joints is influenced by many factors such as method of attachment, details of construction, and material property. In this report three methods of attachment are investigated. They are uniform expansion, mechanical rolling, and welding. Details of construction studied in this report are: the finish of tubesheet hole surface; grooved versus ungrooved tubesheets; and groove geometry. The effect of material property on the joint strength was in­vestigated for carbon steel and titanium tubes attached to carbon steel tubesheet. The results indicate that a theoretical prediction of the behavior of joints is feasible for various materials, methods of attachment, and details of construction.

Introduction The strength level of tube-to-tubesheet attachment in heat

exchangers is important in assuring proper performance of such heat exchangers. The strength of tube attachment depends on many variables such as method of attachment, detail of construction, and material property. This paper presents the summary of a research program that was under­taken to study the effect of various parameters on the strength of tube-to-tubesheet junctions and the interaction between such parameters.

In the construction of heat exchangers, the holes in a tubesheet are drilled slightly larger than the outside diameter of the tubes in order to permit easy installation of the tubes. Methods of attaching the inserted tubes to the tubesheet con­sist of:

(a) uniform expansion, (b) roller expansion, (c) welding to the tubesheet, (d) attaching to the tubesheet by any combination of the above three procedures.

In addition, details of construction vary with different manufacturing processes and have an effect on the attachment strength. The following details of construction were investigated:

(e) surface finish of holes, if) grooved versus ungrooved holes, (g) width of grooves.

Additionally, the effect of materials of construction on the strength of tube attachment was investigated for both titanium and carbon steel tubes attached to a carbon steel tubesheet.

Contributed by the Pressure Vessels and Piping Division and presented at the Pressure Vessels and Piping Conference, Chicago, Illinois, July 20-24, 1986, of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the

Pressure Vessels and Piping Division, September 11, 1985; revised manuscript received February 3, 1986.

Both fabrication and operation conditions were considered. In the operating phase, the following condition was investigated:

(h) temperature effect on strength of tube-to-tubesheet joints.

In this paper the theoretical derivation of the tube-to-tubesheet interaction is developed for each of the foregoing items (a) through (d). This enabled the authors to study each fabrication operation independently. A more general discus­sion of the tube-to-tubesheet interaction has been formulated by many researchers such as K. Uragami, et al. [I] and Soler and Hong [2]. Finite element evaluations have also been discussed by such researchers as Wilson [3].

(a) Uniformly Expanded Tubes

In this method the tubes are expanded by applying a uniform pressure in the tubes over a certain length contained within the tubesheet. The pressure is applied as shown schematically in Fig. 1. Since the annular space between the expander and the tube inside diameter is very small, the axial force due to pressure is negligible and the only force applied on the tubes is in the hoop direction. The mathematical model for predicting the behavior of the tubes is based on the follow­ing four operations:

1 applying pressure until the stress in the tube wall reaches the yield strength of the tube material, 2 increasing the pressure and plastically deforming the tube until the tube wall contacts the tubesheet, 3 increasing the pressure further until the tubesheet-tube composite section is partially yielded, 4 reducing the pressure to zero thereby autofretaging the tubesheet and causing the tubes to be in compression.

The behavior of the tubes and tubesheet due to each of the foregoing four operations is presented next.

Journal of Pressure Vessel Technology FEBRUARY 1987, Vol. 109/19 Copyright © 1987 by ASMEDownloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

HYDRAULIC EXPANDER

TUBESHEET

rc+Afa.

Fig. 2

1 Tube Behavior up to Yield Stress. From the theory of elasticity [4] the strain-stress relationship is given by

1 ih=-^lah~^{or + a,)]

«/=-^rb/-/*K + <^)]

*r=-g\Pr-l*(Oh+al)\

(1)

(2)

(3)

For thin tubes subjected to internal pressure, Ph the average stress is given by

<V Ptr„

- , f f / = 0 " ' " 2 ' " t

Equations (1), (2), and (3) then become

Pi ( 1 ^ \"a\

(4)

(5)

(6)

Equations (4), (5), and (6) can be used to determine the radial growth, tube shortening, and wall thickness reduction due to pressure in the elastic range. From Fig. 2,

final circumference-initial circumference h initial circumference

2T(ra + Ar)-2irra

2irr„

or

~ ^ ( ^ ) (7)

Similarly,

t'-t « r = -

-<hH-b^H (8)

and

or

L'-L

""[3(-H^' (9)

2 Deforming of-Tubes Until They Contact the Tubesheet. When the applied pressure is increased beyond that which causes yielding of the tube wall, the tube deforms plastically until the tube outside surface touches the tubesheet. During this plastic deformation the total volume of the material remains constant. As a consequence, the length of the tube shortens. The amount of shortening can be derived as

N o m e n c l a t u r e

E F f L

L' P

P*

Pi P0

R

radial clearance between tube o .d . and hole diameter, in. modulus of elasticity, psi pushout force, lb friction coefficient length, in. final length, in. pressure, psi internal pressure at which yielding first occurs internal pressure at which total yielding of cross sec­tion occurs inside pressure, psi outside pressure, psi radius at given point in tubesheet

NOTE: Approximate SI Conversion Units—1 in. 2.54 cm,

R,

Rn

r

re

n rn

t V Vi

vf

a

1 lb

= inside radius of tubesheet effective radius, in.

= outside radius of tubesheet effective radius, in.

= radius at given point in tube, in.

= average radius, in. = inside radius = outside radius, in. = thickness, in. = final thickness, in. = initial volume of

material, in3

= final volume of material, in3

= coefficient of thermal ex­pansion, in./in.°F

= 0.4536 kg, 1 psi = 0.00689 MPa.

ArA A

AT 8

e*.«/.«r

°h>al

P P

,<fr

Oy

= change in radius, thickness, and length, respectively, in.

= change in temperature, °F = deflection, in. = strain in hoop,

longitudinal, and radial directions, respectively, in./in.

= Poisson's ratio = radius between elastic and

plastic zones of yielded thick shell, in.

= stress in hoop, longitudinal, and radial directions, respectively, psi

= yield stress, psi

20 / Vol. 109, FEBRUARY 1987 Transactions of the ASME Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

L

L L'

Fig. 3

Fig. 6

Fig. 4

Fig. 7

Fig. 5

follows. Referring to Fig. 3, it is seen that the initial volume, vh of the tube in the tubesheet area is given by

Vi = ir(r02-r?)L

The volume after deformation, vf, is given by

vf = w[(r0 + c)2-(r0+c-t)2]L'

Letting r0 = rt + t, and equating initial and final volumes gives

2r, +1

\2r, + t + 2c/ (10)

This equation is used to determine the tube shortening due to uniform expansion.

3 Partial Yielding of Tubesheet. An increase in pressure, beyond that which causes the tube wall to be in contact with the tubesheet, will stress the tubesheet locally. This local area can be represented by an equivalent thick cylinder of inside radius Rj and outside radius R0 as shown in Fig. 4. From the theory of plasticity [5], the stress in the elastic and plastic por­tions of a thick cylinder, Fig. 5, is given by

Elastic Region

*-(»(£)O-40 *-(-#-)(£)

Plastic Region

•.-(-^0+£+»-r) -(-£-)(-£-»-r) «-(-£-)(£-»-r)

The elastic-plastic interface is expressed by V3 V R0

2 P ' calculated from equati

V3 V R} )

(12)

(13)

(14)

(15)

(16)

V 3 V ^ - p . ™

Initial yielding is calculated from equation (17) by letting p = Rj. This gives

(18) V3

Total yielding occurs by letting p = R0. This gives

„„* ~2ay i R< p* * - ——L. in .

V3 Rn (19)

4 Reduction of Pressure to Zero. When the pressure is reduced to zero, the reduction in deflection and stress values can be calculated from the elastic theory. From thick shell theory [6] and Fig. 6, the deflection due to internal pressure (with a, = 0) is given by

-(-&-)(!&-)('•£) 5=- 'P,R'2 -[RHl-p)+R0Hl+p)]

(11) ER(R2-R?)

and the deflection due to external pressure is expressed as

(20)

Journal of Pressure Vessel Technology FEBRUARY 1987, Vol. 109/21 Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Table 1 Properties of tubes and tubesheet

Theoretical o.d. Theoretical i.d., Theoretical t, in Hole size, in. Hole pitch, in. Nominal length

, in. in.

in. Actual yield stress, ksi Actual tensile strength, ksi E, psi (106) a, in/in°F (10" Poisson'

Tube no.

IT 2T 3T 4T 5T 6T 7T Average IC 2C Average

T = titan

s ratio, 6)

Tube. Carbon Titanium

steel 1.0 0.902 0.049

6 25.0 55.0 30 6.5 0.3

1.0 0.902

Tubesheet

0.049 2-5/8 CS +3/8 Ti

6 61.0 81.0 15.5 4.9 0.34

1.010 1.25

48.6 76.1 30 6.5 0.3

Table 2 Dimensions of installed tubes

um C = carbon steel

tube i.d., in.

0.905 0.906 0.906 0.906 0.905 0.906 0.904 0.905 0.900 0.900 0.900

Tube length,

in. 6.021 6.018 6.007 6.015 6.016 6.014 6.013

5.951 *~ 5.984

t

in. 0.0455 0.0465 0.0450 0.0465 0.0480 0.0470 0.0470 0.0465

* 0.0495 0.0495 0.0495

Table 3 Contraction of tubes due to uniform Tube no. 1 IT 2T 3T 4T 5T 6T 7T Average IC 2T Average

r eq. (7)

2 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020

0.0004 0.0004

Net c 3

0.0045 0.0035 0.0045 0.0035 0.0025 0.0030 0.0040

0.0051 0.0051

1 eq. (9)

4 -0.0035 -0.0035 -0.0035 -0.0035 -0.0035 -0.0035 -0.0035

-0.0007 -0.0007

1 eq. (10)

5 -0.0246 -0.0192 -0.0246 -0.0192 -0.0137 -0.0164 -0.0219

-0.0279 -0.0279

Clearance,

in. 0.0065 0.0055 0.0065 0.0055 0.0045 0.0050 0.0060

0.0055 0.0055

expansion

Columns 4 + 5

6 -0.0281 -0.0227 -0.0281 -0.0227 -0.0172 -0.0199 -0.0254 -0.0234 -0.0286 -0.0286 -0.0286

Table 4 Residual stress in tubes Tube no.

IT 2T 3T 4T 5T 6T 7T Average IC 2C

«-_

Expansion pressure,

ksi

40 40 40 40 40 40 40

28 28

PR2

1 o*Ko

Inside stress

eq. (14), psi

42,370 42,200 42,450 42,200 41,920 42,100 42,100

29,330 29,330

.rj?2n „ i J .

Inside stress

eq. (22), psi

-46,820 -46,860 -46,860 -46,860 -46,710 -46,770 -46,770

-61,420 -61,420

E>.2n -l-„M

Net stress,

psi

-4450 -4660 -4660 -4660 -4790 -4670 -4670

- 32,090 - 32,090

n\\ ER(R„2~R?)1 •" ,y r"

The hoop stress due to pressure is -PtR?+P0R0

2 - (P, -P0) (R?R02/R2)

°h' R}-R} (22)

+ xz^zs £

3" r5

vTt

(A

CM

4 C.5TL.

Fig. 8

From Fig. 7, the compatibility between the tubes and tubesheet requires that

S i U r ^ ' a - * , (23) Equations (20) through (23) are based on the assumption

that free relaxation of the holes in the tubesheet, when expan­sion pressure is released, is greater than the free relaxation of the tubes.

It is of interest to note that thin walled, high strength tubes may remain fully elastic up to and beyond the point of contact with the hole wall. This is especially true when the modulus of elasticity of the tubes is significantly smaller than that of the tubesheet and the yield stress of the tubes is significantly higher than that of the tubesheet. Also, tubesheets with yield stress significantly higher than the tubes may remain fully elastic during application and after removal of the applied pressure.

Comparison of Theoretical and Experimental Data. The results calculated from the theoretical equations were com­pared with experimental data obtained by testing titanium and carbon steel tubes inserted into a carbon steel tubesheet. The tubes were 1 in. o.d. and 18-gage thickness (0.049 in.). The tubesheet thickness was 3 in. as shown in Fig. 8 and Table 1. Actual dimensions of the tubes and the clearances between the tubes and tubesheet are shown in Table 2. From these dimen­sions, the theoretical elastic and plastic tube shortening due to internal pressure over^a length of 2.625 in. was calculated from equations (9) and (10) and is listed in Table 3. The value of P in equation (9) was calculated from the expression Pt = Oyt/Tj where ay is the yield stress of the tubes.

The required internal pressure needed to autofretage the tube and tubesheet is calculated from equation (19) using average values for Rt and R0. Since the yield stress of the tubes and tubesheet are different, an approximate value of the yield stress was used. An average yield stress of the composite sec­tion consisting of titanium tubes and carbon steel tubesheet was assumed to be 71 ksi. This value was the average of the yield stress and tensile strength of the tubes shown in Table 1 and was chosen to assure adequate yielding of the tubes without exceeding the tensile strength of the tubesheet. The assumed yield stress value of 71 ksi resulted in a calculated autofretage pressure of 40,000 psi from equation (19).

The average yield stress of the composite section consisting of carbon steel tubes and carbon steel tubesheet was assumed as 50 ksi. This value is slightly above the yield strength of the tubesheet to allow adequate yielding yet low enough to prevent the tubes from reaching their ultimate strength. This assumed yield stress resulted in an autofretage pressure of 28,000 psi. With the calculated pressures of 40 and 28 ksi, the theoretical stress at the inside surface of the composite section as deter­mined from equation (14) is shown in Table 4.

As the pressure is reduced to zero, the stress distribution due to the pressure reduction can be calculated from the elastic theory. From equations (23) and (22) the stress reduction at the inside surface of the composite section is tabulated in Table 5. The net stress at the inside surface due to the pressurization and pressure reduction is also given in Table 4.

22 / Vol. 109, FEBRUARY 1987 Transactions of the ASME Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Table 5 Pushout force of uniformly expanded tubes Tube no.

IT 2T 3T 4T 5T 6T 7T Average IC 2C

Theoretical contact

pressure, psi 380 410 375 410 435 415 415 406

2990 2990

Theoretical pushout force, lb

2340 2530 2310 2530 2680 2560 2500 2490

13,140<6)

13,140

Actual pushout

force, lb

1860 2220 1500 2000 2040 1380 1880 1840 7530 7130

Maximum<o)

tensile force

11,000 11,270 10,890 11,270 11,640 11,400 11,370

8120 8120

'"'This is the axial tensile force needed to break the tube material and is equal to the tensile strength times the cross sectional area of the tube. ((l)The theoretical contact pressure of 2990 psi results in a maximum hoop stress in the tubes which exceeds the yield stress of the material. Accordingly, the theoretical pushout force was based on a yield stress of 25,000 psi.

Table 6 tubes Tube no.

13 14 15 16 17

Average

Uniformly expanded plus 3 percent roller expanded

i.d. after uniform

expansion, 40ksi

0.921 0.922 0.921 0.920 0.921

i.d. after uniform

expansion us 3 percent

rolling 0.923 0.922 0.923 0.922 0.923

Pushout force,

lb

2460 2880 2660 3280 3140 2880

TUBESHEET

TUBE WALL

Fig. 9

000

000

-

_

-

'////. //// % ^

m

mm

m m V

^-THEO F

UNIFORM EXPANSION UNIFORM EXPANSION ONLY (40 KSI) PLUS 3% ROLLED

Fig. 10

The equivalent pressure that develops between the tube and tubesheet and which results in the net compressive stress shown in Table 4 can be calculated from equation (22) and is tabulated in Table 5. This pressure can be measured indirectly by calculating the total pushout force needed to push the tubes out of the tubehole. The total force on the tube is given by

(P0)(2wr0)(L)

and the required pushout force is given by

F=2irfP0r0L (24)

where, L is taken as 2.625 in. a n d / i s the friction coefficient taken as 0.74. This coefficient of friction [7] is for mild steel on mild steel and is also assumed applicable to titanium on mild steel. Table 5 shows the magnitude of the theoretical pushout force obtained from equation (24) as well as the ac­tual pushout force obtained experimentally.

The pushout force shown in Table 5 for titanium tubes is significantly smaller than the force required to break the tubes. This is due to the fact that the modulus of elasticity of the titanium tubes is less than that for the tubesheet. Hence, the tubes tend to spring back more than the tubesheet material when the uniform expansion pressure is released. For the car­bon steel tubes the pushout force is very close to that needed to break the tubes.

(b) Roller Expanded Tubes Subsequent to Uniform Expansion (Hybrid Expansion)

It was shown in the previous section that uniform expansion increases the tube outside diameter and decreases the length. The decrease in length develops tensile stress in tubes attached to fixed tubesheets or to tubesheets with a large number of tubes. This condition can be minimized or eliminated if the tubes are rolled so that the decrease in thickness is accom­panied by an increase in length. The increase in length due to roller expansion must be the same as the decrease in length due

to uniform expansion. Referring to Fig. 9, it is seen that the in­itial volume can be expressed as

y,= 7r(r02-r,-2)L

While volume after expansion is given by

vf = ir(r02-r?)L'

defining t = r0 — /•,• and t ' =r0 — r- gives

(2/7,-Of L' =L (25)

(2r0-t')f Referring to Table 3, it is seen that the shortening of the tubes due to uniform expansion was 0.0234 in. Hence, from equa­tion (25) the reduction in thickness due to expansion rolling a length of 1.1875 in. along the tube in order to get the tubes to their original length is

r 2 - 2 / y ' + - ^ ( 2 / - o - f ) r = 0

r ' 2 - (1 .01)r ' + 1.1875

1.2109 (1.01-0.0465)(0.0465) = 0

and V = 0.0456 in., which is slightly over 2 percent reduction in wall thickness. Accordingly a 3 percent reduction was ap­plied to the tubes using a 3-roller expander. The axial force needed to push a tube that is uniformly expanded then 3 per­cent roller expanded is shown in Table 6. A comparison be­tween the force needed to push out uniformly expanded tubes versus expanded and rolled tubes is shown in Fig. 10. Also shown is the theoretical average pushout value for a uniformly expanded tube. The figure shows that roller expansion in­creases the precompression pressure between the tubes and the tubesheet. Also, roller expansion substantially fills the grooves with extruded material from the tubes.

Journal of Pressure Vessel Technology FEBRUARY 1987, Vol. 109/23 Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Tube no.

18 19 20 21

Average

Table 7 Pushout force for welded tubes Actual pushout force, (°)

lb 11,400 11,060 11,000 11,520 11,250

<"' Theoretical breaking strength of tubes is 11,800 lb

STICKS OUT

Fig. 11

Table 8 Pushout force for welded and expanded tubes

Tube no.

22 23 24 25 26

Average 27 28 29 30 31

Average

Operation

W+U W+U W+U W+U W+U

W+U+R W+U+R W+U+R W+U+R W+U+R

force, lb

11,520 11,500 11,400 11,780 11,500 11,540 11,160 11,100 11,160 11,160 11,200 11,160

g 10000

„

fj 8000

H 6000

o fc

2000

W= Welded tubes U= Uniformly expanded at 40 ksi hydraulic pressure R = Roller expanded with 3 percent wall reduction

Table 9 Tests

no.

8T-12T 13T-17T 18T-22T 23T-27T 28T-32T 33T-37T 3C-7C 8C-12C 13C-17C 18C-22C 23C-27C 28C-32C

Burnish

No No No Yes Yes Yes No No No Yes Yes Yes

Average finish,

rms

14 168 200

19 95

176 16

172 220

40 72

209

Material

Ti Ti Ti Ti Ti Ti CS CS CS CS CS CS

Expansion pressure,

ksi

40 40 40 40 40 40 28 28 28 28 28 28

Average pushout force,

lb 3430 5000 4600 4990 4410 4840 3720 6570 6130 5260 6020 7660

Table 10 Joint strength in grooved and ungrooved holes Test no.

24T 25T 38T 39T

Material

Ti Ti Ti Ti

Surface finish,

rms 25 25 25 25

Groove

No No Yes Yes

Pushout force,

lb 4920 4960 3600 3560

(c) Welded Tubes

It was shown in Table 5 that uniformly expanded titanuim tubes in a carbon steel tubesheet require a very small force to push them out compared to carbon steel tubes due to their modulus of elasticity. In order to increase the holding strength of titanium tubes to carbon steel tubesheet joints, they have to be welded to the tubesheet. The welds attaching tubes to tubesheet must be made so that they are as strong as the tubes themselves. In this experiment the tubes were welded with a minimum of 1 t thickness as shown in Fig. 11. Results of the push out test are shown in Table 7. The results indicate that titanium tubes welded to carbon steel tubesheets have superior holding power compared to uniformly expanded tubes. This conclusion was also verified by Reynolds [8] and Emhardt [9].

UNIFORM UNIFORM WELDED EXPANSION EXPANSION ONLY ONLY * 3t ROLLED (40 KSI)

WELDED •UNIFORM EXPANSION (40 KSI)

WELDED • UNIFORM EXPANSION 34 ROLLED

Fig. 12

(d) Welded, Uniformly Expanded, and Rolled Tubes

An experiment was conducted to study the effect of uniform expansion and rolling on the strength of welded tubes. The results are shown in Table 8 and Fig. 12. The results indicate that no increase in pushout force is accomplished by uniform expansion or rolling. However, the pattern of failure shown in Fig. 13 indicates that more consistent results are achieved with welded, uniformly expanded and rolled tubes.

(e) Surface Finish of Holes

In order to establish the effect of hole finish on the strength of tube-to-tubesheet joints, a series of uniform expansion tests were conducted using titanium and carbon steel tubes in holes with no grooves. A total of 60 tubes (thirty carbon steel and thirty titanium tubes) were tested in twelve different ex­periments as shown in Table 9. The tests were divided into two parts. Those with burnished holes and those with unburnished holes. Three different hole surface finish values were tested—very smooth, intermediate smoothness, and rough.

The various categories of the tests and their surface finish values, in rms, are shown in Table 9 together with the pushout force required to separate the tubes from the tubesheet. These results are plotted in Fig. 14 for the titanium tubes and in Fig. 15 for the carbon steel tubes. The plots show the average as well as the scatter of measured values. For the titanium tubes, the range of data indicates that the hole surface finish has no significant effect on strength of joints and neither does the burnishing procedure. For the carbon steel tubes, the strength seems to improve with surface finish. Burnishing seems to im­prove the strength of smooth holes but not rough ones.

(f) Grooved Versus Ungrooved Holes

Grooves as shown in Fig. 8 tend to improve the strength of tube-to-tubesheet joints. This is due to the additional locking mechanism that is developed by deforming the tubes into the groove during uniform expansion. Tests conducted with car­bon steel tubes generally confirm this mechanism. However, a limited number of tests conducted with titanium tubes attach­ed to a carbon steel tubesheet showed an opposite effect as shown in Table 10. The tubes tested were inserted in holes with a surface finish of less than 50 rms. Based on these results as

24 / Vol. 109, FEBRUARY 1987 Transactions of the ASME Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

\ ~

7000

6000

5000

4000

3000

2000

1000

1110 OURlIISlI ---r-- BURl/ISH

Effect of hole surface finish on titanium tubesWE.L..D

TEST

FINISH

Fig. 14

14 200 ~S 17E

teract with each other. Figure 16 shows the average results offifteen tests conducted at the stated groove widths. The figureindicates that the best results for titanium tubes are obtainedwhen the width of the groove is equal to the quantity 1.56.Jft.

P'

209n40220In16

,-- NO OURIIISII --r-- BURNISH .1

~l""""'<~'\.'\.'\.'\::

~'l/~

~"

Fig. 15 'Effect of hole surface finish on C.S. tubes

9000

8000

7000

~6000

~5000

lZ5 4000'2

~ 3011Q

2000

1000

TEST

FIfIlSH

(h) Temperature Effect on Strength of TUbe-to­Tubesheet Joints

It was shown in Table 5 that the average pressure betweenthe titanium tubes and carbon steel tubesheet was 406 psi. Thisgives an approximate tube deflection of

fl. Pr2 406 x 0.5052

De ectlOn =--Et 15.5x106 xO.0465

= 1.437 x 10-4

The titanium tubes have a different coefficient of expansionthan the carbon steel tubesheet. Hence, the theoretical rise intemperature needed to give a deflection of 1.437 x 10- 4 is

o 1.437 X 10- 4liT=----

(acs - aTi)r (6.5 - 4.9)10- 6 (0.505)

= 178°F

A test was conducted at room temperature, 160 F, 240 F, and400 F to determine the actual behavior of titanium tubes in

Fig. 13

well as those obtained in the next section, it is concluded thatthe 1/8 in. grooves tend to reduce the surface area of the con­tact pressure and thus reduce the total pushout force. Thisreduction does not occur for wider grooves as discussed in thenext section.

(g) Width of Grooves

Most grooves used in industry are about 1/8 in. in width asshown in Fig. 8. To determine the strength characteristics ofsuch grooves, a series of tests were conducted using 1/8 in.,114 in., and 3/8 in. groove widths. These widths were selectedas multiples of the quantity 1.56.Jft, where r is the radius and tis the thickness of the tubes. For the tubes used in this experi·ment, this quantity is equal to 0.23 in. which is approximatedas 1/4 in. A tube inserted in a hole that has a groove width of1.56.Jft and subjected to internal pressure will deflect andbend such that the effects of the edges of the groove do not in-

Journal of Pressure Vessel Technology FEBRUARY 1987, Vol. 109125

Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

WIDTH, INCH

1/8 1/4 3/8

0.5 1.0 1.5

WIDTH, 1.5vJrT

Fig. 16 Width of grooves

carbon steel tubesheets for various temperatures. The result is shown in Fig. 17 and indicates a reduction in pushout force as the temperature increases.

Conclusion Uniform expansion of tubes results in an excellent tube-to-

tubesheet junction when the modulus of elasticity of the tubes and tubesheet are about the same. The strength of the junction diminishes as the modulus of elasticity of the tube material reduces below that of the tubesheet.

Roller expansion of tubes subsequent to uniform expansion improves the stress in tubes of fixed tubesheets or tubesheets with a large number of U-tubes because it tends to minimize the residual axial tensile stress due to uniform expansion.

Good tube-to-tubesheet junctions can be achieved by welding tubes that have a modulus of elasticity different from that of the tubesheet. For such welded tubes, no structural ad­vantage is achieved by uniformly expanding or rolling the tubes. However, more consistent results are obtained by con­trolling the location of the point of failure and forcing it to oc­cur outside the tubesheet.

Burnishing the holes and improving hole finish does not seem to influence the joint strength when the tubes are of a different material than that of the tubesheet. The strength does seem to improve for tubes and tubesheets of the same material.

Further Research

The theoretical procedure developed in this paper is intend­ed to help the designer predict the behavior of tube-to-tubesheet joints. The numerous tests presented here were per­formed in order to verify the developed theory. Only a limited number of tests were conducted due to available time and funds. Accordingly, further research is needed especially in the following areas:

2200

2000 •

1800 "

1600 "

1400 ~

1200 •

1000 "

800 "

600 "

400 •

200 "

0

\ \ \

> 1

^^THEORETICAL

\ \ \ \ \ \

\ \ \ \ . \ \ \ \ \

i | 4 i i i

100 300 200

TEMPERATURE,°F

Fig. 17 Reduction of pushout force with temperature

1 More testing is needed to study the effect of temperature on joint strength.

2 Additional tube and tubesheet materials need to be tested to substantiate the derived theory.

3 Effect of groove depth and the number of grooves on the strength of joints.

4 More testing is needed to correlate hole surface finish with joint strength.

Tests are in progress at the Nooter Corporation for some of these research topics.

Acknowledgment

This research project was sponsored and conducted by the Nooter Corporation in St. Louis. Acknowledgment is given to Messrs. Dan Kelly and Mark Lunte for preparing and testing the specimens and to all other Nooter Personnel who worked on the different phases of the project and contributed to its success.

References

1 Uragami, K., Sugino, M., Urushibata, S., Kodama, T., and Fujiwara, Y., "Experimental Residual Stress Analysis of Tube-to-Tubesheet Joints During Expansion," ASME Paper No. 82-PVP-61, 1982.

2 Soler, A. I., and Hong, Xu, "Analysis of Tube-Tubesheet Joint Loading Including Thermal Loading," ASME Paper No. 84-APM-15, 1984.

3 Wilson, R. M., "The Elastic-Plastic Behavior of a Tube During Expan­sion," ASME Paper No. 78-PVP-112, 1978.

4 Timoshenko, S., and Woinowsky-Krieger, W., Theory of Plates and Shells, McGraw-Hill Book Company, New York, 1959.

5 Prager, W., and Hodge, P., Theory of Perfectly Plastic Solids, John Wiley and Sons, Inc., New York, 1965.

6 Jawad, M., and Farr, J., Structural Analysis and Design of Process Equip­ment, John Wiley and Sons, Inc., New York, 1984.

7 "D85 Dodge Engineering Catalog," P.H1-29, Reliance Electric Company, Greenville, S.C., 1984.

8 Reynolds, S. D., "Tube Welding for Conventional and Nuclear Power Plant Heat Exchangers," ASME Paper No. 69-WA/HT-24, 1969.

9 Emhardt, F. W., "Heat Exchanger Tube-to-Tubesheet Joints," ASME Paper No. 69-WA/HT-47, 1969.

26/Vol. 109, FEBRUARY 1987 Transactions of the ASME Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 06/15/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use