Whole Body Vibration (WBV) analysis for continuous vibration uses assessment criteria defined in the ISO2631 standard and the EEC vibration directive 2002/44/EC. These assessments are based on the processing of vibration weighted acceleration data (the data must be acceleration data in units of m/s^{2}).

The vibration weighting values are defined in ISO8041:2005. They are basically a set of filters that must be applied to the acceleration data in order to make evaluations and assessments on the effects of vibration on human beings.

The DATS software provides a human biodynamics package that includes a whole body vibration assessment report.

Vibration assessments are made in terms of various vibration quality measures such as the daily 8 hour rms level (A8), the vibration dose value (VDV) and the vibration exposure points (PE). These measures are compared against the standards and the results presented in a report document. The assessments cover health, comfort and perception.

The analysis requires tri-axial (x,y and z) data. Transducers should be oriented using the basicentric axes as illustrated in Figure 1.

Each input signal (x, y and z) is weighted (filtered) by a specific vibration weighting characteristic appropriate to the direction, position and type of assessment.

The weighting curves are defined in ISO 8041:2005 both as frequency functions and as a series of weights at third octave frequencies. The DATS software uses the frequency functions and applies them directly to the input signals.

The rms level of each of these weighted signals is then determined and is multiplied by the appropriate factor, k.

The weighting and multipliers below are applied to the individual acceleration signals. Weighting Wm is used in place of Wd and Wk for building vibrations (ISO2631-2) and Wb is used instead of Wk for fixed guide transport systems (ISO2631-4).

Position | Weighting | Health Assessment Multiplier, k | Comfort & Perception Multiplier, k | ||||||

x | y | z | x | y | z | x | y | z | |

Seated | W_{d} | W_{d} | W_{k} | 1.4 | 1.4 | 1.0 | 1.0 | 1.0 | 1.0 |

Standing | W_{d} | W_{d} | W_{d} | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |

The DATS whole body vibration assessment currently applies to the seated position. Strict ISO8041 compliance imposes a minimum sample rate of 900 samples per second. We would recommend a sample rate of 1200 samples/second. If non-strict compliance is used the minimum required sample rate is 300 samples/second.

The frequency characteristics for health, comfort and perception are principally in the range 0.5 Hz to 80Hz.

ISO2631-1 recommends a minimum sample time (signal duration) of 227 seconds, however for greater reliability a signal of duration 600 seconds or longer is considered more representative.

The final report contains all the relevant assessment information.

## Health Effects Assessment

Vibration exposure assessments are presented according to both IS02631 and EEC directive 2002/44/EC. They are made in terms of the daily eight hour rms level (A8), the vibration dose value (VDV) and Vibration Exposure Points (PE).

ISO2631-1 provides two assessment methods (B1 and B2). One of these (B1) is based on a square root of the time relationship (A8) and the other (B2) is based on a fourth root of the time relationship (VDV). ISO2631-1 gives Health Guidance Zones of ‘unknown’, ‘possible’ or ‘likely’ based upon these relationships. The boundaries between these Health Zones are shown graphically below in Figure 2.

For an exposure time, T_{e} , the B1 and B2 boundaries are given by

T_{e} < 600 seconds | T_{e} ? 600 seconds | |

B1_Upper_Limit | 6.0 | 6.0*(600/T_{e})^{1/2} |

B1_Lower_Limit | (B1_Upper_Limit)/2 | (B1_Upper_Limit)/2 |

T_{e} < 30 seconds | T_{e} ? 30 seconds | |

B2_Upper_Limit | 5.1885 | 5.1885*(30/T_{e})^{1/4} |

B2_Lower_Limit | (B2_Upper_Limit)/2 | (B2_Upper_Limit)/2 |

The analysis checks the weighted rms levels against both the B1 and B2 assessment limits and reports the health assessment risks as follows:

Weighted RMS Level | Health Risk Assessment |

Below the limit | Unknown |

Between the limits (caution zone) | Possible |

Above the limit | Likely |

Note that in the 4 hour to 8 hour exposure the caution zone is essentially the same for both B1 and B2 assessment methods.

The report also gives the additional IS02631 measures of Crest Factor, relative MVEE (Maximum Transient Vibration Value) measure and relative VDV level. To assist in determining the severity of each measure, the report also includes a calculated time to reach individual assessment limits.

The EEC assessment is also based upon the A8 daily exposure criterion and the vibration dose value (VDV). These measurements are checked against defined daily exposure action values (EAV) and daily exposure limit values (ELV).

A8 | VDV | PE | |

EAV | 0.5 | 9.1 | 100 |

ELV | 1.15 | 21.0 | 529 |

If the exposure action values are exceeded then action must be taken to reduce the levels. The exposure limit values must not be exceeded.

## Comfort Effects Assessment

The comfort criterion uses the overall total vibration, , given by

The comfort criterion is assessed accordingly to the following guidelines.

a_{T} ? 2.5 m/s^{2} | extremely uncomfortable |

1.25 < a_{T} < 2.5 m/s^{2} | very uncomfortable |

0.8 < a_{T} < 1.6 m/s^{2} | uncomfortable |

0.5 < a_{T} < 1.0 m/s^{2} | fairly uncomfortable |

0.315 < a_{T} < 0.63 m/s^{2} | a little uncomfortable |

a_{T} ? 0.315 m/s^{2} | not uncomfortable |

Note that the ranges overlap. When making the assessment the analysis works from the top down, for example a value of a_{T}=1.3 would be assessed as ‘very uncomfortable’ and not as ‘uncomfortable’.

## Perception Effects Assessment

The perception assessment is based on the largest weighted rms value of the x, y or z axis vibrations. If the largest weighted rms is a_{w} then the percentage perception is determined assuming a linear relationship

% Perception = (5000 * a_{w} ) – 25

in the range 0.01 > a_{w} > 0.02.

a_{w} < 0.01 | vibration is perceived by less than 25% of people |

a_{w} = 0.015 | vibration is perceived by 50% of people |

a_{w} > 0.2 | vibration is perceived by more than 75% of people |

#### Dr Mike Donegan

#### Latest posts by Dr Mike Donegan (see all)

- How Do I Measure Whole Body Vibration? - March 20, 2015
- Sampling and Filtering Data for ISO8041 Compliance and Human Body Vibration Data Weighting - July 10, 2014
- How To Calculate A Resultant Vector - January 12, 2012

hi,

How do I calculate the VDV(mathematical formula) for a given vehicle?

thanks,

Nikhil.

Hi Nikhil,

As far as I understand, the VDV formula defined in the standard is a general formula to be applied in any vehicle undergoing random vibrations over a time period of T seconds. The vibrations are weighted with weighting filters W, defined in the standard, to give overall frequency weighted RMS acceleration in each rotational or translational direction. Using these weighted accelerations, the total vibration value (aT) as given in the formula above, is calculated as the sum of the squares of the accelerations in each direction, multiplied by a weighting factor k, dependent on the type of weighting used. (see ISO 2631-1 clause 7,8 and 9.

With the total vibration value (aT) you can obtain an indication of the likely level of comfort that would be felt by a passenger in a vehicle.

Evert