NASA/TM-2001-21040 

Structural Analysis of Composite Flywheels: 

An Integrated NDE and FEM Approach 

Ali Abdul-Aziz, George Baaklini, and Jeffrey Trudell 

Glenn Research Center, Cleveland, Ohio 

January 2001 

https://ntrs.nasa.gov/search.jsp?R=20010047389 2018-05-14T14:43:55+00:00Z
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NASA/TM-2001-210461 

Structural Analysis of Composite Flywheels: 

An Integrated NDE and FEM Approach 

Ali Abdul-Aziz, George Baaklini, and Jeffrey Trudell 

Glenn Research Center, Cleveland, Ohio 

Prepared for the 

6th Annual International Symposium on NDE for Health Monitoring and Diagnostics 

sponsored by The International Society for Optical Engineering 

Newport Beach, California, March 4-8,2001 

National Aeronautics and 

Space Administration 

Glenn Research Center 

January 2001 

, 
This report contains preliminary 

findings, subject to revision as 

analysis proceeds. 

Trade names or manufacturers' names are used in this report for 

identification only. This usage does not constitute an official 

endorsement, either expressed or implied, by the National 

Aeronautics and Space Administration. 

Available from 

NASA Center for Aerospace Information 

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Price Code: A03 

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Price Code: A03 

Available electronically at http: //gltrs.grc.nasa.gov IGLTRS 
STRUCTURAL ANALYSIS OF COMPOSITE FLYWHEELS: 

AN INTEGRATED NDE AND FEM APPROACH 

Ali Abdul-Aziz, George Baaklini, and Jeffrey Trudell 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

SUMMARY 

A structural assessment by integrating finite-element methods (FEM) and a nondestructive evaluation (NDE) of 

two flywheel rotor assemblies is presented. Composite rotor A is pancakelike with a solid hub design, and composite 

rotor B is cylindrical with a hollow hub design. Detailed analyses under combined centrifugal and interference-fit 

loading are performed. Two- and three-dimensional stress analyses and two-dimensional fracture mechanics analyses are conducted. A comparison of the structural analysis results obtained with those extracted via NDE findings is 

reported. Contact effects due to press-fit conditions are evaluated. Stress results generated from the finite-element 

analyses were corroborated with the analytical solution. Cracks due to rotational loading up to 48 000 rpm for rotor 

A and 34 000 rpm for rotor B were successfully imaged with NDE and predicted with FEM and fracture mechanics 

analyses. A procedure that extends current structural analysis to a life prediction tool is also defined. 

INTRODUCTION 

Composite flywheels are being developed as an alternative to expensive and short-life chemical batteries. Flywheels promise orders of magnitude increases in performance and service life in many NASA and military applications, including spacecraft, launch vehicles, aircraft power systems, uninterruptible power supplies, and planetary 

outposts and rovers (ref. 1). Although the technology holds great promise, there remain a number of challenges to 

overcome, such as rotor certification for safe life, before these advanced flywheels reach operational status. Carbonfiber-reinforced polymer composites are the materials of choice for energy applications because of the high energy 

and power densities that they can achieve (ref. 2). Flywheel design topology can also allow a burst failure mode that 

is relatively benign in comparison with flywheels made of metallic materials (ref. 3). 

A successful deployment of flywheels must address the long-tern1 durability issue of polymer composites due to 

the limited availability of information about their fatigue characteristics and nonlinear behavior, especially at 

elevated temperatures. Nondestructive evaluation (NDE) in combination with stress, fracture mechanics, and life 

prediction models are expected to set a standardized procedure to accurately assess the applicability of using various 

composite materials to design a suitable rotor-flywheel assembly. 

However, for NDE information to be useful in structural characterization and modeling, the NDE data format 

must be compatible with microstructural and structural models currently being developed (ref. 4). Moreover, to 

enhance the usefulness of the NDE application, qualitative and quantitative computer analysis tools based on NDE 

imaging modalities must be developed. Qualitative tools include two- and three-dimensional visualization methods. 

Quantitative tools include segmentation methods that can send output to commercial finite-element, micromechanical, and/or continuum damage model software (refs. 5 and 6) for the evaluation of composite materials and 

components. 

This report describes the finite-element analyses and the NDE modality undertaken on two flywheel rotors that 

were spun to burst speed. Computed tomography (CT) and dimensional measurements were used to nondestructively evaluate the rotors before and/or after they were spun to the first crack detection. CT data findings of two- and 

three-dimensional crack formation were used to conduct finite-element and fracture mechanics analyses. A procedure to extend these analyses to estimate the life of these components is also outlined. 

NASAffM-2001-210461 
ROTOR TEST CONFIGURATIONS 

Two spin-tested rotor configurations were analyzed and scanned. The fIrst was rotor A, a single thick ring that 

was assembled on a solid aluminum hub. Rotor B, the second configuration, is considered a mass-loaded device. 

The compressive radial stresses induced by the mass-loading hub help to overcome the poor u'ansverse tensile 

strength of filament-wound composites; however, the disadvantage is that the circumferential and edge stresses at 

the inner diameter are increased. The following describes each layout. 

1. Pancake rotor assembly A was assembled by U.S. Flywheel Systems, Inc.

1 and the composite rim was 

manufactured by Toray Fiber, Inc.2 The rim inside diameter (id) is 6.9 in. , the outside diameter is 11.5 in. , and the 

height is I in. (fig. 1). The rim is made of M30G carbon fiber and an epoxy resin system. The radial interference fIt 

between the rotor rim and the solid aluminum hub is 0.014 in. 

2. Composite rotor assembly B was manufactured by U.S. Flywheel Systems and is shown in figure 2. Rotor B 

has an approximate inside diameter of 6.9 in., an outside diameter of 10.5 in. , and a height of 8.5 in. The aluminum 

hub is designed to mass load the rim and with the addition of an interference fIt, to reduce the peak radial tensile 

stresses. The rim is made of Hexel's IM7 carbon and AS4D carbon fIber and a shell epoxy resin mixture. The composite rotor rim is 78.3 percent fiber by weight and 71 percent by volume. IM7 fIber was wound at the inner diameter and outer diameter with AS4D fIber in the central portion. The radial interference fIt between the composite 

rotor rim and the aluminum hub is 0.013 in. 

FINITE-ELEMENT ANALYSIS 

The loading state of a flywheel includes centrifugal, interference, thermal, and residual stresses. For axisymmetric rotors, analytical solutions are available to solve for the rotor stress state. Timoshenko (ref. 7) provided the 

derivation of the stress state in a cylinder subjected to internal and external pressures, temperature, and centrifugal 

loading. In Manson (ref. 8), the axisymmetric stress distIibution is solved via fInite-difference techniques and 

accounts for height, density, modulus, and temperature variations as a function of radius. Genta (ref. 9) modifIed 

Manson's procedure to include orthotropic materials. Gabrys (ref. 10) provides a simple way to solve for the rotor 

stress state by superimposing anisotropic elasticity analytical solutions. Gabrys also provides a simple method to 

predict residual stresses that result from the fabrication process and the experimental correlation of the flywheel 

ring coefficient of thermal expansion. 

The superimposed solutions assume plane stress and are only applicable for constant-axial-height, cylindrically 

orthotropic flywheels. Finite-element analyses are perfornled when the rotors or applied loads are not axisymmetric 

or if fracture mechanics analysis is to be performed. The ANSYS (ref. 11) finite-element code was used to solve the 

nonlinear, two- and three-dimensional contact analysis, whereas the two-dimensional stress and fracture mechanics 

analyses were performed with MARC (ref. 12). The two- and three-dimensional, fInite-element models were generated using MSClPatran Graphics (ref. 13) and ANSYS GUI, and inputs were generated for each FE code accordingly. The ANSYS Paranletric Design Language (ADPL) was implemented to automatic nonlinear solution and data 

recovery with parametric changes in geometry, material, mesh, boundary conditions, and loads. 

Pancake Rotor A 

The MARC pancake rotor A model consisted of 995 nodes and 912 quad4 elements and is shown in figure 3. 

The choice of the planar representation (plane stress) of a disk allows analysis of non axisymmetric rotors (i.e., bolt 

holes for hub-shaft attachment). An alternative approach would use axisymmetric elements to account for variations 

in the radial and hoop stresses as a function of axial height and would decrease the required number of elements 

and run time. The nodes modeling the contact were intentionally offset in the hoop direction and were not radially 

aligned to accommodate the contact condition set by the MARC code. The ANSYS pancake rotor A model consisted of 7065 nodes and 7290 PLANE42 and CONT ACT48 elements and is shown in fIgure 4. A large number of 

elements was generated as run times were only a minute or two and peak stress locations are resolved more 

'u.S. Flywheel Systems, Newberry Park, CA 91320. 

"foray Fiber, Inc., Tacoma, W A 98446. 

NASAfTM-2001-210461 2 
accurately; however, fewer elements by an order of magnitude would give similar results. Using Genta's method 

coded in FORTRAN, the axisymmetric stress distribution of the rotor A was solved and compared with the twodimensional solutions of MARC and ANSYS to benchmark the modeling approaches. 

Rotor B 

The second mass-loaded hub was modeled in both two and three dimensions, which provided guidance to perfoml the fracture mechanics analysis in two dimensions. Both finite-element method (FEM) codes, ANSYS, and 

MARC were utilized to conduct these analyses. The rim stress distribution is clearly tlu'ee dimensional due to the 

axial counterbore and its 1I8th cyclic symmetry, creating a nonunifoml axial and circumferential mass loading of 

the hub. The t1u'ee-dimensional model consists of 1642 eight-node brick elements and 2283 nodes and is shown in 

figure 5. Only half the axial height was included in the model and the X,Y-plane nodes were constrained in the 

Z-direction to represent axial symmetry. The two-dimensional-model assembly consists of 1408 quad4 and quad8 

elements and 2592 nodes and is shown in figure 6. The two reasons for using both quad4 and quad8 elements to 

model the rim were that (1) quad4 elements are needed to model the contact region between the hub and rim since 

higher order elements are not suitable for contact analysis because of a mismatch in stiffness between midside and 

comer nodes and (2) quad8 elements are required for subsequent fracture mechanics analysis. This however creates 

a region in which there is a stiffness mismatch between midside and comer nodes, although it is a region of low 

radial stress and not at the contact surface. Quarter symmetry was chosen to facilitate the application of boundary 

conditions to the X,Y-axes. 

The material properties listed in table I were used for the analyses. The composite properties were generated 

using the software lCAN (Integrated Composite Analyzer, ref. 14) because coupon test data were not available. 

Orthotropic and directionality effects of the material properties were all accounted for in the analyses. 

In performing the analysis, the applied load is divided into a series of small incremental steps to aid in reaching 

a converging solution and to avoid encountering mathematical instabilities typically during contact. However, the 

first load step includes the full amount of interference, with successive load steps applying small increments of all 

other applied loads. 

FRACTURE MECHANICS 

To conduct the fracture mechanics analysis, the J-integral parametric option available in the MARC code was 

applied, resulting in the calculation of the change in strain energy due to nodal movement near the crack tip. This 

quantity is evaluated by numerical integration at each increment for each prescribed nodal movement to determine 

the derivative of the strain energy with respect to the crack length at the end of each increment. 

In addition to overcoming the difficulty that is usually encountered in the finite-element fracture mechanics 

representation of the solution near the crack tip, the mesh must be modeled so that the singularity is approximated 

with sufficient accuracy. Many methods have been established to arrive at such an approximation; however, the 

most commonly employed uses a degenerate fonn of the standard eight-node quadrilateral element. This method, 

usually referred to as the "1I4-point node technique" (ref. 15), is also preferred for analyses conducted with the 

MARC code (ref. 12). It is applied by using an eight-node quarter of the edge length, the edge opposite the crack 

being kept straight. When these steps are followed, a singularity in the stress field exists in all directions going 

outward radially from the crack tip. 

STRESS INTENSITY FACTOR 

The calculation of the stress intensity factor K will allow one to determine at which load increment crack propagation occurs. This is done by calculating the elastic-plastic energy release rate, which is confined to a single parameter: the strength of the singularity in the elastic-plastic stress field at the crack tip. The magnitude of K depends on 

the crack length, the distribution and intensity of applied loads, and the geometry of the structure. Crack propagation 

will occur when any combination of these factors causes K to be equal to or greater than the experimentally determined material threshold value (ref. 16). The equation that relates K to the energy release rate is (ref. 12) 

NASAffM-2001-210461 3 
dW K 2 

G= -=- dA E (1) 

where G is the energy release rate during a small crack extension; W is the strain energy in pounds force per inch per 

inch; K is the stress intensity factor in thousands of pounds per square inch (kpsi); A = a X b where a and b are the 

crack length and width in inches, respectively; and E is the modulus in thousands of pounds per square inch (kpsi). 

The stress intensity factor is given by 

K=~EdW d A (2) 

After the functional forms of K have been determined, the state of the stress and displacement near the crack tip 

region of the structure can be determined. It must be noted, however, that these equations represent a specific provision that describes the general approach to identifying these key parameters. Thus, for polymer matrix composites 

some modification will be required. 

The life prediction computation is based on obtaining the data from the analysis and then applying the Paris 

relation, which ties the number of life cycles to the crack length and the stress intensity factor (ref. 17) and is 

desctibed by 

d N == d a 

C(/lK)" 

(3) 

where N is the number of loading cycles, da is the incremental crack length, c and 11 are material constants determined from experimental data, and I!J( is the stress intensity factor range (Kmay. - KmiJ The loading cycle is defined 

as a combination of the press fit and the rotational speed loading. 

Equations (1) to (3) identify a procedure that would lead to life assessment calculations. However, a fatigue 

crack growth data base would have to be established for these materials to perform a life estimate. 

RESULTS AND DISCUSSION 

The results generated are presented in this section, which includes details covering each rotor assembly and the 

corresponding stress output. 

Rotor A 

The radial and hoop stress distributions of the pancake rotor assembly as predicted by the MARC code are 

shown in figures 7 to 10 for the entire rotor and for the rim section only. The peak hoop stress is 141 kpsi at the rim 

contact region with the hub (fig. 9). The peak radial stress of 3.4 kpsi occurs at a radial location of 4.35 in. as indicated in figure 10. These stresses were generated at a rotational speed of 48 000 rpm. 

The radial and hoop stress distributions as calculated by ANS YS are shown in figures 11 and 12. The peak 

radial stress is 3.52 kpsi and the peak hoop stress 135.30 kpsi. The nodal peak radial stress occurred at a location of 

approximately 1.38 in. (nodal spacing was 0.115) from the inside diameter of the 2.3-in.-thick rim. The variation in 

radial stress versus radius for several speeds is shown in figure 13. Note that the location of peak radial stress moves 

from the outer radius to the center as speed increases because the centrifugal loading continues to offset the compressive preload during assembly. Generally, carbon fiber exhibits an out-of-plane radial strength of 3 to 10 kpsi and 

200 to 300 kpsi in the hoop direction (ref. 18). However, the processing technique for the composite materials 

addressed in this work must be verified in order for these provisions to be held valid. 

NASAfTM-2001-210461 4 
The results of Genta's modification of Manson's finite-difference method are shown in table II. Note that the 

rim peak radial stress is predicted to be 3.52 kpsi at a radial location of 4.83 in. (1.38 in. from the rim id), which is 

in excellent agreement with the ANSYS and MARC results. The fi ber volume ratio (FVR) was then reduced to 0.63 

(but the same density of 0.69 FVR was assumed) to show the sensitivity of reduced stiffness (due to translational 

inefficiencies, fatigue effects, variations in fiber and mauix propenies) on the peak radial stress location. The peak 

radial stress increased to 3.76 kpsi at the radial location of 4.78 in. (1.33 in. from the rim id), a shift of 0.05 in. from 

the 0.69-FVR results. The peak hoop sU'ess decreased to 126.9 from 135.5 kpsi. An estin1ate of residual stress was 

then made (no measurements) based upon the cure cycle of the manufactured ling, and peak radial stress increased 

to 6.4 kpsi at the radial location of 4.67 in. (1.23 in. from the rim id). The residual stress shifted the location of peak 

radial stress 0.15 in. versus 0.05 in. for a 7-percent change in stiffness. 

NDE Findings Versus FEM of Rotor A 

As reponed in the previous paragraph, the finite-element analyses (FEA) of the rotor assembly uncovered the 

stress levels experienced by the unit as a result of the high rotational loading. After spin testing to 48 000 rpm, CT 

images were taken to identify structural damage. Figure 14 shows a CT scan of the rotor after it was spun. An evaluation of the CT image indicated a cracking of the rotor along the entire circumferential direction. The crack is nearly 

symmetlical and is located at a 4.465-in. radial distance. The finite-element analysis reponed in figures 10 and 11 

showed that the maximum radial stress region is at a radial distance range of 4.35 to 5.34 in. Furthermore, the peak 

radial stress occurred at 4.78 in. or with the addition of estimated residual stress, at 4.67 in. With a 7-percent stiffness reduction, the crack would move farther toward the center of the rim to 4.62 in. Because of the symmetlical 

nature of the crack, with accurate estimates or measurements of stiffness and residual stress and assuming no localized stress concentrations, the stress analysis can be cOlTelated to crack location observed by the CT scan, which 

cOlToborates that the FEA is in good agreement with the NDE findings. In addition, both procedures demonstrated 

that obtaining parallel results from both methods is achievable. Additionally, these fi ndings constitute an additional 

means of verifying and confmning service-related damage and design anomalies typically experienced by various 

structural components. 

Mass-Loaded Hub Rotor B 

Figures 15 and 16 illustrate the two-dimensional radial sU'esses and the hoop sU'esses for the rotor. The stress 

distlibution as shown in figure 15 is the result of a complicated combined press-fit centlifugalloading on a 

nonaxisymmetlic structure. Higher hoop stresses are generated at the rim-hub interface as a result of the contact 

effects or mass loading of the hub onto the rim. The cOlTesponding stress magnitude reached 94 kpsi. The radial 

stress profile in figure 16 shows that the maximum stress level in the hub is in the hub holes, which is an indication 

that the hub is very likely to fail at that particular section if a higher rotational load is applied. A nonuniform radial 

stress distlibution shown in the rim near the hub-rim interface has developed because quad8 and quad4 elements 

were used, creating a mismatch in stiffness between the midside and comer nodes. The nonuniform stress distlibution also created convergence problems and tremendous increases in CPU times. 

Figure 17 shows the three-dimensional hoop stress distlibution generated in the flywheel at 34 000 rpm, the 

speed at which the first crack developed in the rim. Note that the hoop stress reaches a maximum value of 113 kpsi 

at the area of contact between the rim and the hub. The radial stress distlibution at 34 000 rpm is shown in figure 18. 

As expected, the peak radial stress is again in the hub holes. Figure 19 shows the Von Mises stresses in the hub with 

a stress level of 32.4 kpsi at the region adjacent to the holes. 

Figure 20 illustrates the three-dimensional hoop stresses for the rim only at 34 000 rpm. Note that a nonuniform 

hoop stress distlibution is clearly shown. The maximum hoop stress occurs at the axial region below the counterbore 

of the hub, which can be explained by examining the radial stress distlibution. Figure 21 illustrates the threedimensional radial stresses. Note the axial shift in radial stress due to the counterbore in the hub, which is also illustrated at 0° and 30° in figures 22 and 23. The compressive radial stresses at the rim inner radius decrease axially 

from the center to the top edge, but this higher radial preload induces higher hoop stresses in the center than in the 

top edge. 

NASAfTM-2001-210461 5 
The peak hoop stress distribution will be reversed as the speed is increased because the centrifugal forces 

decrease the initial interference preload near the center, and the cOllnterbore mass-loading region of the hub induces 

higher compressive radial stresses. The mass loading of the counterbore section of the hub will also create higher 

bending stresses in the rim than that of a solid hub design, and shear stress levels will have to be addressed at the 

higher speeds. With regard to radial stress magnitude, the peak is about 0.3 kpsi at a radial distance of 5.5 1 in. 

(fig. 21). The radial stress, when combined with estimated residual stresses, appears to be at the lower bound of the 

expected transverse strength levels and indicates a critical value that causes failure. Residual stresses will increa e 

and shift the peak radial stresses inward toward the center of the lim as would the decreased hoop stiffness that was 

described in the previous section. 

Figure 24 represents the two-dimensional radial stress distribution of the rotor obtained from the fracture 

mechanics analysis at a rotational speed of 34000 rpm. Figure 25 duplicates figure 24 with the exception that it 

illustrates a closer view of the crack propagation generated. The crack was propagated at the nodal point of the element that exhibited the highest stress as indicated by an earlier three-dimensional stress analysis. An initial crack 

size of 0.005 in. was assumed based upon both data suggested by the CT scan and visual inspection. Furthem10re, 

the crack collected through the CT scan was asymmetric and it replicated the phenomena expelienced by the flywheel while undergoing excessive cenuifugalloading. In this work, however, to simplify the analytical calculations, 

the two-dimensional analyses assumed that the crack was being propagated symmetrically with respect to the radial 

direction and along the circumference of the flywheel. 

Additional observations noted in viewing figure 25 are confined to the fact that the stress magnitude at the crack 

tip grew higher as the crack advanced. The counterbore in the hub is primarily responsible for the high rim bending 

stresses that contributed to the rotor cracking. Figure 26 presents the energy release rate versus the crack length. A 

highlighted linear variation (as anticipated) shows that the higher the energy rate, the higher the crack length. Furthermore, this denotes that a higher energy release rate would ultimately lead to unstable crack growth provided that 

the fracture toughness data of the material demonstrate such a possibility. This scenario will drive the crack to grow 

until it hits the edge or boundaries. Moreover, this information provides a preliminary guide for performing life 

analyses when fatigue crack growth data for these materials become available. 

NDE Findings Versus FEM of Rotor B 

The NDE-FEA results for rotor B are presented in this section. Figure 25 shows a computed CT scan for the 

rotor. The scan is a cross-sectional view taken in a direction parallel to the axis of rotation. The defects detected by 

the CT scan clearly show the two cracks, which vary in axial location because of the variation in the radial stress 

profile created by the mass-loaded hub and the rotational speed of 34 000 rpm. The view indicates that the cracks 

are parallel to the rotor axis of rotation, they are asymmetrical along the entire radial direction, and they fall within 

5.33 to 5.81 in. at the middle section of the rotor. These data are in close agreement with the FEA data without 

residual stresses, which initiated peak radial stresses at a radial distance of 551 to 6.12 in. These findings supported 

the fact that starting crack propagation at that particular location via the fracture mechanics analysis was consistent 

with the CT data. 

Other supporting data relating NDE to FEA are seen in figures 23 and 27. For instance, the stress results shown 

in figure 23, which represents the radial stresses in the rim, clearly indicate that the maximum stress region is within 

the section defined by the CT scan. Figure 23 describes the stress region at the contact side with the hollow hub 

whereas figure 27 shows the crack locations and variations within the rim. The measurements reported, as obtained 

from figure 27, once more show that the NDE data correlate well with those predicted by the FEA. 

Looking at the data collected from the CT scan and the FEA results allows us to conclude that with a good 

degree of accuracy, it was possible to detect the crack origination area and its direction. Furthermore, the NDE data 

assisted us in performing a three-dimensional, finite-element analysis to identify the crack and the maximum stress 

locations. Such information was greatly needed to grow a crack in the rim for life prediction purposes. 

N AS AfTM-200 1-210461 6 
--- 

- ----------

CO CLUSIO S 

Two- and three-dimensional, fi nite-element stress analyses were conducted for two flywheel rotor systems 

with solid and hollow hubs, respectively. Subsequent two-dimensional fracnlre mechanics analysis were conducted 

to trace a crack propagation identified by computed tomography (CT) scans after spin loading to 34 000 rpm. The 

results were discussed and compared with those predicted by CT. The following conclusions are drawn: 

1. The finite-element analyses (FEA) showed that the rotor first crack as detected by the CT scan can be 

modeled with finite elements provided that the material properties and residual loads are adequately quantified. 

2. Indepth FEA modeling and evaluation of two flywheel rotor systems under spin loading conditions was successfully conducted. 

3. Crack location cited via CT corresponded well with that simulated by the fracture mechanics analysis. 

4. Lack of fatigue crack propagation data for the composite materials hindered conducting a life estimate as 

desired. Until a fatigue crack growth data base is established, conducting a life assessment will remain an 

unattainable task. 

5. An aluminum hub design is a crucial factor affecting the durability of the rotor because an improper hub 

design can result in high bending stresses that in tum result in complex crack propagation behavior. Therefore, the 

hub designer must consider bringing the bending stresses to a minimum level. 

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18. Agarwal, Bhagwan D.; and Broutman, Lawrence 1.: Analysis and Performance of Fiber Composites. Second ed., 

l ohn Wiley & Sons, Inc., New York, NY, 1990. 

TABLE I.- FIBER AND COMPOSITES MATERlAL PROPERTI ES 

Properties Aluminum AS4D IM7 M30G 

Density, Ib/in3 0.10 10 0.0584 0.0584 0.0567 

Modulus of elasticity, E, kpsi 

Ell 10.4x 1Ol 13.6x I0' 13.6x I0' 13.3x I0' 

E ll ----------- 29.6x 1Ol 27.8x 1Ol 29.6x 1Ol 

Ell ---------- - 13.6x I0' 13.6x I0' 13.3x I0' 

Poisson's ratio, v 

V l1 0.30 0.01 3 0.0 12 0.0 11 

V21 ----- .24 .24 .25 

VIJ --- -- .38 .39 .39 

Energy release rate, G, kpsi 

Gil - ---- 6.68x 102 6.68x 102 6.44x I0' 

0 22 - - --- 6.68x IO' 6.68x I0' 6.44XIO' 

Gll ----- 3.89x 1O' 3.89x 1O' 3.76x I0' 

NASAfTM- 200l-210461 8 
TABLE II .--PANCAKE ROTOR STRESS : STRAIN DISTRIBUTION USING GENT~ S METHOD (REF . 9) 

Pancake M30G 6 . 9" ID 11 . 5"OD -El e~e ;;t--a""~ci -M-;' e~i~l Ch~~-;'-';te~is ics --------------------------------------------- ------------------------------------

Station Radius Height Tap Ec Er v rho 

o . 000 1 . 000 1 . 1070E+08 . 1070E+08 . 32 . 2617E- 03 AL 7075 - T6 

1 3 . 450 1 . 000 . 1070E+08 . 1070E+08 . 32 . 2617E- 03 AL7075 -T6 

2 3.450 1 . 000 . 2962E+08 . 1326E+07 . 25 . 1471E- 03 fwm30gfv69 

___ ___ ~ __________ _._~ ~9 ________ : ~ _______ _____________ _ ?~~~~:r ~ _____ ~~? ~~Q? ______ ~? _____ _ ~ ~ ~ :} g~ ____ ~~~} 'i ~~ ?~ __ 

BC : Pressure and Interference 

Station Radius Height Pressure Interference 

0 . 000 1 . 000 . 0 . 00000 

1 3 . 450 1. 000 . 0 . 00000 

2 3 . 450 1. 000 . 0 . 00000 

3 5 . 750 1 . 000 . 0 . 00000 

Disk Stress Analysis Using Manson ' s Procedure - LU Solid Disk 

Inner radius [ in.] . 000 

Outer radius [ in .] 5 . 750 

Mass . 0196 

Moment of inertia . 2780 

Angular velocity [ rp~ 48000 . 0 

Angular velocity [ rad/s] 5026 . 5 In~t~al stress [ inner hu~ . 0 

Number of stations 

Number of elements/station 50 

Number of elements 150 -Te-mpe~~ c-ure -~n-d Therma""i -D-;'-t-; ---------- -------- ------------------------------------------------------------------------

Station 

o 

1 

2 

3 

Radius 

. 000 

3 . 450 

3 . 450 

5 . 750 

Stress Distribution 

Station Radius 

0 . 000 

50 3 . 450 

100 3 . 450 

150 5 . 750 

Thick 

1 . 000 

1. 000 

1 . 000 

1 . 000 

Height 

1. 000 

1 . 000 

1. 000 

1 . 000 

Temp Alpha R Alpha C 

312 . 2 . 1300E- 04 . 1300E- 04 

312 . 2 . 1300E- 04 . 1300E- 04 

. 0 - . 3600E- 06 . 1460E- 04 

. 0 - . 3600E- 06 . 1460E- 04 

Sr (ksi) Sc Von Mises 

22368 . 9 22368 . 9 22368 . 9 

- 10312 . 6 3066 . 8 12140 . 1 

- 10312 . 6 135297 . 9 140737 . 9 

. 0 79725 . 2 79725 . 2 

- ;ain/D{sp iac e~,-;;;t. -Dist~ibut;:on -------------------------------------- ---------------------- -------------------------

Station Radius Height er ec ur 

o .000 1 . 000 . 005480 . 005480 . 000000 

50 3 . 450 1.000 . 003003 . 004654 . 016055 

100 3 . 450 1 . 000 -. 008903 . 004654 . 016055 

150 5.750 1.000 - . 000663 . 002692 . 015477 

-Ma-,;}Min--Stress--Oist.r-{butio-n--.:: -Ea-ch -Sta-t"ion --------------------------------------------------------------------------

Station Radius SrMax SrMin ScMax ScMin 

0 . 000 22 . 4 22 . 4 22 . 4 22 . 4 

1 3 . 450 22 . 4 -10 . 3 22 . 4 3 . 1 

2 3 . 450 -10 . 3 -10 . 3 135 . 3 5 . 1 

3 5 . 750 3 . 5 -9 . 0 130 . 5 79 . 7 

-Ma-xiMin--Strai,,--Oistr-{butio-n -.:: -Ea-ch -Assenibiy---------------------------------------------------------------- ---------

I 

AL7075 - T6 fwm30gfv69 

Strain Strain Strain 

KRPM PRELOAD Rad1al Hoop VM Radial Hoop Radial Hoop 

48.00 312.2F Max . 0055 . 0055 . 0055 . 0029 . 0047 

48.00 312 . 2F Min . 0030 . 0047 . 0041 - . 0089 . 0027 

Max/Min Displacement Distribution - Each Assembly 

I 

AL7075 - T6 I fwm30gfv69 

Displacement Displacement 

KRPM PRELOAD Radial Hoop Radial Hoop 

Displacement 

Radial Hoop 

48 . 00 312 . 2F Max . 0161 . 0000 .0161 . 0000 

48 . 00 312 . 2F Min . 0000 . 0000 . 0136 . 0000 -Ma-,;}MIN--Stres-s--Oistr-{bu ti,;;'--'::-Each -Asse-nibiy-------------------------------------------------------------------------

I 

AL7075 - T6 fwm30gfv6 

Stress Stress Stress 

KRPM PRELOAD Radial Hoop VM Radial Hoop Radial Hoop 

48 . 00 312 . 2F Max 22 . 37 22 . 37 22 . 37 3 . 52 135 . 30 

48.00 312 . 2F M1n -10 . 31 3 . 07 9 . 11 -10 . 31 5 . 11 

NASAffM-200 1-2 1 046 1 9 
Figure 1.-Pancake rotor assembly A with aluminum 

hub. 

Figure 2.-Composite rotor assembly B. 

NASArrM-200 1-2L046 1 LO 

Figure 3.-Pancake rotor A two-dimensional, finiteelement model consisting of 912 quad4 elements 

and 995 nodes. Based on MARC analysis. 

L 

x 

Figure 4.-Pancake rotor A two-dimensional, finiteelement model consisting of 7065 nodes and 7290 

PLANE42 elements. Based on ANSYS analysis. 
Figure 5.-Rotor B three-dimensional, finite-element 

model consisting of 1642 eight-node brick elements 

and 2283 nodes. 

Figure 6.- Rotor B two-dimensional, finite-element 

model consisting of 1408 quad4 and quad8 

elements and 2592 nodes. 

NASAfTM-200 1-2 1 0461 " 

Radial 

stress, 

psi 

21757 

18837 • 

15917 

12996 

10076 • 

7155 

4235 

1314 . 

-1606 

L -4527 • -7447 x -10368 • 

Figure 7.-Radial stress distribution for rotor A 

based on MARC analysis. Rotational speed, 

48000 rpm. 

Maximum 

stress 

L 

x 

Hoop 

stress, 

psi 

140725 

127917 I 

115 109 

102301 

89493 

76685 

63877 

51 069 

38261 

25453 

12645 I 

-163 

Figure 8.-Hoop stress distribution for rotor A based 

on MARC analysis. Rotational speed, 48 000 rpm. 
Maximum 

stress ----\\ 

L x 

Hoop 

stress, 

psi 

140725 

136307 I 

131 889 

127471 

123053 

118635 I 

114216 

109798 I 

105380 

100962 I 

96544 I 

92126 I 

87708 I 

83290 I 

78872 I 

Figure 9.-Rim hoop stress distribution for 

rotor A based on MARC analysis. Rotational 

speed, 48 000 rpm. 

Maximum 

stress at 4.35-in. 

axial distance 

L x 0.99 in. 

Radial 

stress, 

psi 

3389 

2477 I 

1565 

652 

- 260 

-1173 I 

-2085 

-2997 

-3910 I 

-4822 I 

-5735 

-6647 I 

-7559 I 

-8472 I 

-9384 I 

-10297 

Figure 1 D.-Rim radial stress distribution for 

rotor A based on MARC analysis. Rotational 

speed, 48 000 rpm. 

NASArrM-2001-210461 12 

Maximum 

stress 

L z x 

Radial 

stress, 

psi 

-9197 

-7784 -

-6370 -

-4957 : -3544 

-2131 -

-717.537 - 695.689 ;;::::] 

2109 -

3522 -

Figure 11.-Rim radial stress distribution for rotor 

A based on ANSYS analysis. Rotational speed, 

48000 rpm. 

Maximum 

stress 

L 

z x 

Hoop 

stress, 

psi 

80034 _ 

86199 

92364 -

98530 -

104695 -

110860 -

117 025 - 123 191 

129356 - 135521 -

Figure 12.-Rim hoop stress distribution for rotor 

A based on ANSYS analysis. Rotational speed, 

48000 rpm. 
·iii 

Q. 

en 

U) 

<IJ 

.... 

..... 

U) 

~ 

'0 

C\I 

100x102 

50 

0 

-50 

a: -1 00 

- 150 

.r:r 

p . 

Speed, 

rpm 

+ - 0 

'* ....... . 22000 

x 36000 

.;) - 48000 

o - .. 58000 

-200~--------L---------L---------L---------L-______ ~ 

0.00 0.50 1.00 1.50 2.00 2.50 

Distance, in. 

Figure 13.-Rim radial stress distribution as function of radius at several speeds for 

rotor A based on ANSYS analysis. 

Crack 

Radial 

distance, 

4.465 in. 

Maximum 

stress 

L x 

Hoop 

stress, 

psi 

96496 

89922 

83349 

76775 

70202 

63628 I 

57 054 

50481 

43907 I 

37 334 

30760 

24 186 

17 613 I 

11 039 

4 466 1 

-2 108 

Figure 14.-Computed tomography scan of tested 

pancake rotor A. 

Figure 15.-Hoop stress distribution for rotor B 

based on MARC two-dimensional analysis. 

Rotational speed, 34 000 rpm. 

NASAffM-200 1-2 1046 1 l3 
Radial 

stress, 

psi 

29969 

27362 I 

24754 

22147 

19539 

16932 I 

14324 

11 717 

Maximum 9109 I 

stress 6502 I 

3895 I 

1287 I 

L - 1320 I 

-3928 I 

-6535 I x -9143 

Figure 16.-Radial stress distribution for rotor B 

based on MARC two-dimensional analysis. 

Rotational speed, 34 000 rpm. 

stress 

Hoop 

stress, 

psi 

113056 

105422 

97788 

90154 

82519 

74885 I 

67251 

59617 

51 983 I 

44348 I 

36714 I 

29080 I 

21 446 I 

13811 I 

6177 I 

-1457 

Figure 17.-Hoop stress distribution for rotor B 

based on ANSYS three-dimensional, finiteelement analysis. Rotational speed, 34 000 rpm. 

NASAffM-200 1-21 0461 14 

Radial 

stress, 

psi 

34446 

31 667 I 

28889 I 

26110 

23332 

20553 I 

17 775 

14996 

12217 I 

9439 I 

6660 

3882

1103 1 x -1675 I Maximum -4454 I 

stress -7232 

Figure 18.-Radial stress distribution for rotor 

B based on ANSYS three-dimensional, finiteelement analysis. Rotational speed, 34 000 rpm. 

Von Mises 

stress, 

psi 

32416 I 

30284 

28152 

26020 

23888 

21 755 I 

19623 

17491 

15359 I 

13227 • 

11 094 I 

Maximum 

8962 I. 

6830 

4698 I stress 

2566 I 

434 

Figure 19.-Von Mises stress distribution 

for hub of rotor B based on ANSYS threedimensional, finite-element analysis. 

Rotational speed, 34 000 rpm. 
Hoop 

stress, 

psi 

113056 

108464 I 

103873 

99281 

94689 

90097 I 

85506 1 

80914 

76322 I 

y L x Maximum 71 730 I 

stress, 67138 I 

region 62547 I 

Figure 20.-Rim hoop stress distribution for rotor B 

based on ANSYS three-dimensional, finite-element 

analysis. Rotational speed, 34 000 rpm. 

Radial 

distance, 

5.51 in. 

initiation 

Radial 

stress, 

psi 

324 

-106 

-534 

-963 

-1392 

-1821 I 

-2250 I 

-2679 . 

-3108 

-3537 

Maximum -3966 

stress, -4395 I 

0.6122 in. 

Figure 21 .-Rim radial stress distribution for rotor B 

based on ANSYS three-dimensional, finite-element 

analysis. Rotational speed, 34 000 rpm. 

NASAffM-200 1-2 1 0461 15 

Radial 

stress, 

psi 

202 

-233 

-649 

-1074 

-1500 

-1925 I 

-2351 

-2776 

-3202 

-3627 

-4053 

~ Maximum -4478 . 

stress and -4904 . x -5339 crack site -5754 

-6180 

Figure 22.-Rim radial stress distribution for rotor 

B 0° slice based on ANSYS three-dimensional, 

finite-element analysis. Rotational speed, 

34000 rpm. 

~ x 

Maximum 

stress and 

crack site 

Radial 

stress, 

psi 

324 

-103 I 

-529 

-956 

-1382 

-1809 I 

-2235 

-2662 

-3088 I 

-3515 I 

-3941 

-4368 I 

-4794 I 

-5221 I 

-5640 • 

-6074 

Figure 23.-Rim radial stress distribution for rotor 

B 30° slice based on ANSYS three-dimensional, 

finite-element analysis. Rotational speed, 

34000 rpm. 
NASAffM- 2001 -210461 

Radial 

Figure 24.-Rim fracture mechanics radial stress 

distribution for rotor 8 based on MARC analysis. 

Rotational speed, 34000 rpm . 

Radial 

Figure 25.-Rim fracture mechanics radial stress 

distribution for rotor 8 based on MARC analysis. 

Rotational speed 34 000 rpm (closeup view of 

crack propagation). 

16 

, 

i 

. 
35 

_ 33 .0 

ai 

~ Q) 31 III 

<Il 

Q) 

~ 29 

>-

e> 

Q) 

c: 

w 27 

• ..... 

• 

25 ~--------~--------~--------~----------~------~ 

0.10 0.20 0.30 0.40 0.50 

Crack length, in. 

Figure 26.-Energy release rate as function of crack length for rotor B. 

NASAfTM- 200 1-2 1 046 1 

Bottom side 

Radial 

distance, 

5.81 in. 

Top side 

Figure 27.-Cross-sectional computed tomography 

scan of rotor B showing cracking. 

17 

0.60 

_ I 
REPORT DOCUMENTATION PAGE I 

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1

3

. 

REPORT TYPE AND DATES COVERED 

January 200 I Technical Memorandum 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Structural Analysis of Compo ite Flywheel 

An Integrated NDE and FEM Approach 

6. AUTHOR(S) 

WU-494-2 I- I 1-00 

Ali Abdul-Azi z, George Baaklini , and Jeffrey Trudell 

7 . PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBER 

National Aeronautics and Space Admini tration 

John H . Glenn Re earch Center at Lewis Field E- 12457 

Cleveland, Ohio 441 35 -3 19 1 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING 

AGENCY REPORT NUMBER 

alional Aeronautic and Space Administration 

Washington, DC 20546- 000 1 NASA TM-2001 -2 1046 1 

11 . SUPPLEMENTARY NOTES 

Prepared for the 6th Annuallnternational Symposium on NDE for Health Monitoring and Di agnostics spon ored by 

The Internati onal Society for Optical Engineering, Newport Beach, Californi a, March 4-8, 200 1. Responsibl e person, 

Ali Abd ul-Aziz, organi zati on code 5920, 2 16-433- 6729. 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Unclas ified - Unlimited 

Subject Category : 24 Distribution : Nonstandard 

Available electronically at hllp:/lgltrs.grc.nasa.gov/GLTRS 

This publication is available from the NASA Center for AeroSpace Informalion, 30 1-62 1-0390. 

13. ABSTRACT (Maximum 200 words) 

A structural assessment by integrating finite-element methods (FEM) and a nondestructive eva luati on (NDE) of two 

fl ywheel rotor a emblie i presented. Composite rotor A i pancakelike with a solid hub design, and composite rotor B is 

cylindrical with a hollow hub de ign. Detail ed analy e under combined centrifuga l and interference-fi t loading are 

performed. Two- and three-dimensional stress analyses and two-dimensional fracture mechanic analyse are conducted. 

A comparison of the structural ana ly is results obtained with those extracted via NDE finding is reported. Contact effects 

du e to pre -fit condition are eva luated. Stre result genera ted from the finite-element analy e were corroborated wi th 

the analytical olution. Cracks due to rotational loading up to 48 000 rpm for rotor A and 34 000 rpm fo r rotor B were 

ucce sfully imaged with NDE and predicted with FEM and fracture mechanics analy e . A procedure that extends 

current structural analy i to a life predi cti on tool is al 0 defi ned. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

23 

Finite elements; Compo ite materials; Flywheels; Nondestructi ve evaluation 16. PRICE CODE 

A03 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT 

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