This article continues from TC-05 and further explains eddy current type displacement transducers. In this issue, the FK Series compliant with API 670 and its applications are mainly described.

5. Sensors for Shaft Vibration Measurements of Industrial Rotating Machinery

　This chapter first describes sensors used for shaft vibration measurements of industrial rotating machinery. As described in TC-05, eddy current displacement sensors can follow and respond not only to static gap measurements (stationary or very slow changes) but also to dynamic gap variations. Therefore, they can be applied not only to positioning and minute displacement measurements, but also to a wide variety of applications including broadband vibration measurements from low to high frequencies and observation of complex dynamic behavior.
　When measuring vibration of rotating machinery, one or more vibration parameters—displacement, velocity, and acceleration—are selected depending on the purpose, machine type, and measurement location. For large high-speed rotating machinery supported by journal bearings and operated above the first critical speed, which are classified as flexible rotors, understanding the dynamic behavior of the shaft is essential for both condition monitoring and vibration analysis. In such applications, non-contact eddy current displacement sensors are commonly used to measure shaft vibration as the relative displacement between the shaft and bearing.

　In particular, API 670 compliant eddy current displacement sensors are essential for shaft vibration monitoring of critical rotating machinery such as centrifugal compressors and steam turbines used in petroleum and petrochemical plants. The FK-202F transducer is designed in accordance with this standard. In addition, API 670 compliant eddy current displacement sensors are widely used not only in petroleum and petrochemical plants but also for turbine-generator shaft vibration monitoring in power plants.

6. API 670 Requirements for Non-contacting Displacement Transducers

　As already introduced in Chapter 3 of TC-02, Table 6-1 summarizes the major requirements specified in the latest edition of API 670 (6th Edition) ⁽¹⁾ for an 8 mm Proximity Probe System. Figures 6-1 and 6-2 show typical sensor configurations conforming to the standard requirements.

　The API 670 standard specifies several accuracy-related terms for proximity probe systems, including Incremental Scale Factor (ISF), Deviation from Straight Line (DSL), and Linear Range. Their definitions are described below, and their relationship is illustrated in Figure 6-3.

• Incremental Scale Factor (ISF)

  For an 8 mm proximity probe system, API 670 specifies a nominal scale factor of 7.87 mV/μm. The Incremental Scale Factor is determined at specified displacement increments, typically 250 μm, throughout the linear range, and its deviation from the nominal value is evaluated.
  API 670 specifies an allowable tolerance of ±5 % relative to the nominal scale factor at the testing temperature. This tolerance corresponds to the Incremental Scale Factor (ISF) error, which directly affects the accuracy of shaft vibration measurements.

  The resulting vibration measurement error can be expressed as ：
  　　[Vibration Measurement Error] = [Measured Vibration] × [ISF Error]

  For example, if the ISF error is ±5 %, a measured vibration amplitude of 100 μm p-p results in a measurement error of ±5 μm p-p, while a measured vibration amplitude of 40 μm p-p results in a measurement error of ±2 μm p-p.

• Deviation from Straight Line (DSL)
  In API 670, linearity is expressed as the Deviation from Straight Line (DSL), which is defined as the maximum deviation of the actual calibration curve from the best-fit straight line based on the nominal scale factor of 7.87 mV/μm, as illustrated in Figure 6-3.
  For an 8 mm proximity probe system, API 670 specifies a maximum DSL of ±25.4 μm at the testing temperature.
  DSL is associated with the accuracy of static displacement measurements, such as axial position measurements and probe gap measurements.
  Unlike ISF error, which produces an error proportional to the measured vibration amplitude, DSL represents an absolute measurement error. Therefore, regardless of the measured displacement value, the measurement may contain an error of up to ±25.4 μm.
  Linearity is often expressed as a percentage of full scale (% of F.S.). For example, if the full scale is 2 mm, a DSL of ±25.4 μm corresponds to approximately ±1.27 % F.S.
• Linear Range
  The Linear Range is the displacement range over which both the Incremental Scale Factor (ISF) and the Deviation from Straight Line (DSL) satisfy the requirements specified in API 670.

　Figure 6-3 illustrates the relationship among the actual calibration curve, the best-fit straight line, ISF, DSL, and the linear range.
　API 670 refers to the non-contacting displacement transducer as a “Proximity transducer”, the sensor portion as a “Proximity probe”, and the converter or driver as an “Oscillator-demodulator.” Accordingly, these terms are also used in Table 6-1.

　Although Table 6-1 summarizes the requirements specified in API 670, many commercially available non-contacting displacement transducers compliant with the standard provide wider operating temperature ranges than those specified. In addition, the total system cable length, consisting of the probe cable length and extension cable length, is commonly available not only in the standard 5 m configuration required by API 670, but also in a 9 m system configuration.

Table 6-1 ： API 670 requirements for displacement transducer ( 8 mm Proximity Probe System )

7. Principle of Vibration Measurement Using a Non-contacting Displacement Transducer

　Although an eddy current displacement sensor is fundamentally a displacement transducer that measures the distance (gap) between the sensor and target, vibration measurement can also be achieved using the same principle. The frequency response of an eddy current displacement sensor is wide, typically extending from DC to approximately 10 kHz. Within the frequency range normally encountered in shaft vibration measurements—from several tens of hertz to several kilohertz—the transducer output follows changes in distance almost one-to-one. As shown in graph area (a) of Figure 6-4, the static characteristic of the transducer provides an output voltage proportional to distance within the linear range. Assuming that the target vibrates between \(x_{1}\) and \(x_{3}\) round \(x_{2}\), the distance variation with time is represented by graph area (b). The corresponding transducer output voltage appears as the waveform shown in graph area (c).

　Since the relationship between \(x_{1}\), \(x_{2}\), \(x_{3}\) and the corresponding output voltages \(y_{1}\), \(y_{2}\), \(y_{3}\) is known and proportional, the vibration amplitude can be calculated from the voltage difference between \(y_{3}\) and \(y_{1}\) using a vibration monitor, and this value is generally used for vibration monitoring. Furthermore, because the transducer output waveform represents the vibration waveform itself—that is, the dynamic behavior of the rotating shaft—it can also be used for shaft motion observation and vibration analysis.

　Here, as examples of the performance characteristics of an actual non-contacting displacement transducer compliant with API 670, Figure 6-5 shows a typical static characteristic of the FK-202F transducer, and Figure 6-6 shows its frequency response. As shown in Figure 6-6, the frequency response remains within -3 dB up to 10 kHz, with virtually no attenuation up to about 2–3 kHz.

　In actual shaft vibration measurements, the vibration frequencies of interest are much lower. For example, for a relatively high-speed machine operating at 12,000 rpm, the rotational frequency (1X) is 200 Hz. Even if vibration components up to the tenth harmonic (10X) are considered, the highest frequency of interest is only 2 kHz. Therefore, the FK-202F transducer provides more than sufficient frequency response for practical shaft vibration measurements.

　Consequently, within this frequency range where attenuation is negligible, the output voltages \(y_{1}\), \(y_{2}\), and \(y_{3}\) in graph area (c) of Figure 6-4 accurately follow the corresponding displacements \(x_{1}\), \(x_{2}\), and \(x_{3}\) in graph area (b). As a result, the dynamic behavior of the rotating shaft can be faithfully reproduced as a voltage waveform.

Figure 6-5 ： Static characteristics of FK-202F displacement transducer

Figure 6-6 ： Frequency response of FK-202F displadement transducer

8. Non-vibration Runout

　Signals that appear similar to vibration signals but are caused by factors other than actual vibration are referred to as runout. These can be divided into mechanical runout, caused by geometric irregularities such as out-of-roundness of the measurement surface, and electrical runout, caused by variations in the material properties of the measurement surface, such as material nonuniformity or residual stress around its circumference.

　API 670 6th Edition states ：
　“The surface areas to be observed by the probes (probe areas) shall be demagnetized or otherwise treated so that the combined total electrical and mechanical runout does not exceed 6 μm (0.25 mil) or as specified in the mechanical equipment standard.”

　Similarly, ISO 20816-1 ⁽²⁾ states ：
　“It is recommended that the total combined electrical and mechanical runout, as measured by the transducer, does not exceed 25 % of the allowable vibration displacement, specified in accordance with 6.3.2.2, or 6 μm, whichever is greater.”

　Although API 670 5th Edition ⁽³⁾ is now superseded and should therefore be regarded only as reference information, the following notes regarding runout treatment were included ：
NOTE 1 ： Diamond burnishing with a tool-post-held, spring-mounted diamond is common. In addition to use in reducing mechanical runout, it has also proven to be effective for electric runout reduction.
NOTE 2 ： Final finishing or light surface-removal finishing by grinding will normally require follow-up demagnetization.
NOTE 3 ： The gauss level of the proximity probe area should not exceed 2 gauss. The variation of gauss level around the circumference of the proximity probe area should not exceed 1 gauss.

　According to the experiments conducted by Asahi et al.⁽⁴⁾, the correlation coefficient between relative permeability and output voltage was \(\gamma\) = 0.93, while the correlation coefficient between residual stress and output voltage was \(\gamma\) = 0.96, indicating strong correlations in both cases.
　The test results also showed that the smaller the surface roughness after finishing, the smaller the variations in relative permeability and residual stress.

　This suggests the following relationship ：
　 “Reducing surface roughness” → “Reducing variations in relative permeability and residual stress” → “Reducing electrical runout”

　Therefore, the diamond burnishing described in NOTE 1 of API 670 5th Edition is considered effective not only because it improves surface finish mechanically, but also because it contributes to homogenization of relative permeability and residual stress, thereby reducing electrical runout.
　The same experiments also showed that changes in residual magnetic flux density before and after demagnetization caused little change in output voltage, and the correlation between magnetic flux density variation and output voltage variation was weak.

　Accordingly, the effectiveness of reducing runout solely by suppressing magnetic flux density and its circumferential variation – as described in NOTE 2 and NOTE 3 of API 670 5th Edition – appears to be limited.

9. Other Applications

　The FK-202F, which has a 2 mm linear range and complies with API 670, is widely used for shaft vibration measurements of large high-speed rotating machinery supported by journal bearings, such as turbines and centrifugal compressors. In addition to the FK-202F, the FK Series includes many models with linear ranges from 3 mm to 26 mm. These eddy current non-contacting displacement transducers are applied not only to shaft vibration measurements but also to shaft position, eccentricity, differential expansion, rotational speed, and phase reference detection in large rotating machinery. In TC-03, these correspond to the [ECD] sensors listed in the “Applicable Sensors” column of Table 3-1 ： TSI monitoring parameters.

　For rotational speed measurements of rotating machinery, electromagnetic speed sensors (magnetic pickups) consisting of a magnet, pole piece, and coil are also widely used in addition to eddy current non-contacting displacement transducers. Therefore, the next technical column, TC-07, will discuss a comparison between these two types of rotational speed sensors.

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