Generation of a Tachometer Signal from a Smart Vibration Sensor Eric Bechhoefer, GPMS Ed Spence, The Machine Instrumentation Group Presented at the MFPT 2018 Virginia Beach, VA, 15-17 May 2018 Introduction TSA, commonly applied for shaft, gear and bearing analysis, requires a Tach A Tach cannot be applied in some applications A novel, 2-process is introduced to generate a high quality Tach signal from the vibration data – Cyclic rate of the shaft is reconstructed by removing extraneous vibration data with an idealized BPF – Then remove jitter from the resulting signal Tach signal can then be used for TSA averaging and TSA resampling algorithms Technique is demonstrated on two data sets Generation of a Tachometer Signal from a Smart Vibration Sensor Some History – S. BRAUN. The extraction of periodic waveforms by time domain averaging. Acustica, 32 (1975) TSA – R, Stewart: Some Useful Data Analysis Techniques for Gearbox Diagnostics, Institute of Sound and Vibration Research, Proceeding of Meeting on Application of Time Series Analysis, Sept. 1977 FM0/1/2/3/4,Residual, Envelope Analysis – Foundation for Modern Gearbox Analysis. Note: Stewart Comments on Tach Jitter, states that there is a limit to the number of Revs for the TSA 3 The Need for a Tachometer • Common to use FFT for Condition Monitoring Analysis – Frequency Magnitude and Phase – Idealized Filtering for Residual Analysis – Hilbert Transform for Amplitude and Frequency Modulation, Envelope analysis. • FFT Assumptions – Infinitely Long Signal (e.g. Gibb’s Effect) • Finite effects mitigated by windowing (Hamming, Hann, etc.) – Signal is Stationary – e.g. Exhibits Stationarity 4 Stationarity and Stationary Signals Implies that the conditions of the signal do not change Shaft rate always changing – Bandwidth limits of the feedback from controller Lack of Stationarity degrades spectral analysis – Spectral smearing Reduces the probability of fault detection 5 The Resample Algorithm • Restores Stationarity by resampling • TSA removes nonsynchronous noise – Reduces Asynchronous Signals by 1/Sqrt(n) is “consistent” – Usually Radix-2 – One Rev based on number of samples measured by the key phasor, e.g. the Tach – ex: 824 samples in a rev is resampled to 1024 TSA Algorithm Set TSA Length m = 2ceil(log2(r)) tsa = zero(m ,1) For i = 1:N Revolutions Resample r data points into M data points tsa = tsa + M Resam ple Algorithm Set Segment Length ceil(log2(r)) m=2 samp = zero(m*N,1) For i = 1:N Revolutions indx = i*m + 1:m Resample r data points into M data points samp(indx ) = M tsa = tsa/ N Get Apparent Sam ple Rate TSA = DFT(tsa) Spectrum = Welches(sam p) 6 The Tachometer Signal Taken as the rising edge of a Key Phasor – Variable Reluctance (e.g. Generator Signal) – NPN or PNP (e.g. Hall or Optical Sensor) Two Method for calculating Zero Cross Time – ADC: Sample the signal and post process for zero cross. Limited to sample rate (e.g. 100,000 sps) – Comparator on Microcontroller GPIO Pin. Essentially the clock speed of the Micro (50 MHz, etc.) Jitter reduces the “consistency” of the Tach signal – Generally, more Revs does not improve TSA 7 Why “Tachless” Vibration Monitoring Some applications cannot implement a Tach – e.g. Glandless Pump due to high temperature and pressure (see BCP paper, MFPT 2018) – Introduction would require expensive re-certification (e.g HUMS) HUMS adoption is an ROI calculation. – Removing Tach reduces cost – One less sensor reduces weight (less rotorcraft fuel) – Smart vibration sensors Local Processing of tachometer and vibration to reduce cost and weight 8 Generating Tach from Vibration is a 2-step process... Tach derived from the vibration signal still includes jitter – Need to reprocess to remove Theory: Vibration is synchronous with a shaft – Pick a Vibration Signal, say a gear mesh (27 tooth) – Count 27 zero crossings, and call that time the ‘Tach Zero Cross’ – Unfortunately, time domain signal is superposition of many signals... Thesis: process the signal to... – Remove extraneous signals (ex. Noise, shaft harmonics, gear mesh frequencies, etc) – Use the Analytic Signal for calculating the Zero Crossing 9 Using Analytic Signal for deriving Time of Zero Cross • Hilbert Transform defined as Gs 0 0 -0.5 -0.5 -1 -1 0 0.4 0.2 0.6 0.8 0 1 0.4 0.2 0.6 1 0.8 Time (sec) Reconstructed Zero Cross Time (sec) (Sa)) unwrap(atan(as)) • Ex: 2 Hz Sine 1 10 0.8 Radians – Imaginary Part of Sa is Signal + π/2 – Zero Cross is the Interpolated Time every 2π 0.5 0.5 Time (sec) S = F{s(t)} Sa(f) = S(f), f = 0 Sa(f) = 0, f < 0 Sa(f) = 2Sa(f), f > 0 sa(t) = F-1 (Sa(f)) 1 Real Image Gs – – – – – Analytic Signal 2 Hz Sine, 1000 sps 1 8 6 4 2 0.6 0.4 0.2 0 0 0 2 4 Angle (Radians) 6 0 2 4 6 Angle (Radians) 10 Prior Art • Bonnardot et. al (2007) demonstrated tach from vibe using the analytic signal – • Implemented a band pass filter filter centered on a gear mesh Band pass filters “leak” – 29 Hz shaft, 32 tooth: 928 Hz Gear Mesh – 120 tap FIR filter – Filter does not reject 1/Rev side bands, corrupts zero cross signal, reducing SNR • • • Phase Error (e.g. zct) is a function of SNR σ[δ]=1/sqrt(2)10-snr/20 6-8dB SNR is typical, or about 6 to 10 degrees of phase error 11 Improved Tach from Vibe Using Idealized Filter (Recipe*) • Calculate radix-2 length for the FFT. • Calculate the low and high bandwidth index (bwlow, bwhigh), which are centered are a know gear mesh • Take the zero padded FFT of the vibration data • Zero the FFT from zero to bwlow, and from bwhigh to nRadix • Take the inverse FFT • Calculate the unwrapped argument of the signal from 1 to n time series • Normalize the time series of radians by the number of teeth of the gear (assuming 1st harmonics) • Interpolate the number of indexes for every 2 radians • Normalized to tachometer zero crossing times by sr. *Much more tractable with a distributed processing approach... 12 Example of Idealized filter vs. FIR filter • 97,656 sps x 6 x sec – 585,936 -> 1,048,576 pt FFT • 29 Hz Shaft, 32 tooth Gear – 928 Hz +/- 29 Hz – Bandwidth of Filter 910 and 960 Hz – bwlow = 920/sr x 1,048,576 = 9771 – bwhigh = 960 / 97,656 * 1,048,576 = 10,308. – Sa(f) = 0, f < bwlow, f > bwhigh 13 Controlling Jitter – Prior Art A previous paper* described a 25% Improvement in analysis by reducing jitter – with Tach... Developed a zero phase IIR filter procedure to remove noise not associated with changed in shaft speed IIR filters are not ideal – New procedure uses Idealized filter... *Improving Gear Fault Detection by Reducing Tachometer Jitter, AHS 2015 14 Application of a New and Improved Jitter Reduction Procedure (Recipe) • • • • • • • • • • Take the pseudo derivative of the tachometer signal Calculate the the radix-2 length of the pseudo derivative signal of length n Zero pad the array from n to the radix-2 length Calculate the bandwidth index of the FFT Idx = floor(bandwidth * radix-2 length / 2); Bandwidth is a normalized value, typically 0.12 Take the real FFT of the zero padded derivative signal Set the real and imaginary parts of the FFT from Idx to the radix-2 length Take the inverse real FFT. Reconstruct the tachometer signal by taking the pseudo integral of the signal Data set from a wind turbine with 8 targets per revolution. The periodic peaks are due to spacing error in the tachometer target, which introduces non-random jitter error. The idealized filter removes all the spectral power (jitter) 15 Ex 1. High Speed Pinion on a Wind Turbine Wind turbine conditions: • SR: 97,656 • 30 Hz Shaft • Cracked Tooth On Pinion • Tach from Hall Sensor Using Comparator • 6 dB SNR data prior jitter reduction Comparison of Tach signal vs. Tach-less Solution 16 TSA Comparison 17 Tach vs. Tachless for Standard CIs Analysis Tach Tach from Vibe SO1 0.0100 g 0.0104 g SO2 0.0013 g 0.0016 g SO3 0.0019 g 0.0018 g TSA RMS 0.5091 g 0.4828 g TSA P2P 2.0887 g 1.8430 g FM0 4.278 4 AM RMS 0.100 g 0.099 g AM Kurtosis 4.242 4.217 FM RMS 0.428 radians 0.426 radians FM Kurtosis 4.995 4.844 18 Tail Rotor Intermediate Gearbox Pinion Fault Comparison of Tach vs. Tach-less Solution • SR: 100,000 • VR Tach on 500 Hz Shaft, 22 tooth • Shaft Under Analysis is ~68.5 Hz • 12 dB SNR • Tach time generated via ADC Note the high level of Jitter on the VR tach 19 TSAs differ only in phase 20 Tach vs. Tachless for Standard CIs Analysis SO1 Tach 0.043g Tach from Vibe 0.043g SO2 0.283 g 0.282 g SO3 1.855 g 1.85g TSA RMS 81.646 g 81.591g TSA P2P 222.77g 223.02g FM0 16.94 15.38 AM RMS 17.06g 17.06g AM Kurtosis 4.126 4.126 FM RMS 3.037 radians 3.048 radians FM Kurtosis 2.46 2.45 21 Implementation Issues Very Difficult to Implement Long FFT on an Embedded System – Floating point (32b) • breaks at 32K points – Double precision (64b) • Uses 2x RAM • 5x slower – Naive implementation (first attempt) 15 minutes; improved to run in 3 minutes 22 Conclusion • Tach-less TSA was demonstrated on two fault cases • Analysis Results Between Tach and Tach-less TSA were indistinguishable • Tach-less Smart Vibration Sensor can be implemented to reduce the cost of a HUMS installation • Goal: lower cost HUMS installation for Type 27 AC (<9,000 lbs) Smart Vibration Sensor 23 24