Discurso de Alcibíades (215a-222a)

Angular position as it pertains to a shaft or appendage can be measured by a number of different techniques. Synchros and resolvers have historically been the most robust and accurate devices, but their requirement for AC power and signal processing can be an issue. Absolute shaft encoders and potentiometers typically use DC power, but these usually do not have the longevity of the AC powered units. As is the case with most measurements, several transducers can serve the purpose. The instrumentation engineer much decide which device type is the best solution for the given situation. A brief discussion for each device type is provided in the following paragraphs.

3.6.1 Synchros. Synchros and resolvers come under the general classification of rotary transformers. In the case of the synchro used for instrumentation purposes, it is usually in the form of a synchro transmitter as illustrated in Figure 3-22.

Figure 3-22. Synchro transmitter.

The three stator windings, which form the secondary portion of the rotary transformer, are mechanically located 120^o apart. The stator windings can be connected in a “wye” or “delta”

fashion. An AC carrier or reference (typically 115VAC or 26VAC, 60Hz or 400Hz) is supplied through leads R1 and R2 to the rotor coil that forms the primary portion of the rotary transformer.

The rotor is mechanically linked by a flexible coupling, belt, chain, or other device to the item for which the angular measurement is to be acquired. The induced AC voltage outputs from the stator windings (S1, S2, and S3) are in time phase with the applied rotor winding input, but will vary in amplitude with respect to rotor position. Therefore, there is only one set of S1, S2, S3

output amplitudes for a given rotor position. These outputs can be connected to another synchro in the form of a synchro receiver for direct display (see Figure 3-23).

Error Voltage R1

Rotor

R2

S1

S2

Stator

S3

R2

Analog meter display

Figure 3-23. Synchro receiver.

The receiver synchro stator windings induce a torque on the receiver rotor until the position matches that of the transmitter rotor. The windings on the receiver rotor will have an induced output “error” voltage that will go to zero as the rotor position matches that of the transmitting synchro. An arm attached to the receiver rotor can then be used as a pointer for a traditional analog meter or as a mechanical link for some other process.

The instrumentation engineer will want to record a time history of the transmitting rotor position rather than providing a remote analog meter display. The S1, S2, S3 synchro transmitter outputs are sent to the synchro to digital (S/D) converter along with the rotor AC supply voltage (see Figure 3-24). The S/D converter “knows” the unique rotor position for the given set of input amplitudes and outputs the angular value in a parallel digital word format. The output resolution (12, 14, 16 bit) in degrees or radians is determined by simply dividing the desired engineering units of measurement for a complete circle (360^o, 2π radians, etc.) by the total number of output counts available (2¹², 2¹⁴,2¹⁶, etc.).

Dn (MSB)

S1

S2

S3

R1 R2

Rotor Stator

Synchro To Digital (S/D) Converter ASIC

D0 (LSB)

D2

D1

12 to 16 typical

AC Reference AC Supply

Figure 3-24. Synchro transmitter.

3.6.2 Resolvers. Resolvers differ from synchros, in that they have a pair of output wires from two isolated stator windings that are mechanically located 90^o apart (Figure 3-25). As with the synchro, the rotor winding is excited with a reference AC supply voltage. Each pair of stator windings has induced voltages in time phase with the input reference. The amplitudes of these induced voltages are proportional to the sine and cosine of the rotor angle with respect to the stator windings. Resolvers have historically been used in systems to perform electrical computations. These computations have historically been used to perform coordinate system transformation between polar and rectangular coordinate systems. Resolver to digital (R/D) Application-Specific Integrated Circuits (ASIC) are commercially available to convert the resolver outputs to an absolute angular measurement. Similar to the S/D converter, the output resolution is typically on the order of 12 to 16 bits.

AC Supply

3.6.3 Absolute shaft encoders. Absolute shaft encoders use an optical-electronic method of measuring angular position (see Figure 3-26). The absolute shaft encoder is constructed with an input shaft to which a disc is attached. The disc is etched with encoded strips of transparent and opaque sectors. The number of concentric strips determines the output resolution of the device (i.e. the number of bits). The encoded strips pass between light sources such as LEDs and photodiodes or phototransistors. The encoded pattern on the disc can be arranged in various schemes. The most basic scheme is binary coded decimal (BCD). Others such as Gray code limit the number of bits that can change state simultaneously. In Gray code, only one bit at a time changes state as the input shaft is rotated. The output, then, is a parallel digital word, typically 12 to 16 bits wide, that directly represents the shaft angle. The zero position is set at the factory when the device is constructed. Power supply requirements range from +5 to +28VDC.

Dn (MSB) 5 to 28 VDC

power input

D0 (LSB) D2

D1

12 to 16 typical

Parallel output

Figure 3-26. Shaft encoders.

3.6.4 Linear variable differential transformer (LVDT). An LVDT is a common type of electromechanical transducer that can convert the linear motion of an object to which it is mechanically coupled into a corresponding electrical signal (Figure 3-27). There are LVDTs readily available that can measure movements as small as a few millionths of an inch up to several inches. There are also LVDTs capable of measuring positions up to ± 20 inches.

Figure 3-27. Linear variable differential transformer (LVDT).

The physical construction of a typical LVDT consists of a movable core of magnetic material and three coils comprising the static transformer (Figure 3-28). One of the three coils is the primary coil and the other two are secondary coils. The moving element of the LVDT is a separate tubular armature of magnetically permeable material called the core, which is free to move axially within the coils’ hollow bore, and mechanically coupled to the object whose position is being measured. This bore is typically large enough to provide substantial radial clearance between the core and bore, with no physical contact between it and the coil.

Figure 3-28. Linear variable differential transformer (LVDT) construction.

During operation, the primary winding of the LVDT is energized by alternating current (AC) of appropriate amplitude and frequency, known as the primary excitation. The LVDT’s electrical output signal is the differential AC voltage between the two secondary windings,

Inside a Transformer

Primary Coil

Secondary Coil

S2 S1

Vin

V^out = Negative

Primary Coil Secondary Coils

Core S1

Vin

V^out = Positive S2

E2 E2

E1 E1

Figure 3-29. LVDT.

Figure 3-29, above, illustrates what happens when the LVDT’s core is in different axial positions. The LVDT’s primary coil is energized by a constant amplitude AC source, Vin. The magnetic flux developed is coupled by the core to the adjacent secondary windings, S1 and S2.

If the core is located midway between S1 and S2, equal flux is coupled to each secondary so the voltages, E1 and E2, induced in each winding are equal. At this midway core position, referred to as the null point, the differential voltage output, (E1-E2), is effectively zero. As shown here, if the core is moved closer to S1 than to S2, more flux is coupled to S1 and less to S2, so the induced voltage E1 is increased while E2 is decreased, resulting in the differential voltage (E1-E2). Conversely, if the core is moved closer to S2, more flux is coupled to S2 and less to S1 and E2 is increased as E1 is decreased, resulting in the differential voltage (E2-E1).

Supplying this excitation power for an LVDT is one of several functions of the support electronics, which is also sometimes known as LVDT signal conditioning equipment. Because the LVDT is an electrical transformer, it is designed for AC power of specific amplitude and frequency (typically 3Vrms at 2.5kHz). The output of an LVDT is an AC waveform. The magnitude of the output of the transducer rises regardless of the direction of movement from the electrical zero position. In order to know in which half of the displacement transducer coil the center of the armature is located, one must consider the phase of the output as well as the magnitude.

One of the most important features of an LVDT is its low friction operation. In normal use, there is no mechanical contact between the LVDT’s core and coil assembly, and there are minimal sources of friction such as rubbing, dragging, or binding. This feature is particularly useful in materials testing, vibration displacement measurements, and high-resolution

dimensional gauging systems. Because there is normally no contact between the LVDT’s core and coil structure, no parts can rub together or wear out. This means that an LVDT features unlimited mechanical life. This factor is especially important in high-reliability applications such as aircraft, satellites, space vehicles, and nuclear installations. It is also highly desirable in many industrial process control and factory automation systems. Additionally, since an LVDT operates on electromagnetic coupling principles in a friction-free structure, it measures

infinitesimally small changes in core position. This “infinite” resolution capability is limited only by an LVDT’s signal conditioner. These same factors also give an LVDT its outstanding repeatability.

The LVDT has only one axis of sensitivity. In other words, the LVDT responds to motion of the core along the coil’s axis, but is generally insensitive to cross-axis motion of the core or its radial position. Thus, an LVDT can usually function without adverse effect in applications involving misaligned or floating moving members, and in cases where the core doesn’t travel in a precisely straight line.

3.6.5 Rotational variable differential transformer (RVDT). The RVDT is used to measure rotational angles and operates under the same principles as the LVDT sensor. Whereas the LVDT uses a cylindrical linear core, the RVDT uses a rotary core (see Figure 3-30).

photo at Figure 3-32. However, potentiometers are not as durable and generally not as accurate as the devices discussed previously. Temperature drift, for example, is a large error source for potentiometers (see RTD section in Chapter 3, paragraph 3.4). For short-term measurements where high accuracy is not of paramount importance, the potentiometer is a good economic solution. Potentiometers with linear taper are used; in other words, a given displacement of wiper position is proportional to a change in resistance between the wiper and the end terminals.

The electrical configuration is also simple. The potentiometer winding can be excited with virtually any level DC voltage within the current capacity of the device. If necessary, the voltage at the wiper can then be directly input to analog signal conditioning equipment for gain and filtering. Often, this signal will be a high-level analog signal that will not require any

amplification. In cases where the range of angular displacement is very small, the potentiometer can be wired into a Wheatstone bridge configuration to increase sensitivity. However, the number of turns of wire used to construct the potentiometer will ultimately determine the resolution that can be obtained. For this reason, potentiometers are better suited for measuring relatively large angular displacements. Potentiometers have historically been constructed with turns of wire with a maximum shaft rotational range of about 300 degrees. Today, additional construction techniques are available such as thin-film deposition. Such developments also permit full 360 degree measurement ranges without the need for end stops.

+

-

DC excitation

Vo R

Figure 3-31. Potentiometer circuit diagram.

Figure 3-32. Typical potentiometer.