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