Vibration Measurement and Analysis

Course overview

The course provides a complete introduction to capturing, processing, and interpreting vibration data using DewesoftX. You’ll start by learning vibration basics—the sources, behavior in mechanical systems, and the common units: acceleration, velocity, and displacement. Sensor selection, wiring configurations, and mounting best practices are covered to ensure accurate measurements.

Next, the course guides you through signal integration and differentiation operations, converting acceleration into velocity and displacement, as demonstrated during a drivetrain ramp test. In the frequency domain section, you’ll configure FFT analysis with proper sampling, window functions, and averaging, and interpret spectral responses using markers and envelope detection methods to find bearing faults.

Advanced modules introduce order tracking and rotational/torsional vibration analysis, essential for rotating machinery assessments like imbalance, misalignment, shaft twist, and coupling diagnostics. You’ll learn how to configure encoders, set angles, and run order vs. RPM and Campbell plots for resonance tracking.

The course also covers modal analysis (ODS, MIMO) and shock response spectrum (SRS) features to explore structural resonances, using FFT and SRS math tools with automatic ISO compliance.

By completion, you’ll be able to design robust vibration test setups with synchronized sensors, apply advanced signal processing techniques, identify mechanical problems, and generate export-ready data and visualizations for reporting or CAE follow-through.

Vibration can be defined as the oscillation or repetitive motion of an object around an equilibrium position. The equilibrium position is the state the object assumes when the net force acting on it is zero.

Vibrations typically occur due to the dynamic effects of manufacturing tolerances, clearances, rolling and rubbing contact between machine parts, and out-of-balance forces in rotating or reciprocating components. Even small, seemingly insignificant vibrations can excite the resonant frequencies of other structural parts, amplifying them into significant sources of vibration and noise.

Sometimes mechanical vibration is necessary. For example, vibration is intentionally generated in component feeders, concrete compactors, ultrasonic cleaning baths, rock drills, and pile drivers. Vibration testing machines are also widely used to apply a controlled level of vibration energy to products and subassemblies. This is done to evaluate their physical or functional response and to determine their resistance to vibration environments.

A vibrating body exhibits oscillating motion about a reference position. The number of times a complete motion cycle occurs within one second is called the frequency, measured in hertz (Hz).

The motion may consist of a single component at one frequency, as with a tuning fork, or several components occurring at different frequencies simultaneously, as in the piston motion of an internal combustion engine.

In the image below, we can see the motion of a tuning fork. A tuning fork is an acoustic resonator in the form of a two-pronged fork. It resonates at a specific constant pitch when set into vibration by striking it against a surface or with an object, emitting a pure musical tone.

The signal from the tuning fork can be observed in the Dewesoft recorder and on the FFT widget.

In the image below, we can see the motion of a piston, as found in internal combustion engines.

The signal from the piston’s motion can also be observed in the Dewesoft recorder and on the FFT widget.

In practice, vibration signals usually consist of many frequencies occurring simultaneously, making it difficult to determine from the amplitude–time pattern alone how many components are present and at what frequencies they occur.

These components can be revealed by plotting vibration amplitude against frequency. The process of breaking down vibration signals into individual frequency components is called frequency analysis, a technique often considered the cornerstone of diagnostic vibration measurement.

A graph showing vibration level as a function of frequency is called a frequency spectrogram. When analyzing machine vibrations, we typically find several prominent periodic frequency components directly related to the fundamental movements of various machine parts. With frequency analysis, we can therefore identify and trace the source of undesirable vibration.

Most of us are familiar with vibration: a vibrating object moves, or oscillates.

There are several ways to recognize when something is vibrating. We can touch a vibrating object and feel its motion. We may also see the movement of the object. Sometimes vibration creates sounds that we can hear, or heat that we can sense.

Machine vibration is simply the back-and-forth motion of machines or machine components. Any component that moves back and forth, or oscillates, is vibrating.

Machine vibration can take different forms. A component may vibrate over large or small distances, quickly or slowly, and with or without perceptible sound or heat. In many cases, vibration is intentionally designed into a machine for a functional purpose. In other cases, vibration is unintended and can lead to machine damage.

Here are some examples of undesirable machine vibration:

What causes machine vibration?

Almost all machine vibration is caused by one or more of the following factors:

• Repeating forces – Most machine vibration results from repeating forces, similar to those that cause a boat to rock. These forces act on machine components and cause the machine to vibrate.

• Looseness – The looseness of machine parts can cause vibration. If components become loose, vibration that is normally within tolerable levels may become unrestrained and excessive.

• Resonance – Machines have natural frequencies at which they tend to oscillate. When external forces excite these frequencies, resonance can occur, greatly amplifying vibration.

Vibration amplitude is the characteristic that describes the severity of vibration and can be quantified in several ways. The diagram shows the relationship between the peak-to-peak level, peak level, average level, and RMS level of a sine wave.

The peak-to-peak value indicates the maximum excursion of the wave. This is a useful measure when the vibratory displacement of a machine part is critical for maximum stress or mechanical clearance considerations.

The peak value is particularly valuable for indicating the level of short-duration shocks. However, as shown in the diagram, peak values only indicate the maximum level that has occurred, without accounting for the time history of the wave.

The rectified average value, on the other hand, does take the time history of the wave into account. Nevertheless, it is of limited practical interest because it has no direct relationship with any significant physical quantity.

The RMS value is the most relevant measure of amplitude because it accounts for the time history of the wave and provides an amplitude value directly related to the energy content— and, therefore, to the destructive potential—of the vibration.

When we observed the vibrating tuning fork, we considered the amplitude of the wave as the physical displacement of the fork ends to either side of the rest position. In addition to displacement, the movement of the fork leg can also be described in terms of its velocity and acceleration.

The form and period of the vibration remain the same, regardless of whether displacement, velocity, or acceleration is being considered. The key difference is that there is a phase shift between the amplitude–time curves of the three parameters, as shown in the drawing.

Velocity is 90° out of phase with displacement, and acceleration is 180° out of phase with displacement.

For sinusoidal signals, displacement, velocity, and acceleration amplitudes are mathematically related by functions of frequency and time, as shown in the diagram. If phase is neglected—as is always the case in time-average measurements—the velocity level can be obtained by dividing the acceleration signal by a factor proportional to frequency, and displacement can be obtained by dividing the acceleration signal by a factor proportional to the square of the frequency.

By detecting vibratory acceleration, we are not limited to one parameter alone. Using electronic integrators, the acceleration signal can be converted to velocity and displacement. Vibration parameters are almost universally measured in metric units in accordance with ISO requirements. However, the gravitational constant “g” is still widely used for expressing acceleration levels, even though it lies outside the ISO system of coherent units.

When a single wideband vibration measurement is taken, the choice of parameter is important if the signal contains components at many frequencies. Displacement measurements give the greatest weight to low-frequency components, while acceleration measurements emphasize high-frequency components.

Experience has shown that the overall RMS value of vibration velocity, measured over the range 10 to 1000 Hz, provides the best indication of vibration severity. A likely explanation is that a given velocity level corresponds to a given energy level, so vibrations at both low and high frequencies are equally weighted from an energy perspective. In practice, many machines exhibit a reasonably flat velocity spectrum.

This leads to a practical consideration that can influence the choice of parameter: it is advantageous to select the parameter that provides the flattest frequency spectrum, in order to fully utilize the dynamic range (the difference between the smallest and largest values that can be measured) of the instrumentation. For this reason, velocity or acceleration parameters are normally chosen for frequency analysis.

Because acceleration measurements are weighted toward high-frequency vibration components, they are often used when the frequency range of interest covers high frequencies. The nature of mechanical systems is such that appreciable displacements occur only at low frequencies; therefore, displacement measurements are of limited value in the general study of mechanical vibration. However, where small clearances between machine elements must be considered, vibratory displacement is an important factor.

Displacement is also often used as an indicator of unbalance in rotating machine parts, since relatively large displacements typically occur at the shaft’s rotational frequency—which is also the frequency of greatest importance for balancing purposes.

Acceleration is the rate at which the velocity of an object changes with respect to time (it is the derivative of the velocity vector as a function of time: a = dv/dt). It is the net result of all forces acting upon an object.

In general, there are two basic measurement tasks for acceleration:

• Acceleration due to vibration of the object under test

• Acceleration due to changes in velocity of the object, such as a vehicle (car, airplane)

There is a significant difference between these two measurement tasks. The most important information when measuring vibration acceleration is the dynamic part of the signal (the object itself does not move). When measuring cornering or acceleration/braking of a vehicle, the most important information is the static part of the signal, which corresponds to changes in speed.

Therefore, sensors designed to measure changes in vehicle motion must be capable of detecting static acceleration (such as gravity), while sensors designed for vibration measurement typically remove the static part by design.

It is also important to note that since velocity is the derivative of displacement (v = ds/dt), acceleration can be measured in different ways:

• by directly measuring acceleration,

• by measuring velocity and deriving the signal, or

• by measuring displacement and taking the second derivative.

The latter is a practical approach when using laser or eddy current probes to measure surface displacement.

It is also common to use acceleration measurements to obtain velocity and displacement through integration. However, the principles of integration differ. When integrating the movement of a vehicle, static acceleration results in changes in velocity and displacement. Since acceleration measurements inherently contain errors, these errors accumulate as drift in speed and distance. The quality of the acceleration sensors determines the magnitude of this drift. For example, submarines with high-quality sensors can operate for weeks while still accurately calculating their position. In everyday applications, however, drift is much more pronounced because the dynamic part of the signal is larger and the rates of change are higher.

To compensate for errors, additional sensors are often used. A common combination is accelerometers, rate-of-turn sensors, and GPS.

When measuring vibrations, the static part of the signal is not relevant and is typically removed during integration using high-pass frequency filters.

Types of measurement

Vibration – An object vibrates when it undergoes oscillatory motion about an equilibrium position. Vibration is common in transportation and aerospace environments or can be simulated by a shaker system.

Shock – A sudden, transient excitation of a structure that generally excites the structure’s resonances.

Motion – A slow-moving event such as the movement of a robotic arm or the motion of an automotive suspension.

Seismic – A form of motion or low-frequency vibration. This type of measurement usually requires a specialized low-noise, high-resolution accelerometer.

Accelerometer

Accelerometers are devices that produce electrical signals (voltage, charge, etc.) in proportion to the experienced acceleration. There are several techniques for converting acceleration into an electrical signal. We will provide a general overview of the most common methods and then briefly look at a few others.

Most accelerometers are based on Hooke’s law and Newton’s first and second laws.

Hooke’s law states that the force (F) needed to extend or compress a spring is proportional to the displacement (x) by a factor of k (a constant characteristic of the spring). The equation is:

F = k × x

Newton’s first law states that an object remains at rest or continues to move at a constant velocity unless acted upon by an external force. Newton’s second law states that the force (F) acting on a moving object is equal to its mass (m) multiplied by its acceleration (a), giving the equation:

F = m × a

The most common way to apply these laws in practice is to suspend a mass on a spring within a supporting frame (as shown in the image below). When the frame is shaken, it moves and pulls the mass along with it. For the mass to undergo the same acceleration as the frame, a force must act on it, which results in elongation of the spring. This deflection can be measured using various types of displacement transducers, such as capacitive transducers.

In general, an accelerometer consists of a mass, a spring (or a similar system), and a displacement transducer.

Two configurations of piezoelectric accelerometers are commonly used:

• Compression type – the mass exerts a compressive force on the piezoelectric element.

• Shear type – the mass exerts a shear force on the piezoelectric element.

Accelerometers are designed using various sensing principles. Here is a quick overview to give you a better understanding of them:

• Piezoelectric – Based on the ability of piezoelectric materials to change their electric potential when under stress. These accelerometers offer unique advantages compared to other types: they have a wide dynamic range, excellent linearity, and a wide frequency range (from a few Hz to 30 kHz). They are the only accelerometers capable of measuring alternating acceleration, but they cannot measure DC responses. Because they have no moving parts, durability is increased. Unlike many other sensors, they also do not require an external power source.

• Piezoresistive – Similar to piezoelectric sensors, but instead of changing electrical potential, they change the electrical resistance of the material. These sensors can measure up to ±1000 g, have a true DC response, and are typically used in micro-machined structures.

• Capacitive – A metal beam or another micromachined feature produces capacitance, which changes when the sensor is accelerated. They are most commonly used in MEMS (Micro-Electro-Mechanical Systems) accelerometers and have characteristics similar to potentiometric sensors in terms of frequency, dynamic range, and DC response.

• Potentiometric – The wiper arm of a potentiometer is attached to the spring-mass system, causing a change in resistance when the spring moves. The natural frequency of these devices is generally less than 30 Hz, limiting them to low-frequency vibration measurements. They also have a limited dynamic range but can measure down to 0 Hz (DC response).

• Hall Effect – A magnet is attached to a spring, and when force is applied, it moves, causing a change in the electric field of the Hall element.

• Magnetoresistive – Works similarly to the Hall Effect sensor, but uses a magnetic resistance element instead of a Hall element.

• Fiber Bragg Grating – Any change in the grating pitch of an optical fiber results in a shift of the Bragg wavelength, from which acceleration can be calculated.

• Heat Transfer – A single heat source is centered on a substrate. Thermoresistors are placed symmetrically on all four sides of the heat source. When the sensor is accelerated, the heat gradient becomes asymmetrical due to convective heat transfer.

Most manufacturers offer a wide range of accelerometers, and at first glance the choice may seem overwhelming. However, a small group of general-purpose types will satisfy most needs. These are available with either top- or side-mounted connectors and have sensitivities in the range of 1 to 100 mV or pC per m/s².

Dewesoft accelerometers

The remaining accelerometers are designed for specific applications. For example, some small-sized accelerometers are intended for high-level or high-frequency measurements on delicate structures, panels, and similar components, weighing only 0.5 to 2 grams.

Other special-purpose types are optimized for:

• simultaneous measurement in three mutually perpendicular planes,

• operation at high temperatures,

• detection of very low vibration levels,

• resistance to high-level shocks,

• calibration of other accelerometers by comparison, and

• permanent monitoring of industrial machines.

Piezoelectricity is the ability of certain materials (notably crystals and specific ceramics—such as quartz, tourmaline, PZT ceramics, and GaPO₄) to generate an electrical potential in response to applied mechanical stress. This may take the form of a separation of electric charge across the crystal lattice. If the material is not short-circuited, the applied charge induces a voltage across the material. Materials that produce an electric charge when a force is applied exhibit what is known as the piezoelectric effect.

Piezoelectric acceleration sensors work on this principle. A piezoelectric material (usually an artificially polarized ferroelectric ceramic) is placed between the bottom of the sensor housing and the seismic mass. When the sensor is moved, the seismic mass compresses the piezoelectric material, producing a very small voltage output. This high-impedance electrical charge, collected on the electrode, can be conditioned by either internal or external electronics for measurement purposes.

Accelerometers with built-in electronics are classified as Integrated Electronic Piezoelectric (IEPE) sensors, commonly referred to as voltage mode accelerometers. Piezoelectric accelerometers that require external charge amplifiers for signal conditioning are called charge mode accelerometers. Voltage mode accelerometers incorporate built-in signal-conditioning microelectronics, making them easier to use. IEPE has been adopted as a standard by many sensor, analyzer, and data acquisition system manufacturers.

Piezoelectric sensors are widely used in modal analysis, environmental stress screening, pyrotechnic testing, aircraft ground and flight vibration tests, and predictive or preventive maintenance.

Voltage mode accelerometers - IEPE

All voltage mode accelerometers are powered by a regulated DC voltage and a constant current excitation of 2 to 20 mA, using a simple two-wire connection scheme. The built-in electronics convert the high-impedance charge signal generated by the piezoelectric material into a usable, low-impedance voltage signal directly inside the transducer.

Because the output is low impedance, the signal can be transmitted over long cable distances and used in harsh field or noisy factory environments with minimal degradation. IEPE sensors require a 4 mA or 8 mA power supply and typically provide a 5 V signal, making them much easier to connect and operate over long cables. Amplifiers for these sensors are simpler and therefore less expensive than those required for charge mode piezoelectric sensors.

However, the amplitude measurement range is limited. Few sensors can measure more than 100 g. Both single-axis and triaxial sensors are available. Recently, very compact designs have been introduced—for example, triaxial sensors in a cube measuring only 10 mm per side and weighing as little as 5 grams.

Measurement with Dewesoft systems:

• Sirius ACC can connect directly to IEPE sensors.

• STG, STG-M, or DEWE-43 systems require a DSI-ACC adapter for use with these sensors.

Charge mode accelerometers

Charge mode piezoelectric accelerometers output the high-impedance electrical charge signal generated directly from the piezoelectric sensing element. These transducers require either an external charge amplifier (preferred option) or an in-line charge converter to transform the high-impedance charge signal into a low-impedance voltage signal suitable for measurement.

Because the output is high impedance, the charge signal is highly sensitive to environmental noise, so several precautionary measures are necessary for accurate measurements. Special low-noise coaxial cables should be used between the transducer and the external charge amplifier. These cables are specially treated (for example, lubricated with graphite) to reduce triboelectric noise—motion-induced noise effects. It is also critical to maintain high insulation resistance of the transducer, cabling, and connectors by keeping them dry and clean.

Given these requirements, and compared with the simpler operation of voltage-mode accelerometers, charge mode accelerometers are typically used only in high-temperature or high-acceleration applications, or in cases where customers continue to use existing stock from before IEPE sensors became widely available.

Piezoelectric accelerometers are self-generating and therefore do not require a power supply. With no moving parts to wear out, they are durable, and their acceleration-proportional output can be integrated to provide velocity- and displacement-proportional signals.

Measurement with Dewesoft systems:

• Sirius CHG supports charge input directly.

• MULTI, STG, or DEWE-43 systems can be used with MSI-BR-CH, but ensure that the dynamic range is sufficient for your application.

The last important characteristic of all piezoelectric transducers (both voltage mode and charge mode) is their AC behavior. Piezoelectric material cannot retain its charge output under a static input. In other words, it only senses dynamic events and therefore cannot be used to measure DC acceleration.

The design of the charge amplifier electronics (whether integrated internally or external) determines the low-frequency AC coupling of the measurement signal. The typical low-frequency performance of piezoelectric accelerometers ranges from about 0.5 Hz to several hertz.

A comparison between IEPE and Charge mode accelerometers

Both charge mode and IEPE sensor types share a common limitation: they cannot measure static acceleration. Their measurement range typically begins between 0.3 Hz and 10 Hz, depending on the sensor. For static or very low-frequency measurements, a different type of sensor is required.

A very popular option is the Micro-Electro-Mechanical System (MEMS) sensor. A MEMS sensor is essentially a microchip that contains a mechanical structure (such as a cantilever beam or seismic mass) that changes its electrical property—usually capacitance—in relation to acceleration.

Capacitive interfaces offer several attractive features:

• In most micromachining technologies, little or no additional processing is required.

• Capacitors can operate as both sensors and actuators.

• They provide excellent sensitivity.

• The transduction mechanism is relatively insensitive to temperature.

• Capacitive sensing is independent of the base material and relies on variations in capacitance caused by changes in the geometry of the capacitor.

A typical MEMS accelerometer consists of a movable proof mass with plates attached to a mechanical suspension system and a reference frame, as shown in the picture below.

MEMS sensors were initially considered very specialized, as they were used to measure earthquakes and other slow movements. However, with the development of airbag technology, there arose a strong demand for low-cost sensors capable of measuring static acceleration. This led to the emergence of single-chip solutions designed for this purpose.

More recently, these sensors have also been used in low-cost gyroscopic systems. Today, MEMS sensors can achieve relatively good bandwidth—up to several kilohertz—and offer low noise levels (though still higher than those of IEPE sensors with the same measurement range).

They have become indispensable in the automobile industry, as well as in computer and audio-video technology.

When choosing any kind of sensor, it is important to answer the following questions:

• What are we measuring, and under which conditions?

• What are the relevant factors affecting our measurements?

• What do we hope to achieve from our measurements in terms of quality, quantity, and cost?

What follows is a short summary of the key characteristics.

Ground isolation

Accelerometers with ground isolation usually have an isolated mounting base and screw, or in some cases, the entire accelerometer case is ground-isolated.

Ground isolation becomes important when the surface of the test article is conductive and at ground potential. A difference in ground voltage levels between the instrumentation and the accelerometer can cause ground loops, resulting in erroneous data.

Sensitivity

Sensitivity is the first characteristic normally considered. Ideally, we want a high output level, but this requires a relatively large piezoelectric assembly, which results in a larger and heavier unit. In most cases, sensitivity is not a critical problem since modern preamplifiers are designed to handle low-level signals.

Low-frequency range

For vibration measurements, the sensor should have a lower cutoff frequency than the frequencies of interest in the devices being tested. For example, a rotating machine running at 50 Hz can be measured with a sensor having a 5 Hz cutoff. For building or ship vibrations, the cutoff frequency must be much lower.

Bandwidth is also important: the lower the cutoff, the longer the recovery time from shocks or overloads. The amplifier should match the bandwidth of the sensor, and ideally, have multiple ranges for flexibility. A typical application is paper mill rolls, which vibrate at 1–5 Hz; here a sensor with a 0.3 Hz (or lower) bandwidth is needed. For such applications, charge or IEPE sensors are most suitable. If static acceleration must be measured, MEMS sensors are required.

In practice, the low-frequency limit is affected by two factors:

1. The amplifier’s cutoff frequency (usually below 1 Hz and rarely problematic).

2. Ambient temperature fluctuations, to which accelerometers are sensitive. Modern shear-type accelerometers minimize this effect, allowing measurements below 1 Hz in normal environments.

Bandwidth (frequency range) 

Mechanical systems often have most of their vibration energy between 10 Hz and 1000 Hz, though measurements are frequently made up to 10 kHz, since interesting vibration components may appear at higher frequencies.

When selecting an accelerometer, its frequency range must cover the range of interest. The upper limit is determined by the accelerometer’s resonant frequency. As a rule of thumb, setting the upper frequency limit to one-third of the resonant frequency ensures measurement errors of no more than +12%.

Small accelerometers can have resonant frequencies as high as 180 kHz, while larger general-purpose accelerometers typically fall between 20 and 30 kHz.

Care must be taken with high-frequency readings, as sensitivity increases near resonance. These artificially high readings can be corrected in the frequency domain using transfer curves (e.g., in Dewesoft).

Amplitude range

Charge sensors offer the widest amplitude ranges (special shock sensors can exceed 100,000 g). IEPE sensors also provide relatively high ranges (up to ~1000 g). MEMS sensors usually have limited ranges (a few hundred g). For general purposes, IEPE sensors are recommended, while piezoelectric charge sensors are better for extreme levels. For seismic applications, high-sensitivity sensors (2 g or lower range) may be required.

Maximum shock level

Charge sensors are the most shock-resistant, sustaining up to 100,000 g. IEPE sensors typically withstand only 5000–10,000 g, while MEMS sensors are even more sensitive to shock.

Noise level

Residual noise defines the lowest measurable amplitude. This is why it is important to select a sensor with the optimal measurement range; higher-range sensors tend to have higher noise levels.

IEPE sensors have very high dynamic range (better than 160 dB below maximum range). Charge sensors are similar, though cable noise must be considered. MEMS sensors typically have worse dynamic range due to internal electronics.

Temperature range

All sensors containing electronics are limited to about 130°C. Charge sensors, however, can operate at much higher temperatures—up to 500°C—with appropriate high-temperature cables.

Piezoelectric materials are temperature-dependent, and changes in ambient temperature affect sensitivity. Small temperature fluctuations can also cause transient outputs. Modern shear-type accelerometers are far less sensitive to these effects, allowing stable measurements below 1 Hz.

For mounting on surfaces above 250°C, a heat sink and mica washer can be inserted between the accelerometer and the surface. This method allows surface temperatures of 350–400°C while keeping the sensor base below 250°C. Additional cooling air can provide further protection.

MEMS sensors are limited by their internal electronics to about –40°C to +125°C.

Weight

In some applications, such as modal testing, sensor weight is critical due to the mass loading effect. Added mass alters the dynamic behavior of the structure. Ideally, the sensor should have negligible mass, though this is practically impossible. In such cases, non-contact sensors like laser systems can be used.

As a rule of thumb, the sensor’s mass should not exceed one-tenth of the dynamic mass of the vibrating component.

Ground loops

Ground loop currents can flow in the shield of accelerometer cables when the accelerometer and measuring equipment are earthed separately. Ground loops can be eliminated by using isolated sensors, isolated amplifiers, or by electrically isolating the accelerometer base from the mounting surface with an insulating stud.

Cable noise

Cable noise is a common issue in piezoelectric accelerometers due to their high output impedance. Disturbances may result from:

• Triboelectric noise – induced by cable motion. It originates from local capacitance and charge changes caused by bending, compression, or tension in the cable layers. This can be minimized by using graphitized accelerometer cables and securing the cable close to the sensor with tape or glue.

• Electromagnetic noise – induced when the cable is placed near running machinery.

Transverse vibrations

Piezoelectric accelerometers are also sensitive to vibrations in directions other than their main axis. In the transverse plane, perpendicular to the main axis, sensitivity is typically less than 1% (and rarely more than 3–4%). Since the transverse resonant frequency is about one-third of the main axis resonant frequency, this effect should be considered when high transverse vibration levels are present.

The sensors can be mounted in several ways. The bandwidth of a sensor is particularly sensitive to the method of mounting. The way the accelerometer is attached to the measuring point is one of the most critical factors in obtaining accurate results from vibration measurements. Improper mounting reduces the mounted resonant frequency, which can severely limit the useful frequency range of the accelerometer.

Stud mounting – The most reliable method is to drill a hole in the test specimen and secure the sensor with a screw. This approach does not affect the sensor’s properties. However, in some cases, customers may hesitate to use this method—for example, on a brand-new prototype of an airplane wing.

Adhesive mounting – Another option, which has less impact on bandwidth, is to use a thin double-sided adhesive tape or beeswax. This method is limited by its temperature range.

Magnet mounting – A widely used technique in machine diagnostics is to attach the sensor with a magnet. This provides good bandwidth, but the surface must be ferromagnetic (not aluminum or plastic). For sensors with a mounting clip, the clip can be glued in place first, allowing the sensor to be easily attached and detached.

Hand-held mounting – A “quick and dirty” method is simply holding the sensor by hand against a rod. This can be useful in hard-to-reach areas, but it reduces the bandwidth to approximately 1–2 kHz.

The accelerometer should always be mounted so that the desired measuring direction aligns with its main sensitivity axis. While accelerometers are also slightly sensitive to vibrations in the transverse direction, this effect can usually be ignored because transverse sensitivity is typically less than 1% of the main axis sensitivity.

The graph below shows the reduction in bandwidth caused by different mounting methods:

Eddy-current sensors are non-contact devices capable of high-resolution measurement of the position and/or displacement of any conductive target. They are sometimes referred to as inductive sensors, but generally, “eddy current” applies to precision displacement instruments, while “inductive” refers to inexpensive proximity switches. Their high resolution and ability to function in dirty environments make eddy-current sensors indispensable in modern industrial operations.

Eddy-current sensors operate using magnetic fields. The driver generates an alternating current in the sensing coil at the end of the probe, creating an alternating magnetic field that induces small currents in the target material—these currents are called eddy currents. The eddy currents, in turn, generate an opposing magnetic field that resists the field produced by the probe coil. The interaction of these magnetic fields depends on the distance between the probe and the target. As this distance changes, the electronics detect variations in the field interaction and produce a voltage output proportional to the displacement between the probe and the target. For accurate, calibrated operation, the target surface must be at least three times larger than the probe diameter.

Eddy-current sensors are widely used to detect surface and near-surface flaws in conductive materials, such as metals. They are also employed for material sorting based on electrical conductivity and magnetic permeability, as well as for measuring the thickness of thin metal sheets and non-conductive coatings such as paint.

Position measurement

Eddy-current sensors are fundamentally position-measuring devices. Their output always indicates the size of the gap between the sensor probe and the target. When the probe is stationary, any change in the output can be directly interpreted as a change in the target’s position. This capability is particularly useful in:

• Automation systems requiring precise positioning

• Machine tool monitoring

• Final assembly of precision equipment, such as disk drives

• Precision stage positioning

Vibration measurement

Measuring the dynamics of a continuously moving target, such as a vibrating element, requires non-contact measurement. Eddy-current sensors are effective in both clean and dirty environments and are well-suited for detecting relatively small motions. They also feature a high-frequency response (up to 80 kHz), enabling accurate tracking of high-speed motion. These sensors can be used for:

• Drive shaft monitoring

• Vibration measurement

Let’s perform some vibration measurements in Dewesoft. Since vibrations are difficult to visualize and many questions often arise about the differences between acceleration, vibration velocity, and displacement, it is helpful to actually demonstrate the vibration.

In this example, a shaker is used with a light plastic structure attached, which has a low natural frequency. At the same time, the movement of this beam was recorded using a high-speed camera. This makes it easier to clearly observe the vibrations as they were measured with the accelerometer.

It is always advisable to use a measurement device equipped with an anti-aliasing filter. Without it, the accuracy of the measurement cannot be guaranteed. High-frequency acceleration (around 20 kHz) is often very large, and if a device without an anti-aliasing filter is used with lower sampling rates, those high frequencies will be mirrored into the lower range. This is particularly critical for measurements such as modal analysis, where the presence of aliasing can severely compromise the results.

There are three ways to set up the sensor:

1. Enter the values manually from the calibration sheet.

2. Calibrate the sensor using a calibrator.

3. Use TEDS technology to automatically read the calibration values.

Entering the setup from the calibration sheet
It is often useful to review the sensor’s calibration sheet. This document provides the sensor sensitivity, expressed either in mV/(m/s²) or mV/g (or both) for IEPE sensors, and in pC/g for piezoelectric (charge) sensors. The example below shows a calibration datasheet for a triaxial sensor. The reference sensitivity is the key value that must be entered into the Dewesoft setup.

First, as usual, we should enter the units of measurement. In this case, we use m/s². Next, go to the Scaling by function section. Check the Sensitivity box and enter 9.863 mV/(m/s²) in the sensitivity field. Also, do not forget to enable IEPE measurements.

The second method is calibration. A standard accelerometer calibrator can be used, which outputs 10 m/s² peak acceleration (equivalent to 7.07 m/s² RMS). The sensor is attached to the calibrator, and the acceleration level is then adjusted according to the sensor mass.

Next, in Scaling by two points, enter the acceleration level of 7.07 m/s² and click Calibrate from RMS. The current measured voltage level in mV is then written into the second point of the scaling.

At this stage, it is already possible to check whether the calibration was successful. In the data preview, the peak level should be approximately 10 m/s² and the RMS around 7.07 m/s². You can also select Scaling by function and compare the measured sensitivity with the calibration datasheet.

The third and relatively new method of sensor setup is the use of an electronic calibration sheet, known as TEDS. With a TEDS sensor, selecting the correct settings is straightforward. Simply plug the sensors into the Sirius ACC, run Dewesoft X, and the sensors should be recognized immediately.

TEDS works only if the amplifier is set to IEPE mode (it does not function in voltage mode). If this mode is enabled later (after the first scan) or if the sensor is connected while Dewesoft X is already open on the setup screen, the TEDS sensors must be rescanned. This can be done by clicking on the AMPLIFIER column header in the basic setup screen and selecting Rescan modules.

TEDS is also supported with MSI-BR-ACC. When a sensor is correctly recognized, its scaling factors, serial number, and recalibration date are automatically read from the sensor. On the setup screen, the user does not need to manually enter the sensitivity, since it is already filled in from the sensor.

This approach is simple and efficient, and it helps prevent user errors.

The second step is to calculate the vibration velocity and displacement. This can be done directly in the channel setup using a filter, since an integrator is essentially just a type of filter.

In the setup, we enable both integration and double integration. The first integrator is used to calculate vibration velocity, and the second (double integrator) is used to measure displacement.

We should select Integration as the math operation. Since the DC offset is simply an error in measurement and calculation, a high-pass filter (in the Flow field) must be applied to remove it. For single integration, the filter order should be at least two. If the filter order is set to one, a static offset will remain in the result; without a filter, the output will drift over time.

Next, we define the units. If integration is performed from acceleration to velocity and the acceleration unit is m/s², the output unit will normally be m/s. With a scaling factor of 1, the units are expressed in m/s. If a scaling factor of 1000 is applied, the units will be in mm/s.

It is also useful to determine the vibration displacement. To do this, we set up another channel by selecting Acceleration and applying double integration. Since the double integrator is essentially a second-order filter, the high-pass filter should be set to an order of at least three or higher.

In most cases, vibration displacement is not visible to the naked eye and is typically measured in micrometers. However, because this measurement produces relatively high values, the output unit was set to mm. The scaling factor is therefore again 1000.

In the preview, we can already observe that the peak-to-peak movement is around 15 mm. Since this value can also be visually confirmed, we can be confident that the scaling factors and filter settings are correct.

In the analysis module, we can review the data. Here, one image is overlaid on another to visualize the movement of the accelerometer. The first image below shows the upper point of displacement.

On the scope to the right, we can clearly see that acceleration, displacement, and velocity are phase-shifted.

In the recorder graph below, the acceleration, velocity, and displacement can be analyzed together. The displacement (blue curve) is shown at its upper position. The velocity (red curve) is zero at this point. This is expected because the upper point represents a turnaround—before reaching it, the velocity decreases, and at the very top, the velocity is zero. The acceleration (green curve), however, is at its maximum in the negative direction. Since acceleration is the rate of change of velocity, this is consistent: the velocity curve shows its steepest change at the top, meaning the acceleration is at its maximum at the top dead point.

Now let’s move to the next significant point of the movement—the center point. We can identify it as the center point because the displacement is in the middle position. At this point, the velocity is at its maximum in the negative direction. The beam passes through the center with maximum velocity and then gradually begins to decelerate.

The acceleration at this point is zero. When a body is either stationary or moving with constant velocity, its acceleration is zero. This can be confirmed by observing the blue acceleration curve.

The third significant point is the bottom point. For reference, the top point is shown in the background. At this position, the displacement is at its lowest value, the velocity is zero but will begin to increase, and the acceleration is at its maximum in the positive direction. This means the speed is changing at the greatest rate at this point.

We conducted a simple experiment to gain a better understanding of vibration measurement. In practice, the measurement process may look different, but the same basic principles demonstrated in this example would still apply.

Let’s perform some vibration measurements in Dewesoft. Since vibration is difficult to visualize, and many questions often arise about the differences between acceleration, vibration velocity, and displacement, it is helpful to actually demonstrate the vibration.

The measurement was carried out using our shaker, where we tested our new product, KRYPTON.

Vibration durability test

The measurement was carried out using our shaker, where we tested our new product, KRYPTON.

The image below shows a screenshot from the software that controls the shaker. We set the frequency sweep from 10 Hz to 250 Hz, with a maximum acceleration of up to 33 g.

On the shaker near KRYPTON, a Dewesoft accelerometer was mounted using glue. Let’s take a look at the signal from the accelerometer.

Let’s examine the maximum acceleration detected by the Dewesoft accelerometer. As shown in the picture, the maximum value was 325.9 m/s², which corresponds to 33 g.

Shock test

The next experiment was a shock test. In this test, the product was exposed to multiple shocks that reached 50 m/s² in our case, but they can go as high as 100 m/s².

Drop test

The next measurement was performed using a drop test. As shown in the video below, the product is lifted and then released, falling under the influence of gravity. When the aluminum plate strikes the ground, the object under test can experience an impact of up to 900 g.

In our case, KRYPTON was subjected to an impact of 957.5 m/s², which is equivalent to almost 100 g.

Envelope detection is a method used for the early identification of faults in ball bearings.

To add a new envelope detection math module, go to the Math section and select Envelope Detection under Add Math Section.

The envelope detector consists of several stages, and parameters must be defined for each stage:

Settings

The Calculation Type defines the principle of calculation:

• Filtering – uses a filtering procedure for envelope calculation. This is a standard method also applied in other implementations.

• Peak Detection – detects peak values in the signal. This method calculates amplitudes more accurately than filtering.

The Use Bandpass checkbox enables or disables the first stage of calculation—bandpass filtering. The acceleration sensor measures the entire frequency range, capturing unbalance, misalignment, and other machine faults. Since ball-bearing faults generate very low energy, their contribution to the overall frequency spectrum is relatively small.

Signal band

In the signal band setup, you must define the lower and upper frequency limits.

Envelope band

In the envelope band setup, you must also define the lower and upper frequency limits.

Bearing database - Kinematic cursor editor

In the bearing database, you can select the type of machinery. If it is not listed, you can add your own using the Kinematic Cursor Editor. The frequency of interest is then automatically calculated based on geometry.

When a ball bearing fault occurs, it produces ringing at a frequency that corresponds to the bearing’s natural frequency. This ringing repeats each time a damaged part of the ball contacts the ring—or vice versa. It is important to note that the inner ring, outer ring, cage, and balls each have their own characteristic repeating frequencies, which depend on the bearing geometry and rotational speed.

To focus only on these high-frequency components of the ringing, we must examine the original frequency spectrum. In our example, we generated a sine wave with small 10 kHz oscillations superimposed on it. In the frequency domain, the repeating frequency of the ringing is not visible; instead, we see only the dominant sine wave (which could result from unbalance) and the very high-frequency components generated by the bearing.

In the envelope detector, bandpass filtering must be configured to remove all components except the ringing of the ball bearing. This ringing is usually found around 10 kHz. In our example, the lower frequency limit was set to 6 kHz and the upper limit to 12 kHz in order to capture the full energy of the signal.

After filtering, the signal appears as follows:

Only the high-frequency components remain, but the main low frequency at which the rings are repeating is still not visible. Therefore, we need to apply an envelope to the signal. The envelope traces a curve around the peaks of the signal, producing only the positive portion of the data.

To obtain the correct amplitude, we must define the Envelope Band frequency. Bearing faults typically occur at frequencies up to 500 Hz. In addition, we may want to enable Remove DC Component to display a clean frequency spectrum without the large DC value caused by offset.

After applying this filter, the signal appears as shown in the picture below, and the frequency spectrum of the envelope signal reveals the fault frequencies (impacts).

This was a simulated case to demonstrate the mathematical procedure behind the calculation. In reality, the signal will appear as follows.

There is not much to observe in the time signal, but by calculating the typical frequencies, we can clearly see that the outer ring frequency appears in the FFT of the envelope signal.

The following picture shows typical damage to the outer ring of a large bearing (courtesy of Kalmer d.o.o., Trbovlje).