Figure "Influences at tip clearances" (Ref 7.0-4 and Ref. 7.1.2-1): Typical influences in an engine that can lead to clearance changes at blade tips (and other seal systems such as labyrinths). These influences can combine in different ways, affect one another, or cancel one another out:

Aerodynamic forces on the engine nacelle: The large bypass ratio of modern fan engines means that the nacelles have large, aerodynamically effective surfaces facing the direction of flight. These can create lifting forces of several tons and act across the suspension to elastically deform the engine core.

Engine thrust: Engine thrust must be transferred across the housing and the suspensions attached to it into the cell. The local force transmission through the engine suspensions can cause
unsymmetrical elastic deformations of the housing.

Heat strain: heat strain is usually responsible for most clearance changes. This can be due to symmetrical changes of the housing and rotor components, as well as distortion of the rotor with extreme imbalances.

Centrifugal force: The centrifugal force acting on the rotor causes synchronal strain. In hot parts, creeping deformations (e.g. of the blading) can shrink clearance gaps or change them through permanent distortion.

Gyroscopic forces: These are created when the engine axle is deflected. These deflections can be created, for example, through flight maneuvers or nacelle vibrations. They cause the rotor to be deformed along with the housing structure in which the bearings are mounted.

Gas pressure: The housings of the engine core, especially the high-pressure region, can be seen as large, thin-walled pressure cookers. The inner gas pressures cause the housings to elastically expand, while stiffness jumps, such as flange, locally affect the deformation.

Vis inertia: This force is created by acceleration of the engine. This acceleration is caused by, for example, flight maneuvers, vibrations, gusts, and landing shocks.

Internal gas forces: Distortion can also occur in stator assemblies due to pressure differences and in housings due to bearing thrust. Axially acting forces primarily affect radial gaps such as those at turbine blades that have stepped labyrinths at the shroud.

Vibrations: Vibrations of the rotor or static assemblies are stimulated by various mechanisms. These vibrations can be self-reinforcing.

Imbalances: These usually occur in connection with damage (e.g. blade failure) or rotor bow.

Rotor bow: This is caused by the cooling process after shut-down and causes dangerous rotor offset and imbalances after premature engine restarts. It must be ensured that the restart time does not result in rubbing.

Stall: Surge shocks can axially and radially deflect the compressor blades and rotor.

Main bearings: Radial play of the main bearings, especially in an elastically-damped bearing assembly, must not be neglected.

Manufacture and assembly: Specific part tolerances and assembly tolerances must be met, especially when the tolerances of several parts add to one another.

Figure "Tip clearance changes at turbines and compressors" (Ref. 7.1.2-3): This diagram shows typical, acceptable clearance changes of individual components in a large fan engine with active HPT and LPT clearance controls. This gives an impression of the designer`s task of limiting component deformation during all operating conditions to this mass. Naturally, the values given here apply to the twin-shaft version shown and are also dependent on the special design philosophy of the OEM.

Figure "Maintaining tip clearances": The radial clearance gaps between the rotor and stator/housing experience various component specific changes during operation (see Fig. "Tip clearance change during operation"). These depend on the strain rates of the blades, disks, and housing. If one considers both the heat strain and the strain due to centrifugal force, the main components exhibit typical behaviors:

Housing: Housings are usually thin-walled and therefore react quickly to temperature changes in the gas flow if they are in direct contact with it. If the wall of the outer housing is separated from the gas flow by an inner housing (double-wall configuration) or coatings with insulating properties (abradables and/or fire containment in the compressor, insulating pads and rub-tolerant assemblies in the turbine), then the reaction to temperature changes is slowed (top diagram). In some cases, mass in the form of flange or circumference racks is used to increase the thermal inertia of the housing (Figs. "Tip clearance control types" and "Thermal adjusting housing expansion").
After internal pressure changes, the housing reacts immediately to the tension/strain increase.

Blades: Since blade leaves are relatively thin and immersed in the gas flow, they react quickly to temperature changes. The size of their strain is linearly dependant on the blade length, and therefore it is, for example, considerably larger in the low-pressure turbine than in the high-pressure compressor. Here, as well, strain due to centrifugal force happens suddenly, yet it is relatively small compared with the heat strain.

Disks: The disks have much greater mass than the blades, and the gas flow causes slow temperature changes. The speed of these changes can be influenced by cooling the rotor. However, strain due to centrifugal force is spontaneous and relatively large.
The temperature changes of the components, and therefore the heat strain, depend not only on temperature changes in the gas flow, but other factors, as well:

Material: Heat conductivity, heat capacity, and heat strain affect the speed at which the temperature of a part changes. For example, titanium alloys have a significantly lower heat conductivity than nickel alloys and steels. On the other hand, the heat strain of titanium alloys is low. Cr-steels lie somewhere between titanium alloys and nickel alloys.
The modulus of elasticity determines the elastic expansion of components under mechanical stress. Titanium has a 30% lower modulus of elasticity than steels and nickel alloys. Therefore, titanium alloy components experience correspondingly larger strain.
Insulating layers made from thermal spray coatings (e.g. ceramic and porous metals) are used in housings to make them more thermally inert.

Flow: Heat transfer is also dependant on pressure, speed, and temperature of the surrounding gas flow. Because of this, the heat transfer in the rear part of a compressor is more intensive than in the front. The opposite is true for turbines.
In the chambers between the disks, there are special flow conditions. In this area, heating-up can occur as a result of agitation losses (inner air friction and friction between the air and the disk surfaces).

Figure "Leakage losses and rub wear behaviour" (Ref. 7.0-7, Ref. 7.1.1-7 and Ref. 7.1.1-8):
Fundamentally, one must distinguish between clearance changes that lead to rubbing and those that occur without rubbing or during standstill (Figs. "Conclusions from clearance shapes" and "why the shortest blades seem to rub first").
For example, in abradable systems with characteristically “soft” coatings relative to the blade tips, local clearance gap shrinkage (denting or ovalizing of the housing) lead to relatively small clearance gaps in the area where the housing has been worn-out (bottom diagram). On the other hand, identical radial infeed in rub-tolerant systems that causes material removal at blade tips results in a circumferential gap with a considerably larger cross-section (top diagram).
The clearance gap cross-section is also influenced (enlarged, shrunk) by factors such as whether deformation that causes clearance loss are reversible (e.g. elastic deformation, heat strain) or if they are permanent (e.g. plastic deformation caused by force, creeping deformation of hot parts).

Figure "Conclusions from clearance shapes": Clearance gaps caused by rubbing have many different forms. Components that contribute to clearance loss are the temporal gap changes in reversible and irreversible deformations and the rubbing behavior of the components. Inversely, conclusions as to the damage mechanism can be made from the clearance gap geometry. Above are schematic gap diagrams with typical causal mechanisms. For example, the far left column shows gaps caused by radial shifting of the rotor shaft relative to the housing (e.g. after unequal deflection of the rotor and housing). In abradable systems, this causes the housing coating to be rubbed out in a small circumferential segment, whereas in rub-tolerant systems, it causes the tips of the entire blading to be worn down.
Deflected rotors with corresponding imbalances (second column) rub out the housing coating along the entire circumference in abradable systems, whereas in rub-tolerant systems it only causes the blade tips of a small rotor segment to be worn down.
In many cases, a combination of these effects results in more complex clearance gap changes (Ref. 7.1.2-15).

Figure "why the shortest blades seem to rub first": Usually, rubbing occurs between rotor blade tips and the stationary housing and/or fixed stator vane tips and the rotor spacer rings (Figs. "Leakage losses and rub wear behaviour" and "Conclusions from clearance shapes").
The radial length of rubbed blades during standstill can have drastically shortened unexpectedly.
Upon inspection of the blade tips of a rotor that has rubbed, one will most often find that the blades with obvious rubbing signs (tarnishing, burrs, and grooves) are shorter than the ones that did not rub, even though it seems that the longest blades would be expected to be the ones rubbing. Of course, the longest blades are the first to rub (phase A), but then the heating-up of the blade tip causes heat strain and increases the intensity of the rubbing. This is followed by correspondingly heavier material removal (phase B). If the blade cools after rubbing, it is shorter than the neighboring blades by the length of the heat strain (phase C).

Figure "Tip clearance change during operation" (Ref. 7.1.2-1 and Ref. 7.1.2-2):
Start-up and idling: The clearance gap sizes during engine start-up are important for rubbing. New engines usually have minimized cold play and it can be expected that the first few engine runs will result in intensive rubbing, until the clearance gaps have reached operating size through material removal. For this reason, special abradable procedures are used in new engines to ensure that the abrasion process goes smoothly. During this time, abrasion takes place progressively. If an engine receives new components during a module change, it can result in especially intensive rubbing in the labyrinths. If the abradable coatings have been damaged by aging and their abradability is worsened, catastrophic damages can occur (Fig. "Labyrinth exchange problems").
If an engine is restarted after too short an interval, a jammed or thermally bowed rotor (see Chapter 7.1.2.2) can cause extensive consequential damages, depending on the engine type.
During engine power-up until idling, depending on the hold time while idling, the engine components are warmed-up. While this does not lead to a stationary temperature distribution, a good warm-up can positively influence the clearance gaps when the engine is accelerated to full power.

Accelerating from idle to full power: Along with the RPM-increase to full power (usually in a few seconds) the strain of the rotor components increases respective to the centrifugal force increase. This is also true for the housing due to the increasing gas pressure.
The blade annulus of compressor and turbine rotors is a relatively small mass with a large surface under gas pressure. The high gas speeds and gas pressure cause the heat transfer to be very intensive. The compression temperature in the compressor and the gas temperature in the turbine increase along with engine output. Also, the blades heat up during the acceleration period of several seconds. The comparatively massive disks are heated up by the blade annulus. It takes several minutes before the disk temperature distribution is stationary.
Rotor blades lengthen radially outward, stator vanes inward. In this way, the expansion of the disk adds to the lengthening of the blades. The stator vane strain partially compensates for the expansion of the housing. This is important because intensive rubbing of the hard rub-tolerant coatings on the rotor or on labyrinth racks between stages can cause serious and dangerous damage.
Housing walls are typically thin and cooled on the outside by the considerably cooler surrounding atmosphere. If the gas flow is in direct contact with the inner side of the housing, the housing heats up considerably faster than the rotor disks, yet slower than the rotor blades. Therefore, during acceleration, the centrifugal strain and heat strain affecting the blades in the first few seconds causes the clearance gap to shrink and sometimes causes rubbing (the first “pinch point”). Afterwards, the gap usually expands. This gap expansion can cause impermissible performance decreases and/or compressor stalls (Example "Unexpected compressor surges" and Example "Reduced compressor stability due to increased compressor blade tip clearance"). Therefore, measures are taken specifically for this operating condition, where the housing expansion is tuned to the rotor expansion in such a way that sufficiently small clearance gaps are ensured.

Cruising flight:
Long-range commercial aircraft engines must have especially low fuel consumption. Therefore, clearance gap leaks should be especially small during long-distance flights. Rubbing should not be expected during this stationary operation, since rubbing already occurred during instationary operation and ensured that the clearance gaps are sufficiently large.

Deceleration: during deceleration, the rotor “shrinks ” synchronously with the RPM decrease due to the lower centrifugal force. The blading also cools at a similarly fast rate and shrinks correspondingly. Initially, the clearance gaps grow in size quickly. However, the massive disks have much thermal inertia, and shrink correspondingly slowly. Although the thin-walled housings shrink slower than the centrifugally-induced rotor shrinkage, their thermal shrinkage is faster than that of the rotor, which causes clearance gap losses and possible rubbing (second “pinch point”). This material removal increases the gaps compared with idling reached from engine start-up. This material removal means that a “zero-gap” is no longer attainable in the following load cycles during full power. For this reason, modern engines are equipped with systems for controlling clearance gaps.

Shut-down and restart: After shut-down, the engine cools off over several hours. The slowest-cooling parts are the massive high-pressure turbine disks and compressor disk zones in the inner rotor with poor heat conduction. This can result in the rotor occasionally jamming. Early restarts can cause extensive damage through self-increasing rubbing or overheating of the hot parts due to high gas temperatures and/or insufficient cooling air flow (see Chapter 7.1.3). A similar effect has been observed, when the rotor has been distorted by heat convection in a standing engine (rotor bow, Chapter 7.1.2).
In military engines, operation at high mach numbers (M>1.8) can lead to high engine temperatures and one-time clearance losses due to especially large heat strain. The correspondingly intensive rubbing process causes permanent play increases that must be considered for all further operation.

Figure "Strain behaviour of engine components" (Ref. 7.1.2-3): The sequence of the operating phases in the diagrams is taken from the cited reference works. It is not clear to what degree this sequence, especially the deceleration to idling and then the acceleration to cruising flight, corresponds to practical operation.
This description shows that bridging of the clearance gap in different engine components occurs during very different phases of operation (“pinch points”). In the 9th high-pressure compressor stage of the depicted eingine, the pinch point is at the end of acceleration to full power. The 15th stage jams when cold during standstill (top diagram).
The high-pressure turbine with ACC (see Chapter 7.1.4) has a pinch point during acceleration from idle to takeoff.
In the low-pressure turbine with ACC (bottom diagrams), clearance gap bridging occurs in the 2nd stage during acceleration and in the 4th stage during deceleration of the engine (compare with Fig. "Active clearance control ACC")

Figure "Tip clearance change during unsteady operation" (Ref. 7.1.2-2): The clearance changes during engine operation can be measured with the aid of a high-energy X-ray assembly (Fig. "X-ray clearance control in engines", Ref. 7.1.2-8). The top diagrams show the movement of a labyrinth tip from the shroud of the HPT-rotor blades of a tactical aircraft engine. The cold radial clearance corresponds to the rotor movement at “0”. As shown in the diagram, radial as well as axial relative movements between the housing and blade shroud soon follow. The axial rotor movements are directed forward or aft, depending on operating conditions. They are primarily affected by thermal strain and thrust load-induced elastic deformations.
Axial relative movements opposite graded or grooved rubbing partners are especially important. Heavy axial rubbing promotes overheating of the rubbing surfaces.
In this case, radial movements do not lead to a bridging of the radial gap under any operating conditions. The tightest radial gaps occur during climb flight and idling.
The bottom diagram shows an effect referred to as a thrust void. The increased clearance gap size after acceleration from idling to full engine loads causes a thrust loss of about 15% after about 30 seconds. At the same time, the RPM of the high-pressure shafts drops slightly. This is the critical moment at which the aircraft should have reached the end of the runway and rotates into climb flight. This maneuver requires the highest engine performance.
However, due to the thrust void, full power is not reached until after abour 10 minutes. The loss of high-pressure RPM can be traced back to the clearance-gap induced performance loss in the high-pressure turbine. This occurs when compensation for the clearance increase by means of increased fuel infeed does not occur due to the shortening effect it has on the life span of the hot parts.

Figure "Tip clearance change after shut-down" (Ref. 7.1.2-8): The clearance at blade tips changes during cooling even hours after shut-down. This is due to the various thermal strains of the engine components. The depicted blade tip movements of a large fan engine were measured with an X-ray process (Fig. "X-ray clearance control in engines").
The top diagram depicts a high-pressure compressor rotor blade tip at the exit edge. The timeline shows that the blade has not reached its resting position even after 4 hours. During full loads, the
rear blade edge is axially in front of its position during rest. This means that, during operationg, the blade moves forward in relation to the housing. This can be explained by the greater heat strain of the housing compared to the rotor and the thrust loads, which act in a forward direction. The axial movements of the tips are greater than the radial movements relative to the housing. After shut-down (“1”), the radial gap shrinks rapidly due to the faster cooling rate of the thin-walled housing (“2”) compared with the relatively thermally inert rotor. The greater axial thermal contraction of the housing can be seen in the relatively large axial movements (from “1” to “3”). The axial movement of the contracting housing (fixed bearing of the rotor to the housing is in the front) in a forward direction to the back edge of the rotor blade tip can be seen in the rearward movement of the rotor blade tip.
The bottom diagram shows the relative movements of a rotor blade tip in a high-pressure turbine blade. During acceleration, the rotor diameter increases considerably faster than the housing diameter, shrinking the gap at the blade tips. During deceleration, the effect is reversed. After shut-down, the gap changes over up to 7 hours, during which time, unlike the high-pressure compressor, the radial changes are considerably greater and therefore similar to the axial ones. Comparing the axial movements of compressor blades and turbine blades makes conclusions as to the proportion of heat strain and axial thrust on the high-pressure shaft (to which both belong) possible.
The gap changes that occur over several hours after engine shut-down explain why, in some engines, rotors jam even several hours after shut-down. During this time, restarting attempts will fail or cause heavy damages.
Necessary minimum time intervals between shut-down and restart must be given in operating manuals. These must then be strictly observed.
In testing-rig operation and trials, the time elapsed from engine shut down until the rotors come to a standstill is measured and the freeness of movement of the rotors is checked. This flow time is indicative of the engine`s condition and the condition of its seals.

Figure "Rotor bow / thermal bending affecting operation" (Refs. 7.1.2-3, 7.1.2-9 and 7.1.2-19): After an engine is shut down, the air inside heats up on the warm engine parts and rises. There it cools against the housing and sinks back down into the lower compressor zone. This creates a circular flow around the rotor (top left diagram). The back, warmer part of a compressor gives this flow an axial component. The combustion chamber also affects this, although its mass is not very large. The warm air causes the top part of the rotor hub to cool slower than the lower part. This causes radial temperature gradients and thermal rotor bow. The rotor bows at the top as the result of the top part expanding as the bottom contracts. High-pressure compressors with large axial length are especially susceptible to this phenomenon. Rotor bow can permanently change shrink-fits. This results in imbalances remaining even after the engine has cooled completely (Ref. 7.1.2-19). There have also been casesin which the low-pressure turbine experienced thermal bow (Example "Late start and early shutdown of tail mounted engine"). Rotor bow causes large imbalances. These can cause damage by overheating, wear, or dynamic fatigue in parts affected by rubbing, such as blading, housings, or rotor hubs. Even those parts not affected by rubbing, such as bearings and bearing casings or labyrinths, can be seriously damaged (Example "Late start and early shutdown of tail mounted engine").
If the rotor hub rubs when the engine is started, it heats up even more at the rubbing point and bow increases (top right diagram) This rubbing process can cause catastrophic destruction of the rotor hub. The engine can only be safely restarted after a sufficiently long cooling period (in hours, depending on the engine; middle left diagram, see also Fig. "Tip clearance change during unsteady operation"). Sufficient cold clearances result in unproblematic hot start behavior. This is a compromise. The eccentricity of rotor bow with corresponding gap changes around the circumference can cause eccentric aerodynamic forces around the rotor (“Whirl”). These increase the eccentricity cause by the imbalances, even if no dangerous rubbing is occurring (middle right diagram). Whirl causes shearing forces that act at roughly 90° to the eccentricity. These forces are due to the increased blade loads and small clearance gaps (low leak flow) compared with blades with large tip clearance around the circumference. During start-up, the radial deflections of the bowed high-pressure rotor occur periodically, depending on the engine type, and are especially large at lower RPM (bottom diagram, Ref. 7.1.2-3). Damped bearings can lessen the oscillations of a bowed rotor. However, the damping must be tuned. For example, in the case of a large fan engine, an 0.2 mm oil film is seen as sufficient. With several minutes of idling operation after start-up and before shut-down, the chances for controlling rotor bow are high. This results in sufficient cooling and temperature distribution without impermissibly high gradiations (Example "Late start and early shutdown of tail mounted engine").
Unlike in steam turbines, there have been no reports of damage to engines caused by housing distortions during standstill. This advantageous behavior is most likely due to the comparatively thin walls of engine housings.

Figure "Engine position influences damages" (Ref. 7.1.2-9, Example "Late start and early shutdown of tail mounted engine"): In this case, the thermal distortion of the low-pressure turbine shaft caused dynamic fatigue cracks in a bearing casing. Interestingly, the shaft bowing was so slight, that the clearance loss did not cause problems. However, the imbalances created were sufficient to dynamically overload the housing structure.

Figure "Compressor blade fracture by thermal bending" (Ref. 7.1.2-7, Example "Rotor bow increases the clearance gaps"): In this engine type, thermal distortion of the high-pressure compressor shaft caused blade failures due to clearance gap bridging in several cases. This typical case of thermally-induced rotor bow illustrates the importance that must be placed on this problem during engine development. It is interesting to note that reconstruction of the compressor housing was chosen as a remedy. (note: it may be that the affected engine version does not correspond to the one depicted above in all details)

Figure "Engine affecting by inertia forces / acceleration" (Ref. 7.0-11 and Ref. 7.1.2-13): Engines, especially those of tactical aircraft (Example "Compressor blade cracks by rubbing"), can be subject to powerful acceleration forces (G-force) during flight maneuvers (curve flight). The suspension, especially, is affected by the inertia forces resulting from the maneuvers and can be noticeably deformed (Example "Compressor blade cracks by rubbing", see also Fig. "Deformations by 'G-forces'"). Engines with a small bypass ratio, i.e. a small fan mass, are less affected by a clearance gap-relevant bowing of the housing outside of the suspension planes. It is mentioned in Ref. 7.1.2-18, that the engine deformation of a tactical aircraft can be influenced by deformation of the nacelle.
The large weight of the fans (usually have bearings on only one side) in modern engines with large bypass ratios noticeably affects the clearance gaps due to maneuver loads during lateral acceleration. Unfortunately, maneuvering loads cannot be adequately simulated during trial runs on the ground and therefore require flight testing. Typical acceleration rates dependent on the turning rate (angle change per second) and the curve radius are given in the top right diagram (Ref. 7.0-4). It is clear that the acceleration rates of tactical aircraft are much higher than those of cargo aircraft. The highest values for tactical aircraft are around 10 G and limited by the endurance of the pilot.
The maneuvering load chart (bottom diagram) shows the allowable angle speeds/G-forces of a cargo aircraft type during flight and landing. From the fields of angle speeds around the maneuver axes, arrows point to the relevant allowable region (border of the grey field). The flight maneuver axes can be seen in the diagram at top left The following definitions apply to the diagram:

• Load factors (G-force values), angle speeds, and accelerations apply to the center of gravity of the engine.

• Lateral load values apply to both sides

• Downward acceleration occurs during aircraft pull out

• Forward accelerations occur during braked landing

Usually the engines of modern tactical aircraft are far behind the pitch axis. During maneuvers with fast tilting movements around this axis, the engine experiences deflections with high negative of positive G-forces and large angle speeds with correspondingly high gyroscopic forces.

Figure "Deformations by 'G-forces'" (Ref. 7.1.2-3): In the bottom diagram, the deformations of the center lines of rotors and housings took place during normal flight maneuvers of a cargo aircraft. The following clearance gap changes in this case were mathematically calculated for a large fan engine and are meant to serve as an example:

• Fan region - several tenths of a millimeter
• Low-pressure compressor (booster) - a few tenths of a millimeter
• High-pressure compressor - several hundredths of a millimeter
• High-pressure turbine - several hundredths of a millimeter
• Low-pressure turbine - about one tenth of a millimeter

Figure "Backbone bending' by aerodynamic forces" (Refs. 7.1.2-1, 7.1.2-15):
In the excerpt, development work to minimize clearance gaps in the depicted engine type is explained as follows:

”…Investigations of historical data on the …engine…, have indicated that a performance loss of 0.7 percent cruise SFC occurs on the first few flights of the aircraft. A substantial portion of this loss occurs during flight acceptance testing of the airplane prior to its delivery to the airline and, therefore, is not part of revenue service deterioration. This deterioration is caused by increased operating clearances between rotating fan, compressor and turbine blade tips and their outer air seals. Engine case and rotor deformation result from aerodynamic loads on the engine inlet cowl and inertia loads on the engine which occur during flight. These deformations cause rubbing on the rotating blade tips on their outer air seals which produce the increased clearances reducing the efficiency of the engine.“
The top diagrams show aerodynamc forces on the nacelle. Depending on the flight conditions, these can be up to several tons and cause correspondingly high moments around the engine suspensions. This causes the front of the engine to be bowed upward (Ref. 7.1.2-4). Moments from engine thrust have the same effect. The housing thus rotates around the front suspension (middle diagram). Normally, the front of the housing is affected by upward forces and is bowed correspondingly (see also Figs. "Clearance changes by flight loads" and "Housing deformations near engine suspension"). At the rear suspension, the housing is pulled downward and ovalized vertically. The bowing of the core engine housing (backbone bending) leads to ovalizing or local deforming of the housing primarily in the area of the engine suspension. Therefore, the design of these suspensions is extremely important for the clearance gaps between the housing and rotor and thus also for deterioration.
The aerodynamic forces are strongly influenced by the nacelle geometry, especially the lip.
Excerpt from Ref. 7.1.2-4:
”…The design of large diameter lightweight fan casings capable of absorbing high nacelle cowl loads while providing good rotor-stator clearance control and blade containment presents a major aerodynamic and structural design challenge.“
The bottom diagram shows the typical deformation process in axes of shaft systems and housings under aerodynamic loads on the engine nacelle. Backbone bending is caused by a moment around the front suspension. It is shown that the axis of the fan housing deviates from that of the LP rotor by Ds in the vicinity of the fan blading. This corresponds to a relatively large clearance gap change at the fan blade tips (see Ref. 7.1.2-4). In the HP rotor, a noticeable gap change takes place, but in the opposite direction. The deviation of the main bearings from the engine axis is also of interest. This indicates corresponding housing deformations, i.e. radial deflection of the bearing chambers.

Figure "Clearance changes by flight loads" (Ref. 7.1.2-11):

Top diagram:
The calculations for the diagram were based on the following excerpt:
”…the…(engine development) program initially suffered airplane delivery schedule slide due to engine installation problems discovered late in the development phase… Substantial engine case ovalization ocurred which caused excessive rotor clearances and high specific fuel consumption. The problem was solved by modifying the engine mount (Fig. "Clearance changes by flight loads") configuration with the help of a sophisticated finite element analysis of the engine and backup testing. At that time (late 70s) this analysis was an advancement in the state of art of engine/airframe integration which had previously relied heavily on the build and test approach.“
The diagram is an example of a deflection contour map (chart of the deformation contour and resulting gap width between housing and rotor on a plane). The calculation includes thrust (“Fs”), aerodynamic loads on the nacelle (“FA”) and maneuvering loads (“FM”). FB1” and FB2“ are the resultant forces on the suspension point of the engine.
The lines connect regions with the same clearance gap width, lines designated with “0” are regions with no gap. The inner “0” line corresponds to the shaft. Understandably, this line touches the axis in the bearing area (in front of the compressor and the low-pressure turbine). If the movement exceeds the provided gap, it causes rubbing and therefore deterioration (grey area). The deformations change axially and across the circumference inside the entire engine. This type of chart is used to estimate the tendency of a specific engine type to short-time deterioration.
The chart also indicates that, from the hub contour, the fan tends to rub in the lower region under the observed conditions. The booster evidently has two areas where the clearance gap is bridged (one at the top and one at the bottom). Evidently, there is no rubbing in the high-pressure compressor. The high-pressure turbine rubs at the bottom similiar to the fan, while the low-pressure turbine rubs at the top.

Bottom diagram:
The calculations for the diagram were based on the following excerpt:
”…the…(engine development) program met their initial delivery schedules, however, the operational flight environment produced engine structural surprises not found on the engine test stand.“
The diagram is an example of an analysis (finite elements) of housing deformation (not gap widths!) in another engine type (Fig. "Housing deformations near engine suspension"). The inspection is of the cold engine structure under 0. The largest deformations occurred around the suspension. The curves represent the horizontal and vertical deformation. In this case, vertical deformation occurred in the compressor region, while horizontal ovalization occurred in the turbine region. The calculated curves correspond closely to measured values. The excerpt does not include the type of loads involved, but a higher thrust proportion would result in the opposite behavior.
The rapid pace of computer software and hardware development has made much more detailed calculations for every type of load possible, especially thermal strain and instationary occurrences.

Figure "Housing deformations near engine suspension" (Ref. 7.1.2-12): The large thrust forces and corresponding moments must be transferred into the aircraft by the engine suspension. This process inceases backbone bending (middle diagram) and typical housing deformations occur, especially near the suspensions (bottom diagram). Special attention must be paid to the constructional design of the suspension.
Bending can be considerably reduced (middle chart) through the use of stiffer materials, designated by a higher modulus of elasticity (e.g. steel instead of a titanium alloy for the housing).

Figure "Problems by deformation of compressor housing" (Refs. 7.1.2-4, 7.1.2-12, and 7.1.2-15): Large fan engines create up to 50 tons of thrust. This force must be transferred by the engine suspension. The thrust is transferred through the main bearings (fixed bearings, see arrows) and the housing to the suspension. This creates a positive moment. This can result in the entire engine structure bending and corresponding deformation (backbone bending) of the components (Ref. 7.1.4-4). A typical consequence is a horizontal ovalizing of the housing at the forward suspension with a noticeable impression (Fig. "Backbone bending' by aerodynamic forces"), the size and shape of which is determined by the design of the suspension.
The bottom diagram shows a large first-generation engine with a retro-fitted stiffener (thrust yoke, see Example "Deformations of the housing under load") intended to minimize bending.

Figure "Rotor axle offset and gyroscopic forces" : It may become necessary, within the frame of a damage inspection or construction design, to know the direction of possible gyroscopic forces. For this, a short graphic description is given: a rotating top sets a moment, i.e. force, against the deflection of its axis. The angular momentum vector of a rotating body has the tendency to adjust itself to match the direction of the vector of the resulting outer moment (middle diagram).
The direction of the deflection (precession), angular momentum, and moment make up the “3 finger rule” (bottom diagram):
The thumb points in the rotor axis (X) in the direction of the angular momentum vector (bent hand indicates direction of rotation). The forefinger points in the direction of the moment axis (Y)The middle finger points in the direction of the precession axis (Z). The rotor deflection occurs in the same direction as the moment direction. For example, if the moment rotates left, then the gyroscopic axis is deflected in left rotation.

Figure "Gyroscopic forces at fan and low pressure shaft" (Ref. 7.1.2-3): This diagram shows deformation of the housing and rotor as axis bending due to gyroscopic forces caused by normal flight maneuvers in a cargo aircraft. The gap changes are typical for a large fan engine, up to 1 mm in the fan region during takeoff and climb; in the booster, several tenths of a millimeter and several hundredths of a millimtere in the high-pressure compressor.
The bottom chart shows that the low-pressure system is the most strongly affected. The fan and low-pressure turbine experience the greatest deflections. This is especially true for the low pressure shaft in the fan region, probably because of the relatively low bending strength. The high-pressure shaft, along with the forward bearing, deflects from the engine axis in the direction of deflection of the low-pressure shaft. This indicates influence on the housing from the high gyroscopic forces from the fan, that tranfer into the bearing chamber of the forward high-pressure bearing (top diagram).

Figure "Gyroscopic forces during military maneuver": The gyroscopic force on the rotor increases with the angle speed of the deflection of the engine axis. This is relatively small during curving flight when compared with the deflections during certain maneuvers of modern tactical aircraft. Quick tilting (on the pitch axis, cobra-maneuver) after almost vertical climbing flight at low speeds leads to simultaneous high G-forces and large gyroscopic forces. These conditions can result in heavy rubbing of rotor components on the housing and/or guide assembly. High gyroscopic forces can also be expected with a deflection of the engine axis in a conical shape around the roll axis. The introduction of thrust vectoring nozzles should benefit these maneuvers and increase the loads from gyroscopic forces.

Fig. "High frequency vibrations of low pressure shafts"