7:72:723:723

7.2.3 Remedies for Labyrinth Rubbing Damage

The design and construction of labyrinth systems must take the following operating loads into account:

Temperature gradient-induced stress (static, LCF):

Thermal strain can occur during steady and unsteady operation. It is caused by the heat ratios in engine parts, which are influenced by leakage air flow and heat created by friction during rubbing. Temperature gradients that change over time cause cyclical heat strain in seal components (thermal fatigue loads) and static loads that, as mean stress, act to lower the tolerable alternating stress levels.
Experience has shown that, contrary to expectations, it is not high rubbing speed that is dangerous for overheating, but rather low rubbing speeds such as during start-up or at normal fan RPM (Ref. 7.2.3-8). New seals are especially susceptible to damage, since they have not been run-in yet, and fresh metal surfaces are especially prone to smearing (depositing). If aged coatings are still present after a module replacement, they will most likely have limited abradability. This increases the probability of overheating, burning, and crack initiation. In extreme cases, the engine may lock or seize. Therefore, rubbing at low speeds must be avoided as much as possible.


Dynamic loads (HCF) due to high-frequency vibrations:

Various factors can incite high-frequency vibrations with large dynamic loads in stationary and rotating labyrinth components (see Table Labyrinth seal vibrations):

  • Flow incitements
    • Pressure changes in the steady flow in circumferential direction.
    • Pressure disruptions running around the circumference along with the rotor RPMdue to the rotor rotating eccentrically relative to its central position, usually due to imbalances.
    • Stator vibrations causing periodically changing aerodynamic forces with fixed nodal diameters in the labyrinth chamber.
    • Pressure waves running around the circumference of the labyrinth chamber (or an air chamber attached to the labyrinth) at the speed of sound relative to the flowing medium.
    • Aeroelastic incitation due to the interplay of seal component vibrations and the periodically changing aerodynamic forces created by the vibrations.
  • Rubbing
  • Incitement from mechanical forces (e.g. vibration of the disk, to which the labyrinth bracket is attached, or vibration of labyrinth stators incited by housing vibrations)
  • A combination of the above factors


Dimensional stability during rubbing:

Rubbing should occur primarily in the static part of the labyrinth, since this creates a smaller leakage gap (Fig. "Operation behaviour by labyrinth clearance"). The leakage air flow differs by a factor of three. Therefore, suitable abradable coatings are necessary on the stator side. Suitable structures have low density and heat up more rapidly than the rotating labyrinth fins (e.g. with pores or honeycomb). This ensures the desired effect of greater wear occurring on the stator side. In this way, the energy exchange takes place along the entire circumference of the labyrinth fin, but only a segment of the static part is involved in the rubbing.
Honeycomb seals (usually on the static labyrinth part) have the advantage that there is always a leakage air flow through the honeycomb (even if the gap is zero, i.e. direct contact with the fins), which helps dissipate the friction heat. The disadvantage this leakage air has for the seal effectiveness, and thus engine efficiency, is not as great as the above mentioned advantage.
Thermal strain caused by friction heat should result in an increase of clearances gap sizes, causing the rubbing to stabilize. If the gap sizes decrease, the rotating labyrinth components may overheat, causing them to plastically deform or fail.
It is important to ensure a minimum of leakage air flow in order to dissipate the friction heat sufficiently quickly and thus prevent unallowable heating of the leakage air due to agitation losses (gas friction) in the labyrinth. If this is not done with overly small labyrinth gaps, the labyrinth will heat-up to dangerous temperatures. In extreme cases, fires may be ignited (e.g. oil fires or titanium fires) or the labyrinth structure may fail (fracture, melt).


Optimizing the heat ratios in labyrinth seals:

Seal diameter:

Large diameters lead to correspondingly high rubbing speeds and more friction heat. On the other hand, the larger diameter also means that the labyrinth mass is larger, lowering the danger of overheating. If centrifugal loads increase with the labyrinth diameter, it also increases the danger of creep overstress during overheating.
In labyrinths, stabile rubbing behavior is marked by an increase of the labyrinth gap during rubbing and can be achieved by faster/larger heat expansion of the outer labyrinth parts. Therefore, the rub coating commonly affixed to the seal stator should be as thin as possible and have good thermal conductivity. However, this measure is not practical in segmented designs (e.g. housing-side seals in high-pressure turbines), since the radial gap is determined primarily by the expansion of the housing, rather than that of the segments.


Geometry of the labyrinth fins:

In any case, dangerous thermal deformation of the supporting labyrinth ring, and thus self-increasing rubbing, must be prevented. Therefore, a basic principle should be keeping the amount of heat transferred from the labyrinth fin to the ring it is mounted on as low as possible. The taller, thinner, and sharper the fins, the lower the heat flow into the relatively massive supporting ring, but also the higher the temperature in the labyrinth fin becomes. Analytical observations have shown that the fin height has twice the influence on the insulating effect (to the ring) as the fin width. On the other and, the local heating-up of the fin increases, along with the risk of overheating and hot cracks in the fin. Because the most dangerous problems have been observed in low fins, the height of the labyrinth fins should always be greater than 0.8 mm (Ref. 7.2.3-8). Labyrinths with stepped cross-sections (Figs. "Operating properties by labyrinth fin geometry" and "Labyrinth seals properties" ) are better than triangular ones with regard to heat creation and ring stiffness, which makes dangerous crack growth less likely.
If the thermally-induced axial movements allow it, stepped labyrinths should be preferred to straight labyrinths due to their improved seal effect (Fig. "Saw like notches used in labyrinth fins"). However, it is becoming more and more difficult to meet these conditions, since the larger axial distance from the thrust bearing and the corresponding larger thermal strain are too great for the axial movements of the step labyrinth.
In order to minimize the amount of friction heat that is created and transferred into the labyrinth fin, the fin is outfitted with suitable armor. Requirements for these coatings are a good cutting effect (matched with the partner surface in order to ensure that a minimum of friction energy is created) and low thermal conductivity, which minimizes the amount of heat flowing into the fin.
In order to minimize leakage air, i.e. maximize seal effectiveness, sharp-edged, right-angled labyrinth fins should be used. Material removal usually results in the leakage air increasing by about 20% relative to the new parts, due to changes to the fin geometry and increased gap size. In order to maintain the geometry of the fin and minimize leakage air, armoring is recommended. The desired fin geometry is largely independent of the part`s size. In honeycomb seals, the thickness of the honeycomb walls should always be considerably smaller than that of the tooth tip, in order to concentrate wear on the stator and spare the fin.
In order to improve the cutting effect during rubbing, labyrinth fins have saw tooth-like notches (e.g. more than 20 well-rounded notches around the circumference, see Fig. "Saw like notches used in labyrinth fins"). This also reduces the centrifugally-induced hoop stress in the tooth and reduces the tendency to bulge and that of radial crack growth from rubbing damage. On the other hand, axial notches cause local increases in tangential tension in the base of the notches, which can lead to fatigue cracks. The notch effect must also be considered when smoothing damaged rubbing zones. Experience has shown that these measures require extensive strength analysis.
The rubbing contact does not usually occur evenly along the entire circumference of the rotor and stator. The friction heat creates large local temperature gradients. These cause the inner labyrinth ring to ovalize
and increase rubbing (unstable behavior). If the labyrinth fins are sufficiently tall and thin, the local heating-up of the supporting ring remains low, keeping ovalization at acceptable levels.
Especially thin, comb-like labyrinth fins (e.g. sheet fins or punched rings) have a high risk of dynamic crack initiation at their base. Therefore, special care must be taken to ensure sufficient vertical curve radii. Spiraled ridges are preferable to ring-shaped closed ridges. However, spiraled ridges have relatively small contact zones and are also affected by axial forces during rubbing. This cutting force can overload filigreed spiral ridges on the stator through bending. A continuous spiral groove creates leakage flow that can cool the labyrinth. Solid circumferential ridges create heat in the contact zone along the entire circumference without corresponding cooling leakage air, which can cause problems.


Important points for preventing thermal instability during rubbing (Refs. 7.2.3-8 and 7.2.3-9):

  • Seal supports that are subject to critically high centrifugal loads should be affixed with an integrated disk shoulder in order to minimize radial expansion.
  • The stator should expand at least as rapidly as the rotor due to temperature changes.

Selection of the rub coating for the labyrinth tips is of primary importance. Only proven material combinations for the tribo-system rub coating/labyrinth fin must be used in serial production. This requires sufficient direct experience by those responsible for development. Reports, documents, and “hearsay” are not sufficient for ensuring safe implementation and operation! This is due to the complex manufacturing procedures and wear processes, which are dependant upon the specific operating conditions. The following experience can be used as a first step in selecting materials:

  • At low and medium temperatures, non-metallic rub coatings made from filled synthetic resins such as epoxide, polyester, silver filling, aluminium filling, and nickel-graphite have been shown to be effective at moderate pressure differences.
  • Open honeycomb structures made from nickel alloy sheeting are suitable for labyrinth seals with high operating temperatures.

The most dangerous thermal deformation of labyrinth seals occurs at low to middle rubbing speeds. The heat created by the rubbing process can be considerably reduced by applying a hard abrasive coating (armor), such as thermally sprayed Al-oxide, to the labyrinth fins. It is necessary for the bond strength of the armor coating to be sufficient for preventing spalling and may require a suitable bond layer between the base material and the armor.


Preventing self-increasing rubbing:

Stabile labyrinth behavior (increase of radial play) during rubbing is best ensured by static parts that heat up more rapidly with more thermal expansion than the rotating parts. This means that the (closed) ring that carries the coating must have thin walls in order to keep the heat capacity and heat dissipation low.


Preventing damage due to thermal fatigue (Ref. 7.2.3-1):

This concerns dynamic fatigue in the LCF region, which is caused by cyclical heat strain in the supporting labyrinth structures. In this case, it does not involve crack initiation in the labyrinth fins due to local heating-up during rubbing.
Constructions in which a thin-walled conical shell carries a relatively thick static seal ring should only have axial temperature gradients. Radial gradients should be avoided. With thin-walled support cones, the following design rules are intended to prevent unallowable heat strain:


Avoid cross-section jumps!

This is especially true for the transition from the support cone to the ring cross-section. Sufficient radii and soft transitions must be ensured. Welds between the ring and the supporting cone should all be sufficiently far from the ring (Fig. "Avoiding labyrinth damages by thermal strain") in order to ensure attenuation of the heat strain-induced flexural stresses.


Sufficient roundness of the stator must be ensured!

Closed labyrinth stator rings: Problems are caused by thermal strain differences between the static labyrinth part and the supporting housing structure during unsteady operation, especially during start-up and shut-down, as well as during large power changes. These radial strain differences should be constructively controlled (e.g. centering braces) in closed labyrinth stator rings. In this case, the fastening flange must have sufficient stiffness across its diameter. Uneven friction forces around the circumference cause correspondingly different radial stressing of the labyrinth stator. This is promoted by distortion and warping of the housing and the flange due to the temperature ratios in the labyrinth ring. Reference 7.2.3-1 mentions about 0.1% unroundness as a guiding value for the seal diameter.
Segmented labyrinth stator rings: Seal segments have been effectively used for a long time. The number of segments can vary greatly. They can be half-rings or correspond to the blade clusters. In this case, the dynamic behaviors of the stator assembly and the seal must be matched to one another.


Preventing damage due to labyrinth vibrations:

Resonance of the labyrinth with the rotor RPM or the acoustic incitation frequency of circumferentially running air vibrations must be avoided through constructive measures. It is essential to analyze and determine potentially damaging natural frequencies of the the labyrinth components. This can be done analytically or through experiments. Especially at risk are metal sheet constructions that tend to torsion and/or bending of the cylindrical labyrinth walls. Closed “box constructions” can give the labyrinth structure the necessary stiffness. One can also make use of the higher torsion stiffness (several decimal powers) of a closed profile compared with an openly-slitted profile with the same cross-section .
Causes of vibration are described in Chapter 7.2.1. Potential resonance is easily recognizable in the frequency diagram (“Campbell diagram”). If resonance occurs in a seal part, then its natural frequency should be altered from the incite frequency or, if this is not possible for constructive reasons, the resonant seal part should be additionally damped by a suitable vibration damper.
According to Alford (see Ref. 7.2.3-7), aeroelastic instability is promoted by long and soft-bending seal structures (with low natural frequencies) if there is a sufficiently large pressure difference and the radial gaps expand due to the low-frequency modes of vibration.
In 1964, Alford gave a criterion regarding aeroelastic instability of a seal part (rotor or stator), into which the length of the seal, the pressure differences throughout the seal, the lowest natural frequency of the seal part, the vibrating mass, and the number of nodal diameters of the respective natural mode (but not the expansion of the radial gaps in direction of the flow at the mode of vibration respective to the lowest natural frequency) all enter. In accordance with this criterion, instability occurs when the radial elastic deformation under pressure loads (modified with the square of the natural frequency and the number of nodal diameters of the mode of natural vibration at the lowest natural frequency) surpasses 0.2% of the seal radius.


Constructive remedies:

With thin conical shells, a multitude of flexural modes of vibration are possible in axial and circumferential directions.
Experience has shown that labyrinth stators are especially at risk if they are braced by a thin-walled cone affixed on one side. Large diameters, length, and large pressure gradients increase the vibration-sensitivity of a seal. In accordance with Alford`s aerodynamic stability criterion, seals in which the elastic deformations under normal operating loads exceed 0.2% of the seal diameter should be avoided.

Another occurrence that should be avoided is expansion of the radial gaps between the seal fins and seal stator in direction of the flow at the mode of vibration corresponding to the lowest natural frequency (e.g. due to low-pressure side fastening of the seal components). According to Abott (Ref. 7.2.3-2), the low-pressure side mounted seal parts must also be sufficiently stiff, so that its lowest natural frequency is greater than the acoustic incitation frequency.
If resonance and aeroelastic instability cannot be sufficiently prevented, friction damping is a possible remedy for dangerous labyrinth vibrations. Friction damping, e.g. with a damping ring/bandage, can be implemented from the very beginning. It can also be retrofitted if the vibration-sensitive configuration only allows this type of remedy. In this way, the log decrement (unit of measurement for damping) can be increased by about one decimal power.
Circumferential profiling or torsion rings with closed profiles can be retrofitted to stiffen support cones and prevent resonance. However, a prerequisite is that all incitement mechanisms are sufficiently understood. If this is not the case, then the endangered seal part must be additionally damped.
A completely different approach is the use of brush seals (Fig. "Brush seal influencing dynamic behaviour"), which only require one constriction in direction of the flow due to their better sealing effect, meaning that they have no (reported) problems due to aerodynamically incited vibrations. If the brush parts (bristles and mounting plates) of a brush seal are jammed against one another, the additional mechanical damping effect of friction inside the seal element is also beneficial.

Figure "Avoiding labyrinth damages by thermal strain" (see also Fig. "Labyrinth design to be avoided", Ref. 7.2.3-1): Cracks due to thermal fatigue (top diagram) or dynamic fatigue under thermally-induced high mean stress must be specifically prevented. There are rules and guiding values for designing static labyrinth carriers, especially labyrinth cones. The transition from the cone to the labyrinth ring should be evenly, conically relieved (top diagram). The distance between a circumferential weld seam and the fastening point of the labyrinth ring should be above the attenuation length of the cone. This distance is necessary in order to reduce flexural stress to acceptable levels (1/e=1/2.7). On the flange side, the attenuation length can be derived from the radius of the cone, the thickness of its wall, and its angle.
Unallowable thermal deformation of the labyrinth support ring can be prevented by installing suitable circumferential stiffeners.

Figure "Saw like notches used in labyrinth fins": Small notches around the circumference of the labyrinth teeth can evidently improve the operation of labyrinths. It can be assumed that the radial chipping surfaces these create make rubbing against metallic honeycomb structures safer (less smearing, less material buildup, less heat development).

Figure "Labyrinth design": The rings of intermediate stage seals can be used to axially affix rotor blades and/or seal or measure cooling air. Since these usually filigreed ring structures tend to high-frequency vibrations and/or the laying-on blades have a vibrating effect, these rings dampen the whole system. They are subject to fretting wear at the contact surfaces. High mean stress can be present in this area if there are large axial loads on the ring, whether they come from the blading or are due to differences in the thermal behavior of the rotating seal part or the neighboring disk. These mean stresses promote dynamic fractures.

Preventing cavity resonators:

Helmholtzian cavity resonators (see Chapter 7.2.2) are caused by chambers that are connected to a gas flow via a duct. This configuration promotes air vibrations in the chambers, which in turn cause dangerous vibrations of the labyrinths and their mountings (e.g. disks or housings). Therefore, these (ring-) chambers (Figs. "Vibration risks at compressor end labyrinths" and "Design details influence labyrinth operation") should be avoided.

General measures for preventing damage during manufacture and repair:
The following is recommended for thin-walled labyrinth carriers (see Fig. "Saw like notches used in labyrinth fins"):

  • Misaligned welded joints must be avoided on static labyrinth cones.
  • When soldering, a sufficiently large fusion surface must be present on static labyrinth carriers.
  • The construction must ensure sufficiently reliable control of the soldering gaps during manufacture, as well as the solder seam. Serially applicable testing procedures must be designed and prepared in time.
  • The fillet of the solder seam must be specified in order to ensure good force transmission and prevent peeling.
  • Brazed metal webbing or metal felts should not be used as rub coatings due to their poor braze- and weldability.
  • Cross-section weaknesses in static labyrinth carriers caused by the manufacturing process (e.g. in bending radii) must not be in heavily stressed areas. Endangered areas must be accessible in order to make verifications of their wall strength possible.
  • In order to prevent distortion and bulging of thin labyrinth structures, it must be ensured that no dangerously high residual stresses (e.g. from welding, metal cutting) are created. If in doubt, suitable after-treatments should undertaken (e.g. heat treatment, shot peening).
  • Armor that is not sufficiently easily removable during overhaul and repair is unsuitable. Materials that cannot be deposit-welded onto severely limit the operational use of the parts they are used in. For example, a labyrinth carrier made from a high-strength material that forms hot cracks during deposit welding may not be suitable for repairs.
  • If a module replacement results in aged rub coatings (poor abradability) being partnered with new surfaces (small gaps), the clearance gaps must be increased (relative to their size when the configuration was new) enough to safely avoid rubbing.

Figure "Labyrinth vibration prevented by design": The tendency of a labyrinth ring to be incited to vibrations by the gap flow (Ref. 7.2.3-8) is clearly influenced by the location of the mountings relative to the pressure progression across the seal (also see Fig. "Labyrinth design to be avoided"). The seal part fastened on the high-pressure side is at risk for vibrations (left diagram). This is only true if no additional stiffening rings have been applied to the low-pressure sides of the labyrinths. This behavior is explained in Fig. "Preventing labyrinth vibration from leakage flow".
Taking into account the normal frequency of the seal part, the following is true:
A seal ring mounted on the low-pressure side of the labyrinth will not be incited to aeroelastic vibrations (Ref. 7.2.3-2), if its lowest natural frequency is higher than the acoustic frequency. If the seal ring is mounted on the high-pressure side, it cannot be incited to such vibrations if its highest natural frequency is lower than the acoustic frequency (see also Fig. "Mechanical labyrinth resonances with rotor").

Example "Mechanical friction damper sleeve" (Ref. 7.2.3-2): “Fatigue cracking of an aircraft engine labyrinth seal occurred during pre-flight factory testing. Tests in a static rig revealed that the seal could be aeroelastically excited by the labyrinth leakage flow….the ratio of acoustic and mechanical natural frequencies was of vital importance in determining if the nature of the pressure fluctuations within the labyrinth seal teeth provided either positive or negative aerodynamic damping to the seal….A mechanical friction damper sleeve was designed to suppress the aeroelastic instability….The aircraft engine was qualified with the newly designed damper which has demonstrated its effectiveness for eight years of service and half a million hours of operation without incident.”

Comment: negative damping is taken to mean an increase of the vibrations

Figure "Preventing labyrinth vibration from leakage flow" (Ref. 7.2.3-7): The sensitivity of a labyrinth seal to aeroelastic vibrations incited by the leakage flow (Fig. "Preventing labyrinth vibration from leakage flow") depends primarily on the gap changes during the vibrating process, i.e. the location of the circumferential nodal line. The location of the phase of the gap changes relative to the phase of the pressure progression in the labyrinth can increase or decrease vibrations, depending on the location of the nodal line. The locations “A” and “B” in the above diagram are sensitive to vibrations, whereas “C” and “D”are not. In Ref. 7.2.3-7, the progression of a vibration incitement is described as follows:
If a circumferential nodal line (here of the static labyrinth side) is located in the vicinity of the intake tooth (pressure side) of a labyrinth (top diagram case “A” and bottom diagram), the flow cross-section in the labyrinth is almost completely constant. The flow rate in the volume between the first and last tooth is almost completely constant. The vibration amplitude of every single tooth is (during a pitching movement of the coating-bearing ring) is almost proportional to the axial distance from the nodal line (see bottom diagrams). Imagine a small segment around the end tooth that oscillates around a central position. In this central location, the outflow at the end tooth corresponds to the inflow at the intake tooth (phase point “1”). If the stator is located radially above the central position, then the outflow exceeds the inflow (phase point “2” in the bottom diagram). In this case, the pressure in the (gap-) volume of the labyrinth between the intake and exit teeth depends on the air mass inside; the less air, the lower the pressure. Now imagine that the stator is in the middle position during the outward movement. During the next 2/4 phase of the vibration, the outflow will be greater than the inflow and the pressure in the gap volume will decrease (phase points “2” to “3” in the bottom diagram). If, on its way radially inside, the stator is located in the central position (phase point “1”), then the pressure in the gap volume will have decreased to a minimum. In the same way, if the stator is in the central position on its way radially outward, the pressure will have reached a maximum and promotes the outward movement of the labyrinth ring. In the described case, the pressure progression in the labyrinth is set against the gap changing phase in such a way that it increases labyrinth movement, i.e. vibrations. The above explanation indicates that a system without noticeable damping will behave unstably (be vibration-sensitive) if the vibrations cause the flow at end of the labyrinth (outflow tooth).
The middle diagram depicts a labyrinth configuration with a damping effect:
Imagine the same thin, cylindrical stator, but fastened by a conical shell on the exit side. This results in the “nodal ring” being located on the side of the exit tooth (labyrinth side with low pressure). The combined bending and torsion (see Fig. "Labyrinth torsion stiffness prevents vibrations") during vibration of the thin cylinder causes the gap size to change at the intake tooth. However, since the nodal line is now located at the exit tooth, the gap changes at the intake tooth. This causes the flow in the gap volume between the intake and exit teeth to change with the radial gap height, but the exit gap stays the same. In the central position (“Sm”), the inflow is the same as the outflow, but if the radial position of the static labyrinth ring is above the central position, then the inflow is greater than the outflow. Imagine a narrow segment of the thin stator ring in the central position (phase point “1”) during the outward

radial movement. During the next 2/4 phase, the inflow is greater than the outflow, increasing the pressure in the gap volume (phase points “2” and “3” in the middle diagram). If the stator is in the central position during inward radial movement, the gap pressure is at a maximum. In the same way, the gap pressure reaches a minimum when the stator is in the central position during outward radial movement. Therefore, labyrinth movement and gap pressure are in phase. The pressure acts against the vibrating motion; it takes energy from the vibration and has a damping effect.
Also see the advantages of brush seals in a tandem arrangement (Fig. "Brush seal influencing dynamic behaviour").

Figure "Stator ring design against vibration by 'coincidence'": By constructively relocating the nodal line that determines the movement of the stator seal surface, the sensitivity to aeroelastic incitements due to interaction with the leakage air flow can be minimized.

Figure "Labyrinth design to be avoided" (Refs. 7.2.3-8 and 7.2.3-9): Reports warn of the depicted labyrinth designs, since they tend to cause dangerous damage.
Thin-walled conical shafts (Example "Mechanical friction damper sleeve" and Fig. "Labyrinth design to be avoided") and filigreed rotor disks (top diagrams) with integrated labyrinth carriers are especially prone to vibrations incited by the labyrinth. This danger is also present in blisk configurations in modern compressors. The blisk blades are integrally bonded to the disk, which means that they do not experience any damping friction in their roots, as is normal with non-integrated, set-in blades.
Poorly located welds (too close to the labyrinth ring) and manufacturing flaws with notch effects increase the danger of crack initiation due to thermal gradients and/or high-frequency vibrations (middle diagrams).
Soldered labyrinth structures can cause dangerous consequential damages (even burst disks) if they separate. Therefore, optimal manufacturing conditions (solder gap!) must be ensured, as well as testing procedures that can certainly analyze the quality of the soldering. If the soldering fails, there must be no dangerous rubbing. This must be ensured by positive fitting (bottom diagrams).

Example "Vibrations at labyrinth on conical hollow shafts" (Ref. 7.2.3-9, Fig. "Vibrations at labyrinth on conical hollow shafts"):

Excerpt: “…One interesting case involved flexural waves propagating in axis-symmetric mode along the slant thin wall of a conical shaft at the compressor discharge labyrinth seal”. There was no wave propagation in the circumferential direction. This was proven because strain gauges on the No. 2 stationary bearing support and strain gauges on the rotating shaft gave the same frequency. A severed damper ring, hollow in this case, was installed and was an effective solution to the problem.“

Comment: The subsequent text indicates that this was an axial mode of vibration without nodal diameters (compare with Fig. "Vibration modes of thin-walled shells")

Figure "Vibrations at labyrinth on conical hollow shafts": In the low-pressure turbine of a large turbofan engine, the compressor discharge labyrinth seal was mounted on the thin-walled conical shaft. Reports (Ref. 7.2.3-1) indicate that, at least during the engine development phase, problems with labyrinth vibrations occurred in this area.

Figure "Damping rings for rotating labyrinth seals" (Refs. 7.2.3-8 and 7.2.3-9): Labyrinth ring vibrations can be prevented by damping rings. In rotating seals, these rings are slitted around their circumference. The damping effect is primarily due to their laying against the inside for the rotating seal due to centrifugal force (top left diagram). They can be mounted on the inside or side as bandages (top middle and right diagrams), or outside as closed bandages on static labyrinth carriers (Fig. "Damping measures in labyrinths"). Damping bandages on static seal rings are elastically stretched and/or riveted on in order to ensure sufficient friction force is created for the damping effect (Fig. "Damping measures in labyrinths"). To ensure that the damping ring maintains its optimal position, it is fixed into special grooves (middle diagrams). This prevents the rings from being unallowably displaced during standstill, for example. This can be ensured by suitable installation, tolerances, and elastic deformations. During installation, it is especially important that the rings are well seated.
Damping occurs primarily due to friction. The friction energy is determined by the surface pressure in the contact zones. Significant damping should be ensured across a wide range of surface pressure (changes due to centrifugal force and decreasing elasticity).

Figure "Configurations of damping in labyrinth systems" (Refs. 7.2.3-8 and 7.2.3-9): In order to dampen vibrations in rotating labyrinth rings as effectively as possible, the damping rings can be positioned in various ways.
The damping ring should be mounted so that the largest friction energy is created, i.e. taken from the vibrating system. This is usually in the area near the end of the labyrinth ring (A,B and D). In rotors, the damping ring is mounted on the inside of the ring, which makes use of the centrifugal force to press it down and increase friction forces (A and B). It is also possible to mount the damping ring on the outer diameter of rotating labyrinth rings (D ).
Variant B has evidently had problems during operation, since newer engine types use type A seals. The torsion-stiffening ring with a box section (Ref. 7.2.3-1) mounted on the protruding static labyrinth section (see Fig. "Labyrinth torsion stiffness prevents vibrations") is conspicuous. Simultaneously, the location of the damping ring was changed relative to the direction of the leakage flow. These characteristics, especially, should be responsible for the improvements.
In case C, the damping ring was mounted on the support cone side. This configuration must be seen in connection with the stiffening effect the ridge has on the ring groove. Perhaps this influenced the mode of vibration in such a way that sufficient friction forces were created even this close to the fastening side. It is interesting that configuration D is part of an older engine variation, which indicates that configuration C has advantages over D under these specific operating conditions.
The stiffening rings mounted underneath the labyrinth fins on the inner diameter in C and D should serve to minimize thermal deformations during rubbing, preventing dangerous self-increasing rubbing.

Figure "Labyrinth torsion stiffness prevents vibrations" (Ref. 7.2.3-1): Cylindrical and conical labyrinth supporting rings can have many different modes of vibration. These can be oriented in an axial direction and/or along the circumference. The radial deflection is dependant on the axial position. This means that the intake and exit fins in a vibrating labyrinth experience different gap changes (top diagrams). These different gap changes lead to corresponding pressure changes inside the seal. If the air inflow is increased by a larger gap while the outflow is simultaneously constricted by a smaller gap, it causes pressure build-up in the labyrinth. If the inflow gap then constricts and the outflow gap expands, the pressure in the labyrinth is relaxed and drops considerably. It must be emphasized that, depending on the frequency of vibration and the number of nodal diameters around the circumference (bottom diagram), this process occurs simultaneously in several places (corresponding to the doubled number of nodal lines). This incites air vibrations that are self-increasing if they resonate with the labyrinth ring. Designs which avoid these axially uneven gap openings are not susceptible to these modes of vibration. However, thin-walled cones with large diameters that are fastened on the low pressure side have been shown to be especially prone to this type of vibration overstress (Fig. "High frequency vibrations of labyrinth cones"). Dangerous constructions can be defined as those in which the deflection due to the pressure drop in the labyrinth is more than 0.02 mm/100 mm of labyrinth diameter.
If one observes the ring above the labyrinth fins during radial deflection, one can see that it forms a changing cone during vibration. This causes the ring to twist in itself. Because it has a flat cross-section, its polar section modulus, which determines its torsion resistance, is relatively low. By fastening a torsion resistant (closed, ring-shaped) hollow section (middle diagram) to the outer surface, the labyrinth carrier can be kept parallel to the axis even during radial deflection. This makes the criterion for the described vibration incitement inapplicable.

Figure "Damping measures in labyrinths" (Ref. 7.2.3-1, Example "Coulomb damping ring"): If static labyrinth rings are subject to a strong vibration incitement, they can be effectively damped by attaching a flat polygonal bandage. The number of corners of the bandage, i.e. the number of attaching points around the circumference, must be odd, since the modes of vibration that it is intended to dampen have fixed nodal diameters that result in an even wave number around the circumference. This ensures that, during vibration, a damping relative movement occurs between the contact surfaces of the labyrinth ring and the damping bandage.

Example "Coulomb damping ring" (Ref. 7.2.3-1, Fig. "Damping measures in labyrinths"): “Designers may need a “fix” for a chronic cracking problem due to flexural vibration fatigue, or may desire to protect an existing part. It has been found that the addition of a dry Coulomb damping ring…will serve the purpose. For example, the initial design of an outer balance piston seal on the (shaft engine type)..turbine developed a fatigue crack in the walls of the cylindrical stator in about one-fifth of the engines during factory testing. A 13-edged polygon damper ring was designed to fit snugly over the cylindrical outer surface of seal stator. (Note that all vibration modes have a diametral node; therefore, use of an odd-sized polygon will ensure coulomb friction, and will result in maximum damping). Comparison of measured log decrement damping with and without the polygon ring indicated that the damping was increased by a factor of about 7. Since the damper ring was applied to production engines over a year ago, no failures have occurred.”

Comment: This example demonstrates the effectiveness of a properly shaped and positioned bandage.

Figure "Preventing bulges in labyrinth arms": In order to avoid dangerous self-increasing rubbing due to deformations caused by heating-up of the rubbing area, stiffening ring braces can be affixed to the inside of the rotors (compare with Figs. "Saw like notches used in labyrinth fins" and "Vibrations at labyrinth on conical hollow shafts"). These braces also increase thermal capacity, slowing the heating-up process.

Figure "Disk fracture risk by labyrinth crack": Disk failures must be avoided due to the catastrophic consequential damages (no containment!). For this reason, the following constructive rules apply to integrated labyrinth carriers:
In case of axial cracks, which characteristically form from hot cracks in the rubbing area of labyrinth fins, the labyrinth carriers should break off of the disk before the axial crack spreads into the disk (middle diagrams).
For this reason, labyrinth carriers should not be fastened to the inside of the disk in the area of the highly-stressed hub, as is shown in the top diagram (see Figs. "Armoring / hard-facing titanium labyrinth tips" and "Danger by position of labyrinth rings"). In this case, the high hub loads characteristic for disks promote axial crack growth from the labyrinth ring, which experiences relatively low centrifugal loads (diagram A).
Diagrams B and C) depict screw-connected labyrinth carriers, from which cracks do not spread into the disk (compare with Fig. "Preventing progress of cracks into disks"). However, the high loads on the disk bores are problematic. Labyrinth rings supported by the disks do not require disk bores (D). In this case, the disks must be braced against one another by tie rods. However, dimensional stability (creeping) in outward lying rings with large diameters can be a cause of problems.

Figure "Armoring / hard-facing titanium labyrinth tips": Armor must have cutting properties, similar to a grinding disk, in order to minimize heat development during rubbing. At the same time, it should insulate against the heat flow. This prevents crack initiation, strength loss, or softening of the rotor.

Figure "Danger by position of labyrinth rings": This labyrinth configuration in the turbine region of a two-shaft engine has characteristics (see Fig. "Disk fracture risk by labyrinth crack") that promote crack growth from the labyrinth into the disk. Evidently, there are operating conditions that make this risk seem tolerable: relatively short life span of the configuration, frequent opportunities for inspection, minimized hot crack risk due to special selection of materials, low rubbing speeds, and sufficient clearances.

Figure "Preventing progress of cracks into disks": Unlike in Fig. "Danger by position of labyrinth rings", this civilian engine was outfitted with a plug connection for fastening the labyrinth carriers in the hub region of the turbine disk. This eliminates the danger of crack growth from the labyrinth ring into the disk. This configuration is suitable for civilian aircraft, given their necessary long operating times and correspondingly long inspection intervals.

Figure "Vibration risks at compressor end labyrinths" (Ref. 7.2.3-10): Usually, and correctly (with regard to avoiding incitements due to air vibration), the compressor-end labyrinth (compressor exit labyrinth) is attached firmly under the inner wall of the exit diffuser (Fig. "Design details influence labyrinth operation"). If the labyrinth is located far inside, as in the depicted case, it has the advantages of lower leakages (smaller gap circumference, lower rubbing speeds) and more varied possibilities of compensating for the axial thrust. However, it also provides the conditions for a (Boys-) resonator (Figs. "Acoustic waves incite labyrinth shafts" and "Labyrinth gas vibration systems"). This is formed by the relatively large chamber between the rotor and labyrinth and a ring opening to the main air flow. Under certain flow conditions in the chamber and between the chamber and the main flow, cellular flow with pressure vibrations can occur (Figs. "High frequency vibrations of labyrinth cones" and "Air pressure vibrations in labyrinths").
Air exchanges between the rotor chamber and the intake of the exit diffuser can cause powerful flows. Effective diffusers are very sensitive to this type of cross flow.

Figure "Design details influence labyrinth operation" (Ref. 7.2.3-10): If the compressor exit labyrinth is located tightly underneath the inner wall of the exit diffuser, the risk of air vibrations in a resonator is minimized (Fig. "Vibration risks at compressor end labyrinths"). Proper shaping of the intake edge of the exit diffuser (see details) reduces the risk of vibration-inciting cross-flows even further.

References

7.2.3-1 J.S. Alford, G.W. Lawson, “Dimensional Stability and Structural Integrity of Labyrinth Seals”, SAE-Paper 660048 of the “Automotive Engieering Congress”, Detroit, Mich. January 10-14, 1966, pages 1-30.

7.2.3-2 D.R. Abott, “Advances in Labyrinth Seal Aeroelastic Instability Prediction & Prevention”, ASME Paper 80-GT-151 of the “Gas Turbine Conference & Products Show”, New Orleans, La., March 10-13, 1980, pages 1-6.

7.2.3-3 H.L. Stocker, “Determining and Improving Labyrinth Seal Performance in Current and Advanced High Performance Gas Turbines”, AGARD-Paper CP-237, pages 13.2-13.22.

7.2.3-4 C.L. Broman, “Energy Efficient Engine, Core Engine Bearings, Drives, and Configuration, Detailed Design Report”, NASA-DR-165376, 1981.

7.2.3-5 M.A. Niemotka, J.C. Ziegert, “Optimal Design of Split Ring Dampers for Gas Turbine Engines”, ASME Paper 93-GT-116 of the “Inernational Gas Turbine and Aeroengine Congress and Exposition”, Cincinnati, Ohio, May 24-27, 1993, pages 1-10.

7.2.3-6 J.S. Alford, “Protecting Turbomachinery From Self Excited Whirl”, periodical “Journal of Engineering for Power”, October 1965, pages 333-339.

7.2.3-7 J.S. Alford, “Protection of Labyrinth Seals From Flexural Vibration”, periodical “Journal of Engineering for Power”, April 1964, pages 141-148.

7.2.3-8 J.S. Alford, ” Labyrinth Seal Designs Have Benefitted from Development and Service Experience“, SAE-Paper 710435, Proceedings of the “National Air Transportation Meeting” Atlanta,Ga. May 10-13, 1971.

7.2.3-9 J.S. Alford, ” Nature, Causes, and Prevention of Labyrinth Air Seal Fractures“, periodical “J. Aircraft”, Vol 12, No. 4, April 1975. page 313-318.

7.2.3-10 J.S.Alford, “Protecting Turbomachinery From Unstable and Oscillatory Flows”, periodical “Journal of Engineering for Power”, October 1967, pages 513-528.

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