A Helicopter Planetary Gear Carrier Plate Crack Analysis and Feature Extraction based on Ground and Aircraft Tests

Transcription

1 A Helicopter Planetary Gear Carrier Plate Crack Analysis and Feature xtraction based on Ground and Aircraft Tests Abstract Panagiotis Sparis Professor Democritus University of Thrace and George Vachtsevanos Professor Georgia Institute of Technology Fatigue cracks of considerable length were discovered in two separate main transmissions planetary gear carrier plates of U.S. Army helicopters. These cracks originated at the blend between the gear post and the plate and later diagnosed as low cycle fatigue. Cracks on the planet carrier plate are a very serious but rare type of fault that may require the redesign of this critical part. In this paper an investigation of the problem is attempted using experimental data from ground and aircraft tests. Two features based on the signal energy are used to distinguish the faulty from the healthy plate using the signals from four one-dimensional accelerometers. A data analysis based on the Time Synchronous Averaging signal transformation tends to indicate that the apart from any machining error or material fault that may have initiated the crack; there is evidence of a non-rotating fault, possibly on the ring gear, as well as a considerable non-uniform distribution of forces among the planet gears that may have been generated by the presence of the crack and or may have promoted its rapid development. Key Words: Fault Diagnostics, Crack Detection, Feature xtraction, Planetary Helicopter Transmission, Planet Carrier Plate.

2 . A Brief Introduction to the Problem The problem in question was initially posed when during routine engine checks caused by ow oil pressure indication, cracks were discovered on two carrier plates of the transmission of an US Army UH-A Blackhawk helicopter. This type of helicopter has two engines rated according to the exact model between -8 HP approximately at rpm. Both shafts converge to the transmission that uses a fiveplanet planetary gear reduction system that reduces the engine speed to approximately rpm. The specific faults were considered very serious, not only because it could lead to a crash, but also because the engine health monitoring system already existing onboard had fail to diagnose this type of failure. The smaller crack of the two plates, illustrated in Fig. courtesy of the US Navy, was used to collect data both on the ground and on the aircraft at the Helicopter Transmission Testing Facility at Patuxant MD and at the Corpus Christ Army Depot respectively, whereas the healthy gearbox data were provided by the Birmingham, Alabama National Guard using several healthy transmissions. The cracked transmission was tested and data were collected with a measuring frequency of khz, using an array of accelerometers. The whole test lasted for 8s that correspond roughly to revolutions of the plate for each engine torque setting. Technical details of the sensors used and the vibration monitoring process were given by Keller [] and will not be repeated here. In this early paper [], an effort was made to investigate the problem using the Kurtosis feature with partial success, because it was not possible to differentiate the healthy from the faulty transmission under certain operating conditions. The location of the four vibration sensors is outlined in Fig.. Input Sensor Input Sensor PortRing Sensor Starboard Sensor Fig.. Crack Length 8 cm approx. Fig.. Sensor Location Illustrations Courtesy of Keller, Johnathan, Grabill, Paul, Vibration Monitoring of a UH-A Main Transmission Planetary Carrier Fault. Most recently Sahrmann presented [] a thorough investigation of the crack development. As it is clearly stated in this paper, the crack growth rates measured were considerably higher than the ones predicted by the analytical models. In fact, the crack grew an additional. inches during the tests that provided the present vibration data.

3 On the basis of the microscopic analysis of the crack has been identified as low cycle fatigue []. In a private communication with the authors, Dr. Sahrmann indicated that there were no visible signs on the bearings that suggested there was a bearing failure or any damage caused by the oil leak.. A physical explanation of the crack development mechanism The initiation of a crack is the result of an interaction between several factors. Firstly, a weak area on the surface or in the crystal microstructure of the material must exist, created during the manufacturing process by a variety of effects, as metal impurities, voids, lattice imperfections during solidification, corrosion, chemical agents, machining errors, etc. Secondly, a crack will not progress further than the microscopic level unless there is a considerably strong time-varying stress field that would promote its growth. To detect a microscopic material fault at a production level is a very expensive enterprise, whereas the elimination of unnecessary vibrations through a careful design process is a more feasible alternative. In the present case the development of the crack near the planet support, in the absence of any serious manufacturing error is an indication that at this region there were considerable tensile stresses that exceeded the plate design specifications to generate low cycle fatigue conditions. The transmission in question uses a five-gear configuration that supposedly will transfer the torque to the rotor shaft by distributing it uniformly to each planet. If during operation the wheel b starts to decelerate, then this action will create tensile stresses on the carrying plate between the wheels (a), (b) and compression stresses between (b), (c). On the other hand, if planet (d) accelerates with respect to its neighbors (c), (e), compression will be created between (c) and (d) and tension between (d) and (e). Since only tensions forces promote crack development of this nature, cracks should be expected between the (a) and the (b) planet posts and or between the (d) and the (e) ones. In principle, friction due to a bearing failure or lack of lubrication can generate strong forces and vibrations that could easily crack the plate, especially when conditions of dry friction exist between moving parts in contact. However, in both faulty plates all planet bearings were in good condition, so friction is not responsible for any planet deceleration that could exaggerate the effects caused by another gear acceleration. If the excessive friction effects are absent, a possible cause for deviation from the equal gear speed condition, which is enforced by the epicyclical motion of the planets between the sun and the ring gear, is the possibility that, due to the extreme loads transmitted from the two engines to the helicopter main blade rotor, there is some form of deformation of the ring gear due to the radial components of the transmitted forces at the contact point. In such a case the planet gear teeth that come into contact with the ring gear teeth would create abnormal vibrations, since the point of contact would not lie at the correct positions in space as prescribed by the kinematics of the teeth geometry. In Fig. the surface of a planet tooth AB is in contact with the corresponding tooth CD of the ring gear. As the planet rotates the point of contact between the two teeth with respect to the planet gear moves along the evolutionary curve AB. On the other hand moves along the evolutionary curve CD with respect to the ring gear. Under normal operating conditions each planet tooth remains in contact with the corresponding

4 tooth of the ring gear for a certain time interval that corresponds to a specific arc described by the planet axis of rotation. For a smooth transfer of torque between the planets, the arcs of contact must be identical for all planets. However, if due to a ring gear deformation, the tooth CD has been misplaced to a new location C D the arc of contact that corresponds to this tooth will decrease or increase, depending on the shape of the deformation. Since the planet has to cover depending on the case arger or a smaller arc it would tend to increase or decrease its speed. However, since the plate carries all the planets, this tendency will be countered by the exertion of stresses on their posts by the following mechanism. b Β a D D Fault f Sensor a a K B A C C b b c e d Α Fig. Fig.. Ring Gear Deformation ffects Considering that the planet teeth are simultaneously in contact with the ring and the sun gear at the point, for a smooth operation these two points of contact must be on a straight line with the center of planet rotation K. If this condition is no fulfilled the result will be the exertion of abnormal stresses at these three points as torque would tend to deform the planet, the sun and the ring gear teeth to satisfy this kinematic condition. In our case the planet post region of the plate has been excessively deformed and cracked to accommodate the geometric constrains of the motion. In the following section we will attempt to examine the power spectrum of the transmission from the ground and aircraft tests and search for traces of evidence that could pinpoint the source of the problem.. Vibration Data Processing a. Ground Tests Since our goal is to investigate the transmission faults that led to the development of the crack, we will now turn our attention to the vibration energy radiated by each planet gear. An estimation of the load distribution that is transferred by each planetary gear can be obtained by examining the corresponding TSA signals [,]. The TSA signal, as

5 its name implies, is actually a time synchronous average of all the signal data collected within the measuring window over the o periphery of a planetary gear carrier plate. The advantage of this numerical procedure is that essentially amplifies all signals that have the same frequency with the plate and its harmonics. In our case the computation of the energy of the TSA signal was performed after the TSA transformation. Taking into account that the input torque generated by the two engines and transmitted by the five planets is constant and that the load at the transmission output for the ground tests is also constant since we do not use a rotor, the TSA for the signal energy that we expect to measure by these two sensors under normal conditions should have peaks every o. These peaks correspond to the passing of each planet from the sensor angular location. In reality, due to the unavoidable angular positioning errors of the planets, the effects of bearing and teeth clearances and unbalances, these peaks under normal circumstances may have slightly unequal heights and be shifted relatively to their geometrically exact angular position. In our case the cracked plates dimensions were measured and found within specification tolerances before the creation of the crack. A much more serious effect that can seriously alter this ideal TSA signal shape is the presence of some vibration generating fault. Consider for example the case that a fault is present on the ring gear, as Fig. indicates. As the planets pass in front of the sensor the vibrations they produce reach a maximum that explains the presence of the five peaks of the TSA signal. On the other hand, the plate crack is essentially a rotating source of vibration, therefore its effect will appear between two successive lobes. However, if a stationary fault exists on the perimeter of the ring gear, then vibrations would be generated every time a planet passes from this point creating five intermediate secondary lobes. If the fault is positioned at an arbitrary location that has not a angle difference of o, o, o, or 88 o with the position of the sensor, then the vibration generated by the planet passing will reach the sensor at two distinct instances that correspond to the time intervals that the sound wave travels the two generally unequal arc(fas) and arc(fbs). This effect will also affect the expected five-lobe structure. Finally, the two sensors that are located far away from the vibration sources would have a considerable lower signal levels due to attenuation effects, but would tend to monitor more clearly the vibration signal since there would by no significant difference in the time delays caused by the unequal lengths of the (fas), (fbs) arcs. Therefore, although the signal coming from these sensors is weaker, it is less confused. a. Ground Tests The helicopter transmissions with the healthy and the cracked plate were tested on the ground for the full range of engine loads. During these tests the load used was constant and did not exhibit the characteristic per revolution variation caused by the four-blade rotor that is present in the case of the aircraft tests; therefore the structure of the TSA signal is simpler than the actual one on the aircraft. Since accelerations are the result of forces, it is natural to assume that the planet that carries the heavier load and stresses will generate the greater percentage of vibration energy. The vibration energy of a signal x=x(t) may be defined as e = e( t) = x'( t) x( t) ()

6 The TSA signals of the signal energy e at the engine torque setting of % for the PortRing and the StbdRing are illustrated for the healthy and the cracked plate in Figs., respectively. Similar results were obtained for the % and % torque settings for these two sensors that will not be presented for brevity. From Fig. we may notice that the overall level of the signal energy in the case of the cracked plate in Fig. is higher than the corresponding for the healthy one, as expected. There is also evidence of a nonuniform distribution of the vibration energy among the five planets, combined with the existence of intricate structures in the valley regions between the lobes. These intermediate lesser lobes are not related to the crack, since, as we previously mentioned, the effect of a rotating crack would appear only once within the interval of two successive planet lobes. 8 x 8 x Ground Tests: % PortRing - Cyan StbdRing - Blue Ground Tests: % PortRing - Cyan StbdRing - Blue 8 8 Fig.. Healthy Plate % 8 8 Fig.. Cracked Plate % x x 9 8 Ground Tests: % Input - Green Input - Red 9 8 Ground Tests: % Input - Green Input - Red 8 8 Fig.. Healthy Plate % 8 8 Fig. 8. Cracked Plate % In Figs., 8 the corresponding TSA for the Input, Input signals are illustrated for % torque. In the case of these sensors the five-lobe structure is more distinct. Due to the different strength of the sensor signals, the scales of the PortRing and StbdRing plots for the y-axis are the same, namely (-8e ), whereas for the Input, Input the scale is reduced to (-e ).

7 Consider now the PortRing TSA signal energy plot in the case of % load for the healthy and the cracked plate, as presented in Fig. 9. There are several interesting observations that can be made. Firstly, as the arrows a, b indicate, the signal energy distribution on each planet of the cracked plate is strongly non-uniform. On the contrary, the five-lobe structure is quite distinct for the healthy plate. Additionally, as the arrows c, and d indicate, among the planet five peaks there are other intermediate peaks that should correspond to some fault on the ring gear. 8 x a g f Ground Tests: % PortRing Sensor Healthy Plate - Cyan c h e b d 8 8 Fig. 9. Healthy vs. Cracked Plate Comparison (PortRing) This is also in agreement with the presence of the peaks f, g ahead of the healthy peaks at e, h. The angle φ that corresponds to this difference of phase is approximately φ=. ο. Τhis angle has considerable magnitude and it is difficult to believe that it is caused only by the crack that developing may cause a displacement of the planet posts. Actually, considering that the mean radius of the plate at the region of the crack is of the order of, an angle increment equal to φ would correspond to inear displacement of the order of that cannot correspond to the planet gear post displacement caused by the crack. Therefore, it must be attributed to other effects. A possible cause that is consistent with the above findings from the TSA signal and the previously described mechanism of crack development is the deformation under load of the ring gear. A deformation of the gear ring could explain the advances of the peaks (g-h), and (f-e) and the delay (c-d), as well as the presence of secondary lobes of lesser magnitude Before closing this subject, it is interesting to see how other sensors describe these phenomena. In Fig. the TSA signal of the StbdRing is presented. In the case of the crack plate, for each planet correspond two peaks, while a similar structure to esser extend is developing also for the healthy plate. As we already mentioned before, the presence of multiple peaks is evidence of a non-rotating fault on the ring gear that generates vibrations when each planetary gear passes from the fault position. There is also evidence of considerable non-uniformity in the planet signal energy distribution.

8 8 x x Ground Tests: % StbdRing Sensor Healthy Plate - Cyan 9 8 Ground Tests: % Input Sensor Healthy Plate - Cyan 8 8 Fig.. Healthy vs. Cracked Plate Comparison (StbdRing) 8 8 Fig.. Healthy vs. Cracked Plate Comparison (Input) In the case of the Input signal illustrated in Fig. a considerable shift of the peaks of some planets from their geometrical exact positions is evident for both the healthy and the crack plate. Also, the number of peaks is greater than five but less than ten, suggesting the possibility of a fault on the ring gear or a plate crack. It is also quite possible that within the mass of the transmission a combination of interference and dissipation effects could attenuate or weaken some signals. The Input signal gave similar results with the Input sensor that are not presented for brevity. The variations of the planet signal energy can be also expressed graphically as a function of the engine torque. For this purpose the TSA signal of each sensor has been shifted in time so that it s maximum coincide with the first of the 8 points per plate revolution. Using this resolution the TSA signal energy that corresponds to each planet can be found if one sums the corresponding values of this signal. x. x n o t i D evia S tḋ gn S i e t P l a n 8 Ground Test Data PortRing Sensor n o t i D evia S tḋ gn S i e t P l a n.... Ground Test Data Input Sensor Fig.. Planet Signal nergy Std. Deviation PortRing Sensor Fig.. Planet Signal nergy Std. Deviation Input Sensor valuating the standard deviation of these measures for each signal, torque and plate we obtain the four plots illustrated in. Figs. -. We observe that there is 8

9 considerable variation of the planetary gear loads for both the healthy and the cracked plate especially between 9% and % torque, even for the uniform loads of the ground tests, that cannot be easily accounted for. x n o t i D evia S tḋ gn S i e t P l a n 8 Ground Test Data StbdRing Sensor n o t i D evia S tḋ gn S i e t P lan 9 8 Ground Test Data Input Sensor Fig.. Planet Signal nergy Std. Deviation StbdRing Sensor Fig.. Planet Signal nergy Std. Deviation Input Sensor. Feature xtraction Ground Tests A useful measure of the signal energy e is its corresponding RMS =sqrt(e *e)/n () Where e is the transposed of the e vector and n is the number of samples. Using () the feature plots can be compiled for each sensor signal and illustrated in Figs. -. We note that for the case of % torque two measurements are available form the healthy plate. The fact that the feature can distinguish the two plates for all signals is an indication that this measure is characteristic of the crack. From these plots we also notice that the values of for both plates and all sensors tend to increase as the torque increases, however this increase is not monotone; therefore some higher torque settings tend to be less noisy for some sensors. These variations may be the result of the operational characteristics of the transmission, but may also be caused by purely geometrical effects, as the location and orientation of the accelerometers in relation to the local acceleration vector. In the present series of tests each sensor measures only one components of the acceleration vector; therefore, for some torque and sensor combinations the computed signal energy is a fraction of the exact magnitude. Another reason that may also cause variation of the signal energy measured by each sensor is the distortion of the signal as it travels from its source to the sensors due to interference, diffusion, focusing, resonance and other wave transmission effects. The four plots, Figs. -9, are suitable for the clarification of the concept of features. Lets now suppose that the goal of the feature was to simply distinguish the healthy from the crack plate. From these plots it is clear that by using the feature, all 9

10 four sensors successfully distinguish the two plates on this basis. However the above logic is not the only one. For example, if we additionally required that the feature should also satisfy the requirement that the cracked plate will generate more vibration energy than the healthy plate, then only the PortRing, StbdRing and Input sensors give the correct answer using the feature...8 Ground Tests Feature Port Ring Sensor Healthy Plate - Blue.8. Ground Tests Feature StbdRing Sensor Healthy Plate - Blue Fig.. PortRing Feature Fig.. StbdRing Feature.. Ground Tests Feature Input Sensor Healthy Plate - Blue.. Ground Tests Feature Input Sensor Healthy Plate - Blue Fig. 8. Input Feature Fig. 9. Input Feature Nevertheless, this hypothesis is not the only physically consistent that we may make. Another reasonable condition is that the noise generated should increase with the engine torque as the stresses of plate increase. In this case only the sensor Input successfully implements all three assumptions. This signal is also superior, because it is also logical to expect that as the engine torque tends to zero the effects from presence of the crack of the crack should also tend to zero. Finally, since the ultimate goal of any feature extraction process is to incorporate it within the architecture of a prognosis algorithm, one would expect that a monotonic function, as the feature for the Input signal, should be more dependable base for a prediction process.. Feature xtraction Aircraft Tests During the aircraft tests data were collected at a slower rate, namely 8 khz using all four sensors. Only four measurements, two for each % and % torque have been

11 carried out for the cracked plate an aircraft # with the aircraft on the ground for safety reasons, and several using healthy plates on different helicopters. Raw vibration data were only available from the PortRing and Input sensors. The following figures, illustrate the feature for these two sensors. From these plots it is clear that the feature using either sensor successfully distinguishes the two plates and satisfies the logical assumption of the noisy cracked plate. It is also evident that the PortRing creates a higher level of distinction between the plates, and is therefore a safer pointer for diagnostic purposes Aircraft Tests Feature PortRing Sensor Healthy Plate - Blue.8.. Aircraft Tests Feature Input Sensor Healthy Plate - Blue Fig.. Signal nergy RMS (PortRing) Fig.. Signal nergy RMS (Input) Conclusions In the present paper an attempt is made to physically explain the generation of the crack near the post of a planetary gear. The radial direction of the crack suggests the presence of high tensile stresses in the tangential direction to the plate periphery. A possible cause for these stresses is the existence of non-uniformities of the torque distribution among the five planetary gears. This phenomenon may be caused, among other factors, by a ring gear deformation that could alter the contact arc of each planetary gear. vidence of this torque distribution non-uniformity was found in the TSA signal recorded by the two acceleration sensors positioned at the vicinity of the carrier plate during the ground tests. Unfortunately, due to the safety requirements during the aircraft tests the engine torque was limited to % and %, so it was impossible to observe similar phenomena at the more critical high torque settings with the rotor shaft present. A non-trivial question may be posed at this point. Is the crack the result of torque distribution non-uniformities among the planets, or is the presence of the crack the reason for the appearance of this phenomenon, or both? Clearly further tests are needed to reach a final conclusion; nevertheless, from the behavior of tensile materials it is well known that when a member fails, before a complete collapse, other members in its vicinity tend to carry the excess load that the failed member is incapable to bear. Therefore, it is natural to expect that the presence of a large crack would force severe load non-uniformities among the planetary gears.

12 On the other hand, the existing experimental data on the ground show expressed as signal energy standard deviation plots imply, the healthy plates exhibit considerable variations of the individual planetary gear load at high torque that could help explain the generation and propagation of a crack. Considerably more convincing is the experimental evidence that a non-rotating fault, possibly a ring gear deformation is present. In many TSA signals there is evidence of a secondary lobe structure between the main lobes that correspond to the planetary gear passing over the sensor position. This structure can be easily explained if we assume the there is a stationary fault causing each planetary gear to vibrate as it passes from its location. As we have previously explained, this type of fault is capable to generate tensile stresses between two planetary gear posts by varying the contact arc of each planet. References. Keller J. and Grabill P., Vibration Monitoring of a UH-A Main Transmission Planetary Carrier Fault, The American Helicopter Society 9 th Annual Forum, Phoenix, Arizona, May -8.. Sahrmann G.J., Determination of the Crack Propagation Life of a Planetery Gear Carrier, Presented at the American Helicopter Society th Annual Forum, Baltimore, MD, June -,.. McFadden, P.D., A Technique for Calculating the Time Domain Averages of the Vibration of the Individual Planet Gears and the Sun Gear in a picyclic Gearbox, Institute of Sound and Vibration, Vol., No., 99, pp. -.. McFadden, P.D., Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibrations, Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 8, No., Apr. 98, pp. -. Acknowledgements With this opportunity Prof. P. Sparis wishes to express his sincerest appreciation to his coauthor, collogue Prof. George Vachtsevanos and friend from the old country for two years of continuous guidance and support at Georgia Tech and for his introduction to the exciting field of engine fault diagnosis and prognosis. The authors wish also to express his gratitude to DARPA for the organization and financial support of this program and to the US Army and Navy for providing all the pictures and the data necessary for the compilation of this work.