As introduced in Column TC-01, rotating machinery can be broadly categorized for condition monitoring into large high-speed machines supported by fluid-film bearings and general-purpose machines supported by rolling element bearings. Columns TC-02 and TC-03 focused on condition monitoring systems for the former category. This column, TC-04, discusses condition monitoring systems for general-purpose rotating machinery with rolling bearings, and the vibration evaluation criteria defined in ISO standards.

1. Condition Monitoring of General-Purpose Rotating Machinery with Rolling bearings

　The target machines for this column are those supported by rolling bearings, operating at speeds below their first critical speed, and classified as rigid rotors. Examples include motors, pumps, fans, and blowers.

　In vibration measurements of such machinery, it is common to install acceleration sensors on bearing housings or similar components where the vibration from the bearing is directly transmitted. The vibration data measured by these sensors are transmitted via wired or wireless means to a vibration monitoring system, as illustrated in Figure 4-1 (the symbol indicates wireless transmission).

　By installing a wireless vibration sensor on a machine that does not originally have a sensor installed, it is possible to automatically collect vibration data more frequently than with a conventional portable vibrometer for patrol inspections, thereby enabling more accurate condition monitoring. In this way, wireless sensors are more suitable for new vibration sensor installations, as they do not require cables to be laid from the site to the monitoring room.

2. Evaluation and Diagnostic Techniques for Machine Vibration

2-1　Evaluation Criteria According to ISO Standards

　The ISO 20816 series, listed in Table 4-1, defines measurement methods and evaluation criteria for machine vibration and is frequently referenced for condition monitoring. Part 1 provides general guidelines, while subsequent parts offer criteria tailored to specific machine types, as indicated by each part’s title.

　Previously, ISO 7919 (focused on shaft vibration) and ISO 10816 (focused on non-rotating parts such as bearing housings) were the standards for vibration measurement and evaluation. Since 2016, these have been replaced or integrated into the ISO 20816 series, and the relevant parts of ISO 7919 and 10816 have been withdrawn. However, Parts 6 and 7 of ISO 10816 remain current, as corresponding ISO 20816 standards have not yet been issued.

Table 4-1: List of ISO 20816 Series Standards

ISO 20816 Series	Mechanical vibration — Measurement and evaluation of machine vibration —
ISO 20816-1:2016	General guidelines
ISO 20816-2:2017	Land-based gas turbines, steam turbines and generators in excess of 40 MW, with fluid-film bearings and rated speeds of 1500 r/min, 1800 r/min, 3000 r/min and 3600 r/min
ISO 20816-3:2022	Industrial machinery with a power rating above 15 kW and operating speeds between 120 r/min and 30000 r/min
ISO 20816-4:2018	Gas turbines in excess of 3 MW, with fluid-film bearings
ISO 20816-5:2018	Machine sets in hydraulic power generating and pump-storage plants
ISO 10816-6:1995	Reciprocating machines with power ratings above 100 kW
ISO 10816-7:2009	Rotodynamic pumps for industrial applications, including measurements on rotating shafts
ISO 20816-8:2018	Reciprocating compressor systems
ISO 20816-9:2020	Gear units
ISO 20816-21:2025	Horizontal axis wind turbines

　Parts 1 through 5 of the ISO 20816 series, which consolidates the ISO 7919 and ISO 10816 series, address the measurement and evaluation of both shaft vibration and the vibration of non-rotating parts. In most practical cases, for general-purpose machines supported by rolling bearings, vibration measurement of non-rotating parts is typically applied. Accordingly, the discussion that follows is limited to the vibration of non-rotating parts.

　A summary of the portion of the Scope of ISO 20816-1:2016 ⁽¹⁾, which provides general guidelines, that concerns the measurement and evaluation of vibration of non-rotating parts is as follows:

• This document establishes general conditions and procedures for the measurement and evaluation of vibration on non-rotating parts of complete machines.
• The general evaluation criteria for both vibration magnitude and change are applicable to operational monitoring and acceptance testing.
• The criteria relate to vibration generated by the machine itself, not externally transmitted vibration.

　In addition, ISO 20816-1 specifies two distinct evaluation criteria – Criterion I and Criterion II—for assessing the severity of machine vibrations.

Criterion I: Vibration magnitude at rated speed under steady operation conditions

　The vibration magnitude of non-rotating parts measured at each bearing or pedestal is assessed against four evaluation zones established from international experience.

　In general, measurements of the broadband rms (root mean square) vibration velocity on structural parts, such as bearing housings, adequately characterize the running conditions of the rotating shaft elements with respect to their trouble-free operation. Therefore, the evaluation zones for vibration measured on non-rotating parts are divided into Zones A to D (see Figure 4-2), and the boundaries of each zone are defined by the rms value of the vibration velocity within the frequency range from \( f_{x} \) to \( f_{y} \).

　Note: Broadband vibration magnitude refers to overall vibration values in a defined frequency band (e.g., 10 Hz to 1,000 Hz) and is also called Overall Amplitude (OA value).

Criterion II: Change in Vibration Magnitude

　This criterion evaluates changes in vibration magnitude relative to a previously established reference. Even if Criterion I zone C is not reached, a significant increase or decrease may still require action. These changes, whether sudden or gradual, may signal damage, impending failure, or other abnormalities. Criterion II applies under steady-state operating conditions.

　Note: In the ISO 20816 series, each part following Part 1 that defines Criterion II describes a guideline for a significant change in vibration magnitude as 25% of the Zone B/C boundary of Criterion I.

　Each part following Part 2 of the ISO 20816 series provides measurement methods and evaluation criteria tailored to the type of machine specified in its title. Among them, ISO 20816-3⁽²⁾ is the standard for the measurement and evaluation of vibration in industrial machinery with a power rating above 15 kW and operating speeds between 120 rpm and 30,000 rpm. Since this includes a wide range of general-purpose rotating machines supported by rolling bearings, Table 4-2 presents the evaluation zone boundaries for vibration measured on non-rotating parts, as specified in ISO 20816-3. The vibration frequency range \(f_{x}\) to \(f_{y}\) defined in ISO 20816-3 is typically 10 Hz to 1,000 Hz.

Table 4-2: Evaluation Zone Boundary for Industrial Machines as Specified in ISO 20816-3

Machine Group		Group 1 (Large machines)		Group 2 (Medium-sized machines)
Support class		Rigid	Flexible	Rigid	Flexible
Zone boundary (mm/s rms)	A/B	2.3	3.5	1.4	2.3
	B/C	4.5	7.1	2.8	4.5
	C/D	7.1	11.0	4.5	7.1
Group 1	Large machines with rated power above 300 kW; electrical machines with shaft height H ≥ 315 mm.
Group 2	Medium-sized machines with a rated power above 15 kW up to and including 300 kW; electrical machines with shaft height 160 mm ≤ H < 315 mm.
Rigid support	Natural frequency of the combined machine and support system is at least 25% higher than the main excitation frequency (typically the rotational speed).
Flexible support	Any support that does not meet the criteria for rigid support.

The machine types covered by ISO 20816-3 are listed in the standard’s Scope, including:

• Steam turbines and generators ≤ 40 MW
• Steam turbines and generators > 40 MW operating at speeds other than 1500, 1800, 3000 or 3600 rpm.
• Rotary compressors
• Industrial gas turbines ≤ 3 MW
• Turbofans
• Electric motors of any type, if the coupling is flexible. When a motor is rigidly coupled to a machine type covered by any other part of ISO 20816, the motor may be assessed either against that other part or against ISO 20816-3
• Rolls and mills
• Conveyors
• Variable-speed couplings
• Blowers or fans

2-2 Diagnosis of abnormalities by frequency analysis

　As explained in Section 2-1, the presence of an abnormal condition can be assessed using the Overall Amplitude (OA) value obtained from vibration measurements. However, this value alone does not provide insight into the specific cause of the abnormality. To estimate the underlying cause of abnormal vibration, it is important to understand the main frequency components (spectrum) contained in the vibration signal. For this reason, in addition to monitoring OA values, frequency analysis using FFT (Fast Fourier Transform) of the vibration waveform data is commonly used as an effective approach.

　By examining the results of frequency analysis and referring to tools such as the vibration cause matrix shown in Table 4-3, it becomes possible to make an educated guess about the source of the vibration⁽³⁾. For example, if a rotating machine running at 3,600 rpm shows an abnormal vibration with a dominant frequency around 60 Hz (known as the 1X component), unbalance is likely to be the cause. If both 60 Hz (1X) and 120 Hz (2X) components are prominent, then possible causes may include a shaft crack, misalignment, or coupling issues.

Table 4-3: Example of the Vibration Cause Matrix

2-3 Damage Detection in Rolling Bearings and Envelope Analysis

　One of the typical types of damage in rolling bearings is the formation of indentations on the inner or outer race due to the intrusion of foreign particles into the bearing. These indentations can initiate micro-cracks, which may grow over time and eventually lead to flaking. When such indentations occur, each time a rolling element (ball) passes over the damaged area, it generates an impact vibration. This impact vibration manifests as a damped free vibration at the natural frequency of the inner or outer race. Since the repetition period of these damped free vibrations depends on the damaged bearing component, the rotational speed, and the bearing’s design parameters, it is possible to identify which component is damaged by analyzing the repetition frequency, which is the inverse of the repetition period. Equations (1) through (4) show the formulas used to calculate each of these characteristic damage frequencies. Equations (1) through (4) are derived from Equations (D.1) through (D.4) in Annex D of ISO 13373-3:2015⁽⁴⁾, under the assumption that the outer race is fixed—that is, the outer race rotation frequency \( f_{o} \) is set to zero—and the inner race frequency \( f_{i} \) is replaced with the shaft rotational frequency \(f_{r}\).

• Ball Pass Frequency of the Outer Race (BPFO)
  \begin{equation}
  BEPO=\frac{N}{2}f_{r}\left( 1-\frac{B}{P}\cos \phi \right) \tag{$1$}
  \end{equation}
• Ball Pass Frequency of the Inner Race (BPFI)
  \begin{equation}
  BPFI=\dfrac{N}{2}f_{r}\left( 1+\dfrac{B}{P}\cos \phi \right) \tag{$2$}
  \end{equation}
• Ball Spin Frequency (BSF)
  \begin{equation}
  BSF=\dfrac{p}{2B}f_{r}\left[ 1-\left( \dfrac{B}{P}\right) ^{2}\cos ^{2}\phi \right] \tag{$3$}
  \end{equation}
• Fundamental Train Frequency (FTF), which is the Frequency of the Cage.
  \begin{equation}
  FTF=\dfrac{f_{r}}{2}\left( 1-\dfrac{B}{P}\cos \phi \right) \tag{$4$}
  \end{equation}

　Where

\begin{alignat}{2}
& N & \; & : & \; & \text{Number of balls or rollers} \\
& f_{r} & \; & : & \; & \text{Rotational frequency} \\
& P & \; & : & \; & \text{Pitch diameter of ball or roller} \\
& B & \; & : & \; & \text{Diameter of ball or roller} \\
& \phi & \; & : & \; & \text{Contact angle} \\
\end{alignat}

The impact vibrations caused by bearing damage are detected by an acceleration sensor (accelerometer). However, the waveform signal typically appears as a ringing signal—i.e., a damped free vibration—at the natural frequency (resonant frequency) of the outer or inner race, with the characteristic damage frequencies modulated onto it. As a result, performing an FFT directly on the raw waveform makes it difficult to detect the damage frequencies. This is especially true in the early stages of damage. In order to detect early signs of bearing faults, it is necessary to perform an FFT on a waveform that has been processed using envelope analysis, as illustrated in Figure 4-3.

References

(1)	ISO 20816-1:2016, “Mechanical vibration – Measurement and evaluation of machine vibration – Part 1: General guidelines”, International Organization for Standardization, 2016.
(2)	ISO 20816-3:2022, “Mechanical vibration – Measurement and evaluation of machine vibration – Part 3: Industrial machinery with a power rating above 15 kW and operating speeds between 120 r/min and 30 000 r/min”, International Organization for Standardization, 2022.
(3)	Matsushita, O., Tanaka, M., Kobayashi, M., Koike, H., Kanki, H., “The Second Volume of Vibration of Rotating Machinery: Applications of Analysis, Troubleshooting and Diagnosis”, Corona Publishing, 2012. (in Japanese)
(4)	ISO 13373-3:2015, “Condition monitoring and diagnostics of machines – Vibration condition monitoring – Part 3: Guidelines for vibration diagnosis”, International Organization for Standardization, 2015.