Quoting vibration levels

3.8.1 Single-value index methods

The following single-value index measures of vibration can be displayed as time histories or runs:

• Vibration acceleration (m/s² or g, where 1g = 9.81m/s²)

• Vibration velocity (m/s, or commonly mm/s)

• Vibration displacement (m, or commonly mm).

In each case any frequency weighting applied to the data must be declared.

Acceleration, velocity and displacement levels (dB) are often used. Care must be taken when quoting vibration levels to:

• distinguish between vibration acceleration, velocity and displacement levels (dB);

• distinguish between peak amplitude, peak-to-peak amplitude (twice peak amplitude – not commonly used), and rms value; and

• quote all units carefully (use SI units where possible, although the use of mm/s for velocity is common).

3.8.2 Acceleration levels (dB)

The usual practice is to measure in rms. Levels are measured in m/s² and the level reference is usually taken as one micrometre per second squared rms (a_ref= 10⁻⁶ms⁻²):

L a

a a

ref

= ⎛ dB

⎝ ⎞

20log10 ⎠ (3.8)

3.8.3 Velocity levels (dB)

The usual practice is to measure in rms. Levels are measured in mm/s and the level reference is usually taken as one nanometre per second rms (= 10⁻⁹ms⁻¹ or 10⁻⁶mms⁻¹):

L v

v v

ref

= ⎛ dB

⎝ ⎞

20log10 ⎠ (3.9)

Note that the time integral:

• of acceleration yields the velocity–time history;

• of velocity yields the displacement–time history.

Numerical methods may be used to post-process time histories and yield the time integral. Alternatively, electrical circuits are available to perform

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the integration at the point of recording the signal. These often become unreliable for double integration of acceleration, limiting signal-to-noise ratio and suffering from DC drift.

For simple harmonic motion analysed in the frequency domain, the inte- gral may be obtained by dividing the amplitude of a spectral component by iω where i is the square root of −1 and ω= 2πf (f is the frequency in Hz).

3.8.4 Assessing vibration levels – human response to vibration

Two ISO standards deal with the human response to vibration. They are:

• ISO 2631 Part 1 (1985) – Mechanical Vibration and Shock: Evaluation of Human Exposure to Whole Body Vibration – Part 1: General Requirements.

• ISO 5349 (1986) – Mechanical Vibration Guidelines for the Measurement of Human Exposure to Hand-transmitted Vibration.

The ISO 2631 Part 1 (General Requirements) offered user-friendly guid- ance on the effects of vibration acceleration amplitude (1–80Hz). Three boundaries are given for various exposure periods between 1 minute and 24 hours. These are:

• Reduced comfort boundary

• Fatigue-decreased profi ciency boundary

• Exposure limits (for health and safety).

The boundaries often still form part of contemporary performance specifi - cations for vehicles. Part 1 of ISO 2631 was revised in 1997. The guidance on safety, performance and comfort boundaries was removed. In its place, there are the following:

• The main body of the text describes a means of measuring a weighted rms acceleration according to:

a T a t t

T w =⎡ w( )d

⎣⎢ ⎤

⎦⎥ 1

∫

₂

0

1 2

(3.10) where a_w(t) is the weighted acceleration time history in m/s², and T is

the duration in seconds.

• Different weightings are given for health, comfort perception, the dif- ferent axes and the position of the human subject (standing, seated and recumbent).

A weighting W_k is used for assessing the effects of vibration on the comfort and perception of a standing person with vertical acceleration in

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the head-to-toe axis. Weighting W_k suggests that a standing person is most susceptible to vertical vibration in the frequency range 4–8Hz. Annexes to the main text give limited guidance on the health, comfort and perception and motion sickness effects of vibration. This guidance is in terms of weighted rms acceleration. The vibration dose value (VDV) is introduced but it is not used in any guidance on the likely effects of vibration. VDV is defi ned as:

VDV=⎡ [ _w( )]⁴d

⎣⎢ ⎤

⎦⎥

∫

^{a t t}

T

0

1 4

(3.11) where the units of VDV are ms^−1.75.

If the VDV is repeated n times during a period, the total VDV period is then:

VDV_total= ⎛ ^total VDV

⎝ ⎞

= ⎠ ×

∑

^t_ti

i n

i 1 4

1

(3.12) Approximate indications of the likely reaction to various magnitudes of frequency-weighted rms acceleration are listed according to ISO 2631 Part 1 as:

• <0.315ms⁻² not comfortable

• 0.315–0.63ms⁻² a little uncomfortable

• 0.5–1.0ms⁻² fairly uncomfortable

• 0.8–1.6ms⁻² uncomfortable

• 1.25–2.5ms⁻² very uncomfortable

• >2.0ms⁻² extremely uncomfortable

Responses of human behaviour to vibration in different frequency ranges are shown in Fig. 3.14 which shows that motion sickness occurs between 0.1 and 0.63Hz. Major body resonances occur between 1 and 80Hz.

Vibration disturbs speech at 2–20Hz, and vibration causes potential annoy- ance between 0.1 and about 400Hz. Vibration may cause spinal damage at about 5 to 20Hz. Figure 3.15 shows that the acceleration of the human body can be written as a weighted acceleration sum:

WAS= (1 4. ax) +² (1 4. ay)²+az² (3.13) If a human is exposed to three different vibration environments, the dose is defi ned as:

Dose = ×

∑

=

^t

ⁱ i i

n

τ

1

100%

(3.14)

where t_i is elapsed time and τi is allowed time.

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EFFECTS ON HUMANS FREQUENCY - Hz

INFRASONICS

+*

STRUCTURE-BORNE VIBRATIONAIRBORNE NOISEKEY ^

AUDIBLE RANGE ULTRASONICS

0.1 1 10 100 10³ 10⁴ 10⁵

Tonal auditory sensation Pulsatile auditory sensation Non-auditory sensation

Vibratory sensation Disequilibrium Motion sickness Major body resonances Disturbance of speech Blurring of vision Interference of tasks Potential annoyance Subjective after-failure Spinal damage+

Frequency range

Uncertain range of occurrence

Pressure Injury (barotrauma) at extreme intensities

Chronic disorders associated clinically with repeated occupational exposure to whole body vibration occupational exposure to vibration from hand-held power tools.

Chronic diseases affecting the blood vessels, bones and joints of the hand and forearm associated with cumulative Gastrointestinal disorders+

Reynaud’s phenomenon etc.^

Potential annoyance Subjective after-failure Speech Interference Loss of work efficiency Hearing loss Middle ear damage*

3.14 Response of human hearing behaviour to vibration.

a_z

a_y

a_x L_y

L_x L_z

3.15 Acceleration of the human body.

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τi

a

a t

i

= ⎛⎝⎜ ⎞

⎠⎟ ×

0 2

0 eq

(3.15) where a0=2 8. × 3=4 85. m s2 (a0x= a0y= 2m/s², a0z= 2.8m/s²) and energy equivalent acceleration is defi ned as:

a T

T a t

T eq( ) = ¹

∫

rms² d

0

(3.16) where T is sampling time and a_rms is root mean square acceleration.

If t₀= 10 minutes, the four-hour energy equivalent acceleration is:

a a t T

eq( )4 eq( )

0 4

= (3.17)

where T t_i

i

= n

∑

= 1

is total exposed time in one event.

The exposure from several events can be calculated from:

a T

a T T

i i i

n

i i eq( ) = ⁼n

=

∑

∑

2 1

1

(3.18)

where Ti is the total elapsed time in the ith event and ai is the equivalent acceleration in the ith event.

Vibration exposure is defi ned by:

• Vibration + time = vibration exposure

• Vibration exposure + time = tissue damage.

Vibration exposure is measured according to national and international standards. In order to avoid breaking occupational health legislation, at lowest cost, you will need to conduct the following monitoring and risk assessment:

• Is there a problem?

• How big is the problem?

• What causes the problem?

• How do we reduce the problem?

• How do we prevent the problem?

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