BWD型擺線針輪減速器設(shè)計(jì)及虛擬裝配研究【說明書+CAD+PROE】

BWD型擺線針輪減速器設(shè)計(jì)及虛擬裝配研究【說明書+CAD+PROE】,說明書+CAD+PROE,BWD型擺線針輪減速器設(shè)計(jì)及虛擬裝配研究【說明書+CAD+PROE】,bwd,擺線,減速器,設(shè)計(jì),虛擬,裝配,研究,鉆研,說明書,仿單,cad,proe Robert B. Randall ,Jerome Antoni a School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia b article info Article history: Received 23 July 2010 Accepted 29 July 2010 Keywords: Rolling element bearings Diagnostics Cyclostationarity Spectral kurtosis Minimum entropy deconvolution Envelope analysis . 486 Contents lists available at ScienceDirect journal homepage: Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 25 (2011) 485520 0888-3270/$-see front matter fax: +61 2 9663 1222. E-mail addresses: b.randallunsw.edu.au (R.B. Randall), jerome.antoniutc.fr (J. Antoni). 1.1. Short history of bearing diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 2. Bearing fault models and cyclostationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 2.1. Localised faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . digital implementations are explained. (b), (e) raw spectra; and (c), (f) envelope spectra. much later shown to be incorrect, and so this approach has not been expanded on in this tutorial, even though it can give R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520 489 satisfactory results in some situations. At around that time, the high frequency resonance technique (HFRT), later called envelope analysis, was developed (see 7 and the first 15 references of 1). Even though this is described in the previous section as solving the problem of smearing of high harmonics (Fig. 2), this was not the main reason for its development, since it probably was not recognised at the time because of the limited resolution of FFT analysis. The main reason for its development was to shift the frequency analysis from the very high range of resonant carrier frequencies, to the much lower range of the fault frequencies, so that they could be analysed with good resolution. The frequency shifting was done using analogue rectifiers. Even in McFadden and Smiths classic paper on the modelling of bearing fault signals 1, the fault pulses are treated as periodic. This concept of demodulating high frequency resonant responses led to the development of a number of bearing diagnostic methods, where the demodulated frequency was the resonance of the transducer itself. This includes the Shock Pulse Meter (SPM), marketed for some time by the SKF bearing company, and the Spike Energy method marketed by IRD. These used the resonance of a conventional accelerometer as the main carrier, in the former case with bandpass filtering around a well-defined frequency of about 32 kHz, and in the latter case a highpass filtering at about 15 kHz, with more tolerance for the transducer resonance. Systems including acoustic emission (AE) transducers, with frequency ranges from 50 kHz to 1 MHz, were also introduced at that time. While often being effective in improving the signal/noise ratio of bearing signal to background noise, this was not universally the case. Ref. 8 describes situations where the transducer resonance happened to coincide with other excitations, such as turbulence and cavitation in pumps, and therefore gave false readings. The authors recommended choosing the appropriate resonance frequency for demodulation in each case. There has long been a discussion on how to choose the optimum bandwidth for the demodulation associated with envelope analysis. Some recommended searching for a peak at high frequency in response spectra, on the assumption that it would be excited by bearing faults, while others suggested that a hammer tap test would be more likely to identify bearing resonances. In the authors opinion, prior to the development of the spectral kurtosis (SK) based methods in the current tutorial, the best approach was to demodulate the band with the biggest dB change from the original condition, although this does require having reference signals with the bearings in good condition. Such methods are not discussed further in this tutorial because the authors believe that the methods proposed herein solve the problems in the vast majority of cases. Another approach to bearing diagnostics that can be found in the literature, but is not discussed here, are statistical methods based on pattern recognition. These rely on training a pattern recognition system with typical signals representing the different classes to be distinguished. There are two main reasons why such methods are not treated here. One is that they require large amounts of data for the training, and it is very rare that sufficient data can be acquired by experiencing actual faults in practice, including all permutations and combinations of fault type, location, size, machine load and speed, etc., in particular for expensive critical machines. Most published results are not non- dimensionalised and would only apply to a particular bearing on a particular machine for which the system was trained. It is likely that some of these problems will be overcome by fault simulation in the future. The other reason is that the authors believe that the quasi-deterministic approach proposed in this tutorial covers the vast majority of situations, as exemplified by the wide range of different cases treated in Section 6, without requiring excessive amounts of data from failures. Even so, the reader is referred to the Tutorial on Natural Computing 9 for a detailed discussion of methods based on pattern recognition. 2. Bearing fault models and cyclostationarity Bearing faults usually start as small pits or spalls, and give sharp impulses in the early stages covering a very wide frequency range (even in the ultrasonic frequency range to 100 kHz). However, for some faults such as brinelling, where a race is indented by the rolling elements giving a permanent plastic deformation, the entry and exit events are not so sharp, and the range of frequencies excited not so wide. They would still generally be detected by envelope analysis, however. Cases have been encountered where faults have not been detected while small and the spalls have become extended and smoothed by wear. Although not necessarily generating sharp impacts any more, this type of fault can often be the response vibrations. He pointed out that at such high frequencies, in the tens of kHz, measurable acceleration levels corresponded to extremely small displacements, which could be accommodated in the clearance space between surface asperities of a bearing ring in its housing, even after fitting, and thus natural frequencies were not greatly modified by the mounting. Shortly after, in 1970, Weichbrodt and Smith 4 used synchronous averaging to expose local faults in both bearings and gears. In the former case they sometimes performed averaging on the (rectified) envelope signals. Braun 5 made a fundamental analysis of synchronous averaging in 1975, and the basic technique was also applied to bearing signals 6. This appears to be one of the first references to the fact that bearing signals are not completely periodic, with a random variation in period. Braun made an analysis of the effects of jitter (of the synchronising signal) and likened this to the random spacing of bearing response impulses. This model, which is effectively Model 1 in the next section (Fig. 4), was detected by the way in which it modulates other machine signals, such as the gearmesh signal generated by gears supported by the bearings. Fig. 3 illustrates the case of an extended inner race spall, where the gearmesh signal is modulated by the type of signal shown, a mixture of a deterministic (local mean) part, and an amplitude modulated noise as the rough section of the race comes into the load zone. It should be kept in mind that the rolling elements are on a different part of this rough surface for every revolution of the inner race. The optimum way to analyse a faulty bearing signal depends on the type of fault present. The main difference is between initial small localised faults, as illustrated in Figs. 1 and 2, and extended spalls, as illustrated in Fig. 3, in particular if the spalls become smoothed. Both fault types give rise to signals that can be treated as cyclostationary. For a signal to be cyclostationary of order n, its nth order statistics must be periodic. Thus, a first-order cyclostationary signal (CS1) has a periodic mean value (e.g. a periodic signal plus noise) while a second-order cyclostationary signal (CS2) has periodic variance (e.g. an amplitude modulated white noise). The statistics are obtained by ensemble averaging over an ensemble of realisations. The consequences of this are summarised in Appendix A, and much more detail can be found in 10,11. 2.1. Localised faults For localised faults, the question arises as to the correct way to model the random spacing of the impacts. Perhaps the first publication to model bearing fault signals as cyclostationary was 12, but the results were not very convincing, possibly because the main resonances excited by the faults may have been outside the measured range up to about 6 kHz. Results are shown below (Fig. 18) where localised faults on a very similar sized bearing only manifested themselves at frequencies above 8 kHz. Good results were obtained in 13, by modelling the vibration signals from localised bearing faults as CS2 cyclostationary. However, the way of modelling the random variation in pulse spacing in Ref. 13 (model 1) was later found to be incorrect, and in 14 a more correct model (model 2) was proposed. As illustrated in Fig. 4, the variation in model 1 was load spalled surface R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520490 Fig. 4. Two models for the variation in period of pulses from a localised bearing fault. distribution Instantaneous reacted force F(t) on the gears t shaft period Fig. 3. Typical modulating signal from the effect of an extended inner race fault on a gear signal. modelled as a random jitter around a known mean period, whereas in the correct model it is actually the spacing itself that is the random variable. In particular, this has implications for the uncertainty of prediction of the location of a future pulse. For model 1, this is constant, and determined by the jitter, whereas in the actual situation, the variation is caused by slip for which the system has no memory, and thus the uncertainty increases with time of prediction into the future (model 2). As pointed out in 14, and put on a firmer mathematical basis in 15, this means that the signals from a localised fault in a bearing are not truly cyclostationary, but are better termed pseudo-cyclostationary. Fig. 5 (from 14) shows the practical consequences of this for a signal with a small amount of random variation. It is seen that in terms of interpreting spectra, in particular envelope spectra, usually only at the low harmonics, there is little practical difference in treating the pseudo- cyclostationary signals as cyclostationary. It was shown in 13 that the spectrum of the squared envelope of a signal (vs cyclic frequency) is equal to the integral of the spectral correlation over all normal frequency. See Appendix A for a discussion of spectral correlation. Fig. 6 shows a typical example. In this case, the (squared) envelope spectrum contains all the diagnostic information required, namely the harmonics of BPFI, with low harmonics and sidebands spaced at shaft speed, and so there is no real benefit in showing the full spectral correlation. 2.2. Extended spalls For extended spalls, there will often be an impact as each rolling element exits the spall, and in that case, envelope analysis will often reveal and diagnose the fault and its type. However, there is a tendency for the spalled area to become worn, in which case the impacts might be much smaller than in the early stages. Such extended spalls can still be detected and diagnosed if the bearing is supporting a machine element such as a gear, as discussed in connection with Fig. 3. The typical modulating signal shown in Fig. 3 contains both CS1 (the local mean value) and CS2 (amplitude modulated noise) cyclostationary components. In contrast, for gears supported in healthy bearings, even with a faulty gear, Force (dB) random contribution -30 R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520 491 0 Frequency periodic contribution -40 5/T 10/T 15/T 20/T 30/T25/T pseudo -periodic contribution random contribution Frequency Force (dB) 10 0 -10 -20 -30 -40 0 5/T 10/T 15/T 20/T 25/T 30/T Fig. 5. Frequency spectra for the two models: (a) model 1 and (b) model 2. the modulating signal tends to be deterministic (CS1 when mixed with noise), because the same profiles mesh in the same way each time. Fig. 7 compares the gearmesh modulating signals for a gear fault and an extended inner race bearing fault, and the spectral correlation of the latter. This has discrete characteristics in the cyclic frequency direction, but a mixture of discrete and continuous characteristics in the normal frequency direction. This is because a periodic signal has a periodic autocorrelation function (in the time lag or t direction) so the Fourier transform in this direction also gives discrete components. Thus the spectral correlation has discrete components in both directions (a bed of nails). If the periodic 10 0 -10 -20 R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520492 0 100 200 300 400 500 Frequency f Hz components are removed (by one of the methods described below), then only the CS2 components will be left, and they could only come from an extended bearing fault in a case such as this. Note that the continuous lines in the spectral correlation of Fig. 7 are at the low harmonics of shaft speed (O) but also in principle at the harmonics of BPFI and sidebands spaced at shaft speed around them. For an inner race fault the shaft speed is probably the best to use to extract this information, but for an unmodulated outer race fault, components may be found in the spectral correlation at harmonics of BPFO. Note that where the shaft speed is the modulating frequency, the signal is truly second-order cyclostationary (since the cyclic frequency is completely determined) whereas if the modulating frequency is BPFO or BPFI, the signal would be pseudo-cyclostationary. Fig. 8 (from 14) shows the spectral correlation, for cyclic frequency equal to shaft speed O, for two cases of inner race faults in the same type of bearing. For the localised fault, the difference manifests itself at high frequencies above Fig. 7. Spectral correlation for a mixture of first and second-order cyclostationarity, illustrated using modulation by gear and bearing signals: (a) gearmesh modulation by a gear signal; (b) gearmesh modulation by an extended inner race bearing fault; and (c) spectral correlation for case (b). From 14. 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 0 0.5 1 1.5 2 2.5 3 x 10 6 Frequency afii9825 Hz Frequency afii9825 Hz Integrated CSD 9.5 Hz 120Hz 240Hz Fig. 6. Spectral correlation and spectrum of the squared envelope for a local inner race bearing fault. BPFI=120 Hz, shaft speed=9.5 Hz. made on a gearbox test rig, the spall had become smoothed and did not reveal itself by envelope analysis at BPFI, only at R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520 493 the harmonics of shaft speed, and so could have been misinterpreted as a gear fault if this analysis (with removal of deterministic components) had not been done. 3. Separation of bearing signals from discrete frequency noise One of the major sources of masking of the relatively weak bearing signals is discrete frequency noise from gears, since such signals are usually quite strong, even in the absence of gear faults. Even in machines other than gearboxes, there will usually be strong discrete frequency components that may contaminate frequency bands where the bearing signal is 1000 shaft orders, whereas for the extended fault the differences are concentrated at lower frequencies up to 15 times the gearmesh frequency. In the former case the fault was easily detected by envelope analysis, but in the latter case it was much less clear. Fig. 9 (also from 14) shows an actual case from the input pinion bearing of a helicopter gearbox, where the extended inner race spall was not detected until very late. There was no on-board vibration monitoring, and metal particles were getting trapped in an oil dam, and not reaching the chip detector. By the time these measurements were Fig. 8. Spectral correlation evaluated for cyclic frequency equals shaft speed: (a) localised fault and (b) extended fault. otherwise dominant. It is usually advantageous therefore to remove such discrete frequency noise before proceeding with bearing diagnostic analysis. A number of methods are available, with different pros and cons. The notational convention used throughout the presentation is to denote the measured vibration signal either by x(t)orbyx(n) depending on whether continuous-time or discrete-time is most convenient. Filtered versions of x will be systematically denoted by y. For convenience, the spectrum of any signal, say s, will be denoted by S(f) independently of whether s is continuous or discrete-time. 3.1. Linear prediction Linear prediction is basically a way of obtaining a model of the deterministic (i.e. predictable) part of a signal, based on a certain number of samples in the immediate past, and then using this model to predict the next value in the series. The residual (unpredictable) part of the signal is then obtained by subtraction from the actual signal value. The model used for linear prediction is an autoregressive or AR model as described by the following equation: ynC0 X p k 1 akxnC0k 5 where the predicted current value y(n) is obtained as a weighted sum of the p previous values. The actual current value is given by the sum of the predicted value and a noise term: xnynen 6 As described in 16 the a(k) can be obtained using the YuleWalker equations, often using the so-called Levinson Durban recursion (LDR) algorithm. R.B. Randall, J. Antoni / Mechanical Systems and Signal Processing 25 (2011) 485520494 0 1.2 2.4 3.6 4.8 6.0 7.2 8.4 9.6 10.8 10 20 30 40 50 60 70 Frequency kHz dB 12 = 0 60 70 = Note that Eqs. (5) and (6) can be combined and written as xn X p k 1 akxnC0ken 7 which can be Fourier-transformed to XfAfEf 8 or Xf Ef Af 9 which can be considered as the output X(f) of a system with transfer function A C01 (f) when excited by the forcing function E(f). The transfer function is thus an all-pole filter, and can be interpreted as an autoregressive (AR) system. The forcing function E(f) is white, containing stationary white noise and impulses, and its time domain counterpart e(n) is said to be prewhitened. Thus, removing the deterministic (discrete frequency) components leaves a prewhitened version of the residual signal, which includes the bearing signal because of the randomness of the latter. 3.2. Adaptive noise cancellation Adaptive noise cancellation (ANC) is a procedure whereby a (primary) signal containing two uncorrelated components can be separated into those components by making use of a (reference) signal containing only one of them. The reference 0 1.2 2.4 3.6 4.8 6.0 No fault fault 7.2 8.4 9.6 20 30 40 50 Frequency kHz 1210.8 A c c e l e rat i on (dB ) Fig. 9. Comparison