Table of Contents
23.2 Gears and spline couplings
23.2.1 Gears
Problems or failures at gears can, besides results of the drop
out of the power transmission, also trigger
dangerous loads at other components. Does it come to the
disruption of the power transfer, at least the outage of the function of following
components/equipmaent (e.g. control units, generators, stators, pumps), must be expected. With thisA; the chance of an engine
shut/failure down exists. Develop fragments
(e.g., of teeth), the likeliness is given, that these get
between the gear wheels in the failure region or neighbouring gears and trigger there extensive
secondary failures.
Even if it doesn't come to an outage, seemingly little
damages can act dangerously through the service or other influences (e.g., assembly, production). To these belong
exitations of vibrations, which also act over long distances (Fig. "Fracture by resonance vibration of grars"). Here especially the, for the aeroengine
operation, typical high-speed rotation
becomes noticeable. Therefore problems concentrate, in contrast
to the common engineering, rather on fatigue processes
as at overloads by shocks (forced cracks, forced fractures) and high transferring torques with a penetration of the oil film at the tooth
flanks (seizing/galling).
Gear failures and/or failures in causative connection with gears, demand targeted and
effective remedies. Precondition is an identification of the failure mechanism and its causes as certain
as possible. The experience shows, that for this, at gears are better chances as for anti friction
bearings. In contrast to these the likelihood is less, that the failure origin is no more analyzable due to
a damage by a pass on process or overheating with plastic deformations. Not less that is caused
from primary fracture surfaces which are in an analzable condition. This is often the cause, when
the fragment has been centrifuged, or if there are not yet fractured primary cracks.
Fig. "Increasing use of gears" (Lit. 23.2.1-1 and Lit.
23.2.1-2): For propeller drives, planet gears
are preferred. They must transfer high powers with lowest weight and smallest volume.
A special problem is the dissipation of the produced
heat in gear wheels and bearings. Even best performance efficiency produces in the range of `upteen' KW during transferring high power.
This problem will even icrease for future big geared
fans. The heat must be discharged to the highest
portion into the oil. The thermal and mechanical load of the oil demands
special oil properties (Fig. "Lubrication oils"). Even little disturbances of the oil flow can trigger catastrophic failures. Thereby the even load
distribution at the planetary gear wheels is an especial challenge. It is crucial for the life of the teeth flanks and
the bending stress at teeth the roots. For this it is necessary, to distribute the load equal on all
planetray gears. This requirement can be achieved with features, which permit a
self adjustment of the gear wheels. Therefore, depending from the design principle of the planetary gear, wheels on a carrier
or engaged with a static geared ring (hollow wheel) are floating, respectively mounted by means of
a hydrulic element.
Failures of planetary gears are type specific, corresponding with the weak points. Anyway
emerged failures can get instructional and point at highly loaded components. Also „minor“ failures like
break outs of tooth edges, lead to extensive secondary failures if the fragments get between the gears.
Tooth fractures, influenced by the material
at the flanks in the area of the pitch cicle, occur
during typical high loads, caused by fatigue cracks. It should be mentioned, relatively big gear wheels
of propeller gears are concerned. With the size, the required
material homogenity and cleanness is a problem. The tooth flanks are usually
surface hardened. So high strength can ve achieved
ond compression stresses can be induced. This increases the fatigue strength. Do anyway fatigue
cracks develop, they will start beneath the tooth flank (Fig. "Development of fatigue puittings"). In this case the cracss get first
visible, when they exit to the surface. Then they have already the size, which triggers the short-term
failing, caused from fast crack propagation to the critical crack length (forced fracture).
Failures by overload at planet wheels can be also the result of failures of the related bearings
(Fig. "Skidding by unsuitable bearing tolerances"). Then these failures are rather traced back at a changed engagement, as at forced fractures.
Weak points with the danger of fatigue are, be also
bores of the oil supply.
Lightning strike is a typical danger for the deterioration of planet gear wheels from
turboprop aeroengines (volume 1, Ill. 5.1.3-4). Here the blade tips of the propeller are the favored strike
area (volume 1, Ill. 5.1.3-3 ).
During circuit continuity, small arcs can develop. Concerned are the the tooth flanks, because they
are separated by an electrical insulating lubricant film, comparable anti friction bearings (Ill.
23.1.1-21). Weld puddles develop with notch effect, changes of the material structure (embrittlement, drop
of strength) and bell mouths (local load transmission). They form a weak point which triggers a
fatigue fracture.
For this reason, if there is the suspicion of a lightning
strike the instructions of the manual must be strictly complied. Mostly these go up to the
diassembly of the gear and the visual check of
potential affected components. To these primarily belong gear wheels. Not only their tooth flanks are suspect.
At planet gear wheels, also the races of the bearings (anti friction bearings, friction bearings) must
be checked most exactly for damages from a lightning strike.
Fig. "Abrasive and chips in starter generator" (Lit. 23.2.1-3, Lit. 23.2-4 and Lit. 23.2.1-5): Gears of aeroengines are accordant of the top of the gear technology of its time. the requirements for
- transfer of high power,
- high rotation speed,
- small volumes and
- low weight
Usually the toothing
is case hardened. For very high circumferential speeds and low transmission torques the teeth are nitrided.
For weight saving at gearshafts the inner rings of the bearings can be integrated (Fig. "Failures of gear wheels").
Gear boxes/casings consist of sand casting from aluminium alloys or magnesium alloys. These
have disadvantages which however can be controlled.
- Considerably different thermal expansions and elasticity (modulus of elasticity), compared with the gear wheels, complicate the exact adherence of the axis-centres of the gearshafts.
- Low fatigue strength demands according low loads.
- Because of the low static strength, the transfer of loads like at bolts and bearing seats must be carried out by steel inserts (volume 4, Ill. 16.2.1.7-6). This complicates the overhaul, because the inserts must be sufficient covered or removed before the paint stripping and etching processes.
- Corrosion susceptibility, especially of magnesium alloys, demands appropriate protection (volume 1, Ill. 5.4.1.2-9 ).
- The disposition of light metal alloys for porosity can require sealing measures (e.g., infiltration, volume 4, Ill. 15.2-9).
Primarily there are three applications of gears in aeroengines:
Accessory gear (sketch above) serves the drive of auxilary devices like generators, pumps (oil,
fuel) and at older aeroengine types, the mechanical/hydraulic control unit. These gears are driven by
bevel gears from a main shaft, usually the high pressure rotor (radialdrive). Contrary, through this
connection the starting process can occur. In the accessory gear itself spur gears are used.
Gears for the power output (output
side) serve at turbo thaft engines the power extraction.
Typical example are smaller aeroengines for helicopters (sketches middle). At two shaft aeroengines they
take the power over spur gears directly from the shaft of the power turbine. At single shaft engines there
is usually a clutch between. Also the gear has often simultaneously the function of an accessory gear
and drives the auxilary devices (Fig. "Fracture by resonance vibration of grars").
Reduction gear at starters are highly loaded and use mainly a planet design (Lit. 23.2.1-3 and
Lit. 23.2.1-4). They are covered in detail in Fig. "Reduction gears in starter motors".
Propeller gears, which are integrated in the aeroengine (sketch below), are covered in Fig. "Increasing use of gears".
Fig. "Reduction gears in starter motors" (Lit. 23.2.1-5): The use of reduction gears at
starters are designed for a relative short running
time. This is for the start procedure, till the automatic de-clutching when the
aeroengine ramps up autonomous. If the gear casing is not integrated into the oil system of the aeroengine, an
oil change has to be carried out, according to the maintenance manual (Lit. 23.2.1-5). The `waste oil'
must be controlled for unusual abrasive and
chips. If the starter, as normally, is mouted near the
gas producer also high surrounding
temperatures must be expected.
The gears of starters/starter generators are exposed to especially demanding operation conditions.
- Very high rotation speeds.
- Often the lubrication is not optimal e.g. oiltemperature unfavourable.
- Shocklike loads.
- Danger of overspeed and continuous loading, caused by failing of the clutch function. Thereby the starter will be carried along by the aeroengine.
- Failing of the valve from the pressure airsupply (Lit. 23.2.1-19) at devices with airturbine drives. The starter then contiues running without load (Lit. 23.2.1-19).
At malfunctions during decoupling (Lit. 23.2.1-20) or during stiffness of the rotor to drive (e.g.,
very cold surrounding temperatures, volume 1, Ill. 5.1.5-3.2), overload of the teeth flanks and
according features must be expected. To these belong „gray staining” (Fig. "Failure modes at gear wheels"), seizing/galling and
overheating at the driven/loaded teeth flanks.
Gear wheel failures develop also from failing
bearings (Lit. 23.2.1-20). Thereby the consequences
are not only limited to a failing of the starter, respectively skipping of the starting process. If gear
teeth fracture, fragments can penetrate the
casing and trigger extensive secondary failures (Lit.
23.2.1-19). The location of the starter in the region of the accessory devices can
- trigger electric disruptions and shorts.
- If leaks of fuel and oil develop, the danger of fires exists (Lit. 23.2.1-20).
Fig. "Failures of gear wheels" (Lit.23.2.1-9): Gear wheels of the aeroengine technology are frequently designed
as gearshafts with integrated shaft lugs. These take the function of bearing inner rings, sliding
surfaces for oil selas and coupling spline toothings. At bolted versions, flange connections are used.
These characteristics of the lightweight design, form
potential weak points besides the usual problems
of gears of the mechanical engineering.
The toothing can, besides the in Fig. "Gear wheels failure mechanisms" described load depending failures, hint at further failures.
Effect of foreign objects, mostly as secondary failures,
if a fragment (e.g., of an oil jet or a seal)
gets into the tooth engagement. This produces plastic
deformations. Thereby often form metallic
particles. In an extreme case, forced fractures of the teeth occur. The consequence is a catastrophic failure of
the whole gear wheel. Symptomes and
features of sucgh a failure are
- noticeable vibrations,
- Loss of oil at damaged seals,
- metallic particles/chips in the oil.
Before the wheel fails catastrophic, a limited failure can be identified at deposits on magnetic plugs and filters (Fig. "Ol filter helping for diagnistics").
Particles in the lubrication oil (Fig. "What deposits of magnet plugs can tell"). Concerned are contaminations, which also
trigger failures at anti friction bearings. These produce wear and fatigue pittings at the tooth flanks.
During oil shortage, because of the high circumferential speed, the direct danger of
seizing/galling damages exists (Fig. "Gear wheels failure mechanisms"), which in a short period of time, during heavy chip production, means
the outage of the toothing.
Material problems in the tooting are rather seldom. Concerned are:
- Grinding deteriorations (soft/overheated locations, cracks).
- Faulty surface hardening (too thin/unfavourable hardness profile, deviations of the material structure).
- For an inner crack formation by hydrogen embrittlement, especially small case hardened teeth with a small cross section are prone (Fig. "Tooth fracture by hydrogen enbrittlement", volume 1, Ill. 5.4.4.2-3).
- Contaminations/inhomogenities of the material. This danger rises with the size of the wheel (e.g., propeller gears) and the load.
Region of the geared rim: The lightweight design
of gear wheels from aeroengines causes thin
cross sections. This means for the membrane and the rim
a very low stiffness. Such a disk shaped
structure is extremely susceptible for disk
vibrations (Fig. "Tooth contact patterns at gears"). In such a case the rim can perform an
axial bending vibration. Thereby the outer edges at the tooth root are dynamically so high loaded,
that fatigue cracks develop. Do these propagate far enough into the rim, the
break out of whole segments, up to the separating of the whole rim occurs.
In the region of the gear rim caused by the production
stress corrocsion cracking (SCC) can
develop. It is about so called „burnishing
cracks“ (volume 1, Ill. 5.4.2.2-4 and volume 4, Ill.
16.2.1.8.3-11). This danger exists especially, when these zones have not been at all or not sufficient shot peened.
Further problems are grinding failures and
hardening failures (too soft, too hard, crack
formation, high internal tension stresses).
Vibration wear (fretting) in grooves of
damping rings: To damp vibrations in the appropriate area
in the inner side of a rim, a circimferential groove is applied. In it a slotted springy ring
(damping ring) is introduced which is pressured by the centrifugal force (volume 2, Ill. 7.2.3-7). The cross section of
this rings can be square (piston ring) or circular (wire ring).
Necessary for the function are friction
movements against the wheel respectively the nut/groove. Thereby markedly wear is possibly at
the ring and/or the the groove.
Weel membrane: Mostly fatigue
cracks are concerned. They can develop during dynamic oveload
with unusual heavy membran vibrations. Typical causes are
- unfavourable engagement conditions,
- damages of the toothing or
- failing of the damping.
Production caused failures from which fatigue cracks start are
- burnishing cracks,
- cracks by hydrogen embrittlement,
- Welding failures (Fig. "Gear wheel fracture by welding failure", volume 4, Ill. 16.2.1.3-32).
- Hardening failures (e.g., soft areas, crack formation, internal tensile stresses).
Bearing supporting shaft attachments can be formed as welded joined
integral bearing rings or as bearing
seats. The race of integrated bearing seats underlay the failure mechanisms of anti
friction bearing inner rings (chapter 23.1.1). With convenient design and arrangement from experience,
the weldseam (electron beam welding, friction welding, volume 4, Ill. 16.2.1.3-32) is sufficient
fail-proof. At slided on inner rings, with an unsufficient tight seat and/or too large elastic deformation of the
shaft (e.g., bending), fretting wear and
loosening is possible.
Sliding surfaces of shaft seal rings run in by wear (form a groove) during long operation times.
This indeed influences the function acceptable, however demands a repair during overhaul. Usually
the sliding surface will be grinded (Fig. "Problems of radial sealing rings"), coated/plated (hard chromium) and dimensional
ground. Is the surface befor the chrome
plating not sufficient shot peened, the
danger of burnishing cracks (stress corrosion cracking=SCC) below the chromium layer in the base material exists (volume 4,
Ill. 16.2.1.8-3).
Spline toothings are usually located at gear wheels
in der hollow shaft. During unsufficient
lubrication and(or too large vibration movements,
they can wear in a so heavy, that
failing/overrun occurres (Fig. "Damage influences at multispline shafts" and Fig. "Problems by changing a proven spline surface").
Are the gear wheels burnished, the danger exists, that cracks develop by SCC in the
serrations of the spline toothing. Then a sufficient certain non destructive proof is no more possible. This applies
also the usual penetrant inspection or magnetic testing, used at gear wheels.
Fig. "Gear wheels failure mechanisms" (Lit. 23.2.1-6 and Lit.
23.2.1-15): At the teeth of gears different
failures, respectively failure mechnisms can occur. They can be specified as component specific load limits. For this
a diagram serves, in which the threshold torque versus the circumferential speed is shown.
The pitting threshold rises with the
strength of the tooth flank. Pittings are
fatigue break outs in the contact zone, i.e. at the pitch circle (detail right, Fig. "Development of fatigue puittings"). They can be compared with the
race fatigue at anti friction bearings (Fig. "Fatigue pittings at bearings"). The pitting threshold is basis of the
gear wheel life time. It rises with the circumferential,
respectively the relative speed of the tooth
flanks, in the region of the load transfer. The reason is a bearing and separating lubrication film. It forms during
sufficient high sliding velocities and enables an EHL (elastohydrodynamic lubrication , Fig. "Micropittings and life time").
The wear threshold is in the region of
low circumferential velocities. It comes to mixed friction
with metallic contact and abrasion. The threshold torque, from which a failure occurs, rises after a
minimum steep with the circumferential velocity. This may be seen in connection with the formation of a
favourable sliding film. The wear threshold may only be important during
run-up, because of the typical high circumferential speeds of the gear wheels in aeroengines (e.g., start). A deterioration takes place
above the pitch circle (detail left).
The threshold of seizing/galling is established at high torques and high circumverential speeds. In
this region the torque produces such high teeth forces, that the
loading capacity of the lubrication film is no more
sufficient. It will be penetrated and metallic
contact at high relative velocities occurs.
The consequence are locally weldings
/seizures which are forced separated. Radial scratches/grooves
form, which increase to the tooth tip (detail right). The failure mechanism explains, why the
threshold torque drops significant with the circumferential
speed.
The fracture threshold is reached, when the
fatigue limit of the tooth is surpassed (Ill.
23.2.1-5). Critical load is the pulsating tooth bending. The crack plane is located near the root, depending
from the tooth geometry and strength (detail right). It drops only slight with the circumferential speed and
determines for relevant operation speeds the threshold torque
of gear wheels with hardened toothing.
A failing by forced fracture occurs from unusual high loads during secondary failures. Thereby it can
be about foreign object damage (FOD, OOD), shocklike loads and extreme torques (e.g., after
bearing failures).
„Grey staining” (Lit. 23.2.1-21) is a fatigue failure in the surface region (Fig. "Development of fatigue puittings"). It was
first about 1975 conciously identified at case hardened, ground tooth wheels of turbo gears. A
generally usable certain calculation is obviously yet outstanding. Grey staining develops during mixed friction
at the tooth flanks. Will the fatigue limit (under pulsating stresses) be surpassed at the roughness tips by
a metallic contact, the development of micro pittings
will occur and with this the grey staining.
Especially endangered are the flank regions with negative slippage below the pitch
circle. Typical is a grey zone with wear (scour), which begins in the root region and grows to the pitch circle. Microscopic (SEM)
the surface is cliffy with axial oriented micro deteriorations (mikcro pittings). Gray staining is governed
of several, connected influences.
- Oil composition/condition.
- Flank roughness.
- Toothing geometry.
Fig. "Development of fatigue puittings" (Lit. 23.2.1-9 and Lit. 23.2.1-10): The so called
„pitting formation“ is at high-speed gears of the aeroengine technology the life determinant
factor. Concerned is vibration fatigue of the tooth flanks. It is compearable with fatigue cracks and fatigue out breaks/pittings at the race tracks
of anti friction bearings (Fig. "Fatigue pittings at bearings"). Independent, if due to load a crack starts from the surface
or beneath, the crack growth accelerates if
surrounding air and lubricant have access. Supporting
acts the pumpeffect of the crack during the load cycles. Thereby act several effects which will be
later discussed in the illustration text.
Failure modes:
In most cases the pitting formation begins first at the driving wheel
(bevel). The favoured position of the fatigue cracks usually is located
in the region of negative slippage. Here the circumferential speed by the slippage is lower as at
the mating wheel. This condition exists nearer the tooth
root (sketch below). There the cracks begin
shallow and deepen accelerating to the pitch circle. Usual are several parallel orientated cracks (sketch above).
At case hardenings, as they are usual at toothings in the aeroengine technology, form
large-scale connected pittings. This can be explained with the failing of the less strength from the base material
in the area of the detached hardening layer, after the beak out of a pit. At a case hardening, the bottom
of the pit is heavily cliffed. Here, microscopically,
firmly sticking beads with a smooth surface and
the chemical composition of the base material, can be observed (Fig. "Spherical oil contaminations"). It is under
consideration, if these develop by dispersing inside the crack, or if these are slugs from locally „temperature
flashes”. Are such beads found in the
oil, they are a hint at an advanced fatigue process in the pitch surface.
The vibration load gets failure effective with the periodic tooth load during every wheel
turn.Two types of stresses develop from the friction forces between the tooth flanks. A
shear stress and the hertzian stress. They codetermine, if the cracks start directly from the contact surface
or below. For the forces, the lubrication
conditions and the relative movements between
the tooth flanks play the essential role.
The decline of the crack relatively to the tooth flank
is similar to the race surfaces of the anti friction bearings (Fig. "Stresses between rolling elements and race"), determined
from the relation of friction forces/shear
forces and compression forces.
At high relative velocity between the load transferring tooth flanks, the separating
lubricant film can induce overloading tensile stresses. These can
surpass the fatigue strength of the tooth flanks in the micro
region (see `grey staining', Fig. "Gear wheels failure mechanisms" and Fig. "Gray staining of turbogears").
The pressure distribution in the lubrication gap is very different, similar to a friction bearing.
Thereby the hydraulic pressure, especially for high speed gear wheels can locally drop as far,
that cavitation occurres (volume 1, Ill. 5.3.1-11.2). This reinforces the fatigue deteriotration process.
With the mechanical loads, further effects act:
During the fatigue process the metal is activated and oxidises
increasingly. So obviously oxide nests can form
below the surface (inner oxidation).
In connection with aging processes in the lubricant (Fig. "Formation mechanisms and oil coke features") and/or from
contaminations like water (Fig. "Problems by water in lubrication oil"), hydrogen
can develop and diffuse into the material (volume 1,
Ill. 5.4.4.1-3). A thereby developing embrittling effect can also promote the crack formation.
Influences at the pitting formation:
- Crucial is the fatigue strength in the region of the tooth flanks. This depends decisive from the homogenity (fine material structure) and cleanliness of the material. An essential influence has the heat treatment, expecially the surface hardening.
- The internal stresses in hight and distribution act together with the operation determined stresses. So the resulting stress can vary as well in height as also in distribution. To aspire are compression stresses. These can be obtained with a surface hardening like the case hardening (Fig. "Start of cracks from inside") and/or with shot peening (volume 4, Ill. 16.2.1.6-5 and Ill. 16.2.2.4-11).
In the lubrication gap, friction heat develops. It heats locally the tooth flank. Thereby, near the
surface, thermal stresses arise.
Toothing properties and service conditions
are important for the behaviour.
- The design conforming tooth form influences by the conditions in the lubrication gap the load transfer.
- The dimensional accuracy of the tooth geometrry decides about the bearing surface. Correlates this rather a point contact rises the maximum stress and approaches the surface.
- The surface quality of the tooth flanks essential influences processes in the lubrication gap. A higher roughness promotes mixed friction and with this deteriorating peak stresses in the micro region (Fig. "Gear wheels failure mechanisms" and Fig. "Influence of lubrication gap at lifetime"). This applies especially for start procedures and unfavourable oil condition (high temperature, decreasing bearing capacity, contamination with water etc.). With With lower roughness the pitting formation also decreases.
- Service conditions act indirectly at the material loading through the lubrication condition. A higher load acts in two ways unfavourable. The forces at the tooth increase and the lubrication gap gets tighter.
A rise in the rotation speed respectively the circumferential speed triggers counter effects: Positive is, that the lubrication film becomes thicker. Besides this heat is produced. With this the temperature in the lubricant film rises. This lowers the viscosity and so its bearing capacity, the lubrication film gets thinner.
- The lubrication oil influences the pitting formation through the processes in the lubrication gap. The relevant maximum shear stress in the tooth flank decreases first with a growing film thickness (up to about 5µ), but then markedly rises. This optimal, design according viscosity and with this thickness of the lubrication film, should aspired for the elasto hydrodynamic lubrication condition (EHL).
Additives in the oil (Fig. "Micropittings and life time" and Fig. "Mechanisms of rolling wear") can have a considerably effect at the pitting formation. Especially important for gear wheels are chemically acting
- extreme-pressure (EP-) components,
- Wear decreasing additions (anti-wear = AW).
These can act absolutely different at the wear. They react with the material of the tooth flanks and enable a controlled abrasion. i.e. they improve the surface finish.
Fig. "Start of cracks from inside" ( Lit. 23.2.1-2 and Lit. 23.2.1-15): At
surface hardened gear wheels (case hardened, nitrided) frequently can be observed during vibrtion fatigue the crack origin below the hardening
zone. Below the flank surface, thereby play non metallic inclusions as weak points (imperfections, inside
the specifications) or flaws a crucial roll. They are limited from the specified and to be kept
degree of purity. This complies reasonable with the
sufficient safe limit of the non destructive testing
method. Less safe is a failure limitation by monitoring the rough material production.
Appear at several, especially neighboured
teeth fatigue cracks, then this indicates a
high service load as main cause. In such a case in the crack origin rather weak points than failures are to expect.
There are soft inclusions (e.g., manganese sulfides) with low nothch effect and
hard/brittle inclusions (e.g., aluminium oxide/alumina)
with high notch effect. Also internal stresses, which form during
the heat treatment as effect at the fatigue crack initiation must not be neglected. They arise because
of different thermal expansion of the matrix from the base material aroud the inclusions.
An important influence at the development of
inner cracks obviously has hydrogen. It can be
supposed, that it forms during the diffusion in the case hardening process or nitriding and gets so into the
material. The compression stresses in the case hardening layer
hinder the escape by diffusion, respectively make a desembrittlement more difficult. Hard particles (e.g., carbides or aluminium oxide in
mitriding steels) with high notch effect
widen the lattice under tensile stresses in the inner of the tooth. Here
the hydrogen diffuses and recombines. Over longer operation times,
inner brittle cracks occur. At the beginning, this zone with typical micro features for hydrogen embrittlement (volume 1, Ill. 5.4.4.1-2),
is positioned concentric around the origin (Fig. "Tooth fracture by hydrogen enbrittlement"). Gear wheels in aeroengines, with typical
small/slim teeth, are especially predestined for such failures. This can be explained with, for a stress
balance necessary, high tension stresses in the
inner. For this the relative thick compression zone of
the hardnening layer is responsible. Typically the incipient cracks are located in the inner of the tooth
cross section near the neutral fibre/axis. This excludes a too high operation load (bending stresses) as cause.
Fig. "Failure modes at gear wheels" (Lit. 23.2.1-8): In this schema and in the following text
typical failure types/modes at tooth wheels are discussed. The
failure appearance is shown in the illustrations 23.2.1-8.1, 23.2.1-8.2, 23.2.1-8.3.
Tooth fracture failures: Fractures of the whole tooth
in the root area lead in the most cases to
extensive secondary failures. Than a failing of the whole gear must be expected. In contrast
break-outs at the tooth edges or spallings at the tooth tip trigger rather no spontaneous failing.
Forced fractures are mostly secondary failures from damages and/or overload. They develop
through foreign objects between engaged teeth. Typical are features of a bending overload. The fracture
surface of high strength materials mostly appears brittle. However, if not embritled, it is micro
ductile (microscopical provable in the SEM). There are shear planes at the component surface.
Surface hardenings (case hardening, case nitriding) can emerge at the fracture surface.
Fatigue fractures (HCF, LCF) usually show a macroscopic pronounced structure with arclike,
concentric to the fracture origin positioned beach
marks (lines of rest). The residual
fracture then occurres as forced fracture, mostly with pronounced shear planes to the surface. The relation of the residual
fracture surface to the fatigue crack area permits an estimation of the load of the gear wheel. Dark
discoloured zones of the fatigue fracture are caused by
fretting wear (`friction rust') and/or oil
residues. The crack origin usually is located at the surface of the tension side of the bending loaded tooth. However
there are cases, where the fatigue fracture starts from a flaw, respectively incipient crack
(hydrogen embrittlement, Fig. "Tooth fracture by hydrogen enbrittlement") far inside the cross section of the tooth. In this case the crack may
develop accelerating in the direction of the tensile zone, i.e. the loaded tooth flank.
Pittings are pit like break-outs on the bearing tooth flanks (Fig. "Gear wheels failure mechanisms"). Mostly they are
located beneath the pitch cycle. Running-in pittings
(see `grey staining') develop in contact zones of
mixed friction („hard bearing areas“) after the
first bringing into service. The usual running-in wear
leads to an even bearing of the flanks. After this process running-in pittings increase no more.
In this connection the, frequently in the specialist literature so called
`grey staining' must be mentioned („micropittings”, Lit. 23.2.1-17). Concerned are grey appearing zones. Mostly these proceed over
the width of the contact area and are displaced to the tooth root. Mikroscopically these can be identified
as fatigue caused tiny break-outs. Preferred they appear in
case hardened tooth flanks during loads below the formation of macroscopic fatigue break-outs. With this
mechanism correlates the mechanism of the running-in
pittings on race tracks of anti friction bearings (Fig. "Mechanisms of rolling wear"). Grey staining
is promoted by
- high load,
- high slippage velocity/circumferential speed,
- unsufficient bearing capacity of the oil film.
These conditions are rather to expect in highly loaded
starter gears (e.g., planetary gears, Fig. "Reduction gears in starter motors").
Proceeding pitting formation decreases the bearing flank area and
so increases the flank load. Additionally it means a
dangerous notch effect. Both influences favor fatigue fractures.
Flank peelings, flakings appear at surface hardened teeth.
Gas nitrided gear wheels show, instead pronounced pitting formation, a
peeling of the tooth flank. Rather there can be found sharp edged splinterings. Gas nitriding layers wear with gradings up
to about 10µm by overloading or vibrations. These also lead to
ripplet flank wear, transverse to the direction of
sliding/slippage, e.g. in radial direction.
Case hardenings and induction hardenings
get a spill like appearance.
Wear is named as normal, if merely a smoothening of the tooth flanks occurs. Cause is the
removal of roughness tips during mixed friction.
Heavy wear is called, if already the tooth flange geometry
is markedly changed. It develops during lubricant shortage or unsuitable lubricant.
Grinding wear forms under the acting of hard abrasive particles in the oil.
Seizing/galling: The initial stage shows
scratches in the direction of the sliding
movement. Does it come to a halt, we speak of `running-in seizing'. The grooves in the range of 10 µ depth form. In
the final stage streaky roughenings develop. At first tooth root or tooth tip are
concerned, because in the region of the pitch cycle the lubrication film forms best.
Plastic deformations can be observed during high overload e.g., a
shock load or extreme gear vibrations
(flutter). The failure mode are rippled deformations of the tooth
flanks. Thereby often form burrs at the tip and the faces
surfaces.
Surface cracks, as far these arn't production caused (hardening cracks, grinding cracks), form
during overload with plastic deformations of a surface
hardening.
Annealing can be traced back to extreme heat production (oil deficiency, overload). The
toothening shows annealing colours (mostly blue). The hardness has dropped. Frequently seizing and
plastic deformations can be observed.
These annealing colours must not be confused with production caused usual discolourations of
gas nitriding layers.
Corrosion arises during storage with unsufficient corrosion
protection. Rusting will occur. Vibrations during stand still produce fretting corrosion with the development of puce stains (Fig. "True and false brinelling").
Here oxygen from the atmosphre and/or condensate acts. This is supported from the air expansion
cycles during temperature changes. This produces o pump effect in the gearbox.
Electrical continuity (lightning) during operation, produces in a very short period of time small
weld puddles like at anti friction bearings (Fig. "Bearing failure by lightning strike"). Over a longer period of time, e.g., during a
short in the generator (Fig. "Bearing failure by electric continuity"), circuit conttinuity leaves at the loaded flank a broad
zone similar to sandblasting („frosting“, Fig. "Electrically caused bearing failure"). This consists of many microscopic small craters.
Overheating features like `recast layer' and drop of hardness in the deterorated zone ensure the confirmation.
Cavitation also produces zones which appear like sand blasted and can be easy
confused with electrical continuit. It can
also arise at the unloaded flank. Microskopical (SEM) a differentiation is
possible because the bottom of cavitation pits is more smooth. Also the deteriorated zone shows no features
of overheating. In the final stage, the toothing will be damaged from abrasion.
Fig. "Operation marks and damages on gears 1", 23.2.1-8.2, 23.2.1-8.3 (Lit. 23.2.1-8 and
Lit. 23.2.1-11 up to -13): In these illustrations it
is attempted to enable the practitioner a first evaluation of
toothening failures. An exact description of failures contain Fig. "Gear wheels failure mechanisms"
and Fig. "Development of fatigue puittings". So the understanding of informations in the
overhaul manual and specifications should be easier. In cases
of doubt, basically an expert, respectively the OEM should be consulted and
approached according to the instructions.
Fig. "Tooth contact patterns at gears" (Lit. 23.2.1-2, Lit. 23.2.1-8, Lit. 23.2.1-9 and Lit. 23.2.1-15): The sketches show
typical tooth contact patterns at spur-toothed and skew gears. The upper half of the sketches shows the
aktive flank (loaded flank). The sketches below shows, respectively the rear side. The
counter wheel is supposed accurate.
Contact patterns are itself no failure/damage. They develop on the tooth flanks in the region of
the engagement, i.e. normally around the pitch cycle. The
contact track usually appears
bright because of micro deformations of the roughness tips. Exists an initial deterioration, similar running-in
pittings (grey staining, Fig. "Failure modes at gear wheels"), this can appear
dull. Contact patterns can allow important
conclusions in the context of problem
analysis.
Typical causes for contact patterns which deviate from the
optimum:
- Differences in heat expansion between casing (light metal) and gear wheels (steel). Thereby a change of the centre distance or the alignment of the gear shafts can become appearent.
- Elastic deformations of the light metal casing because of the low stiffness (modulus of elasticty/Youngs modulus).
- Elastic bending of gear shafts by unbalances or under high transfer torques. Thereby the one-sided acting force at the gear rim becomes noticeable.
- Unsymmetrical force application by a worn spline toothing of the shaft coupling (Fig. "Material caused wear at a spline coupling").
- Assembly depending problems like the local damage of tooth flanks. Bending of the shaft during the axial push together of the toothening (Ill. .2.1-17).
- Loosening of screw joints (fretting) from a wheel with flange-mounted shaft.
- Production failure as dimension fault and geometry deviations. From experience, such causes are in the aeroengine engineering rather unlikely.
- Vibrations which run relatively to the gear wheel and lead to a markedly deflection of the rim. They are either the result of unusual heavy exitation and/or the breakdown of the damping ring, e.g., the fracture of the damper ring (Fig. "Vibration fatigue at gear wheels").
Faulty contact patterns caused from seemingly minor deviations, can trigger in the high speed
accessory gears dangerous vibrations (toroidal modes, disc modes). The tooth frequency is very high and
reaches the ultrasonig range. Accordingly high are the
resonance frequencies which can be excited.
Concerned are vibrations of higher modes (Fig. "Vibration fatigue at gear wheels"). This causes, that already tiny deflections
correlate dangerous high vibration stresses (volume 3, Ill. 12.6.3.1-7).
Gear vibrations can proceed through several gear
chains. So in seemingly independent
components, especially in the region of accessory gears, failures can be triggered (Fig. "Fracture by resonance vibration of grars"). About this,
here some examples:
Accessory devices:
- Fatigue fractures at blades of turbopumps and rotors of blowers/compressors (Fig. "Damages from exitation by tooth flanks").
- Erratic electrical voltage of generators. Effect at elektronical devices like control units (Fig. "Bearing failure by Interaction with accessories").
- Malfunctions of mechanical control units.
- Increased vibration wear (fretting, Fig. "Damage influences at multispline shafts") up to the separation of spline toothings of couplings from the drive shafts of the accessory devices (Fig. "Material caused wear at a spline coupling").
- Fatigue fractures of components from the main shafts/rotors. Triggering of dangerous, high frequency disk vibration modes. Known are also cases, which can be brought in causative connection with the fracture of centric tension bolts (Fig. "Fracture by resonance vibration of grars", volume 2, Ill. 6.3-3).
- Fractures of shafts and gear wheels, caused by vibrations, which are induced through a power drain (Fig. "Vibrations caused by the test rig").
Fig. "Vibration fatigue at gear wheels" (Lit. 23.2.1-2): High speed
gear wheels are extremely prone for
vibrations. To control this, gear wheels are equipped with a
friction damping. The location must be choosen
at a suitable point, according the vibration mode which must be dampened (volume 2, Ill. 7.2.3-7 and Ill.
7.2.3-8). These are zones of the componet, where a relative movement as large as possible, between the
wheel and the damping contact surface can be expected.(sketch below). Usually
springy slotted rings in a circumferential groove are concerned (detail below).
So always first the failure causing vibration mode must be
identified. This can be carried out by a test on a electro dynamic shaker at not too high frequiencies. Very high frequencies can afford special
test setups like air sirens. Also the use of computers can be helpful.
Criteria are the primary fatigue crack
zones. Promising are thereby measurements of stresses with strain gauges. The evaluation of the
exitation risks takes place with help of the so called
Campbell Diagramms (volume 3, Ill. 12.6.3.4-1).
Gear wheel vibrations are usually, according to the tooth frequencies, very high frequency. This leads
to high order modes of disk vibrations (several nodes, right sketch).
Especially at bevel gear hollow shafts, failures caused by vibration fatigue arose (sketch above left).
Dangerous gear wheel vibrations can be already triggered from very small irregularities in
the engagement, during unsufficient damping. To this also belong damages from the assembly like
tiny ridges at the tooth flanks (Fig. "Damages from exitation by tooth flanks").
Dual tilted shafts are used at test rigs
for the simulation of a power drain with the
connection of auxilay drives from aeroengines in the fuselage of fighters. For this the shafts need
interconnected flexible couplings. Fore example this can be
cardan joints (Ill. 24-1.2) or couplings with a
flexible intermediate member (rubber, sheet metal lamellas). Already during slight
elbowing, angular accelerations during rotation can induce dangerous vibrations into the gear wheel system up to
the accessory devices.
Fig. "Fracture by resonance vibration of grars": The assembly technique of the centeric tension
bolt from the gas producer turbine of this helicopter engine was
changed seemingly without risk. With this it should be prevernted, that
this touches the bore wall in the hub of the turbine wheel of the 1st gas producer stage. So strength
decreasing fretting schould be avoided in this extremely high stressed zone. However, over years already no
failure which had emerged, was triggered from fretting. Therefore this was a precaution measure. To
prevent the touching, the tension bolt was more precise than usual centered during assembly of the rotor.
After about one year in service with this change at several aeroengines occurred
fatigue fractures in the tension bolt. An investigation showed as failure cause an
extremely high frequency resonance
vibration of the tension bolt (volume 2, Ill. 6.3-3). This had been possible, because the
damping of the bolt failed due to the new assembly
technique. Obviously the vibration was transfrered from the output
gearbox through the shaft system. In one case a
suboptimal contact pattern of a gear weel could be seen.
This was caused from the assembly, but absolutely acceptable. At the former assembly technique,
obviously the contact of tension bolt and turbine wheel damped unknowigly such inevitable exitations. After the
reintroduction of the `old' assembly technology, no such failures occurred any more.
This example reveals, that also typical extremely high frequent vibrations orginating from the
gear wheels can be transferred through the gear chains and shafts to remote regions. Even, when at the
first sight, there is no connection.
Fig. "Damages from exitation by tooth flanks": The oil cooler of a small gas turbine is feeded with the air from a
blower. The used blower wheel has a diameter of about 12 cm and a rotation speed of about 20 000 r.p.m. The
drive takes place with a chain of gears. The wheel consists of pressed thermosetting
glass fibre reinforced resin. This material was choosen because of
its high inner damping and good fatigue
strength. Before, the wheels have been milled from a high strength aluminium alloy. Its blades suffered frequently
fatigue fractures. After a longer time since the introduction of the reinforced plastic wheels, also a
fracture occured. A segment from the bladed rim was centrifuged. The investigations allowed to conclude at
a fatigue fracture.Vibration tests on an elektrodynamic exciter (shaker) pointed at an extremely
strong vibration exitation with a very high frequuency. As probable
vibration exitation, a small mechanical produced bulging at the flank edge of a gear wheel was
identified (detail). It may be formed during an assembly, a few operation hours before.
This example gives an impression from the extremely intense vibration exitation, caused from a small nonuniformity respectively damage of a gear wheel.
Fig. "Gear wheel failure by lightning strike": It shows the apparance of a damage from a lightning strike (volume 1, Ill. 5.1.3-3 and Ill. 5.1.3-4). Remarkable is the coinciding position of the weld puddles, produced by the arc during the electric circuit at the neighboured teeth.
Fig. "Tooth fracture by hydrogen enbrittlement": After longer operation periods, (ca. 1000 hours) it came in several cases at the bevel gears of the radial drive (tower shaft) of the accessory gear to tooth fractures (sketch right). Get these fragments into the toothing, it came to dangerous failures with shut down of the aeroengine. The investigation showed, that fatigue fractures are concerned, which started fom an embrittled zone inside the tooth. The structure of the fracture at the incipient crack showed typical features of hydrogen embrittlement (volume 1, Ill. 5.4.4-2). The hydrogen diffuses into the material during the case hardening and lead over a long period of time to delayed crack formation. With sufficient crack size the fatigue crack occurred. As remedy all gear wheels are checked with a special ultrasonic testing during every overhaul. Thereby several cracks could be identified in time and the wheels scrapped.
Fig. "Gear failures by burnishing cracks": Burnishing cracks
in gear wheels are known and formidable since long time.
Concerned is a type of stress corrosion (causic embrittlement, volume 1, Ill. 5.4.2.2-4). Therfore, now some
OEM forbid, at least during overhaul, the use of this process.
In the example above, it came to the cracking
in the region of the inside located spline
toothing (Fig. "Failures of gear wheels"). From this, during service, a fatigue crack started. In the shown case it was identified due
to vibrations, before the complete failure of the wheel. In other cases, the wheel fractured and
separated the drive. The consequence was the overspeed of the gas
producer with the fracture of the turbine
wheel (volume 1, Ill. 5.4.2.2-4).
The example below shows the failure of a bevel gear to the radial shaft (tower shaft). In this case
in the shaft accretion a fatigue crack started from a
burnishing crack. Such burnishing cracks
developed expecially frequent during overhaul. Concerned from the cracks have been ground and
chromium plated wear surfaces (volume 4, Ill. 16.2.1.8-3). The burnishing cracks formed under the
chromium layer. These have been sliding surfaces of the sealing lip from a
radial seal ring (Fig. "Problems of radial sealing rings"). A preventing protection against cracks is
shot peening of the grinding surface before the
chromium plating. The compression stresses protect the repair zone from the effect of the burnishing bath,
which can penetrate through the typical cracks in the chromium layer to the base material.
Fig. "Gear wheel fracture by welding failure": Welding joints at gear shafts
(sketch left) are potential weak points. Therefore these are positioned, if possible, in less high loaded zones. The
intense process monitoring and the non destructive testing from experience guarantees
the quality. So with sufficient certainty, dangerous flaws can not get to the assembly.
In the shown case, it came during the development phase to a fatigue crack at a
flaw (incomplete fusion, detail) of the elektron beam
weld in the disc membrane (volume 4, Ill. 16.2.1.3-32).
Fig. "Assembly fault causes gear wheel fracture": The experience teaches, that obviously during the assembly of a gear, an increased risk of a dangerous damage of a gear wheel exists (bath tub curve). A critical phase exists, if gear wheels must be axially pushed for latching. Do thereby the faces of the tooth collide they can be damaged (sketch left). Above this, a high bending moment can plastically bend the shaft. In the shown case, at the accessory gear of the mounted aeroengine, assembly work was done. This took place at the drive shaft from the scavenge pump, mounted at the front of the aeroengine. Visibility and accessibility have been hindered during this work. During assembling of the cover together with the gearshaft it came to the contact of the gear faces. This was not noticed because the gear wheel was very slim. So, also the gap between cover and casing was not identified as unusual. The gap was closed with the tightening of the flange bolts. Thereby the filigree shaft was unnoticed bend, before the gear wheels „snapped in place”. During a flight, the shaft fracturend, corresponding the deformation with a onesided bending fatigue fracture. The fighter airplane was destroyed during emergency landing (Ill. 19.1.4-5.2). A failure investigation could clear the described cause. During an inspection of the airplanes with the same assembling process, sevreal further cases have been found. The bend shafts could be exchanged before failing.
Fig. "Gear pump failures" (Lit. 23.2.1-16): Gear pumps
take a special position under the gears. Different to
gears they seve the delivery of a fluid/liquid (oil or fuel). From experience these are extremely
fail-proof components. However, they are endangered besides from function caused problems, especially
from secondary failures. These are traced back to primary failures of other components. Thereby the
oil system (Fig. "Oil system components") differs from the fuel system by a closed loop with a circulating medium (Ill.
22.2-18 and Fig. "Identification of water in fuel"). So time dependent effects like aging, coke formation or wear can increase over
the time and trigger „creeping
failures“ in the pump. Even if filters and sieves can withhold
dangerous foreign objects, still the danger exists during a disturbance of the oil flow. For example, if the
pressure is lowered, cavitation damages can occur.
Rises the pressure behind the pump, accordingly increases the mechanical load. This can lead to
ovreload failures. Typical short time effects are seizing/galling of the teeth flanks
or LCF fatigue fractures at the tooth
root. Long time effects are abrasion, forming of fatigue pits at the tooth flanks or
HCF vibration fatigue.
The toothing is endangered from foreign objects. At sealing gaps and bearings a self-energizing
failure by jamming during unacceptable heating
can occur in very short time.
Fig. "Influence from a gear at the operation" (Lit. 23.2-18): Sensor data will be combined for analysis with
vibration readings (mearuring of acceleration and frequency) in a
computer based analysis (e.g., DPTOCC, Fig. "Engine health management"). So,
features of the gear due to design will be included. With this, informations about the conditions are
possible. This enables conclusions at wear, fatigue and fracture.
From the OEM specified limits decide about an
exchange.
Besides vibration based analysis, further
symptoms, expecially on site, can be evaluated from
an experienced practitioner:
- Oil leaks.
- Traces of overheating.
- Wear/damages (e.g., seals, multisplinetoothings, Fig. "Damage influences at multispline shafts"; tube clamps, Fig. "Causes of pipe line vibration").
- Chips at magnetic plugs and sieves/filters.
References
23.2.1-1 L.Kerber, „Deutscher Start für eine sowjetische Triebwerksepoche, Das
PTL-Triebwerk Kusnezow TW-2”, Zeitschrift „Fliegerrevue“, Edition 06, 1996, 6 pages.
23.2.1-2 C.Albrecht, J.Mack, „Drive System Technology Advancements”, Zeitschrift „Journal
of the American Helicopter Society“, April 1981, page 18-24.
23.2.1-3 I.E.Traeger, „Aircraft Gas Turbine Engine Technology, Second Edition”, Verlag :
Glencoe/McGraw-Hill 1994, ISBN 0-07-065158-2, page 307-321 and 559-562
23.2.1-4 „The Jet Engine“, Rolls-Royce.plc. 1986, 994, ISBN 0-902121-2-35, Ausgabe
1996, page 81 and 121-128.
23.2.1-5 M.J.Kroes, T.W.Wild, „Aircraft Powerplants, Seventh Edition”, Verlag :
Glencoe/McGraw-Hill 1990, ISBN 0-02-801874-5, page 354, 367, 372, 470.
23.2.1-6 J.Broichhausen, „Schadenskunde, Analyse und Vemeidung von Schäden in
Konstruktion, Fertigung und Betrieb“, Carl Hanser Verlag München, 1985, chapter 10.
23.2.1-7 T.E.Tallian, „Failure Atlas for Hertz Contact Machine Elements”, ASME Press, ISBN
0-7918-0008-3, 1992.
23.2.1-8 Allianz Versicherungs-AG, „Allianz-Handbuch der Schadenverhütung“, 3. Auflage,
1972, page 388-410.
23.2.1-9 V.Krüger, W.J.Bartz, „Untersuchungen des Einflusses moderner Schmierstoffe auf
die Pittingbildung bei Wälz-und Gleitbeanspruchung”, Abschlussbericht, Forschungsheft 39
der Forschungsvereinigung Antriebstechnik e.V. 1976.
23.2.1-10 L.Engel, H.Klingele, „Rasterelektronenmikroskopische Untersuchungen von
Metallschäden“, 2. Auflage, Carl Hanser Verlag München Wien 1982, ISBN
3-446-13416-6, 160,161, page 149-150, 158, 159.
23.2.1-11 H.Huppmann, „Aus Schäden Erfahrungen sammeln - Fehlerquellen und
Fehlerstatistik, Übersicht über Schadensarten an Zahnrädern”, Zeitschrift „asr. Digest für angewandte
Antriebstechnik“, Heft 1, April 1973, 1. Jahrgang, page 53-56.
23.2.1-12 P.Lynwander, „Gear Drives for Turbomachinery” in J.W.Sawyer,
„Sawyer's Turbomachinery Maintenance Handbook“, First Edition, 3. Band, page 11-1 up to 11-22.
23.2.1-13 Metals Handbook Ninth Edition, „Volume 11 Failure Analysis and Prevention”,
Verlag ASM, ISBN 0-871170-007-7, Kapitel von L.E.Alban„Failures of Gears“, page 586-601.
23.2.1-14 „Gear Design, Manufacturing and Inspection Manual, Design Guidelines for
High-Capacity Bevel Gear Systems”, AE-15, SAE, page 112-121.
23.2.1-15 J.Holland, „Zur Schmierfilmausbildung bei Evolventenverzahnungen“, Zeitschrift
„Schmiertechnik + Tribologie” 29. Jahrgang, 5/1982, page 195.
23.2.1-16 P.M.Farwell, „Vermeiden Sie Pumpenreparaturen“, Zeitschrift „ Fluid”, 6 Juli 1978, page
18-20.
23.2.1-17 Wikipedia, „Graufleckigkeit“, de.Wikipedia.org., Stand 27.05.2007, page 1.
23.2.1-18 W.Bartelmus, „Gearbox Diagnostics Fault Detection”, Zeitschrift „Maintenance
World“, www.maintenanceworld.com, May 17, 2004, page 1-10.
23.2.1-19 Transportation Safety Board of Canada (TSB), „TSB Report Number A96o0125,
Engine Fire”, 18. July 1996, page 1-3.
23.2.1-20 AAIB Bulletin No: 5/2002, Ref: EW/C2001/09/01, „ Allison AE3007A turbofan
engine, starter failure“, 6.Sept. 2001, page 1-5.
23.2.1-21 J.Theißen, „ Graufleckenbildung an Zahnrädern - Ursachen, Prüfverfahren,
Berechnung, Praxiserfahrungen”, www.ib24.de/images/ib-gregorius-PDF's/…/Vortragsmanuskript.pdf, page
1-21.
23.2.1-23 E.Bauer, „Beispiele für Verzahnungsschäden, ausgehend von innenliegenden
Fehlstellen“, Zeitschrift „ Allianz Report” 68 (1995), Heft 6 , page 230-238.