2015 HBM ncode Products User Group Meeting
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1
2 Looking at Measured Data in the Frequency Domain Kurt Munson HBM-nCode
3 Do Engineers Need Tools? 3
4 What is Vibration? 4
5 Some Statistics Amplitude PDF y Measure of central tendency Mean: most commonly used measure of central tendency Measures of Spread Variance = square of deviation from the mean. 2 Measures of combined spread and central tendency Mean square = average moment of inertia of PDF relative to zero. y 2 1 N yn y n 1 Standard deviation = Square root of variance makes dimensions consistent with input units N 1 2 N y n n 1 RMS = Square root of above. How far from typically the mean? Makes dimensions consistent with input units. N 2 5
6 Resonance and Vibration: Large Scale Wind turbine tower (nacelle mass = M, tower bending stiffness = K ) natural resonant frequency Small amount of energy near natural frequency huge response possible failure Collapse Excessive deflections = Force M = K M 6
7 Complicated Structures Consider a multi-story building. This elastic body can be thought of as a series of lumped masses connected by structural elements of some stiffness. How many different ways can it move? M M M M 7
8 Modes of Vibration This elastic body can respond in a number of ways called modes. Each mode has its own natural frequency. M M M M Mode 1 Mode 2 Mode 3 Mode 4 8
9 Introducing the Frequency Domain
10 Understanding Dynamic Response Dynamic response can be made of the superposition of many vibration modes. How do we learn what vibration modes are present? How do we learn about the source of these vibration modes? Engineers need a way to decompose measured data into frequencies and modes. How many ways can this piping system shake? 10
11 What s a Fourier Transform? A way of converting from time domain to frequency domain. Time Domain Fourier Transform Frequency Domain Inverse Fourier Transform 11
12 How Does Fourier Work? The Fourier transform decomposes a signal into individual sinusoidal waves Each sinusoidal wave is described by 3 properties: Amplitude Frequency Phase Frequency Amplitude A Phase 12
13 Fourier Transform X ( t) k a k cos( k t) i sin( k t) k a k e ik t 13
14 Fourier s Sum When all the sinusoidal waves are added together, they recreate the original signal. Consider a square wave. Is it periodic? Is it a sine wave? =Σ 14
15 What s a Power Spectral Density (PSD)? Created by electronics engineers in the 1940s to characterize noise in electronic circuits. They were interested in the average amplitude of noise at different frequencies but couldn t calculate the Fourier transform at that time. g 2 /Hz Y axis units are engineering units squared per Hertz. Square root of the area under the PSD is the RMS of the time series data. 15
16 Example Time Series and PSDs Sine wave Broad band process Time history PSD frequency Hz Narrow band process Time history PSD White noise process frequency Hz frequency Hz frequency Hz 16
17 Loading Frequencies Typical loading frequencies for mounted equipment Type of environmental force Frequency (Hz) Loading type Wave forces PSD / time domain Wind turbulence PSD / time domain Earthquake PSD Automotive road-induced loading 1 30 PSD / time domain Automotive powertrain Swept sine Swept sine on random Helicopter rotor-induced vibration Sine on random Helicopter gearbox and engine Sine on random Jet Aircraft PSD Propeller Aircraft PSD Train - Body PSD Train - Bogie PSD Train - Axle PSD 17
18 The Use of Buffers The Fast Fourier Transform (FFT) breaks the time series into buffers for faster calculation. Each buffer is 2 n points long, i.e. 32, 64, 128, 256,..., points. Each buffer has its own frequency spectrum. Buffer 1 Buffer 2 Buffer 3 Buffer 4 18
19 Combining Buffers Results All buffer s spectra are then combined. Methods: Average: For each spectral line, report the average of all spectra Peak hold: For each spectral line, report the worst case of all spectra Joint time-frequency: stack all spectra into a 3D or color plot Peak hold Average 19
20 Buffer Size and Frequency Resolution The FFT s frequency resolution is set by buffer size and sample rate. f = sample rate/buffer size Longer buffers = finer frequency resolution = peakier spectrum Shorter buffers = coarser frequency resolution = smoother spectrum f=0.25 Hz f=2.0 Hz 20
21 Amplitude Spectrum vs. Power Spectral Density Both the amplitude spectrum and the PSD tell the same story. The y-axis magnitudes and units are drastically different. Area under the PSD = RMS 2 of a random time series = constant Area under the AS = variable = depends on buffer size AS PSD 21
22 Frequency Domain Results Time domain Peaks represent high response magnitude at that frequency, either because of High input magnitude, or Dynamic amplification from resonance Frequency domain 22
23 Frequency Domain Results Time domain Frequency domain 5 laps in the time domain. Same frequency spectrum! The frequency domain doesn t have any consideration of time or duration. 23
24 Comparison of Time and Frequency Domains Domain Advantages Disadvantages Time Easy to visualize Describes transient behavior Can understand phase and relationships between many channels It s how we live our lives Frequency Easy to see patterns and periodicity Small data files Averaging can be used to understand statistics of a process Time is most people s independent variable. All data look like squiggly lines Hard to see patterns and periodicity Large data files Time duration is lost Transient behavior is lost Hard to get amplitudes right for a broadband process There may be others like rotational position, or frequency, or. 24
25 Summary: The Frequency Domain All structures want to vibrate at some frequency their natural frequency. The frequency domain and time domain are two different ways of looking at varying signals. The Fourier Transform breaks down a time series into many sinusoidal waves of varying amplitude, frequency, and phase. A PSD (power spectral density) is a common way of reporting Fourier transform results. It reports vibration energy levels versus frequency and can be used to identify frequencies of interest. 25
26 Connect with us on: linkedin.com/company/hbm-ncode +ncode measure and predict with confidence
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