When testing for vibration effects, the following test methods are most widely used:
Fixed frequency sinusoidal vibration method;
Sweeping frequency method;
Broadband random vibration method;
Narrowband random vibration method.
Sometimes in laboratory conditions carry out tests for the effects of real vibration.
Fixed Frequency Sinusoidal Vibration Tests carried out by setting specified values of vibration parameters at a fixed frequency. Tests can be carried out:
At one fixed frequency;
At a number of mechanical resonance frequencies;
At a number of frequencies specified in the operating range.
Tests at one fixed frequency f(i) for a given time t p with a certain acceleration (displacement) amplitude are ineffective. Because the likelihood that a product during operation or transportation is exposed to vibration at one frequency is very small. This type of testing is carried out during the production process to identify poor-quality soldered and threaded connections, as well as other manufacturing defects.
Tests using the fixed frequency method at mechanical resonance frequencies. The products under test require preliminary determination of these frequencies. The product under test is sequentially exposed to vibration at resonance frequencies, maintaining it in each mode for some time. Dignity This method is that tests are carried out at frequencies that are most dangerous for the tested electrical system. Disadvantage is the difficulty of automating the testing process, since during testing the resonant frequencies may change slightly.
Tests at a number of specified frequencies in the operating range It is advisable to carry out to determine the characteristics of the product at points in the operating frequency range. Theoretically, the interval between two adjacent frequencies is chosen to be no greater than the width of the resonant characteristic structural element. This is done in order not to miss the possible occurrence of resonance. In case of detection of resonant frequencies or frequencies at which deterioration of the controlled parameters of the product is observed, an additional shutter speed at this frequency is recommended to clarify and identify the causes of the discrepancy.
Sweeping frequency testing are carried out by continuously changing the vibration frequency towards its increase and then decrease. The main parameters characterizing the sweep frequency method are:
Time of one swing cycle T c;
Swing speed nk;
Test duration T p.
An important indicator of the sweep frequency method is the speed of the frequency swing. Based on the fact that the range of high vibration frequencies (1000...5000 Hz) is much wider than the range of low vibration frequencies (20...1000 Hz), it follows that when the frequency swings at a constant speed within the operating range, the low frequency region will pass in less time, than the high frequency region. As a result, detection of resonances at low frequencies will be difficult. Therefore, usually the frequency change within the operating frequency range is carried out according to an exponential law.
f in =f 1 ×e kt,(3)
Where f in– vibration frequency at time t, Hz; f 1– lower frequency of the operating range, Hz; k is an exponent characterizing the swing speed.
When choosing a high swing speed, the properties of the tested ES will be assessed with large errors, because the amplitude of the resonant oscillations of the product will reach lower values than at low speed, and omissions (non-detection) of resonances are also possible. When choosing a low swing speed, prolonged passage of the operating frequency range may cause damage to the test product at resonant frequencies and increase the test duration. The rate of change of frequency must be such that the time of frequency change in the resonant frequency band t D f was no less than the time it took for the vibration amplitude of the product to rise at resonance to a steady-state value t nar and the time of final establishment of the moving part of the measuring or recording device t y. Those. The rate of change of frequency will be limited by the following conditions:
t D f > t nar,(4)
t D f > t y .
The time for the vibration amplitude to rise at resonance to a steady-state value can be approximately calculated using the formula:
t ad =k 1 ×Q/f 0, (5)
Where f 0 – resonant frequency, Hz; Q - quality factor of the product; k 1 – coefficient that takes into account the increase in the time of amplitude rise to a steady-state value as a result of deviation of amplitude changes from the linear law.
Taking into account all of the above, the rate of change of frequency is calculated using the formula:
n k =2000×lg(2×Q+1/2×Q)/t D f ,(6)
Where t D f - selected in accordance with conditions (4). If the rate of change of frequency found by the formula exceeds 2 octaves/s, then it is still accepted as 2 octaves/s - this is the maximum maximum rate of change of frequency.
Broadband random vibration testing. In this case, simultaneous excitation of all resonances of the test product is realized, which makes it possible to identify their joint influence. Tightening the test conditions due to the simultaneous excitation of resonant frequencies reduces the test time compared to the sweeping frequency method.
The severity of broadband random vibration testing is determined by a combination of the following parameters:
Frequency range;
Spectral acceleration density;
Duration of the test.
The degrees of cruelty are shown in Table 5.1.
Table 5.1
TO merits This method includes:
Proximity to mechanical stress during actual operation;
Ability to identify all mechanical effects various elements designs;
Shortest test duration.
TO shortcomings concerns the high cost and complexity of the equipment being tested.
Narrowband random vibration testing. This method is also called the frequency band scanning random vibration method. Random vibration in this case is excited in narrow strip frequencies, the central frequency of which, according to an exponential law, slowly scans across the frequency range during the test.
This method is a compromise between the wideband and swept sine wave test methods.
To ensure equivalence between the sweep band random vibration test and the broadband random vibration test, the following condition must be met:
g=s/(2×pi×f) 1/2 =const,(7)
where g is the acceleration gradient, g×с 1/2; s – root-mean-square vibration acceleration in a narrow frequency band, measured at the control point, g; f is the center frequency of the band.
The degree of test severity in this case is determined by a combination of the following parameters:
Frequency range;
Scanning frequency bandwidth;
Acceleration gradient;
Test duration.
The value of the acceleration gradient is found using the formula:
g=0.22×S(f) 1/2 ,(8)
Where S(f) – spectral density of vibration acceleration when tested by the broadband random vibration method.
Related information.
Test methods for random narrow-band vibration with a time-varying average frequency have become widespread. They have the following advantages:
1) the ability to obtain significant load levels using less powerful equipment;
2) the possibility of using simpler control equipment that requires less qualified personnel.
Rice. 8. Control circuit for testing for narrowband random vibration: a - spectral densities of narrowband and broadband vibration, b - block diagram of the system: 1 - frequency scanning drive, 2 - vibrometric equipment, 3 - sensor, 4 - product under test, 5 - vibration exciter, 6 - amplifier; 7 - automatic gain control, 8 - accompanying filter; 9 - white noise generator
The main tasks are to determine the law of change in average frequency over time and the law of change in vibration depending on frequency. When determining these laws, they are guided by considerations of some equivalence between tests for narrow and broadband random vibrations. It is installed, for example, for fatigue strength tests, which require identical distribution of maximum and minimum loads under narrow and broadband vibrations. Installed
where is the root-mean-square value of the vibration overload (in terms of acceleration in units with narrow-band excitation. If it must be proportional to VI, then the acceleration gradient when testing for narrow-band vibration is a constant value. Test time with a logarithmic change in frequency
Accordingly, the highest and lowest frequencies of the range in which scanning is performed; testing time for narrow and broadband vibration; scale factor.
To reproduce the conditions that arise during broadband vibration with uniform spectral density in the frequency band (see Fig. 8, a), the acceleration gradient is calculated using the formula
where On the average transmission coefficient of the vibration system; its transfer function.
In accordance with (18) and (19), the test mode for narrow-band vibration is determined by the coefficients. The coefficient can vary from 1.14 (for simple tests) to 3.3 (for accelerated tests). The coefficient changes accordingly within the limits
In Fig. 8a shows the spectral densities of narrowband and broadband vibrations. The slope of the dashed line, which determines the rate of increase in the spectral density when the average frequency changes, is equal to the square of the acceleration gradient.
A large number of industrial automation systems are known to test for narrowband random vibration. They are built according to the scheme shown in Fig. 8, b. A narrow-band random process with a time-varying central frequency is obtained using a white noise generator and an accompanying filter, the central frequency of which is varied by a frequency scanning drive. The rotation speed is adjustable within wide limits. The RMS value of narrow-band vibrations at the output of the vibration system is stabilized using an automatic gain control (AGC) system. The AGC feedback signal comes from the output of the vibration measuring equipment
What is SKZ (and what is it eaten with)?
The easiest way to determine the condition of the unit is to measure the RMS vibration with a simple vibrometer and compare it with the standards. Vibration standards are defined by a number of standards, or are indicated in the documentation for the unit and are well known to mechanics.
What is SKZ? RMS is the root mean square value of a parameter. Standards are usually given for vibration velocity, and therefore most often the combination of RMS vibration velocity is used (sometimes they simply say RMS). The standards define a method for measuring RMS - in the frequency range from 10 to 1000 Hz and a number of RMS vibration velocity values: ... 4.5, 7.1, 11.2, ... - they differ by approximately 1.6 times. For units of different types and power, the norm values from this series are set.
Mathematics SKZ
We have a captured vibration velocity signal with a length of 512 counts (x0 ... x511). Then the RMS is calculated using the formula:
It is even simpler to calculate the RMS from the spectrum amplitude:
In the spectrum RMS formula, index j is moved not from 0, but from 2, since the RMS is calculated in the range from 10 Hz. When calculating RMS from a time signal, we are forced to use some filters to select the desired frequency range.
Let's look at an example. Let's generate a signal from two harmonics and noise.
The RMS value for the time signal is slightly higher than for the spectrum, since it contains frequencies less than 10 Hz, and in the spectrum we threw them out. If in the example we remove the last term rnd(4)-2, which adds noise, then the values will exactly match. If you increase the noise, for example rnd(10)-5, the discrepancy will be even greater.
Other interesting properties: the RMS value does not depend on the frequency of the harmonic, of course, if it falls in the range of 10-1000 Hz (try changing the numbers 10 and 17) and on the phase (change (i+7) to something else). Depends only on the amplitude (numbers 5 and 3 before the sines).
For a signal from one harmonic:
It is possible to calculate the RMS vibration displacement or vibration acceleration from the RMS vibration velocity only in the simplest cases. For example, when we have a signal from one return harmonic (or it is much larger than the others) and we know its frequency F. Then:
For example, for a rotation frequency of 50 Hz:
SKZusk=3.5 m/s2
RMS speed=11.2 mm/s
Additions from Anton Azovtsev [VAST]:
The general level is usually understood as the root mean square or maximum value of vibration in a certain frequency band.
The most typical and common value is the vibration velocity in the range of 10-1000 Hz. In general, there are many GOSTs on this topic:
ISO10816-1-97 - Monitoring the condition of machines based on the results of vibration measurements on
non-rotating parts. General requirements.
ISO10816-3-98 - Monitoring the condition of machines based on the results of vibration measurements on
non-rotating parts. Industrial machines with rated power over 15 kW and
rated speed from 120 to 15000 rpm.
ISO10816-4-98 - Monitoring the condition of machines based on the results of vibration measurements on
non-rotating parts. Gas turbine installations with the exception of installations based on
aviation turbines.
GOST 25364-97: Stationary steam turbine units. Vibration standards for supports
shafting and General requirements to carry out measurements.
GOST 30576-98: Centrifugal feed pumps for thermal power plants. Norms
vibrations and general requirements for measurements.
Most GOST standards require measuring root-mean-square values of vibration velocity.
That is, you need to take a vibration velocity sensor, digitize the signal over some time, filter the signal in order to remove signal components outside the band, take the sum of the squares of all values, extract the square root from it, divide by the number of added values and that’s it - that’s the general level !
If you do the same, but instead of the root mean square you just take the maximum, you get “Peak value.” And if you take the difference between the maximum and minimum, you get the so-called “Double swing” or “peak-peak.” For simple vibrations, the root mean square value is 1.41 times less than the peak value and 2.82 times less than the peak-to-peak value.
This is digital, there are also analog detectors, integrators, filters, etc.
If you use an acceleration sensor, you must first integrate the signal.
The bottom line is that you simply need to add up the values of all components of the spectrum in the frequency band of interest (well, of course, not the values themselves, but take the root of the sum of squares). This is how our (VAST) device SD-12 worked - it calculated the RMS general levels from the spectra, but now the SD-12M calculates the real values of the general levels, using filtering, etc. numerical processing in the field of time signals, so when measuring the overall level, it simultaneously calculates RMS, peak, peak-to-peak and crest factor, which allows for correct monitoring...
There are a couple more comments - the spectra, naturally, should be in linear units and those in which the overall level needs to be obtained (not logarithmic, that is, not in dB, but in mms). If the spectra are accelerated (G or mss), then they must be integrated - divide each value by 2 * pi * frequency corresponding to this value. And there is also some complexity - spectra are usually calculated using a certain weighting window, for example Hanning, these windows also make corrections, which significantly complicates the matter - you need to know which window and its properties - the easiest way is to look in a reference book on digital signal processing.
For example, if we have a spectrum of vibration acceleration obtained with a Hanning window, then in order to obtain the RMS vibration acceleration, we need to divide all channels of the spectrum by 2pi*channel frequency, then calculate the sum of the squares of the values in the correct frequency band, then multiply by two thirds (window contribution Hanning), then extract the root from the resulting one.
And there are other interesting things
There are all sorts of peak and cross factors that are obtained if you divide the maximum by the root mean square value of the overall vibration levels. If the value of these peak factors is large, it means that there are strong single impacts in the mechanism, that is, the condition of the equipment is poor, for example, devices such as SPM are based on this. The same principle, but in a statistical interpretation, is used by Diameter in the form of Kurtosis - these are humps in the differential distribution (what a clever name it is!) of the values of the time signal in relation to the usual “normal” distribution.
But the problem with these factors is that these factors first grow (with the deterioration of the condition of the equipment, the appearance of defects), and then begin to fall when the condition worsens even more, and here is the problem - you need to understand whether the peak factor with excess is still growing, or already falling...
In general, you need to keep an eye on them. The rule is rough, but more or less reasonable, it looks like this: when the peak factor began to fall, and the overall level began to rise sharply, then everything is bad, the equipment must be repaired!
And there is a lot more interesting things!
Depending on the nature of the vibrations, they differ:
deterministic vibration:
Changes according to the periodic law;
Function x(t), describing it, changes values at regular intervals T(oscillation period) and has an arbitrary shape (Fig. 3.1.a)
If the curve x(t) changes over time according to a sinusoidal law (Fig. 3.1.b), then periodic vibration is called harmonic(in practice - sinusoidal). For harmonic vibration the following equation holds:
x(t) = A sin (wt), (3.1)
Where x(t)- displacement from the equilibrium position at the moment t;
A- displacement amplitude; w = 2pf- angular frequency.
The spectrum of such vibration (Fig. 3.1. b) consists of one frequency f = 1/T.
Fig.3.1. Periodic vibration (a); harmonic vibration and its frequency spectrum (b); periodic vibration as the sum of harmonic oscillations and its frequency spectrum (c)
Polyharmonic oscillation - private view periodic vibration; :
Most common in practice;
A periodic oscillation by Fourier series expansion can be represented as the sum of a series of harmonic oscillations with different amplitudes and frequencies (Fig. 3.1.c).
Where k- harmonic number; - amplitude k- th harmonics;
The frequencies of all harmonics are multiples of the fundamental frequency of the periodic oscillation;
The spectrum is discrete (line) and is presented in Fig. 3.1.c;
It is often classified, with some distortions, as harmonic vibrations; the degree of distortion is calculated using harmonic distortion
,
where is amplitude i- harmonics.
Random vibration:
Cannot be described by precise mathematical relationships;
It is impossible to accurately predict the values of its parameters at the nearest point in time;
It can be predicted with a certain probability that the instantaneous value x(t) vibration falls into an arbitrarily selected range of values from to (Fig. 3.2.).
Fig.3.2. Random vibration
From Fig. 3.2. it follows that this probability is equal to
,
where is the total duration of the vibration amplitude in the interval during the observation time t.
To describe a continuous random variable, use probability density:
Formula 
;
The type of distribution function characterizes the distribution law of a random variable;
Random vibration is the sum of many independent and slightly different instantaneous influences (subject to Gauss’s law);
Vibration can be characterized:
mathematical expectation M[X]– arithmetic mean of instantaneous values of random vibration during the observation period;
general dispersion - the spread of instantaneous values of random vibration relative to its average value.
If oscillatory processes with the same M[X] and differ from each other due to different frequencies, then the random process is described in the frequency domain (random vibration is the sum of an infinitely large number of harmonic oscillations). Here it is used power spectral density random vibration in the frequency band
OCTAVES AND RATE OF CHANGE OF FREQUENCY
Octaves are used to determine the difference between two frequencies. For example, the difference between frequencies of 10 Hz and 500 Hz is 490 Hz. Octaves represent this difference on a logarithmic scale.
Almost all of us have heard of the concept of octave being used in music. On a piano, the frequency difference between two nearest notes of the same name is exactly an octave. International standard note for tuning musical instruments is the note A, whose frequency is 440 Hz. The frequency of a note one octave higher is 880 Hz, and one octave lower is 220 Hz. Thus, we see that the octave has the property of doubling, in other words it is a logarithmic ratio.
To determine the number of octaves between two frequencies, you can use the following formula:
where f n – lower frequency, f в – upper frequency.
When testing with a sliding sine wave, a logarithmic scale of frequency change is used. This is done in order to ensure conditions for equal loading of the test object at different frequencies. So, at a frequency of 10 Hz, 10 oscillation cycles occur in 1 second. These same 10 oscillation cycles take one hundredth of a second at a frequency of 1000 Hz. This means that to ensure an equally loaded state (equal number of oscillation cycles) at different frequencies, as the frequency increases, the oscillation time at this frequency must decrease.
The most commonly used frequency change rate is 1 oct/min. If the tests start at 10 Hz, then the first minute will go through the range 10 Hz - 20 Hz, in the next minute - 20 Hz - 40 Hz, etc. For the frequency range 15 Hz – 1000 Hz, the number of octaves is 6.1. At a speed of 1 octave per minute, the test time will be 6.1 minutes.
WHAT IS RANDOM VIBRATION?
If we take a structure consisting of several beams various lengths and we begin to excite it with a sliding sinusoid, then each beam will oscillate intensely when its own frequency is excited. However, if we excite the same structure with a broadband random signal, we will see that all the beams will begin to sway strongly, as if all frequencies were simultaneously present in the signal. This is true and at the same time not true. The picture will be more realistic if we assume that for some period of time these frequency components are present in the excitation signal, but their level and phase change randomly. Time is the key point in understanding a random process. In theory, we should consider an infinite period of time to have a true random signal. If the signal is truly random, then it never repeats.
Previously, to analyze a random process, equipment based on bandpass filters was used, which isolated and evaluated individual frequency components. Modern spectrum analyzers use a Fast Fourier Transform (FFT) algorithm. A random continuous signal is measured and sampled in time. Then, for each time point in the signal, sine and cosine functions are calculated, which determine the levels of the frequency components of the signal present in the analyzed signal period. Next, the signal is measured and analyzed for the next time interval and its results are averaged with the results of the previous analysis. This is repeated until an acceptable averaging is obtained. In practice, the number of averagings can vary from two to three to several tens and even hundreds.
The figure below shows how the sum of sinusoids with different frequencies forms a signal of a complex shape. It may appear that the total signal is random. But this is not so, because the components have a constant amplitude and phase and vary according to a sinusoidal law. Thus, the process shown is periodic, repeatable and predictable.
In reality, a random signal has components whose amplitudes and phases vary randomly.
The figure below shows the spectrum of the sum signal. Each frequency component of the total signal has a constant value, but for a truly random signal, the value of each component will change all the time and spectral analysis will show time-averaged values.
frequency Hz
The FFT algorithm processes the random signal during the analysis time and determines the magnitude of each frequency component. These values are represented by root mean square values, which are then squared. Since we are measuring acceleration, the unit of measurement will be the overload gn sq, and after squaring it will be gn 2 sq. If the frequency resolution in the analysis is 1 Hz, then the measured quantity will be expressed as the amount of acceleration squared in a frequency range 1 Hz wide and the unit of measurement will be gn 2 /Hz. It should be remembered that gn is gn well.
The unit gn 2 /Hz is used in the calculation of spectral density and essentially expresses the average power contained in a frequency range 1 Hz wide. From the random vibration test profile, we can determine the total power by adding the powers of each 1 Hz wide band. The profile shown below has only three 1Hz bands, but the method in question can be applied to any profile.
Spectral density,
g RMS 2 /Hz
frequency Hz
(4 g 2 /Hz = 4 g rms 2 in each 1 Hz wide range)
The total acceleration (overload) gn of the RMS profile can be obtained by addition, but since the values are root mean square, they are summed up as follows:
The same result can be obtained using a more general formula:
However, the random vibration profiles currently used are rarely flat and more like a cross-section of a rock mass.
Spectral density,
g RMS 2 /Hz
(log scale)
Frequency, Hz (log scale)
At first glance, determining the total acceleration gn of the shown profile is a rather simple task, and is defined as the root-mean-square sum of the values of the four segments. However, the profile is shown on a logarithmic scale and the slanted lines are not actually straight. These lines are exponential curves. So we need to calculate the area under the curves, which is a much more difficult task. We will not consider how to do this, but we can say that the total acceleration is equal to 12.62 g rms.
Why do you need to know the total acceleration during random vibration?
In random vibration mode, the vibration test system has a rated pushing force, which is expressed in Nsq or kgfsrm. Note that the force is determined by the RMS value, unlike sine vibration, which uses the amplitude value. The formula for determining force is the same: F = m*a, but since force has a root-mean-square value, then the acceleration must also be root-mean-square.
Force (N sq.) = mass (kg) * acceleration (m/s 2 sq.)
Force (kgfs.) = mass (kg) * acceleration (gns.)
Remember that mass refers to the total mass of all moving parts!
What is meant by movement during random vibration?
It is important for us to know the displacement for a given test profile, since it may exceed the maximum permissible displacement of the vibrator. Without going into details, we know how to calculate the total rms acceleration and there is no reason that prevents us from determining the rms velocity and rms displacement for a given profile. Difficulties arise when we want to move from the root mean square value to the amplitude or peak-to-peak value. Let's remember that the ratio of the amplitude value to the root mean square value is called the crest factor, which for a sinusoidal signal is equal to the square root of 2. The coefficients of transition from the root mean square value to the amplitude value and back are equal to 1.414 (2) and 0.707 (1/2), respectively. However, we are not dealing with a sinusoidal signal, but with a random process whose theoretical crest factor is equal to infinity, since the amplitude value of a random signal can be equal to infinity. In practice, the crest factor value is taken to be 3. The figure shows the normal distribution curve of a random signal. According to statistics, if we limit ourselves to the width of the interval 3, then this will cover 99.73% of all possible values of the amplitudes of a true random signal.
Probability Density
Bell curve
Therefore, if we assume that with a crest factor of three, the random vibration controller will generate a random signal with a maximum amplitude of three times the rms value, then it follows that the calculated displacement will be equal to the total rms displacement multiplied by the crest factor value and multiplied by by 2. This calculated movement should not exceed the maximum permissible movement of the vibrator.
Practical aspects of choosing the crest factor value
We can make the random vibration controller generate a signal with a crest factor of 3, which will be transmitted through the vibrator to the test sample. Unfortunately, both the vibrator and the sample are essentially nonlinear systems and have resonances. This nonlinearity with resonances will cause distortion. Ultimately we will see that the crest factor measured on the vibrator table or test object will be significantly different from what was originally specified! Random vibration controllers do not correct for this automatically.
Out-of-band power
It is necessary to pay attention to the effect that can appear when a sample designed for operation in the frequency range, for example, up to 1000 Hz, is excited by a random signal. The signal generated by the controller can excite resonant frequencies well above 1000 Hz. These frequencies are excited by harmonics. Therefore, it is useful to control the signal power above the test range, since it can cause destruction of a sample that is operational in a given frequency range (in this case, up to 1000 Hz).
Narrowband random vibration
The pushing force of vibrators in random vibration mode is measured under the following conditions:
the load mass is approximately twice the mass of the fittings (the moving part of the vibrator)
test profile complies with ISO 5344 standard
the ratio of the amplitude value to the root mean square value of the acceleration is at least 3.
Vibration testing systems have a non-linear frequency response (at some frequencies their efficiency is higher, at others they are lower), and the random process at frequencies below 500 Hz is reproduced with less efficiency. In this case, the amplifier may not have enough power to create the necessary pushing force. Choosing a more powerful amplifier will solve this problem.
UNITS OF MEASUREMENT OF SPECTRAL DENSITY
The most commonly used units of power spectrum density are:
gn²/Hz | ||||
(m/s²)²/Hz | ||||
gn/Ö Hz |
In any case, you need to remember that acceleration is expressed in root mean square values.
To convert units of measurement:
g²/Hz V m²/s³ | multiply by 9.80665² | those. ´ 96.1703842 |
m²/s³ V g²/Hz | divided by 9.80665² | those. ¸ 96.1703842 |
g/Ö Hz V g²/Hz | square g/Ö Hz | those. (g/Ö Hz)² |
g²/Hz V g/Ö Hz | extract sq. root of g²/Hz | those. Ö (g²/Hz) |
HOW DOES VIBRATION AFFECT MY PRODUCTS?
All products are subject to vibration, which in most cases we know little about. The cause of vibration is the operating conditions of the product, its transportation, or the product itself. For example, electronic components washing machine exposed to strong vibration. We need to understand the effects of vibration to help us create products. High Quality and reliability.
If we consider a car radio installed on the dashboard, it is subject to vibration. The sources of vibration are the engine, transmission, and road profile. The vibration frequency range is usually between 1 Hz and 1000 Hz. For example, a motor speed of 3000 rpm corresponds to a frequency of 50 Hz. This vibration is transmitted to the instrument panel even if the engine is mounted on vibration-isolating mounts, which theoretically should not transmit vibration to the car body. So, we have a vibration source that excites the instrument panel and car radio.
Dashboard
Vibration
The vibration created by the source may be small, but by the time it reaches the radio, the vibration level can increase significantly due to resonances of the car body and dashboard.
Resonance
A good example of resonance is the sound a glass makes when you run a wet finger along its rim. The walls of the glass begin to vibrate at their own frequency. These vibrations produce the sound waves that we hear. The vibrations themselves are caused by the friction of the finger on the glass. There is a well-known story about an opera singer who broke a glass with his voice. If the frequency of sound vibrations coincides with the natural frequency of vibrations of the walls of the glass, the vibrations can become so intense that the glass will burst.
Edge of a wine glass at resonance
The resonant frequency of an object is the frequency at which the object will naturally vibrate if disturbed from its state of equilibrium. For example, when a guitar string is plucked, it will vibrate at a resonant frequency; after being struck, a bell will also vibrate at a resonant frequency.
Beam at resonance
impact
Gain = 20
The figure shows how resonance amplifies vibrations. In this example, an exciting movement with an amplitude of 1 mm causes vibrations of the beam with an amplitude of 20 mm, the magnitude of which to a certain extent depends on the quality factor of the beam. Excessive bending of a beam can lead to fatigue failure.
The sharpness of the resonance, known as the quality factor (quality criterion), is determined by the amount of damping. The effect of damping can be heard by touching the sounding bell with your hand: the hand will dampen its vibration, i.e. the amplitude of vibrations and the sound of the bell will change and quickly fade.
The figure below shows the resonant peak at frequency f. The greater the damping, the lower and wider the resonant peak. Damping is expressed through the quality factor Q, which determines the width of the resonance curve at half power level (A/2) or level -3 dB from A, where A is the maximum amplitude. (-3 dB is a rounded value, the exact value is –3.0102299957 dB).
Level
Frequency
How does resonance affect a car radio?
Weakening of the casing (chattering)
Cable break
Hit
Dashboard
Damage
boards
This picture illustrates:
A poorly secured circuit board will bend and eventually crack or break.
At resonance printed circuit board she conveys high levels vibrations to electronic components, which can cause premature failure.
Cables and wires can break over time at the point of attachment to the board due to fatigue stress.
If the entire device is not carefully secured, it can hit other parts of the dashboard, causing annoying rattling, but more dangerously, shocking electronic components and causing them to vibrate resonantly.
Since the car radio contains a cassette recorder, vibration of the tape mechanism can cause howling and rattling sound, and damage to the film.
VIBRATOR ISOLATION
When operating in a vertical position, the vibrator creates a pushing force directed vertically. According to Newton's third law, every action causes a reaction. It follows from this that when we apply force to our test object, we exert the same force on the floor.
Test object
Force
Since most buildings have a natural frequency of about 15 Hz, the resonant frequencies of not only the objects surrounding the vibrator are excited, but also the resonant frequencies of the building, and this in some cases can lead to damage to the building.
To prevent such a problem, you can use a seismic mass - usually a large one concrete block, the weight of which must be at least 10 times the maximum pushing force developed by the vibrator,
or use some other insulation methods such as pneumatic mounts or rubber mounts.
Armature
Moving reinforcement
Air spring
Moving the body
Most vibrators come with vibration isolation elements. However, this raises another problem related to the movement of the vibrator body. Due to the fact that the vibrator body is isolated from the floor using “springs”, when the vibrator armature moves upward with a load, the vibrator body tends to move downwards. Moving the vibrator body reduces the movement of the vibrator table relative to the floor and, therefore, the acceleration of the table, which has an absolute value. The amount of movement of the housing is related to the ratio of the total moving mass to the mass of the vibrator housing. The heavier the payload, the greater the body movement. The maximum movement of the table relative to the floor can be determined by the following formula:
Unfortunately, vibration isolators have resonances at frequencies of 2.5 Hz, 5 Hz, 10 Hz or 15 Hz depending on the type of isolator. If the vibrator operates large with movement at the resonance frequency of the insulator, then the above formula does not make sense, since the test object will remain motionless while the vibrator body moves.
Tipping TORQUE
There is a rule according to which the center of gravity of the test object and equipment should be placed on the longitudinal axis of the reinforcement. If this rule is not followed, then you can:
overload the test object
damage the vibrator
The design of the vibrator ensures the transmission of pushing force along the axis of the reinforcement, therefore, the displacement of the payload and equipment from the longitudinal axis causes the reinforcement to “tip over”. This overturning movement is perceived by the reinforcement guides and loads them, which, in as a last resort may cause damage to the guide bearings and moving coil. The test object is also subjected to lateral loads that are not provided for by the test modes. If the equipment is not rigid enough, it may experience resonance in the transverse direction, in which the test object is subject to significant uncontrolled vibration. For example, with a lateral acceleration of 5g caused by displacement of the load and equipment having a quality factor at the resonance frequency Q = 50, the test object at this frequency will have an acceleration of 250g!
Control
To prevent this situation, a good rule of thumb is to control the lateral acceleration. In cases where the lateral acceleration is not negligible, the control strategy can reduce the vertical movement to avoid overloading the test object. This method is used in multichannel control, when the control signal is generated based on the reaction of the tested object at several points.
If your equipment is rigid, carefully designed and manufactured, the centers of gravity of the equipment and the test object lie on the longitudinal axis of the vibrator table, then the overturning moment will be minimal and can be ignored.
Note. When vibration complex design the position of its center of gravity may depend on the excitation frequency, so at different frequencies the position of the center of gravity will be different.
DocumentIn vocal parts Richard often used, rather, ..., drummer Ginger Baker, pianist Johnny... back in administered, rock is subdivided... simple scenes of semi-heroic content. Adam Ent, ... notes, especially large vibration at the end of the sentence...