Measuring with light

Nov. 1, 2007
Author/Title Polytec Inc. Tustin, Calif. Laser Doppler vibrometers (LDVs) measure vibrations where other sensors can't. They accurately track up to 30

Author/Title Polytec Inc. Tustin, Calif.

Laser Doppler vibrometers (LDVs) measure vibrations where other sensors can't. They accurately track up to 30 MHz with linear phase response, as well as vibrations of liquid surfaces and small structures. These units measure both vibrational velocity and (depending on configuration) displacement.

The Doppler effect

So how do LDVs work? Everyone has experienced the Doppler effect, when a moving vehicle's acoustical tone changes as it passes on the road. Well, the propagation of light, the principle behind LDVs, is similar, and the same physical principles apply.

If a wave is reflected by a moving object and tracked, the measured frequency shift of the wave can be described as:

where υ = Object's velocity and

λ = Wavelength of the emitted wave.

To determine the velocity of an object, the Doppler effect (frequency shift) must be measured at a known wavelength. This is done in LDVs with a laser interferometer.

Interferometry

Inferometers work by optical interference (overlapping) of two coherent light beams with intensities I1 and I2. The resulting intensity is not just the sum of the single intensities, but is modulated:

With a so-called interference term relating to the path-length difference of the beams. If this difference is an integer multiple of laser wavelength, then overall intensity is four times a single intensity; overall intensity is zero if the two beams have a path length difference of half of one wavelength. In the former case, the two beams interfere constructively; in the latter, it is destructive interference.

Interferometer modulation frequency is directly proportional to object velocity. But because objects moving away from an interferometer generate the same interference pattern (and frequency shift) as objects approaching an interferometer, these alone cannot determine motion direction.

For that added functionality, an acousto-optic modulator (or Bragg cell) can be placed in the reference beam. Say the laser light frequency is 4.74 × 1014 Hz and a setup with a Bragg cell modulates fringe pattern frequency at 40 MHz when the object is at rest. If an object moves towards the interferometer, modulation frequency is reduced; movement away, and the detector collects a frequency higher than 40 MHz. In this way, it's possible to not only detect the amplitude of movement, but its direction as well.

Displacement as well

Besides reporting velocity, LDVs can also measure displacement. Here, the Doppler frequency is not transformed into a voltage proportional to velocity. Instead, the LDV circuitry counts the bright/dark fringes on the detector. With interpolation programming, resolution can reach 2 nm, and with digital demodulation techniques, it can reach the picometer range. Note that displacement demodulation is better suited for low-frequency measurements, and velocity demodulation is better for higher frequencies, because the maximum amplitudes of harmonic vibrations is:

And as frequency increases, a given vibration generates higher velocities at lower displacement amplitudes.

Round and round

Besides linear motion consistency, LDVs can also monitor rotary movement. A frequency range of 0.5 Hz to 10 kHz provides sufficient bandwidth for processing even fast transients — as those of a suddenly accelerating shaft upon a gearshift, for example.

This is useful, because other mechanical systems (engines, power trains, gearboxes) and mismatched gearing, unbalanced shafts, and poorly aligned articulate joints are also significant sources of rotational vibration. These systems transmit torque, movement, speed, and acceleration from one place to another — but they also create torsional and bending vibration. Their vibration results in noise and premature fatigue of mechanical systems.

So to minimize rotational vibration and its harmful effects on engineering designs, measurements reveal how torque and kinematics are carried across drive systems, and uncover the nature of deviations in terms of elasticity, inertia, torque, and contact. Traditional measurement of torsional and rotational motion is not easy because system components are continually moving relative to the sensor platform and large portions of systems reside in inaccessible places.

Invasive methods use devices mounted to the rotating part that transmit a signal to an opposing receiver or sensor — for instance, RF telemetry combined with shaft-mounted strain gauges or accelerometers. Though these techniques give direct physical measurements, they are maintenance sensitive. (Too, transducers that need physical contact with objects often fail to measure high amplitudes.) Conventional contact transducers are also subject to wear and slippage.

In contrast, noncontact technologies like laser interferometers are easy to mount, even in crowded places. The vibrometer's large standoff distance makes repositioning the laser probe fast and convenient, and enables precision measurement of operating machinery at several locations without interruption. Some units can measure between -7,000 to +11,000 rpm including directional changes, torsional transients, and rotational vibrations around a rest position.

How it works

Many rotational vibrometer setups use two parallel laser beams, which exit a front lens and strike the rotating surface. Each back-scattered laser beam is Doppler shifted in frequency by the surface velocity vector in the beam direction. This velocity consists of rotational and lateral components. Raw velocity information from each beam is independently sent to downstream for processing. The difference between the two velocity components is a direct measure of the pure rotational velocity of the object and eliminates lateral vibrations.

Another approach is to use one interferometer operating in an optically differential mode. But these systems are not as sensitive and cannot track poorly reflecting surfaces very well.

Optical setup

A differential technique utilizes both to track only angular vibration, independent of the shape of the monitored object. Twin laser interferometers each emit a measurement beam that are parallel and come to a focus at a specified distance from the sensor head, where they strike the rotating object with a separation d. One beam strikes the rotating object above the axis of rotation while the other strikes it at an approximately equal distance below. Each point on the circumference of the rotating part with angular velocity ω has a tangential velocity υt — dependent on the rotational radius R. This tangential velocity can be broken down into two orthogonal translational velocity components.

It's possible to determine angular velocity ω by measuring two parallel, translational-velocity components. Projecting the tangential velocity vectors along the measurement beam means that:

So, the velocity components along the measurement beam direction produce Doppler frequencies ƒDA and ƒDB in the back-scattered beams. For example, in our figure (right) the lower beam measures a Doppler shift from the surface moving towards the sensor head. The upper beam measures a Doppler shift with opposite sign from the surface moving away from the sensor head. Here the following apply:

The geometrical relationship between the beam separation distance d and angles α and β at radii RA and RB is given by:

d = RAcos + RBcos β

So, the frequency difference between the two Doppler-shifted beams depends on the system constants d, λ, and the angular velocity ω:

ƒD = ƒDA + ƒDB = 2d ω/λ

So, angular velocity is:

ω = ƒD λ/2d

Signal processing

Sensor signals are processed by its controller, which gives complete angular velocity information. In short, the frequency of the analog output signals from both interferometers are separated into a static component (dc fraction) and a dynamic component (ac fraction) of rotational speed.

After signal conditioning, the output signals of both interferometers are merged in a mixer stage, followed by a preprocessing block. Here, static and dynamic frequency components are sent to separate decoders, which operate as frequency-to-voltage converters.

Then, the static rpm and the dynamic signal are fed to separate outputs:

• Dc stationary rotation ωDC: A constant component of the tangential velocity, which is proportional to the speed or rpm. The combination of both beams yields the correctly scaled rpm information, independent of radius.

• Ac rotational vibration ▲ω: The fluctuating component of the shaft rotation, which indicates the angular or rotational vibration.

• The vibrational velocity signal is also sent to an integrator block to provide angular displacement▲φ.

Any gross, lateral, non-vibration movement of the shaft is not measured, because it's detected by both laser beams, and discarded in the differencing process.

Data processing

Rotational vibrometers together with data processing software can identify individual vibration frequencies, solve problems with noisy signals (and closely spaced and crossing orders) and create plots and tables of the situation.

Angular vibrational velocity, displacement, and rpm are sent downstream as analog output. These outputs can be used by signal processing software, such as order tracking analyzers. Or, some software analyze s noise and vibration from time waveform and tachometer signals. This generates post-process vibration data and high-resolution spectral and order-based analyses for detailed diagnosis of machinery problems. Other features include spectrograms, color-contour plots, phase plots, 2 and 3D plotting, and Bode diagrams.

Measuring out-of-plane single-point vibration

Single-point vibrometers measure the vibrations of an object in the laser beam direction. If aligned at a right angle to the object surface, it's termed an out-of-plane vibrometer.

Measuring out-of-plane differential vibration

Differential vibrometers measure vibration between two points vibrating relative to each other. Specialized fiber-optic probes even examine locations difficult to access.

Measuring in-plane vibration

Measurements of vibrations in the surface plane — for example, at right angles to the optical axis. Some sensor-controller combinations can even monitor V belts or pistons.

Measuring rotational vibrations

For measuring torsional vibrations of continuously rotating surfaces or angular vibrations of fixed surfaces. Output is independent of the surface shape.

Measuring 3D vibration

Three independent laser beams intersecting at the focus point allow vibration characterization in three dimensions.

Mapping vibration over surface

Scanning vibrometers and video microscopy systems automate surface vibration measurement and visualization. Productivityis boosted by fast, comprehensive, and accurate acquisition and data handling.

Mapping 3D vibration over surface

In this complete three-dimensional structural dynamics, a scanning vibrometer measures 3D vibration characteristics, and motion analyzers characterizes microstructures.

LDVs work by shooting a laser through a beamsplitter BS1, which divides it into reference and measurement beams. After passing through a second splitter BS2, the measurement beam is focused onto the object under investigation, which reflects it. This reflected beam is then deflected by BS2, merged with the reference beam by BS3, and sent to the detector. As the reference beam's path length r2 is constant over time, a movement of the object — r1 = r(t) — generates a dark-and-bright fringe pattern on the detector. One complete pattern on the detector corresponds to object displacement of exactly half the wavelength of the light used. In the case of a helium neon laser (used almost exclusively in vibrometers) this corresponds to a displacement of 316 nm.

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