FAQ

Modal testing is a form of vibration testing of an object where the natural (modal) frequencies, modal masses, modal damping ratios and mode shapes of the object under test are determined.

A modal test not only consists of an acquisition phase, but also of an analysis phase as well. The complete process is often referred to as a Modal Analysis or Experimental Modal Analysis.

There are several ways to do modal testing. The most widely used are Impact Hammer modal testing and Shaker modal testing. In both cases energy is supplied to the system with a known frequency content. Where structural resonances occur there will be an amplification of the response, clearly seen in the response spectra. Using the response spectra and force spectra, a transfer function can be obtained. The transfer function (or frequency response function (FRF)) is often curve fitted to estimate the modal parameters; however, there are many methods of modal parameter estimation and it is the study of much research.
 

Resonance is simple to understand if you view the spring and mass as energy storage elements – with the mass storing kinetic energy and the spring storing potential energy. As discussed earlier, when the mass and spring have no force acting on them they transfer energy back and forth at a rate equal to the natural frequency. In other words, if energy is to be efficiently pumped into both the mass and spring the energy source needs to feed the energy in at a rate equal to the natural frequency. Applying a force to the mass and spring is similar to pushing a child on swing, you need to push at the correct moment if you want the swing to get higher and higher. As in the case of the swing, the force applied does not necessarily have to be high to get large motions; the pushes just need to keep adding energy into the system. The damper, instead of storing energy, dissipates energy. Since the damping force is proportional to the velocity, the more the motion, the more the damper dissipates the energy. Therefore a point will come when the energy dissipated by the damper will equal the energy being fed in by the force. At this point, the system has reached its maximum amplitude and will continue to vibrate at this level as long as the force applied stays the same. If no damping exists, there is nothing to dissipate the energy and therefore theoretically the motion will continue to grow on into infinity.

In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies and not others in order to suppress interfering signals and reduce background noise. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: a. analog or digital; b. discrete-time (sampled) or continuous-time; c. linear or non-linear; d. passive or active type of continuous-time filter; e. infinite impulse response (IIR) or finite impulse response (FIR) type of discrete-time or digital filter.

Digital signal processing (DSP) is concerned with the representation of signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of systems, biomedical signal processing, seismic data processing, etc. The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling it using an analog-to-digital converter (ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analog converter (DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression. DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), or on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.

Computers are digital devices, meaning they perform all calculations using ones and zeros. This method of computing is referred to as the "binary system," and is the heart of all digital technology. Devices such as hard drives, CD recorders, and Mini DV camcorders are digital devices, and therefore record data digitally, as ones and zeros. VCRs, tape players, and record players, on the other hand, are analog devices. This is because they record data linearly from one point to another. Imagine a bumpy line moving from left to right -- that is what an analog audio recording would look like. Analog devices read the media, such as tapes or records, by scanning the physical data off the media.

For example, a record player reads the bumps and dips in the grooves of the record and translates the information into an audio signal. An audio CD player, however, reads ones and zeros off a compact disc and translates that information into an audio signal. However, the ones and zeros only estimate the actual soundwave, whereas a record player records the exact sound. When you hear terms like "sampling rate" or "bit rate," these refer to how many times per second the digital signal is sampled. The higher the number, the more accurate the estimate is, which translates into higher quality sound or video.

So why is digital technology used if analog provides a better representation of the recorded information? Well, since computers perform digital computations, they can only work with digital media. Therefore, all analog audio or video media must be converted to digital to work on a computer. Once the information is digital, computers can be used to edit the data and create effects that were never possible with analog media. Digital media is non-linear, which means it can be edited or played back starting at any point, which can be a huge timesaver compared to working with tape. Digital information also does not "wear out" after repeated use like tapes or records do, which results in much better longevity for digital media.

To summarize, a digital signal is an estimation of analog data. Digital recordings are made with ones and zeros, while analog recordings are made with linear bumps and dips. While digital information is not as exact as analog information, it can be used with other digital devices, such as computers, making editing and reproduction of the information easier and faster. Because digital media is more compatible and does not degrade over time, it has become the common choice for today's audio and video formats.
 

Structural test engineers use modal analysis to understand the dynamic behavior of structures, including airframes, buildings, and automobile frames. Basically, the procedure is to excite the structure with a force of known frequency and amplitude and measure the response of the structure by measuring the output of accelerometers placed in various locations on the structure. Using the data acquired from the accelerometers, structural test engineers construct a modal model of the structure under test. Then, using this model, they calculate important modal parameters, including resonant frequencies, mode shapes, and damping values.

The key to building accurate modal models for structures is having the proper excitation force. An important part of the process is determining a structure's frequency response function (FRF), which you calculate by dividing the response of the structure (measured with the accelerometers) by the excitation force (provided by a shaker). As in all areas of engineering, the principle “garbage in, garbage out” applies. If you don't have a clean input, then it will be impossible to obtain good results.

To ensure a good excitation force, the test engineer must:
• choose the right shaker,
• set up the shaker in a good location,
• build a fixture that minimizes the mechanical impedance between the shaker and the structure under test, and
• generate a clean waveform.

Choose the right shaker technology
There are four different shaker technologies in use today: electro-dynamic, servo-hydraulic, mechanical, and pneumatic. The type most often used for modal analysis is the electro-dynamic shaker. Electro-dynamic shakers are versatile and relatively inexpensive. Using technology similar to the technology used in audio speakers, electro-dynamic shakers convert electrical energy into dynamic motion. Typically, the frequency range is 5 Hz-20 Hz, and you can use them with nearly any test waveform. They provide a sufficient stroke for modal analysis tests (typically 0.5-in. to 2-in. displacement).
In general, you must choose a shaker that provides a high force-to-weight ratio-for automotive applications, this ratio should be greater than 8. To ensure that you choose a shaker that can generate enough force, you must know the masses of your test structures and the accelerations specified for your tests. You can then use Newton's law of dynamics-force = mass * acceleration-to calculate how much force the shaker will have to generate. When calculating this force, be sure to include the mass of the shaker armature in your calculation. The total mass that the shaker must accelerate is the mass of the armature plus the mass of the test structure.

Another important shaker specification is frequency range. The low frequency limit will determine the shaker's maximum displacement. Because modal analysis tests low frequencies (low frequency modes being the most relevant ones in a structure), the maximum stroke of the shaker has to be chosen judiciously. Be sure to choose a shaker with a stroke of at least one inch.

Set up the shaker in a good location
Often, you will have to evaluate many different locations before choosing the final shaker location. The best locations are at a point where you will be able to excite many different modes simultaneously, including bending, torsion, and compression. Avoid placing them on node lines or node points (stationary modal degrees of freedom).
Remember also that shakers for automotive tests tend to be big, as the shaker needs to be about as big as the size of the structures you are going to shake. So, when choosing a location you need to have enough room for the shaker, as well as the test structure.

Building fixtures and measuring the input force
Although fixtures are a necessary evil when it comes to modal analysis, you need to take steps to minimize their influence. The fixture must transfer the excitation force to the structure under test with as little mechanical impedance as possible.
For example, side loads and bending moments are undesirable when performing a modal analysis, as the desired direction of force is purely axial. To minimize these transverse effects, you can use a pre-tensioned piano wire, or stinger, in your fixture. Stingers have high axial stiffness and very low bending stiffness, minimizing the influence of transverse force components. They also help to position the shaker and protect the shaker and input force transducer by acting as a “mechanical fuse.”

To obtain accurate frequency response measurements, you must accurately measure the input force to the structure under test. You do this by mounting a piezoelectric force transducer, sometimes called an impedance head, on the test fixture. The impedance head not only will measure the force at the excitation point, but the acceleration as well.
How you attach the transducer to the structure influences the vibration characteristics of the test specimen. It constrains the structure, primarily because it affects the stiffness of the fixture/structure system. This is another consideration in building a fixture that will transmit the input force as transparently as possible.

Generate a clean waveform
Another consideration when using shakers for modal analysis is the type of waveform and the cleanness of the waveform. There are five different types of waveforms used for modal analysis. They are swept-sine, sine, random, burst-random, or pseudo-random.

When choosing the type of input waveform, you must consider:
• the application,
• the non-linearity in the structure,
• the time available for test,
• the dynamic range of the measurement,
• whether the noise is present mostly at the input or output, and
• the type of shaker you are using.

Using more than one shaker
In certain applications, you may need to use more than one shaker to better distribute loading forces. There also may be applications where it is necessary to drive the structure at very high force levels. These force levels will generate non-linear behaviors that you cannot easily analyze using modal analysis. For these applications, you can use MIMO (Multiple-Inputs Multiple-Outputs) analysis.
MIMO analysis is also well suited for cases where the structure exhibits local modes that occur only when excitation forces are high. It is also used in analyzing symmetrical structures that exhibit separate mode shapes but have the same resonance frequency (repeated roots case).
Taking into account all the considerations mentioned in this article definitely leads to a good understanding of the dynamics of a shaker’s structure. They also will help you obtain accurate results that you can use in the future, whether or to refine your finite element models.
 

As you develop an error budget for a circuit or data-acquisition system, you also must think about the accuracy and resolution of the measuring device. Unfortunately, some people confuse accuracy and resolution or think they mean the same thing.

I use a Fowler digital caliper in my workshop and its digital display indicates measurements with a resolution of five ten-thousandths of an inch or one hundredth of a millimeter. But this display resolution can lull you into a false sense of accuracy. The caliper data sheet notes an accuracy of ±0.001 inch or ±0.02 mm. So, the number of displayed digits doesn't reflect the accuracy of the instrument. In other words, a display of 0.500 inches most likely indicates a dimension between 0.501 and 0.499 inches. Think of accuracy as the "correctness" of measurements.

In short, resolution describes how small a measurement an instrument can make. And accuracy defines how well the instrument makes those measurements. Suppose I use a 3½-digit DMM with an accuracy of ±1 mV (±1 count) to measure a known 0.1667-V signal. In this case, the meter probably displays 0.167, so the voltage could range from 0.166 to 0.168 mV. The measurement is not accurate because the DMM doesn't offer enough resolution. If you want a better measurement use a 4½-digit DMM with an accuracy of ±100 μV (±1 count) to provide a reading of 0.1666 to 0.1668V. If thatmeasurement doesn't come close enough, you could use a 5½-digit DMM with an accuracy of ±10 µV (±1 count). But, if you have a 5½-digit DMM that no one has calibrated in years, you will still see a 5½-digit resolution, but probably not an accuracy of ±10 µV. Always check manufacturers' data for instrument-accuracy information.

When you build a measurement circuit from scratch or assemble one from modules you must budget for errors that can occur within an analog-to-digital converter and its front-end components such as amplifiers and multiplexers. You can have more resolution than accuracy, but not more accuracy than resolution.

Although accuracy and resolution dominate conversations about electrical measurements, engineers should also know about precision, which determines whether they can make reliable and repeatable measurements. As shown in the diagrams you can have precision and accuracy independently, but you should aim to have them simultaneously.
 

 Data-acquisition systems need signal conditioning to prevent unwanted signals from masking important data.

Identifying gear, shaft, or bearing quality problems in rotating systems such as automobile transmissions typically requires laser vibrometers, microphones, or accelerometers. During a test, these sensors produce analog signals that can represent defects as the mechanical system rotates. Each rotating part transfers energy, or vibrates, at a frequency associated with its rotating speed and its physical characteristics. The number of teeth, number of vanes on a pump, bearing dimensions, and gear-set design all contribute to the vibration characteristics of the rotating component.

Defective components produce a set of energies, or vibrations, different from those generated by good parts. Some of these defects appear at certain speed and torque conditions only. Thus, tests are performed while the speed or torque is ramped very quickly, typically from several hundred rpms to several thousand rpms within a few seconds, throughout the assembly's operating range.

To eliminate measurement errors, you must collect and analyze data in a way that eliminates errors by aliasing, which produces distortion and unwanted frequency components. To remove aliasing, the signal needs filtering to reduce its bandwidth to a frequency range lower than the Nyquist frequency, which is defined as one-half the data-acquisition sampling rate? 

 
Figure 2. This plot shows the intensity of the energy relative to rotational speed and order. Courtesy of Bauer Controls.
You can overcome this problem by using a position-based data-acquisition system with a low-pass anti-aliasing filter. Figure 1 shows the measurement system. The accelerometer signal consists of frequency components that contain low frequencies and other irrelevant content (two sine waves in the upper left box). The filter dynamically adjusts its cutoff frequency as the transmissions rotational speed changes under software control.

The speed signal—a TTL-level pulse train—passes through the FPGA that multiplies the signal's frequency by 100 so it can become the input to the programmable low-pass filter. The filter limits the accelerometer signal's bandwidth, keeping it below the Nyquist frequency. The filtered signal goes to a National Instruments' analog input card (box in the upper right).
As the speed of the system changes, the pass bandwidth changes dynamically, eliminating data distortion.
After filtering and digitizing the signal, the system converts the data from the raw time-based domain into the frequency domain through FFTs (fast Fourier transforms).  

The FFT shows the energy generated by the gears, bearings, and shafts making up the physical system. Because the speed is known, the software can divide all the frequencies of the FFTs by the speed, which converts frequency to "order." Order is the number of times a vibration is produced per revolution of the tracking shaft. The equation is:
Order = Frequency / Speed
where Speed is revolutions/s.