The Differential Transformer

The basic form of a differential transformer is three coils wound on a common bobbin, where the center coil is the primary, and the two end coils are the secondaries. Aligned in the center of the bob bin is an iron core that can be displaced linearly (ill. 1). The position of this iron core relative to the primary and secondary coils controls the flux linkage into the secondaries and , hence, the voltages induced in them.

Connecting the secondary coils differentially, that is, start-to start, as in ill. 2, the induced voltages in secondaries S1 and S2 with the core in the central position will be equal in plane and magnitude and cancel each other out. There will thus be no volt age appearing across the output terminals.

If the core is now displaced, the voltage induced is one secondary will increase, and that induced in the other secondary will decrease. The result will be a difference signal, the output of which is in linear proportion to the core movement.

ill. 10-1. A differential transformer. The core is movable. This is a linear de vice (LVDT).

ill. 10-2. When the core is centered and the secondaries connected as shown here, the output is zero.

In fact, it will be linear only over a proportion of the core movement. Output voltage will fall away as the core approaches the end(s) of the coil system due to reducing magnetic field at these points (ill. 10-3). When used as a practical measuring device to give accurate linear response, a long coil assembly is needed to pro vide a relatively short linear range. This may be quite acceptable in many applications, and it represents the basic design of a linear variable displacement transformer (LVDT) for general use, measuring smaller displacements (short strokes). To achieve linear out put with longer strokes, you can use various modified forms of coil windings, although they are inevitably more expensive to produce. These are:

Balanced Linear-Tapered Secondaries (ill. 10-4). In practice, a complicated form of winding where the secondary coils are wound over the primary and tapered in section from center to end. Provided the two secondary coils are perfectly symmetrical, good balance is achieved, but the magnetic field is still not maintained to the ends of the coils. Thus, linearity of output is not maintained over the whole of the possible stroke.

ill. 10-3. The variation in output from a differential transformer is linear only within a certain core-displacement range.

ill. 10-4. Balanced linear-tapered secondary.

Over-wound Linear-Tapered Secondaries (ill. 10-5).

This is an even more complicated form of winding to reproduce in practice, and it can exhibit unbalance. However, it does provide a better length of magnetic field and , thus, a greater linear range for the same length of coil.

Balanced Over-wound Linear-Tapered Secondaries (ill. 10-6). This form of winding splits the primary into two separate coils, an inner coil and an outer coil, with tapered secondary windings between. It has better balance than the second type, but it retains some of the basic limitations of the first type. it's also more costly to wind than either type.

ill. 10-6. Balanced overwound linear-tapered secondary.

Balance Profiled Secondaries (ill. 10-7). This is really a variation on the first type with the section profile of the secondary windings adjusted to maintain a greater length of magnetic field and a corresponding greater linear range.

ill. 10-7. Balanced profiled secondary.

Note: Some LVDTs are available with alternative cores: for ex ample, a plain core for general applications or a core fitted with low-friction sleeves (usually PTFE rings). The latter eliminate core skewing and would be the preferred choice where alignment is difficult or vibration is present.

INSTRUMENTATION

The linear variable-displacement transformer itself is only a signal generator requiring interfacing to an electrical circuit to pro vide indication or readout in analog or digital form. Such associated instrumentation can be relatively expensive. Because it's a transformer, ac excitation is essential. If a dc signal is required, ac output must be converted to dc when demodulation of the transformer output is required.

Two basic methods of achieving this are:

- Use of a transducer with a bifilar wound primary so that primary inductance controls oscillation, when a multivibrator circuit may be used for dc conversion.

- The ac output signal is “read” by a fixed-frequency oscillator.

In both cases the frequency response will be limited by the excitation frequency and the filter circuits employed. The manufacturer chooses the excitation frequency with performance, cost, and convenience criteria in mind, and the user has the usable frequency governed by this and the output filter. This filter is usually passive and is, therefore, less effective and efficient than an active filter.

In some cases the necessary electronic circuitry may be contained within the transducer itself. Those transducers that have integral dc input-dc output electronics are, in the main, available for excitation from 10-, 12-, and 24-V stabilized supplies. The use of electronics limits the temperature range; -200 C. to +1000 C. is typical, with thermal coefficients of 0.04 percent to 0.01 percent of full range per degree Celsius for both zero and span.

The dc transducer with integral electronics contains a considerably larger number of components than its ac counterpart. Cost is also relatively high, but it's usually less than a full ac system.

In the case of ac transducers, excitation can be at any voltage level up to 26 V (rms), depending only upon the impedances of the windings, at frequencies from 50 Hz to 20 kHz. The operable temperature range is much wider than the dc type, being typically 55° C. to + 1500 C., but the temperature effects are difficult to define. For any particular transducer the thermal coefficients tend to be a function of frequency, but zero coefficient is affected to a large extent by the core/extension rod assembly. Thus, where any temperature effects are important, it's best to calibrate the transducer at the selected frequency with the actual core/extension rod assembly in place. However, with variable excitation frequency, optimum performance can be obtained, and then the frequency can be fixed.

The usable frequency response of the unit can be determined by the user, because he is free to choose his excitation frequency. In addition, the external electronics can more easily utilize high- quality, active filtering, thus ensuring better characteristics. Frequency response can, therefore, be a function of the quality of the associated electronics.

The majority of ac transducers provide lead-out wires from both secondaries, which enables them to be connected either differentially or in series. When connected in series, the output remains constant, regardless of core position within the designed displacement range. This can be used as a self-test facility. Many users are unaware of this interesting facility, and it's most useful in applications where the integrity of the transducer is essential, and in some systems the connections are automatically switched to check the prime signal source. If, e.g., the insulation were to break down on any turn in either of the secondaries or the primary, the output would change the value.

LVDT GAUGE HEADS

A typical LVDT gauge head consists of an LVDT whose core is connected to a spring-loaded probe shaft having a removable tip. The probe shaft is guided in a sleeve bearing that is retained in a case that also encloses the LVDT coil windings. The case is of ten threaded externally to simplify mounting.

There are several possible ways to classify LVDT gauge heads, but the most meaningful classification is according to performance capabilities. This leads to three general categories of LVDT gauge heads: economy, precision, and ultra-precision. Considerations of bearing precision and linearity are the principal variables from one class to another.

ECONOMY GAUGE HEADS

The economy classification is applied to gauge heads that are designed to give a reasonably good level of performance at moderate cost. Economy gauge heads incorporated a lower-cost LVDT having a linearity of better than 0.5 percent of full range. The shaft is loosely fitted in a sleeve bearing, typically of nylon, and is free to rotate. Shaft loading is accomplished by an external helical compression spring. The cases of economy gauge heads are usually not threaded, so they require an external mounting clamp.

The loose bearing fit and rotatable shaft may cause core skewing and core rotation. These contribute to a somewhat larger repeatability error, typically 0.00254 mm (0.0001 in.), than more precise types of gauge heads. The typical life of economy gauge heads exceeds 5 million cycles with no significant degradation in performance. Economy gauge heads are not recommended for operation in severe environments because special sealing and protection techniques are required.

PRECISION GAUGE HEADS

The majority of LVDT gauge heads fall into the precision category. Precision gauge heads are characterized by good linearity, typically 0.25 percent of full range, and excellent repeatability, typically 0.00127 mm (0.00005 in.). They incorporate more precise bearings that have a closer fit to a non-rotating shaft. In spring- loaded units the spring is located internally. Most precision gauge heads have an externally threaded case. Precision gauge heads in corporate either ac or dc LVDTs.

The life of a precision gauge head is comparable to that of an economy type but depends on operating environment to a greater extent.

ULTRAPRECISION GAUGE HEADS

An ultraprecision LVDT gauge head combines a special ac LVDT with a honed-and-lapped, selectively fit sleeve bearing or ball bushing to produce a linearity of up to 0.05 percent of full range and a repeatability of 0.0001016 mm (0.00004 in.). Such gauge heads have the lowest error from shaft play and core skewing. The non-rotating shaft can be spring loaded to produce tip loads from 10 grams to several pounds. The close fit of the probe shaft to the shaft bearing may cause bearing friction that can shorten the useful life of an ultraprecision gauge head. For this reason the operating environment must be carefully controlled to prevent dust, dirt, moisture, oil, and similar contaminants from affecting the bearing of an ultraprecision gauge head.

PNEUMATICALLY ACTUATED GAUGE HEADS

In a pneumatically activated gauge head the probe spring is deleted and low-pressure air is introduced to the end of the core opposite the probe shaft. The probe-shaft load force is proportional to applied air pressure. By changing the applied pressure, the probe contact force can be varied as needed to suit a variety of gauging requirements. Once the actuating pressure is set, usually by means of an external pressure regulator, the probe contact force remains constant; it does not vary with shaft position. This gives the effect of a zero-rate compression spring.

The probe shaft may be retracted between gauging cycles by applying a low vacuum—127 to 254 mm (5 to 10 in.) of mercury—instead of pressure. Alternatively, the probe shaft may be spring biased in the retracted position, and the air pressure can be released to retract the probe. However, this method loses the constant force effect of a zero-rate spring.

Pneumatic actuation is normally used with certain types of ultraprecision gauge heads. For this reason the applied air must be entirely dry and free of oil. It should also be filtered with a 10-um (nominal) filter to prevent the introduction of contaminants into the bearing. Some LVDT gauge heads have a bleed orifice on the connector to facilitate low-pressure regulation. Typically, the probe- shaft force is 0.00175 gram per kg/cm^2 (0.4 oz per lb/in.^2) of applied air pressure.

LEVER- OR FINGER-PROBE GAUGE HEADS

In some gauging applications the dimension being checked is not directly accessible to the probe of an ordinary LVDT gauge head. For such measurements LVDT gauge heads incorporating lever- or finger-style probes are useful.

There are two types of finger-style gauge heads. One has a probe with a flexural pivot. A rotational (cosine) error is inherent in gauge heads using a flexural-pivot probe. In addition, the core of the LVDT also cocks, introducing other errors. For these reasons the parallel-flexure probe is preferred for most precise measurement applications.

ENVIRONMENT EFFECTS

The environmental considerations, with some restrictions, for an LVDT also apply to the LVDT gauge head. Economy and precision gauge heads can be operated over temperature ranges from -7° C. to 93° C. (-20° F. to 200°F.). The operating temperature of ultraprecision gauge heads should be restricted to the range from 40 C. to 60° C. (40° F. to 140° F.). The local environment should be clean and free from fluids or particles that could contaminate or otherwise affect the gauge-head bearing. Low relative humidity is desirable. In applications where cleanliness is difficult to maintain, a suitable environmentally protected gauge head should be used. No attempt should be made to lubricate the bearing of a gauge head.

Mechanical vibrations don't generally pose a problem under ordinary conditions and may even provide useful dither that reduces the effects of static friction. As with any standard LVDT, gauge heads are magnetically shielded and are not particularly affected by proximate magnetic fields or materials.

ADVANTAGES OF LVDTS

The LVDT has characteristics that make it a very useful (and, often, first choice) transducer for a wide variety of applications. Some of its features are unique to the LVDT:

Frictionless Measurement: Ordinarily, there is no physical contact between the movable core and coil structure, which means that the LVDT is a frictionless device. This permits its use in critical measurements that can tolerate the addition of the low-mass core but can't tolerate friction loading. Two examples of such applications are dynamic deflection or vibration tests of delicate materials and tensile or creep tests on fibers or other highly elastic materials.

Infinite Mechanical Life: The absence of friction and con tact between the coil and core of an LVDT means that there is nothing to wear out. This gives an LVDT essentially infinite mechanical life. This is a paramount requirement in applications such as the fatigue-life testing of materials and structures. The in finite mechanical life is also important in high-reliability mechanisms and systems found in aircraft, missiles, space vehicles, and critical industrial equipment.

Infinite Resolution: The frictionless operation of the LVDT combined with the induction principle by which the LVDT functions gives the LVDT two outstanding characteristics. The first is truly infinite resolution. This means that the LVDT can respond to even the minutest motion of the core and produce an output. The readability of the external electronics represents the only limitation on resolution.

Null Repeatability: The inherent symmetry of the LVDT construction produces the other feature, null repeatability. The null position of an LVDT is extremely stable and repeatable. Thus, the LVDT can be used as an excellent null-position indicator in high- gain, closed-loop control systems. it's also used in ratio systems where the resultant output is proportional to two independent variables at null.

Cross-Axis Rejection: An LVDT is predominantly sensitive to the effects of axial core motion and relatively insensitive to radial core motion. This means the LVDT can be used in applications where the core does not move in an exactly straight line (for ex ample, when an LVDT is coupled to the end of a Bourdon tube to measure pressure).

Extreme Ruggedness: The combination of the materials used in an LVDT and the techniques used for assembling them result in an extremely rugged and durable transducer. This rugged construction permits an LVDT to continue to function even after exposure to substantial shock loads and the high vibration levels often encountered in industrial environments.

Core and Coil Separation: The separation between LVDT core and LVDT coil permits the isolation of media such as pressurized, corrosive, or caustic fluids from the coil assembly by a nonmagnetic barrier interposed between the core and the inside of the coil. It also makes the hermetic sealing of the coil assembly possible and eliminates the need for a dynamic seal on the moving member. Only a static seal is necessary to seal the coil assembly within the pressurized system.

Environmental Compatibility: An LVDT is one of the few transducers that can operate in a variety of hostile environments. e.g., a hermetically sealed LVDT is constructed of materials such as stainless steel that can be exposed to corrosive liquids or vapors. Because it's hermetically sealed, the same LVDT can also be used in a hazardous location containing flammable vapors or particles if the external connections to the LVDT are made in an approved manner. LVDTs constructed with the proper materials and techniques can operate at cryogenic temperatures immersed in media such as liquid nitrogen or liquid oxygen. Other appropriately constructed LVDTs are available for operation at elevated temperatures (1100° F. or 600° C.) and in nuclear reactors with high radiation levels (10^20 NVT total integrated flux). LVDTs are available to operate continuously in fluids pressurized to 3000 psi (210 bars). Suitably designed LVDTs can be used in various combinations of these hostile environments.

Input/Output Isolation: The fact that the LVDT is a transformer means that there is complete isolation between excitation input (primary) and output (secondaries). This makes an LVDT an effective analog computing element without the need for buffer amplifiers. It also facilitates the isolation of the signal ground from excitation ground in high-performance measurement and control loops.

ROTARY VARIABLE-DIFFERENTIAL TRANSFORMERS

A modified form of differential transformer can be used for measuring angular rather than linear displacement. This type is known as a rotary variable-differential transformer or RVDT.

A typical RVDT is illustrated in ill. 10-8. The primary and secondary windings are wound symmetrically on a coil form (stator).

ill. 10-8. Rotary variable differential transformer (RVDT).

A cardioid-shaped cam of magnetic material (rotor) is used as a core. The input shaft goes across the middle of the coil form at the plane of winding symmetry and is fastened to the cardioidal core. The shape of the rotor is carefully chosen to produce a highly linear out put over a specified range of rotation.

The output curve of a typical RVDT is shown in ill. 10-9. There are two linear operating ranges 180° apart for any RVDT, but only one is calibrated by the manufacturer. The factory- calibrated linear region is identified by markings on both the shaft and the RVDT case for the nominal zero-degree shaft position (null angular position) of the shaft.

ill. 10-9. Output curve of a typical RVDT. Only one-half (180°) of the rotation range is needed.

The input shaft is usually supported by precision ball bearings to minimize friction and mechanical hysteresis. Because the bearing loads are ordinarily so low, the life of an RVDT transducer is comparable to the life of an LVDT. An important feature of the RVDT is the absence of any contact brushes in its construction. Also, like the LVDT, and RVDT is not affected by mechanical travel.

CHARACTERISTICS OF THE RVDT

Although the RVDT is a continuous (360°) rotation device, the range of most linear operations for a typical RVDT is only about ± 40°; operating range is better than 0.5 percent of full range. How ever, the linearity over smaller angular displacements is correspondingly improved. Thus, if an RVDT is used to measure a small angle of displacement, say ±5°, the linearity is found to be better than 0.1 percent of full range. The practical upper limit of angular measurement with an RVDT is about ± 60°.

The resolution of the RVDT is theoretically infinite. Resolution to very small fractions of a degree is commonly achieved in practice.

APPLICATIONS

RVDTs are available in both ac and dc types; dc units may con tam integral thick-film signal conditioning. Both types are used extensively to measure angular position and offer significant advantages over other types of angular position transducers. The foremost advantage is the lack of physical contact between rotor and stator. Another major advantage is the absence of brushes and slip rings. The only limitation on mechanical life is the shaft bearing, but the bearing loads under normal operating conditions are so insignificant that the operating life of an RVDT is comparable to that of an LVDT.

Another advantage of the RVDT is its truly infinite electrical resolution. The bearing play is usually so negligible that an RVDT exhibits practically no mechanical hysteresis.

PREV: Magnetic and Inductive Transducers
NEXT: Digital Transducers

Fundamentals of Transducers (all articles)