Machine Design

Dynamic sensing with LVDTs

LVDTs may not be new. But frictionless measurement and nearly infinite resolution never go out of style.

Martin Aronow
Senior applications engineer
Sensors Measurement Specialties Inc.
Hampton, Va.

Edited by Miles Budimir

A cutaway LVDT shows its primary and secondary windings. The core material is usually a 50/50 nickel-iron alloy which has good permeability after heat treating.

The LVDT is used to measure time and displacement of a shaker head in a vibration tester. The core movement accurately represents mechanical displacement, with typical linearity of 0.025% of full range.

A linear-variable-differential transformer, or LVDT, is basically a transducer that converts mechanical motion into an electrical signal through mutual induction. A typical two-element LVDT consists of a fixed frame containing primary and secondary coils, and a movable core. The frame usually contains one primary winding sandwiched between the two secondary windings. A voltage of constant amplitude and frequency is applied to the primary.

Centering the movable core between the primary and secondary windings produces an identical magnetic flux on both sides. Equal flux induces equal voltages on the two secondary windings. However, as the core moves, the ratio between the two voltages changes. The change in voltage turns out to be proportional to the mechanical displacement of the core.

The fact that the movable core is not mechanically connected to the frame of the LVDT makes it essentially a no-contact transducer. The no-contact measurement assures a nearly infinite life as well as input/output isolation. And although many other transducers have one or more of these features, only the LVDT combines them all into one package.

LVDTs are often used to measure the displacement/time function of a singular event, as in shock-testing machines, projectiles fired into ballistic pendulums, or a pressure pulse resulting from a shock tube. The core of the LVDT is attached to the moving element while the coil assembly is fastened to a stationary reference frame. Displacement of the core precisely represents the movement of the forcing element when one ignores the plastic deformation of materials.

LVDTs are also used in dynamic gaging. Here we define a gage head as a sensor consisting of the LVDT plus a probe, bearings, a spring, and a probe tip. Conventional LVDTs generally attach the core to the moving element of the system being monitored by a connecting rod. Therefore, the core movement represents exactly the displacement/time function of the moving element regardless of applied mechanical frequency. Springs used in gage heads to maintain the probe against the moving surface must be strong enough to maintain contact with the surface. If not, the probe will lose contact with the surface, providing false position information. The spring constant and the mass of the probe assembly will define the natural frequency of the mechanical system, establishing the maximum frequency the gage head will follow.

Consider three factors when using LVDTs in dynamic situations: the characteristics of the mechanical system under test, the LVDT carrier frequency, and filtering or signal conditioning.

The mechanical system is best understood as a spring-mass system with one degree of freedom whose natural frequency, w, is

where k = spring constant and m = mass. The natural frequency is the most likely limiting factor on the measurement system. Natural frequency is the frequency in cycles per second (Hz) at which an undamped spring-mass system will continue oscillating after a single disturbance.

As the frequency of the measured vibration increases, attenuation error may become large enough to affect the measurement. If possible, the natural frequency of the mechanical measuring system should be at least 2.5 times greater than the highest frequency of the displacement being measured. Although in practice, it's best to work well below the natural frequency of the mechanical system. A sufficient amount of viscous damping may allow measuring frequencies up to 50% of the natural frequency before encountering significant errors.

The excitation voltage for an LVDT is usually between 1 to 10 Vac. The carrier frequency of the excitation voltage should be chosen keeping in mind the highest frequency of the expected measurement. Typically, a frequency of 400 to 20 kHz. An amplifier or demodulator is also needed to provide a stable dc output signal. Here, several rules of thumb apply. For one thing, the carrier frequency of the excitation voltage should be at least 10 times the mechanical frequency being measured. At this carrier frequency, there will be an attenuation of –3 dB (–36.8%) of a step function input. Increasing the carrier frequency to 2p 10 times the natural frequency will reduce the attenuation of a step function to 0.2%.

However, the carrier frequency cannot be increased without limit. Increasing the frequency makes the system more sensitive to lead length and other sources of stray capacitance which degrade signal integrity. Also, if wide temperature variations are expected, the carrier frequency should be kept close to the optimum value for minimum temperature coefficient.

Dynamic instrumentation systems often employ filtering to suppress unwanted noise. If the band of frequencies over which the information occurs is known, a filter can be designed to attenuate unwanted signals occurring at higher or lower frequencies. In most cases, attenuating frequencies higher than those of interest with a low-pass filter is usually enough to ensure a clean output signal.

Dynamic errors can result from the inability of a measuring system to accurately follow a time varying output. The errors are often caused by friction, damping, or inertia of the moving elements of the sensor. Dynamic errors also come from using an excitation frequency not sufficiently greater than the maximum frequency of the moving element being measured. Errors can also stem from cut-off or band-pass filters in the sensor, signal conditioning, or the readout instrument that filters out noise and a portion of the signal itself.

Also consider the rise time, overshoot, and decay-time of the output signal that distorts the output to some degree. Response time is typically specified as the time for the output to reach 63.2% of the final value in response to a step input. If a response time 2p times longer can be tolerated, the output will reach 99.8% of the final value, a result far more satisfactory for most work in instrumentation and measurement.

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