- Email: [email protected]
A new method used in assembly of the stator component and its limit fluid pressure determination
Nuclear Engineering and Design 256 (2013) 256–263
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A new method used in assembly of the stator component and its limit fluid pressure determination Huahan Liu, Wei Jiang ∗ , Ming Hao School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, PR China
h i g h l i g h t s
Tube hydroforming as a method to assembly the stator core and can of AP1000. Establishing a three-dimensional assembly model for the stator core and can. The maximum tensile stress criterion is presented to indicate the burst of the can. Obtained the limit internal pressure during the hydroforming by using ABAQUS.
a r t i c l e
i n f o
Article history: Received 20 October 2011 Received in revised form 29 July 2012 Accepted 1 August 2012
a b s t r a c t The AP1000 reactor coolant pump is a single-stage, hermetically sealed centrifugal canned motor pump with high-inertia. The assembly of the can on the stator is one of the most important and difficult techniques in the manufacturing of reactor coolant pumps. In this paper, methods currently used in this process are reviewed first, and an assembly method based on the theory of tube hydroforming is presented and discussed in detail. In order to establish an experiment rig to test the proposed assembly method in the future, a three-dimensional assembly model with reduced size is established to simulate this process in this paper. The limit fluid pressure is preliminarily predicted by using ABAQUS, and the maximum tensile stress criterion is presented as the criterion of the burst of the can. It is expected that the research could provide helpful guidelines for the establishment of the experiment rig and eventually the actual assembly of the can and stator. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The AP1000 reactor coolant pump (RCP) is one of the key components in the primary loop of a nuclear plant. The primary loop consists of two circuits, each with one steam generator, two cold leg main pipes, two heat leg main pipes, and two reactor coolant pumps. Additionally, a pressurizer is directly connected to one of the heat leg main pipes. The AP1000 RCPs are single-stage, hermetically sealed, high-inertia, centrifugal, canned motor pump (Ma, 2007). The RCPs are designed to pump large volumes of reactor coolant with high pressure and temperature to circulate in the reactor core, coolant loops and steam generator. In order to avoid coil corrosion, it is very important to shield the motor and stator components from the coolant. Therefore, the stator and rotor are encased in corrosionresistant cans which could prevent the contact of the rotor bars and
stator windings from the reactor coolant. The cans are designed for this purpose, but this will result in eddy current losses. The thinner the shielding sleeve is, the less eddy current losses it will be. Therefore, the can has to be selected as thin as possible within the limits of mechanical strength. In this paper, a new method for the assembly of the stator core and the can, which has an extra thin-wall and a high ratio of length to diameter, is first discussed in detail. This method is based on the theory of tube hydroforming and relies on the plastic deformation of the can. A three-dimensional finite element model of the can and stator core with reduced size is then established to simulate the process. Finally, the maximum tensile stress criterion is presented to indicate the burst of the can, and the limit fluid pressure is predicted by using ABAQUS. It is expected that the research could provide helpful instructions for the establishment of experiment rig and eventually the actual assembly process. 2. Methods of assembly
∗ Corresponding author. Tel.: +86 411 84706741; fax: +86 411 84706741. E-mail addresses: [email protected] (H. Liu), [email protected], jiangwei [email protected] (W. Jiang), [email protected] (M. Hao). 0029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.08.038
Cans can be produced in two ways: welding (Jiang, 2010) and spinning (Li et al., 2010). Welding method is proceeded by rolling
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
257
Fig. 1. The theory of tube hydro forming (a) free bulging and (b) bulging with artificial axial feeding.
the roll-formed tubular material into tube first and then welding its sides. During the spinning process, the tube blanket is clamped between the mandrel and a backplate. These three components rotate synchronously at a specified spindle speed. A local plastic deformation zone is generated at the roller contact area. So we can get the pre-shaped formation. The spinning technology is typically classified into two types with different blanket shapes: common spin-forming and power spinning (Wang and Liu, 1986). Thin-wall tube spinning, forward spinning, is one kind of method used to produce the can. In order to insert the can into the stator core easily, there is a clearance between the stator core and can initially. The clearance of 1 mm is assumed in this paper.To install the can and stator together, precise assembly methods currently available include: (1) Vacuum technique (vacuum pumping). After putting the can into the stator, pumping the air out of the clearance between the can and the stator core. The can will deform plastically, and the clearance will be reduced or even disappear (Feng, 2011). (2) Hydrostatic test. This assembly method relies on the hydrostatic test of the can, and can produce pressure large enough to make the can deform plastically to attach to the inner side of the stator core closely (Guan and Gao, 2008). The test pressure is 1.25 times greater than the design pressure, and the test time is 8–9 h. There are some disadvantages of these two methods. For the first one, since air has properties such as low density, large fluidity and compressibility, when we pump the air out, uneven deformation distribution of the can will happen along the axe of stator core. More important, we cannot obtain the desired deformed can, as the load generated by this process is too small to make the can deform to the expected shape. As for the second method, since the hydraulic pressure path corresponding to the time cannot be controlled precisely step by step, we still cannot obtain the desired effect. Therefore, this paper presents a method based on the theory of tube hydroforming.
is a reality today in mass production of these components in the automotive industry. Application of this process is driven mainly by the need for weight reduction, part consolidation, and dimensional tolerance improvement. The best advantages that make it available in the assembly process are the controllability of the load path and the uniformity of the plastic deformation of the whole part. Usually, there are two kinds of tube hydroforming methods: the free bulge method and the method with artificial axial feeding. These methods are shown in Fig. 1(a) and (b), respectively. Filled with liquid in the hollow part and depending on the pressure of the liquid by keeping injecting liquid into the part are the common features of these two methods. Therefore, the main difference between the two methods is that there exists the displacement or force along the axial direction during the bulging process in the second method. Tube hydroforming used in this process is more complicated than that used in the automation industry. The thickness of the can is only 0.5 mm with large diameter and length. The application of the axial force may introduce the wrinkle failure of the can, then the failure of the assembly. The best choice for us to use in this process is the first method. There are three stages through the whole process: (1) Before the can contacts with the stator gear. (2) After the can attaches to the stator gear and before it contacts with the stator slots. (3) After the can attaches the slots and the gear. It can be seen that it is a nonlinear problem concerning contact and large deformation. The wedges along the axial direction of the stator core are the same, and distribute evenly along the circumference direction. Therefore, free bulging is chosen as the assembly method in this study, only applying internal pressure without artificial axial feeding during the process, and the uniformed internal pressure inside the can makes it attached inside the stator core evenly depending on plastic deformation of the can. Fixing one side or two sides of the can’s axial end surface are the two cases to be considered during the assembly process in the research. By this theory, we can control the process easily through the load-time curves. By changing the loading time, loading path and other parameters, we can control the loading path to get the proper shape of the can. It is expected that useful conclusions could be obtained for the future practical production from current research.
2.1. Theory of tube hydroforming used in this process 3. FE model establishment The tube hydroforming process is used commercially to form a wide variety of automotive components, such as camshafts, front and rear axial parts, crankshafts, space frames, engine cradles, roof rails, seat frames (Dohmann and Hartl, 1996; Bartley and Evert, 2000; Chu and Xu, 2004a,b). Advanced hydroforming machinery
3.1. Elastic–plastic constitutive The material of the can is assumed to be elastic–plastic. According to the theory of elastic–plastic, we know that when the material
258
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
Table 1 Dimensions of the stator core and the can and the stator slot at reduced size. Stator core
Can
Stator slot
Number of stator slot
Outer diameter (mm)
Inner diameter (mm)
Stator core length (mm)
Diameter of the can’s middle surface (mm)
Can thickness (mm)
Can length (mm)
a (mm)
b (mm)
h (mm)
r (mm)
48
236
113
630
110.5
0.5
730
1
4
44
0.5
enter into the plastic deformation stage, the stain εij contains two p components: the elastic strain εeij and the plastic strain εij . The strain increment can be described in the following equation: p
dεij = dεeij + dεij .
(1)
The Von Mises yield criterion for isotropic material is used in this simulation. Therefore we can get the tensor form of the elastic–plastic constitutive (Lei et al., 2006) as: ep
ij = Dijkl εkl .
(2)
ep Dijkl
(3)
=
p e Dijkl − Dijkl . ep
e where ij is the stress increment, Dijkl is the stiffness matrix, Dijkl p
is the tensor form of the elastic stiffness matrix, and Dijkl is the tensor form of the plastic stiffness matrix. 3.2. Simplified model of the assembly The dimensions of the stator core and the can used in the simulation in this paper are shown in Table 1. This data is from the actual size (Feng, 2011) by reduced size. Fig. 2 displays the dimensions of the groove of the large stator. It is assumed that the coils and the slot wedges are already put into the slots before the can and the stator are assembled. The clearance between the slot wedges and the internal diameter of the stator is 1 mm (Fig. 2). The coils and the slot wedges are neglected in the paper and the groove is assumed as a square, so we can find the limit deformation capability of the can. Generally, groove width is larger than gear teeth of the stator core in the canned motor pump (Ma, 2005). If we choose larger external diameter and the groove shape, not only material
Fig. 3. Shapes of the stator and the can.
consumption, but also the efficiency of the motor will be improved. Table 1 and Fig. 2 show the dimensions of the groove (slot wedges and the coils are neglected) used in the current research. Fig. 3 displays the three-dimensional assembly model of the stator core and the can. To avoid the numerical singularity in the FEM analysis, the fillet is assumed 0.5 mm along the length of the core in the gear teeth sides. In the analyses, it is assumed that the can is homogeneous and isotropic and the stator core is a rigid body. The effect of welding is also neglected. No thermal effect is considered. Gravity of the liquid is neglected. Based on the above assumptions, the assembly model is established in Fig. 3.
3.3. Material model The can is made by rolling hastelloy C-276 blank. However, the anisotropy of this material through the process is neglected in this paper, since the effect of the anisotropy is very small and the pressure is focused on in one single direction during the whole assembly process. The Von Mises criterion of the isotropic material is used in this simulation. Fig. 4 presents the stress–strain curve of hastelloy C-276 obtained from tensile tests. It is the true stress–strain curve based on transforming by equations. Table 2 shows other mechanical properties of the hastelloy C-276.
4. Analysis step and contact condition
Fig. 2. Shape of the stator groove.
A single step with the step time of 0.1 s is used in this analysis. Because of the complexity and size of the whole model, the analysis time will be very long. A mass scaling technology (ABAQUS, 2008) is selected to reduce the computational time. The mass scaling factor of 100 is chosen in the condition of quasi-static analysis. Surface to surface contact is used between the stator core and the can with non-friction effect.
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
259
Table 2 Mechanical properties of hastelloy C-276. Young’s modulus E [MPa]
Poisson’s ratio
Yield strength s [MPa]
Ultimate tensile strength b [MPa]
Density (kg m−3 )
208,000
0.375
363
758
8900
The process is completed by internal high fluid pressure, that is, liquid is firstly filled into the can and then injected continually to increase the pressure we need to form the desired shape. The internal pressure will be applied radially to the zone where there may be contact with the stator core in the process along the axial direction. During the simulation, the internal pressure is increased linearly to the maximum value as a function of time. (1) Fixing one end surface side. The range of the internal pressure of free bulging can be decided by the following empirical formula (Wang, 1997): 2Kb ı 2Ks ı ≤P≤ R1 R0
Fig. 4. Diagram of stress–strain behavior obtained by test.
4.1. Finite element mesh In the finite element model, the stator core is considered to be rigid and 103,000 4-node shell elements-S4R is adopted for the can. The hydraulic pressure is imposed normally on the inner surface of the tube incrementally and non-friction is assumed. As to the stator core mesh, the process involves first splitting the stator model, and then refining the mesh in the zone which is close to the can. The total number of element of the stator core is 217,700 with element type R3D4. Fig. 5 shows the meshes of the model. 4.2. Boundary and load conditions The stator core is modeled as rigid body. All degrees of freedom will be encased in the reference point. As to the can, one side of the end surface is encased, and fixing the two end surface sides is also analyzed. Fig. 6 displays the boundary condition of the assembly model.
Fig. 5. Meshes of the assembly.
(4)
where R0 = 55.25 mm, R1 = 57.25 mm, K = 2, then the range of P is: 6.57 MPa ≤ P ≤ 13.183 MPa. (2) Fixing two end surface sides. The internal pressure can be decided by the following empirical formula (Wang, 1997):
s ı
1 R2
+
1 R1
≤P≤
b ı ((1/R2 ) + (1/R1 ))
(5)
It is assumed that the wall thickness is not changed after the hydroforming process and the shape of this deformed zone is arc (this is to the free tube hydroforming). Then R2 − R1 ≈ ı. Select the maximum external radius of the can after deformation 57.5 mm as R1 , the range of pressure is from 6.189 MPa to 12.9027 MPa. Here the internal pressure of 10 MPa is chosen for the initial simulation in both the two cases. More simulations are then conducted with different final internal pressures ranging from 10 MPa to the pressure limit with an increment of 10 MPa.
Fig. 6. Boundary and load conditions.
260
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
5.1. Criterions for the decision of the can’s forming limit Currently, there are several forming limit criterions for the can as follows:
Fig. 7. The ratios of the kinetic energy to the internal energy (KE, kinetic energy; IE, internal energy).
5. Results and discussion The initial clearance between the stator core and can is 1 mm in all the simulations, and the step time is 0.1 s. The quasi-static analysis is assumed.
(1) Generally, when the ratio of the wall thickness thinning of the can is higher than 20%, the wall can be considered burst. (2) The theory of the thickness gradient can be chosen as the forming limit criterion (Liu and Zhou, 2006). (3) So far, forming limits diagram (FLD) (Keeler, 1965) and forming limits stress diagram (FLSD) (Stoughton and Zhu, 2004) are two promising methods for predicting the forming limit of the shell. Unfortunately, FLD and FLSD are hard to get because of the high experiment costs and time consuming. (4) Since there is no axial material feed, uniaxial stressed state can be assumed through the whole process. Therefore, the maximum tensile stress criterion (Liu, 2007) could be used as the form limit. The ultimate tensile stress b is the limit stress. When the maximum principal stress increases up to this value, the can will burst. The internal pressure value corresponding to this value will be chosen as the load limit. According to the discussions above, the maximum tensile stress criterion is chosen as the limit criterion in this paper.
Fig. 8. The forming results and the displacement distributions in the x direction. (a) Before bulging process. (b) Forming result (P = 50 MPa). (c) Forming result (P = 60 MPa). (d) Forming result (P = 70 MPa).
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
261
Table 3 Certain variation distributions in the snap time. Maximum load [MPa]
Time [s]
KE/IE
Corresponding load [MPa]
Node displacement u1 [m]
50 60 70
0.00900066 0.00750400 0.00650120
0.080633 0.0843669 0.0895823
4.50033 4.50240 4.55084
0.00103231 0.00104693 0.00105499
5.2. Verification of the quasi-static analysis Normally it is unfeasible to run a quasi-static analysis in real time scale, because of the unacceptable computational time (Harewood and McHugh, 2007). Mass scaling is one of the techniques to speed up the analysis. But by artificially increasing the mass scaling factor, the corresponding inertial forces will affect the
mechanical response and provide unrealistic dynamic results. To ensure that the inertial effects due to mass scaling do not significantly affect the simulation results, the kinetic energy of the can should be no greater than 10% of its internal energy during most of the time of the assemble process (ABAQUS, 2008). In this paper, a mass scaling factor of 100 has been applied in order to speed up the computation.
Fig. 9. Max. principal stress distribution at different finally internal pressure. (a) Max. principal stress distribution (P = 50 MPa). (b) Max. principal stress distribution (P = 60 MPa). (c) Max. principal stress distribution at 0.085 s (P = 70 MPa). (d) Max. principal stress distribution at 0.090 s (P = 70 MPa). (e) Max. principal stress distribution at 0.095 s (P = 70 MPa). (f) Max. principal stress distribution at (P = 70 MPa).
262
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
As it can be seen from Fig. 7, during the process the ratio of the kinetic energy to the internal energy of the can is below 10%. Therefore, the dynamic effects caused by mass scaling are well controlled. It is also noticed that there is a cusp in each curve where is the maximum values in the whole process with the time: 0.00900066 s (P = 50 MPa), 0.00750400 s (P = 60 MPa), 0.00650120 s (P = 70 MPa), corresponding cusp values are 8.0633%, 8.4367%, 8.9582% respectively. But all the mutation values are lower than 10%, so we can consider these simulations as quasi-static analysis. Table 3 displays certain variation distributions at that moment (node 64,419), the displacement along the x direction are all about 1 mm. We can conclude that this moment is the first time that the can contacts the stator core. It may cause large non-linearity and is also the reason for the rapid increase of kinetic energy. After contacting, the analysis process becomes steady as before. We can still conclude from Table 3 that the internal pressure is also almost the same in the crest where there is the max value. If we can ensure the simulation is quasi-static analysis and the load type is the internal pressure (not displacement), the step time almost does not affect the radial displacement of the can in this process. The internal pressure is the key factor that makes the can deform. That is, we can get the same radial displacement if we use the same internal pressure, no matter what the step time is in the process (with the condition of quasi-static analysis). 5.3. Bulging analysis Fig. 8 displays the final results with different internal pressure. Fig. 8(a) is the initial condition that no internal pressure is applied, and there is a clearance between the stator core and the can. When the internal pressure P = 50 MPa is applied, the maximum displacement along the 1 direction is 1.468 mm, which indicates that the can is getting into the stator grooves. The displacement is increased with the increase of the internal pressure: from 1.581 mm at P = 60 MPa rising to 1.744 mm at P = 70 MPa. It can be concluded that with the increase of the internal pressure, the increment of the plastic deformation of the can is slow. Therefore, a desirable loading path could be found. Fig. 9(a) and (b) shows that the maximum principal stress are 695.6 MPa and 739.2 MPa respectively with the final internal pressure 50 MPa and 60 MPa. Both the two conditions are not up to the ultimate strength stress. But when P = 70 MPa, the maximum principal stress reaches to 806.2 MPa, this value is more than ultimate strength stress 758 MPa. It shows that the can is bursting before 70 MPa. The maximum principal stress distribution at time 0.085 s, 0.090 s, 0.095 s when the final internal pressure is 70 MPa is also shown in Fig. 9(c)–(e). The corresponding maximum principal stress are 735.9 MPa, 754.9 MPa, 775.7 MPa, respectively. Then we can know that the limit internal pressure is between the 0.090 s and 0.095 s (P = 70 MPa), the range of the limit internal pressure is: 63 MPa < P < 66.5 MPa. Then the limit internal pressure of 63.75 MPa corresponding to the maximum tensile stress (758 MPa) can be obtained by using linear interpolation. From Fig. 9 we can see that there is stress concentration zone in the can contacting with the stator gear sides along the axial direction, and this is also the place where excessive thinning of the can happens. Therefore, filleting the sides is necessary in order to avoid the cusp to lead to the can burst. In summary, the reduction of stress concentration and friction is necessary in this process not only in numerical simulation but also in actual production. 5.4. The result analysis of the second case (fixing two end surface sides) Case two has the same conditions as case one, such as geometry dimensions, load path, mesh condition, mass scaling factor, except
that the boundary condition of the can is fixed at both ends. The range of the limit internal pressure obtained by the same method as case one is 59.5 MPa < P < 63 MPa, and the limit internal pressure of 62.52 MPa can also be obtained. From overall observation, it can be noted that there are some differences between different boundary conditions. The one with one end fixed has the larger limit internal pressure than the one with both ends fixed. This is attributed to the fact that with one end fixed more material will get into the stator core to compensate for rapid thinning of the can. The carrying capability of the can is improved, and it is due to the fact that the feeding of the material can avoid the rapid excessive thinning of the can which should be responsible for the burst of the can. Therefore, because of the characteristics of the present model, the large length of the can correspond to the stator core and the small thickness of the can, the differences of the limit internal pressure of the two cases are small. Besides, from the simulation results, the thickness of the can after applying load in case two is more uniform than case one in the axial direction. 6. Conclusion In this study, several methods that could be used to assemble the stator component and the can are firstly discussed and a method based on the theory of tube hydroforming is then presented and discussed in detail. A three-dimensional model with reduced size was established with limited available data and the size of the slot and wedges are developed according to the ordinary motor. Finite element analyses were carried out by using ABAQUS/EXPLICIT to determine the limit pressure of the can preliminary. The maximum tensile stress criterion was presented as the forming limit criterion and the range of the limit internal pressure of 63 MPa < P < 66.5 MPa for fixing one end and 59.5 MPa < P < 63 MPa for fixing both ends were found based on this criterion with the clearance of 1 mm, and the limit internal pressures calculated by using linear interpolation for two cases are 63.75 MPa and 62.52 MPa respectively. Then the differences between the two cases are discussed. The intensified stress concentration along the stator gear sides are observed. This must be paid more attention to in the practical production. In the future work, experiment rig will be established according to the analysis results of this paper. Then experiments will be performed to validate the simulation results in the internal pressure equipment developed by our research team. Furthermore, more FEA simulations will be carried out by considering the effects of springback. The influences of different clearances and friction coefficient to the limit internal pressure will also be investigated. Acknowledgements Financial support for this work has been provided by the National Key Basic Research Program of China (Grant No. 2009CB724307). The author also would like to acknowledge Mr. Yuquan Guo and Mr. Zhi Zhu for providing the material parameters for hastelloy C-276 used in this research. The insightful comments on the manuscript by the reviewers are also highly appreciated. References ABAQUS, 2008. ABAQUS Analysis User’s Manual. Version. 6.8. ABAQUS Inc., Botha, USA. Bartley, G., Evert, R., 2000. Hydroforming of aluminum extrusions for automotive applications. Light Met. Age 8, 1–8. Chu, E., Xu, Y., 2004a. Hydroforming of aluminum extrusion tubes for automotive applications. Part I: buckling, wrinkling and bursting analyses of aluminum tubes. Int. J. Mech. Sci. 46, 263–283. Chu, E., Xu, Y., 2004b. Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram. Int. J. Mech. Sci. 46, 285–297.
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263 Dohmann, F., Hartl, C., 1996. Hydroforming – a method to manufacture lightweight parts. J. Mater. Process. Technol. 60, 669–676. Feng, Y.H., 2011. Mechanical Analyses of the Cans in AP1000 Reactor Coolant Pump. Shanghai Jiao Tong University, Shanghai, China. Guan, R., Gao, Y.J., 2008. Brief analysis on fabrication process of the AP1000 reactor coolant pump can. China Nucl. Power 1, 49. Harewood, F.J., McHugh, P.E., 2007. Comparison of implicit and explicit finite element methods using crystal plasticity. Comput. Mater. Sci. 39, 481. Jiang, L.J., 2010. Effect of Laser Welding Quality of Nuclear Reactor Coolant Pump Can on Eddy Current Losses. Dalian University of Technology, Dalian, China. Keeler, S.P., 1965. Determination of forming limits in automative stamping, SAE. Report 650535. Li, X.H., Deng, R., Zhang, H.L., He, J., Wang, Y.F., Yang, X.Q., 2010. Effect of friction condition on the process for spinning of shielding cover with extra thin-wall and height diameter/thickness ratio. Acta Sci. Nat. Univ. Sunyatseni 49, 1.
263
Lei, Y.C., Wang, M.J., Jia, Z.H., 2006. Theory of Metal Forming. China Chemical Industry Press, Beijing, China. Liu, C.L., Zhou, X.B., 2006. Experimental and numerical investigation on sheet metal forming limit prediction with thickness related criteria. China Forging & Stamping Technol. 5, 1. Liu, H.W., 2007. Mechanics of Materials. China Higher Education Press, Beijing, China. Ma, X.P., 2007. Discussion on design scheme of frequency-conversion for AP1000’s main-coolant pumps. Electr. Equip. 8, 20. Ma, D.X., 2005. Summary of electromagnetic design of ADFLPH-(55–160) kW/2p canned motor. Explosion Proof Electr. Mach. 40 (126), 1–3. Stoughton, T.B., Zhu, X.H., 2004. Review of theoretical models of the strain based FLD and their relevance to the stress based FLD. Int. J. Plasticity 20, 1460–1481. Wang, C.H., Liu, K.Z., 1986. Spinning Technology. China Machine Press, Beijing, China. Wang, D.Y., 1997. Study on the bulging process technology of the thin-walled products. China Heavy Mach. 6, 37.
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A new method used in assembly of the stator component and its limit fluid pressure determination Huahan Liu, Wei Jiang ∗ , Ming Hao School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, PR China
h i g h l i g h t s
Tube hydroforming as a method to assembly the stator core and can of AP1000. Establishing a three-dimensional assembly model for the stator core and can. The maximum tensile stress criterion is presented to indicate the burst of the can. Obtained the limit internal pressure during the hydroforming by using ABAQUS.
a r t i c l e
i n f o
Article history: Received 20 October 2011 Received in revised form 29 July 2012 Accepted 1 August 2012
a b s t r a c t The AP1000 reactor coolant pump is a single-stage, hermetically sealed centrifugal canned motor pump with high-inertia. The assembly of the can on the stator is one of the most important and difficult techniques in the manufacturing of reactor coolant pumps. In this paper, methods currently used in this process are reviewed first, and an assembly method based on the theory of tube hydroforming is presented and discussed in detail. In order to establish an experiment rig to test the proposed assembly method in the future, a three-dimensional assembly model with reduced size is established to simulate this process in this paper. The limit fluid pressure is preliminarily predicted by using ABAQUS, and the maximum tensile stress criterion is presented as the criterion of the burst of the can. It is expected that the research could provide helpful guidelines for the establishment of the experiment rig and eventually the actual assembly of the can and stator. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The AP1000 reactor coolant pump (RCP) is one of the key components in the primary loop of a nuclear plant. The primary loop consists of two circuits, each with one steam generator, two cold leg main pipes, two heat leg main pipes, and two reactor coolant pumps. Additionally, a pressurizer is directly connected to one of the heat leg main pipes. The AP1000 RCPs are single-stage, hermetically sealed, high-inertia, centrifugal, canned motor pump (Ma, 2007). The RCPs are designed to pump large volumes of reactor coolant with high pressure and temperature to circulate in the reactor core, coolant loops and steam generator. In order to avoid coil corrosion, it is very important to shield the motor and stator components from the coolant. Therefore, the stator and rotor are encased in corrosionresistant cans which could prevent the contact of the rotor bars and
stator windings from the reactor coolant. The cans are designed for this purpose, but this will result in eddy current losses. The thinner the shielding sleeve is, the less eddy current losses it will be. Therefore, the can has to be selected as thin as possible within the limits of mechanical strength. In this paper, a new method for the assembly of the stator core and the can, which has an extra thin-wall and a high ratio of length to diameter, is first discussed in detail. This method is based on the theory of tube hydroforming and relies on the plastic deformation of the can. A three-dimensional finite element model of the can and stator core with reduced size is then established to simulate the process. Finally, the maximum tensile stress criterion is presented to indicate the burst of the can, and the limit fluid pressure is predicted by using ABAQUS. It is expected that the research could provide helpful instructions for the establishment of experiment rig and eventually the actual assembly process. 2. Methods of assembly
∗ Corresponding author. Tel.: +86 411 84706741; fax: +86 411 84706741. E-mail addresses: [email protected] (H. Liu), [email protected], jiangwei [email protected] (W. Jiang), [email protected] (M. Hao). 0029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.08.038
Cans can be produced in two ways: welding (Jiang, 2010) and spinning (Li et al., 2010). Welding method is proceeded by rolling
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
257
Fig. 1. The theory of tube hydro forming (a) free bulging and (b) bulging with artificial axial feeding.
the roll-formed tubular material into tube first and then welding its sides. During the spinning process, the tube blanket is clamped between the mandrel and a backplate. These three components rotate synchronously at a specified spindle speed. A local plastic deformation zone is generated at the roller contact area. So we can get the pre-shaped formation. The spinning technology is typically classified into two types with different blanket shapes: common spin-forming and power spinning (Wang and Liu, 1986). Thin-wall tube spinning, forward spinning, is one kind of method used to produce the can. In order to insert the can into the stator core easily, there is a clearance between the stator core and can initially. The clearance of 1 mm is assumed in this paper.To install the can and stator together, precise assembly methods currently available include: (1) Vacuum technique (vacuum pumping). After putting the can into the stator, pumping the air out of the clearance between the can and the stator core. The can will deform plastically, and the clearance will be reduced or even disappear (Feng, 2011). (2) Hydrostatic test. This assembly method relies on the hydrostatic test of the can, and can produce pressure large enough to make the can deform plastically to attach to the inner side of the stator core closely (Guan and Gao, 2008). The test pressure is 1.25 times greater than the design pressure, and the test time is 8–9 h. There are some disadvantages of these two methods. For the first one, since air has properties such as low density, large fluidity and compressibility, when we pump the air out, uneven deformation distribution of the can will happen along the axe of stator core. More important, we cannot obtain the desired deformed can, as the load generated by this process is too small to make the can deform to the expected shape. As for the second method, since the hydraulic pressure path corresponding to the time cannot be controlled precisely step by step, we still cannot obtain the desired effect. Therefore, this paper presents a method based on the theory of tube hydroforming.
is a reality today in mass production of these components in the automotive industry. Application of this process is driven mainly by the need for weight reduction, part consolidation, and dimensional tolerance improvement. The best advantages that make it available in the assembly process are the controllability of the load path and the uniformity of the plastic deformation of the whole part. Usually, there are two kinds of tube hydroforming methods: the free bulge method and the method with artificial axial feeding. These methods are shown in Fig. 1(a) and (b), respectively. Filled with liquid in the hollow part and depending on the pressure of the liquid by keeping injecting liquid into the part are the common features of these two methods. Therefore, the main difference between the two methods is that there exists the displacement or force along the axial direction during the bulging process in the second method. Tube hydroforming used in this process is more complicated than that used in the automation industry. The thickness of the can is only 0.5 mm with large diameter and length. The application of the axial force may introduce the wrinkle failure of the can, then the failure of the assembly. The best choice for us to use in this process is the first method. There are three stages through the whole process: (1) Before the can contacts with the stator gear. (2) After the can attaches to the stator gear and before it contacts with the stator slots. (3) After the can attaches the slots and the gear. It can be seen that it is a nonlinear problem concerning contact and large deformation. The wedges along the axial direction of the stator core are the same, and distribute evenly along the circumference direction. Therefore, free bulging is chosen as the assembly method in this study, only applying internal pressure without artificial axial feeding during the process, and the uniformed internal pressure inside the can makes it attached inside the stator core evenly depending on plastic deformation of the can. Fixing one side or two sides of the can’s axial end surface are the two cases to be considered during the assembly process in the research. By this theory, we can control the process easily through the load-time curves. By changing the loading time, loading path and other parameters, we can control the loading path to get the proper shape of the can. It is expected that useful conclusions could be obtained for the future practical production from current research.
2.1. Theory of tube hydroforming used in this process 3. FE model establishment The tube hydroforming process is used commercially to form a wide variety of automotive components, such as camshafts, front and rear axial parts, crankshafts, space frames, engine cradles, roof rails, seat frames (Dohmann and Hartl, 1996; Bartley and Evert, 2000; Chu and Xu, 2004a,b). Advanced hydroforming machinery
3.1. Elastic–plastic constitutive The material of the can is assumed to be elastic–plastic. According to the theory of elastic–plastic, we know that when the material
258
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
Table 1 Dimensions of the stator core and the can and the stator slot at reduced size. Stator core
Can
Stator slot
Number of stator slot
Outer diameter (mm)
Inner diameter (mm)
Stator core length (mm)
Diameter of the can’s middle surface (mm)
Can thickness (mm)
Can length (mm)
a (mm)
b (mm)
h (mm)
r (mm)
48
236
113
630
110.5
0.5
730
1
4
44
0.5
enter into the plastic deformation stage, the stain εij contains two p components: the elastic strain εeij and the plastic strain εij . The strain increment can be described in the following equation: p
dεij = dεeij + dεij .
(1)
The Von Mises yield criterion for isotropic material is used in this simulation. Therefore we can get the tensor form of the elastic–plastic constitutive (Lei et al., 2006) as: ep
ij = Dijkl εkl .
(2)
ep Dijkl
(3)
=
p e Dijkl − Dijkl . ep
e where ij is the stress increment, Dijkl is the stiffness matrix, Dijkl p
is the tensor form of the elastic stiffness matrix, and Dijkl is the tensor form of the plastic stiffness matrix. 3.2. Simplified model of the assembly The dimensions of the stator core and the can used in the simulation in this paper are shown in Table 1. This data is from the actual size (Feng, 2011) by reduced size. Fig. 2 displays the dimensions of the groove of the large stator. It is assumed that the coils and the slot wedges are already put into the slots before the can and the stator are assembled. The clearance between the slot wedges and the internal diameter of the stator is 1 mm (Fig. 2). The coils and the slot wedges are neglected in the paper and the groove is assumed as a square, so we can find the limit deformation capability of the can. Generally, groove width is larger than gear teeth of the stator core in the canned motor pump (Ma, 2005). If we choose larger external diameter and the groove shape, not only material
Fig. 3. Shapes of the stator and the can.
consumption, but also the efficiency of the motor will be improved. Table 1 and Fig. 2 show the dimensions of the groove (slot wedges and the coils are neglected) used in the current research. Fig. 3 displays the three-dimensional assembly model of the stator core and the can. To avoid the numerical singularity in the FEM analysis, the fillet is assumed 0.5 mm along the length of the core in the gear teeth sides. In the analyses, it is assumed that the can is homogeneous and isotropic and the stator core is a rigid body. The effect of welding is also neglected. No thermal effect is considered. Gravity of the liquid is neglected. Based on the above assumptions, the assembly model is established in Fig. 3.
3.3. Material model The can is made by rolling hastelloy C-276 blank. However, the anisotropy of this material through the process is neglected in this paper, since the effect of the anisotropy is very small and the pressure is focused on in one single direction during the whole assembly process. The Von Mises criterion of the isotropic material is used in this simulation. Fig. 4 presents the stress–strain curve of hastelloy C-276 obtained from tensile tests. It is the true stress–strain curve based on transforming by equations. Table 2 shows other mechanical properties of the hastelloy C-276.
4. Analysis step and contact condition
Fig. 2. Shape of the stator groove.
A single step with the step time of 0.1 s is used in this analysis. Because of the complexity and size of the whole model, the analysis time will be very long. A mass scaling technology (ABAQUS, 2008) is selected to reduce the computational time. The mass scaling factor of 100 is chosen in the condition of quasi-static analysis. Surface to surface contact is used between the stator core and the can with non-friction effect.
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
259
Table 2 Mechanical properties of hastelloy C-276. Young’s modulus E [MPa]
Poisson’s ratio
Yield strength s [MPa]
Ultimate tensile strength b [MPa]
Density (kg m−3 )
208,000
0.375
363
758
8900
The process is completed by internal high fluid pressure, that is, liquid is firstly filled into the can and then injected continually to increase the pressure we need to form the desired shape. The internal pressure will be applied radially to the zone where there may be contact with the stator core in the process along the axial direction. During the simulation, the internal pressure is increased linearly to the maximum value as a function of time. (1) Fixing one end surface side. The range of the internal pressure of free bulging can be decided by the following empirical formula (Wang, 1997): 2Kb ı 2Ks ı ≤P≤ R1 R0
Fig. 4. Diagram of stress–strain behavior obtained by test.
4.1. Finite element mesh In the finite element model, the stator core is considered to be rigid and 103,000 4-node shell elements-S4R is adopted for the can. The hydraulic pressure is imposed normally on the inner surface of the tube incrementally and non-friction is assumed. As to the stator core mesh, the process involves first splitting the stator model, and then refining the mesh in the zone which is close to the can. The total number of element of the stator core is 217,700 with element type R3D4. Fig. 5 shows the meshes of the model. 4.2. Boundary and load conditions The stator core is modeled as rigid body. All degrees of freedom will be encased in the reference point. As to the can, one side of the end surface is encased, and fixing the two end surface sides is also analyzed. Fig. 6 displays the boundary condition of the assembly model.
Fig. 5. Meshes of the assembly.
(4)
where R0 = 55.25 mm, R1 = 57.25 mm, K = 2, then the range of P is: 6.57 MPa ≤ P ≤ 13.183 MPa. (2) Fixing two end surface sides. The internal pressure can be decided by the following empirical formula (Wang, 1997):
s ı
1 R2
+
1 R1
≤P≤
b ı ((1/R2 ) + (1/R1 ))
(5)
It is assumed that the wall thickness is not changed after the hydroforming process and the shape of this deformed zone is arc (this is to the free tube hydroforming). Then R2 − R1 ≈ ı. Select the maximum external radius of the can after deformation 57.5 mm as R1 , the range of pressure is from 6.189 MPa to 12.9027 MPa. Here the internal pressure of 10 MPa is chosen for the initial simulation in both the two cases. More simulations are then conducted with different final internal pressures ranging from 10 MPa to the pressure limit with an increment of 10 MPa.
Fig. 6. Boundary and load conditions.
260
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
5.1. Criterions for the decision of the can’s forming limit Currently, there are several forming limit criterions for the can as follows:
Fig. 7. The ratios of the kinetic energy to the internal energy (KE, kinetic energy; IE, internal energy).
5. Results and discussion The initial clearance between the stator core and can is 1 mm in all the simulations, and the step time is 0.1 s. The quasi-static analysis is assumed.
(1) Generally, when the ratio of the wall thickness thinning of the can is higher than 20%, the wall can be considered burst. (2) The theory of the thickness gradient can be chosen as the forming limit criterion (Liu and Zhou, 2006). (3) So far, forming limits diagram (FLD) (Keeler, 1965) and forming limits stress diagram (FLSD) (Stoughton and Zhu, 2004) are two promising methods for predicting the forming limit of the shell. Unfortunately, FLD and FLSD are hard to get because of the high experiment costs and time consuming. (4) Since there is no axial material feed, uniaxial stressed state can be assumed through the whole process. Therefore, the maximum tensile stress criterion (Liu, 2007) could be used as the form limit. The ultimate tensile stress b is the limit stress. When the maximum principal stress increases up to this value, the can will burst. The internal pressure value corresponding to this value will be chosen as the load limit. According to the discussions above, the maximum tensile stress criterion is chosen as the limit criterion in this paper.
Fig. 8. The forming results and the displacement distributions in the x direction. (a) Before bulging process. (b) Forming result (P = 50 MPa). (c) Forming result (P = 60 MPa). (d) Forming result (P = 70 MPa).
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
261
Table 3 Certain variation distributions in the snap time. Maximum load [MPa]
Time [s]
KE/IE
Corresponding load [MPa]
Node displacement u1 [m]
50 60 70
0.00900066 0.00750400 0.00650120
0.080633 0.0843669 0.0895823
4.50033 4.50240 4.55084
0.00103231 0.00104693 0.00105499
5.2. Verification of the quasi-static analysis Normally it is unfeasible to run a quasi-static analysis in real time scale, because of the unacceptable computational time (Harewood and McHugh, 2007). Mass scaling is one of the techniques to speed up the analysis. But by artificially increasing the mass scaling factor, the corresponding inertial forces will affect the
mechanical response and provide unrealistic dynamic results. To ensure that the inertial effects due to mass scaling do not significantly affect the simulation results, the kinetic energy of the can should be no greater than 10% of its internal energy during most of the time of the assemble process (ABAQUS, 2008). In this paper, a mass scaling factor of 100 has been applied in order to speed up the computation.
Fig. 9. Max. principal stress distribution at different finally internal pressure. (a) Max. principal stress distribution (P = 50 MPa). (b) Max. principal stress distribution (P = 60 MPa). (c) Max. principal stress distribution at 0.085 s (P = 70 MPa). (d) Max. principal stress distribution at 0.090 s (P = 70 MPa). (e) Max. principal stress distribution at 0.095 s (P = 70 MPa). (f) Max. principal stress distribution at (P = 70 MPa).
262
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263
As it can be seen from Fig. 7, during the process the ratio of the kinetic energy to the internal energy of the can is below 10%. Therefore, the dynamic effects caused by mass scaling are well controlled. It is also noticed that there is a cusp in each curve where is the maximum values in the whole process with the time: 0.00900066 s (P = 50 MPa), 0.00750400 s (P = 60 MPa), 0.00650120 s (P = 70 MPa), corresponding cusp values are 8.0633%, 8.4367%, 8.9582% respectively. But all the mutation values are lower than 10%, so we can consider these simulations as quasi-static analysis. Table 3 displays certain variation distributions at that moment (node 64,419), the displacement along the x direction are all about 1 mm. We can conclude that this moment is the first time that the can contacts the stator core. It may cause large non-linearity and is also the reason for the rapid increase of kinetic energy. After contacting, the analysis process becomes steady as before. We can still conclude from Table 3 that the internal pressure is also almost the same in the crest where there is the max value. If we can ensure the simulation is quasi-static analysis and the load type is the internal pressure (not displacement), the step time almost does not affect the radial displacement of the can in this process. The internal pressure is the key factor that makes the can deform. That is, we can get the same radial displacement if we use the same internal pressure, no matter what the step time is in the process (with the condition of quasi-static analysis). 5.3. Bulging analysis Fig. 8 displays the final results with different internal pressure. Fig. 8(a) is the initial condition that no internal pressure is applied, and there is a clearance between the stator core and the can. When the internal pressure P = 50 MPa is applied, the maximum displacement along the 1 direction is 1.468 mm, which indicates that the can is getting into the stator grooves. The displacement is increased with the increase of the internal pressure: from 1.581 mm at P = 60 MPa rising to 1.744 mm at P = 70 MPa. It can be concluded that with the increase of the internal pressure, the increment of the plastic deformation of the can is slow. Therefore, a desirable loading path could be found. Fig. 9(a) and (b) shows that the maximum principal stress are 695.6 MPa and 739.2 MPa respectively with the final internal pressure 50 MPa and 60 MPa. Both the two conditions are not up to the ultimate strength stress. But when P = 70 MPa, the maximum principal stress reaches to 806.2 MPa, this value is more than ultimate strength stress 758 MPa. It shows that the can is bursting before 70 MPa. The maximum principal stress distribution at time 0.085 s, 0.090 s, 0.095 s when the final internal pressure is 70 MPa is also shown in Fig. 9(c)–(e). The corresponding maximum principal stress are 735.9 MPa, 754.9 MPa, 775.7 MPa, respectively. Then we can know that the limit internal pressure is between the 0.090 s and 0.095 s (P = 70 MPa), the range of the limit internal pressure is: 63 MPa < P < 66.5 MPa. Then the limit internal pressure of 63.75 MPa corresponding to the maximum tensile stress (758 MPa) can be obtained by using linear interpolation. From Fig. 9 we can see that there is stress concentration zone in the can contacting with the stator gear sides along the axial direction, and this is also the place where excessive thinning of the can happens. Therefore, filleting the sides is necessary in order to avoid the cusp to lead to the can burst. In summary, the reduction of stress concentration and friction is necessary in this process not only in numerical simulation but also in actual production. 5.4. The result analysis of the second case (fixing two end surface sides) Case two has the same conditions as case one, such as geometry dimensions, load path, mesh condition, mass scaling factor, except
that the boundary condition of the can is fixed at both ends. The range of the limit internal pressure obtained by the same method as case one is 59.5 MPa < P < 63 MPa, and the limit internal pressure of 62.52 MPa can also be obtained. From overall observation, it can be noted that there are some differences between different boundary conditions. The one with one end fixed has the larger limit internal pressure than the one with both ends fixed. This is attributed to the fact that with one end fixed more material will get into the stator core to compensate for rapid thinning of the can. The carrying capability of the can is improved, and it is due to the fact that the feeding of the material can avoid the rapid excessive thinning of the can which should be responsible for the burst of the can. Therefore, because of the characteristics of the present model, the large length of the can correspond to the stator core and the small thickness of the can, the differences of the limit internal pressure of the two cases are small. Besides, from the simulation results, the thickness of the can after applying load in case two is more uniform than case one in the axial direction. 6. Conclusion In this study, several methods that could be used to assemble the stator component and the can are firstly discussed and a method based on the theory of tube hydroforming is then presented and discussed in detail. A three-dimensional model with reduced size was established with limited available data and the size of the slot and wedges are developed according to the ordinary motor. Finite element analyses were carried out by using ABAQUS/EXPLICIT to determine the limit pressure of the can preliminary. The maximum tensile stress criterion was presented as the forming limit criterion and the range of the limit internal pressure of 63 MPa < P < 66.5 MPa for fixing one end and 59.5 MPa < P < 63 MPa for fixing both ends were found based on this criterion with the clearance of 1 mm, and the limit internal pressures calculated by using linear interpolation for two cases are 63.75 MPa and 62.52 MPa respectively. Then the differences between the two cases are discussed. The intensified stress concentration along the stator gear sides are observed. This must be paid more attention to in the practical production. In the future work, experiment rig will be established according to the analysis results of this paper. Then experiments will be performed to validate the simulation results in the internal pressure equipment developed by our research team. Furthermore, more FEA simulations will be carried out by considering the effects of springback. The influences of different clearances and friction coefficient to the limit internal pressure will also be investigated. Acknowledgements Financial support for this work has been provided by the National Key Basic Research Program of China (Grant No. 2009CB724307). The author also would like to acknowledge Mr. Yuquan Guo and Mr. Zhi Zhu for providing the material parameters for hastelloy C-276 used in this research. The insightful comments on the manuscript by the reviewers are also highly appreciated. References ABAQUS, 2008. ABAQUS Analysis User’s Manual. Version. 6.8. ABAQUS Inc., Botha, USA. Bartley, G., Evert, R., 2000. Hydroforming of aluminum extrusions for automotive applications. Light Met. Age 8, 1–8. Chu, E., Xu, Y., 2004a. Hydroforming of aluminum extrusion tubes for automotive applications. Part I: buckling, wrinkling and bursting analyses of aluminum tubes. Int. J. Mech. Sci. 46, 263–283. Chu, E., Xu, Y., 2004b. Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram. Int. J. Mech. Sci. 46, 285–297.
H. Liu et al. / Nuclear Engineering and Design 256 (2013) 256–263 Dohmann, F., Hartl, C., 1996. Hydroforming – a method to manufacture lightweight parts. J. Mater. Process. Technol. 60, 669–676. Feng, Y.H., 2011. Mechanical Analyses of the Cans in AP1000 Reactor Coolant Pump. Shanghai Jiao Tong University, Shanghai, China. Guan, R., Gao, Y.J., 2008. Brief analysis on fabrication process of the AP1000 reactor coolant pump can. China Nucl. Power 1, 49. Harewood, F.J., McHugh, P.E., 2007. Comparison of implicit and explicit finite element methods using crystal plasticity. Comput. Mater. Sci. 39, 481. Jiang, L.J., 2010. Effect of Laser Welding Quality of Nuclear Reactor Coolant Pump Can on Eddy Current Losses. Dalian University of Technology, Dalian, China. Keeler, S.P., 1965. Determination of forming limits in automative stamping, SAE. Report 650535. Li, X.H., Deng, R., Zhang, H.L., He, J., Wang, Y.F., Yang, X.Q., 2010. Effect of friction condition on the process for spinning of shielding cover with extra thin-wall and height diameter/thickness ratio. Acta Sci. Nat. Univ. Sunyatseni 49, 1.
263
Lei, Y.C., Wang, M.J., Jia, Z.H., 2006. Theory of Metal Forming. China Chemical Industry Press, Beijing, China. Liu, C.L., Zhou, X.B., 2006. Experimental and numerical investigation on sheet metal forming limit prediction with thickness related criteria. China Forging & Stamping Technol. 5, 1. Liu, H.W., 2007. Mechanics of Materials. China Higher Education Press, Beijing, China. Ma, X.P., 2007. Discussion on design scheme of frequency-conversion for AP1000’s main-coolant pumps. Electr. Equip. 8, 20. Ma, D.X., 2005. Summary of electromagnetic design of ADFLPH-(55–160) kW/2p canned motor. Explosion Proof Electr. Mach. 40 (126), 1–3. Stoughton, T.B., Zhu, X.H., 2004. Review of theoretical models of the strain based FLD and their relevance to the stress based FLD. Int. J. Plasticity 20, 1460–1481. Wang, C.H., Liu, K.Z., 1986. Spinning Technology. China Machine Press, Beijing, China. Wang, D.Y., 1997. Study on the bulging process technology of the thin-walled products. China Heavy Mach. 6, 37.