Further developments on gear transmission monitoring

Transcription

1 Further developments on gear transmission monitoring Niola V., Quaremba G., Avagliano V. Department o Mechanical Engineering or Energetics University o Naples Federico II Via Claudio 21, 80125, Napoli, ITALY vincenzo.niola@unina.it Abstract This work shows how it is possible to improve the algorithm used or the duration test. Generally, it shows some requencies in the spectrum o signal obtained by an accelerometer. Several considerations on requencies appears when an unexpected event occurs are presented. In the irst part o the paper it is described the typical requencies due to the vibration o the gearbox. In the second part it is illustrated the concept o harmonics, side bands and their meaning. In the third part a new index or monitoring the duration test is introduced. This index, as explained below is very important, because it gives the opportunity o checking the various aspects o the spectrum o the signal o an accelerometer. A warning starts i a damage on a gear wheel is detected. Key-Words: - Assembly-Phase-Passage Frequency, Tooth Repeat Frequency, Harmonics, Side Bands. 1 Introduction During some tests o duration o gear transmission perormed in laboratory, we ound out some undamental characteristics on the spectrum derived rom an accelerometer signal. These aspects careully investigated led the research or the gear transmission monitoring to a urther improvement. As it showed in ollowing pages, a new index or monitoring was proposed, which can be used in parallel with the ollowing one (see [1] or details): Index =Δ %( Area _ cur / Area _ re ) It gives more strength to the monitoring because by means o its more speciicity and sensitivity we can stop earlier the duration test. 2 Typical requencies o gear transmission vibration The vibrations o gear transmission system are characterized by certain "typical" requencies (signatures) that can be determined beore starting the monitoring. Usually, the spectrum o vibrations o a gear system is dominated by peaks belonging to typical requencies, but in some cases, it shows other requencies that don t coincide with typical ones. However, this irregularity is not true; in act these requencies can be made in relation to the typical ones. Below we can ind the deinitions o our requencies that usually occur as dominant peaks in the spectrum o vibrations o gearbox. The ormulas or the calculation o these requencies are valid both or a cylindrical gear with straighttoothed and or those with helical teeth, and or the wheel crown gear. As we show, beore using the ollowing ormulas to calculate these requencies, it is necessary to know the number o teeth and the speed o rotation o all wheels under testing. Frequency o rotation: let s consider a typical pair o wheels, where Z 1 is the number o teeth o drive wheel, n 1 its rotation speed (rpm), Z 2 the number o teeth o the driven wheel and n 2 its speed o rotation (rpm). We deine, or both the wheels, the requency o rotation or the drive wheel, and n = (1) n = (2) or driven wheel. Geared Frequency: it is well known that, during the rotation, teeth are subjected to collision, sliding and bending. These phenomena are repeated every time that a pair o teeth comes in contact, and thereore they appear as a vibration which undamental requency, characteristic o the pair o wheels, is the gear mesh requency (GMF or ). mesh Using the same symbolism adopted beore, the gear mesh requency is given by [2,3] GMF = Z n 60 = Z n 60 (3) The second equivalence concerns the act that or a pair o gears, the gear ratio is given by ISSN: ISBN:

2 and thereore, ε = n1 n2 = Z2 Z1 (4) Z 1 n1 = Z 2 n2 (5) and rom this ormula we can iner immediately the equivalence (3). From the deinition o rotational speed, it is possible to rewrite the expression o GMF GMF = Z = Z (6) Gear mesh requency and its harmonics are the dominant components in the spectrum o vibration as well as the noise o any gear transmission system [2,4]. Assembly-Phase-Passage requency: this requency could occur in the spectrum o vibrations o a gearbox when it is disassembled (e.g., or a detection or a repair) and then reassembled. For that reason the contact o teeth is never the same. Beore showing the ormula to calculate this requency, it is necessary to introduce the concept o Phase Assembly [2,3]. Let s take in consideration a typical pair o wheels, and let s suppose to numerate all teeth o both wheels starting rom the real point o contact, as it is showed in Fig. 1. Fig. 2 - Sequence o contact between the teeth Z 1 =Z 2 =6 During the rotation each tooth o the wheel 1 (pinion) comes in contact with a single tooth o the wheel 2 (gear). In this case, the teeth showing the same number develop during their contact, a complementary wear so that it compensate the imperections due to manuacturing and/or assembling operation. I ater a certain working period these two wheels are disassembled and then reassembled without taking the right sequence into consideration o the numbered teeth, each tooth would no longer be in contact with its "complementary" and it would bring out a changing in the vibration. We say that this pair o wheels has 6 Assembly Phases (). Fig. 1 - Teeth numeration or a generic pair o wheels Fig. 2 shows the sequence o teeth involved during their contact. Each wheel has 6 teeth. Fig. 3 - Sequence o contact between the teeth Z 1 =6, Z 2 =7 The Fig. 3 shows the sequence or two gears having respectively 6 and 7 teeth. In this case the situation is completely dierent. Ater 7 rotation, all the teeth o the pinion are in contact with all the teeth o the wheel; all teeth o both gears wear in the same way, and thereore, even i two gears have to be disassembled and then reassembled in a dierent way, there will be no change in vibration. This pair o gears has a single. Thereore, the number o (N ) o a pair o gearwheels can be considered as the number o ISSN: ISBN:

3 types o wear" (wear patterns) developed by the contact o teeth o the pair o wheels. Thereore the type o wear depends on the combinations o contact between the teeth. Numerically speaking, N is the highest common actor o the number o teeth or two wheels tested [2,3]. The "Assembly-requency Phase-Passage", is given by = GMF N (7) where GMF is gear mesh requency (Hz), N is the number o Assembly Phases or pair o wheels tested. Note that i N =1, coincides with the gear mesh requency. Tooth Repeat requency: this requency (Hunting- Tooth requency [2]) usually occurs when each o the two wheels has a deect localized on a tooth [2,3,5]. In this case, the pair o damaged teeth comes into contact one more time, with a requency equal to [2,3] TR ( ) ( ) = GMF N Z Z (8) 1 2 where: GMF is the gear mesh requency (Hz) N is the number o Assembly Phases Z 1 and Z 2 represent the number o teeth o the drive and driven wheel respectively. Once more, the value o the requency under consideration depends on N. 3 Harmonics and side bands It was already observed that in the spectrum o gearbox peaks appear requencies which are dierent rom the typical ones. These requencies are "unknown" and are oten reerable to one or more typical requencies because: they are multiple o a characteristic requency (in this case they are called typical harmonic requency) or they are the sum or the dierence o the typical requencies. The rotation requency or each wheel usually occurs when there is a residual imbalance, which causes a vibration and thereore harmonic component around the rotation requency [4,6]. Usually, the residual imbalance (static and/or dynamic) is always present, more or less, in all types o rotor. Static imbalance appears as a radial vibration characterized by a requency equal to N/60 (where N is the speed o rotation o the rotor expressed in revolutions per minute) and then, in the spectrum, it appears as a harmonic component at this requency [4]. However, it is well known the non-linearity o some components (e.g., lubricant ilm, bearings), may change the eedback o the system to generate components at higher requencies [6]. The amplitude o vibration due to imbalance growths with the square o the rotation speed. Usually, in the spectrum o vibrations o a gearbox, there are also the harmonics belonging to the requencies o rotation. In particular, a wide second harmonic o the rotation requency is usually taken as a signal due to the shat damage [2]. This points out the situations in which the shats o a pair o gears are not perectly parallel, or those in which the axes o the shats o two generic machines are not perectly coincident, in this case there are two types o problems: parallel and angular. Such situations usually are generated by errors realized during the assembling process. The peaks due to GMF and their harmonics are usually dominant in the spectrum. In some cases, in the neighbourhood o GMF, may appear peaks due to, or example, a small eccentricity o the drive/driven wheel. The peak requencies are: GMF ± 1 or GMF ± 2. (9) where and 1 2 are the requencies o drive and driven wheel respectively. The presence o these requencies is due to the act that the eccentricity modulates the amplitude o the orces acting during the mesh [2,6,7]. Localized deects on the teeth, such as cracks or broken part determine the apparition o several peaks in the neighbourhood o the GMF and its harmonics, due to changing o delection o the tooth during the mesh. This happens once or each rotation o the damaged wheel. This change could be seen as an amplitude modulation while the requency modulation is the requency o rotation o the damaged wheel. Thereore, the distance rom the side o the peak o the GMF can identiy the modulated requency, and then the wheel generating the deect [7,8]. In [7] (Chapter 16), talking about peak side, it is stated that: or localized deects such as cracks or broken on teeth, the side peaks are smaller than the gear mesh requency and they cover a very wide range o requencies or distributed deects such as wear or errors in working-process, the peaks side are more extended and are more clustered around the gear mesh requency and its harmonics. In a gearbox, each wheel can be a source o vibration and thereore o side peaks, in order to ISSN: ISBN:

4 measure, with low error, their distance rom the GMF, it is necessary that the spectra have, at least, the same resolution equal to the lower rotation requency. However, even this kind o resolution might not be enough, to dier rom neighbourhood o GMF, because o its very low value. This is a negative aspect, because it would mean a loss o inormation i two gears show a well localized damage [4]. In this case, i it is impossible a urther improvement o the resolution, it is undamental to carry out an analysis based on the techniques o the close-up. The requencies and TR could appear as peaks side o the GMF, where, respectively, the pair o wheels is disassembled and reassembled in a dierent sequence and contemporary both the wheels are damaged. It should be remarked that i both wheels have the number o teeth such as N = 1 their =GMF, and thereore the Assembly-Phase-requency Passage is no more distinguishable rom the GMF. The Tooth-Repeat requency, however, because o its very low value, could hardly be distinguished, especially when N = 1. 4 Index o Side Bands The idea to improve a new index or monitoring the duration test o a gearbox was born starting rom the ollowing considerations. First o all we thought to monitoring only the most important requency (or their orders [1]). But it should be a very expensive system. A new index has been proposed to enorce the previous index in [1]. For each order the index o Side Bands is the ratio, between the "current spectrum" and the target spectrum. This index doesn t overthrow the threshold level o 3. So this index, takes on account how the instantaneous spectrum is related to the target spectrum: the index should ideally be close to "1" or each order. As it is well known in the literature, and as we reported beore, the presence o side-band and the changing o the spectrum, due to typicall requencies dierent rom the typical ones o gearbox, indicate the presence o deects. In these cases the Index_SideBand> 1. Moreover, reerring to the irst threshold [1] Δ %( Area _ cur / Area _ re ) (10) meaningul changes o some orders could not stop the test (e.g., the order o bearing changes, which has no weight on the overall spectrum). In these cases, i the Index_SideBand> 3 we stop the test and we also have an indication on which order is increased. For this type o monitoring is not required the use o additional sensors and this is a great additional beneits or us. So, on the algorithm proposed in [1], we thought to modiy the STEP 5 only, in which the Index_SideBand must be controlled. So the process is modiied as in Fig. 4: Fig. 4 - How the algorithm stop the test where Index_SB stands or Index_Side_Band. Using this method the monitoring control the energy content o the whole spectrum does not overthrow the threshold. In addition an order doesn t overthrow the other threshold. Note that i an order growths signiicantly, but not the irst index in [1] then the Index_SideBand should be employed in order to solve this kind o problem. In the next paragraph it will be showed how the above index should be used or stopping earlier the test. 5 Experimental results Taking now the same test showed in [1], we can see that the duration test is stopped to the 13% o the total test. Vice versa, by means o the index proposed in [1] the perormance was less good, in act the test-run was stopped at 16% o the total test. The diagrams reported below, obviously, show only a part o the test results. They are selected to best underline the duration test perormed with this technique. We analyze the 6 th cycle (in particular, two seconds: the instants corresponding to 40s and 80s). Later it will be shown 2 seconds o the 13 th cycle where the test-run was stopped. ISSN: ISBN:

5 In order to see the Index_SideBand, in Fig. 8 it is represented the ratio between these two spectra. Fig. 5 - Comparison at 40s In the Fig. 5 it is represented the target spectrum and the actual spectrum (at 40s). To check the eectiveness o the Index_SideBand, it must be done the ratio between these two spectra as it is shown in the Fig. 6 Fig. 8 - SideBand at 80s It s clear again that the test can go on. Fig. 9 shows the 13 th cycle: at the second 1 the order 1 has already overthrown the target Fig. 6 - SideBand at 40s It s clear that the Index_SideBand doesn t overthrow the threshold level, so the test-run can go on. In Fig. 7 it is shown the spectrum at 80s. Fig. 9 - Comparison at 1s At this moment the order 1 o the actual spectrum overthrow the amplitude o the same order o the target spectrum. It s quite clear looking at the Fig. 9, but it is more clear looking at the Fig. 10 in which it is reported the Index_SideBand. The threshold imposed to stop the duration test. Fig. 7 - Comparison at 80s ISSN: ISBN:

6 Fig. 10 SideBand at 1s Using Vibration Analisys, Application Note [5] A. V. Barkov, N. A. Barkova, Diagnostic o Gearing and Geared Couplings using Spectrum Methods, Proceedings o the 20 th Annual Meeting o the Vibration Institute, Saint Louis, Missouri, USA [6] R. B. Randall, State o the art in monitoring rotating machinery Part I, Sound & Vibration, March [7] C. M. Harris, Shock and Vibration Handbook, 4a ed., McGraw-Hill [8] K.WANG Phase inormation at tooth mesh requency or gear crack diagnosis, Proc. 2nd IEEE Conerence on Industrial Electronics and Application, So looking at the last diagram the duration test must be stopped at the 13 th cycle, with all beneits. 6 Conclusions The new index proposed in this paper allows new perormance. In act, the algorithm is designed or detecting earlier the gearbox damage. The Index_SideBand monitoring each order gives us inormation about each one o these orders. So it helps to ind the reasons o damage. In act, as we showed in the above paragraphs, each event is showed like requency. Observing the requencies which overthrow the threshold level, we can detect the wheel to which requency corresponds. Note that test is also stopped i one order overthrows o the threshold level. The Index_Area leads to stop the duration test only i the total contribution, given by the area o spectrum, overthrows the threshold level. The proposed algorithm, using two index, oers a better control o the test and gives more inormation about an unexpected event that can cause a serious damage to the gearbox. Reerences [1] V. Niola, G. Quaremba, V. Avagliano, Vibration monitoring o gear transmission in press. [2] G. F. Lang, S&V Geometry 101, Sound & Vibration, March [3] J. G. Winterton, Component identiication o gear-generated spectra, Machinery Diagnostic Services, Bently Nevada Corporation, 1991 [4] Hewlett-Packard, Dynamic Signal Analyzer Applications. Eective Machinery Maintenance ISSN: ISBN: