The preload analysis of screw bolt joints on the first wall graphite tiles in East AO ei( 曹磊 ), SONG Yuntao( 宋云涛 ) Institute of plasma physics, hinese academy of sciences, Hefei 230031, hina Abstract The first wall in Experimental Advanced Superconducting Tokamak (EAST) has used many graphite tiles to face the plasma. All graphite ties have been mounted on heat sink using screw bolts which had been preloaded to produce clamp force. The clamp force is very important to keep the graphite tiles on the surface of the heat sink tightly because the heat flux will cross this contacting surface in a small thermal resistor. Without the clamp force the small gap between graphite tiles and heat sink will lead thermal power can not be carried away by cooling water. The worse is some bolts turned out with the loss of clamp force. rom the mathematical models the process of the loss of clamp force has been studied. Research results explain how the different thermal expansion of three members of the screw joint leads to the clamp force decrease to zero under temperature rise and external force and how the stiffness affect the relationship between the clamp force and temperature. The research also gets the critical temperature point that the clamp force can remain above zero. Research results indicated this screw joint is absolute to lose their clamp force during the EAST running so that the bolt joints should be redesign to improve its reliability. eywords: clamp force, preload, residual preload, thermal expansion PAS:52.55.a 1. Introduction Experimental Advanced Superconducting Tokamak (EAST) is one of the most important steady-state plasma physics experimental devices in the world. The first wall in EAST has been employed to protect the vacuum vessel and other components which can t withstand high thermal power from plasma. The first wall has installed 4896 graphite tiles on the heat sink to face the plasma. It means the graphite tiles have to face high heat flux from plasma. Graphite can be used as first wall material because it is a good material to withstand high temperature. The graphite is also a good thermal conductive material, so heat flux on the first wall can be transfer rapidly to heat sink that at last is cooled by water. In order to make the heat transfer effectively, graphite tiles should be pressed on the heat sink tightly by a clamp force [1]. All Graphite tiles have been mounted on the heat sink using screw bolts. Though all bolt joints have been preloaded to provide the enough clamp force, in EAST or some other similar Tokamaks, the clamp force on graphite tiles was disappear during plasma burning [1]. Table.1 shows that there is about 1~1.5% of total graphite tiles loosed their clamp force. igure.1 shows the screw bolt escaped from the first wall and graphite tiles fall down from the heat sink. (Table.1) (igure.1) Author s email: caolei@ipp.ac.cn
Obviously the clamp force has been disappeared under high temperature during plasma burning. With the disappearing of clamp force a very small torques resulting from electromagnetic force can turn the screw bolt out [2-3]. With the disappearing of clamp force there will be a small gap between the graphite tiles and heat sink with the electromagnetic force acted on first wall. So it is necessary to study the process of the loss of clamp force to improve the designs intended to increase the quality and reliability of the first wall. It is well known that for material under high temperature creep can lead to stress relaxation with the plastic deformation [4-5]. How ever though some parts were serious erosion by sudden very large thermal energy, the results of careful measurement of the dimensions proved that most components of first wall have not exceeded their elastic limit. It means the bolt joints on first wall loose its clamp force without creep. In fact though none of material exceed their elastic limit the elastic deformation of all components will change under high temperature and external force. The expansion and stiffness of the material may affect such a process. 2. The analysis of the process of clamp force change for the bolt joints East has got a loop vacuum vessel with D shape section as igure.2 shown. The first wall was installed on the Vacuum vessel to face the plasma. All bolt joints on first wall in EAST have the same design. The detailed structure of bolt joints is shown in igure.2. Each bolt joint has three members: a heat sink, a graphite tile and a screw bolt. The material of all components and its properties are in Table.2 [6-7]. (igure.2) (Table.2) 2.1 The relation between deformation and preload A typical bolt joint can be present by an elastic-deformation model. igure.3 shows the structure of the mechanical model. The model shows that the strength and stiffness of a single bolt joint depends on the physical and geometrical properties of the members. Each member of the bolt joint was seen an elastic unit which can be described by stiffness and deformation. In igure.3 the graphite tile. is the stiffness of the heat sink. is the stiffness of the screw bolt. is the stiffness of X are their deformation caused by preload P. The interface shown in igure.3 between graphite tile and heat sink should contact very well under the preload. Here preload P P acts as clamp force and all members have to withstand the preload. It means that the different member will be different deformation as they have different stiffness as igure.4 shown. (igure.3) The deformation on each components depend on there stiffness and force. The stiffness of each component can be presented in such equation (1) [6-8] EA (1) Where: E is the elastic modulus and A is the cross section area of the bolt or load area. is the equivalent length of each component. Here the cross section area depends on the equivalent diameter. or 6 bolt the equivalent diameter is its bottom diameter. or heat sink and graphite tile the equivalent diameter can be
calculated on assumption of cylinder effective area [7]. So the effective outer diameter of heat sink and graphite tile equal to the diameter of head of 6 bolt (10mm) and the inner diameter equals to diameter of cross hole (6.5mm).. The deformation of each member can be calculated by equation (2) [6-8] P (2) The preload on a bolt has been defined as 500N to prevent that the graphite tile was broken. The 500N P associated with the torque T 0.4N has been provided by a definite torque wrench. In this case the specific P calculated parameters are listed in Table.3. (Table.3) The mechanical model showed in igure.3 indicates that the heat sink and graphite tile are connected in series. They are parallel with bolt. So the stiffness of heat sink and graphite tile can be considered together. Define is P the equivalent stiffness of and [8-10]. N/ 62.2E6 (3) Define X is the equivalent stiffness of X and X is the equivalent deformation: X (4) 8.03E 3 2.2 The process of clamp force loss affected by external force When the external force acts on the graphite tile, the total force does not equal to the sum of the preload and external force [11-12]. The total load t will equal to the sum of external force and residual preload P. igure.4 illustrates how the external force affects the connection system. (igure.4) In igure.4 left slash (solid line) present the deformation of the bolt and right slash (dash line) present the deformation of graphite tile and heat sink. With the increasing of the external force, the left slash extend to a higher position which mean that the clamp force p reduces to deformation x and the follow equations can be deduced: P. The external force brings the external ( x) P ( x) P (5) (6)
x (7) P P The equation (5) (6) and (7) (8) are equivalent. Equation (7) indicates that the ax external force should not large than 1624N or the external deformation will exceed. Equation (8) indicates that if the ax external force X should not large than 1667 N or the residual preload will reduce to zero. oth above case means the clamp force reduces to zero and the interface will get a small gap. The equation (8) also indicates that a high stiffness bolt with a low stiffness joint the bolt would sustain the majority of the applied force. ecause the stiffness slope of the bolt is greater than that of the joint. 2.3 The process of clamp force loss affected by thermal expansion All first wall components are installed at normal room temperature and then they must be heating to about ax 200 during the period of plasma burning. Under such a high temperature the deformation of each member of the bolt joint will change and then the clamp force will be changed too. igure.5 illustrates how the thermal expansion affects the clamp force. (igure.5) In igure.5 is the expansion of the bolt and is the sum of the expansion of the heat sink and graphite tile. Obviously as the total deformation remains constant the expansion reduces the respective elastic deformation. There for the sold line becomes dash-dot dot line and dash line becomes dash-dot line. P and P are respective preload and residual preload changes. rom igure.5 the expansion equation can be deduced: (9) ( * * * ) T (8) * * (10) Where: are thermal expansion of bolt graphite tile and heat sink. rom equation (9) (10) can get equation (11) (12) and the specific curve equation (13) (14) with substitution of numerical values. 6 74.8*10 T (11) (12) 6 23*10 * T 6 51.8*10 * T (13) (14)
Obviously if thermal deformation is less than the original elastic deformation the clamp force will remain on the bolt joint. Thus the conditions of keeping the clamp force on the bolt joints is equation (15) without external force and (16) with external force. (15) x (16) With substitution of numerical values the limit temperature to keep the clamp force is: ( Without external force ) (17) T 2 155 1620 T1 10.45 ( With the external force) (18) In fact for equation (18) let =0, it can get the equation (17) at once. If =500N the limit temperature will be 107. As the clamp force should have a min value the reliable region to keep the graphite stay at its original position may very narrow and can not meet the requirements for the EAST running. igure.6 shows two critical temperature points. (igure.6) 2.4 The process of clamp force loss affected by stiffness of bolt Above analysis proves that stiffness also plays a very important role on joint. In fact the often used method to adjust the stiffness is simply put a spring washer on the bolt. It means the stiffness will be changed. et become a variable equation (15) and (16) present curve equations as igure.7 and igure.8 shown. (igure.7) (igure.8) igure.7 and igure.8 shows how the stiffness igure.7 without external force use affects the lock conditions at different temperature. urves in X as boundary curve which means that thermal expansion should be less than X. urves in igure.8 with external force use X as boundary curve which means that thermal expansion should be less than X. The curves indicate that even the small will increase the critical temperature without the external force acting on joint but it almost can not change the lock condition when the external force act on joints. 3 onclusion and discussion The main cause to reduce the clamp force is that three members of bolt joint have different thermal expansion. Thermal expansion will reduce the elastic deformation and make the clamp force become small. The mathematic model of clamp force proved that the adjustment of stiffness of bolt can not improve the lock conditions of bolt joint with the external force. As the limit temperature point to keep the clamp force is very low (less than 107 ),
the bolt joint will loose their clamp force during plasma burning. It is necessary and important to redesign and assessment the joints on first wall in EAST to improve the performance of bolt joints. The connection system may need a special part or structure to compensate the most thermal expansion. Acknowledgments The authors would like to appreciate the EAST design team. The work was supported by all team members. References [1].. axi, E.E. Reis,.A. Ulrickson. 2003, usion Engineering and Design, 66 :323 [2] i Yinong, Zheng ling, Wen angchun. 2003, Journal of Vibration Engineering, 16 :137(in hinese) [3] Zhu hen. 1990, Natural Science Journal of Xiangtan University, 13 :51(in hinese) [4] John, H. ickford. 1981, An introduction to the design and ehaviour of olted joins, arcel Dekker Inc, New York [5] Jin Yao, Sun Xun ang. 1998, Journal of Southwest Jiaotong University, 33 :46 [6] N. Ravi P. haudhuri, P. Santra, D. henna Reddy. 2001, usion Engineering and Design, 56 :355 [7] Zongze Wu. 1991, Advanced mechanical design. Tsinghua university press, engjing (in hinese) [8] T. Jaglinski, A. Nimityongskul, R. Schmitz. 2007, Transaction of ASE, 129:48 [9] A. Strang. 1994, Performmance of bolting materials in high temperature plant Applications. Institute of materials, odon [10]. Tendo,. Yamada, Shimura. 2001, ASE Journal of Engineering aterial Technolgy, 123:198 [11] Zhu hen. 1992, Natural Science Journal of Xiangtan University, 14 :21(in hinese) [12] Zhu hen. 1995, hinese Journal of echanical Engineering, 31 :77 (in hinese)
Table 1: The quantity of failed graphite ties in EAST graphite tiles date 2008 date 2009 Total 4896 4896 oosed 46 38 Escaped 25 12 Total failed 71 50 Scale 1.5% 1% Table 2: The properties of material Parameters Screw olt (6) Graphite tile Heat sink aterial Stainless steel 316 Graphite urzr Elastic modulus GPa 200 14 127.5 Thermal expansion (10E-6) 15.3 2.4 16.72
Table 3: The stiffness and deform of each components 6 bolt Graphite tile Heat sink aterial Stainless steel Graphite urzr 316 Elastic modulus E / 200 E /14 E /127.5 GPa Thermal expansion (10E-6) Equivalent Diameter mm Equivalent length mm ross section area /15.3 /2.4 /16.72 /5 /10 /10 /28 /8 /20 A /19.6 A / 45.3 A /45.3 2 mm Stiffness /140 / 79.3 /288.8 6 10 N/ m Deform 3 10 mm /3.57 /6.3 /1.73 X X X igure.1 Escaped and loosed graphite ties in EAST
Graphite tile Screw bolt Heat sink igure.2 The structure of graphite ties connection in EAST fixed P X Interface igure.3 The mechanical model of the bolt joint orce p x p t Deform igure.4 The relation between force and deformation
orce P P Deform igure.5 The clamp force loss process Deform x T 1 T2 T igure.6 limit temperature point
Deformation (mm) 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 boundary curve 50k temperature rise 100k temperature rise 150k temperature rise 200k temperature rise Xc 0 0 50 100 150 200 250 300 350 400 450 500 c (E6 N/) igure.7 how the stiffness affect the clamp force (without external force) Deformation (mm) 0.016 0.014 0.012 0.01 0.008 boundary curve 50 temperature rise 100 temperature rise 150 temperature rise 200 temperature rise Xm 0.006 0.004 0 50 100 150 200 250 300 350 400 450 500 c (E6N/) igure.8 how the stiffness affect the clamp force (with external force)
East 第一壁石墨瓦螺纹副的预紧力分析 曹磊, 宋云涛 中科院等离子体物理所, 合肥 1126 信箱, 邮编 230031 摘要 :EAST 面向等离子体的第一壁使用大量石墨瓦面对等离子体 所有的石墨瓦均使用螺栓紧固在热沉上 螺栓加载了预紧力作为石墨瓦和热沉贴合的夹紧力 保持石墨瓦和热沉紧密贴合的夹紧力非常重要, 因为紧密贴合使得热流通过石墨瓦穿越接触界面抵达热沉的热阻保持最小 没有夹紧力, 微小的间隙都可能造成石墨瓦上的热量无法被热沉里的冷却水有效带走 更糟的是夹紧力丧失使得一些螺栓在很小的外力扰动下被旋出, 从而造成石墨瓦位置变动甚至掉落 夹紧力消失的过程可以使用数学模型研究 研究结果解释了螺纹副构件不同的材料热膨胀系数是如何影响到夹紧力的变化以及螺纹副的刚度如何影响加紧力和温度之间的关系 研究给出了保持夹紧力大于零的温度极限 研究结果显示现有设计和条件使得在等离子体放电过程中第一壁的螺纹副不可避免丧失其夹紧力, 因此需要对连接副进行设计优化以提高连接的可靠性 关键词 : 夹紧力, 预紧力, 残余预紧力, 热膨胀系数