Library / Vibration exposure / VIB-04
Vibration exposure
Combined vibration dose value of separate segments
Total vibration dose value of several non-overlapping exposures on the same axis.
- Ref
- VIB-04
- Rev
- v1
- Field
- Vibration exposure
- Result
- VDVtotal [m/s^1.75]
For non-overlapping exposures on the same axis, the doses combine by their fourth powers: VDVtotal = (ΣVDVj⁴)1/4. The fourth power makes the largest single exposure dominate, so shocks count far more than steady vibration. Units are m/s1.75. Apply an axis multiplier only where the assessment method requires it, and only once. VDV cannot in general be reconstructed exactly from the RMS and the duration. The lecture’s VDV values (9.1, 21 and 15 m/s1.75) belong to their own frameworks and are not interchangeable with the UK daily exposure A(8) limits.
Total vibration dose value of several non-overlapping exposures on the same axis. The fourth power makes the largest single exposure dominate, so shocks count far more than steady vibration.
Calculator
- Share of the fourth-power sum from the largest segment68.07 %
- Simple sum of the three doses, for comparison19 m/s^1.75
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.
- Segment doses of 6, 8 and 5 combine to 8.807, only 0.807 above the largest single dose, not the simple sum of 19. The biggest segment supplies 68.1 % of the fourth-power sum.
- Doubling the largest dose doubles the total almost exactly, while doubling the smallest barely moves it. VDV is most useful for rides with shocks and bumps.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s^1.75) | Local step | Change in result |
|---|---|---|---|---|---|---|
| VDV2 Dose value, segment 2 | 0 to 20 m/s^1.75 | 6.62 | 20.06 | 13.44 | +10% | +7.1 % |
| VDV1 Dose value, segment 1 | 0 to 20 m/s^1.75 | 8.289 | 20.15 | 11.86 | +10% | +2.41 % |
| VDV3 Dose value, segment 3 | 0 to 20 m/s^1.75 | 8.569 | 20.17 | 11.6 | +10% | +1.18 % |
Sweep of Dose value, segment 2
| Dose value, segment 2 (m/s^1.75) | Total vibration dose value (m/s^1.75) |
|---|---|
| 0 | 6.62 |
| 2.5 | 6.654 |
| 5 | 7.103 |
| 7.5 | 8.445 |
| 10 | 10.45 |
| 12.5 | 12.74 |
| 15 | 15.14 |
| 17.5 | 17.59 |
| 20 | 20.06 |
Sweep one variable
Variables and how each one contributes
Total vibration dose value
What the equation gives you. Everything else feeds it.
Dose value, segment 1
The vibration dose value of the first segment, in m/s^1.75. Raises the total, with a share that grows with the fourth power of this segment’s share. Raising it by 10 % (to 6.6) moves the result by +2.41 %, from 8.807 to 9.02 m/s^1.75.
Dose value, segment 2
The vibration dose value of the second segment, in m/s^1.75. Raises the total, with a share that grows with the fourth power of this segment’s share. Raising it by 10 % (to 8.8) moves the result by +7.1 %, from 8.807 to 9.433 m/s^1.75.
Dose value, segment 3
The vibration dose value of the third segment, in m/s^1.75. Raises the total, with a share that grows with the fourth power of this segment’s share. Raising it by 10 % (to 5.5) moves the result by +1.18 %, from 8.807 to 8.912 m/s^1.75.
Worked example with the values above
- Fourth powers: 6⁴ = 1,296, 8⁴ = 4,096, 5⁴ = 625.
- Sum: 6,017.
- VDVtotal = (sum)1/4 = 8.807 m/s1.75.
Assumptions and limits
- Non-overlapping segments on the same axis, each with a measured dose value.
- The same frequency weighting and axis for every segment.
Common mistakes
- Adding the doses directly instead of combining fourth powers.
- Treating the result as interchangeable with the UK A(8) exposure limits.
Statistics and uncertainty
VDV values from short records are sensitive to whether a rare large shock happened to fall inside the record, and can vary by ±20 % between repeated runs. Use enough runs to capture the typical worst events.
Where it is used
- Combining the dose from separate runs or road sections into one number.
- Assessing shock-dominated ride exposure.
Maths you need
- Fourth power: emphasises the largest values
- Vibration dose value: fourth-power time integral of acceleration