Frequency Response Function (FRF)

A common application of dynamic signal analyzers is the measurement of the Frequency Response Function (FRF) of mechanical systems. This is also known as Network Analysis, where both system inputs and outputs are measured simultaneously. With these multi-channel measurements, the analyzer can measure how the system “changes” the inputs. If the system is linear, which is a common assumption, then this “change” is fully described by the Frequency Response Function (FRF). In fact, for a linear and stable system, the response of the system to any input can be predicted just by knowing the Frequency Response Function. The relationship between the input and output is known as the transfer function or frequency response function and represented by H(y,x). In general, a transfer function is a complex function that describes how the system modifies the input signal magnitude and phase as a function of the excitation frequency. With various excitation, the characteristics of the UUT system are measured experimentally. These characteristics include:

• Frequency Response Function (FRF), which is described by:
  • Gain as a function of frequency
  • Phase as a function of frequency
  • Resonant Frequencies
  • Damping factors
  • Total Harmonic Distortion
  • Non-linearity

Single Response                              

Two responses

Frequency response is measured using the FFT, cross power spectral method with broadband random excitation. Broadband excitation can be a true random noise signal with Gaussian distribution, or a pseudo-random signal of which the amplitude distribution can be defined by the user. The term broadband may be misleading, as a well implemented random excitation signal should be frequency band-limited and controlled by the upper limit of the analysis frequency range. That is, the excitation should not excite frequencies above that which can be measured by the instrument. The random generator will only generate random signals up to the analysis frequency range. This will also concentrate the excitation energy on the useful frequency range.

Products we recommend:

Modal Analysis

Standard Modal Analysis:

EDM Modal Standard Modal Analysis provides the user with a complete arsenal of tools, from FRF data selection and parameter identification to results validation and mode shape animation. Upon completion of the Modal testing, the set of FRF data is made available for the next step: Modal Analysis. You can also add/replace individual FRF signals. The complete set of FRF test signals can be exported, or imported from other sources. These operations are managed by ‘Modal Data Selection’. The FRF signals are organized for a rapid comprehensive review, one by one, or multiply in one graph window.

With one click, the Modal Parameter Identification process can be started. With the help of a Mode Indicator Function (MIF), the natural frequencies can be labeled. The Multivariate, Complex, Real, and Imaginary Sum MIFs are available.  MIF indicators aide identifying repeated roots (repeated poles) and closely-space distinct roots.

A Stability Diagram is employed with modal parameter identification. With the Standard Modal Analysis option, the proven Least Square Complex Exponential (LSCE) fitter is implemented for pole identification. The physical poles sought are stable (as opposed to ‘computational poles’ sometimes produced by the LSCE) and can be selected from the Stability Diagram for the next step mode shape calculation, using the Least Square Frequency Domain (LSFD) algorithm.

The resulting mode shape table can be saved and used for mode shape animation. Modal Assurance Criterion (MAC) function and FRF synthesis are also available. These provide means for modal parameter validation.

Features of Standard Modal Analysis

• Ease of use modal data selection
• Signal Smoothing with Deconvolution (for OMA testing only)
• MIF: Multivariate MIF, Complex MIF, Real MIF, Imaginary sum MIF
• User selectable frequency band for parameter identification
• Stability Diagram
• Proven curve fitting method: LSCE
• Least square frequency domain (LSFD) algorithm for mode shape calculation
• Save/append modes to the shape table
• Auto/Cross MAC calculation and display
• Import/export modes: UFF format
• Animation equation editor for unmeasured DOFs
• Mode Shape Animation: wireframe, surface contour, FFD, animation with interpolation
• Contour edit, Contour value
• Animation smoothing
• Node lines
• Animation with un-deformed elements
• Mode Shape Animation speed control (fast, slow), magnitude control (increase, decrease)
• Animation format: Single, Left/Right, Upper/Lower
• Modal Shape video saving, graph saving
• Synthesized FRF vs. measured FRF, with Correlation and Error values

Advanced Modal Analysis:

EDM Modal Advance Modal Analysis includes all the features of Standard Modal Analysis. On top, it provides the Poly-reference modal analysis algorithm to curve fit the FRF matrix from the MIMO FRF testing results. The time domain curve fitting algorithm for the pole identification is Poly reference time domain method (PTD), which is sophisticated and proven.

src=”https://ayyappatelugusongs.com/flamboyant/wp-content/uploads/2019/04/gggggg-300×164.png” alt=”” width=”300″ height=”164″ />

The selection of the curve fitting method, PTD or LSCE, is automatic based on the type of FRF signal set selected, whether it is the single reference or multi-reference.

Features of Advanced Modal Analysis:

• Includes all features of Standard Modal Analysis, plus,
• Poly reference time domain (PTD) curve fitting
• Auto selection of curve fitter per single or multiple references from the FRF data set

Premium Modal Analysis (with Poly-X):

EDM Modal Premium Modal Analysis includes all the features of Standard and Advanced Modal Analysis. On top, it provides Poly-X, which is the poly reference Least Square Complex Frequency domain (p-LSCF) modal analysis algorithm to curve fit the FRF matrix from the MIMO FRF testing results. This frequency domain modal parameter estimator is more efficient and neater on the stability diagram.

The selection of the curve fitting method, Time Domain or Poly-X, is available from the EDM Modal software. It applies to either single reference or poly reference FRF data sets.

Features of Premium Modal Analysis:

• Includes all features of Standard and Advanced Modal Analysis, plus,
• Poly-X – Poly reference Least Square Complex Frequency Domain (p-LSCF) curve fitting
• Neat Stability Diagram with emphasis on stable poles

Products we Recommend:

Octave Analysis and Sound Level Meter (SLM)

Acoustics measurements are performed for a variety of reasons, including product design, production testing, machine performance, and process control. have capable acoustic measurement facilities including real-time octave, 1/3 octave filters, and sound level meter functions. CI provides an easy to use yet powerful toolbox for acquiring and viewing acoustic signals. Digital octave band filters and raw time data recording can be performed simultaneously for a detailed investigation of noise problems. Onboard IEPE (ICP®) transducer power capability allows for direct connection to pre-polarized microphones when used with an ICP microphone pre-amplifier. Traditional condenser microphones are also easily accommodated by connecting the direct voltage signal from the microphone power supply into an input channel. White and pink noise signals can be produced using the waveform generator. This feature is very useful when performing absorption measurements using a speaker.

Acoustic Measurement: Sound Level Meter

The Sound Level Meter (SLM) is a related application in the acoustic data acquisition software. This module is also referred to as an Overall Level Meter. The SLM applies a frequency weighting filter to the input signal and time weighting to the filter’s output. Various acoustic measurements are then extracted from both the input and output signals of this frequency weighting filter.

All of the features that you would expect from an acoustic measurement device are present…and then some! A, B, C, and Linear weighting functions; Fast, Slow, Impulse, and Peak detectors; and user selectable high and low-pass filtering. The tremendous dynamic range that all CI instruments offer to take the worry out of setting voltage ranges precisely to avoid under-range or overload conditions.

1/3^rd Octave Band Analysis

Products we Recommend:

Shock Response Spectrum

A Shock Response Spectrum (SRS) is a graphical presentation of a transient acceleration pulse’s potential to damage a structure. It plots the peak acceleration responses of a bank of single-degree-of-freedom (SDOF) spring, mass damper systems all experiencing the same base-excitation as if on a rigid massless base. Each SDOF system has a different natural frequency; they all have the same viscous damping factor. A spectrum results from plotting the peak accelerations (vertically) against the natural frequencies (horizontally).An SRS is generated from a shock waveform using the following process:

• Specify a damping ratio for the SRS (5% is most common)
• Use a digital filter to model an SDOF of frequency, f_n and damping ξ.
• Apply the transient as an input and calculate the response acceleration waveform.
• Retain the peak positive and negative responses occurring during the pulse’s duration and afterward.
• Select one of these extreme values and plot it as the spectrum amplitude at fn.
• Repeat these steps for each (logarithmically spaced) f_n desired.

Illustration of a multi-degree of freedom system model used to compute SRS.

Products we recommend:

CoCo-80X

Spider-80X

Order Tracking

Order Tracking is a general term describing a collection of measurement functions used for analyzing the dynamic behavior of rotating or reciprocating machinery for which the rotational speed can change over time. Unlike the power spectrum and other frequency-domain analysis functions where the independent variable is frequency, Order Tracking functions present the data against multiples (Orders) of the variable shaft running speed.The most useful measurements are Order Spectra and Order Tracks. An Order Spectrum displays the amplitude of the signal as a function of harmonic orders of the reference shaft’s rotation frequency. This means that a harmonic or sub-harmonic order component remains in the same analysis line (at the same horizontal position) regardless of the speed of the machine.The technique that observes the changes of a measured quantity at a given order vs. RPM is called tracking, as the rotation frequency is being tracked and used for analysis. Most of the dynamic forces exciting a machine occur at multiples of the rotation frequency, so interpretation and diagnosis is greatly simplified by use of order analysis.An Order Track is simply the history of measured amplitude at a single order versus the machine shaft speed (in RPM). There are other types of tracking functions. For example, you can track the FFT-based PSD spectra, a fixed band or an octave band versus RPM; all of these are tracking functions.

Applications of Order Tracking

There are several different applications for order tracking.  A discussion of some is given below.

The first application, often referred to as Run Up/Run Down, is used to survey a machine’s dynamic response when the operating RPM is varied across the entire operating span. In this case, the RPM range can be very large, from a few RPM to 10,000 RPM. Such tests are run on automotive or aircraft engines and when commissioning new or refurbished stationary processing equipment. The measurements can be any physical quantities such as sound, displacement, velocity, acceleration, torque, etc. The analysis measure can be the amplitude or the power of an order, the energy over a fixed frequency band, a bin of octave filter, etc.  The most important result for this type of measurement is the magnitude of the response versus RPM.

The second application is monitoring measured machine displacement, velocity, acceleration, pressure, current or sound while the machine is performing its normal duty. The instrument measures the amplitudes of specific orders and their phase relative to a reference tachometer input signal. The phase is calculated relative to the tachometer input or a separate reference input. This application is common for machine diagnosis and balancing. In this case, the operating RPM is relatively stable. Order tracking technology is useful to increase the accuracy of the estimation of orders.

Order Track signals with phase are useful in the study of rotating machine during Run Up/Run Down. This is often presented as a “Bode Plot”, useful in characterizing resonance/excitation intersections. The Bode Plot is a concept borrowed from control theory; it provides simultaneous Amplitude and Phase data over a changing speed range (i.e. Run Up or Coast Down). Some of the setup information depends on the rate of change of the RPM.  The Run Up or Coast Down could take anywhere from a few minutes to a few hours (such as for a cold startup on a turbine).

Remote Condition Monitoring

Remote Condition Monitoring is designed for the remote monitoring of equipment or structures that are inaccessible to configure within a local network. Common applications and examples of remote condition monitoring include the monitoring of vibrations during the transportation of equipment, monitoring vibrations on bridges and structures close to rails or roadways, and monitoring vibrations caused by rotating windmills on the ground.

The type and intensity of these vibrations can potentially cause a multitude of problems; from damaged equipment during transportation to structural damages on a bridge.Continuous monitoring with auto alarms and notifications assists in monitoring the health while also providing alerts to unusual and potentially catastrophic behavior on systems or structures.Crystal Instruments has developed EDM – Remote Condition Monitoring (RCM) to extend the capabilities of Dynamic Signal Analysis (DSA). The integration of these features with the Spider platform achieves reliable results in monitoring remote equipment and devices.When operating in EDM-RCM mode, multiple Spider front-ends featuring any channel count can be remotely mounted and connected through a mobile wireless gateway using cellular data connectivity. Each Spider system is accessible through EDM-RCM software by using a Static Public IP address with a connected modem. The use of a Static Public IP address with the modem ensures remote connectivity across the world.

The specially designed EDM-RCM software simultaneously connects multiple such Spider systems in addition to providing updated results of essential data for all Spider front-ends located throughout the world. The software provides a live view of data from any Spider system as needed and downloads recordings from any or all Spider front-ends for further analysis and inferences.

The capability of Spider systems to operate in Black Box mode has been fully utilized to ensure the continued operation of Spider front-ends regardless of their connection to the host software. This ensures the reliability of RCM during times when cellular connectivity is poor or nonexistent.

This paper discusses the key elements of setting up different Spider front-ends with a Public IP address provided by a cellular network provider. Also discussed is the procedure to set up EDM-RCM mode to simultaneously connect to and track the status of all devices.

Products we recommend

Passive Dampers

TMD Pipe has been specifically developed for industrial use in facilities such as those within the chemical industry or in power plants. All components have increased corrosion protection. In addition, it operates reliably even under rough and changing environmental conditions.

Active Dampers

Active dampers are based on the principle that accelerating a suspended mass results in a reaction force on the supporting structure. An embedded sensor monitors the supporting structure vibration. The sensor readings are sent to an external feedback controller that drives the internal electromagnetic actuator of the active damping device.

As it does not rely on a model of the structure to be controlled, a rather simple control algorithm can be implemented. It will work theoretically on any type of structure and will damp any vibration mode that is observable in its open-loop transfer function. The only selectable parameters for the control system are the actuator/sensor location and the feedback gain.

Anti-Noise

Anti-Noise consists in canceling the vibration by generating a force opposite to the incoming perturbation

Whenever the sensitive area cannot be isolated from the vibration excitation forces and whenever the vibrations are not amplified by the mechanical structure but mainly transmitted, the only remaining method to reduce the vibration (without a complete re-design of the system) is the anti-noise where a force opposite to the vibration excitation (same frequency, same amplitude but opposite phase) is generated resulting in a destructive interference process at the location where the control forces are applied. It is important to note that anti-noise is a local vibration reduction method that lower the modal shape; applying to damp locally will only reduce the vibration at this point and may lead to a vibration amplification elsewhere.

Passive anti-noise systems are mainly based on the use of Tuned Mass Absorbers or TMA where an oscillating spring-mass system is mounted on the target structure, i.e. at the location where the vibration is to be canceled. This TMA will absorb the vibration energy at the resonance frequency of the oscillating appendice. It is well suited for stationary harmonic excitations.

Active anti-noise systems are open-loop devices, relying on actuators, sensors and a feedforward control algorithm. Two sensors are necessary in this control scheme: a reference signal correlated to the incoming perturbation (e.g. the engine speed) and an error signal located where the vibration is to be attenuated. The control algorithm (usually an x-filtered LMS) will filter the reference signal and apply the resulting signal to the actuator; the filter parameters being continuously adapted in such a way that the error signal is minimized. Because of the computation and adaptation, this control scheme is well suited for slowly varying harmonic excitations.