Creep Analysis of Aluminum Alloy Disk Experiment for High Speed Energy Storage Flywheel

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1 Creep Analysis of Aluminum Alloy Disk Experiment for High Speed Energy Storage Flywheel YangXU, HanYU, ZupeiSHEN Tsinghua Univ. CHINA Abstrat: In order to ahieve higher speed and higher energy density, aero aluminum alloy and arbon fiber are used in building the Flywheel Energy Storage System (FESS). When FESS s energy is stored in or released out quikly, the system temperature would notably rise up. To the aluminum alloy part of the rotor, thermal reep effet in this high temperature environment has to be arefully onsidered. Even though the temperature rising does not often our, it will definitely depresses the FESS s operating lifetime and reliability. Through a speial experiment devie, this reep phenomenon ould be observed and the reep deformation ould be obtained as well. This paper disusses a omputer simulation of this aluminum alloy reep performane, by using the traditional reep model and Nonlinear Finite Element Analysis (solved in ANSYS). The simulation result an not only well repeat the experimental result, it an also simulate the unmeasured struture stress redistribution under reep effet. This reep analysis has a very important ontribution to the further researh of FESS s optimum design, reliability design and its lifetime estimation. Introdution Now a day, Flywheel Energy Storage System has already been deeply researhed and widely used. High speed and high energy density are two of the most important harateristis that people have been researhing for a long time. The struture of high strength aero aluminum alloy rotor with outside arbon fiber winding has been proved to be a very reasonable struture whih an highly improve the flywheel rotor s performane. A typial strutural is shown in Figure Aluminum alloy rotor.carbon fiber winding Figure 1. Typial Strutural of Aluminum alloy rotor with arbon fiber winding Flywheel rotor The motor/generator and the bearing are diretly fixed to the Al alloy part in the extending axial plae. When the energy is stored in or released out quikly, the eletri urrent density in the motor/generator would be extremely high, and the loal temperature would notably rise up as well, and soon, the whole system would be heating-up. Experiment shows that the temperature in Al alloy may even rise up from 0 to about 70. Under this high temperature environment, reep effet will obviously our in Al alloy, whih is a rate dependent material nonlinearity in whih the material ontinues to deform under a onstant load as we have known.

In order to easily understand this reep effet s influene to the flywheel rotor, a simple reep experiment was taken by using the separated Al alloy end ap, where the maximum stress and reep effet

2 In order to easily understand this reep effet s influene to the flywheel rotor, a simple reep experiment was taken by using the separated Al alloy end ap, where the maximum stress and reep effet would happen. Firstly, the end ap is reshaped and speially designed to be prototype disk, show in Figure. And then, fixed up the same motor/generator and the same bearing as the flywheel, this disk an aelerate to a very high stati speed of 60,000rpm, whih makes the disk perform in a same stress level as in the flywheel. The axial displaement of the outer edge, point [A] showed in Figure - b), is then deteted by an optial devie. In this reep experiment, the rotating disk s temperature ould be ontrolled to stati 70 by adjusting the ooling water s temperature inside the motor stator, and ould be deteted by a fixed infrared temperature sensor. Under above onditions, the reep experiment was well performed and the reep deformation was obviously observed and quantitatively reorded. a) A a). 3D model of the experiment disk b) b). Cross session of the experiment disk Figure. Speially designed disk for reep experiment In this paper, the parameters in traditional reep funtion were setup through experiment data reord, and this reep funtion was used to desribe the Al alloy s material model in ANSYS program to simulate and analyze the Al alloy disk s reep phenomenon, and the simulating result was very exiting. Here, the simulation method and the result analysis would be disussed in detail. It is very helpful for the further reliable researh and lifetime estimation. ANSYS Modeling Before doing the reep analysis, built up a reasonable finite element model is neessary for getting an aurate result. Here, several key aspets are listing out. 1). -D Axisymmetri Solid Element Under finish mahining, the experimental prototype disk shape is an exatly axisymmetri geometrial solid body. So, in this reep analysis, -D ross setion model and axisymmetri 8 node quadrilateral solid

3 element PLANE18 is used. It is muh simple than using a 3-D model, it also an save a lot of omputer time, it is quite enough for this speial ase, and it an even get muh better result. ). Multilinear Kinemati Hardening Material Model In omputer simulation, reep analysis proedure uses two time steps, stati strutural analysis and then reep analysis. In the speed of 60,000rpm, the stress level in some part of the Al alloy disk would be extremely high, over the proportional limit and exhibit nonlinear stress-strain relationship. Finally, the Multilinear Kinemati Hardening plasti and nononservative material model is hosen for this strutural analysis. The stress-strain relationship urve is showed in Figure 3, whih is defined by 7 points ome from a speial material experiment. The data showed in Table 1 following Figure3 is the 7 plotted stress-strain points. 700 Multilinear Stress-Strain Curve Stress ( σ / MPa ) Strain ( ) Figure 3. Multilinear Stress-Strain Curve of Aluminum Alloy Table 1 Stress-Strain Point of Multilinear Curve Sign No Strain () Stress (σ / MPa) Using this multilinear plasti material model, stress distribution of the experimental disk an be muh better simulated and the result will be muh more reasonable for the oming step of reep analysis. 3). Impliit Creep Model Creep is a rate dependent material nonlinearity in whih the material ontinues to deform under a onstant load. In a traditional theory, reep ould be divided into three stages, whih are shown in Figure 4. The ANSYS program has the apability of modeling the first two stages (primary and seondary). The tertiary stage is usually not analyzed sine it implies impending failure.

4 Figure 4. Three Stages of Creep The impliit reep proedure is used in solving this disk rotating reep problem. And the reep model an be desribed by this funtion. Where, C 1 -C 4 = Constants 4 C C3 T = C1σ t e = Strain aused by reep σ= t = T = e = Struture stress Time Temperature Constant, (base of natural logarithms) In the omputer simulation analysis, and σ are alulated as elements Mises strain and Mises stress. 3 ( ) + ( ) + ( ) + ( + ) = x y y z z x xy yz σ = σ σ + σ σ + σ σ + τ + τ + τ ( x y) ( y z) ( z x) 6( xy yz zx ) Beause of the temperature is also a onstant (70 ) in this experiment, the reep model funtion an be abbreviated like C C3 = C1σ t zx

5 Using the experiment testing displaement result data, through iterative testing method, the three onstants in this reep funtion is worked out, and the final experimental reep funtion is = In this funtion, stress unit is Pasal, and the time unit is minute. The impliit reep method is hosen in this ase, beause it is robust, fast and aurate, whih is reommended for general use. Further more, it an handle temperature dependent reep onstants, as well as simultaneous oupling with isotropi hardening plastiity models. And of ause, the final analysis results prove that this hoie is right. Analysis Results & Disussion Using the above finite element model and impliit reep method, the reep analysis of Al alloy disk experiment is performed. 1). Axial Displaement Result The axial displaement result of disk edge, [A] point showed in Figure, is the only physial parameter an be well deteted and reorded during this experiment. Drawing the experiment data and the simulating data in a same figure, the urve of displaement-time relationship is showed in Figure 5. σ t 00 Axial Displaement d /10 - mm Exper i ment al Dat a Si mul at i on Cur ve Time t / min Figure 5. Creep Displaement-Time Data Compare The elasti-plasti strutural axial displaement at 60,000rpm rotating speed is 150e-mm, whih is the beginning reep displaement when the time equal to 0, showed in this figure. And at the time about 3300min, the large deformation ause the disk broken. The maximum reep axial displaement is about 47e-mm. It is showed that the reep effet in this rotating Al alloy disk an be well simulated by omputer. At the beginning, the reep deformation performs very quikly, and about 10 hours later, the axial displaement goes more and more slowly, and even goes down after long period s reep. But the omputer simulation shows that the reep effet ontinues enlarging the radial displaement, till the end, the disk breaks up. The

6 relative error in this reep simulation is less than 15%, whih is a wonderful result in reep analysis. ). Redistribution of The Strutural Stress During the strutural reep period, not only the deformation, the unmeasured stress distribution will also largely hange. Through the omputer simulation, the redistribution of the strutural stress (Mises Stress) after a long period of reep is showed in the following Figure 6. a) b) a). Mises Stress ontour before reep b). Mises Stress ontour after reep Figure 6. The Mises Stress Redistribution After A long Period of Creep After the stress redistribution, the maximum Mises stress hanges from about 605MPa to 330MPa. And from this figure, suh a onlusion ould be draw: the stress goes to average. The stress redistribution result an only work in alulation and imagination, and it annot read in experiment diretly. But, its existing an be proved by some other experimental phenomenon. To prove this stress redistribution result, the disk rotor was stopped and taken out to measure its marosopial surfae remainder deformation. The remainder axial deformation of the upper surfae result is plot in Figure 7. The experimental deformation and the omputer simulation result an fit eah other very well.

7 Axi al Remai nder def or mat i on d/ mm Radi at i on Pl ae Exper i ment Measur ement Comput er Si mul at i on Resul t r / mm Figure 7. The Surfae Axial Remainder Deformation of Creep Disk When stopping the disk rotor after a long period of reep, the alulated result shows that the axial displaement will not goes down, on the ontrary, it goes up a little as the rotor speed down. This interesting phenomenon an also be observed in the experiment. The quantitative deformation testing data and the simulating data are showed in Figure 8. Axial Displaement d/10 - mm Computer Simulation Result Experiment Data Speed Down Rotating Speed v/rpm Figure 8. The Axial Deformation Inreasing When The Speed Down This is said that the strutural stress redistribution under reep effet may really happen.

3). Critial Cross Setions The high strength aero Al alloy is a kind of fragile material. It is said that large strain would make this material unstable.

The large strain is seen to be the main reason of system fail, whih happens in two ritial ross setions loated in different radius plaes. See Figure 9.

8 3). Critial Cross Setions The high strength aero Al alloy is a kind of fragile material. It is said that large strain would make this material unstable. In this experiment, reep strain will ontinually enlarge under the 60,000rpm high speed, even over several times of the elasti strain, up to 10% at some speial part of the disk. The large strain is seen to be the main reason of system fail, whih happens in two ritial ross setions loated in different radius plaes. See Figure 9. One is at a smaller radiation plae, here is the maximum strain plae, but here the large strain an only be deep into half of the ross setion. The other ritial ross setion is loated in the middle radius plae, here the strain is not the largest, but it an really over the strain limit of this kind of Al alloy material. And, at the seond plae, the high strain will go through the whole ross setion. 1 1, The Two Cross Setions Figure 9. Creep Strain Contour and The Two Critial Cross Setions Experiment shows that the disk is finally broken from the seond ritial ross setion plae, but at the first ritial plae of the broken fragment, the marosopi rivel aused by very large strain an be easily seen, the photo showed in Figure 10. Marosopi Rivel Figure 10. Marosopi Rivel of Very Large Strain At The First Critial Cross Setion Plae Conlusion 1. Creep effet an be well desribed through traditional reep funtion and ANSYS Finite Element Analysis, and this effet ertainly should be arefully onsidered in the reliability design and lifetime estimation.. Large reep strain makes the strutural unstable. There are two ritial plaes should be taken are of, they really make the whole system muh more weak when the reep effet our.

9 Referenes 1) Xiaying MU, Creep Dynamis, XiAnJiaoTong Univ. Press, 1990, XiAn, Chinese. ) Majumdar et al, A Unfied and Mehanial Approah to Creep Fatigue Damage, ANL ) M.J.Manjoine, Elevated Temperature Mehanis of Metals, Symposium on Mehanial Behavior of Material, 1974, Kyoto, Japan.

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