Motion System Design

# Measuring motion with light

Laser Doppler vibrometers (LDVs) measure vibrations in ways that other sensors can't. From large aircraft structures to microscopic MEMS sensors, and vacuum enclosures to red-hot mills, LDVs measure both vibrational velocity and displacement with linear response and 30-MHz bandwidth. Because they don't introduce any mass loading, they don't affect dynamics.

### 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 is similarly affected by motion, and the same physical principles apply.

If light is reflected by a moving object and then captured, the measured frequency shift of the light is:

where v = Object's velocity and λ = Wavelength of the incident laser light.

To determine the velocity of an object, the frequency shift of the Doppler effect must be measured. 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 individual intensities, but is modulated with a so-called interference term relating to the path-length difference of the beams:

If the intensities are equal and the path-length difference is an integer, 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.

The 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.

### Displacement as well

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.

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 amplitude of harmonic vibration is:

### Round and round

Besides linear motion, LDVs can also be configured to monitor rotary movement. A frequency range of 0.5 Hz to 10 kHz provides sufficient bandwidth for processing most fast transients — as those of a gear shift's suddenly accelerating shaft.

Rotational vibration measurement is useful in designing drive systems in which connected powertrains are mismatched. Gearing, unbalanced shafts, and poorly aligned articulate joints are 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. This vibration results in noise and premature fatigue of mechanical systems.

So to minimize rotational vibration and its harmful effects on engineering designs, rotational 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. Conventional contact transducers are also subject to wear and slippage.

In contrast, noncontact laser vibrometers 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

Most rotational-vibrometer setups use two independent and 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 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 generally, these systems are not as sensitive and cannot track poorly reflecting surfaces very well.

### Optical Setup

The better approach uses two independent laser beams and an electronic differential technique 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 v t — 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 f DA and f DB 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 R A and R B is given by:

d = R A cos α + R B cos β

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

f D = f DA + f DB = 2d ω/λ

So, angular velocity is:

ω = f D 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 dynamic signal Δω are fed to separate outputs:

• Dc stationary rotation ω DC : A constant component of the tangential velocity, which is proportional to the speed or rpm. Together, the beams yield correctly scaled rpm information, independent of radius.

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

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

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 plot 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 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 all types of motion

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 vee 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 out-of-plane vibration over a surface:
Deflection shapes

Scanning vibrometers automate surface vibration measurement and visualization. Productivity is enhanced, eliminating the gluing, wiring, and processing of other methods, and improving accuracy.
Mapping 3D vibration over a surface:
Deflection shapes

Complete 3D structural dynamics can be captured for an entire test object. This is useful for FE correlation and model validation; animations give excellent visualization of experimental results.