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Monitoring wear of gear wheel of helicopter transmission using the FAM-C and FDM-A methods
ScienceDirect ScienceDirect Structural Integrity Procedia 00 (2019) 000–000
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ScienceDirect
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Procedia Structural Integrity 16 (2019) 184–191
6th International Conference “Fracture Mechanics of Materials and Structural Integrity” 6th International Conference “Fracture Mechanics of Materials and Structural Integrity”
Monitoring wear of gear wheel of helicopter transmission using the Monitoring wear ofFAM-C gear wheel of helicopter transmission using the and FDM-A methods FAM-C and FDM-A methods Andrzej Gęburaa, Sylwester Kłysza,b, Tomasz Tokarskia* a a,b01-494 Warsaw, post box. 96, Poland a Air Force Institute of Technology, Księcia Bolesława St. 6, University of Warmia and Mazury, Faculty of Technical Science, Oczapowskiego St. 11, 10-719 Olsztyn, Poland a Air Force Institute of Technology, Księcia Bolesława St. 6, 01-494 Warsaw, post box. 96, Poland b University of Warmia and Mazury, Faculty of Technical Science, Oczapowskiego St. 11, 10-719 Olsztyn, Poland a
b
Abstract
Andrzej Gębura , Sylwester Kłysz , Tomasz Tokarski *
Abstract This article is devoted to observation results of gear wheel wear of two different types of helicopter transmission: reduction gear of Mi-2 helicopter engine as well as accessory gearbox (AGB) of Mi-24 helicopter using proprietary FAM-C and FDM-A This articleThe is devoted to observation of gear wheel wear differentphenomena types of helicopter transmission: methods. substantial sensitivity results and complementarity of of thetwo observed was established – it reduction is possiblegear to of Mi-2 helicopter engine as well gearbox (AGB) Mi-24 helicopter usingas,proprietary FAM-C and FDM-A simultaneously observe a given pair as of accessory a gear wheel and also otherofmechanical points, such e.g. the worn out bearing of the methods. substantialrotor. sensitivity and complementarity of the observed was established it is possible to main shaftThe of helicopter The authors based their deliberations on the phenomena results of laboratory tests and– complex tests on simultaneously observe a given pair of a gear wheel and also other mechanical points, such as, e.g. the worn out bearing of the helicopters during their operation. The article is addressed at subsequent destruction stages of a gear wheel in helicopter main shaft ofThe helicopter The authors deliberations of laboratory tests and observed complex in tests on transmission. authorsrotor. paid high attentionbased to thetheir observed wear dueontothe theresults so-called structural resonance some helicopters during their operation. The of article is addressed at subsequent destruction of gear a gear wheel in gear helicopter helicopters, where the worn out bearing helicopter rotor results in the destruction of thestages pair of wheels. The wheel transmission. The authors high attention observedrolling wear bearing due to the so-called resonance observed in some equalizes its frequency of paid free vibrations withtothethedamaged in the line ofstructural rotation axis. Due to this, occurs the helicopters, where the worn out bearing of helicopter rotor results in the destruction of the pair of gear wheels. The gear wheel synchronous acceleration and deceleration of rotational speed of the wheel under consideration, which leads to material fatigue equalizes frequency of free vibrations with the damaged bearing inand thehelicopter line of rotation wear at theitsroot of two teeth. Such wear may contribute to gearrolling teeth breakage crash. axis. Due to this, occurs the synchronous acceleration and deceleration of rotational speed of the wheel under consideration, which leads to material fatigue wear at the of two teeth. Suchby wear may contribute to gear teeth breakage and helicopter crash. © 2019 Theroot Author(s). Published Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Author(s). Published by Elsevier organizers Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers Keywords: transport; aviation; gear wheel; fatigue wear; technical diagnostics; frequency modulation; angular speed modulation; characteristic set; helicopter transmission. Keywords: transport; aviation; gear wheel; fatigue wear; technical diagnostics; frequency modulation; angular speed modulation; characteristic set; helicopter transmission.
* Corresponding author. Tel.: +48-22-261-851-642; fax: +48-22-261-431. E-mail address: [email protected] * Corresponding author. Tel.: +48-22-261-851-642; fax: +48-22-261-431. E-mail address: [email protected] 2452-3216 © 2019 The Author(s). Published by Elsevier B.V.
Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” 2452-3216 organizers© 2019 The Author(s). Published by Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers. 10.1016/j.prostr.2019.07.039
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1. Introduction The first transmissions were made of wood, and there were initially friction gears (mentioned already by Aristotle in ‘Mechanics’), but soon afterwards (as far back as in IV B.C.), they transformed to gear wheels. II B.C. is a period, during which gear wheels found a broad scope of applications in the whole Mediterranean. There were still wooden wheels, where one of them was loaded with pegs, and the other resembled a basket. Simon Stevin (1548÷1620) – the Flemish engineer, economic activist, mathematician and scientist, worked on increasing the efficiency of such transmission mechanism combined with the windmill for pumping water from polders, which was typical for the Netherlands. Thanks to the mathematical analysis of the whole power unit (windmill, transmission and power transmission to pumps), having considered the radial and longitudinal movements of transmission wheels, he modified the system in such a way that it became three times more efficient. Wooden transmission wheels survived in windmills until the beginning of the 20th century. Gear transmissions with metal gear wheels were already known in Ancient times in precise mechanisms with low power made of bronze to reflect the movement of planets and in the Middle Age (from the VIII century) in clock mechanisms. The first steel gear wheels transmitting substantial power were applied in England already from the XVII century in some machines based on water drive and in some agricultural machinery. However, in general use, transmissions with steel gear wheels appeared only in the XIX century along with the invention of the steam engine. Nowadays, the treatment of gear wheels attained perfection – the quality of mechanical and chemical treatment of these wheels guarantees its silent operation, while carburization and nitration ensure a considerably increased abrasion resistance. It is, however, worth noting that after the long operation, especially under fast-changing loads, it may result in the inequality of the wear of wheels and inequality of output angular speed of transmission. Due to the variable forces acting on the tooth of such a wheel, cases of its breakage are sometimes reported, developed by Augustyn and Gębura ( 2012), Dudziński et al. (2011), Gębura and Stefaniuk (2017). 2. Theory of meshing Evolvent shape of teeth guarantees the cooperation of gear teeth during power transmission between a driving wheel and a drive wheel without the displacement of the point of contact (contact line) of the teeth’ surface. Since there is no displacement in such a situation, there is also no friction. If there is no friction, there is also no abrasive wear. However, it is only a theory. In reality, gear wheels have their own manufacturing defects advancing throughout the wear process. These defects include: shape defect, scale defect, eccentricity defect. Moreover, rotation axes are not stable due to the wear of bearing supports, by which gear wheels make complex movements: wheels move further away and then come closer due to the eccentricity of suspension, frequent axis skew is observed, which results in the surface skew of the contact surface, shafts of gear wheels are characterized by frequent longitudinal clearances, which results in post-axial movements of the cooperating gear wheels, angular speed of input shaft of gear transmission may be substantially modulated (most often caused by the power unit), which results in accumulating mechanical stresses at the teeth’ surface during acceleration and deceleration of angular speed. The complex character of the movement of gear wheels in real conditions in a power unit (windmilltransmission-water pump) was already addressed by Simon Stevin in XVII century. The mathematical description, which he utilized, enabled to improve the efficiency of pumping water from polders in the Netherlands. 3. Teeth breakage process in the transmission – reasons and effects There are many publications concerning the computer simulation of wear of gear wheels i.a. due to fatigue cracks devoleped by: Bukowski and Kłysz (1993), Jakielaszek and Nowakowski (2014), Kłysz and Lisiecki (2009),
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Ghaffari et al. (2015). Apart from a precise mathematical model describing the wear process of individual teeth, including the development of fatigue crack, it is possible to derive many practical guidelines such as: for the onset of wear process it is necessary to wipe the hardened layer at the tooth’s surface, wear of bearing supports of the shaft, on which the gear wheels are mounted, is very important – the approaching rotation axis of the cooperating gear wheels leads to undercutting the tooth’s root, whilst by moving away, there is an increased bending moment contributing to breakage, fatigue cracks develop directly proportional to rotational speed and the number of meshings, to initialize cracks, instantaneous overloads are needed (increase in driving torque or braking torque). In this article, which presents the monitoring of real mechanical elements (in laboratory conditions and during normal operation of aircraft transmissions), all of these suggestions have been confirmed. However, there is also another phenomenon here – resonance impact of the damaged power plant on the pair of gear wheels. The authors believe that the conditions of weakening the structure of a tooth and creating conditions for fatigue cracks at the tooth’s root forms over a long time and thus, it should be subject to the in-depth monitoring. The subsequent process of initiating the fatigue crack is usually short, especially in the case of aircraft transmissions, angular speeds and variable loads distinguishably accelerate this process in the way which substantially hinders from taking the countermeasures. Such opinions are also shared in other publications by: Bukowski and Kłysz (1993), Padfield (1998), Żurek (2006). 4. Resonance of bearing support system and its impact on the wear of transmission gear wheels Helicopter power plants are characterized by diverse rotational speeds of shafts and, thus, also the journals of rolling bearings – Fig. 1: engine n = 250 rev/min; main shaft of helicopter rotor n = 4 rev/min. The authors frequently observed the resonances of individual bearings. The most loaded element, or even overloaded, is the upper bearing in the main transmission – Fig.1, element 3a. It is the principal support of the main shaft (Fig. 1, element 3c) – the helicopter rotor with substantial structural unbalances changing significantly during flight direction control due to changing angles of attack (system of the so-called periodic control) developed by: Barszewski (1956), Padfield (1998), Żurek (2006).
Fig. 1. Arrangement of transmission elements between the engine and generator in Mi-24 helicopter: 1. – TW3-117MT propulsion engine, 2. – mechanical fan, 3. – WR-24, 3a. main transmission – upper bearing, 3b. – main shaft of helicopter rotor, 3c. – rotor blade, 4,5,7. – power transmission shaft, 6. – accessory gearbox, 8. – left GT-4PCz6 generator (behind it, a right GT-4PCz6 generator is installed to the same accessory gearbox), 9. – intermediate transmission, 10. – tail transmission, 11. – auxiliary rotor.
During operation, such bearing deteriorates – spallings in the inner ring raceway developed by Augustyn and Gębura (2012). Then, the waveform in the angular frequency component observed by the FAM-C method – Fig. 2, Fig. 3 is modified. From these diagrams, it can be calculated that the pulsation frequency for the upper bearing working correctly (‘positive standard’) amounts to fp = 13 ÷ 23 Hz (Fig. 2, fp = 13 since there are 13 oscillations/s), and for the bearing with a spalling, it equals fp = 51÷ 64 Hz (Fig. 3, fp = 51 since there are 51 oscillations/s).
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Andrzej Gębura, Sylwester Kłysz, Tomasz Tokarski / Structural Integrity Procedia 00 (2019) 000–000 fi [s]
4 rotations - 13 oscillations
Δt = 1 s
t [s] Fig. 2. The waveform of the instantaneous frequency from Mi-24 – ‘positive standard’. fi [s]
4 rotations - 51 oscillations
Δt = 1 s t [s] Fig. 3. The waveform of the instantaneous frequency from Mi-24– ‘negative standard’.
5. Selected operational problems of aircraft transmissions 5.1. General information on aircraft transmissions Mechanical transmission is a mechanism or a system of machines used for transferring motion from an active element (driving element) to the passive element (drive element) with the simultaneous change of motion parameters, that is speed and force or the moment of force developed by Jakielaszek and Nowakowski (2014). The transmission may be: a) reduction gear – when the drive element rotates with the lower speed than the driving element, b) step-up gear – when the drive element rotates with the higher speed than the driving element. In modern aviation based on turbine engines, reduction gears with different velocity ratio are most frequently used. The highest reduction values have helicopter propulsion with turbine engines. The reduction gear is aimed at reducing the rotational speed of the main shaft of the turbine engine – Fig. 1, element 1 (this speed is maximised by construction engineers to obtain a high engine efficiency) to the rotational speed of helicopter rotor shaft – Fig. 1, element 3a (this speed is optimized by construction engineers to obtain a high aerodynamic lift i.e. to achieve a subsonic speed at the end of the main rotor blade developed by Barszewski (1956), Padfield (1998), Żurek (2006). 5.2. Skews of shafts and their importance Skews of couplings manifest itself in the form of a sinusoidal modulation of the waveform of the instantaneous angular speed of driving element with the frequency of the second harmonic of the rated speed of individual shaft. It can be observed that skews of shafts result in dynamic excesses, which are two times more frequent (one full
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rotation cycle of a kinematic pair) than in the case of the eccentricity defect. If tribological phenomena are considered (excessive abrasion due to the contact point of spline causing the accumulation of stresses and temperature increase), then the skews of splined couplings shall be treated as a dangerous manufacturing defect leading to intensive abrasion of a splined coupling in the form of ‘barrel-shaped’ defects developed by Gębura (1999), Gębura and Stefaniuk (2017). During operation, the clearance-free skew (skew without clearances in bearing supports) of splined couplings or toothed couplings is almost non-present – most frequently it is associated with radial clearances. Such combination of two defects: skew and radial clearances is exhibited in the FAM-C method in the first form of a subharmonic rated rotational speed, i.e. pulsation component of angular speed will be two times longer – Fig. 4b, detail Ti = 80 ms – than the duration period of the full shaft rotation – Fig. 4a, detail Ti = 4 ms. 5.3. Structure of Mi-24 accessory gearbox Fig.5 illustrates a diagram of the accessory gearbox of Mi-24 helicopter. This diagram also shows a transmission system in the accessory gearbox. It can also be noted that a gear wheel Z70 cooperates only with one gear wheel (Fig. 5 detail Z30), i.e. there is an asymmetry of dynamic forces during operation. It can pose a threat to the transmission system since such displacement can constitute an unbalance of the mechanical system. Gear wheel Z35 no. 1, and Z30 are installed on the so-called intermediate shaft – Fig. 5, element 6. On one side, the shaft is hollowed internally and has internal splines. These splines are used to ensure the connection with the drive shaft of GT-4PCz6 generator no. 1 – Fig. 5, element 1. The rotor of this generator has a significant moment of inertia and constitutes a reliable spatial fixation of the extension of the intermediate shaft.
Fig. 4. The waveform of the instantaneous frequency by the changes in skew value of transmission shaft by angle: a) β = 0,2o, b) β = 0,5o obtained with the FAM-C method on a reduction gear from Mi-2 helicopter (TUN-75/R) in laboratory conditions: Ti – period of modulations of pulsation component of angular speed (here: on the waveform reflected with the FAM-C method synchronized with the waveform of instantaneous rotational speed).
From the other side of the intermediate shaft, a centrifugal fan (Fig. 5, element 3) with a little moment of inertia is installed. In the centre of this shaft, as it was previously mentioned, gear wheels Z30 and Z35 no. 1 are mounted. Thanks to them, mechanical power is transferred to the tail rotor. The anti-torque of tail rotor changes depending on the angle of attack of its blades and sometimes obtains the significant values developed by: Padfield (1998), Żurek (2006). The input power (from main transmission WR-24) is transferred on the gear wheel Z66. From here, there is a flow of power, through gear wheels Z35 to two generators TG-4PCz6 in the direction of a tail rotor. The wheel Z33 has a symmetrical loading but on the power output in AGB there is no such symmetrical loading – gear wheel Z70 is loaded on one side by wheel Z30 – Fig. 5, element Z70. If there are radial clearances in bearing mounting of the axle of gear wheel Z70, then they will cause the undamped radial movements of this axle. The mutual radial
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movements of the rotation axis of the Z70 wheel will contribute to the oscillations of angular speed of tail rotor, thus, the oscillatory movements of the direction of helicopter flight.
Z70.
Fig. 5. Block diagram of a complete accessory gearbox (GT-4PCz6 generators) from Mi-24 helicopter: 1 – right generator-converter GT-4PCz6 No. 1, 2 – accessory gearbox, 3 – generators’ fan, 4 – left generator-converter GT-4PCz6 No. 2.
6. Spatial resonance between the upper bearing of the main transmission and intermediate shaft of accessory gearbox of Mi-24 helicopter Phenomena described in the previous chapters include: resonance of the upper bearing of the main transmission – causing false brinelling on its inner ring raceway (in the form of spallings with the depth of 2,1 mm) – they induce the increase of free-running frequency of this bearing f ≥ 51 Hz, specificity of the asymmetric dynamic load of the intermediate shaft (in the accessory gearbox) results in its skew. This skew, in combination with the increased radial clearances, manifests itself in the form of the decrease in angular frequency (Fig. 4) of this node with fp = 102 Hz to fp = 51 Hz. It causes the synchronous acceleration and deceleration – Fig. 6 – of the angular speed of intermediate shaft (Fig. 6, element 6). On this shaft, from the side of a fan (i.e. from the greatest radial clearance of the bearing support), a gear wheel Z30 is mounted – Fig. 5, element Z30. The toothed-wheel rim is subject to asymmetric abrasion due to: 1. synchronous acceleration and deceleration of the angular speed of the intermediate shaft (Fig. 6.), 2. wheel Z30 moving closer and further away from wheel Z70. Instantaneous increase of the frequency and amplitude of the envelope of the instanteous frequency course fi [Hz]
t [s]
Fig. 6. Waveform of frequency in time function obtained from the pilot exciter generator Mi-24 No. 456 test No. 31, measurement No. 2 – visible instantaneous increase in frequency and amplitude of envelope of frequency with fp ≈ 100 Hz – observation time: 0,2 s.
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Contact edge and the root of two teeth of wheel Z30 are subject to intensive abrasion. It may result in the fracture of these two teeth. Then, it may end in the loss of the continuity of transferring the mechanical power to the tail rotor. In consequence, the helicopter loses its directional maneuverability, and its fuselage starts to rotate around the vertical axis in the opposite direction to the direction of rotations of the main rotor. Such a case (helicopter crash) was reported in 2011.
7. Development of destruction process of gear wheels according to AFIT research Due to the disassembly and investigations conducted in Air Force of Institute of Technology (AFIT) of helicopter destroyed in 2011 – Fig. 9 – the following conclusions were formulated: 1. the reason for the loss of kinematic attachment of helicopter transmission between the main transmission and tail rotor hub was the destruction of gear wheels of the drive shaft and intermediate shaft of the accessory gearbox; 2. the destruction of the gear wheels consisted in fatigue fracture of two subsequent teeth of drive wheel mounted on the intermediate shaft (Fig. 5, element 6). The initiation of fracture occurred most likely under the influence of a short-term growth of loading of a gear wheel. A crucial factor, which impacted the initiation of cracks, was a defective shape of the teeth of this wheel done during the mechanical treatment – the root of all 30 teeth was not polished, and as a result, a dent was created, which contributes to fatigue failures. Driving wheel mounted on the intermediate shaft transmits torque on the above – mentioned drive wheel. Driving gear wheel (Fig. 5, element Z30) was subject to greater destruction than the drive wheel (Fig. 5, element Z70), which is illustrated in figure 10. In gear wheel Z30, all 30 teeth of this wheel were damaged. Due to the macroscopic observations developed by Dudziński et al. (2011), two modes of teeth failure were identified. First of them is milling of 14 teeth on the length of the junction with the teeth of wheel Z30 – Fig. 5, element Z30. The second mode of teeth destruction was its breakage at the tooth’s root. In this way, 16 teeth of wheel Z30 were damaged. Macroscopic observations of fracture surfaces found out that 14 fractures, amongst 16 fractures of broken teeth, are distinguished by features of temporary destruction. The surface of these fractures is characterized by coarseness and relief in the form of ‘ridges’ and ‘valleys’ of ‘rivers’ crossing perpendicularly to the length of teeth, i.e. circumferential relative to the axle of the gear wheel – Fig. 7, elements a2. Such form of fracture indicates temporary destruction (breakage) of teeth. This type of failure and the afore-mentioned milling is known as secondary teeth damage. fatigue fracture
a1
temporary fracture
a2
Fig. 7. Macrostructure of gear wheel’s fractures – upper view: a1 – fatigue fracture a2 – temporary fractures of dynamic destruction (Dudziński et al. (2011)).
The fractures of two teeth show macroscopic features of fatigue cracking – Fig. 7, elements a1. In this elaboration, it was concluded that:
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The earliest failure of all examined failures was initiated a fatigue cracking of two subsequent teeth of a gear wheel (the same by which other teeth suffered from being broken or milled). The initiation of fatigue cracks occurred at the teeth’ root at approximately two-thirds (2/3) of its length. The region of fatigue cracking occupies 85–90% of the fracture area, which signifies low loads accompanying the development of fatigue cracks. In the region of the initiation of fatigue cracks, the presence of micro-areas of fracture of temporary character was found, which indicates that the cracks were initiated presumably by short-term exposure to high loads of teeth (load impulse). Duration of this impulse, assuming that it simultaneously initiated the cracking of both teeth, was estimated at approx. 1/3 ms. 8. Summary 1. Resonance phenomena in the mechanical power transmission system are dangerous and lead to the accelerated destruction of bearing nodes and gear wheels. 2. Resonance phenomena in rolling bearings are difficult to detect with the use of traditional methods, e.g. vibroacoustic methods since the increased energy absorbed from the drive unit is closed in the bearing, and reduces the vibration energy emitted from outside. The situation looks different in the case of detecting resonances with the FAM-C method. This method distinguishes them without any difficulty by tracing the dynamics of angular speed. 3. For the power plants, a crucial aspect is to provide parallelism of the rotation axis of shafts, on which gear wheels are mounted. Failure to comply with this parameter may contribute to the mutual skew of the abovementioned shafts and undercutting the root of teeth. 4. The skew of the shaft and increased radial clearances decrease its angular frequency to the first subharmonic. If this angular frequency will equal the frequency of other subassembly, e.g. the upper bearing of the main transmission, then, the spatial resonance of both subassemblies is created. 5. In spatial resonances, the subassemblies with smaller constructional offcuts are the first, which are subject to destruction. 6. Synchronous interaction of rolling bearing during resonance on the pair of gear wheels may end in undercutting of two teeth, production of focal points of fatigue cracks at the root and its breakage. References Augustyn, Sł., Gębura, A., 2012. Capabilities of the FAM-C method to diagnose the accessory gearboxes and transmission - train assemblies of the Mi-24 helicopters. Aviation Advances & Maintenance, 30.30: 199÷220. ISSN 1234-3544. Barszewski, W., 1956. A helicopter in flight. Wyd. MON, Warszawa. (in Polish) Bukowski, L., Kłysz, S., 1993. Fatigue of aircraft structures against the background of a 4-year experience activity. Biuletyn Wojskowej Akademii Technicznej, XLII, 3(487), Warszawa. (in Polish) Dudziński, A., Dudzińska, A., Flotyńska, A., 2011. Report No. 03/36/2011 from damage to the gearbox components of agreements, bearings and components of the helicopter rear shaft Mi-24W No. 410737 and two intermediate shafts with toothed wheels of the accessory gearbox 24-512-00 – type. ITWL, Warszawa. (in Polish) Gębura, A., 1999. Skew of splin connections and frequency modulation. Scientific Problems of Machines Operation and Maintenance, 34.4 (120): 763–772. (in Polish) Gębura, A., Tokarski, T. 2009. The monitoring of the Bering nodes with excessive radial clearances using the FAM-C and FDM-A methods. Research Works of Air Force Institute of Technology 25, 89–127. (in Polish) Gębura, A., Stefaniuk, M., 2017. Monitoring the helicopter transmission using the FAM-C diagnostic method, Diagnostyka 2, 75–85. Ghaffari, M.A., Pahl, E., Xiao, S., 2015. Three dimensional fatigue crack initiation and propagation analysis of gear tooth under load conditions and fatigue life extension with boron/epoxy patches. Engineering Facture Mechanics 135, 126–146. Jakielaszek, Z., Nowakowski, M., 2014. Selected characteristics of the electric propulsion system of aircraft as found out the ground-based laboratory tests, Journal of KONES Powertrain and Transport 4, 203–210. Kłysz, S., Lisiecki, J., 2009. Strength testing and analysis of fatigue crack growth in selected aircraft materials, in: Niepokólczycki A.: Fatigue of aircraft structures, monographic series, pp. 74–83, Institute of Aviation Scientific Publication, Warsaw. Padfield, G.D., 1998. Helicopter Flight Dynamic. The theory and Application of Flying Qualities and Simulation Modelling. WKiŁ, Warszawa. (in Polish) Żurek, J., et al., 2006. Helicopters life. Warszawa. (in Polish),
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Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Structural Integrity 16 (2019) 184–191
6th International Conference “Fracture Mechanics of Materials and Structural Integrity” 6th International Conference “Fracture Mechanics of Materials and Structural Integrity”
Monitoring wear of gear wheel of helicopter transmission using the Monitoring wear ofFAM-C gear wheel of helicopter transmission using the and FDM-A methods FAM-C and FDM-A methods Andrzej Gęburaa, Sylwester Kłysza,b, Tomasz Tokarskia* a a,b01-494 Warsaw, post box. 96, Poland a Air Force Institute of Technology, Księcia Bolesława St. 6, University of Warmia and Mazury, Faculty of Technical Science, Oczapowskiego St. 11, 10-719 Olsztyn, Poland a Air Force Institute of Technology, Księcia Bolesława St. 6, 01-494 Warsaw, post box. 96, Poland b University of Warmia and Mazury, Faculty of Technical Science, Oczapowskiego St. 11, 10-719 Olsztyn, Poland a
b
Abstract
Andrzej Gębura , Sylwester Kłysz , Tomasz Tokarski *
Abstract This article is devoted to observation results of gear wheel wear of two different types of helicopter transmission: reduction gear of Mi-2 helicopter engine as well as accessory gearbox (AGB) of Mi-24 helicopter using proprietary FAM-C and FDM-A This articleThe is devoted to observation of gear wheel wear differentphenomena types of helicopter transmission: methods. substantial sensitivity results and complementarity of of thetwo observed was established – it reduction is possiblegear to of Mi-2 helicopter engine as well gearbox (AGB) Mi-24 helicopter usingas,proprietary FAM-C and FDM-A simultaneously observe a given pair as of accessory a gear wheel and also otherofmechanical points, such e.g. the worn out bearing of the methods. substantialrotor. sensitivity and complementarity of the observed was established it is possible to main shaftThe of helicopter The authors based their deliberations on the phenomena results of laboratory tests and– complex tests on simultaneously observe a given pair of a gear wheel and also other mechanical points, such as, e.g. the worn out bearing of the helicopters during their operation. The article is addressed at subsequent destruction stages of a gear wheel in helicopter main shaft ofThe helicopter The authors deliberations of laboratory tests and observed complex in tests on transmission. authorsrotor. paid high attentionbased to thetheir observed wear dueontothe theresults so-called structural resonance some helicopters during their operation. The of article is addressed at subsequent destruction of gear a gear wheel in gear helicopter helicopters, where the worn out bearing helicopter rotor results in the destruction of thestages pair of wheels. The wheel transmission. The authors high attention observedrolling wear bearing due to the so-called resonance observed in some equalizes its frequency of paid free vibrations withtothethedamaged in the line ofstructural rotation axis. Due to this, occurs the helicopters, where the worn out bearing of helicopter rotor results in the destruction of the pair of gear wheels. The gear wheel synchronous acceleration and deceleration of rotational speed of the wheel under consideration, which leads to material fatigue equalizes frequency of free vibrations with the damaged bearing inand thehelicopter line of rotation wear at theitsroot of two teeth. Such wear may contribute to gearrolling teeth breakage crash. axis. Due to this, occurs the synchronous acceleration and deceleration of rotational speed of the wheel under consideration, which leads to material fatigue wear at the of two teeth. Suchby wear may contribute to gear teeth breakage and helicopter crash. © 2019 Theroot Author(s). Published Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Author(s). Published by Elsevier organizers Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers Keywords: transport; aviation; gear wheel; fatigue wear; technical diagnostics; frequency modulation; angular speed modulation; characteristic set; helicopter transmission. Keywords: transport; aviation; gear wheel; fatigue wear; technical diagnostics; frequency modulation; angular speed modulation; characteristic set; helicopter transmission.
* Corresponding author. Tel.: +48-22-261-851-642; fax: +48-22-261-431. E-mail address: [email protected] * Corresponding author. Tel.: +48-22-261-851-642; fax: +48-22-261-431. E-mail address: [email protected] 2452-3216 © 2019 The Author(s). Published by Elsevier B.V.
Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” 2452-3216 organizers© 2019 The Author(s). Published by Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the 6th International Conference “Fracture Mechanics of Materials and Structural Integrity” organizers. 10.1016/j.prostr.2019.07.039
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1. Introduction The first transmissions were made of wood, and there were initially friction gears (mentioned already by Aristotle in ‘Mechanics’), but soon afterwards (as far back as in IV B.C.), they transformed to gear wheels. II B.C. is a period, during which gear wheels found a broad scope of applications in the whole Mediterranean. There were still wooden wheels, where one of them was loaded with pegs, and the other resembled a basket. Simon Stevin (1548÷1620) – the Flemish engineer, economic activist, mathematician and scientist, worked on increasing the efficiency of such transmission mechanism combined with the windmill for pumping water from polders, which was typical for the Netherlands. Thanks to the mathematical analysis of the whole power unit (windmill, transmission and power transmission to pumps), having considered the radial and longitudinal movements of transmission wheels, he modified the system in such a way that it became three times more efficient. Wooden transmission wheels survived in windmills until the beginning of the 20th century. Gear transmissions with metal gear wheels were already known in Ancient times in precise mechanisms with low power made of bronze to reflect the movement of planets and in the Middle Age (from the VIII century) in clock mechanisms. The first steel gear wheels transmitting substantial power were applied in England already from the XVII century in some machines based on water drive and in some agricultural machinery. However, in general use, transmissions with steel gear wheels appeared only in the XIX century along with the invention of the steam engine. Nowadays, the treatment of gear wheels attained perfection – the quality of mechanical and chemical treatment of these wheels guarantees its silent operation, while carburization and nitration ensure a considerably increased abrasion resistance. It is, however, worth noting that after the long operation, especially under fast-changing loads, it may result in the inequality of the wear of wheels and inequality of output angular speed of transmission. Due to the variable forces acting on the tooth of such a wheel, cases of its breakage are sometimes reported, developed by Augustyn and Gębura ( 2012), Dudziński et al. (2011), Gębura and Stefaniuk (2017). 2. Theory of meshing Evolvent shape of teeth guarantees the cooperation of gear teeth during power transmission between a driving wheel and a drive wheel without the displacement of the point of contact (contact line) of the teeth’ surface. Since there is no displacement in such a situation, there is also no friction. If there is no friction, there is also no abrasive wear. However, it is only a theory. In reality, gear wheels have their own manufacturing defects advancing throughout the wear process. These defects include: shape defect, scale defect, eccentricity defect. Moreover, rotation axes are not stable due to the wear of bearing supports, by which gear wheels make complex movements: wheels move further away and then come closer due to the eccentricity of suspension, frequent axis skew is observed, which results in the surface skew of the contact surface, shafts of gear wheels are characterized by frequent longitudinal clearances, which results in post-axial movements of the cooperating gear wheels, angular speed of input shaft of gear transmission may be substantially modulated (most often caused by the power unit), which results in accumulating mechanical stresses at the teeth’ surface during acceleration and deceleration of angular speed. The complex character of the movement of gear wheels in real conditions in a power unit (windmilltransmission-water pump) was already addressed by Simon Stevin in XVII century. The mathematical description, which he utilized, enabled to improve the efficiency of pumping water from polders in the Netherlands. 3. Teeth breakage process in the transmission – reasons and effects There are many publications concerning the computer simulation of wear of gear wheels i.a. due to fatigue cracks devoleped by: Bukowski and Kłysz (1993), Jakielaszek and Nowakowski (2014), Kłysz and Lisiecki (2009),
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Ghaffari et al. (2015). Apart from a precise mathematical model describing the wear process of individual teeth, including the development of fatigue crack, it is possible to derive many practical guidelines such as: for the onset of wear process it is necessary to wipe the hardened layer at the tooth’s surface, wear of bearing supports of the shaft, on which the gear wheels are mounted, is very important – the approaching rotation axis of the cooperating gear wheels leads to undercutting the tooth’s root, whilst by moving away, there is an increased bending moment contributing to breakage, fatigue cracks develop directly proportional to rotational speed and the number of meshings, to initialize cracks, instantaneous overloads are needed (increase in driving torque or braking torque). In this article, which presents the monitoring of real mechanical elements (in laboratory conditions and during normal operation of aircraft transmissions), all of these suggestions have been confirmed. However, there is also another phenomenon here – resonance impact of the damaged power plant on the pair of gear wheels. The authors believe that the conditions of weakening the structure of a tooth and creating conditions for fatigue cracks at the tooth’s root forms over a long time and thus, it should be subject to the in-depth monitoring. The subsequent process of initiating the fatigue crack is usually short, especially in the case of aircraft transmissions, angular speeds and variable loads distinguishably accelerate this process in the way which substantially hinders from taking the countermeasures. Such opinions are also shared in other publications by: Bukowski and Kłysz (1993), Padfield (1998), Żurek (2006). 4. Resonance of bearing support system and its impact on the wear of transmission gear wheels Helicopter power plants are characterized by diverse rotational speeds of shafts and, thus, also the journals of rolling bearings – Fig. 1: engine n = 250 rev/min; main shaft of helicopter rotor n = 4 rev/min. The authors frequently observed the resonances of individual bearings. The most loaded element, or even overloaded, is the upper bearing in the main transmission – Fig.1, element 3a. It is the principal support of the main shaft (Fig. 1, element 3c) – the helicopter rotor with substantial structural unbalances changing significantly during flight direction control due to changing angles of attack (system of the so-called periodic control) developed by: Barszewski (1956), Padfield (1998), Żurek (2006).
Fig. 1. Arrangement of transmission elements between the engine and generator in Mi-24 helicopter: 1. – TW3-117MT propulsion engine, 2. – mechanical fan, 3. – WR-24, 3a. main transmission – upper bearing, 3b. – main shaft of helicopter rotor, 3c. – rotor blade, 4,5,7. – power transmission shaft, 6. – accessory gearbox, 8. – left GT-4PCz6 generator (behind it, a right GT-4PCz6 generator is installed to the same accessory gearbox), 9. – intermediate transmission, 10. – tail transmission, 11. – auxiliary rotor.
During operation, such bearing deteriorates – spallings in the inner ring raceway developed by Augustyn and Gębura (2012). Then, the waveform in the angular frequency component observed by the FAM-C method – Fig. 2, Fig. 3 is modified. From these diagrams, it can be calculated that the pulsation frequency for the upper bearing working correctly (‘positive standard’) amounts to fp = 13 ÷ 23 Hz (Fig. 2, fp = 13 since there are 13 oscillations/s), and for the bearing with a spalling, it equals fp = 51÷ 64 Hz (Fig. 3, fp = 51 since there are 51 oscillations/s).
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Andrzej Gębura, Sylwester Kłysz, Tomasz Tokarski / Structural Integrity Procedia 00 (2019) 000–000 fi [s]
4 rotations - 13 oscillations
Δt = 1 s
t [s] Fig. 2. The waveform of the instantaneous frequency from Mi-24 – ‘positive standard’. fi [s]
4 rotations - 51 oscillations
Δt = 1 s t [s] Fig. 3. The waveform of the instantaneous frequency from Mi-24– ‘negative standard’.
5. Selected operational problems of aircraft transmissions 5.1. General information on aircraft transmissions Mechanical transmission is a mechanism or a system of machines used for transferring motion from an active element (driving element) to the passive element (drive element) with the simultaneous change of motion parameters, that is speed and force or the moment of force developed by Jakielaszek and Nowakowski (2014). The transmission may be: a) reduction gear – when the drive element rotates with the lower speed than the driving element, b) step-up gear – when the drive element rotates with the higher speed than the driving element. In modern aviation based on turbine engines, reduction gears with different velocity ratio are most frequently used. The highest reduction values have helicopter propulsion with turbine engines. The reduction gear is aimed at reducing the rotational speed of the main shaft of the turbine engine – Fig. 1, element 1 (this speed is maximised by construction engineers to obtain a high engine efficiency) to the rotational speed of helicopter rotor shaft – Fig. 1, element 3a (this speed is optimized by construction engineers to obtain a high aerodynamic lift i.e. to achieve a subsonic speed at the end of the main rotor blade developed by Barszewski (1956), Padfield (1998), Żurek (2006). 5.2. Skews of shafts and their importance Skews of couplings manifest itself in the form of a sinusoidal modulation of the waveform of the instantaneous angular speed of driving element with the frequency of the second harmonic of the rated speed of individual shaft. It can be observed that skews of shafts result in dynamic excesses, which are two times more frequent (one full
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rotation cycle of a kinematic pair) than in the case of the eccentricity defect. If tribological phenomena are considered (excessive abrasion due to the contact point of spline causing the accumulation of stresses and temperature increase), then the skews of splined couplings shall be treated as a dangerous manufacturing defect leading to intensive abrasion of a splined coupling in the form of ‘barrel-shaped’ defects developed by Gębura (1999), Gębura and Stefaniuk (2017). During operation, the clearance-free skew (skew without clearances in bearing supports) of splined couplings or toothed couplings is almost non-present – most frequently it is associated with radial clearances. Such combination of two defects: skew and radial clearances is exhibited in the FAM-C method in the first form of a subharmonic rated rotational speed, i.e. pulsation component of angular speed will be two times longer – Fig. 4b, detail Ti = 80 ms – than the duration period of the full shaft rotation – Fig. 4a, detail Ti = 4 ms. 5.3. Structure of Mi-24 accessory gearbox Fig.5 illustrates a diagram of the accessory gearbox of Mi-24 helicopter. This diagram also shows a transmission system in the accessory gearbox. It can also be noted that a gear wheel Z70 cooperates only with one gear wheel (Fig. 5 detail Z30), i.e. there is an asymmetry of dynamic forces during operation. It can pose a threat to the transmission system since such displacement can constitute an unbalance of the mechanical system. Gear wheel Z35 no. 1, and Z30 are installed on the so-called intermediate shaft – Fig. 5, element 6. On one side, the shaft is hollowed internally and has internal splines. These splines are used to ensure the connection with the drive shaft of GT-4PCz6 generator no. 1 – Fig. 5, element 1. The rotor of this generator has a significant moment of inertia and constitutes a reliable spatial fixation of the extension of the intermediate shaft.
Fig. 4. The waveform of the instantaneous frequency by the changes in skew value of transmission shaft by angle: a) β = 0,2o, b) β = 0,5o obtained with the FAM-C method on a reduction gear from Mi-2 helicopter (TUN-75/R) in laboratory conditions: Ti – period of modulations of pulsation component of angular speed (here: on the waveform reflected with the FAM-C method synchronized with the waveform of instantaneous rotational speed).
From the other side of the intermediate shaft, a centrifugal fan (Fig. 5, element 3) with a little moment of inertia is installed. In the centre of this shaft, as it was previously mentioned, gear wheels Z30 and Z35 no. 1 are mounted. Thanks to them, mechanical power is transferred to the tail rotor. The anti-torque of tail rotor changes depending on the angle of attack of its blades and sometimes obtains the significant values developed by: Padfield (1998), Żurek (2006). The input power (from main transmission WR-24) is transferred on the gear wheel Z66. From here, there is a flow of power, through gear wheels Z35 to two generators TG-4PCz6 in the direction of a tail rotor. The wheel Z33 has a symmetrical loading but on the power output in AGB there is no such symmetrical loading – gear wheel Z70 is loaded on one side by wheel Z30 – Fig. 5, element Z70. If there are radial clearances in bearing mounting of the axle of gear wheel Z70, then they will cause the undamped radial movements of this axle. The mutual radial
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movements of the rotation axis of the Z70 wheel will contribute to the oscillations of angular speed of tail rotor, thus, the oscillatory movements of the direction of helicopter flight.
Z70.
Fig. 5. Block diagram of a complete accessory gearbox (GT-4PCz6 generators) from Mi-24 helicopter: 1 – right generator-converter GT-4PCz6 No. 1, 2 – accessory gearbox, 3 – generators’ fan, 4 – left generator-converter GT-4PCz6 No. 2.
6. Spatial resonance between the upper bearing of the main transmission and intermediate shaft of accessory gearbox of Mi-24 helicopter Phenomena described in the previous chapters include: resonance of the upper bearing of the main transmission – causing false brinelling on its inner ring raceway (in the form of spallings with the depth of 2,1 mm) – they induce the increase of free-running frequency of this bearing f ≥ 51 Hz, specificity of the asymmetric dynamic load of the intermediate shaft (in the accessory gearbox) results in its skew. This skew, in combination with the increased radial clearances, manifests itself in the form of the decrease in angular frequency (Fig. 4) of this node with fp = 102 Hz to fp = 51 Hz. It causes the synchronous acceleration and deceleration – Fig. 6 – of the angular speed of intermediate shaft (Fig. 6, element 6). On this shaft, from the side of a fan (i.e. from the greatest radial clearance of the bearing support), a gear wheel Z30 is mounted – Fig. 5, element Z30. The toothed-wheel rim is subject to asymmetric abrasion due to: 1. synchronous acceleration and deceleration of the angular speed of the intermediate shaft (Fig. 6.), 2. wheel Z30 moving closer and further away from wheel Z70. Instantaneous increase of the frequency and amplitude of the envelope of the instanteous frequency course fi [Hz]
t [s]
Fig. 6. Waveform of frequency in time function obtained from the pilot exciter generator Mi-24 No. 456 test No. 31, measurement No. 2 – visible instantaneous increase in frequency and amplitude of envelope of frequency with fp ≈ 100 Hz – observation time: 0,2 s.
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Contact edge and the root of two teeth of wheel Z30 are subject to intensive abrasion. It may result in the fracture of these two teeth. Then, it may end in the loss of the continuity of transferring the mechanical power to the tail rotor. In consequence, the helicopter loses its directional maneuverability, and its fuselage starts to rotate around the vertical axis in the opposite direction to the direction of rotations of the main rotor. Such a case (helicopter crash) was reported in 2011.
7. Development of destruction process of gear wheels according to AFIT research Due to the disassembly and investigations conducted in Air Force of Institute of Technology (AFIT) of helicopter destroyed in 2011 – Fig. 9 – the following conclusions were formulated: 1. the reason for the loss of kinematic attachment of helicopter transmission between the main transmission and tail rotor hub was the destruction of gear wheels of the drive shaft and intermediate shaft of the accessory gearbox; 2. the destruction of the gear wheels consisted in fatigue fracture of two subsequent teeth of drive wheel mounted on the intermediate shaft (Fig. 5, element 6). The initiation of fracture occurred most likely under the influence of a short-term growth of loading of a gear wheel. A crucial factor, which impacted the initiation of cracks, was a defective shape of the teeth of this wheel done during the mechanical treatment – the root of all 30 teeth was not polished, and as a result, a dent was created, which contributes to fatigue failures. Driving wheel mounted on the intermediate shaft transmits torque on the above – mentioned drive wheel. Driving gear wheel (Fig. 5, element Z30) was subject to greater destruction than the drive wheel (Fig. 5, element Z70), which is illustrated in figure 10. In gear wheel Z30, all 30 teeth of this wheel were damaged. Due to the macroscopic observations developed by Dudziński et al. (2011), two modes of teeth failure were identified. First of them is milling of 14 teeth on the length of the junction with the teeth of wheel Z30 – Fig. 5, element Z30. The second mode of teeth destruction was its breakage at the tooth’s root. In this way, 16 teeth of wheel Z30 were damaged. Macroscopic observations of fracture surfaces found out that 14 fractures, amongst 16 fractures of broken teeth, are distinguished by features of temporary destruction. The surface of these fractures is characterized by coarseness and relief in the form of ‘ridges’ and ‘valleys’ of ‘rivers’ crossing perpendicularly to the length of teeth, i.e. circumferential relative to the axle of the gear wheel – Fig. 7, elements a2. Such form of fracture indicates temporary destruction (breakage) of teeth. This type of failure and the afore-mentioned milling is known as secondary teeth damage. fatigue fracture
a1
temporary fracture
a2
Fig. 7. Macrostructure of gear wheel’s fractures – upper view: a1 – fatigue fracture a2 – temporary fractures of dynamic destruction (Dudziński et al. (2011)).
The fractures of two teeth show macroscopic features of fatigue cracking – Fig. 7, elements a1. In this elaboration, it was concluded that:
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The earliest failure of all examined failures was initiated a fatigue cracking of two subsequent teeth of a gear wheel (the same by which other teeth suffered from being broken or milled). The initiation of fatigue cracks occurred at the teeth’ root at approximately two-thirds (2/3) of its length. The region of fatigue cracking occupies 85–90% of the fracture area, which signifies low loads accompanying the development of fatigue cracks. In the region of the initiation of fatigue cracks, the presence of micro-areas of fracture of temporary character was found, which indicates that the cracks were initiated presumably by short-term exposure to high loads of teeth (load impulse). Duration of this impulse, assuming that it simultaneously initiated the cracking of both teeth, was estimated at approx. 1/3 ms. 8. Summary 1. Resonance phenomena in the mechanical power transmission system are dangerous and lead to the accelerated destruction of bearing nodes and gear wheels. 2. Resonance phenomena in rolling bearings are difficult to detect with the use of traditional methods, e.g. vibroacoustic methods since the increased energy absorbed from the drive unit is closed in the bearing, and reduces the vibration energy emitted from outside. The situation looks different in the case of detecting resonances with the FAM-C method. This method distinguishes them without any difficulty by tracing the dynamics of angular speed. 3. For the power plants, a crucial aspect is to provide parallelism of the rotation axis of shafts, on which gear wheels are mounted. Failure to comply with this parameter may contribute to the mutual skew of the abovementioned shafts and undercutting the root of teeth. 4. The skew of the shaft and increased radial clearances decrease its angular frequency to the first subharmonic. If this angular frequency will equal the frequency of other subassembly, e.g. the upper bearing of the main transmission, then, the spatial resonance of both subassemblies is created. 5. In spatial resonances, the subassemblies with smaller constructional offcuts are the first, which are subject to destruction. 6. Synchronous interaction of rolling bearing during resonance on the pair of gear wheels may end in undercutting of two teeth, production of focal points of fatigue cracks at the root and its breakage. References Augustyn, Sł., Gębura, A., 2012. Capabilities of the FAM-C method to diagnose the accessory gearboxes and transmission - train assemblies of the Mi-24 helicopters. Aviation Advances & Maintenance, 30.30: 199÷220. ISSN 1234-3544. Barszewski, W., 1956. A helicopter in flight. Wyd. MON, Warszawa. (in Polish) Bukowski, L., Kłysz, S., 1993. Fatigue of aircraft structures against the background of a 4-year experience activity. Biuletyn Wojskowej Akademii Technicznej, XLII, 3(487), Warszawa. (in Polish) Dudziński, A., Dudzińska, A., Flotyńska, A., 2011. Report No. 03/36/2011 from damage to the gearbox components of agreements, bearings and components of the helicopter rear shaft Mi-24W No. 410737 and two intermediate shafts with toothed wheels of the accessory gearbox 24-512-00 – type. ITWL, Warszawa. (in Polish) Gębura, A., 1999. Skew of splin connections and frequency modulation. Scientific Problems of Machines Operation and Maintenance, 34.4 (120): 763–772. (in Polish) Gębura, A., Tokarski, T. 2009. The monitoring of the Bering nodes with excessive radial clearances using the FAM-C and FDM-A methods. Research Works of Air Force Institute of Technology 25, 89–127. (in Polish) Gębura, A., Stefaniuk, M., 2017. Monitoring the helicopter transmission using the FAM-C diagnostic method, Diagnostyka 2, 75–85. Ghaffari, M.A., Pahl, E., Xiao, S., 2015. Three dimensional fatigue crack initiation and propagation analysis of gear tooth under load conditions and fatigue life extension with boron/epoxy patches. Engineering Facture Mechanics 135, 126–146. Jakielaszek, Z., Nowakowski, M., 2014. Selected characteristics of the electric propulsion system of aircraft as found out the ground-based laboratory tests, Journal of KONES Powertrain and Transport 4, 203–210. Kłysz, S., Lisiecki, J., 2009. Strength testing and analysis of fatigue crack growth in selected aircraft materials, in: Niepokólczycki A.: Fatigue of aircraft structures, monographic series, pp. 74–83, Institute of Aviation Scientific Publication, Warsaw. Padfield, G.D., 1998. Helicopter Flight Dynamic. The theory and Application of Flying Qualities and Simulation Modelling. WKiŁ, Warszawa. (in Polish) Żurek, J., et al., 2006. Helicopters life. Warszawa. (in Polish),