Fatigue strength analysis of titanium and steel flange connection bolts for ships
[Objective] the new ship and titanium alloy bulbous bow deflector are generally connected by bolts. Due to the influence of bow slamming and wave load, it is necessary to analyze the fatigue performance of titanium and steel connection structure.
[Method] firstly, the stress of titanium and steel connection structure was analyzed by finite element method, and the stress of titanium and steel marine flange connection bolt was calculated. Then, based on fatigue cumulative damage theory and S-N curve method, the titanium and steel connection structure was calculated.
At the same time, according to the stress analysis of the titanium and steel connection structure of the real ship, the corresponding fatigue test scheme is formulated to carry out the fatigue test of the titanium and steel connection structure.
[Result] the results show that the theoretical calculation of fatigue strength of titanium steel joint bolt is basically consistent with the experimental results, and the analysis method of fatigue performance of titanium steel joint is reasonable.
[Conclusion] the established fatigue performance analysis method of titanium steel connection interface can provide useful reference for the connection type, bolt selection and connection structure optimization of titanium steel connection.
With the improvement of technical performance requirements of naval equipment in modern war, many surface ships have installed large Hull Sonar and deflector in bulbous bow. In order to give full play to the performance of sonar, it is necessary to apply certain pressure inside the dome, which puts forward the requirements of high strength, water tightness and sound transmission performance for the dome. Because of its excellent sound transmission performance and high strength, titanium alloy structure is more and more used in Ship Hull Sonar Dome.
At present, the calculation and research of titanium alloy bulbous bow deflector are mainly based on the static strength at home and abroad, mainly focusing on the yield strength [2-3] and impact resistance [4-5] of the body of the deflector, while the research on the fatigue strength of titanium and steel joint of titanium alloy bulbous bow deflector is less. This kind of alternating slamming load in the bulbous bow area can not be ignored, which may lead to the fatigue failure of the bolts at the connection between the titanium alloy bulbous bow deflector and the steel structure of the bow. Therefore, it is of great significance for the safety of the structure to carry out the stress analysis and fatigue life assessment of the bolts at the joint of titanium alloy and steel structure.
In this paper, the fatigue life of the connecting bolts between the titanium alloy bulbous bow deflector and the steel hull structure is evaluated. Through the analysis of the stress of the connecting bolt, the appropriate S-N curve is selected, and the fatigue life of the structure is calculated according to the fatigue cumulative damage theory. At the same time, the fatigue test is carried out to verify the fatigue strength of the joint. In the follow-up design, through the fatigue stress calculation of titanium and steel connection under slamming and other cyclic loads, combined with the fatigue test data of connecting bolts, it can provide reference for optimizing the connection type of titanium and steel connection and guiding the selection of connecting bolts, so as to meet the anti fatigue requirements of football bow deflector.
Stress calculation of connecting bolt
As an important part between titanium and steel structures, connecting bolts need to ensure sufficient strength, tightness and insulation. The connection structure type is shown in Figure 1.
Figure 1 Schematic diagram of bolted titanium and steel structures
Stress calculation of marine flange connection bolt
The finite element analysis software is used for calculation, and the finite element model of the whole titanium alloy dome is established according to the structural scheme of the titanium alloy dome (Fig. 2). The model includes titanium structure, steel structure and titanium steel connection interface structure. The grid size is bolt spacing. The shell element is used to simulate the shell plate of titanium and steel structure, and the beam element is used to simulate the stiffeners, stiffeners and connecting bolts of titanium and steel structure. By applying Slamming Loads on the wet surface of the hull under the conditions of water entry and water exit respectively, and setting fixed boundary conditions at the top and tail boundaries of the bulbous bow, the distribution of tensile stress and shear stress of bolts are calculated, so as to obtain the structural performance of main connecting components such as marine flanges and bolts.
Fig.2 FE model for titanium-steel connection of bulb bow domes
According to the finite element calculation results, the normal stress and shear stress of bolt under slamming pressure can be obtained, as shown in Table 1.
Table 1 bolt stress at the most dangerous position of each marine flange
|Stress components||Numerical value|
|Maximum normal stress σ / MPa||44.2|
|Maximum shear stress τ / MPa||27.1|
Calculation of bolt preload
The bolt connection must be tightened during assembly, and a certain pre tightening force must be applied. The purpose of preloading is to increase the rigidity, reliability and tightness of the connection, so as to prevent the gap or relative slip between the connected parts after loading. Proper control of preload is the key to ensure the quality of threaded connection. Reasonable pre tightening force can not only improve the anti loosening ability of bolts, but also improve the fatigue strength and fatigue life of bolts under alternating load. For alloy steel bolts, the preload QP (unit: n) is usually determined according to the following relationship :
Where: σs is the yield strength of bolt material; A1 is the dangerous section area of bolt, A1»πd2/4, where D is the nominal diameter of bolt. The connecting bolts of titanium and steel structure of bulbous bow deflector are made of 2Cr13 material, with yield strength of 410mpa and bolt diameter of 20mm. Then the tensile stress (unit: MPa) produced by bolt preload is
The pre tightening force of titanium and steel structure connecting bolts is controlled by torque wrench, and the pre tightening torque T = 280n · M. The bolt pre tightening force QP is obtained by T=KQPd.
In the formula, K is the coefficient of tightening force, and the value is 0.2 according to reference .
Therefore, the tensile stress σ 1 generated by the preload QP in the axial direction of the bolt is 0.
By comparing the calculation results of formula (2) and formula (4), it can be seen that the axial tensile stress of the bolt produced by the pre tightening force controlled by the tightening torque of the bolt connection is consistent with the stress value calculated by the pre tightening force calculation method commonly used in formula (1) to formula (2). Therefore, the subsequent bolt stress analysis is the bolt pre tightening force calculated according to formula (3) ~ formula (4) and the bolt axial tensile stress generated by it, and the pre tightening stress is 223 MPa.
Calculation of nominal stress of connecting bolt
According to the third strength theory , the nominal stress of bolt under complex stress condition is . In this calculation, the normal stress should be superimposed on the normal stress produced by the bolt preload, so the nominal stress of the bolt in this calculation is .
The calculation results of are summarized in Table 2.
Table 2 nominal stress of each marine flange connecting bolt
|Maximum normal stress σ / MPa||44.2|
|Maximum shear stress τ / MPa||27.1|
|Pretension tensile stress σ 1 / MPa||223|
|Nominal stress σ von / MPa||272.5|
Life calculation of connecting bolt
Selection of S-N curve
According to the report of reference , the S-N curves of 2Cr13 steel obtained by test method according to GB 3075 standard at different tempering temperatures are shown in Fig.3.
It can be seen from Figure 3 that the S-N curve of 2Cr13 stainless steel varies greatly under different tempering temperatures. The S-N curve of 2Cr13 steel tempered at 710 ℃ is selected as the S-N curve of bolt from the point of view of partial safety.
Fig. 3 S-N curve of 2Cr13 steel at different tempering temperatures
The S-N curve of 2Cr13 steel tempered at 710 ℃ was fitted, and the mathematical expression of S-N curve was obtained
In the formula: s is the stress range; n is the number of stress cycles.
It can be seen from the figure that the fatigue limit is 386mpa, that is, when the stress ratio r = – 1, the stress is lower than 386mpa, and the structure has infinite life and will not fatigue failure.
Fatigue life estimation
Mean stress correction
The initial tensile stress of bolt preload at the first thread is σ1=223mpa, so the minimum stress of bolt is 223mpa.
In order to calculate the fatigue life of bolts by using the standard S-N curve, it is necessary to modify the average stress, that is, the equivalent life of bolts with stress ratio is converted to the stress level with stress ratio r = – 1 by Goodman equation, and then the fatigue life can be calculated by using the standard S-N curve.
The Goodman equation is
In the formula: SA (R) is the stress amplitude when the stress ratio is R; SA (r = – 1)
Is the stress amplitude when the stress ratio r = – 1; SM is the average stress; Su is the ultimate strength of the material.
Fatigue life calculation
According to formula (7), the hot spot stress corrected by average stress is combined with S-N curve for fatigue calculation, and the fatigue life of bolt is obtained. The summary of calculation results is shown in Table 3.
Table 3 fatigue life of bolt structure on marine flange
|Initial stress S0 / MPa||223|
|Maximum stress S1 / MPa||272.5|
|Stress ratio R / MPa (r = S0 / S1)||0.818|
|Stress amplitude s / MPa (s = （S1 – S0）/2 ）||24.75|
|Stress amplitude / MPa (r = – 1)||62.54|
|Fatigue limit / MPa||386|
It can be seen from table 3 that for the bolts at the marine flange position, the corrected stress is less than the fatigue limit of 386 MPa, so the fatigue life of the bolts is infinite.
Fatigue test of 3 connecting bolts
In order to verify the fatigue life calculation of the connecting bolts, accumulate the fatigue strength data of the joint between the titanium alloy deflector and the steel hull, and provide the necessary data support for the corresponding structural design and reliability evaluation, the fatigue test of the connecting bolts of titanium and steel structures is carried out.
Fatigue test samples
In the design of fatigue test pieces of titanium and steel structure connecting bolts, it is necessary to ensure that the test pieces are consistent with the actual ship as far as possible, and at the same time, it is also necessary to consider the conditions under which the test can be realized. The connection bolt, titanium flange, steel flange, non-metallic insulation transition layer between the connection bolts, flange installation and connection process and bolt spacing used in the fatigue test piece are consistent with those of the real ship. Considering the loading capacity of the fatigue testing machine, the number of bolts in the model is less than that in the real ship. Figure 4 is the effect picture of titanium and steel flange connection fatigue specimen, and figure 5 is the processed fatigue specimen.
Fig. 4 effect picture of fatigue specimen of titanium and steel flange connection
Figure 5 connecting bolt specimen after machining
Determination of load of connecting specimen
When designing the loading mode and force application point of the fatigue test of the connecting specimen, the force application direction of the experimental equipment is set in the same line with the axis of the bolt in the center of the specimen in Fig. 5. Therefore, during the fatigue test, all the connecting bolts on the specimen can bear the normal stress approximately. In this way, the external load exerted by the experimental equipment can be calculated by the maximum nominal stress on the titanium marine flange flange in Table 3.
During the fatigue test, according to table 3, the maximum stress σ max = 272.5-223 = 49.5 MPa and the minimum stress σ min = 0 MPA on the single bolt of the connection specimen under the applied load. Therefore, the maximum load (unit: n) exerted by the test equipment on the soft interface connection specimen is
In the formula, n is the number of bolts on the specimen.
Test equipment and installation
The fatigue test of titanium and steel flange connection structure is carried out on the structure fatigue test system of fatigue testing machine (MTS). The bottom of the connecting specimen is rigidly connected with the cross beam of MTS fatigue test system by the strong bolt, and the upper part of the connecting specimen is connected with the force application ball head by the strong bolt through the base, which is used as the loading part of the fatigue test. The installation of connecting specimen on MTS test system is shown in Figure 6.
Fig. 6 connection specimen installed on MTS test system
According to the calculation in Section 3.2, the maximum external load control is 77715n and the minimum external load control is 0n. According to the simulation test results, when the minimum load is set to 0n, the test system will have small fluctuations. Therefore, the minimum load is set to 200N, and the test loading frequency is set to 4Hz.
Test data recording and processing
After debugging, the test system can be started when everything is normal. During the test, necessary inspection and records should be made, including whether the load changes abnormally and whether the connection interface of the test structure changes abnormally. Table 4 shows the change of relative displacement in the loading direction of the structure in the typical cycle during the test. The data show that the deformation of the specimen is stable during the test
Table 4 record of fatigue test data
After the test cycle reaches 3.0 × 106 times, the bolted joint structure is removed from the test system, the surface of the specimen is carefully cleaned, the adhesive on the bolt surface is removed, and then the visual inspection is carried out with a 10 times magnifying glass. There is no abnormal phenomenon in the material interface, insulating sleeve and bolt connection components of the connection interface, which indicates that the fatigue damage of the connection bolt will not occur during the service life.
In the practical engineering application, the anti fatigue design of products should try to ensure that the actual stress is below the fatigue limit of materials, so as to ensure that the fatigue life meets the design requirements. In this paper, the stress analysis and fatigue strength calculation of titanium and steel flange connecting bolts of bulbous bow deflector of a ship are carried out by theoretical method combined with finite element analysis, and the fatigue test of typical bolt interface is carried out according to the stress condition of the ship. The results of theoretical calculation and test method are basically consistent. At the same time, this paper also establishes the calculation method for the fatigue strength research of the titanium and steel connection interface of the bulbous bow deflector, accumulates the necessary fatigue test data of the connection interface, and the results can be used for the fatigue design reference of the titanium and steel connection interface of the bulbous bow deflector.
Author: SONG Zhenwei，CAO Junwei，LIU Ling，ZHENG Shaowen，XU Feng
Source: China Marine Flange Manufacturer – Yaang Pipe Industry (www.steeljrv.com)
(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)
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- ［1］ BAI X F，ZHU X，XU S Q，et al. Design and model test of joining structure of spheroidal sonar dome on bow［J］. Shipbuilding of China，2002，43（3）：32-39（in Chinese）.
- ［2］ LI Y Y. Structural design exploration in new type bul⁃ bous bow of navel ship［J］. Ship Engineering，2007，29（3）：58-60（in Chinese）.
- ［3］ JIANG L S. Analysis of structure strength of sonar dome［J］. Ship Engineering，2004（4）：41-44（in Chinese）.
- ［4］ CHENG X D. Research on anti-shock characteristics of ship bulbous bow［D］. Harbin：Harbin Engineering University，2012 .
- ［5］ WANG S P，CHENG X D，ZHANG A M，et al. Tests for interaction of underwater bubbles and a ship bul⁃ bous bow［J］. Journal of Vibration and Shock，2012，31（22）：96-100，162（in Chinese）.
- ［6］ XU H. Machine design handbook-Vol.2［M］. Beijing：China Machine Press，1991（in Chinese）.
- ［7］ LIU X Y，ZHANG H C，HE X M，et al. Effect of tem⁃ per temperature on fatigue strength of 2Cr13 steel［J］. Physical Testing and Chemical Analysis（Part A：Phys⁃ical Testing），2007，43（9）：446-448（in Chinese）.
- ［8］ Smansky. Handbook of ship structural mechanics Volume 3. Trans. Sun Haitao. Shanghai: Shanghai Science and Technology Press, 1980