Library / Vibration exposure / VIB-09
Vibration exposure
Daily vibration exposure A(8), governing axis
Daily whole-body vibration exposure for one task at constant weighted levels on the three axes.
- Ref
- VIB-09
- Rev
- v1
- Field
- Vibration exposure
- Result
- A(8) [m/s²]
For one task at constant weighted RMS levels on three axes, the daily exposure is A(8) = max(1.4 awx, 1.4 awy, 1.0 awz) √(T/8). The three axes are not added; the axis with the largest multiplied level governs. With several tasks, combine every task for x, y and z separately and only then select the maximum, because the governing axis can change from task to task. The UK Health and Safety Executive gives daily exposure action and limit values of 0.5 and 1.15 m/s² A(8). Use current applicable guidance for an actual exposure evaluation.
Daily whole-body vibration exposure for one task at constant weighted levels on the three axes. The axes are not added; the axis with the largest multiplied level governs.
Calculator
- Governing axis value, max(1.4awx, 1.4awy, awz)1.1 m/s²
- Time to reach the action value 0.5 m/s²1.653 h
- Time to reach the limit value 1.15 m/s²8.744 h
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- For weighted RMS levels of 0.3, 0.15 and 1.1 m/s² over 0.5 h the partial values are 0.105, 0.0525 and 0.275 m/s², so the z axis governs with A(8) = 0.275 m/s², below both the action value and the limit. At these levels the action value is reached after 1.653 h and the limit value after 8.744 h of exposure.
- These are exposure arithmetic, not guaranteed symptom-free operating times. Normalising to eight hours does not erase a long exposure, and a stationary period does not undo earlier dose.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Exposure time | 0.1 to 12 h | 0.123 | 1.347 | 1.224 | +10% | +4.88 % |
| awx Weighted RMS, x axis | 0 to 3 m/s² | 0.275 | 1.05 | 0.775 | +10% | 0 % |
| awy Weighted RMS, y axis | 0 to 3 m/s² | 0.275 | 1.05 | 0.775 | +10% | 0 % |
| awz Weighted RMS, z axis | 0 to 3 m/s² | 0.105 | 0.75 | 0.645 | +10% | +10 % |
Sweep of Weighted RMS, z axis
| Weighted RMS, z axis (m/s²) | Daily exposure A(8) (m/s²) |
|---|---|
| 0 | 0.105 |
| 0.375 | 0.105 |
| 0.75 | 0.1875 |
| 1.125 | 0.2813 |
| 1.5 | 0.375 |
| 1.875 | 0.4688 |
| 2.25 | 0.5625 |
| 2.625 | 0.6563 |
| 3 | 0.75 |
Sweep one variable
Variables and how each one contributes
Daily exposure A(8)
What the equation gives you. Everything else feeds it.
Weighted RMS, x axis
The weighted RMS acceleration on the x (fore and aft) axis, in m/s². Raises A(8) only if the x axis is the governing one, where 1.4 awx is the largest. Raising it by 10 % (to 0.33) moves the result by +0 %, from 0.275 to 0.275 m/s².
Weighted RMS, y axis
The weighted RMS acceleration on the y (side to side) axis, in m/s². Raises A(8) only if the y axis is the governing one, where 1.4 awy is the largest. Raising it by 10 % (to 0.165) moves the result by +0 %, from 0.275 to 0.275 m/s².
Weighted RMS, z axis
The weighted RMS acceleration on the z (vertical) axis, in m/s². Raises A(8) in proportion while the z axis governs, as it does at the default. Raising it by 10 % (to 1.21) moves the result by +10 %, from 0.275 to 0.3025 m/s².
Exposure time
The exposure time, in hours. Raises A(8) with the square root of time. Raising it by 10 % (to 0.55) moves the result by +4.88 %, from 0.275 to 0.2884 m/s².
Worked example with the values above
- Multiplied levels: 1.4 × 0.3 = 0.42, 1.4 × 0.15 = 0.21, 1.0 × 1.1 = 1.1 m/s². The largest governs.
- Time factor: √(T/8) = √(0.5/8) = 0.25.
- A(8) = 1.1 × 0.25 = 0.275 m/s².
Assumptions and limits
- Constant weighted RMS on each axis for the whole exposure time, with Wd weighting on x and y and Wk on z.
- The multipliers 1.4, 1.4 and 1.0 of the health assessment; the lecture’s VDV values and the 6 W ride criterion belong to other frameworks and are not interchangeable.
Common mistakes
- Adding the three axes together instead of choosing the governing one.
- Applying the axis multiplier twice.
Statistics and uncertainty
Weighted RMS levels are uncertain by ±10 % or more, which maps straight into A(8). A result within ±10 % of the action or limit value cannot be said to be on one side or the other without further measurement.
Where it is used
- Checking a task against the UK daily exposure action value and limit value.
- Choosing which axis to attack to reduce the exposure.
Maths you need
- Weighted RMS: frequency-weighted root mean square acceleration
- Axis multipliers: 1.4 for x and y, 1.0 for z