Library / Vibration exposure / VIB-08
Vibration exposure
Daily vibration exposure from three tasks on one axis
Daily eight-hour exposure on one axis from several tasks.
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- VIB-08
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- v1
- Field
- Vibration exposure
- Result
- Ai(8) [m/s²]
For several tasks on one axis, the partial exposures Aij(8) combine as a root sum of squares: Ai(8) = √(ΣAij(8)²) = ki √(Σaj²Tj/T0), with T0 = 8 h. The task with the highest level can dominate the day even if short. Combine every task for the x, y and z axes separately before choosing the governing axis. A stationary period does not undo earlier dose, and adding zero-exposure time does not reduce an already accumulated A(8).
Daily eight-hour exposure on one axis from several tasks. The partial exposures add as squares, so the task with the highest level can dominate the day even if it is short.
Calculator
- Total time on tasks3.5 h
- Share of the squared exposure from the strongest task (task 3 by default)57.14 %
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.
- Three tasks at 0.5, 1 and 2 m/s² for 2, 1 and 0.5 h give 0.6614 m/s². The 2 m/s² task lasts only 0.5 h but supplies 57.1 % of the squared total.
- The UK daily action value is 0.5 m/s² and the limit is 1.15 m/s², so this day is above the action value and below the limit.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T3 Time on task 3 | 0 to 8 h | 0.433 | 2.046 | 1.613 | +10% | +2.82 % |
| a1 Weighted RMS, task 1 | 0 to 3 m/s² | 0.6124 | 1.62 | 1.008 | +10% | +1.49 % |
| a2 Weighted RMS, task 2 | 0 to 3 m/s² | 0.559 | 1.199 | 0.6399 | +10% | +2.96 % |
| T2 Time on task 2 | 0 to 8 h | 0.559 | 1.146 | 0.5866 | +10% | +1.42 % |
| a3 Weighted RMS, task 3 | 0 to 3 m/s² | 0.433 | 0.866 | 0.433 | +10% | +5.83 % |
| ki Axis multiplier (1.4 for x and y, 1.0 for z) | 1 to 1.4 | 0.6614 | 0.926 | 0.2646 | +10% | +10 % |
| T1 Time on task 1 | 0 to 8 h | 0.6124 | 0.7906 | 0.1782 | +10% | +0.712 % |
Sweep of Weighted RMS, task 3
| Weighted RMS, task 3 (m/s²) | Daily exposure on the axis (m/s²) |
|---|---|
| 0 | 0.433 |
| 0.375 | 0.443 |
| 0.75 | 0.4719 |
| 1.125 | 0.5163 |
| 1.5 | 0.5728 |
| 1.875 | 0.6381 |
| 2.25 | 0.7099 |
| 2.625 | 0.7862 |
| 3 | 0.866 |
Sweep one variable
Variables and how each one contributes
Daily exposure on the axis
What the equation gives you. Everything else feeds it.
Axis multiplier (1.4 for x and y, 1.0 for z)
The axis multiplier: 1.4 for the x and y axes and 1.0 for z. Raises the daily exposure in proportion. Raising it by 0.1 (to 1.1) moves the result by +10 %, from 0.6614 to 0.7276 m/s².
Weighted RMS, task 1
The weighted RMS acceleration during task 1, in m/s². Raises the exposure by a share of the total that depends on that task’s mean square. Raising it by 10 % (to 0.55) moves the result by +1.49 %, from 0.6614 to 0.6713 m/s².
Time on task 1
The time spent on task 1, in hours. Raises the exposure with the square root of the combined mean-square-times-time. Raising it by 10 % (to 2.2) moves the result by +0.712 %, from 0.6614 to 0.6661 m/s².
Weighted RMS, task 2
The weighted RMS acceleration during task 2, in m/s². Raises the exposure by a share of the total that depends on that task’s mean square. Raising it by 10 % (to 1.1) moves the result by +2.96 %, from 0.6614 to 0.681 m/s².
Time on task 2
The time spent on task 2, in hours. Raises the exposure with the square root of the combined mean-square-times-time. Raising it by 10 % (to 1.1) moves the result by +1.42 %, from 0.6614 to 0.6708 m/s².
Weighted RMS, task 3
The weighted RMS acceleration during task 3, in m/s². Raises the exposure by a share of the total that depends on that task’s mean square. Raising it by 10 % (to 2.2) moves the result by +5.83 %, from 0.6614 to 0.7 m/s².
Time on task 3
The time spent on task 3, in hours. Raises the exposure with the square root of the combined mean-square-times-time. Raising it by 10 % (to 0.55) moves the result by +2.82 %, from 0.6614 to 0.6801 m/s².
Worked example with the values above
- Mean square times time for each task: 0.5 + 1 + 2 = 3.5 (m/s²)² h.
- Divide by 8 h and take the root: √(0.4375) = 0.6614.
- Ai(8) = k × that = 0.6614 m/s².
Assumptions and limits
- Steady weighted RMS during each task, on the same axis, with the multiplier applied once.
- T0 = 8 h reference and the UK-style weightings.
Common mistakes
- Averaging the RMS values instead of combining their squares weighted by time.
- Adding the exposures of different axes.
Statistics and uncertainty
The weighted RMS for each task is usually uncertain by ±10 % or more. The root-sum-square means the strongest task controls the result: a 10 % error in its level changes the day’s exposure by about 5 to 6 %.
Where it is used
- Assessing a working day made of several different driving tasks against action and limit values.
- Deciding which task to shorten to reduce the daily dose.
Maths you need
- Weighted RMS: frequency-weighted root mean square acceleration
- Root sum of squares: combining independent contributions