Vibration Introduction

Over the last couple years we’ve learned a great deal about shock and vibration to support our Slam Stick data logging line and its customers. We’ve had a lot of questions on various aspects of shock and vibration testing; so I’m excited to share with everyone what we’ve learned!

This eBook provides a practical overview on some of the key components of shock and vibration testing; everything will be covered from sensor selection to analysis. Engineers have limited time; so links will be provided to supplemental information and suppliers to keep this eBook as quick hitting and brief as possible. You’ll learn:

• Sensor Selection.
  We’ll go through different accelerometer types and alternatives to accelerometers.
• Data Acquisition System Selection
  Learn what to look for in a data acquisition system.
• Equipment Setup
  We’ll discuss best practices of equipment setup (sensors, electronics, and wiring).
• Analysis Overview
  We’ll define some theoretical background on vibration followed by some analysis examples such as FFTs, PSDs, and spectrograms for real world data and applications.
• Response Spectrums
  We’ll give some background on how to use response spectrums and modal analysis as part of the design process.
• Simulating Shock and Vibrations in the Laboratory
  We’ll give some different methods of exciting and testing your system in a controlled environment.
• Analysis Software Options
  We’ll discuss different software options available to the vibration test engineer.

If you’re new to shock and vibration measurement or if you just need a quick refresher, use this as a guide. We’ll update this book, so please send suggestions and best practices you’ve learned. I hope you enjoy it.

Stephen Hanly, Senior Mechanical Engineer, Midé Technology

All bodies possessing mass and elasticity are capable of vibration; which basically means everything you see and touch can vibrate and are impacted from shock events. As the world around us gets increasingly more automated with more and more powerful machinery, vibration and its destructive strength is on the forefront of any mechanical engineer’s mind during the design and testing process.

I’m sure everyone knows what vibration is; the device in your pocket probably reminds you far too frequently throughout the day! But here’s the technical definition: vibration is an oscillating motion about a point of equilibrium. Mechanical shock is a sudden change of acceleration that generally excites a structure’s resonance. A shock event is basically a type of vibration where the excitation is non-periodic; much of the test setup and analysis between shock testing is similar to vibration testing. Plus, the tendency for shock events to induce a vibratory response in the structure makes it worthwhile to discuss the shock and vibration testing together. Mechanical shocks and vibrations have become very pervasive in our ever day lives, so measuring and measuring and understanding their impact on your system is an important part of mechanical design.

Shock and vibration measurement can be defined as “the art and science of measuring and understanding a structure’s response to a dynamic environment.” Shock and vibration testing goes beyond simply data acquisition, it is only effective when you are able to understand what the data means for your application. And it takes some creative skill to properly gather and analyze your shock and vibration data.

The frequency range will drive hardware; I’ve seen far too many engineers have the wrong sensor and even the wrong DAQ (data acquisition) system for their application that can lead to erroneous results.

Obviously you’ll need to select a sensor with a measurement range that includes the amplitudes you or your customer care about; but it also heavily influences your DAQ selection. Very small vibrations/accelerations like those in seismic applications will require not only a very low noise and high sensitivity accelerometer; you’ll also need a DAQ system with very low noise and ultra-high resolution. On the higher amplitude end, it’s important to bear in mind what type of acceleration levels the DAQ hardware will see. When measuring a wider range, resolution will also be important.

You’ll need to lean towards higher quality systems if your customer has a particular test standard they need to have the system qualified to. The United States military has a testing standard, MIL-STD-810 (vibration is section 514.6 and shock is 516.6) for example; you won’t be able to qualify your system to meet such a standard with low quality equipment. On the other hand, if you just need a rough handle of the shock and vibration levels in your environment to get started in the design process or if you’re trying to satisfy a curiosity, lower quality systems may be adequate. There are other applications, such as health monitoring, that aren’t necessarily looking for absolute vibration values. Rather, relative vibration levels and how it changes with time is important.

Will this be in the lab or in the field? If testing will be limited only to the lab then more complicated test equipment can be used. Conversely though, if the testing is done in the field, ease-of-use will be a driver of your hardware selection. The type of environment will also heavily influence sensor selection such as temperature range, humidity, electromagnetic noise; and even corrosive or radioactive conditions.

All too often engineers realize they need testing once a problem has already presented itself. Lead time of equipment now becomes incredibly important especially because they can have 6 to 8 week lead times. Often times the engineer won’t have that time available to wait.

This may drive your software selection. If you have a limited time to perform the analysis you may want to go the route of simpler and cheaper software packages to give you that quicker overview of the data. On the other hand if you have a development effort that has a heavy emphasis on analysis and the time available to support that analysis effort then a more complex software package may be warranted. Along that same vein, it may be worthwhile to use a programming language like MATLAB or Python to develop your own analysis scripts specific to your analysis needs.

Accelerometers are by far the sensor of choice for shock and vibration measurement. Accelerometers mount directly to (or in) the vibrating structure and proportionally converts mechanical energy to electrical when experiencing acceleration. Acceleration is generally represented with the gravitational constant ‘g’ which equals 9.81 m/s2. There are three main types of accelerometers:

1. Piezoelectric Accelerometer

   Piezoelectric accelerometers are the most popular and widely used for industrial applications. They typically use lead zirconate titanate (PZT) sensing elements that product electric charge or output under acceleration. Piezoelectric accelerometers have very low noise and offer superior performance over capacitive MEMS or piezoresistive accelerometers in all vibration and most shock applications. Piezoelectric accelerometers come in many different variants: triaxial or single axis, high sensitivity for seismic applications down to low sensitivity for shock testing, and even have some types that can handle extreme environments including nuclear. The major downside of piezoelectric accelerometers is that they are AC coupled so they can’t measure the gravity vector or sustained accelerations. This also prevents the engineer from integrating the data for velocity or displacement information because of their intrinsic decay properties (although it can be integrated for higher frequency vibration). But again, piezoelectric accelerometers are generally the preferred choice for industrial testing applications for their performance benefits.

   Because piezoelectric accelerometers are so popular there are many different companies that sell these including: Measurement Specialties, Meggitt’s Endevco Corporation, PCB Piezotronics, Bruel & Kjaer, and Dytran. Generally the cost of a piezoelectric accelerometer will be in excess of $1,000 and they typically have long lead times of over 4 weeks.

2. Capacitive 

   MEMS (micro-electro-mechanical systems) accelerometers more than likely refer to capacitive accelerometers; MEMS is just the fabrication technology. This fabrication technology has brought capacitive accelerometers into the mainstream though! They are by far the cheapest and smallest accelerometer options (as the name implies!); and capacitive MEMS accelerometers are the type found in your smart phone. These accelerometers can be mounted directly to printed circuit boards which has made capacitive MEMS accelerometers the preferred choice for electrical engineers. Their low cost (typically less than $10) and small size has made them popular but capacitive MEMS accelerometers have much poorer data quality, especially on the higher frequency and amplitude end. They should generally be avoided for industrial applications; but they are a DC coupled and a great option for human-based applications. Their low cost and power consumption does also make them a good choice for health monitoring.

   Capacitive MEMS accelerometers are very easy to purchase; and have short lead times. Using one will require some electrical design on your part though. The leading manufacturers of capacitive MEMS accelerometers include Analog Devices, Bosch Sensortec, and InvenSense.

3. Piezoresistive Accelerometer

   Piezoresistive accelerometers are the premier type for shock testing. Piezoresistive accelerometers are strain gauge based so they require amplifiers and temperature compensation; but they have a very wide bandwidth (0 hertz to several thousand hertz) and low noise characteristics. Piezoresistive accelerometers can be gas or fluid damped which protects the accelerometer and prevents it from reaching its internal resonant frequency. Because they are DC coupled their output can be integrated to calculate velocity and displacement during shock events. Again, they are the premier type for shock testing; but piezoelectric accelerometers are preferred for vibration testing.

   The same companies that sell piezoelectric accelerometers also offer piezoresistive options. Piezoresistive accelerometers also tend to be in excess of $1,000 each and have longer lead times of over 4 weeks.

   Figure 1 provides a reference table that recommends an accelerometer type for different applications. If you want to dive a bit deeper into accelerometer selection check out Midé’s blog post. Endevco also has a nice white paper on selecting the right accelerometer. 

   

Vibration meters offer real time vibration analysis in a handheld unit so that maintenance decisions can be made quickly in the field. They either wire to a traditional accelerometer or some even, like the one shown in Figure 2, incorporate the accelerometer into the unit cutting down on wiring requirements and complexity. Vibration meters typically don’t allow the user to log long duration events (they may give you access to the last couple thousand points for some analysis); but they give RMS and peak-to-peak levels in real time. They also will typically have an algorithm to rate the overall vibration of your bearing or machine. Vibration meters can be a bit pricey at around $1,000 which sometimes won’t include the cost of the accelerometer (the Fluke 805 is over $2K that has the embedded accelerometer). If you are looking to do some more in depth vibration analysis or any shock testing, a vibration meter is probably not your best option. But for that quick go/no-go vibration testing of a piece of machinery, a vibration meter is unbeatable. Fluke is the leader in hardware and software for vibration meters; here is their vibration testing homepage.

An often overlooked option for shock and vibration measurement is to use a data logger that combines the accelerometer with the data acquisition system, power, and memory into one package. This is the preferred option for engineers who need ease-of-use and portability. Apps on your smart phone can be considered simple data loggers but they tend to have a maximum sample rate of 100 Hz and poor data quality. Higher end data loggers like Midé’s Slam Stick X effectively bridge the gap to the more expensive shock and vibration measurement systems by incorporating a high quality piezoelectric accelerometer as opposed to the cheaper capacitive MEMS accelerometers found in most vibration data loggers.

Shock and vibration data loggers generally have much shorter lead time (a few days) and lower cost ($500 to $2,000) than building your own vibration measurement system. There are a lot of different companies that make shock and vibration data loggers and a lot of different options; here’s a post comparing 6 different products.

Although accelerometers are the most popular choice in shock and vibration measurement, displacement sensors measure the displacement of a vibrating structure. Calculating between displacement, velocity, and acceleration is accomplished with integration/differentiation (here’s a calculator for simple harmonic motion applications). The downside to using these is that it’s measuring relative motion between two structures. These are near impossible to use in the field because a fixed mounting and distance is required between the sensor and equilibrium position of the vibrating structure. They can also be quite a bit more expensive and complex than accelerometer based systems. That being said, displacement sensors can be preferred in some applications that prevent the use of accelerometers such as rotating components (although a data logger could be used), or when the accelerometer’s mass would too greatly influence the motion of the system. Generally displacement sensors should be avoided for shock testing for fear of damaging the sensors.

Laser displacement sensors (KEYENCE is the leader) and capacitive displacement sensors would be the two main sensor types that would be useful for vibration testing. These systems will typically be upwards of $5,000 and lead times over 4 weeks.

Sound is not often thought of as a way to measure vibration; but it should be! After all sound, by definition, is a vibration that travels through the air in the form of pressure waves. Microphones offer a cost effective means of measuring high frequency vibration and is especially useful to determine how a system’s vibration changes with time. Health monitoring applications can greatly benefit from using a microphone on cost and simplicity.

Microphones aren’t limited to applications where cost is a concern; some acoustics applications will use high end microphones for vibration testing and analysis. You’ll notice a lot of the accelerometer companies also offering high end microphones, like PCB Piezotronics. Microphones and acoustic analysis can be a great option for some applications; but if you need absolute shock and vibration data, not relative change, then microphones probably won’t work. They also won’t be able to analyze modal shapes and specific/discrete points along your structure. But again, they are very effective for overall frequency analysis.

Often times the end goal of vibration testing is determining the stress and strain in your structure. Strain gauges can be an effective sensor type to directly measure the strain of your test article. A change in capacitance, inductance or resistance is proportional to the strain experienced by a strain gauge so that mechanical energy can be converted to an electrical signal. Strain gauges do present some challenges though; they can be very sensitive to temperature change, material properties of your structure, and the adhesive used. Instrumenting a structure with strain gauges is very much an art and difficult to do. They also require strain gauge amplifiers which are also difficult to work with. That being said, strain gauges are cost effective (from a material point-of-view, not labor), and allow the engineer to directly measure the strain in his/her structure.

Now that you have the sensor, something needs to capture and record the sensor’s output! Data acquisition systems do just as the name implies: collect/acquire data. The global leader in DAQ systems is National Instruments; but there are many other options out there too. National Instruments offers unparalleled customization options with both their modular hardware and their software program, LabVIEW. Measurement Computing offers some more cost effective alternatives to National Instruments; but they’re less well-known and trusted. For the more advanced user there are systems like m+p International’s VibRunner that can capture 100s of channels for modal analysis applications on larger structures. Something like this will cost tens of thousands of dollars, whereas low-channel systems will cost hundreds or thousands of dollars.

The sensor selection will often dictate the type of DAQ system that will work based upon the sensor’s output. Does the sensor have a digital output? Is it 0 to 30 volts, is ±5 volt? Low sensitivity sensors may require amplification of their output. It will simplify your shock and vibration measurement system setup significantly too if the DAQ system can provide the excitation voltage to your sensor to power it so that clunky power supplies can be avoided.

It’s good practice to sample at a rate 10 times greater than the upper interested frequency range to accurately capture the vibration profile. For most shock and vibration measurement applications a DAQ system will need a sample rate of at least a few thousand hertz; but it all depends on what frequency range that your or customer is concerned about. Take for an example an excerpt of vibration data recorded on a test aircraft shown in Figure 5. The data sampled at 2,500 Hz is made up of many different frequencies ranging from 50 to 600 Hz. Now if this same dataset is sampled only at 500 Hz (shown in the dashed red line), the vibration environment looks much different and would be inaccurately represented.

General guidelines on sample rate are over 10,000 Hz for shock testing, over 5,000 for general vibration, and around 1,000 Hz for slower vibration or movement.

Resolution is generally specified as bits which can then be used to calculate the resolution in acceleration units. For example let’s say that an accelerometer system has 16-bit resolution; this means that it has 2¹⁶ (65,536) acceleration levels or bins it can measure. Figure 6 illustrates the importance of resolution on a simple 60 Hz sine wave with two lines of different resolutions. 5-bit resolution provides 2⁵ discrete acceleration levels that can be detected while 5-bit resolution only provides 2³ or 8 discrete levels.

When looking for a DAQ system they will typically have a resolution on the order of 16 or 24 bits. The lower quality shock and vibration data loggers however may only have a resolution of 12 bits or less which may not be adequate for your application.

Filtering can be used to remove unwanted frequency content and should be an important part of your evaluation of different DAQ systems. High pass filters remove lower frequency vibration and is inherent to all piezoelectric accelerometers (resistor and capacitor in series) which gives these accelerometers the AC response. Low pass filters are more important however to prevent aliasing which can’t be filtered out in software. Aliasing causes a signal to become indistinguishable or to look like a completely different signal as shown in Figure 7. It’s important to realize that an analog lowpass filter is needed to prevent aliasing. Once a signal is aliased, it can’t be filtered out digitally in software.

Now the question remains as to what type of filter should you use? An ideal filter would uniformly pass all frequencies below a specified limit and eliminate all above that limit. This ideal filter would have a perfectly linear phase response to the same upper frequency limit. But ideal filters don’t exist; there is some compromise that needs to be made on a filter’s amplitude and phase response. There are four main different types of filters:

1. Butterworth 

   A Butterworth filter is known for its maximally flat amplitude response and a reasonably linear phase response. The Butterworth filter is the most popular for vibration testing.

2. Bessel

   The Bessel filter has nearly perfect phase linearity so it is best suited for transient events like shock testing. It has a fairly good amplitude response but its amplitude roll-off is slower than the Butterworth or Chebyshev filter.

3. Chebyshev

   The Chebyshev has a faster roll-off in the amplitude response which is achieved by introducing a ripple before the roll-off. They have a relatively nonlinear phase response.

4. Elliptic

   The Elliptical filter has the steepest roll-off in the amplitude response but it has a ripple in both the pass band and stop band. In addition, its phase response is highly nonlinear. This is only used for applications where phase shift or ringing is not of a concern; it should generally be avoided to the common test engineer because of its tendency to distort complex time signals.

In Figure 8 the performance of these filters are compared for a 1,000 Hz cut off frequency and 5^th order filters. The plots were generated in MATLAB using the Signal Processing Toolbox and the analog filter functions. Figure 9 takes a closer look at the filter performance in the passband (0 to 1,000 Hz). The Chebyshev and Elliptical filters offer that sharper amplitude roll off but at the expense of large ripples in the passband and nonlinearity. Butterworth filters offer the best of both worlds with a relatively sharp amplitude roll off. Bessel has the best phase response and a reasonably good amplitude response but note how early it begins filtering; and in the stopband it still allows over 10% of the single until roughly 2.5x the cut off frequency.

Figure 8: Different filter types are compared on their amplitude response and phase for a 1,000 Hz 5^th order filter.

Which filter you choose will depend on your application; but in general, the Butterworth filter is best for vibration and the Bessel is best for shock testing. And above all, you should avoid a system that does not offer some low pass filtering to avoid aliasing.

The method of mounting the accelerometer to the vibrating structure and the coupling between the sensor and the measurement point is a critical factor in obtaining accurate results. Mounting types and methods influence the resonant frequency of the accelerometer. If/when the accelerometer’s mounting results in a reduction of its natural frequency the bandwidth (or useful frequency range) is reduced. Accelerometers, piezoelectric in particular, have a very high amplification factor at resonance too; so it’s important to avoid using a mounting method that shifts the resonance into the frequency range of your vibration environment. There are six main mounting methods listed below; their frequency response is compared in Figure 10.

1. Stud Mounting

   This represents the best mounting method in terms of accelerometer performance and will maximize the frequency response of the accelerometer. It’s important to torque the accelerometer down to the manufacturer’s specifications; inadequate mounting torque can reduce the frequency response. Perhaps the most important factor when stud mounting is to use a coupling fluid such as grease, oil, petroleum jelly or beeswax. Using a coupling fluid solves a lot of mounting problems including inadequate mounting torque, surface flatness, and surface roughness. Figure 11 provides a comparison on the frequency response for when an accelerometer is under torqued and/or no coupling fluid is used. The data presented is from an excellent MEGGITT/Endevco presentation and resource on accelerometer mounting.

   

2. Adhesive

   There are several different adhesives to consider when mounting your accelerometer. Surprisingly though, the most important parameter for accelerometer performance is not the adhesive type, rather it is the thickness of the adhesive that plays the largest role. Figure 12 provides a few plots of the frequency response of different adhesives (data is taken from that same Endevco presentation) which illustrates what little difference there is.

   

   • a. Loctite or Epoxy

     Loctite or a two part epoxy offers a permanent mounting option which improves repeatability and testing time. There are many different types of Loctite; but 454 is a popular type for accelerometer testing. Must times the accelerometer can also be dismounting with a small shear load from the tap of a hammer (be careful not to damage the sensor or test article though!). Accelerometer manufacturers will recommend using a de-bonding agent like Acetone and gently twisting the accelerometer.

   • b. Wax or Duct Seal Putty

     Wax or duct seal putty are other popular adhesives that aren’t as effective as Loctite or epoxy but still offer surprisingly good frequency response. The major benefit of using this type of adhesive is that removal of the accelerometer is much easier. Hi-Test, who does much of the shock and vibration testing for large military systems, recommends using duct seal putty for shock testing because it can mechanically filter out high frequency (and thus low energy) vibration content that could risk exciting an accelerometer’s internal resonance. Petroleum wax would have similar benefits; but note that this can have adverse effects for an application that is interested in higher frequency vibrations. Blanchard wax is a much stiffer adhesive and may be preferred for these applications.

   • c. Double Sided Tape

     Double sided tape is often thought to not be strong or stiff enough to be used as an effective mounting method for accelerometers. They do offer the lowest frequency response of all the adhesives but for many applications it is still plenty effective enough. Midé’s has had good luck with the 3M 950 adhesive transfer tape for its Slam Stick products (a 5 yard roll is actually included with each unit). Endevco’s study found that the thickness of the adhesive is the most important factor and this is only 0.005” thick (0.1 mm). If the 950 tape is adequately compressed then there is no discernable difference in the Slam Stick’s performance compared to mounting with bolts. The downside of this particular tape is that it’s quite tacky and can be difficult to remove. 3M offers an adhesive eraser wheel which is effective at removing this tape and other adhesives.

3. Adhesive Mounting Pad

   Adhesive mounting pads offer the very high frequency response of adhesives and stud mounting; but allow the engineer to easily swap out accelerometers. For large structures when you may be doing modal analysis it is much easier to instrument the structure with adhesive mounting pads first (no wiring, and less expensive) then attach the accelerometers for your test. At the end of testing the accelerometers can easily be taken off and brought to the next test. If, after analyzing the data, the team determines more testing is needed then having the mounting pads remain on the structure ensures that the tests can be repeatable. Adhesive mounting pads also help prevent epoxy from damaging expensive accelerometers. Here are some accelerometer mounting bases from PCB; but there are many accessory options out there.

4. Magnetic Mounting Base

   For ferrous magnetic structures a magnetic mounting base allows easy and mess-free accelerometer mounting. There are two types of magnetic bases: flat, and curved; flat offers the best frequency response. You should use caution with magnetic mounting bases to not damage your structure or injure yourself. But these are a great solution for short term testing applications. Here are some accelerometer magnetic mounting bases from PCB.

5. Hand Held or Probe Tip

   Some applications can be difficult to reach for proper mounting and/or have sensitive coatings or materials that prevent adhesives or bolting. A probe tip can be utilized to press the accelerometer to the structure by hand. This obviously drastically reduces the measurable frequency range to less than 100 Hz or so. Because humans can’t remain perfectly still either, they are not recommended for frequency ranges less than 10 Hz.

One of the biggest pains of vibration measurement is typically how to deal with wiring. Wiring can sometimes require modifications to the test environment to accommodate the wiring from sensors to DAQ systems to a power source. This can limit where testing occurs and can sometimes require special “test samples” that are systems specifically designed for testing, not field use. Often test data is required on site, on a fielded unit, not a glorified laboratory! !

Wiring also can introduce mechanical, electrical, and electromagnetic noise so great care should be taken to mitigate the chances of the wiring introducing such noise. Generally a reduced cable length offers the best practice of minimizing unwanted noise and is where a high quality vibration data logger offers unique benefits.

1. Ground Loops

   Unwanted differences in the electrical potential between the sensor and the instrumentation will result in erroneous DC offsets and voltage drops. The entire measurement chain should be grounded at only one point (which is the very purpose of grounding!). To prevent these ground loops there should be sufficient insulation between the accelerometer body and ground. Unfortunately this insulation may mechanically dampen the coupling of the accelerometer which will also influence vibration data. Another way to mitigate this issue is to shorten the cable length as much as possible.

2. Electromagnetic Noise

   In particular EMI laden environments (like those found on surface ships) electromagnetic noise can greatly sully the data quality. Again, the best practice is to avoid long cable lengths where possible; but sometimes special cabling may be needed that is has reinforced shielding to offer EMI protection. This of course comes with an added price tag; but of only a few hundred dollars in most instances.

3. Mechanical Noise

   Cable motion will literally induce mechanical strain on the accelerometer which the accelerometer will measure and erroneously report as vibration in your structure. This strain and acceleration will influence the data quality of the sensor as it tries to measure the vibrating structure directly without interference. To prevent this motion which causes erroneous data the cable should be secured as close as possible to the accelerometer. O-rings, cable clamps, and adhesive cable clamps are typically used.

4. Risk of Losing Connection

   The last challenge wiring presents is the possibility that you may lose connection during a test. So strain relieving your cabling is very important to prevent mechanical noise but also to help ensure connection is not lost. In large setups there can be a concern about wire mismatching where the engineer may think he/she is analyzing data from one accelerometer when in fact he/she may be looking at data from a completely different area of the structure. It’s very important to double check that all accelerometers are properly wired, labeled, and strain relieved to prevent losing or confusing data sources.

MEGGITT offers a nice resource on sensor wiring and cabling that is worth a read.