Figure "Ways exciting vibrations at blading": This primarily concerns four types of vibration excitement. Recognizing the excitement and type of vibration is a prerequisite for targeted solutions and elaborate verification tests in compressors.

Wake vortex excitement (Ref. 12.6.3-5): This is an excitement that occurs frequently in flows. A zone of low flow speed forms ahead of and behind blades and braces (Fig. "Excitement mechanisms of flutter"). The wake vortex behind the stator vanes reduces the aerodynamic forces on the following running blade in the interference zone. The static pressure builds ahead of the inlet edge of the stator vane. Running blades of the upstream stages pass through these interference zones. The stator vanes are also struck by the flow disruption of the running rotor blades and thus excited. In some cases, this impulse frequency or the harmonic frequency are equal to the resonant frequency of the blade. This results in resonance and the danger of high vibration amplitudes.
This type of excitement becomes more pronounced in modern compressors. The high aerodynamic loads and the long blade chords promote the intensity of the disturbances. The tendency to continually reduce the axial spacing of the stages, in order to reduce compressor length and save weight, allows the disturbrances to act even more effectively.
The wide, slim integral welded stator blade rows in the fan area of fighter engines are especially susceptible to excitement. These can experience high-frequency torsional vibrations that result in cracks along the blade edge (Fig. "Dynamic fatigue cracks by higher order vibrations").
Flutter excitement: Flutter vibrations can occur as flexural modes (fundamental flexural modes) and/or as torsional vibrations. This is a self-inciting process. It is determined by the ascending force and point of attack of the aerodynamic forces (Figs. "Blade fractures by flutter" and "Overloading blades by flutter"). If flutter occurs, it is difficult to escape this condition. Blade fractures can occur in seconds (Fig. "Flutter problems at a fan").

Excitement through rotating stalls: Even before the surge limit is reached, local stalls occur at single or several neighboring blades (Figs. "Stall at compressor blades" and "Damages by rotating stall"). There can be several circumferential zones with this type of flow disturbance (Fig. "Uneven pressure and temperature in compressor inlet"). These zones rotate in the direction of rotation of the disk with roughly half the circumferential speed.
The ascending force of the rotor blade drops in the area of the stall. When the blade passes out of the stall zone, the aerodynamic force picks up again. This puts a pulsating force on the rotor blades as they pass through the stalls. If the impulse frequency or its harmonic match the resonant frequency of the blade, it can result in resonance with dynamic fatigue and blade fractures. Prediction of the number of occurring stall zones and their rotating speed is still not completely understood. This makes it difficult to design specific preventive measures for susceptible compressor stages.

Combined excitements: Ref. 12.6.3-2 describes a case in which a rotating flow instability near the rotor blade tips of the first compressor stage excited the blades to dangerously large vibrations. The vortex stall in the affected blade zones creates pressure waves similar to those in a rotating stall, but they travel around the circumference at a fraction of the rotor speed (Fig. "Stall at compressor blades").
In the case of FOD with blade deformations, serious flow disturbances can occur near the deformations and cause a rotating stall in an otherwise stable operating zone.

Non-systematic excitements: Experience has shown that flexural modes and torsional vibrations with dangerously high amplitudes can occur in compressor blade rows even without any of the described excitement mechanisms. It is assumed that these vibrations are due to sporadic mechanical excitements and/or random disturbances and vortices in the flow.
These excitements include surge shocks, which can cause extreme blade deflection together with high-frequency vibrations (LCF at high-frequency).

Unfavorable inlet flow: Uneven pressure, flow, velocity, and temperature in the inlet flow (Fig. "Dynamic loads by disturbance of the inlet flow") lead to changing aerodynamic forces on rotor blades that pass through these zones. These disturbances occur in S-shaped long inlet ducts of fighter aircraft engines (Figs. "Secondary flow in the intake duct" and "Dynamic loads by disturbance of the inlet flow"). In two-engine fighter aircraft with inlets on both sides of the fuselage, these disturbances can partially block the inlets if the flow is at an angle (Fig. "Surge by flow disturbances at the compressor inlet"). If the inlet is located below the fuselage, vortexes that come from the lip of the duct at sharp angles can disrupt the inlet flow. If a ground vortex develops, it will cause a massive flow disturbance in a very limited area in the compressor (Fig. "Compressor problems by ground vortex"). The result is a vibration excitement of the fan stages (not only the first stage). If hot gases are sucked in during landing after thrust reverser activation, or steam is sucked in during a catapult takeoff from an aircraft carrier (Fig. "Factors increasing intake temperature"), it will lead to uneven temperatures in the inlet flow. In extreme cases, this can cause blade vibrations in the fan area (Fig. "Ground vortex caused by thrust reverser").

Mechanical excitement: Blades can be dangerously mechanically excited. Mechanisms include vibrations coupled with the disk (Fig. "Shaft loading by gyroscopic effects") and excitements of stator vanes via the housing. The housing is subject to high-frequency excitements from the blade passing frequency, due to the pressure differences on the pressure and suction sides of the blade tips. These vibrations are transmitted into the stator assemblies, which are fastened in the housing. If the blades are axially fixed by labyrinth rings, then labyrinth vibrations (Volume 2, page 7.2.1-9) can excite blade vibrations.
A unique type of excitement occurs during blade tip rubbing (Volume 2, Ill. 7.1.3-4, Ref. 12.6.3.1-21). This can cause dynamic overstress in a very short time. In order to prevent this from occurring, the rubbing systems must be optimized accordingly. Typical influences on the blade loads during rubbing are:

• rotor bearings (location, type)
• damping and stiffness of the system (rotor, blades, housing, bearings)
• blade fastening in the rotor (integral or inset: jammed, loose, glued-in)
• blade bracing (e.g. with/without shrouds, closed shroud, braced shrouds, etc.)
• feed motion (size, speed)
• contact areas (number, length)-gaps (symmetry, width, length)
  
• run-in behavior of the tribo-system (coating in housing, blade tip).

Possible consequential damages include extreme blade vibrations with fatigue fractures within seconds. This is the case, for example, if a fractured blade lays against the housing and is run over by the rotor blades. These experience LCF flexural modes (Fig. "Rotor blade fracture by LCF") in the plastic zone.

Figure "Flow disturbances exciting vibrations": The orientation of the cross-section and braces of housings that direct the gas flow have an influence on flow disturbances, and therefore also affect the vibration excitement of the blading in the compressor and turbine.
There are many interesting examples of flow disturbances that can have a dangerous vibration-inciting effect not only in the direction of the flow (left and right diagrams), but also against the flow (middle diagram; Fig. "Disk fracture by flow vibrations"). Typical flow disturbances are caused by the braces of inlet and exit housings. Radial engines with side-mounted inlets (right diagram) and one-sided and two-sided inlets are usually chosen for smaller shaft-power engines of the type typically used in helicopters. In these engines, the flow is disturbed by the power-shaft or its central housing, which juts out from the front of the engine. This must be considered in vibration-technical designing of the disks and stator assemblies.

Figure "Excitement mechanisms of flutter" (Ref. 12.6.3.1-27): The relative movement of the rotor and stator blade rows excites vibrations. The rotor blades are periodically influenced by the wake vortices of the upstream blades and also by the turbulence in front of the inlet edges of the immediately following stator vanes (top diagram). During supersonic flow, shockwaves lead to a similar effect (bottom diagram, Fig. "Flutter needs specific remedies"). Because the excited vibrations are controlled by the behavior of the vibrating structure, it is referred to as a forced response.
A fundamentally different type of excitement is flutter vibration, which is self-excited (Fig. "Blade fractures by flutter"). However, under unfavorable conditions, flutter can be caused by forced response vibrations.

Figure "Blade fractures by flutter" (Ref. 12.6.3.1-27): The left diagram shows the cooperation of the three technical fields required to analytically treat the field of aeroelasticity and the flutter phenomenon. These technical fields are determined by the acting forces of this process.
The left diagram shows the fundamental process of flutter excitement (aeroelastic instability).
Blades will always vibrate somewhat during operation (Ills. 12.6.3.1-2.1 and 12.6.3.1-2-2). These normally allowable vibrations change the flow around neighboring blades (Fig. "Overloading blades by flutter"). For example, changing the angle of inflow causes blade torsion. The vibration amplitude depends on the inciting aerodynamic forces. If the inciting loads are greater than the loads that are neutralized by damping, the vibration will increase in strength (self-increasing process).

Figure "Development preventing vibrations" (Ref. 12.6.3.1-3): The so-called Campbell diagram makes it possible to recognize resonances and indentify sources of vibration excitement, not only during investigation of causes following damage, but also much earlier, during the design phase (also see Fig. "Resonance condition during development"). In this diagram, the rotor frequency (Hz), i.e. the number of rotations per second, is plotted on the abscissa, and the resonant frequencies of the vibrating components and their incitations are plotted on the ordinate. For every disturbance, a line can be drawn in this diagram that corresponds to the disturbances around the circumference. The curve of the resonant frequency (not a horizontal line because it also contains the centrifugal force influence and the temperature dependency of the E modulus) intersects with these lines in possible resonance points in the operating RPM range (here, in a single point, see arrow). Typical disturbances in the gas flow include braces, stator vanes, and bleed valves (vent openings). In the case of damage, experimental vibration analyses (e.g. modal analysis) are used. The damage-causing mode of vibration is most likely to be the one in which the highest loads occur in the crack initiation zone of the damaged part. This is the location with the greatest surface strain (smallest radius of curvature between the nodal lines). Measurements with strain gauges make verification possible. The influence of operation on the actual height of the occurring loads is estimated on the basis of experiential values. Naturally, during design, one will attempt to place the resonance possibilities of important components outside of the operating RPM range of the rotor. During engine development, the resonant frequencies of the components are designed in a way that prevents dangerous resonance from occurring. However, since it is impossible to prevent all potential resonances between startup and full power due to the large number of flow-influencing components, engine operation will ultimately have to provide definitive information. In other words, the engine will tell us.

Figure "Dynamic fatigue by missing damping": Minor damping can enable dangerous vibration excitements and therefore also lead to dynamic fatigue fractures (Volume 2, Ill. 6.3-3).
Even if no specific damping measures (Chapter 12.6.3.4) are implemented, there are many protective damping effects acting on engine parts, such as air damping. These effects are usually rubbing processes between contact surfaces of the root fastening, shroud- and root platforms, and clappers. Another damping effect is provided by coatings that are actually used for a different purpose (e.g. erosion or corrosion protection). If these damping effects, the use of which is generally not a conscious decision, are lost, it can result in dynamic fatigue fractures. Typical mechanisms that break down damping effects include:

• Mechanical jamming of socket connections
• Cold welding (galling) of contact surface under fretting stress
• Soldering-up or fusing-together of parts by melted contaminants (dust, detached silver, Fig. "Thermal barrier coatings temperature influence").
• Aging and/or spalling of coatings

These mechanisms can be attributed to very different causes, including

• Construction
• Assembly
• Repair
• Operation

Figure "Forms of typical blade vibrations": The fundamental flexural mode (top left diagram) is the most common damage-causing dynamic mode in blades without shrouds. It causes fatigue cracks near the root platform. The first flexural harmonic is in the second diagram from left. Depending on the blade profile, a dynamic fatigue crack is located in this area closer to the center of the blade. The first torsion vibration mode is shown in the third diagram from left. However, there are also a large number of vibration forms of higher orders with especially complex nodal line patterns that can lead to dynamic fatigue fractures (Fig. "Vibration models of disks"). The top right diagram symbolizes a flexural mode around the vertical axis (vertical edge vibration), which puts especially large amounts of stress on the edges of dovetail roots. In addition, the blade is bent due to its twist.
Bracing the blades at the tips (shrouds) and or middle (clappers, snappers, see Ill. 12.6.3.4-6) stiffens them and raises the resonant frequencies. However, important factors include the contact surfaces of the shrouds, and whether these are twisted against one another (Fig. "Design of rotor blade tip shrouds"). Experience has shown that these measures are no guarantee for the prevention of dangerous blade vibrations. For example, if a flexural mode causes all blades to be deflected in unison (“Aehrenfeld vibration”; bottom left diagram), then an axially segmented shroud is evidently not very effective. (Segmented) shrouds will not have a significant effect in the case of coupled blade/disk vibrations in which the tip deflection is primarily axial (bottom center diagram).
In a “soft” shroud, a higher-order flexural mode can develop in the blading and cause cracks below the shroud and/or in the upper half of the blades (Ref. 12.6.3.1-26).
The bottom diagram shows a cast turbine disk from a small shaft-power engine in which many different variations of a cast shroud (non-segmented, segmented with various segment sizes) were unable to prevent frequently repeated dynamic fatigue fractures (HCF) in the blades. The fractures were located both near the shroud and near the annulus.

Figure "Dynamic fatigue cracks by higher order vibrations": The most common damage-relevant vibrational mode in rotor blades without shrouds (left diagram) is the fundamental flexural mode. This puts especially high stress on the transition between the blade leaf and root platform. However, fatigue cracks can also occur in the root itself if a significant fretting influence sufficiently reduces the dynamic strength (Volume 2, Chapter 6). The blade profile (curvature, distribution of thickness) and probability of FOD notches (Volume 1, Chapter 5.2.1.2) determine whether dynamic fatigue cracks in the blade will occur primarily at the edges or in the center, and whether they will be on the pressure or suction side. Torsional vibrations put more stress on the edges (right diagram) and are related to blade bending loads in blades with very twisted profiles.
Among higher-order vibrations, “Lyre” modes (nodal line shape) are especially well known as damage-relevant modes (left diagram). The typical damage symptom in this case is a radial crack that originates in the blade tip (especially if this has been damaged by rubbing; Volume 2, Chapter 7.1.3) and runs in a bow-shaped path to the blade edge. Other cracks are also initiated at the blade surface. Lyre cracks cause the corners to break off. This type of damage is generally not sufficient to cause engine failure. However, the subsequent damage caused by the impact notches from the corner fragments leads to further blade failures with extensive consequential damages (in extreme cases, titanium fires; Volume 2, Chapter 9.1.1).
Special torsional vibrations of higher orders (“tremline mode”) threaten filigreed stator vanes of integral (attached) fan stage stators through cracks that run parallel to the edges and cause large edge fragments to break out in the final stages of damage (right diagram). Experience has shown that this type of crack initiation is promoted by production-specific weak points, especially splashed material from welding (e.g. electron-beam joining of integral stators) and grinding procedures (Example "Mishap during grinding operation").
If serial delivery has already taken place and no constructive changes are possible, the only options for solving these problems are often cutting off the affected corners or shortening the profile chord over the blade length (cutting off corners; see Ill. 12.6.3.4-6).

Figure "Fatigue fractures by high frequency vibrations": The highest stresses in a vibrating part occur in the region of the maximum of the antinodes. If one imagines a bending rod, it is understandable that its bending radius becomes smaller as the bending force increases. The antinodes experience a similar deflection and are highly stressed. The nodes/nodal lines are in zones with no deflection and minor bending loads. One exception is the unilaterally fixed bending beam (top diagram), in which the highest vibration amplitude occurs in the fixed end at rest, and the lowest stress is in the tip, which is the most deflected section.
In general, the following is true: with an equal maximum deflection amplitude, the dynamic loads on a part increase along with the order of the excited natural frequency.

Figure "Vibration models of disks" (Ref. 12.6.3.1-7): Disk-shaped parts such as rotor disks or labyrinth carriers can be excited to very different vibrational forms. These can be classified into three basic types:

• Vibrations with nodal diameters (top diagrams)
• Vibrations with node circles (bottom diagrams)
• Combinations of vibrations with nodal diameters and node circles (bottom diagrams).

The ideal nodal line patterns depicted here are changed to polygon-like shapes in real parts due to the cross-section shapes and geometric characteristics (stiffness changes such as a balance band on a turbine disk or a labyrinth carrier; top diagram). This also influences the location and progress of dynamic fatigue cracks that are to be expected in the range of antinodes (Fig. "Fatigue fractures by high frequency vibrations").
The use of blisks, in which the blades are integrally connected to the carrying disk, is becoming more common in engines in the upper performance range. These systems are not damped by friction at the blade roots, as is the case with inset blades. This means that the problem of mistuning is especially noticeable in blisks. This problem is caused by small production-related deviations within the otherwise acceptable geometric tolerances. This means that unfavorable frequency combinations with neighboring blades can cause individual blades to experience several times greater dynamic loads than the mean value experienced by the blading (Fig. "Influences on damping of parts"). Therefore, mistuning is problematic as a measure for preventing resonant vibrations. It can, however, be a useful remedy for flutter vibrations.

Figure "Friction damping influencing vibrations": Generally, it is assumed that friction in a vibrating system will dampen the system and retard vibration. However, this example shows a case (also see Fig. "Tip clearance influencing 'orbiting'") in which the friction in a rotating system can dangerously increase vibrations (Ref. 12.6.3.1-10, Example "Flow disturbance"). This case concerns so-called friction-induced vibrations (Ref. 12.6.3.1-9). In order for this to occur in a rotating system, such as a fan stage with clappers that brace the blades, a coupled blade-disk vibration must run against the direction of rotation (Ref. 12.6.3.1-8). This excitement mechanism is described by Klompas (Ref. 12.6.3.1-9) with the aid of an example of friction in an interlocking shroud or between supporting clappers (top left diagram) of an overhung fan. The excitement principle is explained in the following:
The middle diagram depicts the progress of the contact forces of the clapper over time. These forces are a backward-running wave of a vibration with a nodal diameter. This vibration arises from the gyro effect of a component with elliptical deflection (“whirl”, Ills. 12.6.3.1-11, -12, -13; bottom diagram). The circumferential speed of the gyroscopic forces is below the eigenfrequency of the bladed disk. The gyroscopic moment of the bladed fan disk, which is usually considered to be rigid, is increased by the vibration deflection. In addition, the friction moment resulting from the deflection of the disk must be overcome. The friction energy “used up” by the system is replaced via the low-pressure shaft. The friction moment is determined by the relative movements of different circumferential speeds of the shaft deflection (whirl, 2/rotation) and the eigenfrequency of the bladed disk.
In the vibration phase, in which the friction forces prevent the contact surfaces from slipping, the system is warped, storing elastic energy. If the deflection in a vibration phase is large enough to exceed the friction forces at the contact surfaces and cause them to slip (discontinuity in the vibration curves), the stored elastic energy is released. Under suitable conditions, an impulse is created that increases the vibrations of the bladed disk.
A simplified model of the described excitement mechanism is shown in the top right diagram. The vibration of a system, in this case a swing, can be maintained or increased if a suitable impulse is introduced into the system at the right moment. In a swing, this occurs through the person shifting their center of gravity, which introduces necessary energy. In the same way, when the contact surfaces in a rotating system slip at the right time, it inputs energy that promotes the vibrations. In the case of the fan, sufficient energy is provided by the low-pressure turbine.

Figure "Exciting shaft vibrations" (Ref. 12.6.3.1-12): Shafts and rotors with their bearing system can be excited to unallowable vibrations in various different ways. The following provides an overview of important factors, but makes no claims to completeness.

Inciting forces on housings:

• from vibrations that are transmitted into the housing suspension,
• accelerations (G forces) from maneuvers, landing shocks, rotation during startup.
• housing damage (e.g. bearing brace fracture)

Inciting forces on the rotor and bearings:

• Forces due to rotor movement:
• Imbalances due to insufficient balancing (only static, not dynamic), imbalances due to asymmetrical elasticity, rotor bow (Volume 2, Ill. 7.1.2-9), jigging motions at joined points, collection of media such as leakage oil or condensation water in the rotor drum, foreign object damage (bird strikes, Volume 1, Chapter 5.2.2), part fractures (Volume 2, Chapter 8.2), plastic deformations (e.g. oil fires; Volume 2, Chapter 9.2).
• Friction forces around flanges (Fig. "Tip clearance influencing 'orbiting'") and blade contact surfaces (Fig. "Friction damping influencing vibrations").
  
• Aerodynamic effects: Uneven tip clearances (Fig. "Self exciting rotor vibration"), flight through extremely heavy rain (Volume 1, Ill. 5.1.1-1), air vibrations around the disks (Fig. "Vibrations excited in ring shaped spaces 1"), rotating stalls, surge shocks (Chapter 11.2.1), wake vortices (Ill. 12.6.3.1-2), and forward-acting flow disturbances (Fig. "Disk fracture by flow vibrations").
  
• Gyroscopic forces (Volume 2, Ills. 7.1.2-18 and 12.6.3.1-17).
  
• Forces over the shaft:
  
  • Torsion moments in shaft-power engines.
    
  • Vibrations from a connected gearbox, e.g. tooth frequency (Volume 2, Ill. 6.3-3), powering aggregates via a cardan shaft.
    
  • Combustion vibrations from the combustion chamber (Ill. 11.2.2.1-4).
    
  • Poorly aligned shafts (e.g. when a module is replaced)
    
  • Aerostatic effects: Pressure distribution in the air system influences the axial thrust (leakage influence, Volume 2, Ill. 7.2.1-3).
    
  • Rubbing: Blade tips (Volume 2, Chapter 7.1) and labyrinths (Volume 2, Chapter 7.2)
    
• Forces from the bearings:
  
  • Contact surface fatigue
  • Problems with bearing damping (in elastically suspended, damped bearings).

Gyroscopic forces:
If gyroscopic forces deflect a shaft, it can promote orbiting (Fig. "Orbiting by gyroscopic forces") and lead to vibrations. In multi-shaft engines, shaft deflections can act through the bearings.

Figure "Characteristics for identifying vibration ecitements" (Ref. 12.6.3.1-16): If characteristic effects are observed within the context of a damage-relevant rotor vibration, then it becomes possible to draw conclusions regarding the excitement mechanism. This makes it possible to define specific inspections to determine the cause of damage and strategies for solving the problem. The definitions are given in Fig. "Self exciting rotor vibration".

Figure "Self exciting rotor vibration" (Ref. 12.6.3.1-16): There is a difference between (externally excited) forced vibrations or resonant vibrations, which depend on the frequency of the excitement forces that are acting on the vibrating system from the outside, and self-excited or instability-vibrations, which are independent of an external excitement or its frequency.

Forced vibrations or resonant vibrations: If, in addition to restoring force and resistance, another inciting, periodically changing external force acts on a system, it is called a forced vibration, in contrast to a free vibration. If the eigenfrequency of the part and the excitement frequency are the same, resonance occurs.
The exciting frequency is either the rotor RPM or many times greater. A cricial RPM is at hand when the rotary frequency of a natural oscillation is equal to the natural frequency of the rotor. Excitement frequencies can also be several times greater than the rotor RPM (harmonic). Such high excitement frequencies originate in stators or toothed gears, for example. In the case of an externally-excited resonant vibration, as a first approximation, the critical frequency remains constant at every shaft RPM rate. Deviations from this behavior are possible if the stress in the part (e.g. centrifugal force in a rotor blade) increases with the RPM (similar to a tightened violin string) or if the temperature increases with the power output (a drop in the E modulus with temperature leads to a drop in frequency; Fig. "Temperature influence on material properties").

Self-exciting vibrations: These are causally related to mechanisms that orbit at a critical frequency without an external excitement. In this form of rotor instability, the characteristic, radially deflected orbiting (Fig. "Orbiting mechanism and cause") of a shaft creates a force that acts on the rotor in a direction that is tangential to the radial deflection. This deflecting force grows corresponding to the deflection. This process is referred to as whirling or whipping. If the RPM level is reached, at which the externally-acting stabilizing damping is not sufficient for the forces, it causes a shaft deflection that increases more and more (shaft flutter). This is called a coupled self-increasing instability. The inciting RPM must not correspond with any special circumferential frequency (Fig. "Rotor deflection during flexural mode"). Even if the damping shifts the frequency, it does not lead to a smaller amplitude, which would be the case in an external excitement. A self-increasing vibration system is driven (reinforced by internal friction in the rotor assembly, rubbing of the rotor against static parts, or aerodynamic effects (Fig. "Orbiting mechanism and cause"). The orbiting movement can occur either in or against the direction of rotation (Ill. 12.6.3.1-15).

“A” Hysteretic whirl caused by friction in the rotor assembly: This dynamic instability is caused by internal friction in the rotor (Ref. 12.6.3.1-18). Internal friction occurs primarily at the contact surfaces of the rotor. These include centering collars (Fig. "Overheating and fusing at shafts by vibrations"), flange surfaces (Figs. "Vibrations by friction between flanges" and "Vibrations excited in ring shaped spaces 2"), and fan blade clapper assemblies (Fig. "Tip clearance influencing 'orbiting'"). Internal friction causes neutral strain and stress axes to shift and induce a tangential force that acts perpendicular to the deflection, i.e. whirl instability (Fig. "Friction damping influencing vibrations"). The deflection thus increases the stresses, which in turn increase the deflecting force. The deflection can often be induced by a small initial impulse, such as the seating of detachable connections (e.g. centering seats). This phenomenon of a whirl instability only occurs at RPM above the first critical RPM. It can be prevented by avoiding plug-and-socket connections.

“B” Orbiting caused by rubbing: Experience has shown that this whip instability occurs during warm-up procedures with considerable friction forces of the type that occur at blade tips and labyrinths (Fig. "Tip clearance influencing 'orbiting'"). As soon as the rotor and rubbing surface come into contact, the friction force puts tangential loads on the rotor. The friction force is roughly proportional to the radial force (m=0.5). This creates conditions for a dynamic instability that moves against the direction of rotation.
Because the friction forces usually occur at specific times (periodic in/out type), the dynamic stiffness of the system is also time-dependent (Ref. 12.6.3.1-20). The coupling effect with the friction process depends on the following influences:

• Contact forces perpendicular to the friction surface, depending on the angle of infeed, rubbing speed, tribo-system, etc.
• Contact surface
• Resiliency (degrees of freedom) of the rubbing elements (e.g. elastic, damped bearings)
• Dynamic stiffness of the structure under normal operating conditions, and the structure that is additionally coupled to it through the friction process
• Contact time in relation to the contact-free time (gap development).

“C” Orbiting caused by the flow in Von der Strömung in plain bearings (lubricants) and labyrinth seals (leakage medium, Refs. 12.6.3.1-17 and 12.6.3.1-19): Because problems with labyrinth seals have already been covered in Volume 2 (Chapter 7.2) and plain bearings are rarely used in aircraft engines, the following concerns air bearings. Their use is probably of greater importance in the engines of unmanned aircraft. For air bearings, half frequency whirl, in which the shaft is deflected with half of the RPM, is a considerable problem.
The instability is created when the air between the shaft and bearing surface circulates with half the mean speed of the shaft surface. Due to the toughness of the air in the very tight space, higher pressure builds up ahead of the gap than at the gap exit. This leads to a tangential force on the rotor. A whirl-movement begins when this tangential force exceeds the inner damping. Experience has shown that this effect occurs when the shaft runs at approximately twice the critical RPM. Therefore, remedies include reducing the RPM and/or suitable structuring of the bearing surface (segmented bearings, foil bearings).

“D” Aerodynamically-induced orbiting: The mechanism of this phenomenon is evidently not yet completely understood. Aerodynamically effective rotor components such as bladed compressor and turbine stages can induce coupled shearing forces due to the motion of the disk. In principle, the acceleration or deceleration of the air flow leads to a tangential force on the blading. This is also the case if the clearance at the circumference changes (Fig. "Orbiting mechanism and cause").

“E” Orbiting due to media caught in the rotor drum: If liquid media get into the rotor (leakage oil, cleaning fluids, condensation water) and are not expelled by specifically provided drainage holes, it can result in a dynamic instability. The fluid moves in a tangential direction at the circumference. This creates friction forces and corresponding tangential forces that act on the rotor. This instability occurs between the first and second critical RPM (1st and 2nd harmonic).

Figure "Orbiting mechanism and cause": Bowed elastic shafts can turn into themselves. One example is flexible shafts for powering tools (bottom diagram). If the RPM “W” of a deflected shaft around an eccentric axis is lower than the shaft RPM “w”, it is called orbiting (right diagram). This situation is quite common in technical fields. A typical case of this is rubbing (Volume 2, Chapter 7).
Especially intense rubbing processes (bottom right diagram) are to be expected in the case of consequential damages with large imbalances (e.g. containment situation). During this process, the rotor rolls on the housing with slip, similar to a powered wheel on a road (radius of the orbit ¥, right diagram). The housing (i.e. the road) experiences an equally large, yet opposite force (F_G or F_s) as the rotor (F_R or F_A).
The influences on the whirl effect during rubbing (also see Fig. "Tip clearance influencing 'orbiting'") change during the rubbing process (Ref. 12.6.3.1-20) due to:

• Wear (increased clearances, deflection)
• Changes to the friction conditions (e.g. creation of a lubricating melt, etc.)
• Changes in the stiffness of the system
• Impingement speed due to the radial infeed speed (creation of vibrations)
• Changes in flow conditions in the area of the system.

The rubbing process is also influenced by the number of radial and axial positions of the rubbing surfaces around the rotor (one radial, several radial, around the entire circumference, one axial, several axial) and their orientation relative to the axis (radial, axial, conical).

Figure "Tip clearance influencing 'orbiting'" (Ref. 12.6.3.1-19): Orbiting (Ills. 12.6.3.1-13 and 12.6.3.1-15) and the Alford force can excite and reinforce each other. This deflecting force acts on the shaft that rotates with the angular speed “w”. It results from different circumferential forces (left diagram), i.e. not-counterbalanced moments. An unequal clearance distribution between the blade tips and housing or in labyrinths will suffice. These conditions are given in, for example, a rotor with axial deflection relative to the housing or in the case of housing warping. If the Alford force is large enough, it will lead to orbiting.
Creation of the Alford force: The efficiency of the blading changes in circumference areas with different tip clearances. A smaller clearance gap means less leakage losses and a higher aerodynamic efficiency of the blade. This means that more compression work is accepted. This leads to higher torque, i.e. higher circumferential force (“F₁”) in the affected circumferential areas. Conversely, less work can be brought into the blades in circumferential areas with a wide gap, i.e. larger leakage losses and poorer efficiency. The result is a decrease in circumferential force (“F₂”). The opposing equal and oppositely acting forces cancel each other`s deflecting influence at equal clearances (“F₂” and “F₄”). The difference (“F_A”) between these two forces deflects the shaft in the direction of orbiting (W ) and thus increases it.
The same is true for labyrinths. Here, it is the uneven pressure distribution around the circumference in the labyrinth gap. The air friction also changes with the pressure. The various circumferential forces this creates act as Alford forces (also see Volume 2, Chapter 7.2).

Figure "Orbiting movement" (Refs. 12.6.3.1-15, 12.6.3.1-22, and 12.6.3.1-16 ): The shaft deflection during the orbiting movment (orbital movement) usualy occurs as a fundamental flexural mode (top diagram). The vibration is reinforced by the forces and moments in an orbital direction (F_S2 ), as well as by the excited vibrations. The deflecting forces include the Alford force (Fig. "Tip clearance influencing 'orbiting'") and forces from the inner hysteresis of the rotor (friction forces, see Fig. "Orbiting mechanism and cause").
On the other hand, forces and moments in the opposite direction have a damping effect on the orbital movement (middle diagram). These are external dampings, for example, due to a damped suspension.
The orbit movement “W” orients itself in the direction of rotor rotation (“w”) in vibration-sensitive systems under the influence of Alford forces (inner hysteresis, gas forces).
In rubbing systems (Fig. "Orbiting mechanism and cause"), an opposite direction of rotation occurs.
Imbalances are typical, outward-deflecting forces (“F_s1”) that act on the rotor in a radial direction.

Figure "Orbiting by gyroscopic forces": A deflection of the axis of rotation should be seen in connection with gyroscopic forces. The angle speed “W” of the deflected axis of rotation creates gyroscopic forces that can be directed in the direction of the orbiting movement, depending on the direction of rotation of the orbiting movement and shaft (also see Volume 2, Ill. 7.1.2-18). In this way, they increase reciprocally with the orbiting movement (self-increasing process).
On the other hand, forces with a stabilizing effect are those such as the elastic reset, which are directed against the deflection towards the center (“F_d1”).

Figure "Vibrations by friction between flanges" (Refs. 12.6.3.1-18 and 12.6.3.1-23): Orbiting can be caused and reinforced by elastic deformation (inner friction) following a hysteresis in shaft systems. This is evidently a type of stick-slip effect.
In this case, the friction evidently does not have the typical damping effect on vibrations, but rather has an inciting influence (also see Figs. "Friction damping influencing vibrations", Self exciting rotor vibration" and "Vibrations excited in ring shaped spaces 1").
The elastic bowing of a rotor or shaft causes micro-movements and friction forces at flange surfaces or fitting surfaces (Fretting, Volume 2, Chapter 6). At ring-shaped contact surfaces (flange) of shafts with circumferential bow, the surface pressure decreases on the outer side, and increases on the inside, where the surfaces are pressed together (right diagram). In the sectional drawing, the progress of the surface pressure is schematically depicted with grey tones. The friction forces, which can transmit shaft torque, also change with the surface pressure. In this way, during slipping (micro-movements!) in the relaxation phase, different circumferential forces occur opposite one another, and an Alford force results from these, as depicted in Fig. "Tip clearance influencing 'orbiting'". This Alford force acts in the direction of the orbital movement, and therefore has a reinforcing effect. The direction of the Alford force can be explained by the time offset of the neutral axes of stress and strain caused by the combination of hysteresis and rotary motion. Without the rotation of the rotor, this phase-shifting would not occur, and the hysteresis (friction in the rotor) would have a damping effect.

Figure "Shaft loading by gyroscopic effects": Gyroscopic forces usually act against a deflection of the axis of rotation (also see Fig. "Orbiting by gyroscopic forces"). Disks with a large polar moment of inertia stiffen under the influence of gyroscopic force. This increases the dynamic stress in the areas of shaft shoulders. For example, it is thinkable that, at the same amplitude of flexural modes in a shaft, more dangerous dynamic loads will be induced during flight than in a rotating bending test in a laboratory using a solidly fastened shaft. Similar overstress can occur during deflection of the axis of rotation during a flight maneuver (Volume 2, Ill. 7.1.2-7).
A damage mechanism related to gyroscopic forces is indicated by cracking in the flange region with a slowing growth rate. In this case, it can be assumed that the cracking makes the shaft connection more elastic and breaks down the effect of the gyroscopic forces.

Figure "Vibrations by imbalance": A bladed rotor disk usually forms a coupled vibration system. This is true not only for blisks, in which the blades and disk are integrally connected, but also for disks with inset blades. Under the typical high centrifugal forces common in operation, the blades sit very firmly in the disk. Due to the lack of damping in the blade root, the exciteability of blisks to dangerous vibrations is seen as especially dangerous. At the typical high frequencies of coupled vibrations, the deflections and, therefore, the air damping, are relatively small. The excitement possibilities that are provided as examples have already been covered in different sections (Fig. "Exciting shaft vibrations"):

Excitement through the blading:

• Flow disturbances (Figs. "Development preventing vibrations" and "Disk fracture by flow vibrations")
• Rubbing (Ref. 12.6.3.1-31, Volume 2, Ill. 7.1.3-4)
• Foreign object damage (e.g. bird strikes, Volume 1, Chapter 5.2)
• Consequential damages (e.g. after a blade fracture, Volume 2, Ill. 8.1-15)
• Alford forces (Fig. "Tip clearance influencing 'orbiting'")

Excitement due to gas forces on the disk:

• Gas vibrations in ring ducts (Figs. "Exciting of disk vibrations " and "Vibrations excited in ring shaped spaces 1", Volume 2, Chapter 7.2)
• Hydrodynamic paradox (Figs. "Vibrations of flat seals" and "Fraction of turbine disk by nodal cycle vibration")
• Cooling air supply for the rotor (TOBI, Figs. "Vibrations excited in ring shaped spaces 1" and "Vibrations excited in ring shaped spaces 2")

Excitement through labyrinths:

• Labyrinth vibrations (Volume 2, Chapter 7.2)
• Gas vibrations in the labyrinth area (Figs. "Exciting of disk vibrations " and "Vibrations excited in ring shaped spaces 1")
• Alford forces (Volume 2, Chapter 7.2)

Mechanical excitements:

• From the shaft system (Figs. "Friction damping influencing vibrations", Imbalance by fan blade dynamic fracture" and "Rotor deflection during flexural mode")
• From clamping bolts (Fig. "Fixing of centered rotor damping bolts")
• Tooth forces from a gearbox (Fig. "Gear excited fatigue fractures at cooler disk")

Disk vibrations are especially dangerous due to the possibility that fatigue cracks could result in fragments that cannot be contained by the housing (Volume 2, Chapter 8). This problem has become even more pronounced in the compressors of large engines with the introduction of blisk constructions (no friction damping at the blade-disk connection).

Figure "Exciting of disk vibrations " (Ref. 12.6.3.1-24): Ring ducts near rotor disks and labyrinths (also see Volume 2, Chapter 7.2) can act as resonators with the gas flow and excite dangerous vibrations in disks (Fig. "Vibrations excited in ring shaped spaces 1").

Figure "Ring duct as resonator": A heavy, multiple-disk clutch was used on the power takeoff side of a single-shaft small gas turbine for powering a helicopter. During the development phase, the clutch evidently reached a critical RPM on the testing rig and was thrown clear after the shaft fracture within seconds. The externally measured vibrational mode of the entire system is shown in the bottom diagram. An additional supporting bearing was introduced as a corrective measure.

Figure "Vibrations of flat seals" (Ref. 12.6.3.1-19): In structures that act like disk springs and are unilaterally exposed to gas pressure loads, the hydrodynamic paradox can occur (also see Fig. "Vibrations at seal membrane"). This effect occurs when the gas pressure at least periodically overcomes the pressing force of the “lid” and escapes through the created circumferential gap. This causes the pressure to drop (Bernoulli), the lid closes, and the process begins again.
This system can be created by a coverplate. There is a small additional compressor for the cooling air that is usually located on the front side of the first high-pressure turbine stage. If the spring effect is unallowably weakened through unfavorable mass distribution due to centrifugal forces, incidental resonance conditions can cause vibrations to be excited in the disk through the hydrodynamic paradox Similar examples can be found in static, laminar seals made from elastic plates.