As mentioned in Chapter 9, “Other Applications,” of the previous TC-06, eddy current displacement transducers are used not only for shaft vibration measurement in industrial machinery but also for rotational speed measurement. On the other hand, electromagnetic pickups, also referred to as magnetic speed sensors, are widely used for rotational speed measurement in industrial machinery. This column explains the characteristics and points to consider when using eddy current displacement transducers and electromagnetic pickups for rotational speed measurement.

1. Application of Eddy Current Displacement Transducers to Rotational Speed Measurement

　As described in TC-06, an eddy current displacement transducer measures the distance (gap) between the target metal surface and the sensor tip. In addition to displacement measurements, it can also be applied to non-contact vibration measurements because it typically has a frequency response up to approximately 10 kHz. How, then, can it be applied to rotational speed measurement? More specifically, an eddy current displacement transducer detects rotational speed pulses—pulse-like signals with a repetition frequency proportional to rotational speed—which are used to measure rotational speed. The following explains how these rotational speed pulses are detected.

　To detect rotational speed pulses with an eddy current displacement transducer, its sensor is installed facing a metallic sensing gear having rectangular or trapezoidal teeth, as shown in Figure 7-1(a). As the sensing gear rotates, the surface facing the sensor alternates between the gear teeth and tooth spaces. The gap therefore alternates between a large gap (tooth space) and a small gap (gear tooth). In accordance with the static characteristic shown in Figure 7-1(b), the transducer consequently outputs a pulse-like signal such as that shown in Figure 7-1(c). (See NOTE.)

　Because the repetition frequency of this pulse train is proportional to rotational speed, the rotational speed can be measured by waveform shaping in the speed monitor followed by signal processing such as pulse-frequency or period measurement.

　A major characteristic of an eddy current displacement transducer is that it responds from DC (that is, a stationary gap measurement) up to high frequencies of about 10 kHz. It can therefore detect rotational speed pulses at essentially the same voltage level over a very wide speed range, from extremely low to very high rotational speeds. This also allows it to be used as a sensor for zero-speed detection, to determine when the rotor is virtually at rest.

　Eddy current displacement transducers are also used to detect phase-reference pulses (phase markers) for vibration analysis and eccentricity measurement. In this application, rather than using a sensing gear with multiple teeth such as that shown in Figure 7-1(a), the target is provided with either one projection per revolution [Figure 7-2(ii)] or a keyway-like notch [Figure 7-2(iii)]. This produces one pulse per revolution.

　The following describes the requirements for an eddy current displacement transducer when it is applied to rotational speed pulse detection.

(1) It must have a high frequency response even for large-amplitude pulse waveforms.

　For shaft vibration measurement, even a relatively large vibration amplitude is generally only several hundred μm p-p, corresponding to an output-voltage amplitude of several V p-p, and the frequency is usually no more than several hundred Hz. In rotational speed pulse detection, however, the amplitude is commonly around 10 V p-p, as shown in Figure 7-1(c). In addition, a sensing gear with 60 teeth is commonly used, resulting in a repetition frequency of several kHz. A high frequency response is therefore required even for large-amplitude signal waveforms.

(2) If the sensor or extension cable becomes open-circuited, the output voltage must shift toward zero volts (corresponding to an excessively small gap).

　For a shaft vibration monitor, upper and lower limits are normally defined for the acceptable input-voltage range, and excessively high or low displacement-transducer output voltage is interpreted as an input fault such as a sensor open circuit. For rotational speed pulse detection, however, reaching the saturation voltage (high output voltage) at the tooth-space portion, as shown in Figure 7-1(c), is a normal measurement condition. The speed monitor must therefore detect an input fault only on the zero-volt side (the excessively small-gap side).

　Accordingly, to detect an open circuit in the sensor or extension cable, the output voltage must shift toward zero volts when an open circuit occurs.

　The FK-202F transducer satisfies the above requirements and can therefore be used not only as a sensor for shaft vibration and shaft position measurement, but also as a rotational speed pulse detection sensor and a phase-reference sensor (phase marker). For reference, Figure 7-2 shows the recommended sensing-gear tooth dimensions when the FK-202F transducer is used for rotational speed pulse detection.

2. Application of Electromagnetic Pickups to Rotational Speed Measurement

　As shown in Figure 7-3(a), an electromagnetic pickup consists of a pickup coil, pole piece, and magnet, and uses an involute gear made of steel as the sensing gear. As the sensing gear rotates, each tooth of the magnetic sensing gear repeatedly approaches and moves away from the pole piece of the electromagnetic pickup. This changes the condition of the magnetic circuit formed by the magnet and pole piece, thereby changing the magnetic flux passing through the pickup coil. The magnetic flux increases as a gear tooth approaches and decreases as it moves away. If the magnetic flux is \(\phi\) and the number of turns in the pickup coil is N, the induced electromotive force e generated in the pickup coil is expressed by Faraday’s law of electromagnetic induction, as shown in Equation (7-1).

\begin{align}
e=-N\dfrac{d\phi }{dt} \tag{7-1} \\
\end{align}

　From Equation (7-1), the electromotive force e generated in the pickup coil is proportional to the time derivative of the magnetic flux, that is, the rate of change of the magnetic flux. Therefore, as rotation of the sensing gear causes the magnetic flux through the coil to increase and decrease continuously, the electromotive force generated in the coil also varies while alternating in polarity, producing a waveform such as that shown in Figure 7-3(b).

　Because the repetition frequency of this pulse train is proportional to rotational speed, the rotational speed can be measured, as with the eddy current displacement transducer described in Chapter 1, by waveform shaping in the speed monitor followed by signal processing such as pulse-frequency or period measurement.

　With an electromagnetic pickup, however, the output voltage (V p-p), which is the peak-to-peak amplitude of the rotational speed pulses shown in Figure 7-3(b), is affected by both the setting gap and rotational speed. As an example, Figure 7-4 shows the output-voltage (V p-p) characteristic of the MS-1601 electromagnetic pickup versus detection frequency. The characteristic shows that the output voltage decreases as the setting gap increases and also decreases as the frequency decreases. Electromagnetic pickups are therefore unsuitable for measuring very low rotational speeds. Conversely, at high rotational speeds with a small setting gap, a very high output voltage may be generated. The input circuit of the speed monitor receiving this signal must therefore be designed with protection against the expected high input voltage.

3. Effect of Cable Length on Electromagnetic Pickup Characteristics

　As shown in Figure 7-3(a), electrically an electromagnetic pickup consists essentially of only a coil, which is connected directly to the output cable (or connector). The electromagnetic pickup and speed monitor are connected through a twisted-pair shielded cable. This loop can be represented by the equivalent circuit shown in Figure 7-5, from which it can be seen that the system forms a resonant circuit.

　Using typical specification values for the MS-1601 electromagnetic pickup and VM-5S speed monitor, Rs = 110 Ω, Ls = 35 mH, and Ri = 5 kΩ, and assuming Cc = 100 pF/m as a representative capacitance for a general instrumentation cable, the calculated gain response of Vi relative to e has the frequency characteristics shown in Figure 7-6.

　When the characteristic for Gap = 1.0 mm in Figure 7-4 is combined with this calculated result, the speed monitor input voltage has the frequency characteristic shown in Figure 7-7. This is a simulation result based on a simplified equivalent circuit in which the individual elements are treated as lumped, ideal inductances and capacitances. Although the result does not quantitatively reproduce every actual installation, it indicates the qualitative and relative behavior of the system.

　Accordingly, if the cable becomes sufficiently long or a cable having relatively high capacitance per unit length is used, resonance may occur within the rotational-speed measurement range. This can create a range in which the speed monitor input voltage becomes very high, followed by substantial attenuation in the high-speed region. Therefore, when selecting the cable and determining its length, particular attention should be paid to the total cable capacitance, which depends on the cable capacitance per unit length and the cable length.

4. Problems with Rectangular-Tooth Gears for Electromagnetic Pickups

　An involute gear made of steel is typically used as the sensing gear for an electromagnetic pickup. This is because, as the gear rotates, the gap changes continuously and smoothly, allowing the magnetic flux \(\phi\) in Equation (7-1) to increase and decrease continuously.

　Now consider what occurs if a rectangular-tooth gear is used as the sensing gear. Figure 7-8 illustrates the electromotive force generated in the pickup coil and the input voltage to the speed monitor when the sensing gear has rectangular teeth.

　The electromotive force in the pickup coil shown in Figure 7-8(e), corresponding to the gear and pole-piece positions (a) through (d) as the shaft rotates, can be explained as follows.

　As the shaft rotates, (a) through (d) are repeated, and ideally, the electromotive force takes the form of repeated pairs of positive and negative pulses, as shown in (e). In practice, however, various factors may prevent the waveform from having completely zero intervals or sharp pulses, but theoretically it tends to have such a waveform.

　The rising and falling pulses of the coil electromotive force contain a broad range of frequency components. Components near the resonant frequency of the system comprising the electromagnetic pickup, cable, and speed-monitor input circuit can be amplified, producing a damped oscillation. As a result, a ringing waveform such as that shown in Figure 7-8(f) may appear: an initial large positive or negative change, followed by an overshoot of the opposite polarity, and then an oscillation that decays over several cycles.

　The resulting problem occurs in the processing from the speed-monitor input signal to generation of the shaped pulse. For an electromagnetic-pickup input, 0 V is normally used as the trigger level, with a specified hysteresis applied to determine the ON/OFF state of the shaped pulse. If the overshoot or ringing exceeds this hysteresis, multiple shaped pulses may be generated for the passage of a single gear tooth, preventing correct rotational speed measurement.

　For this reason, the use of a rectangular-tooth gear as the sensing gear for an electromagnetic pickup is not recommended.

　The same issue applies to phase-reference targets such as those shown in Figure 7-2(ii) and (iii). Because such targets contain edge regions where the magnetic flux changes rapidly and regions where it remains nearly constant, multiple pulses may be generated during one revolution. The use of an electromagnetic pickup for phase-reference detection is therefore not recommended.

5. Comparison of Eddy Current Displacement Transducers and Electromagnetic Pickups for Rotational Speed Pulse Detection

　Finally, Table 7-1 compares eddy current displacement transducers and electromagnetic pickups when applied to rotational speed pulse detection.

　As explained above, an eddy current displacement transducer is fundamentally a displacement-measuring device that responds from DC to approximately 10 kHz. Provided that the shape and dimensions of the sensing gear are appropriate, it can be applied over a very wide range, from zero-speed detection at extremely low rotational speeds to overspeed detection at high rotational speeds. However, it requires a dedicated transducer system consisting of a sensor, extension cable, and driver, making it more complex and expensive than an electromagnetic pickup.

　In contrast, an electromagnetic pickup requires no power supply, operates as a stand-alone sensor, has a simple construction, and is less expensive than an eddy current transducer system. However, as shown in Table 7-1, it requires greater care in application and cannot be used as a phase-reference sensor or a zero-speed sensor.

　When selecting either an eddy current displacement transducer or an electromagnetic pickup for rotational speed measurement or phase-reference detection on rotating machinery, the characteristics and application precautions of each should be fully understood.

Table 7-1 : Comparison of Eddy Current Displacement Transducers and Electromagnetic Pickups for Rotational Speed Pulse Detection

Item	Eddy Current Displacement Transducer (FK-202F)	Electromagnetic Pickup (MS Series)
Appearance
Principle	Eddy current principle Outputs a voltage proportional to the distance (gap) between the sensor and target.	Electromagnetic induction principle Generates an induced electromotive force proportional to the change in magnetic flux passing through the pickup coil.
Sensing Gear Type	Rectangular-tooth gear made of magnetic or non-magnetic metal	Involute gear made of steel
Features	Stable detection from low to high rotational speeds Constant amplitude even when rotational speed changes	No power supply required Simple construction
Points to Consider	An involute gear is unsuitable as a sensing gear. Depending on the gear module, a certain output voltage amplitude can be obtained, but it is not recommended for stable rotational speed pulse detection.	A rectangular-tooth gear can produce damped oscillation in the output waveform, causing erroneous rotational speed detection. Unsuitable as a phase-reference sensor. The output voltage amplitude is affected by the setting gap, rotational speed, and cable capacitance. At low rotational speeds, sufficient output-voltage amplitude cannot be obtained.
Applications	Overspeed detection General rotational speed measurement and monitoring (from low to high rotational speeds) Zero-speed detection Phase-reference detection (phase marker)	Overspeed detection General rotational speed measurement and monitoring (not applicable at low rotational speeds)

Column related products

FK Series

MS Series