Library / Vibration exposure / VIB-07
Vibration exposure
Partial daily vibration exposure on one axis
Contribution of one task to the eight-hour daily whole-body vibration exposure on one axis, from the axis multiplier, the weighted RMS level and the time spent.
- Ref
- VIB-07
- Rev
- v1
- Field
- Vibration exposure
- Result
- Aij(8) [m/s²]
The daily exposure A(8) normalises a day’s vibration to an eight-hour reference T0 = 8 h. The contribution of one task j on axis i is Aij(8) = ki aw,ij √(Tj/T0), with ki the axis multiplier (1.4 for x and y, 1.0 for z in the usual health assessment) and aw,ij the weighted RMS (Wd or Wk weighting). A(8) includes the actual duration through the dose accumulation; normalising to eight hours does not erase a long exposure. Apply the axis multiplier once only.
Contribution of one task to the eight-hour daily whole-body vibration exposure on one axis, from the axis multiplier, the weighted RMS level and the time spent. Doubling the time raises it by only the square root of two.
Calculator
- Time for the same axis at this level to reach 0.5 m/s²1.653 h
- Time to reach 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.
- The lecture’s z-axis case, 1.1 m/s² for 0.5 h with k = 1, adds 0.275 m/s² to the day’s exposure; the x and y cases of 0.30 and 0.15 m/s² with k = 1.4 add 0.105 and 0.0525 m/s². The z axis is the largest.
- At this level the exposure would reach 0.5 m/s² after 1.653 h and the limit of 1.15 m/s² after 8.744 h. These are exposure arithmetic, not guaranteed symptom-free operating times.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Tj Time on the task | 0.1 to 8 h | 0.123 | 1.1 | 0.977 | +10% | +4.88 % |
| aw,ij Weighted RMS acceleration | 0.1 to 3 m/s² | 0.025 | 0.75 | 0.725 | +10% | +10 % |
| ki Axis multiplier (1.4 for x and y, 1.0 for z) | 1 to 1.4 | 0.275 | 0.385 | 0.11 | +10% | +10 % |
Sweep of Time on the task
| Time on the task (h) | Partial exposure (m/s²) |
|---|---|
| 0.1 | 0.123 |
| 1.088 | 0.4056 |
| 2.075 | 0.5602 |
| 3.063 | 0.6806 |
| 4.05 | 0.7827 |
| 5.037 | 0.8729 |
| 6.025 | 0.9546 |
| 7.013 | 1.03 |
| 8 | 1.1 |
Sweep one variable
Variables and how each one contributes
Partial exposure
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 in the usual whole-body assessment. Raises the partial exposure in proportion. Raising it by 0.1 (to 1.1) moves the result by +10 %, from 0.275 to 0.3025 m/s².
Weighted RMS acceleration
The weighted RMS acceleration for this task and axis, in m/s². Raises the partial exposure in proportion. Raising it by 10 % (to 1.21) moves the result by +10 %, from 0.275 to 0.3025 m/s².
Time on the task
The time spent on this task, in hours. Raises the partial exposure with the square root of time: doubling the time raises it by about 41 %. 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
- Time ratio: Tj/T0 = 0.5/8 = 0.0625, with square root 0.25.
- Multiply the level and multiplier: k a = 1 × 1.1 = 1.1 m/s².
- Aij(8) = 1.1 × 0.25 = 0.275 m/s².
Assumptions and limits
- A steady weighted RMS level on one axis for the duration of the task.
- The multiplier and weighting suit the assessment method in use.
Common mistakes
- Applying the axis multiplier twice, once in the RMS and once in the formula.
- Reading the result as a pass or fail without combining all tasks and axes.
Statistics and uncertainty
The weighted RMS is typically uncertain by ±10 %, so the exposure is too. Because time enters under a square root, a 20 % error in duration gives only a 10 % error in exposure.
Where it is used
- Working out how much of the daily exposure budget a single task uses up.
- Planning task durations for a shift.
Maths you need
- Weighted RMS: frequency-weighted root mean square acceleration
- Square roots: time enters as √(T/8)