Library / Vibration exposure / VIB-11
Vibration exposure
Remaining time to an exposure value with prior dose
Time still available at a constant weighted level before the daily exposure reaches a target, once part of the day has already been used.
- Ref
- VIB-11
- Rev
- v1
- Field
- Vibration exposure
- Result
- Trem [h]
If part of the day’s exposure has already been used, Aprior(8), the time still available on an axis at a constant weighted level is Trem = T0 max(0, Atarget² − Aprior²)/(k aw)², with T0 = 8 h. Exposures add as squares, so a high earlier dose uses up the remaining time quickly. The result is zero if the target has already been reached. Take the shortest time across axes with a non-zero ongoing exposure; a zero ongoing level contributes no further dose on that axis.
Time still available at a constant weighted level before the daily exposure reaches a target, once part of the day has already been used. Exposures add as squares, so a high earlier dose uses up the remaining time quickly.
Calculator
- Time from zero prior dose (no earlier exposure)8.744 h
- Share of the target already used (by squares)18.9 %
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.
- With 0.5 m/s² already accumulated and a limit of 1.15 m/s², there are 7.091 h left at 1.1 m/s². Without the earlier dose the figure would be 8.744 h; only 18.9 % of the squared budget is used, which costs 18.9 % of the time.
- If the prior dose were 1.0 m/s², only 2.132 h would remain. A dose of 1.15 m/s² or more leaves 0 h.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (h) | Local step | Change in result |
|---|---|---|---|---|---|---|
| aw Weighted RMS acceleration | 0.1 to 3 m/s² | 0.9533 | 858 | 857 | +10% | −17.4 % |
| Atarget Target daily exposure | 0.2 to 1.5 m/s² | 0 | 13.22 | 13.22 | +10% | +25.9 % |
| Aprior Exposure already accumulated | 0 to 1.5 m/s² | 0 | 8.744 | 8.744 | +10% | −4.9 % |
| k Axis multiplier | 1 to 1.4 | 3.618 | 7.091 | 3.473 | +10% | −17.4 % |
Sweep of Weighted RMS acceleration
| Weighted RMS acceleration (m/s²) | Remaining time (h) |
|---|---|
| 0.1 | 858 |
| 0.4625 | 40.11 |
| 0.825 | 12.61 |
| 1.188 | 6.084 |
| 1.55 | 3.571 |
| 1.913 | 2.346 |
| 2.275 | 1.658 |
| 2.638 | 1.233 |
| 3 | 0.9533 |
Sweep one variable
Variables and how each one contributes
Remaining time
What the equation gives you. Everything else feeds it.
Target daily exposure
The target daily exposure value, in m/s²: for example 0.5 or 1.15. Raises the remaining time, with the square of the target minus the squared prior dose. Raising it by 10 % (to 1.265) moves the result by +25.9 %, from 7.091 to 8.927 h.
Exposure already accumulated
The daily exposure already accumulated before this period, in m/s² A(8). Lowers the remaining time; the effect grows as the prior dose approaches the target. Raising it by 0.1 m/s² (to 0.6 m/s²) moves the result by −10.3 %, from 7.091 to 6.364 h.
Axis multiplier
The axis multiplier: 1.4 for x and y, 1.0 for z. Lowers the remaining time with the square of the multiplier. Raising it by 0.1 (to 1.1) moves the result by −17.4 %, from 7.091 to 5.86 h.
Weighted RMS acceleration
The weighted RMS acceleration on the axis for the remaining period, in m/s². Lowers the remaining time with the square of the level. Raising it by 10 % (to 1.21) moves the result by −17.4 %, from 7.091 to 5.86 h.
Worked example with the values above
- Squares: Atarget² − Aprior² = 1.322 − 0.25 = 1.072.
- Divide by (k aw)² = 1.21 and multiply by 8 h.
- Trem = 7.091 h.
Assumptions and limits
- A constant weighted RMS on one axis for the remaining period, with the earlier dose measured as A(8) on the same axis.
- These are arithmetic times, not guaranteed symptom-free operating times.
Common mistakes
- Subtracting Aprior from Atarget directly instead of subtracting their squares.
- Assuming a rest period reduces the dose already accumulated.
Statistics and uncertainty
Both the earlier dose and the ongoing level carry uncertainty of ±10 % or more. Because prior dose enters as a square, the remaining time is least certain when the prior dose is close to the target, where a small error in Aprior changes the answer a lot.
Where it is used
- Planning the rest of a driver’s shift after an earlier task has built up exposure.
- Deciding how long a vehicle can continue on a rough route.
Maths you need
- Daily exposure A(8): normalised to eight hours
- Adding as squares: independent exposures combine in quadrature