Figure "Resonance condition during development" (Ref. 12.6.3.4-1): With the aid of the Campbell diagram (Fig. "Development preventing vibrations"), possible resonances, such as those between flow disturbances (Ill. 12.6.3.1-2) and eigenfrequencies of the parts, can be identified during the engine development phase, and specific remedies can be implemented by mistuning the eigenfrequencies and/or exciting frequencies. If dynamic fatigue damage occurred due to resonance, causal relationships can be analyzed with the help of the Campbell diagram.
This example is from the early days of engine development. The turbine rotor blades of a high-thrust variant of the engine in the top diagram suffered dynamic fatigue fractures. In the corresponding Campbell diagram the grey horizontal lines represent the frequencies of the vibrational modes of the turbine rotor blade. As one can easily recognize, the exciting frequencies from the 10 can-type combustion chambers approach the operating RPM of 100% (arrows). In the high-thrust engine variant with longer blades, these eigenfrequencies were somewhat lower and therefore in the resonance range, which explains the damage.

Figure "The 'Monte Carlo Method' technique": The operating properties of modern engine parts are becoming more and more utilized. This is true for mechanical loads, especially dynamic ones, as well as for aero- and thermo-dynamic demands. Higher aerodynamic loads lead to increased vibrational loads in the HCF range (stronger and more frequent excitement possibilities).
In order to sufficiently safely avoid problems, the statistical scattering of the properties must be taken into consideration. One must only consider the large number of blades in an engine, which is then multiplied by the number of engines in serial operation. In this case, it is not sufficient to merely act in accordance with the maxim “the engine will tell us”, since the expense of serial implementation of corrective measures can be far too great. Therefore, the statistic behavior of the parts and operating influences must also be considered. This includes manufacturing influences such as tolerances (see depicted example), as well as statistical scattering of design-relevant material data (e.g. HCF and LCF) and operating parameters such as dwell times at certain RPM, temperatures, and load cycles.
One tool that can be used to achieve greater safety in design and/or better understanding of operating behavior is the Monte Carlo method. This is done in the following steps:

• Creating a model that mathematically describes the relevant operating behavior of the part in question (e.g. eigenfrequencies of a blade).
• Selecting of relevant input parameters (variables: length, thickness, density, E modulus, etc.) and determining statistical scattering.
• A value is taken at random from the scattering of each parameter, and an analysis is done with the model.
• The necessary results of the output parameters (eigenfrequencies, etc.) are selected and recorded.

These steps are repeated until the output parameters stabilize (i.e. converge on recognizable values) and/or the number of simulations seems sufficient. The methodology used makes all simulations completely independent of one another, and they can be depicted in a three-dimensional diagram (meta diagram) as a scatter plot. By considering random occurrences, one is able to recognize relationships that remain concealed during normal calculations, but more closely reflect the reality of the large number of parts in serial operation.

With this method, parameters with the strongest influence (e.g. the worst), or the worst combination of parameters, can be identified and determine reliability. In addition, one will gain an understanding of the relationships in the behavior of the system.

Figure "Configurations for Measuring blade vibrations": Measuring compressor rotor blade vibrations in running engines is an important task and requires a great deal of experience. It is useful for controlling design and determining unwanted effects. Typical measuring procedures are described in the following:
The deflection (amplitude) or vibration rate of a blade tip is characteristic for the fundamental flexural mode. Therefore, measuring these values conversely permits conclusions regarding the dynamic loads (left diagram). This is done by inserting a small magnetic plate into the blade tip and firmly anchoring it so it cannot come loose due to centrifugal force. The position of the magnets must not correspond to the nodal lines (detail diagram), or no measurable deflection will occur despite the presence of large vibrational loads. In the housing, a meandering conductor (copper band) is affixed above the blade being measured. When the blade rotates, the magnet creates a current in the conductor that changes characteristically during blade tip vibrations according to the velocity changes (circumferential speed + parallel and counter-acting vibrations), and can be analyzed to determine the vibration amplitude and frequency. The difficulty with this procedure is measuring higher order vibration modi. It is advantageous that there are no measured values that must be transferred from the rotating system. This allows measurements to be made even in areas where transmitters or rotary joints are problematic (such as on the high-pressure rotor of multi-shaft engines). An additional advantage is the robustness and minimal danger of overstress due to high vibrational loads.
Measurements with strain gauges (DMS) require a difficult application of the gauges and measuring lines to the transmitter, which brings the measurement values from the rotor (radio, slip rings, right diagram). Strain gauges are sensitive, and can fail before or during measurement (e.g. dynamic overstress of the gauge and/or measurement lines, bonding problems). The strain gauges themselves can have an unallowable influence on the vibration behavior of blades (damping, Fig. "Unsuitable blade vibration measurement").
Some of the advantages of strain gauges are:

• specific measurement of different vibrational modes in vibration-stressed areas
• simultaneous measurement with multiple gauges
• direct indication of the measured strains or stresses.

Figure "Unsuitable blade vibration measurement": Experience has repeatedly shown that even if strain gauge measurements of compressor blades do not show any alarming vibrational loads during the development phase of an engine, dynamic fatigue damage can occur during serial operation. The HCF cracks can not always be plausibly explained by a decrease in dynamic strength following operation-specific damage such as erosion or FOD.

The explanation is as follows:
Normally, during testing runs, only a few stator vanes and/or running blades of a stage are equipped with DMS strain sensors in the vibration-critical zones. The reasons for this are the cost, the influence of the measuring lines on the airflow, and the increased risk of failure of the many measuring points. It has been shown that the measuring lines and components of DMS can have a disruptive influence on the vibration behavior of parts, especially the filigreed blades of modern compressors. The primary influence is the damping of the measuring probe. This becomes an even greater problem if the integral construction of the stators and rotors (bling), which have minimal inner damping and reciprocal influencing with the blading through the cohesive fastening, react especially sensitively to additional damping. Even the minimal mass of the DMS can change the resonant frequency of the neighboring blades in a stage so much that it is clearly noticeable in the vibrational loads. This occurred in a case in which only one blade was outfitted with DMS. After the test run, this was the only blade without a dynamic crack. This is largely due to the following effect:
Small differences in the eigenfrequency means that the blades in a stage do not begin to vibrate simultaneously. If a single blade in an integral system (e.g. stator) starts to vibrate in resonance, it absorbs a great deal of the saved excitement energy and prevents dangerous vibrations of the neighboring blades.
If the blade being measured is altered by the DMS and measuring lines so that it is not as easily excited to vibration as the other blades in the stage, then the blades without DMS vibrate and prevent vibration of the measured blade.
A solution to this problem would be to outfit all blades equally with DMS and measuring lines, although they do not all have to be hooked up. However, this procedure is only practical if the large number of flow disturbances do not unallowably alter the behavior of the entire system.

Figure "Understanding with stroboscope vibration problem": Despite high-power calculation methods and modal analyses, in complicated cases with deflections similar to those during operation (e.g. with friction influences that are dependent on the amplitude and wear), supplemental part inspections with a boroscope are still recommended. This is especially true for cases in which engines are serially retrofitted as a remedy for damage. With very old engine types and licensed products, especially, there are no longer any sufficiently relevant existing design or construction data of the type required for meaningful calculations.
The fastenings of auxiliary components have unexpectedly proven to be an especially challenging task. The complex interplay of the different masses and their distribution (e.g. gearboxes and auxiliary components, pipes), damping (e.g. friction in the suspension, pipe clips), and stiffnesses (combinations of complex parts such as gearboxes, mechanical regulators, and pumps made from different materials) leads to suprising deviations from the calculated behavior during operation. It is also very difficult to realistically predict and incorporate into calculations the changes during operation, such as wear or changes in the damping or coefficient of friction.
Experience has shown that in those cases in which an external visual evaluation is possible, the following experimental procedure has proven itself to be very effective:

Elastic suspension of the engine or parts being inspected (e.g. a housing with all relevant auxiliary components, top diagram). Excitement of all operation-relevant vibration frequencies with the aid of an electrodynamic exciter. At the same time, the concerned area is monitored with a stroboscope.
Specialists such as designers are thus given an ideal opportunity to intuitively recognize deformations, loads, and load-relevant relationships. If necessary, changes can be implemented immediately and their effectiveness verified.
Similar inspections can also be conducted in a running engine in a testing rig. A prerequisite for on-site inspections is protective measures such as hearing protection.

Figure "Methods preventing blade vibrations 1": There are many methods based on various principles that can be implemented to prevent dangerous blade vibrations:

• Constructive design of blades:
  Avoiding resonances. This is primarily a question of design. Important tools for this are currently available analytical methods (FE calculations). However, these are generally not sufficient to prevent all potentially dangerous resonances (also see Campbell diagram, Fig. "Resonance condition during development"), especially those caused by required RPM changes. Ultimately, experience of the part in the engine must verify damage-free operability (“the engine will tell us”).
  If HCF fractures occur in spite of conscious design, corrective measures should be considered. Cracking along the rear edge is often treated by shortening the blade chord, and in the case of corners breaking off (lyra mode vibrations, Volume 2, Chapter 7.1.3), the corners are removed.
  In general, larger axial spacing between rotor and stator blades increases the intensity of the reciprocal excitement (rotor wake and stator wake). This may decrease the compressor efficiency and increase the length and weight of the engine, but it has been shown to reduce the risk of later unexpected problems. For this reason, it is highly recommended that appropriate design regulations are set in construction manuals.
  A suitable configuration of the stator vanes around the circumference can suppress reciprocal excitement with the rotor blades (cyclic spacing).
  Vibrations can be prevented by braces that are tuned for dangerous vibration modes, such as shoulders attached to the center of blades in a circumferential direction (clappers, snappers), segmented or closed shrouds (e.g. in compressor stators or turbine rotor blades), and axial stiffeners (a flat axial rib on the pressure side of compressor stator vanes).
  

• Constructive design of housings:
  The flow-disturbing effect of housing braces can excite blade vibrations. On the other hand, damping measures and optimized stiffness properties can also dampen vibrations (Fig. "Damping bearings against rotor vibrations") and prevent resonances.
  Due to their relatively thick cross-section, bearing braces cause pronounced flow disturbances that spread with and against the direction of the flow (Ill. 12.6.3.1-2). The number and arrangement of the braces should be chosen in a manner that prevents resonances with the rotor components.
  In compressor housings, air extractors are generally integrated and/or bleed valves are attached. These potential flow disturbances should be positioned and shaped in a way that ensures that no dangerous vibrations are excited in the axially neighboring blades.
  Housing strengths (stiffness and mass) can influence the vibration of the affixed stator vanes. Blade vibrations and dynamic strength-decreasing structural changes at blade tips can be indirectly controlled by preventing dangerous clearance changes and the possibility of rubbing.
  

• Preventing local flow disruptions (stalls) at the blading:
  Profile changes due to erosion (Volume 1, Chapter 5.3.2), roughening of the blade surfaces (Volume 1, Chapter 5.3.2), and increasing tip clearances (Volume 2, Chapter 7.1.2) promote limited local flow disruptions (rotating stalls, Fig. "Types of flutter excitement"). This flow disturbance can lead to vibration excitement. Measures to prevent erosion of blades (erosion-proof materials, protective coatings, and robust blade profiles) and abradable coatings (erosion-resistant coatings) reduce the probability of dynamic fatigue fractures.
  

• Damping (Fig. "Blade shape and aerodynamic damping") can prevent dangerous vibrational loads by using up the stored energy. There are several methods for accomplishing this:
  
  • Blade materials with pronounced inner damping. A prerequisite is that a sufficient volume is involved in the dynamic deformation process (Fig. "Temperature influences inner damping of materials"). Materials with high inner damping are
    • Synthetics, especially fiber-reinforced synthetics
      
    • Precipitation-hardened alloys
    • Memory metals
    • Specially treated, fiber-reinforced metals can also have a usable damping effect.

• An additional form of damping can be caused by external effects. These include:
  • Friction damping, e.g. at the blade contact surfaces or with dampers such as damping wires, piston rings, friction dampers at the root platforms (cowbells, Fig. "Influences on damping of parts").
  • Damping inserts or poured-in materials (e.g. in compressor stator vanes) made from elastomers (Fig. "Damping materials for passive damping"). In this way, the aluminum alloy dovetail roots of compressor rotor and stator blades in older engine types were glued in with silicon gum, which made the normally vibration-sensitive material suitable for operation (bottom right diagram). A damping effect can also be used when the aluminum fan outlet blades of large bypass engines are encased in elastomers on both sides.
    
    • Metal foils that are affixed to the surface being damped (Fig. "Damping of casings with elastomers").
    • Damping coatings such as synthetics, enamels, sprayed memory metals, or piezo composites.
    • Damping bandages made from elastomers (Fig. "Damping bearings against rotor vibrations"). Uses include stretching them around a housing or glueing them into the circumferential shroud of a compressor stator.• Suitable rubbing systems can prevent dynamic fatigue cracks in rotor blades (Volume 2, Ill. 7.1.4-13). Blade fractures are promoted by damage to the blade tips caused by rubbing. The typical high friction temperatures lead to embrittlement, strength loss, smeared material, and burring (see Volume 2, Ill. 7.1.3-4). A vibration excitement due to the rubbing increases the danger of dynamic fatigue fractures. Proper rubbing systems (tribo-systems) should minimize this threat. For example, rubbing forces and friction heat can be minimized by armoring blade tips or suitable shaping (e.g. feather edging, etc.).
      

• Mistuning blades (Fig. "Mistuning of blisks"): By changing the mass, mass distribution, and/or stiffness (material, Fig. "Single crystal material for mistuning" or part geometry), the eigenfrequencies can be specifically changed in order to prevent resonances. This is referred to as mistuning. It is especially useful for poorly damped integral structures that consist of a large number of identical elements (e.g. welded or cast integral stators and blisks; Ref. 12.6.3.4-17). Typical production-dependent deviations of 1-2% can lead to statistical scattering of the dynamic blade loads of up to 100%, and result in correspondingly high dynamic stress (Ill. 12.5.3.1-18). This unwanted effect can be prevented through targeted variation of the blades. The influence of the changes on the eigenfrequency must be considerably greater than the usual production-dependent deviations (roughly an order of magnitude). This even makes it possible to lower the maximum dynamic loads considerably. In milled disks, the production costs of the different blades can be reduced to a tolerable amount relative to inset blades. However, mistuning remains a problematic solution for resonance vibrations due to the aforementioned issues. Flutter vibrations, on the other hand, are more easily prevented through mistuning.
  

Fig. "Damping ring for turbine disk" (Ref. 12.6.3.4-18): This damping ring is recommended for suppressing fundamental flexural modes of the blades of an integral turbine rotor (top right diagram). The turbine disk mentioned in the reference most likely belongs to the pump drive of a rocket engine. The blade profiles are evidently unusually thick (bottom right diagram). The relatively thin annulus closely follows the axial component of the vibration movement of the very stiff blade. In addition, the mass of the annulus which supports the damping ring is small relative to the massive blades, especially in comparison with a turbine disk from a typical turbine engine. Therefore, an important issue in this case is whether this damping measure is suitable for the typically relatively thin blade profiles of integral turbine disks in small gas turbines (e.g. helicopter engines). The long term behavior (e.g. fretting in contact surfaces, creep loads, oxidation) is also especially important in gas turbine engines, but not in rocket engines. However, due to the increased use of blisks, this method may provide inspiration for a solution to blade and disk vibrations, especially in acute cases.
The damping principle of tuned masses is based on the well-known dual-mass dual-spring system (top left diagram). The interplay in this system gives a considerably different resonant frequency than the individual subsystems (“1” and “2”). Proper selection of masses and spring stiffnesses, i.e. the relationship of the eigenfrequencies of the subsystems, can considerably increase the resistance of mass “1” (blade annulus) against the exciting force. For example, if one selects the spring stiffness and mass of subsystem “2” (damping ring) so that the resonance of the damping ring occurs with the external excitement, the vibration of mass “1” (blade annulus) could, in principle, be completely suppressed. However, complete suppression of the vibration is not possible in practice because the friction damping takes place in the contact surfaces of the damping ring. In addition, a slight mistuning of the damping ring out of resonance is recommended (danger of dynamic fatigue of the damping ring?).
The one-piece damping ring should elastically snap into a flat circumferential groove (detail; assembly problems?). Centrifugal force presses the ring onto the annulus from below. Each blade is assigned a contact surface. This is intended to make the ring act like a correspondingly large number of individual tuned damping masses. The location of the damper ring must use the axial deflection of the blade annulus, which occurs with the fundamental flexural mode of the blades, as well as possible. This requires a corresponding coupled blade-disk vibration. The contact surfaces of the damping ring should create nodes in the plane of the vibration (amplitude = 0), thus having a damping effect.

Figure "Single crystal material for mistuning": Technical single-crystals of the turbine blades have very different stiffness properties in different crystal directions. The eigenfrequencies of the parts depend on the stiffness. Lower stiffness means lower eigenfrequencies. Targeted orientation of the single crystals in a turbine blade can influence its eigenfrequency. This can be used to avoid dangerous resonances. The depictions show an expansive model of the direction-dependence of the elasticity modulus (left diagram) and glide modulus (G-modulus, shear modulus) of a single crystal of a typical Ni-based material. The E-modulus influences flexural modes, the G-modulus controls torsional vibrations.
If multi-crystal turbine blades with fir tree roots are replaced by single-crystal blades (e.g. during retrofitting, etc.), there is a danger of undesirable stress distributions in the fir tree teeth (Ill. 12.6.3.4-23). This reduces LCF life.
In addition, the dynamic strength of single-crystal materials is better than that of multi-crystals under optimal solidification conditions (minimal pore formation; Ref. 12.6.3.4-2). This is attributed to better controlled solidification conditions with smaller growth-capable defects.

Figure "Damping mchanisms" (Ref. 12.6.3.4-3): In engines, not all resonance possibilities of a part are avoidable. For example, rotor blades have flexural and torsional eigenfrequencies, the excitement of which cannot be avoided during operation (Ill. 2.6.3.1-1) as the engine passes through different RPM ranges. Therefore, one must attempt to use sufficient damping to prevent dangerously high dynamic loads.
The effect of passive damping is based on dissipation of the vibration energy of the part and occurs during the cyclical straining of the part. At this point, the vibration energy turns into heat. During active damping, controlled forces act on the vibrating system. The passive damping effect can be achieved in very different ways with specific effects on the total structure (top diagram):
Constructively inserted damping: Constructively inserted passive damping (e.g. coatings) is, with few exceptions, considerably more effective than the inner damping of the base material in the case of local vibration problems (about 10%) or local vibration forms (up to 40%).
There are a great number of energy-dissipating mechanisms available to the designer that are suitable for damping vibrations in engine components. The bottom table provides an overview and is intended to aid in selection. It shows characteristic properties of the damping effects. These are usually damping coatings (Fig. "Constrained layers 'damping foils'") and friction dampers such as damping wires, rings, and bandages, clapper rivets, riveted wall sections, and stiffeners (Volume 2, Ills. 7.2.3-8 and 7.2.3-10).
Intrinsic damping: This effect is created by friction in a system, but does not determine constructive design. This includes the inner damping of materials. It can act in many different ways (Ill. 12.5.3.4-12). Especially pronounced inner damping is observed in metallic materials with particle damping (precipitation-hardened alloys, Fig. "Temperature influences inner damping of materials"). The damping effect of the homogenous metallic material is not especially great in comparison with contact surfaces with relative movements. Exceptions include fiber-reinforced synthetics and fiber-reinforced ceramics. Their inner damping is very high, and usually increases when the typical dynamic fatigue mechanism of delamination begins. Integral parts such as welded constructions (e.g. compressor stators), cast parts (e.g. small turbine disks, Fig. "Disk fracture by flow vibrations"), and milled forged parts (e.g. blisks) have especially low damping. Better damping properties can be expected from assembled structures such as disks with inset blades (friction at contact surfaces), bolted flanges and riveted plates (e.g. sheet metal covers in the gas flow), and surfaces that move against one another, as are found in adjustable thrust nozzles.

Figure "Passive damping effects in engine components" (Ref. 12.6.3.4-3): Passive damping can be used in many different ways. When passing through resonances or during rubbing, it prevents unallowably strong buildup of vibrations (top diagram). Vibrations of sheet metal constructions such as combustion chambers and housings are minimized (bottom right diagram) and the sound emission (e.g. of housings and gearboxes) can be reduced considerably (bottom left diagram).

Figure "Blade shape and aerodynamic damping" (Ref. 12.6.3.4-3): In compressor blades that are vibrating in the fundamental flexural mode (Fig. "Forms of typical blade vibrations"), air damping accounts for the lion`s share of damping relative to the intrinsic damping of the material and the friction in the contact surfaces (see beam depth). In the fundamental flexural mode, the blade makes relatively large movements against the surrounding medium (air or gas flow) thus transferring its energy into it. In contrast, higher order vibrational modes (Fig. "Resonance condition during development") have relatively small amplitudes. For this reason, as with disk vibrations, not much damping can be expected. The damping effect of the air flow is decisively dependent on the pressure in the surrounding medium and the vibrational mode of the blade. One possible result of this is that during test runs on the ground during the development stage, no dangerously high vibrational stresses on the blades are detected, but dynamic fatigue fractures occur in altitude testing rigs or during flight at high altitudes, where the air damping is considerably weaker.
The bottom diagrams show the influence of blade geometry on air damping, and therefore on the vibration sensitivity. Rotor blades with a high aspect ratio (left) can be found in older engine types and tend to fundamental flexural modes. This creates high aerodynamic damping, providing a certain amount of protection from dynamic fatigue. The wide chord blade (low aspect ratio) at right is typical for the rotor blades in modern compressors. These blades have a relatively thin profile and tend to high-order high-frequency vibrations. Due to the small amplitudes, these vibrations are only slightly damped by the surrounding air. This promotes development of dynamic cracks in the edges (lyra mode cracks).

Figure "Damping seals between turbine blade feet": Dampers under the root platforms between the turbine rotor blades have performed admirably for a long time as a protective measure against unallowable blade vibrations (Ref. 12.6.3.4-4). Example "Failing dampers" shows that dynamic fatigue fractures in the blading can be expected if the dampers fail. These dampers are known as friction dampers, cottage-roof dampers, under-platform dampers and cowbells. In addition to damping, these inserts are also used to seal out hot gases and can also axially fix the blades. Naturally, these additional functions must not unallowably influence the damping effect. The mass, arrangement, and shape of the contact surfaces of the dampers must be optimized for the specific vibrations and operating conditions. This means that the fretting effect that is necessary for damping must be ensured (Volume 2, Chapter 6). Experience has shown that dampers can be subjected to several damage-relevant influences (Example "Failing dampers") :

• gas forces (seal action)
• axial forces from the blade fastening
• fretting wear (functional)
• vibrational loads
• thermal fatigue
• damage during installation

The damping effect is only assured within certain limiting conditions. The pressing force must not be too low, or the friction force will be too weak to take sufficient energy out of the vibrating system. If, on the other hand, the friction is too great, the necessary relative movements of contact surfaces will not occur. Also, if the dampers make a rolling motion, effective damping will not occur. This is the case with coupled blade/disk vibrations with few nodal diameters (Ref. 12.6.3.4-5).

Figure "Influences on damping of parts" (Ref. 12.5.3.4-7): In cases with small exciting forces and/or minimal air and friction damping, limitation of resonant vibrations can be decisively determined by the inner damping of the material. The inner damping capacity of a material is given as the amount of energy that is absorbed by a unit of volume during a dynamic load change (or strain load change). The damping capacity D=k.sⁿ applies to many materials. “s” is the dynamic load. “n” is roughly 3 for the usual metallic materials, and “k” is a material constant that is dependent on the load type (flexure, torsion, shear, tension, pressure). The volume dependence of the damping effect has an important implication:
Because only volumes under sufficient dynamic stress contribute to inner damping, the damping effect is strongly dependent on the vibrational mode. The volume of a blade does not experience a homogenous dynamic load, and is only of limited use for damping. The bottom diagram (Ref. 12.6.3.4-8) shows the proportions of volume that are usable for inner damping in several examples. In the extreme case of a notched rod under tension and flexure (“a”), only the small highly stressed volume in the notch base contributes to damping. The damping effect is thus very small. Even a rotor blade (“b”) only has very little usable inner damping. A rod under pure pulsating axial force (“g”), on the other hand, has a maximum of usable inner damping.
The inner damping of a material depends on a large number of factors, the most important of which are:

• frequency of the loads
• load levels (top left diagram)
• structure (e.g. grain size, grain structure,precipitation particles, strengthening structure)
  
• operating temperatures (Fig. "Temperature influences inner damping of materials"),
• previous dynamic damage (top right diagram).

The inner damping of a metallic material (Ref. 12.6.3.4-7) is not linearly dependent on the size of the dynamic loads. For steels, the top left diagram shows a sudden increase in damping together with the appearance of macroscopic plastic deformations. This behavior corresponds to the stress-strain hysteresis in the LCF range (Fig. "LCF lifespan estimation"). In contrast, in the HCF range the damping is relatively minimal.
Cast iron has high inner damping even at low load amplitudes, but it does not increase significantly as load levels increase. This behavior can be explained by the inhomogenous structure (e.g. graphite lamella), and can also be expected in precipitation-hardened alloys. The damping of materials with heavily distorted structures (hardened steels) can have an inflection point, as shown in the schematic depiction.
The inner damping changes with the number of load cycles, and is most likely influenced by mechanisms of dynamic fatigue (Fig. "Material changes during crack development"). In general, it has been observed that, near the fatigue strength, the damping approaches a material-specific threshold value. Until this value is reached, the damping behavior of the materials can vary greatly. Under high micro-residual stresses (Fig. "Definition of residual stress types") damping first increases and then drops to the limiting value of damping (e.g. hardened carbon steels). The opposite behavior can be seen in materials with low yield strengths and thus lower inner stress (e.g. CrNi steels). If the material is free of residual stresses in the structural area, it will result in a monotone decrease in damping as load cycles increase.
The load frequency only has a clear influence on the inner damping if it is high enough to cause the material to heat up and the temperature influence becomes a factor (Fig. "Temperature influences inner damping of materials"). This is the case, for example, in titanium alloys with typical low thermal conductivity. In this case, the fatigue zone can experience tarnishing, structural changes, and even melting. Fiber-reinforced synthetics have similar behavior and can heat up to high temperatures under sufficiently intense excitement.

Figure "Temperature influences inner damping of materials": Because the inner damping is usually dependent on the plastic deformations in the micro-level (Fig. "Material changes during crack development") of a material under dynamic loads, it increases along with ductility and the decrease of the deformation resistance (right diagram). This can be seen in the temperature influence. The damping of metals usually increases with temperature. Large, material-specific jumps in the damping can be observed if the deformability (e.g. Mg) and/or the structure (collapsing instable structural components in steels) change (Ref. 12.6.3.4-7).
Many synthetic resins and elastomers have very high inner damping, which can be up to 1000 times greater than that of metals. Unfortunately, the inner damping of synthetics is extremely temperature-dependent. The left diagram shows the behavior at a constant frequency (Ref. 12.6.3.4-9). Three typical zones can be identified. The elastomers differ in their transition temperatures, i.e. the temperature with the maximum inner damping, and also in their range of temperatures. At low temperatures, the E modulus is high and the damping is low. These properties are also seen in adhesives and must be considered when using systems such as constrained layer damping, for example (Ref. 12.6.3.4-10, Fig. "Constrained layers 'damping foils'"). Fiber-reinforced synthetics exhibit a similar, matrix-dependent behavior (Ref. 12.6.3.4-10).

Figure "Damping materials for passive damping" (Ref. 12.6.3.4-3): Effects that are suitable for the passive damping of engine components are:

“1” Constrained layers: These foils are bonded to the surface of the part in need of damping, such as a compressor stator vane (Fig. "Damping seals between turbine blade feet"). Their function is different from that of a simple lacquer or elastomer coating. Their damping effectiveness is achieved due to the two-layer application (top left diagram). At the surface, there is a thin foil with a high modulus of elasticity. Metal foils made of CrNi steel sheets or Ti alloys are usually used. The adhesive (synthetic resin, elastomer) that bonds the foil to the surface must use shear stress to transfer the deformation forces (antinode) into the foil. During this process, energy is absorbed by the soft middle layer, which causes the damping effect.
A special form of this technology is damping bandages, which are used, for example, around thin-walled compressor housings in order to suppress high-frequency vibrations.
A configuration that has proven itself in practice (Fig. "Damping of casings with elastomers") consists of a bandage, which is made of carbon fiber-reinforced synthetic/epoxide and is several millimeters thick and a few centimeters wide. This bandage is wrapped around the affected housing and tangentially fastened. As a constraint layer, a belt of silicon gum several millimeters thick is inserted between the housing wall and the carbon fiber-reinforced bandage.

Advantages:

• very good damping effect
• usually tolerable alteration of surface geometry (profile, roughness)
• can be used in serial applications
• operating experience in engines.

Drawbacks:

• poor spherical deformability for the typical arched leaf surfaces of modern compressor blades
• limited temperature stability, therefore only used in front compressor zone
• damping effect very dependent on temperature (see section 2)
• sensitive to aging and loss of bond strength due to creep (delamination). Damage through media such as fuel, oil, and cleaning agents
• sensitive to foreign object impacts and erosion. Experience has shown that the impact of a grain of sand can cause cracking and local delamination of the foil (Volume 1, Ill. 5.3.2-6).

“2” Coatings made from visco-elastic materials (VEM): These materials can be used as relatively thin coatings, but also as massive bandages and fillings for hollow spaces (Ill. 12.6.3.4-6). These are materials that only have optimal damping properties in certain temperature ranges. In high-temperature areas, such as high-pressure compressors, experiments were conducted with enamels as stator vane dampers in the 1970s (Ref. 12.6.3.4-16). Evidently the erosion-sensitivity of these coatings prevented their serial implementation (also see Volume 1, Ill. 5.3.1-7). The attendant diagram shows that at low temperatures, in which a glassy state occurs, the shear modulus of the coating is high. However, the loss factor that characterizes damping is low. The range in which these material properties are useful is limited to very high frequencies. Enamel has an additional drawback in that the viscous behavior at operating temperatures prevents its use on rotor blades. After a short time, the enamel flows away under the centrifugal forces and gas forces. Even on stator vanes, the flow can shift the enamel layer.
In a transition zone with a sharply dropping shear modulus, there is a zone “A” with an increasing loss factor and a zone “B” with a decreasing loss factor. These zones with the maximum loss factor are the most suitable areas for optimal damping.
In zone “C”, with a rubber-like coating behavior, the shear modulus and loss factor are very low. This zone is at material-specific high temperatures and is only useful for low frequencies.

Advantages:

• very good damping in suitable temperature and frequency ranges
• good availability
• relatively inexpensive to obtain and process
• can be applied to complex shapes

Drawbacks:

• temperature sensitivity
• aging (embrittlement, strength losses)
• damage and delamination due to foreign media (e.g. cleaning agents, oil, fuel)
• bond strength problems during production, as well as over long operating times
• damage due to dynamic overstress (inner cracking, delamination)
• erosion sensitive (flat impact angles, see Volume 1, Chapter 5.3).

“3” Viscous Fluids: In this case, the flow resistance, i.e. viscosity, of a fluid is used in a manner similar to the function of an automobile shock absorber. This type of damper is used, for example, in attached aggregates. Examples include vibration dampers of high-RPM flat belt- and chain drives.
One special application is elastically damped bearings (Fig. "Damping bearings against rotor vibrations"). In this case, an oil film is pressed between the outer bearing ring and the housing wall, damping the radial movement of the bearing ring due to the flow resistance in the tight ring gap. In addition to damping the bearing and rotor/shaft, the oil film also acts as a cushion against the transmission of vibrations into the housing.

Advantages:

• good constructively configurable damping. Dampens both vibrations with high frequencies, and large movements at low frequencies
• can be integrated into an oil system (e.g. elastically damped bearings)

Drawbacks:

• retrofitting can be difficult due to reconstruction
• limited to operating temperatures that are suitable for oils

“4” Magnetic materials: Here, the damping principle is based on the excitement of eddy flows. These are created in a (not necessarily) magnetic conductor that is moved through a magnetic field (principle of electricity meters). The faster the movement, the greater the resisting force, i.e. the greater the damping. There have been no known applications of this type of damping in turbine engines.

“5” Smart materials: These materials are still largely in the fundamental development phase.
In materials with a piezo effect, elastic deformation causes an electric current that can be broken down through a resistor with a current flow. This electrical energy is removed from the system as vibration energy and has a damping effect (middle right diagram). Potential uses include bearing dampers.
Electro- and magneto-rheological fluids change their inner friction (toughness) with the introduction of electrical or magnetic fields.
Magneto-restrictive materials change their length under the influence of a magnetic field.
Memory metals reversibly alter their shape when the temperature changes, provided the shape was “programmed” earlier. They have high inner damping. If it becomes possible to use these materials as coatings, a good damping effect can be expected.

“6” High-damping alloys: These include precipitation-hardened alloys (e.g. the high-temperature alloy Mar M2000, Ill. 12.5.1-12). There has been no reported specific use of the damping properties.

“7” Impulse- and particle damping: Impulse damping has been used for a long time in turbo-machines (industrial turbines, turbochargers) in the form of clapper rivets (bottom right diagram). The rivet, which vibrates out of sync with the blade, dampens through opposite impulses and friction in the mounting bore. This type of damping method is not used in modern engines. Drawbacks include flow disturbances, weakening of the blade due to the mounting bore, and the danger of
rivet fractures (fretting wear, dynamic loads) with consequential damages (OOD). One possible use might be as a temporally and numerically limited emergency measure in case of damage.
Particle damping consists of a hollow space filled partially with particles. The particles can move against one another and against the wall of the hollow space, thus absorbing friction energy. This type of damping is evidently being investigated and discussed for use in blisks.

Figure "Constrained layers 'damping foils'" (Ref. 12.6.3.4-10): This diagram depicts the case of a fighter engine compressor inlet stator which suffered HCF damage that had a decisive influence on its availability and operation. This case was a typical application of constrained layer technology (Fig. "Damping materials for passive damping"). A thin sheet of metal was bonded to the vibration-stressed part, in this case the inlet stator vanes, with the aid of a high-damping synthetic adhesive. Strain dynamically stresses the adhesive between the rigid metal sheet and the part surface through shearing with high damping. This technology has proven itself for suppressing dangerously high dynamic loads. However, it also has serious drawbacks. FOD and erosion can cause cracking and delamination (Volume 1, Ill. 5.3.2-6). Over long running periods, the operating temperatures and/or the influence of damaging media (fuel, solvents, cleaning agents, hot engine oil) promote delamination of the foil. It is virtually impossible to bond the foil to spherically arched surfaces without delamination-promoting warping.

Figure "Damping of casings with elastomers" (Ref. 12.6.3.4-13): A damping technology for large cylindrical surfaces, and which is related to the constraint layer method (Figs. "Constrained layers 'damping foils'" and "Damping of casings with elastomers"), can be realized with a highly stiff bandage and an elastomer insert. For weight reasons, the bandage consists primarily of carbon fiber-reinforced synthetic material. It is stretched over the thin rubber layer on the part (e.g. housing). Due to the difference in stiffness between the housing and bandage, the elastomer layer experiences strain during housing vibrations. The vibration energy is turned into heat by the inner damping. Suprisingly, this damping system is effective with high-frequency vibrations with small amplitudes. Experience has shown that it can even dampen vibrations in the blades of integrated (welded) stators. The depicted example (Ref. 12.6.3.4-14) shows a bandage that was able to prevent dynamic fatigue cracks in titanium alloy walls of a compressor inlet housing that was several tenths of a millimeter thick.

Figure "Damping bearings against rotor vibrations" (Ref. 12.6.3.4-11): Oil-damped bearings have proved excellent for preventing unallowable rotor vibrations (Fig. "Vibrations excited in ring shaped spaces 1") and are widely used in modern engines.
Between the outer ring of the bearing and the housing there is a sealed oil cushion several tenths of a millimeter thick. Twisting of the ring is prevented by flanges or an elastic cage (with axial braces) that is firmly fastened to the ring. Radial resetting occurs due to the shaft elasticity or the cage.

Figure "Estimating allowable fatigue loads" (Ref. 16.6.3.4-12): In the cited text, H. Huff states that:

“One of the greatest challenges of material science is determining the allowable fatigue loads. This difficulty is on the one hand due to the large statistical scattering of the dynamic strength and the large number of influencing values, and on the other hand due to the margin of deviation of the loads that machines are generally subjected to.”

The following text concerns causes for the statistical scattering of HCF strengths, not uncertainties in the determination of operating loads (a corresponding estimate for LCF loads is shown in Fig. "When is a weak point a flaw limiting LCF"). It would be interesting to run the following realizations through a Monte Carlo analysis (Fig. "The 'Monte Carlo Method' technique").
The subject is the life-determining dynamic loads on a part, in this case the hub area of an integral turbine disk (blisk). In this case, the loads are LCF stress, but the procedure is suitable for both LCF and HCF. A procedure in accordance with the numbers is recommended (arrows).
Flaws and weak points are defined as follows: Flaws are not allowed by the design-relevant regulations. Weak points are allowable and typical for materials (Ill. 12.6.3.4-19).

“1” Estimating the fatigue strength of <U>flawless </U>material: The attainable fatigue strength “F_D” can be estimated based on the general relationship of hardness and strength. The relationship shown in the diagram applies to steels. In order to attain the designed dynamic fatigue strength (specific dynamic strength), the hardness must be greater than a certain minimum value. If the HCF strength is lower than the hardness would indicate, then flaws are dominant.

“2” Estimating the fatigue strength of <U>flawed </U>material: Weak points must always be expected in a material. The weak point size “a” must be below a threshold value that is determined by the relationship F_D = 6 . a^-1/2. This means that it is not practical to attempt to reduce the weak point size if the fatigue strength cannot be raised accordingly in the design.

“3” Considering the mean stress: In general, the fatigue strength decreases with the tension mean stress s_m (Figs. "Terms and examples of dynamic loads" and "Dynamic strength at temperature and notches"). Because this approach does not apply to the operating loads, this section only deals with the influence of residual stress on the mean stress (Fig. "Definition of residual stress types"). Pressure residual stresses act against the fatigue strength-lowering tension residual stresses, increasing dynamic strength. Residual stresses can be induced in parts in many different ways during the production process. They can be limited to the surface (e.g. through machining) or found in the entire cross-section (e.g. forging and hardening stresses). For this reason, it is vital that the production processes and their parameters are firmly established. This is the only way of attaining reproducable, acceptable residual stress conditions in parts.

“4” Considering the stress drop: The fatigue strength increases with the stress drop “c”, which is size-dependent, unlike the form factor “a_k”, which does not change with geometric similarity to the notch (c = 2/notch radius).

“5” Material condition at crack initiation: Dynamic fatigue fractures always occur in places where the dynamic strength is lower than the dynamic loads, i.e. in weak points. Because dynamic loads can often be traced back to flexural modes, and the more highly stressed surface is subjected to potential dynamic strength-reducing influences from production processes (e.g. machining), dynamic fatigue cracks are usually located at the surface. Evaluating these influences must be left to an experienced specialist. A prerequisite for sufficiently safe dynamic strength values is a specified, reproducable production process and quality assurance of the semi-finished products. In addition, the data that are the basis for the design must be determined using representative specimens. Naturally, special material- and load-specific behavior is important. This is true, for example, of damage accumulation (Fig. "Dynamic fatigue life span estimations (Miner rule)").

Figure "Material specific minimum damping fatigue" (Ref. 12.6.3.4-12): Unavoidable material-specific inhomogeneities can determine the dynamic strength of a material and must be present at part-relevant levels in the specimens used for determining design data (Fig. "Dynamic strength differing at samples and parts"). This means that these are not flaws, but weak points that must be expected in the part due to the manufacturing process and/or the limits of serially implementable non-destructive testing. In Ni-based cast alloys, the most common turbine blade material, these weak points include cavities from the solidification process (bottom detail). These cause a typical scattering of the dynamic strength, and result in a relatively low “safe” fatigue strength. If cavities smaller than 1 mm cannot be detected with sufficient accuracy, then fracture-mechanical estimates for this material result in a usable fatigue strength of 180 MPa (bottom diagram), which corresponds closely to the specimen results.

Figure "Fatigue strength of coated parts and blades": If parts are coated, their dynamic strength under operating conditions can be reduced considerably relative to laboratory tests, especially if the coatings behave brittly in certain operating temperature ranges (Fig. "Influences on thermal fatigue"). These coatings include diffusion coatings for protection from oxidation and hot gas corrosion, as well as hard erosion-resistant coatings such as TiN.
If cracking occurs in a coating during operation, the dynamic strength values determined with the aid of uncoated specimens or specimens with undamaged coatings will be too high. The discrepancy will be greater, the stronger the coating is bonded with the substrate (bottom detail). Experience has shown that dynamic fatigue fractures in operation will then increase. This is especially unpleasant because a large number of engines with coated parts will have been delivered by the point at which the statistic clustering is noticed.

Cracking in a brittle coating on a ductile material can be initiated in various ways:

• plastic deformations:
  • loads in the LCF range (right middle detail)
  • FOD (left detail)
• thermal strain differences between the coating and substrate (top right detail, Fig. "Coatings sensitive to thermal fatigue").

Figure "Residual stresses influencing LCF behavior" (Ref. 12.6.3.4-12): Residual stresses from manufacturing processes must always be expected in parts. Heat treatments and solidification processes (e.g. casting, welding) create residual stresses that act across large part cross-sections. Machining processes (e.g. turning, milling, grinding) induce residual stresses near the surface (see Fig. "LCF fracture of a fan disk").
If a part is plastically stressed (Ill. 12.6.1-13), residual stresses are reduced when the yield limit (flow limit) is reached. Naturally, this is also the case under LCF loads, which by definition occur with plastic deformations. Creep strain has a comparable effect (Ill. 12.5.1-14). In the case of disk damage shown in Fig. "LCF fracture of a fan disk", dangerous residual stresses in the part were evidently not safely reduced through creep. If the part has protective compressive residual stresses at the surface, they can be weakened, whether they are intentional (e.g. shot peening) or not (warping). This also reduces the HCF strength at the surface.

Figure "Multiple fatigue cracks point at high dynamic loads": Important conclusions regarding causal influences can be made based on dynamic fatigue fracture surfaces. This fulfills a requirement for specific corrective measures (also see Figs. "Crack size and number point to operation loads" and "Crack growth can reveal causal influences").
Multiple dynamic fatigue fractures and/or dynamic cracks in the same parts (e.g. blades in a stage) indicate simultaneously acting, short-duration, high dynamic loads (Ills. 12.2-18 and 12.2-19). The cracking must occur almost simultaneously, or the first cracked part would have fractured before the others began cracking. The order of lines of rest (number and spacing) may be able to confirm this conclusion. The load may be, as in the depicted example, a temporary flow disturbance. One example is the malfunctioning of a bleed valve or a rotating stall (Fig. "Axial compressors operating characteristics").
A large residual fracture can indicate a high, possibly unusual, mean stress. In contrast, a small residual fracture can indicate a low mean stress to the end of the dynamic fatigue fracture. This may indicate relaxation during crack growth, which is a typical behavior under heat stress or residual stresses. Another possibility is an operating state with low mean stress, such as dynamic loads at unusually low RPM. This also indicates a specific operating state.
If lines of rest indicate uneven crack growth, it may be possible to attribute this to specific operating states and times. A dynamic fatigue fracture without lines of rest indicates steady crack growth. This would make the dynamic overstress a very brief occurrence (seconds) immediately before fracture. This permits very precise specification of the time when the dynamic overstress occurred. If the damage occurred during the development phase, i.e. in an engine equipped with sensors, the documented data of this time frame should be closely analyzed.
If different part types (e.g. rotor blades and stator vanes) have dynamic fatigue fractures or cracks, an explanation for the excitement of various resonances may be required.
Of course, unique conditions in the crack initiation zone are indicators of overly low dynamic strength. These can be anomalies from the production process or operation (e.g. FOD, erosion, corrosion, fretting). Here, as well, it is important whether only one or multiple parts were affected, or if different crack initiation causes were found in parts with otherwise similar damage symptoms. Different symptoms in the crack initiation zones of multiple parallel damages indicate that the actual cause of damage was dynamic stress.

Figure "Fatigue cracks in firtree roots": In fir tree roots, which are typical for turbine rotor blades, it occasionally happens that several dynamic cracks are initiated in the root. The location, arrangement, and number of the dynamic cracks in the teeth allow important conclusions to be drawn regarding the damage-causing loads.
Cracks on the pressure side of the top tooth (left diagram) are usually HCF cracks due to the flexural modes of the blade. Flexural modes primarily stress the top tooth. The crack occurs on the pressure side if the gas bending loads increase the mean stress as usual.
In the case of a crack in the bottom tooth (middle diagram), the most likely stress is LCF, since fir tree roots are generally designed in a way that increasing RPM and centrifugal forces cause the bottom tooth to make contact first, followed by the others in order. This means that the bottom tooth is subjected to relatively high LCF loads.
If the fir tree has several cracks (left diagram), it can be assumed that the bottom-most crack initiated under LCF, followed by the next with the same damage mechanism, since the second tooth now had to absorb a part of the centrifugal force of the lower tooth which was already cracked. The outermost crack occurred last, under LCF and/or HCF. If this crack had occurred first, it would have relaxed the loads on the other teeth, and they would not have cracked due to LCF.
If dynamic cracks occur on the suction side of a fir tree root, one must investigate whether this root side was overstressed through flexure as a consequential damage, which would have pre-damaged it (e.g. rubbing).

Figure "Testing flutter behavior in rigs" (Ref. 12.6.3.4-15): Damage due to flutter can usually be prevented through appropriate actions taken at the beginning of engine development. However, one must remember that testing rig runs alone are not necessarily sufficient for verifying flutter resistance (top diagram and Fig. "Flutter problems at a fan"). In the depicted case, testing rig runs showed flutter occurring at considerably lower frequencies than during actual flight operation. This should be related to different flow conditions in the flight envelope relative to the testing rig conditions.
The design tools also do not seem to rule out a residual uncertainty.
Despite testing rig runs and consideration of flutter when designing fan blades (1975!), dangerous flutter vibrations with dynamic fatigue cracks occurred during flight tests. This resulted in redesigning of the affected fan blade.
The profile thickness at the blade tip (in bottom diagram, “t/b”) was increased by 3 to 5.25%.
The clapper was moved from a position near the outlet edge to the center of the chord.
The greater profile thickness improved the normalized inflow angle along with the loss characteristic of the blade. Because the thickening of the blade profile necessary for strengthening affected the blade beyond the clapper to the tip, the inflow was improved by moving the clapper to the center of the chord. The changed clapper position was also intended to have a stabilizing effect on flutter resistance by helping to prevent the causal torsional vibrations.
Thickening the blade profile and moving the clapper to the chord center increased the eigenfrequency, which had an additional stabilizing effect. This lowered the reduced flow speed by 20%.
These changes proved effective in later operation.

Figure "Flutter needs specific remedies" (Ref. 12.6.3.4-19): According to the literature, the fan blades of this Russian engine, which are bent backwards, have this unique shape in order to prevent flutter. One explanation is that the problem was supersonic flutter (Figs. "Types of flutter excitement" and "Excitement mechanisms of flutter"). The bent front edges reduce the effect of the shockwaves on the neighboring blades.