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Finite element analysis of tooth load distribution on P-110S conic threaded connections
International Journal of Pressure Vessels and Piping 88 (2011) 88e93
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Finite element analysis of tooth load distribution on P-110S conic threaded connections Shoujun Chen a, Qiang Li a, Yi Zhang b, Qi An a, * a b
School of Mechanical and Power Engineering, East China University of Science & Technology, Shanghai, China Wuxi Seamless Oil Pipe Co., Ltd, Wuxi, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2009 Received in revised form 10 December 2010 Accepted 21 January 2011
Based on elastic mechanics and by use of thick cylinder theory, this paper presents a finite element analysis model with interference fit and axial load on P-110S conic threaded connections and the tooth load distributions on contact threaded surfaces were investigated. A 2D finite element model with elastic-plastic axisymmetric contact threaded surfaces was established and the tooth load distributions on its thread teeth were analyzed under different interference fit and axial load. Results for the loads on every engaged tooth are obtained. These indicate that the load distribution on the engaged teeth is not uniform, with the maximum tooth load concentrated on the first three pairs or the farthest two pairs of engaged teeth from the pin end and the middle teeth only bear a very small load. Such results are identical to the practical situation and indicate that the finite element model proposed in this paper is reasonable. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Finite element analysis Conic threaded connections Interference fit Axial load Tooth load distribution
1. Introduction Conic threaded connections are widely used in the oil industry and this kind of connection has advantages of well assembly, high joint strength and good seal ability. However, failure on threaded connections is the main factor in oil tubing and casing accidents. According to a survey, thread failure mostly happens on the joints of threaded connections in oil industry. Thus, improving the quality of threaded connections has a positive effect on deep oil drilling project. Researches in the past indicate that every thread tooth was under a different load, which leads to the damage or destruction of threaded connections. Stromeyer [1], Den Hartog [2], Goodier [3] and Sopwith [4] analyzed threaded connections subjected to axial load to find out the load distribution on the teeth and they observed that the maximum load occurs at the first tooth pair from the tool joint shoulder or the farthest loading tooth pair from the pin end. Heywood [5] concluded that the variation of stress concentration factor along the teeth is due to two different mechanisms. The first is tooth bending like a cantilever beam, and the second is notch stress effects. More recent investigations into the distribution of load in threaded connections have involved the use of finite element methods. Yuan and Yao [6] made a non-linear finite element analysis in API round threaded connections under make-up torque and axial tensile * Corresponding author. Tel.: þ86 21 64251834. E-mail address: [email protected] (Q. An). 0308-0161/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2011.01.004
load. Tafreshi and Dover [7] analyzed threaded connections using FEM to obtain the location of maximum stress concentration at the drill string tool joint under axial load, pure torsion and bending. Bahai [8] used 2D finite element modeling to calculate the SCFs for API thread connectors used in drill string applications. The threaded joint was subjected to preloading, axial loading and bending loads. Baryshnikov and Baragetti [9] determined the percent of load bearing of each tooth to calculate allowable loads for API drill string threaded connections under bending, axial and combined loading. They concluded that in different conditions of loading, the first engaged tooth has the greatest contribution in load bearing and bears 20% of the total load. Chen and Shih [10] performed a finite element stress analysis under the conditions of make-up torque and axial tension load and proposed a theoretical guide to enhance the API tubing performance. Brennan and Dover [11] made analysis in stress strength on both pipe threaded and conic threaded connections. Placido [12] conducted some experiments on full and reduced scale samples of aluminum drill pipes under cyclic bending and constant tensile loads to investigate their fatigue mechanism. Tanaka [13,14] introduced a modified two-dimensional finite element method to analyze such cases as threaded connections subjected to a transverse displacement and flange coupling under an arbitrary type of loading for typical examples of the threaded connections subjected to an external load. Fukuoka [15] used an axisymmetric finite element method with four types of model that included the effects of friction on two contact surfaces between threads of the bolt and nut, and between fastened plate and nut.
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
89
Nomenclature
d N P
4 T E
n ss r PL
Value of interference Tighten cycle Thread pitch Taper angle Taper Young’s modulus Poisson’s ratio Ultimate strength Density Axial load Fig. 2. The schematic of P-110S conic threaded connections with interference fit.
Newport and Glinka [16] investigated the effect of changing a dimension of the thread geometry on the maximum local stress occurring in a threaded tether connection. They used a previously validated numerical technique and presented the results for changes in thread fillet radius, pitch, wall thickness and the number of engaged threads. Shahani and Sharifi [17] established a 3D finite element model and different types of loading composed of tension and compression, pure preload and a combination of these was applied to the model. Based on the above mentioned references, it is found that some researchers have performed much work on the influences of load distribution on contact threaded surfaces under make-up torque and axial load and some conclusions have been obtained. But we have not found researches on the influences of interference fit caused by tighten cycles on the tooth load distribution on contact threaded tooth. In this paper, in order to assess various effects of interference and axial load on tooth load distribution of P-110S conic threaded connections, the FE standard code, ABAQUS 6.5 [18] has been used and a model has been discretized using structured elements. In these analyses, various types of interference and axial load (10 cases) are considered, tooth load distribution on threaded connection teeth is analyzed and the effects on the contact surface teeth of pin and box are investigated. 2. Definition of interference on conic threaded connections The loading analysis and calculations on conic threaded connections were mainly on the basis of Lame stress analysis and thick cylinder theory. This kind of fitting could be regarded as assembling two cylinders together. In manufacturing, the inner
radius of the outer ring is a little smaller than the outer radius of the inner ring. So the differential d is the value of interference. Fig. 1 shows a schematic of the thick cylinder theory. In Fig. 2 we can see that, when the pin and box contact smoothly with each other in the right position, there are no loads occurring on the thread tooth. If we still screw the pin after the pin reaches the right position, the interference d will be created on the thread tooth in pin and box and the value of interference d is
d ¼ NPtan4 ¼ NPT=2
(1)
where N is the tighten cycle, P is the thread pitch and T is the taper of the conic threaded connections. 3. Finite element modeling 3.1. Assumptions The variation of friction coefficient values between threaded surfaces does not affect the maximum value of the contact stress considerably [19]. In this analysis, the friction coefficient of contact surfaces has been assumed to be 0.02. Also, it is assumed that after tightening the conic threaded connections, 17 pairs of thread teeth are engaged together. In the finite element modeling, whole geometric parameters with all of the details have been considered. According to the API standard [20], the geometric parameters of P-110S conic threaded connection are presented in Table 1. 3.2. Modeling approach The geometry was created in ABAQUS 6.5. The element type selected for mesh generation is CAX8R, which is an 8-node biquadratic axisymmetric quadrilateral and reduced integration element. In ABAQUS, while in the definition of Interaction, there is an option called “Interference Fit” that can simulate the interference. With input of the value of interference fit calculated by Eq. (1) into this option, ABAQUS will define the contact pairs of pin and box tooth with interference fit. Also surface-based contact approach has been used for modeling the contact between engaging tooth pairs on both sides of the thread. Because of the non-linear nature of the contact problem, a standard method has been chosen to solve the
Table 1 Geometric parameters of P-110S conic threaded connection.
Fig. 1. The schematic of thick cylinder theory.
Pipe Thread specification pitch P (mm)
Young’s modulus E (GPa)
Poisson’s Ultimate strength ss ratio n (MPa)
Density r (kg/m3)
P-110S
206
0.3
7850
2.54
758
90
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
problem. Fig. 3 shows the finite element model of the problem in the whole parts of threaded connections and Fig. 4 shows the finite element mesh of thread teeth on pin and box. 4. Evaluation of results Because of the importance of interference fit effects on the conic threaded connections, several analyses have been performed either with or without interference fit. For this to be accomplished, 10 loading conditions presented in Table 2 are applied to the model. 4.1. Tooth load distribution on the thread surfaces subjected to interference fit In this case, loading of the structure conforms to cases 2, 3 and 4 of Table 2. The boundary condition used in this analysis is clamping the box end. With different value of interference, tooth load distributions on contact tooth surfaces are complex and Fig. 5 shows the tooth load on oriented flank and loading flank with different tighten cycle. In Fig. 5 we can observe that, to the oriented flank, the maximum tooth load is sustained by the first two pairs and the farthest two pairs of the engaged teeth from the pin end. When the tighten cycle (or interference) is not large, the tooth load on each contact threaded tooth does not change significantly and the load distribution on conic threaded connections is uniform. With increase of the tighten cycle (or interference), the tooth load on oriented flank increase gradually, especially on tooth numbers 1, 2, 16 and 17, the loads change rapidly. But to the loading flank, the maximum tooth load is concentrated on the first three pairs of engaged teeth and the load on the next thirteen pairs of teeth is relatively stable. This nonuniformity of load distribution on conic threaded connections will have a negative effect on loading capacity and the higher load distribution will also possibly create some failures on thread teeth. 4.2. Tooth load distribution on the thread surfaces subjected to the axial load
Fig. 3. Finite element model.
In this case, loading of the structure conforms to the cases 1, 6 and 9 of Table 2. The boundary condition used in this analysis is
Fig. 4. Finite element mesh of thread teeth on pin and box.
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
91
Table 2 Various cases of loading conditions. Load case
Tighten cycle N
Value of interference d (mm)
Axial load PL (MN)
1 2 3 4 5 6 7 8 9 10
0 1 2 3 1 2 3 1 2 3
0 0.079375 0.15875 0.238125 0.079375 0.15875 0.238125 0.079375 0.15875 0.238125
1.96784 0 0 0 0.7025 0.7025 0.7025 2.5125 2.5125 2.5125
clamping the box end and application of an axial load on the pin end. In order to validate the finite element model established in this paper, we compared the results with Shahani’s analysis [17]. Fig. 6 shows the comparison of tooth load between analysis in this paper and Shahani’s analysis. In Fig. 6, Shahani and Sharifi found from a 2D analysis of an NC50 tool joint with 15 engaged teeth that the first tooth bears the maximum percent of tooth load. The tool joint in this paper is P-110S with 17 engaged teeth. It can be observed that the results of these two analyses are very close suggesting that the finite element
Fig. 5. Tooth load distribution on oriented and loading flank with different tighten cycle. (a) Oriented flank; (b) Loading flank.
Fig. 6. Comparison of tooth load distribution between analysis in this paper and Shahani’s analysis.
Fig. 7. Tooth load distribution on oriented and loading flank with different axial load. (a) Oriented flank; (b) Loading flank.
92
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
In Fig. 8(a) we can find that, when the tighten cycle (or interference) and axial load is not large, the tooth load distribution on the loading flank is relatively uniform. When increasing the tighten cycle (or interference), the load distribution on the loading flank changes rapidly. In Fig. 8(b) we can find that, when the axial load reaches 2.5125 MN and tighten cycle N is 3, the load on tooth 1 decreases while the load on tooth 2 has a large increase. The reason is that the load on tooth 1 has exceeded the ultimate strength of P-110S and plastic deformation has been taken place on the thread tooth. The load that thread tooth 1 should bear has been transferred from the first thread tooth to the second one. According to the analysis above, we can find that the tooth load concentrates on the first three pairs or the farthest two pairs of engaged teeth from the pin end. This phenomenon is identical to the practical situation because thread failure mostly happens on both sides of threaded connections. Such results suggest that more care is needed on the highest loading teeth and it is desirable to find ways to strengthen these teeth and make the middle teeth bear more loads. 5. Conclusions Tooth load distributions on contact threaded surface have been analyzed by using the FEM for P-110S conic threaded connections under different interference fit and axial load. Some results for the loads on every engaged tooth are obtained. The results show that the loading on the engaged thread teeth is not uniform. The tooth load concentrates on the first three pairs or the farthest two pairs of engaged teeth from the pin end and the middle teeth only bear a small load. Such results suggest that it is desirable to find ways to strengthen these highest loaded teeth and make the middle teeth bear more load. The following conclusions can be presented from the analysis:
Fig. 8. Tooth load distribution on loading flank with different tighten cycle and axial load. (a) PL ¼ 0.7025 MN; (b) PL ¼ 2.5125 MN .
model proposed in this paper is reasonable. The discrepancy in these two curves may be attributed to the different geometric parameters. Fig. 7 shows the effect of axial load on the load distribution in threaded connection. To the oriented flank, when the applied axial load reaches 2.5125 MN, the first nine pairs of engaged teeth are out of touch and the load on the oriented flank decreases to zero. To the loading flank, the load on the contact surface increases with increase of applied load and the load was mostly carried by the first three pairs of engaged teeth. It can be observed that in the existence of interference, when the axial load increases, the value of the load on the first three teeth increases more than the other teeth. 4.3. Tooth load distribution on the thread surfaces subjected to combination of interference fit and axial load For more comprehensive investigation of interference fit effects on the tooth load distribution under axial load and especially when variable axial load exists, various combinations of axial load with interference fit are considered. In this case, loading of the structure conforms to cases 5 to 10 of Table 2. Applying axial load under the different interference fit, the tooth load on the loading flank changes significantly and the tooth load on the contact surface is not symmetrical along the thread tooth. The results are shown in Fig. 8.
(1) In the case of interference fit, on the oriented flank, the main portion of the tooth load was sustained by the first two and the farthest two pairs of the teeth from the pin end and on the loading flank, the main portion of load was sustained by the first two pairs. (2) In the case of axial load, on the oriented flank, the pin tooth and box tooth lost contact under a large axial load. On the loading flank, when the axial load increases, the load on the first three teeth increased more than the other teeth. (3) For combination of interference fit and axial load, when the tighten cycle (or interference) and axial load is not large, the tooth load distribution on the loading flank is relatively uniform. If the axial load is large enough to make the tooth load exceed the ultimate strength of threaded connections, plastic deformation will take place on the thread teeth and the tooth load will transfer to the next thread tooth. References [1] Stromeyer CE. Stress distribution in bolts and nuts. Trans Last Nav Arch 1918;60:112e21. [2] Den Hartog JP. The mechanics of plate rotors for turbo-generators. J Appl Mech ASME 1929;51(1):1e11. [3] Goodier JN. The distribution of load in threads of screws. J Appl Mech ASME 1940;62:A10e6. [4] Sopwith DG. The distribution of load in screw threads. Proc Inst Mech Engrs; 1948:373e83. [5] Heywood RB. Tensile fillet stresses in loaded projections. Proc Inst Mech Engrs; 1948:384e91. [6] Yuan GJ, Yao ZQ, Wang QH, Tang ZT. Numerical and experimental distribution of temperature and stress fields in API round threaded connection. Engrg Fail Anal 2006;13(8):1275e84. [7] Tafreshi A, Dover WD. Stress analysis of drill string threaded connection using the finite element method. Int J Fatigue 1993;15(5):429e38.
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93 [8] Bahai H. A parametric model for axial and bending stress concentration factors in API drill string threaded connectors. Int J Press Vessels Piping 2001;78:495e505. [9] Baryshnikov A, Baragetti S. Rotary shouldered thread connections: Working limits under combined static loading. J Mech Design 2001;123(9):456e63. [10] Chen JJ, Shih YS. A study of the helical effect on the thread connection by three dimensional finite element analysis. Nucl Eng Des 1999;191:109e16. [11] Brennan FB, Dover WD. Stress intensity factors for threaded connections. Engrg Fracture Mech 1995;134:545e67. [12] Placido JCR, Miranda PEV, Netto TA, Pasqualino IP, Miscow GF, Pinheiro BC. Fatigue analysis of aluminum dirll pipes. Cater Res 2005;8(4):409e15. [13] Tanaka M, Yamada A. The behavior of fasteners under external loading. Bull JSME 1986;29(248):617e27. [14] Tanaka M, Hongo K, Asaba E. Finite element analysis of the threaded connections subjected to external loads. Bull JSME 1982;25(200):291e8.
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[15] Fukuoka T, Yamasaki N. Kitagawa H at el. Stress in bolt and nut. Bull JSME 1986;29(256):3275e9. [16] Newport A, Glinka G. Reducing the loacal stresses in threaded tether connections. Proceedings of the International Offshore Mechanics and Arctic Engineering Symposium 7th 1988; 1: 141e147. [17] Shahani AR, Sharifi SMH. Contact stress analysis and calculation of stress concentration factors at the tool joint of a drill pipe. Mater Des 2009;30: 3615e21. [18] Hibbitt. ABAQUS finite element code, Version 6.5. Karlsson and Sorensen Inc; 2003. [19] Macdonald KA, Deans WF. Stress analysis of drill string threaded connection using the finite element method. Engrg Fail Anal 1995;2(1):1e30. [20] American Petroleum Insitute. API Specification 7 (Spec 7) specification for rotary drill stem elements. 38th ed.; 1994. Washington, DC.
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Finite element analysis of tooth load distribution on P-110S conic threaded connections Shoujun Chen a, Qiang Li a, Yi Zhang b, Qi An a, * a b
School of Mechanical and Power Engineering, East China University of Science & Technology, Shanghai, China Wuxi Seamless Oil Pipe Co., Ltd, Wuxi, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2009 Received in revised form 10 December 2010 Accepted 21 January 2011
Based on elastic mechanics and by use of thick cylinder theory, this paper presents a finite element analysis model with interference fit and axial load on P-110S conic threaded connections and the tooth load distributions on contact threaded surfaces were investigated. A 2D finite element model with elastic-plastic axisymmetric contact threaded surfaces was established and the tooth load distributions on its thread teeth were analyzed under different interference fit and axial load. Results for the loads on every engaged tooth are obtained. These indicate that the load distribution on the engaged teeth is not uniform, with the maximum tooth load concentrated on the first three pairs or the farthest two pairs of engaged teeth from the pin end and the middle teeth only bear a very small load. Such results are identical to the practical situation and indicate that the finite element model proposed in this paper is reasonable. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Finite element analysis Conic threaded connections Interference fit Axial load Tooth load distribution
1. Introduction Conic threaded connections are widely used in the oil industry and this kind of connection has advantages of well assembly, high joint strength and good seal ability. However, failure on threaded connections is the main factor in oil tubing and casing accidents. According to a survey, thread failure mostly happens on the joints of threaded connections in oil industry. Thus, improving the quality of threaded connections has a positive effect on deep oil drilling project. Researches in the past indicate that every thread tooth was under a different load, which leads to the damage or destruction of threaded connections. Stromeyer [1], Den Hartog [2], Goodier [3] and Sopwith [4] analyzed threaded connections subjected to axial load to find out the load distribution on the teeth and they observed that the maximum load occurs at the first tooth pair from the tool joint shoulder or the farthest loading tooth pair from the pin end. Heywood [5] concluded that the variation of stress concentration factor along the teeth is due to two different mechanisms. The first is tooth bending like a cantilever beam, and the second is notch stress effects. More recent investigations into the distribution of load in threaded connections have involved the use of finite element methods. Yuan and Yao [6] made a non-linear finite element analysis in API round threaded connections under make-up torque and axial tensile * Corresponding author. Tel.: þ86 21 64251834. E-mail address: [email protected] (Q. An). 0308-0161/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2011.01.004
load. Tafreshi and Dover [7] analyzed threaded connections using FEM to obtain the location of maximum stress concentration at the drill string tool joint under axial load, pure torsion and bending. Bahai [8] used 2D finite element modeling to calculate the SCFs for API thread connectors used in drill string applications. The threaded joint was subjected to preloading, axial loading and bending loads. Baryshnikov and Baragetti [9] determined the percent of load bearing of each tooth to calculate allowable loads for API drill string threaded connections under bending, axial and combined loading. They concluded that in different conditions of loading, the first engaged tooth has the greatest contribution in load bearing and bears 20% of the total load. Chen and Shih [10] performed a finite element stress analysis under the conditions of make-up torque and axial tension load and proposed a theoretical guide to enhance the API tubing performance. Brennan and Dover [11] made analysis in stress strength on both pipe threaded and conic threaded connections. Placido [12] conducted some experiments on full and reduced scale samples of aluminum drill pipes under cyclic bending and constant tensile loads to investigate their fatigue mechanism. Tanaka [13,14] introduced a modified two-dimensional finite element method to analyze such cases as threaded connections subjected to a transverse displacement and flange coupling under an arbitrary type of loading for typical examples of the threaded connections subjected to an external load. Fukuoka [15] used an axisymmetric finite element method with four types of model that included the effects of friction on two contact surfaces between threads of the bolt and nut, and between fastened plate and nut.
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
89
Nomenclature
d N P
4 T E
n ss r PL
Value of interference Tighten cycle Thread pitch Taper angle Taper Young’s modulus Poisson’s ratio Ultimate strength Density Axial load Fig. 2. The schematic of P-110S conic threaded connections with interference fit.
Newport and Glinka [16] investigated the effect of changing a dimension of the thread geometry on the maximum local stress occurring in a threaded tether connection. They used a previously validated numerical technique and presented the results for changes in thread fillet radius, pitch, wall thickness and the number of engaged threads. Shahani and Sharifi [17] established a 3D finite element model and different types of loading composed of tension and compression, pure preload and a combination of these was applied to the model. Based on the above mentioned references, it is found that some researchers have performed much work on the influences of load distribution on contact threaded surfaces under make-up torque and axial load and some conclusions have been obtained. But we have not found researches on the influences of interference fit caused by tighten cycles on the tooth load distribution on contact threaded tooth. In this paper, in order to assess various effects of interference and axial load on tooth load distribution of P-110S conic threaded connections, the FE standard code, ABAQUS 6.5 [18] has been used and a model has been discretized using structured elements. In these analyses, various types of interference and axial load (10 cases) are considered, tooth load distribution on threaded connection teeth is analyzed and the effects on the contact surface teeth of pin and box are investigated. 2. Definition of interference on conic threaded connections The loading analysis and calculations on conic threaded connections were mainly on the basis of Lame stress analysis and thick cylinder theory. This kind of fitting could be regarded as assembling two cylinders together. In manufacturing, the inner
radius of the outer ring is a little smaller than the outer radius of the inner ring. So the differential d is the value of interference. Fig. 1 shows a schematic of the thick cylinder theory. In Fig. 2 we can see that, when the pin and box contact smoothly with each other in the right position, there are no loads occurring on the thread tooth. If we still screw the pin after the pin reaches the right position, the interference d will be created on the thread tooth in pin and box and the value of interference d is
d ¼ NPtan4 ¼ NPT=2
(1)
where N is the tighten cycle, P is the thread pitch and T is the taper of the conic threaded connections. 3. Finite element modeling 3.1. Assumptions The variation of friction coefficient values between threaded surfaces does not affect the maximum value of the contact stress considerably [19]. In this analysis, the friction coefficient of contact surfaces has been assumed to be 0.02. Also, it is assumed that after tightening the conic threaded connections, 17 pairs of thread teeth are engaged together. In the finite element modeling, whole geometric parameters with all of the details have been considered. According to the API standard [20], the geometric parameters of P-110S conic threaded connection are presented in Table 1. 3.2. Modeling approach The geometry was created in ABAQUS 6.5. The element type selected for mesh generation is CAX8R, which is an 8-node biquadratic axisymmetric quadrilateral and reduced integration element. In ABAQUS, while in the definition of Interaction, there is an option called “Interference Fit” that can simulate the interference. With input of the value of interference fit calculated by Eq. (1) into this option, ABAQUS will define the contact pairs of pin and box tooth with interference fit. Also surface-based contact approach has been used for modeling the contact between engaging tooth pairs on both sides of the thread. Because of the non-linear nature of the contact problem, a standard method has been chosen to solve the
Table 1 Geometric parameters of P-110S conic threaded connection.
Fig. 1. The schematic of thick cylinder theory.
Pipe Thread specification pitch P (mm)
Young’s modulus E (GPa)
Poisson’s Ultimate strength ss ratio n (MPa)
Density r (kg/m3)
P-110S
206
0.3
7850
2.54
758
90
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
problem. Fig. 3 shows the finite element model of the problem in the whole parts of threaded connections and Fig. 4 shows the finite element mesh of thread teeth on pin and box. 4. Evaluation of results Because of the importance of interference fit effects on the conic threaded connections, several analyses have been performed either with or without interference fit. For this to be accomplished, 10 loading conditions presented in Table 2 are applied to the model. 4.1. Tooth load distribution on the thread surfaces subjected to interference fit In this case, loading of the structure conforms to cases 2, 3 and 4 of Table 2. The boundary condition used in this analysis is clamping the box end. With different value of interference, tooth load distributions on contact tooth surfaces are complex and Fig. 5 shows the tooth load on oriented flank and loading flank with different tighten cycle. In Fig. 5 we can observe that, to the oriented flank, the maximum tooth load is sustained by the first two pairs and the farthest two pairs of the engaged teeth from the pin end. When the tighten cycle (or interference) is not large, the tooth load on each contact threaded tooth does not change significantly and the load distribution on conic threaded connections is uniform. With increase of the tighten cycle (or interference), the tooth load on oriented flank increase gradually, especially on tooth numbers 1, 2, 16 and 17, the loads change rapidly. But to the loading flank, the maximum tooth load is concentrated on the first three pairs of engaged teeth and the load on the next thirteen pairs of teeth is relatively stable. This nonuniformity of load distribution on conic threaded connections will have a negative effect on loading capacity and the higher load distribution will also possibly create some failures on thread teeth. 4.2. Tooth load distribution on the thread surfaces subjected to the axial load
Fig. 3. Finite element model.
In this case, loading of the structure conforms to the cases 1, 6 and 9 of Table 2. The boundary condition used in this analysis is
Fig. 4. Finite element mesh of thread teeth on pin and box.
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
91
Table 2 Various cases of loading conditions. Load case
Tighten cycle N
Value of interference d (mm)
Axial load PL (MN)
1 2 3 4 5 6 7 8 9 10
0 1 2 3 1 2 3 1 2 3
0 0.079375 0.15875 0.238125 0.079375 0.15875 0.238125 0.079375 0.15875 0.238125
1.96784 0 0 0 0.7025 0.7025 0.7025 2.5125 2.5125 2.5125
clamping the box end and application of an axial load on the pin end. In order to validate the finite element model established in this paper, we compared the results with Shahani’s analysis [17]. Fig. 6 shows the comparison of tooth load between analysis in this paper and Shahani’s analysis. In Fig. 6, Shahani and Sharifi found from a 2D analysis of an NC50 tool joint with 15 engaged teeth that the first tooth bears the maximum percent of tooth load. The tool joint in this paper is P-110S with 17 engaged teeth. It can be observed that the results of these two analyses are very close suggesting that the finite element
Fig. 5. Tooth load distribution on oriented and loading flank with different tighten cycle. (a) Oriented flank; (b) Loading flank.
Fig. 6. Comparison of tooth load distribution between analysis in this paper and Shahani’s analysis.
Fig. 7. Tooth load distribution on oriented and loading flank with different axial load. (a) Oriented flank; (b) Loading flank.
92
S. Chen et al. / International Journal of Pressure Vessels and Piping 88 (2011) 88e93
In Fig. 8(a) we can find that, when the tighten cycle (or interference) and axial load is not large, the tooth load distribution on the loading flank is relatively uniform. When increasing the tighten cycle (or interference), the load distribution on the loading flank changes rapidly. In Fig. 8(b) we can find that, when the axial load reaches 2.5125 MN and tighten cycle N is 3, the load on tooth 1 decreases while the load on tooth 2 has a large increase. The reason is that the load on tooth 1 has exceeded the ultimate strength of P-110S and plastic deformation has been taken place on the thread tooth. The load that thread tooth 1 should bear has been transferred from the first thread tooth to the second one. According to the analysis above, we can find that the tooth load concentrates on the first three pairs or the farthest two pairs of engaged teeth from the pin end. This phenomenon is identical to the practical situation because thread failure mostly happens on both sides of threaded connections. Such results suggest that more care is needed on the highest loading teeth and it is desirable to find ways to strengthen these teeth and make the middle teeth bear more loads. 5. Conclusions Tooth load distributions on contact threaded surface have been analyzed by using the FEM for P-110S conic threaded connections under different interference fit and axial load. Some results for the loads on every engaged tooth are obtained. The results show that the loading on the engaged thread teeth is not uniform. The tooth load concentrates on the first three pairs or the farthest two pairs of engaged teeth from the pin end and the middle teeth only bear a small load. Such results suggest that it is desirable to find ways to strengthen these highest loaded teeth and make the middle teeth bear more load. The following conclusions can be presented from the analysis:
Fig. 8. Tooth load distribution on loading flank with different tighten cycle and axial load. (a) PL ¼ 0.7025 MN; (b) PL ¼ 2.5125 MN .
model proposed in this paper is reasonable. The discrepancy in these two curves may be attributed to the different geometric parameters. Fig. 7 shows the effect of axial load on the load distribution in threaded connection. To the oriented flank, when the applied axial load reaches 2.5125 MN, the first nine pairs of engaged teeth are out of touch and the load on the oriented flank decreases to zero. To the loading flank, the load on the contact surface increases with increase of applied load and the load was mostly carried by the first three pairs of engaged teeth. It can be observed that in the existence of interference, when the axial load increases, the value of the load on the first three teeth increases more than the other teeth. 4.3. Tooth load distribution on the thread surfaces subjected to combination of interference fit and axial load For more comprehensive investigation of interference fit effects on the tooth load distribution under axial load and especially when variable axial load exists, various combinations of axial load with interference fit are considered. In this case, loading of the structure conforms to cases 5 to 10 of Table 2. Applying axial load under the different interference fit, the tooth load on the loading flank changes significantly and the tooth load on the contact surface is not symmetrical along the thread tooth. The results are shown in Fig. 8.
(1) In the case of interference fit, on the oriented flank, the main portion of the tooth load was sustained by the first two and the farthest two pairs of the teeth from the pin end and on the loading flank, the main portion of load was sustained by the first two pairs. (2) In the case of axial load, on the oriented flank, the pin tooth and box tooth lost contact under a large axial load. On the loading flank, when the axial load increases, the load on the first three teeth increased more than the other teeth. (3) For combination of interference fit and axial load, when the tighten cycle (or interference) and axial load is not large, the tooth load distribution on the loading flank is relatively uniform. If the axial load is large enough to make the tooth load exceed the ultimate strength of threaded connections, plastic deformation will take place on the thread teeth and the tooth load will transfer to the next thread tooth. References [1] Stromeyer CE. Stress distribution in bolts and nuts. Trans Last Nav Arch 1918;60:112e21. [2] Den Hartog JP. The mechanics of plate rotors for turbo-generators. J Appl Mech ASME 1929;51(1):1e11. [3] Goodier JN. The distribution of load in threads of screws. J Appl Mech ASME 1940;62:A10e6. [4] Sopwith DG. The distribution of load in screw threads. Proc Inst Mech Engrs; 1948:373e83. [5] Heywood RB. Tensile fillet stresses in loaded projections. Proc Inst Mech Engrs; 1948:384e91. [6] Yuan GJ, Yao ZQ, Wang QH, Tang ZT. Numerical and experimental distribution of temperature and stress fields in API round threaded connection. Engrg Fail Anal 2006;13(8):1275e84. [7] Tafreshi A, Dover WD. Stress analysis of drill string threaded connection using the finite element method. Int J Fatigue 1993;15(5):429e38.
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