INTRODUCTION TO VIBRATION TESTING
By Wayne Pauly
1) INTRODUCTION: Vibration testing is the process of applying a controlled amount of vibration to a test specimen, usually for the purposes of establishing reliability or testing to destruction. In practice the test article is securely mounted on a shaker table or actuator, which may be operated by electro-dynamic or hydraulic force; typically hydraulic force is used at very low frequencies because of the large displacements involved, and electro-dynamic force is used where higher frequencies are involved.
An electro-dynamic shaker is a linear motor: a moving coil in a fixed magnetic field that is the same principle used in the construction of a loud-speaker. The magnetic field is generated either by permanent magnets or a DC current in a field coil, and audio power is provided by an amplifier of suitable rating, typically requiring about 10 watts of audio/ pound force generated.
Some type of signal source is necessary to drive the amplifier, and an accelerometer is needed to measure the vibration response of the test article. Accelerometers are referred to as "Integrated", meaning they have a built-in amplifier and need a current source for power, or "Charge" type, requiring an external charge-converter to make a usable signal from their output. If the test article is large, then the response may vary across it’s surface and multiple accelerometers may be used and the outputs averaged.
The overall response curve is usually VERY non-uniform due to the response curves of the amplifier and shaker, and mechanical resonances of the shaker, test article, and mounting fixtures. To cure this, a controller us used to servo the actual measured response to the desired response curve. Controllers may be rack-mounted analog instruments or digital computer-based products.
The signal source usually attempts to simulate the real-world environment that the test article will operate in. Two methodologies are commonly used: Swept-sine and Random testing. In the Swept-sine approach the frequency is swept back and forth with amplitudes corresponding to the desired test levels. In Random testing the frequency spectrum of a noise source is shaped to represent the environment that the article will operate in. An additional test approach is Classical shock testing where the article is subjected to one or more high level shock pulses; this is similar to a one time drop-test that might occur in shipping. In all three approaches the test level can be increased until destruction occurs, thus establishing the safety margins.
2) SHAKERS: Vibration may be accomplished with hydraulic actuators or high-level acoustics for specialized testing, but only electro-dynamic type will be discussed here. All are variations on the common audio speaker design, i.e., they are a coil moving linearly in a magnetic field; instead of a speaker cone attached to the coil, a mounting plate is attached to which test articles are mounted. There are very tiny ones for accelerometer testing, but the most popular size is around 100 force-pounds. A shaker is rated at the maximum force it can apply to the total moving mass, which is the sum of the shaker moving parts, the fixture and the test specimen; a shaker could apply a 100# force at 100 G’s to a 1# total mass or 10 G’s to a 10# mass. Remember force = mass times acceleration. A 100# system is well suited for testing circuit cards and small devices up to a few pounds, as tests are frequently specified up to 10 G’s or so test level.
Shakers are available in much larger sizes though, up to about 50,000# force. Systems of 1000# rating are well sized for test articles of 10-50# or so, whereas the largest systems can handle a complete missile or equipment rack The complete systems seem to weigh about one pound per pound of force rating, so you can see that the largest systems will fill a room and require fork-lifts to install.
The magnetic field is generated by permanent magnets in the smaller systems or by a field coil in the larger ones; DC current flows through the field coil. The coil moves within this magnetic field and is referred to as the armature, and if a current flows through the armature coil, a force will be exerted on it and coupled up to the test article mounted on the armature head. The head is usually machined very flat with numerous threaded mounting holes patterned around it’s surface.
The current flowing through both the field and armature coils results in a lot of heat being generated and it is important that the heat be removed or the shaker will quickly overheat. Small and medium sized systems are usually air-cooled by a blower operating as a vacuum cleaner pulling the heat out of the shaker, whereas the larges systems are water-cooled with the coils being hollow-tubing with chilled water circulating through them.
3) AMPLIFIERS: The armature current is generated by the amplifier; since we are dealing with signals in the audio-frequency range, it is essentially an audio amplifier, and in fact industrial audio amplifiers are commonly used with small systems. It typically takes about 10 watts of audio power to result in 1 pound of force, so you can see that 1000 watt amplifiers would be typical in small systems going up to 500 KW in the largest systems.
Linear amplifiers are common with the smaller systems, but quickly get impractical with larger systems due to their low efficiency; switching amplifiers are utilized instead, which are much more efficient, but noisy and have higher distortion. Vintage systems used large glowing vacuum tubes that were steam-cooled and a few are still in existence today. Large water-cooled transistorized linears became popular in the 1970’s, but lost out to the more efficient switchers. Normally all types of amplifiers are designed to produce their full output voltage with a drive signal of 1 to 3 Vrms and the output voltage may range from 30 Vrms on small systems to 240 Vrms on large systems. The amplifier may also provide the DC voltage for the field coil, and these voltages are similar in magnitude to the armature coil voltages.
Small amplifiers operate from a standard 120 V wall receptacle, but above about 1000 watts higher voltages are required and 3-phase power is desirable; these installations will require an electrician to install and may require bringing a special power line to the test station. The larger amplifiers are usually modular in design, allowing a faulty module to be removed from the system and returned for repair while only diminishing the system capabilities.
4) ACCELEROMETERS: The measurement of the force applied to the test article is usually done with an accelerometer, commonly shortened to accel; it essentially a sliver of piezo-electric crystal with a mass attached to the free end. It appears electrically to be a charged capacitor and a change of acceleration results in a change of charge. To convert this charge into a useful voltage, an integrator is used; if the integrator is internal to the accel body, it is referred to as an “integrated”, or ICP type, and is powered by a current source of nominally 4 MA. The current biases the electronics at a DC level of typically 6-10 volts with the signal riding on the DC level. The sensitivity is expressed in units of MV/G with a nominal 10 MV/G being a common type for tests up to 200 G and 100 MV/G and 500 MV/g being better suited for low-level testing. Thus a 10 G peak test with a 10 MV/G accel would show a signal of 100 MV peak ( 200 MV p-p ) riding on the DC bias level as viewed on a scope. Because of the large DC bias, the scope must be AC coupled to see the signal on a useful scale.
If there is no electronics in the accel body, it is referred to as a “charge” type and some signal conditioning is required to convert the charge into voltage. A charge amplifier is the device used, which is just an integrator with gain adjustments and metering; some are multi-channel fully-metered rack-mount types and others are simple battery-powered single channel types. All convert the charge into voltage, typically at a scale of 10 MV/G with no DC bias level on the output. The length of cable used from the accel to the charge amp is critical to the accuracy of a charge type accelerometer.
5) FIXTURES: Unless you are very lucky, your test article won’t easily mount to the armature head and some type of adapter will be needed. These adapters are referred to as fixtures, and I cannot emphasize enough the importance of good fixture design to get good test results. At the frequencies of interest to the vibration tester, mechanical items have many modes of motion, all detracting from the desired result. While the fixture must be very light be avoid using up all the system capability just moving the fixture, it must be incredibly stiff and have no modes of motion in the frequency range of interest. It is a specialized design skill.
Large fixtures are commonly made of an arrangement of welded pieces cut from 2” plates of magnesium. For the amateur, starting with a cube of aluminum and machining out the unnecessary parts is a good beginning; do not expect to use angle brackets to do the job, but be equally careful not to overload the shaker with too much weight. Also it is very important for the center of gravity of the fixture and load to fall in line with that of the shaker. Mating surfaces must be dead flat with multiple screws torque’d down and rechecked periodically.
6) CONTROLLERS: The controller’s job is simply to control, in other words to run the desired test within the capabilities of the system, and to stop the test if those capabilities are exceeded or the test fails to perform properly. Early controllers were analog and even motorized, but virtually all have been replaced by PC based versions. A good controller should start with multiple input channels and current sources for each one of them so that additional equipment is not needed to set up a test. It should offer the option of controlling on the average of the desired channels or the Extremal, or highest of those channels. It should have a wide dynamic range with pre-scaling to fully resolve signals from less than a millivolt to several volts.
The control methodologies differ whether the desired test is sine, random or shock and a more detailed description of each approach follows, but they share common requirements. The drive signal always starts out at zero and slowly rises, looking for an appropriate response from the system If there is no feedback signal from the accelerometer, the test wants to be aborted rather than destroy the shaker, so at some point an “open-loop” determination is made and the test aborted. If the response seems insufficient, the controller may sense that something is wrong and trip out with “low-gain” rather than keep pushing. If these situations are encountered, see the troubleshooting section that follows.
Once started, the controller should force the system to produce the desired response over time in random or as the system sweeps frequency in sine, compensating for changing responses from all the various elements in the system that may change with frequency, temperature or time. Should the response exceed pre-set abort limits, the system should safely shut down. If the test runs successfully, the controller should allow plotting, printing, or saving the results or exporting them in a format recognizable by Microsoft Excel or Word.
7) SWEPT-SINE TESTING: Sine testing is the easiest to understand since all the waveforms are sine waves and the resulting audio tone from the shaker is easy to recognize. In practice the frequency is swept back and forth between a lower limit and an upper limit at a pre-determined rate; the rate may be specified as linear, logarithmic, or stepped. Logarithmic is most prevalent, with a specification of 3.0 Oct/Min being a common number, meaning the frequency will double 3 times per minute of sweep ( or halve 3 times if the frequency is counting down.
While the frequency is sweeping, the controller is varying the test level to conform with the specified test. Shaker systems have physical and electrical limitations which restrict the range of permissible tests; these are expressed as displacement, velocity and acceleration limits. You must remember that velocity is the integral of acceleration and displacement is the integral of velocity; if you refer to a vibration nomograph, you will be able to understand the seemingly odd-shaped tests.
At low frequencies the displacement is very large for a given acceleration level and hence there is a displacement limit at lower frequencies equal to the system displacement limit, which is typically specified as 1” or 2” peak-to-peak. The moving coil also generates a voltage referred to as back EMF; this voltage is proportional to the velocity of the coil which is expressed in units of IPS ( inches-per-second ) with 70 IPS being a typical maximum number. Since the amplifier has a maximum output voltage before clipping, this defines the velocity limit. Force generated is proportional to current flowing through the armature coil, but at some point the coil will overheat or become separated from the armature head, or the coil will come apart and turn into a slinky; this point is the acceleration limit and is typically 100 G’s.
Thus for a test to stay within the safe limits of the shaker system, it will have to conform to these restrictions. Starting at low frequencies, it will be in a displacement limit mode, transitioning into a velocity limit mode typically around 40 Hertz, and finally into an acceleration mode around 150 Hertz. A specified test does not have to follow this shape, but it must stay within the system limits. As the frequency is swept, the drive level to the amplifier must be continuously adjusted to take account of changes in test level, amplifier gain, shaker response, and fixture and test article response. This changing of drive or servo level is referred to as compression, as in reduction of drive level and measured in Db and displayed on a bar graph.
Shakers, fixtures and loads all have resonances, and when sweeping the frequency through these resonances wild response changes will occur. While it is the controller’s job to compensate for these changes, there are practical limits to what can be accomplished. The seasoned test engineer will do everything possible to keep the resonances above the test frequency range or to damp the Q of the resonances; this can sometimes be accomplished by adding stiffeners, drilling irregular hole patterns, or gluing damping material to fixture flat surfaces.
The resonances are obviously excited when passing through those frequencies, but less obviously so at sub-harmonics. Amplifiers all have distortion and an analysis of the distortion usually shows 2nd, 3rd, 5th, 7th harmonics, etc, in diminishing amplitude; as the frequency passes any of these sub-multiples of the resonances, the distortion will excite them, resulting in visible acceleration distortion and audible impurities. Other than at these frequency points, the resulting acceleration waveform and audio tone should be pure, or something is wrong.
8) RANDOM TESTING: Random testing is harder for the neophyte to understand since the results appear to be random. Sine testing is a good engineering tool to measure a system, but it doesn’t duplicate the actual conditions that occur in the field. Random testing was started to duplicate field conditions and it dates back to when a bank of different length tuning forks with pencil leads attached were mounted to a test article and it was then driven or flown in the usual manner; the resulting pencil marks recorded the amount of vibration that occurred in actual use over the various frequencies that the tuning forks measured.
From these pencil marks an outline would be drawn that indicated the frequency spectrum and amplitudes that the article was subjected to in actual use. It is obviously better to have an airplane wing fail on a test table instead of the air and the military took a great deal of interest in developing random testing to make flight safer. Their efforts resulted in the creating of MIL-STD-810 Environmental Test Methods, of which every test engineer should have a copy.
Thus random testing is not at all random, but tries to duplicate a noise output that has been spectrally-shaped. Since the response of the amplifier, shaker, fixture and test article all vary widely with frequency, it is not enough to just generate this spectrally-shaped signal; it must be altered at every individual frequency for the result to be correct, and this process is called equalization. Modern controllers use the fast-Fourier Transform or FFT to do the frequency analysis and digital signal processing or DSP for the spectrum generation; the resolution of the controller is expressed in lines. Thus a 400 line system has a resolution of 5 Hertz on a 2000 Hertz frequency range, and not every individual frequency gets adjusted, but every 5 Hertz, limiting how sharp a correction can be achieved.
Test levels are specified in units of acceleration spectral density ( ASD ) which is the same thing as power spectral density on a spectrum analyzer. The RMS of the ASD curve is the actual test level expressed in G-rms; note that this differs from swept-sine testing where the levels are expressed in units of G-peak. A proper random test should have a Gaussian distribution of amplitudes to appear random with a peak-to-RMS ratio of at least 3:1, so you should see occasional acceleration peaks of at least 3X the RMS level.
9) SHOCK TESTING: There are two types of shock testing- classical shock and shock spectrum. We will only deal with classical shock here; shock spectrum is an attempt to duplicate the results of a shock test with a shaped random spectrum that matches what was generated during a classical shock test.
Classical shock duplicates real world conditions where an object gets dropped or banged, or perhaps jarred when a gun was fired. It was originally accomplished by mounting the article on a pendulum that was raised to a pre-determined height and dropped. Pads were placed against the stop to shape the resulting impact; rubber pads would result in a sinusoidal impact, whereas crushable pads might yield a triangular result. Thus a family of geometrical shaped tests resulted characterized by the pulse shape, duration, and peak amplitude.
Since a shock test is a one-time event, the controller must first characterize the system to “know” what drive waveform to produce to result in the desired test. This learning process is referred to as equalization and usually consists of a train of low-level pulses or random noise; the results of the equalization are analyzed to predict the drive requirements. If multiple pulses are ordered, the controller will home in on the desires response after each pulse. Since a pulse is generally in one direction, only half of the shaker displacement could get used, but by pulling the armature down before the test starts, the whole displacement range can be used; this is referred to as pre-compensation. Since the armature is still moving at the end of the test, it would continue to move until it hit the stops unless it was returned to center position, and this process is called post-compensation. Actually the goal is for acceleration, velocity and displacement to all integrate to zero at the end of the test and a low-level pulse train is used for both the pre- and post- test pulses to maximize the system capabilities.
There is a mathematical relationship with the returned pulse response and it’s “shock spectrum” and some controllers will display that calculated response spectrum if desired.
10) TROUBLESHOOTING: A shaker system may appear to be a rugged heavy mass, but it is as fragile and mistakes can be very expensive and difficult to repair. NO AMOUNT OF CAUTION IS TOO MUCH WHEN OPERATING A SYSTEM; this is even more true when diagnosing a problem In a normally operating system both the controller and amplifier safety limits are at work to save the day if something goes wrong, but if something is already wrong, all bets are off and you should proceed very cautiously.
The most common problems relate to the accelerometer. If the current source is turned off, the accel cable bad or cables switched, or the accel was super-glued down and popped loose, then there will no feedback signal to the controller and it will keep trying to drive the shaker harder until safety checks shut it down. If they don’t shut it down , it will drive the shaker to destruction accompanied by very audible indicators.
The next most common errors are human: disconnecting cables or turning the computer off during a test. DO NOT TOUCH ANYTHING WHILE A TEST IS RUNNING! Stop the test and TURN THE AMPLIFIER GAIN DOWN before disconnecting anything or changing programs. The most common error here is to leave the amplifier gain turned up and later disconnect something or turn the pc off, resulting in a bang. Remember that the controller can only control if the computer is turned on and everything is hooked up.
If a system once worked and now doesn’t, stop and carefully look for all of the obvious things mentioned above. Also, check all the setup parameters for the controller to be sure that you are not asking for something that cannot be done. If nothing is found, the safest way to diagnose a problem is to use a sine-wave signal source to excite the system at a low level. If a frequency of 200 Hertz is used, there will be no appreciable displacement or velocity to worry about, and by monitoring the armature current, the system can safely be controlled. You will need an audio range sine generator, a clamp-on current meter, a scope and some BNC tees; the controller can be used as the signal source if needed, but a separate source will eliminate the controller from question. Tee the accelerometer signal and drive signal out so that you can monitor the drive signal, amplifier output and accelerometer feedback as needed.
Start out by knowing what to expect; you should know what is the maximum acceleration rating with the load that is currently on the table, and the approximate voltage and current to be expected at those levels and then limit yourself to 10-20% of those numbers initially. If you have no knowledge of the voltages and currents, small systems usually require 30-60 Vrms and maybe 10 Arms at full rating and large systems100-200 Vrms and a current in amps roughly 10% of the system rating in pounds. With the amplifier gain turned down, increase the 200 Hertz source to about 1 volt output; have the clamp-on ammeter around an armature lead and slowly increase the amplifier gain until 10% of rating. You should be hearing a low tone and observing the acceleration signal at this point; if there is no acceleration signal, trouble-shoot that until the expected response is observed. Remember that you are looking for a signal roughly 10% of maximum, maybe 10 G’s times the accelerometer sensitivity, or 100 MV for a typical accel. If the field power is missing, there will be no noticeable response even if everything else is OK.
If the accelerometer waveform is distorted, next check the drive waveform and then the amplifier output to see if either is causing the distortion; if the amplifier output waveform is clean and you are getting a distorted acceleration waveform or impure audio tone, then the problem most likely is in the shaker itself. Some problems will only manifest themselves at higher levels, with heavy loads that imbalance the shaker, or at lower frequencies where the displacement results in internal rubbing, but you have achieved a safe approach to look for them. Remember that you now have a purely manual system now, with you as the controller; be ready to turn the gain down at the first sign of trouble!
You can gradually increase the level to verify full force capability or reduce the frequency to 20 Hertz and gently increase the level to look for any noises that occur with displacement, but be very cautious when doing so as to not overdrive the shaker. At 20 Hertz, only a few G’s will be needed to reach maximum displacement and the current will be very low at that point, so observe the shaker table at all times.
By now you should have observed something wrong and fixed it, and be ready to put the controller back to work; if you did not find anything wrong, then the controller itself may be at fault, or more probably some improper setup condition that will not allow the test to run. Run a controller self check referred to as a “closed-loop” test by connecting the drive or servo output to channel #1 input and try to run the test; it should control perfectly if the controller is operating properly. Now you should be ready to re-connect the system and start with a low level test initially and build up to the desired test as your confidence grows, but not so low a level as to be unobservable; 2 to 5 G’s is a good place to start.
11) TRAINING: Training may appear to be expensive, but it can prevent much more expensive mistakes; keep in mind that a uniquely trained teacher must come to you along with the usual travel expenses. A user can educate himself by taking advantage of available materials. The military Environmental Test Handbook MIL-STD-810E is available for free online; a Google search found www.weibull.com offering it for a free download and it will explain vibration testing from a requirements viewpoint. Also a series of training courses are available on www.equipment-reliability.com as well as Wayne Tustin’s excellent new book “Random Vibration & Shock Testing” which sells for around $250; the book covers everything in this paper and much more in great detail.
Rev 4/29/05 RWP