ISO 2041:2018 機械的振動、衝撃、状態監視—用語, 語彙 | ページ 2

3.5.1

data

sampled measurements of a physical quantity

3.5.2

sampling

measurement of a varying physical quantity at a sequence of values of time, angle, revolutions or other mechanical, independent variable

Note 1 to entry: Other meanings of this term may be used in particular fields, for example in statistics.

3.5.3

sampling frequency

number of samples with respect to time for uniformly sampled data

3.5.4

sampling period

duration of time between two successive samples

3.5.5

sampling rate

number of samples with respect to time, angle, revolutions or other mechanical, independent variable for uniformly sampled data

3.5.6

Nyquist frequency

maximum usable frequency available in data taken at a given sampling rate

Note 1 to entry: The Nyquist frequency is f_N = f_s/2 ここで, f_s is the sampling frequency.

3.5.7

sampling interval

number of physical or engineering units (e.g. time, angle, revolutions) between two successive samples

3.5.8

frequency resolution

difference of frequency between two adjacent spectral lines

Note 1 to entry: This is equal to the reciprocal of the total time of a block of data that is Fourier transformed.

3.5.9

Fourier transform

frequency description of a transient vibration

Note 2 to entry: The Fourier transform of vibration data x(t) measured over an interval T is given by:

where and m is an integer.

3.5.10

Fourier series

frequency description of a set of sampled vibration data

3.5.11

rms spectrum

amplitude spectrum used to quantify the components of sinusoidal, harmonic and non-harmonic signals, such as vibrations from an unbalanced rotor, gears or rolling bearings

Note 2 to entry: The physical or engineering units of the rms spectrum are U rms.

3.5.12

power spectral density

auto-spectral density

magnitude of the frequency domain description of random, continuous signals

Note 2 to entry: The physical or engineering units of the power spectral density are U²/Hz.

Note 3 to entry: Power spectral density is a generic term used regardless of the physical process represented by the time history. The physical process involved is indicated in referring to particular data, e.g. the term “acceleration power spectral density” or the term “acceleration spectral density” is used instead of power spectral density when the acceleration spectrum is to be described.

3.5.13

energy spectral density

magnitude of the frequency description of a transient signal

Note 2 to entry: If the data x(n) are measured from a random process, the average of the preceding equation is taken.

3.5.14

cross spectral density

magnitude of the frequency domain relationship between the two signals

3.5.15

coherence function

dimensionless measure of the relationship between two signals in the frequency domain

Note 3 to entry: The value of the coherence function ranges between 0 and 1.

3.5.16

statistical degrees of freedom

number of independent variables in a statistical estimate of a probability

Note 1 to entry: The number of degrees of freedom determines the statistical accuracy of an estimate.

3.5.17

aliasing error

aliasing

false representation of the spectral energy caused by the mixing of spectral components above the Nyquist frequency with those spectral components below the Nyquist frequency

3.5.18

window function

window

pre-defined mathematical function that multiplies a data block and improves some characteristics of the frequency description

Note 1 to entry: If a window function is used, an amplitude scaling constant shall be used.

Note 2 to entry: A window function is used for reducing the errors in processing weighted data points.

3.5.19

amplitude scaling factor

constant derived from window function that corrects the amplitude of the frequency description of a narrowband signal

Note 2 to entry: where w(n) is the window function.

3.5.20

effective noise bandwidth

bandwidth between frequency lines for a windowed signal, to be used to quantify the frequency description of a noise

3.5.21

time history

sequence of values of a physical or engineering quantity as a function of time

3.5.22

sidelobes

spurious peaks in the frequency domain caused by the use of a finite time window with the Fourier transform

3.5.23

spectral leakage

broadening of a peak in the frequency domain caused by window function with the Fourier transform

3.5.24

leakage error

error in frequency spectrum caused by a mismatch of the recording time to the frequency of interest

3.5.25

deterministic vibration

vibration for which the instantaneous value at a certain time can be predicted

Note 1 to entry: The vibration can be produced as a response to a known input, such as an impact, or predicted from another measured quantity, such as shaft position.

3.5.26

ensemble

set

collection of time histories

3.5.27

number of lines

number of spectral lines that are displayed

3.5.28

record length

<time histories> number of data points comprising a contiguous set of sampled data points

3.5.29

stationary process

ensemble of time histories such that their statistical properties are constant with respect to time

3.5.30

ergodic process

stationary process that possesses statistical properties that permit averages over time to replace averages over ensemble

Note 1 to entry: It follows that these time averages from any time history are then equal to the corresponding statistical averages over the ensemble.

3.5.31

random process

stochastic process

ensemble of time histories that is characterized through statistical properties

3.5.32

autocorrelation function

average of the product of the data’s value at one time with its value at another time

Note 2 to entry: If the vibration is stationary, the autocorrelation is a function only of the time difference τ. If the vibration is ergodic, the average can be taken over time. If it is non-ergodic, averages shall be taken over statistically independent samples.

3.5.33

cross-correlation function

average of the product of the values of two physical or engineering quantities at different times for two sets of data x(t) and y(t), the mean of the product of the value of one set of data at one time and the value of the other set of data at another time

Note 2 to entry: See Note 2 to entry for autocorrelation function (3.5.32) .

3.5.34

normalized autocorrelation function

ratio of the autocorrelation function to its value with zero time delay

3.5.35

normalized cross-correlation coefficient

ratio of the cross-correlation function to the square root of the product of autocorrelations at zero time delay

Note 2 to entry: At any delay τ, the cross-correlation coefficient satisfies −1 ≤ ρ_xy (τ) ≤ 1.

3.5.36

effective bandwidth

<specified band pass filter> bandwidth of an ideal filter which has a flat response in its passband and transmits the same power as the specified filter when the two filters receive the same white-noise input signal

Note 1 to entry: The effective bandwidth may be measured by dividing the mean-square response of the filter to white-noise excitation by the product of the excitation spectral density and the square of the maximum transmission.

3.5.37

signal bandwidth

interval over frequency between the upper and lower frequencies of interest

3.5.38

confidence level

value of the probability associated with a confidence interval or a statistical interval estimator

3.5.39

probability

expression of the likelihood of occurrence of a vibration event

Note 1 to entry: The probability of occurrence of a particular event is generally estimated as the ratio of the number of occurrences of the particular event to the total number of occurrences of all types of events considered.

Note 2 to entry: For a stationary random vibration, the probability that the magnitude will be within a given magnitude range is taken to be equal to the ratio of the time that the vibration is within that range to the total time of observation.

Note 3 to entry: A large number of events or a long observation time shall be involved in the probability determinations.

Note 4 to entry: A unit probability means that the occurrence of a particular event is certain. Zero probability means that it will not occur.

Note 5 to entry: The probability that the magnitude of a vibration will be within a given range is equal to the integral of the probability density function of that vibration integrated over the given range. See probability density function (3.5.41) .

3.5.40

probability density

<vibration theory> ratio, at a specified vibration magnitude, of the probability that the vibration magnitude will be within a given incremental range, to the size of the incremental range, as the increment size approaches zero

Note 2 to entry: The probability density, p(x), is the derivative of the cumulative probability distribution function, P(x), with respect to x (see 3.5.41).

3.5.41

probability density function

<vibration theory> expression of the probability density associated with a stated vibration

Note 1 to entry: The functions p(x) given under probability density, normal distribution and Rayleigh distribution are probability density functions.

Note 2 to entry: The probability density distribution curve is a graphical representation of the probability density function. The total area under the probability density curve is equal to unity.

3.5.42

confidence interval with confidence level 100(1-α) %

interval bounded by a lower and upper statistical limit

3.5.43

Bode plot

pair of rectangular plots, one displaying the amplitude of the vibration on the vertical axis with appropriate units and frequency on the horizontal axis with appropriate units, and the other displaying the phase of the vibration on the vertical axis with units of degrees and frequency on the horizontal axis with the same units as those in the amplitude plot

Figure 4 — Bode plot

Key

Y1	displacement
Y2	angle (°)
X	frequency (Hz)

Note 1 to entry: The plots are placed so that the horizontal frequency axes are aligned to clearly display related phase and amplitude behaviour.

Note 2 to entry: In machinery assessment, a special case of the Bode plot is sometimes used which uses speed as the horizontal axis and plots corresponding vibration features such as magnitude and phase. One such use is to plot the filtered 1x turning speed vibration magnitude and phase as the machine RPM changes.

3.5.44

Nyquist plot

square plot that displays the amplitude and phase of a vibration over a range of frequencies with the imaginary components of the vibration are displayed on the vertical axis and the real components on the horizontal axis

Figure 5 — Nyquist plot

Key

Y	imaginary displacement
X	real displacement

Note 1 to entry: Frequency is implicitly displayed along the length of the resulting curve.

Note 2 to entry: Square Nyquist plots clearly display the phase angle along the curve.

Note 3 to entry: The Nyquist plot is particularly useful for displaying transfer functions, such as transfer compliance.

3.5.45

orbit plot

plot displaying two perpendicular displacements of a rotating shaft over one rotation

Note 1 to entry: The displacements are sometimes measured with proximity sensors.

Note 2 to entry: A third sensor is used to establish a phase reference to the angular position of the shaft.

Note 3 to entry: The average shaft centerline plot and orbit plot indicate shaft dynamics that reveal malfunctions before failure.

3.5.46

average shaft centreline plot

plot displaying the average shaft position for several frequencies

Note 1 to entry: The average shaft centerline at each frequency is determined from the orbit plot.

3.5.47

cascade plot

waterfall plot

diagram that provides a simple comparison of several frequency analyses

Note 1 to entry: It is a three-dimensional form of spectra display that clearly shows vibration signal changes related to another parameter (such as rotational speed, load, temperature, time) taken for specified parameter values, such as time.

3.6.1

ball pass frequency, inner

f_BPFI

frequency of the inner race (BPFI), which appears when all the rolling elements pass on a defect on the inner race

3.6.2

ball pass frequency, outer

f_BPFO

frequency of the outer race (BPFO), which appears when all the rolling elements pass on a defect on the outer race

3.6.3

ball spin frequency

f_BSF

frequency (BSF), which is the circular frequency of each rolling element as it spins

3.6.4

fundamental train frequency

f_FTF

frequency (FTF), which is the frequency of the cage

Note 2 to entry: If both the inner and outer races rotate, the terms are additive or subtractive depending on the relative rotational direction.

3.6.5

primary belt frequency

f_b

number of times per second that a belt makes one complete circuit

3.6.6

gyroscopic moment

cross effect which yields a vibratory whirling torque on a shaft that can increase or decrease natural frequencies

Note 1 to entry: In rotor dynamics, the gyroscopic effect results from the whirling of an inclined spinning shaft of a rotor having angular momentum.

3.6.7

flexural vibration

vibration of a body in which the resultant deflections cause elastic (or plastic) deformation within the body

Note 1 to entry: It is related to the mode shape of a vibrating system.

Note 2 to entry: In a shaft or beam supported by two bearings (supports), the flexural vibration is the displacement of the neutral axis of the shaft or beam from that in the static equilibrium condition.

3.6.8

whirling

motion of a rotor in which individual elements of the rotor are deformed from the static deflection line due to the influence of, for example, unbalanced forces

Note 1 to entry: The motion of the deformed shape about the static deflection is described as “whirling” of the shaft.

3.6.9

oil whip

self-excited vibration of a rotor supported by fluid bearings due to an increase in tangential force of the fluid bearings

3.6.10

surging

vibratory movement of fluid in fans or compressors due to the system back pressure instability

3.6.11

flutter

self-excited vibration of a structure caused by the dynamic interaction with motion of the surrounding gas or fluid

3.6.12

sloshing

free surface oscillation of liquid in a partly filled moving container

Note 1 to entry: Examples of partly filled moving containers include mobile liquid storage tanks, seismic slosh tanks and marine fuel oil tanks.

3.6.13

flow induced vibration

vibration induced by fluid flow fluctuations

Table 1 — Equivalent definitions to be used for various kinds of output/input ratios

	Motion expressed
Characteristic	Displacement resonance	Velocity resonance	Damped natural frequency
Frequency
Amplitude of displacement
Amplitude of velocity
Phase of displacement with reference to applied force

NOTE 1 In the case of a linear single-degree-of-freedom system, the motion can be described by the formula

where

t is the time;

x is the displacement;

ω is the angular frequency;

F₀ is the magnitude of the exciting force;

m is the mass of the system;

c is the coefficient of linear (viscous) damping of the damping element in the system;

k is the stiffness of the spring in the system.

The characteristics of the different kinds of resonance in terms of the constants of the above formula are as given in the table.

NOTE 2 For values of c which are small compared with there is little difference between the three cases.

The frequency at velocity resonance is equal to the natural frequency of the system. Other symbols are employed for electrical resonance.