Charles Lawrence and Kelly Carney

Glenn Research Center, Cleveland, Ohio

Vicente Gallardo

Ohio Aerospace Institute, Brook Park, Ohio

A Study of Fan Stage/Casing

Interaction Models

NASA/TM—2003-212215

March 2003
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Charles Lawrence and Kelly Carney

Glenn Research Center, Cleveland, Ohio

Vicente Gallardo

Ohio Aerospace Institute, Brook Park, Ohio

A Study of Fan Stage/Casing

Interaction Models

NASA/TM—2003-212215

March 2003

National Aeronautics and

Space Administration

Glenn Research Center
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Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2003-212215 1 

A Study of Fan Stage/Casing Interaction Models 

Charles Lawrence and Kelly Carney 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Vincente Gallardo 

Ohio Aerospace Institute 

Brook Park, Ohio 44142

 Introduction 

One of the primary concerns of aircraft structure designers is the accurate 

simulation of the blade-out event. Simulation of the blade-out event is 

required to pass Federal Aviation Administration (FAA) certification and to 

insure that the aircraft is safe for operation. Typically, the most severe 

blade-out occurs when a first stage fan blade in a high bypass gas turbine 

engine is released. Structural loading results from both the impact of the 

blade onto the containment ring and the subsequent instantaneous unbalance 

of the rotating components. Reliable simulations of the blade-out event are 

required to ensure structural integrity during flight as well as to guarantee 

successful blade-out certification testing. The loads generated by these 

analyses are critical to the design teams for several components of the 

airplane structures including engine, nacelle, strut, and wing, as well as the 

aircraft fuselage. 

Currently, a collection of simulation tools is used for aircraft structural 

design (References 1,2,3). Detailed high fidelity simulation tools are used to 

capture the structural loads resulting from blade loss, then these loads are 

used as input into an overall system model that includes complete structural 

models of both the engines and the airframe. The detailed simulation (Figure 

1) includes the time dependent trajectory of the lost blade and it’s 

interactions with the containment structure while the system simulation 
NASA/TM—2003-212215 2 

includes the lost blade loadings and the interactions between the rotating 

turbomachinery and the remaining aircraft structural components. Generalpurpose finite element structural analysis codes are typically used and 

special provisions are made to include transient effects from the blade loss 

and rotational effects resulting from the engine’s turbomachinery. 

An area of particular importance to the simulation process is capturing the 

interactions between the fan blades and the casing. Typically, the system 

simulation will employ some form of interaction model to characterize the 

fan blade to case interactions during impact and post impact rub that occurs 

as a result of the rotor being out of balance. High fidelity simulation tools 

(e.g. LS-DYNA) have the potential to capture the details of fan blade-case 

interactions including effects such as rub, damage, wear and friction, 

however, the interaction must be characterized in a simpler manner that is 

compatible with the large scale system simulation. While the detailed 

simulation may predict the three-dimensional nonlinear behavior of the 

blades contacting the case, the system model needs to simulate the gross 

macro behavior using a simpler model that consists of a flexible rotor 

modeled with beam elements and lumped concentrated masses for the 

bladed disk, since this is the type of modeling that is normally used for the 

system simulation. The purpose of the present study is to investigate the 

performance of several existing and new, blade-case interactions modeling 

capabilities that are compatible with the large system modeling strategy but 

are able to capture the complex blade-case interactions with enough fidelity 

for an accurate system simulation. 

Comparison of NASTRAN Nonlinear Radial Gap Element and 

CGAP Elements 

The first two interaction models that are studied in the present study are 

the Nonlinear Radial Gap (NLRGAP) and the CGAP Elements currently 

available in NASTRAN (References 4, 5). The CGAP is a one dimensional 

element used to model a gap and associated friction between two nodes 

while the NLRGAP element is used to model a gap and friction in a plane such 

as might occur with a shaft moving inside a bearing support. These two 

models are commonly used by the industry to simulate blade-case 

interactions. In practice both of these element types may be used to model 
NASA/TM—2003-212215 3 

the interactions between the rotor and stationary components (e.g. bearing 

housing or shroud) resulting from steady state or sudden unbalance. The 

NLRGAP provides a convenient modeling tool for these problems in that only 

a single element is needed to model the interactions. The major limitation of 

the NLRGAP is that since only a single NLRGAP is used the rotor must be 

connected to only a single point on the supporting structure. For structural 

supports having symmetry this limitation may not present a problem but for 

non-symmetric bearing supports or rotor shrouds simplifying approximations 

must be made. Unlike the single NLRGAP, the use of the CGAP element to 

model rotor interactions requires that a number of CGAP elements be placed 

around the circumference of the rotor. Since this element is one 

dimensional, a number of them must be distributed around the 

circumference of the rotor to support rotor motion in all the radial 

directions. There are three parameters associated with the CGAP and 

NLRGAP elements; gap clearance, gap radial stiffness, and gap friction 

coefficient. The radial stiffness produces a radial force once the gap 

clearance is closed while the friction force produces a tangential force that 

is proportional to the radial force and in the direction opposite to the 

rotation of the rotor. In general, the NLRGAP element is simpler to 

implement than the CGAP and is effective for modeling contact, however, as 

mentioned previously it can only be connected to a single point on the case so 

the NLRGAP element cannot accommodate flexible cases where the shape of 

the case does not remain round. 

A simple cantilevered rotor was used to compare the NLRGAP to the CGAP 

element. Figure 2 shows the finite element model. The model consists of 5 

beam elements, 6 nodes and 36 degrees of freedom. Relatively rigid springs 

attach node 6 to ground in both the translational and rotational directions. 

Although axial and torsional degrees of freedom are included in the finite 

element model they are not used in the present study. All of the rotational 

inertias ( p θ I ,I ,I α ) are concentrated in the disk at the rotor attachment 

point. The present model is identical to the model used by Boeing in 

“Sample Problem One” of their documentation for rotordynamic analysis 

(Reference 6). 

Transient simulations of a blade loss event were performed to compare the 

NLRGAP to the CGAP elements. A blade loss event is simulated by applying a 

mass unbalance at the rotor tip at time = 0.0 seconds. Initially, the rotor is 
NASA/TM—2003-212215 4 

spinning at full speed. Just beyond 0.0 seconds, after the blade loss, the 

rotor begins to slow until it reaches zero speed at 1.0 seconds. Since the 

centrifugal force from the unbalance is a function of rotor speed it also 

diminishes to zero at 1.0 seconds. Gyroscopic effects are included in the 

simulation. 

Figures 3a and 3b show results from the simulations. Displacement curves 

are shown for the NLRGAP and for three different CGAP configurations 

consisting of 4, 8 and 32 CGAP elements. The sum of the stiffnesses of the 

CGAP elements was made to equal the stiffness of the single NLRGAP for a 

zero gap condition in an attempt to match the results from the CGAP models 

to those of the NLRGAP. The gap in both the NLRGAP and CGAP was set to 

0.4 inches and no friction forces were implemented. 

The results show that for up to approximately 0.08 seconds the results for 

all of the models are identical. This is expected since the magnitude of the 

displacement is less than the gap opening of 0.4 inches and the NLRGAP and 

CGAP’s are having no effect. Beyond 0.08 seconds the rotor displacement 

exceeds the gap opening and the NLRGAP and CGAP’s begin to exert a radial 

restoring force on the rotor. At this point, the results from the NLRGAP 

model show an additional displacement of approximately 0.05 inches before 

the displacements decay downward to near zero at 1.0 seconds. 

The trajectory of the rotor tip for the CGAP models with 8 and 32 CGAP 

elements follow the same path as the trajectory for the NLRGAP model 

except that the magnitude of the trajectory is slightly larger for the CGAP 

models. It was expected that as the number of CGAP’s increased the 

solution obtained with the CGAP’s would converge to the solution obtained 

with the NLRGAP. However, after further consideration it was realized that 

the two approaches will never be exactly identical since the NLRGAP gap 

opening is always in the direction of the rotor motion while the gap in the 

CGAP’s may or may not be parallel to the direction of the rotor motion. As a 

result of this geometric nonlinear effect, for a given rotor displacement the 

gap in the NLRGAP may be closed while the gap in some of the CGAP may 

still be open, or not closed as much, and therefore not applying the same 

force as the NLRGAP. 
NASA/TM—2003-212215 5 

The results for the model with only four CGAP elements do not match the 

results of the other models. With only four CGAP elements, the proper 

rotor tip trajectory is not computed since the distribution of the elements 

does not provide a fine enough distribution of the gap or restoring forces. 

As a result, while some rotor lateral displacements are oriented in the 

direction of a gap element and are resisted by the gap restoring force other 

displacements are “between” elements and do not experience any, or 

experience less, effect from the gap elements. Because of this off and on 

effect from using too few gap elements there also is an impacting effect 

that causes the rotor displacements to oscillate more than if the gap 

elements were more evenly distributed around the circumference of the 

rotor. 

The next step in the present study was to examine the effects of element 

parameters (e.g. radial stiffness, friction coefficient and gap distance) on 

the rotordynamic response. To perform this part of the study a stand-alone 

rotordynamic FORTRAN code was developed. A separate rotordynamic code 

was developed because some features associated with fan stage-case 

interactions models are not readily available in commercial codes such as 

NASTRAN. The code was validated by comparing a Campbell diagram 

generated from the FORTRAN code to results obtained from NASTRAN. 

Figure 4 shows the Campbell diagram comparison for the first forward and 

backward mode of the sample rotor. The 1/rev line shown in this figure 

indicates the first critical speed at 3000 RPM. As shown in the figure, there 

is perfect agreement between the NASTRAN and FORTRAN program 

generated results thus verifying that the rotordynamic code is correctly 

predicting the rotordynamic response, at least where there is no interaction 

between the fan stage and case. 

A gap element, which is identical to the CGAP element currently available in 

NASTRAN, was incorporated into the code to assess the effects of the gap 

parameters and rotor speed. Figure 5 shows orbit plots at the rotor tip for 

four rotor rotational speeds (2000, 4000, 6000, and 8000 RPM). For these 

results the gap clearance was made large so there is no contact between the 

rotor and case and therefore no radial contact or tangential friction forces. 

The orbits are minimum at 2000 RPM, increase at 4000 RPM then decrease 

up to 8000 RPM. Even though the unbalance load is greatest at 8000 RPM, 

this decreased response is expected since the rotor first critical speed 
NASA/TM—2003-212215 6 

which is at 3000 RPM is close to 4000 RPM, and no critical speed near 8000 

RPM exists. 

Figure 6 shows orbit plots where the gap clearance and radial stiffness was 

set to 0.20 inches and 5.0 x 105

 lb./inch, respectively. The friction 

coefficient remained at 0.0 so although there is a radial gap force present 

when the gap clearance is exceeded a tangential friction force is never 

produced. As expected the orbits in this figure are smaller and more 

contained than the orbits in the previous figure since there is a restoring 

force whenever the rotor displacements exceed the gap of 0.20 inches. The 

resonant condition that was evident in the previous figure does not appear in 

this figure since the restoring force disrupts the resonant behavior. Unlike 

the previous figure where the largest orbits matched the critical speed, the 

maximum orbits for these results coincide with the maximum unbalance 

force at 8000 RPM. 

Figures 7 and 8 show transient and orbit plots where the gap clearance and 

radial stiffness was set to the same values as in the previous figure but the 

friction coefficient was 0.10 thus introducing a tangential friction force. 

Similarly to the previous simulations where the friction coefficient was set 

to 0.0 and there was no friction force, the rotor displacements are 

constrained by the casing. However, for this case the orbits are much more 

chaotic as a result of the friction force. The friction force, which is 

proportional to the rotor displacement but 90 degrees out of phase with the 

displacement appears similar to internal rotor damping and causes chaotic 

motion in more extreme cases. When the rotor speed is higher or the 

friction force is greater the rotor motions will become unstable. In practice 

this phenomenon may be somewhat tempered since for real rotors as the 

rotor motion becomes large the radial stiffness and overall damping may 

actually increase and/or the rotor may become damaged so it can no longer 

sustain as large a tangential destabilizing force. This phenomenon poses a 

limitation for the currently used interaction elements, such as the CGAP or 

NLRGAP, since they do not account for these nonlinear effects. 
NASA/TM—2003-212215 7 

Rigid Bladed Disk Model with Friction Rub 

The model used for the previously discussed results utilized a rigid disk 

without blades. The next step in the present study is to implement discrete 

rigid blades into the rigid disk. For this model the contact between the 

bladed disk and case is intermittent occurring only where blades are located 

and the gap is closed, whereas in the previous model the contact is 

continuous as long as the gap is closed. Figure 9 depicts the methodology 

used for the rigid bladed disk. The penetration distance, pr

r is calculated 

using the displacement of the center of the disk, the angular position of the 

blade of interest and the radius of the case. 

The distance from the origin to the blade tip is: 

 

rc rp ru rb r r r r + = + (1) 

Where cr

r is the radius of the case, prr is the penetration of the blade into 

the case, ur

r is the displacement of the bladed disk at the rotor attachment 

point (obtained directly from the rotor degrees of freedom) and br

r is the 

radius of the blade tip. For the present study the case is assumed to be 

rigid and fixed to ground so cr

r is a constant 

Since pr

r and crr are collinear, the penetration distance may be obtained by 

rearranging equation (1) as: 

p c p c r r r r r r r r = + − (2) 

The distance rc rp

r r

+ can be determined by: 

2 b y 2 b x ( ) ( ) c p r + r = r cosβ+ u + r sinβ+ u r r r r (3) 

Where β is the angle to the blade (assuming synchronous vibration, β = ψ), 

and u and x u are the horizontal and vertical displacements of the rotor at y

the disk attachment point (Figure 9). 
NASA/TM—2003-212215 8 

Substituting equation 3 into 2 yields: 

c ) ( ) x ( p

r r cos u r sin u r 2 b y 2 b

r r r r = β+ + β+ − (4) 

At each point in time every blade on the disk is checked to see if the blade 

has penetrated the case. If penetration exists, then a radial force that is 

parallel to the vector, cr

r and a tangential force which is perpendicular to crr

, is 

calculated. 

Figure 10 shows results for the rigid disk with 16 rigid blades. Figure 10a 

can be compared to Figure 6c and Figure 10b can be compared to Figure 8c. 

These comparisons are relevant because the simulations were generated 

with the same loadings and rub characteristics, the only difference being 

the results in Figures 6 and 8 used the rigid disk without blades while the 

results in Figure 10 were generated using a disk with rigid blades. The 

comparison of these results shows that there is negligible difference 

between using a model with a rigid disk versus a model with a rigid disk with 

rigid blades. A likely explanation for the similarity is that the bladed disk 

has a large enough number of blades such that the spacing between blades is 

small and the bladed disk behaves as a continuous disk. Although not shown, 

a similar simulation with only four blades on the disk did exhibit very 

different results from the results for the disk without blades. 

Individual Blade Plowing Model

Limited data and experience with rub tests on turbofan engines and test 

rigs indicate that blade tip rub forces, resulting from blade tip and case 

interactions, are in a direction that is perpendicular to the blade tip 

chordline. This phenomenon is similar to the behavior of an airfoil traveling 

through a fluid where the airfoil motion generates a lift and drag forces. 

From tests, the tangential rub blade force was found to have an axial 

component that would move the blade forward (or aft), and a 

circumferential component that opposes the rotor rotation. The 

hydrodynamic analogy expresses the blade rub force as proportional to the 

blade tip’s mean velocity and the instantaneous angle of attack or incidence. 

It differs from the typically used friction model of rub in that the friction 

model only generates a force in the direction opposing the rotor spin (i.e. 
NASA/TM—2003-212215 9 

drag) while the plowing model generates this drag force, as well as a “lifting” 

force that is perpendicular to the direction of rotor spin.

An analytical expression, analogous to the dynamic pressure force from a 

change in momentum is used to develop the plowing model. This model is 

consistent with expressions of impact forces and hydrodynamic pressure. 

(Reference 7) This was necessitated by the observed directionality of the 

blade tip “tangential” rub forces, i.e., perpendicular to the blade chordline. 

The hydrodynamic force is defined as: 

f DV γtA 2 = (5) 

where f is the total tangential force on the blade from rubbing, V is the 

blade tip velocity, t γ is the blade chordline angle of incidence in the rotating 

frame, and A is the frontal area of the rubbing material (i.e. chord length * 

rub depth). D is a coefficient that must be determined from test or some 

other analysis procedure. It is most likely a function of several factors such 

as the material’s Young and Shear moduli, density, hardness, machinability, 

feed depth, dynamic shear strength, smoothness and probably others. 

For the present study, a beam rotor with rigid blades and disk will be 

utilized. The rigid bladed disk is just a localized extension of the rotor, and 

has no separate degrees of freedom. Thus the vibration of the bladed disk 

is only the motion imparted by its attachment point on the rotor. 

The incidence angle for a rigid bladed disk in the orbiting disk frame is 

(Reference 8): 

γt = γ0 + αsinβ + θcosβ - w& /ψ&R (6) 

Where 0 γ is the blade tip chordline mean (i.e. initial) incidence angle, α and 

θ are yaw and pitch displacements, β is the azimuth position of the blade 

from the fixed horizontal axis (Figure 9). ψ& is the rotor spin speed, R is the 

blade tip radius, and w and w& are the blade tip axial position and velocity, 

respectively and are defined as: 
NASA/TM—2003-212215 10 

 w = − αRcosβ + θRsinβ (7) 

So that: 

w = − αRcosβ + θRsinβ βR(αsinβ + θcosβ) & & & & (8) 

Substituting (8) into (6) the blade tip chordline angle of incidence is: 

)

ψ

β ( sin θcosβ)(1- ψαcosβ - θsinβ γ γ - t 0 &

&

&

& & = + α β + (9) 

For synchronous vibration, β ψ& & = and equation (9) reduces to: 

ψ

αcosβ - θsinβ γ γ - t 0 &

& & = (10) 

Substituting the total incidence angle, equation (10) into (5) yields the 

tangential plowing force in the orbiting reference frame: 

 )A

ψ

αcosβ - θsinβ (γ - 2 R2 f Dψ 0 &

& & = & (11) 

Assuming that the vibratory components of the incidence angle are negligibly 

small, compared to the mean incidence, the axial and circumferential 

components of the force on the blade in the orbiting frame are: 

a 0 f = fcosγ (axial) (12) 

 

t 0 f = fsinγ (circumferential) (13) 

The forces and moments in the rotor degrees of freedom in an inertial 

frame of reference can be obtained by resolving the plowing force, equation 

(11), into the three orthogonal components corresponding to the rotor 

translational degrees of freedom. 
NASA/TM—2003-212215 11 

Axially, 

a 0 f = fcosγ (axial) (12) 

Horizontally, 

f x = ftsinβ (14) 

Vertically, 

f y = − ftcosβ (15) 

The horizontal and vertical forces yield shear forces in the direction of the 

rotor translational degrees of freedom, whereas the axial force produces 

moments about the yaw and pitch axes. The moments about the yaw and 

pitch axis, respectively are: 

fα = − f aRcosβ (16) 

fθ = f aRsinβ (17) 

Individual Blade Radial Forces 

In addition to the previously described plowing force, there is a radial force 

on the blades and an equal and opposite force on the case resulting from 

radial motion of the rotor blades. When the radial motion of the blades 

exceeds the gap distance, the blade tips push against the case and a 

restoring force is exerted back against the blades. This restoring force 

tends to re-center the bladed disk and its magnitude is proportional to the 

casing stiffness. The radial force is defined as: 

r p f kr

r = − (18) 
NASA/TM—2003-212215 12 

Where k is the case stiffness and pr

r is the penetration depth at the point 

of blade contact with the case. In practice pr

r may vary not only from the 

rotor displacement, but also from the rub material getting worn away from 

blade contact, but in the present study only rotor displacement will be 

considered and blade and case displacements will not be considered. 

The horizontal and vertical components of the radial force are: 

ry py f kr

r = − (19a) 

rz pz f kr

r = − (19b) 

Where py

r

r and pz

r

r are the horizontal and vertical components of the 

penetration of the blade tip into the case.

Summing of Forces and Moment on all Rubbing Rigid Blades

Once the plowing and radial force is computed for each blade, the total 

force and moment acting on the rotor degrees of freedom are obtained by 

summing the forces for each of the individual blades. Each blade will 

contribute a different force and moment since the penetration depth and 

incidence angle is different for each blade.

Results for Rigid Bladed Disk Using Plowing Model 

The results in Figure 11 are for an overhung rotor with a disk at the free 

end. The disk has 16 blades and an initial clearance of 0.2 inches between 

the blade tips and case. The blade tip radius is 10.0 inches. A radial 

restoring spring is used to model the radial behavior while the plowing model 

is used for the tangential loads. 

For the initial results, the plowing force was kept simple by setting the 

blade angle of attack to a constant 90 degrees (the change in angle resulting 

from any vibrations was not included). The 90 degrees is not realistic, 

however, it eliminates any loads in the axial direction and overturning 
NASA/TM—2003-212215 13 

moments so a comparison could be made to the friction model that was 

previously discussed in this report. The only difference between this 

simulation and the friction model is that in the previous model the tangential 

friction force is proportional to the penetration depth while in the present 

model the plowing force is proportional to the penetration depth and the 

blade tip velocity. Both the friction and plowing forces are in the same 

direction and oppose rotor rotation. 

As shown in the figure, the simulation was run at three different speeds; 

3000, 6000, and 9000 RPM. Regardless of the rotor speed, the shapes of 

the curves are very similar. The difference between the curves is that the 

displacements are larger for faster rotor speeds which are expected since 

the plowing force is proportional to rotor speed squared. (The loading is an 

unbalance that also increases with rotor speed squared). For small Dynamic 

Coefficients the orbital displacement is small since a small Dynamic 

Coefficient generates a small plowing force. As expected, as the Dynamic 

Coefficient increases the orbital displacement increases. For very large 

Dynamic Coefficients the rotor response/displacements grow very large but 

do not go unstable because of the 5% level of structural damping provided in 

the model. If the level of structural damping was decreased, or eliminated, 

an unstable response is obtained. Obviously, the results in this figure are not 

realizable since the displacements are orders of magnitude larger than the 

structural dimensions; however, the results do demonstrate the effect of 

the dynamic coefficient for extreme cases. 

Figures 12 and 13 show the effect of the Dynamic Coefficient and structural 

damping on the displacement response. The only difference between the 

models used for these two figures is that the results in Figure 12 were 

generated using 3% structural damping while the results in Figure 13 used 

1% structural damping. As previously discussed, the Dynamic Coefficient 

determines the magnitude of the destabilizing skew symmetric plowing 

force. Conversely, the structural damping provides a stabilizing force that 

helps to reduce the displacement response. 

For smaller Dynamic Coefficients the displacement response is relatively 

small and levels off to a steady state in a short amount of time. (Figure 12a, 

12b, Figure 13a) The steady state displacement exceeds the gap clearance 

because the centrifugal force is large in comparison to the stiffness of the 
NASA/TM—2003-212215 14 

radial restoring spring. For this level of plowing force structural damping 

has minimal effect on the magnitude of the displacements. 

For larger Dynamic Coefficients the plowing force is more forcibly driving 

the response unstable. The only reason the response does not grow 

exponentially is because of the structural damping. Without any structural 

damping the response does in fact grow exponentially, however with just 1% 

damping the response, although possibly quite large, is still stable. With 3% 

structural damping the magnitude of the response is less than with 1% 

damping, however the onset of large displacements is greatly 

influenced by the level of damping. While the onset of large 

displacements occurs with a Dynamic Coefficient of 5.0E-5 lbm/in**3 

and 1% damping (Figure 13b), it does not occur until the Dynamic Coefficient 

is 1.0E-4 lbm/in**3 when the damping is 3%. (Figure 12c) 

Figure 14 shows the effect of a 30 degree blade angle of attack for various 

values of Dynamic Coefficient. For this angle of attack, unlike an angle of 

attack of 90 degrees, there is a component of plowing force in both the 

axial, as well as the circumferential direction. The axial component produces 

an oscillating moment about the rotor y and z axis (Figure 9). The results in 

Figure 14 follow the same trend as Figure 12 where all the parameters are 

the same except for the angle of attack. The onset of the larger 

displacement is delayed for the smaller angle of attack which is 

expected since the magnitude of the plowing force is smaller when 

the angle is 30 degrees than when the angle is 90 degrees. 

Figure 15 shows the gyroscopic and plowing force moments and the resulting 

transient response for a Dynamic coefficient of 1.e-4 lbm/in**3 and a rotor 

speed of 9000 RPM. For this combination of rotor speed and Dynamic 

Coefficient the plowing force moment is considerably smaller than the 

gyroscopic moment. For slower rotor speeds and large Dynamic Coefficients 

the moments will be closer in magnitudes. Regardless of the magnitude of 

these moments, the plowing force moment is always 180 degrees out of 

phase with the gyroscopic moment and therefore has an offsetting effect. 

The rotations shown in Figure 15b depict this effect by showing how the 

rotations are smaller when the plowing force moment is included in the 

simulation. 
NASA/TM—2003-212215 15 

A major challenge for all of the simulations presented in this work is that 

although the numerical simulation is able to produce a reliable transient 

response for a given set of input parameters, the fidelity of the response is 

only as good as the quality of the input parameters (e.g. Dynamic 

Coefficient, structural damping). Unfortunately, these parameters are very 

difficult to predict in practice and as shown in the present results a small 

variation in the parameters may lead to large variations in the resulting 

response. 

Summary 

Three contact models have been examined for simulating the interactions 

between a rotor bladed disk and a case: a radial and linear gap element and a 

new element based on a hydrodynamic formulation. All three models were 

assessed using results from unbalance loadings and transient simulations. 

The first two models are currently available in commercial finite element 

codes such as NASTRAN and have been showed to perform adequately for 

simulating rotor-case interactions. The hydrodynamic model, although not 

readily available in commercial codes, may prove to be better able to 

characterize rotor-case interactions. Future work includes adding flexibility 

to the rotor case and incorporating vibratory motions into the coordinates 

used to define the rotor blade position, as well as experimental testing to 

determine which of the models are best suited for simulating rotor-case 

interactions. 
NASA/TM—2003-212215 16 

References 

1. Lawrence, C., Carney, K., Gallardo, V., “Simulation of Aircraft Engine 

Blade-Out Structural Dynamics,” NASA/TM—2001-210957/REV1, 

September 2001. 

2. Vasco, T.J. (2000). “Fan Blade Bird Strike Analysis and Design,” 6th

International LS-DYNA Users Conference. 

3. Carney, K.S., Lawrence, C., Carney, D.V., “Aircraft Engine Blade-Out 

Dynamics,” 8th International LS-DYNA Users Conference. 

4. Sitton, G., ”MSC/NASTRAN Basic Dynamic Analysis,” The MacNealSchwendler Corporation, 1997. 

5. Herting, D.N., “MSC/NASTRAN Advanced Dynamic Analysis User’s 

Guide,” The MacNeal-Schwendler Corporation, 1997. 

6. Heidari, M.A., Carlson, D.L., Yantis, T.F. (2000), “Documentation for the 

Boeing Rotor Dynamics Analysis Procedure,” Boeing D6-36663. 

7. Streeter, V.L., Wylie, E.B., “Fluid Mechanics,” McGraw-Hill, 1975. 

8. Bisplinghoff, R.L., Ashley, H., “Principles of Aeroelasticity,” Dover 

Publications, Inc., 1962. 
NASA/TM—2003-212215 17 

Figure 1: Detailed blade-fan case interaction model. 

Figure 2: Rotor finite element model.

Translational & Rotational DOF’s

Beam Elements (5)

Rigid Disk

Nodes (6)

Grounded Springs

Location of Rub
NASA/TM—2003-212215 18

Figure 3: Comparison between nonlinear radial gap (NLRGAP) 

and CGAP elements 
NASA/TM—2003-212215 19

Figure 4: Rotor Campbell diagram. 
NASA/TM—2003-212215 20

 

 

Figure 5: Rotor tip orbits for increasing rotor speed (open gap). 
NASA/TM—2003-212215 21

 

 

Figure 6: Rotor tip orbits for increasing rotor speed. 

Gap = 0.20 inches, Stiffness = 5e05 psi, Friction coefficient = 0.0 
NASA/TM—2003-212215 22

 

 

Figure 7: Rotor tip displacement for increasing rotor speed. 

Radial stiffness = 5.E05, Friction = 0.10, Gap = 0.20. 
NASA/TM—2003-212215 23

 

 

Figure 8: Rotor tip orbits for increasing rotor speed. 

Radial stiffness = 5.E05, Friction = 0.10, Gap = 0.20. 
NASA/TM—2003-212215 24

z

fx, f

x

A

A

y

w, w, fa

, 

Displaced rotor

Case

Blade tip

r



u

r



c

r



b

r



p

, 

fy, f

, 

Blade

tip

Section A-A

z

fa

ft

y

x

R

f

T

Figure 9: Schematic of rotor blade, degrees of freedom, 

and tip penetration. 
NASA/TM—2003-212215 25

Figure 10: Bladed disk model with 16 blades. Rotor speed = 6000 RPM. 
NASA/TM—2003-212215 26

Figure 11: Maximum displacement versus dynamic coefficient. 

Blade angle of attack = 90 degrees, 5% damping. 
NASA/TM—2003-212215 27

 

 

Figure 12: Effect of dynamic coefficient on transient response 

(3% structural damping, 90 degree angle of attack). 
NASA/TM—2003-212215 28

 

 

Figure 13: Effect of dynamic coefficient on transient response 

(3% structural damping, 30 degree blade angle of attack). 
NASA/TM—2003-212215 29

 

 

Figure 14: Effect of dynamic coefficient on transient response 

(3% structural damping, 30 degree blade angle of attack). 
NASA/TM—2003-212215 30

Figure 15: Effect of plowing force axial component on rotor response 

(3% structural damping, 30 degree blade angle of attack, 

dynamic coefficient = 1.e-4 lbm/in**3). 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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E–13836

WBS–22–728–30–07

36

A Study of Fan Stage/Casing Interaction Models

Charles Lawrence, Kelly Carney, and Vicente Gallardo

Turbomachinery; Structural dynamics

Unclassified -Unlimited

Subject Categories: 39 and 07 Distribution: Nonstandard

Charles Lawrence and Kelly Carney, NASA Glenn Research Center; Vicente Gallardo, Ohio Aerospace Institute,

Brook Park, Ohio 44142. Responsible person, Charles Lawrence, organization code 5930, 216–433–6048.

The purpose of the present study is to investigate the performance of several existing and new, blade-case interactions

modeling capabilities that are compatible with the large system simulations used to capture structural response during

blade-out events. Three contact models are examined for simulating the interactions between a rotor bladed disk and a

case: a radial and linear gap element and a new element based on a hydrodynamic formulation. The first two models

are currently available in commercial finite element codes such as NASTRAN and have been showed to perform

adequately for simulating rotor-case interactions. The hydrodynamic model, although not readily available in

commercial codes, may prove to be better able to characterize rotor-case interactions.