Abstract
In order to evaluate human exposure whole-body vibration and shock the ISO 2631 is the most common used standard. The human body presents different sensitivity of the body in different axes. ISO 2631 offers different frequency weightings and multiplying factors to predict discomfort. [DOI:10.12866/J.PIVAA.2016.19]
Keywords: International Standard, Whole-body vibration
Introduction
The International Standard ISO 2631 defines reasonable procedures for quantifying the severity of the complex vibration and shocks to which people are exposed. The International Standard ISO 2631 concerns all forms of multi-axis, multi-frequency, random, stationary and non-stationary vibration and repeated shock in the frequency range 0.5-80 Hz ISO [1997]. Annexes of the ISO 2631 provide guidance on the interpretation of the measurements.
The paper seeks to identify the aspects of the measurement, evaluation and assessment of exposures to vibration and shock. We analyze several aspects: time-dependency, crest-factor limitation, frequency weighting, number of axes, the summation methods over axes, the evaluation of discomfort and the vibration limits. In addition, the discussion evaluates the apparent inadequacies in the International Standards ISO 2631.
The International Standard ISO 2631 affirms that
The duration of measurement shall be sufficient to ensure reasonable statistical precision and to ensure that the vibration is typical of the exposures which are being assessed. The duration of measurement shall be reported.
Where complete exposure consists of period of different characteristics, separate analysis of the various periods may be required.
In contrast to the standard, common experience suggests that human responses are dependent on duration of exposure below 4 mins [Griffin, 1998, p.896].
. A note in the standard suggests that for statistical reasons the minimum measurement duration will be 227 s (assuming a lower limiting frequency of 0.5 Hz). The measurement duration will be representative of the vibration exposure.
The standard should have identified how to measure and evaluate all possible exposures, either: (i) from a measurement over the full period of exposure (however short), or, (ii) by calculating a value using one or more measurements obtained over shorter periods [Griffin, 1998, p.901].
Frequency weightings
The frequency range, considered in ISO 2631, is divided into following fields:
0.1 to 0.5 Hz for motion sickness;
0.5 to 80 Hz for health, comfort and perception.
ISO 2631 suggests that vibration is measured in the three translational axes on the seat pan. The frequency weightings and multiplying factors are defined in ISO 2631 Table 1 for axes x, y and z and for different locations. The ISO defines contours for each axis over the 1-80 Hz frequency range. One contour is defined limits for z-axis vibration and another one is defined limits for both x- and y-axis vibration.
We can remark the following aspects:
The weighting W_{k }indicates greatest sensitivity to vibration acceleration between 4 and 8 Hz.
The acceleration limits increases in proportion to frequency at frequencies above 8 Hz. The z-axis acceleration limits advances in inverse proportion to the square root of the frequency below 4 Hz.
The weighting W_{d }gives greatest sensitivity to vibration acceleration between 0.63 and 2.0 Hz. The acceleration limits increases in proportion to frequency from 2-80 Hz.
The weighting W_{c }attributes greatest sensitivity to vibration acceleration between 1.0 and 6.3 Hz.
Axes vibration
International Standard ISO 2631 requires the measurement of vibration in three translational axes on the supporting seat. ISO 2631 does not propose rules about the rotational vibration of the seat, on the translational vibration at the back or at the feet. The assessments, evaluated by International Standard 2631, is based on the axis giving the greatest frequency-weighted acceleration on the seat pan. If no dominant axis of vibration exists, ISO 2631 requires the use of multiplying factors for the horizontal axes. The x- and y-axes frequency-weighted values have to be multiplied by 1.4 for the comparison with the z-axis frequency-weighted value (Table 1).
The value of acceleration should be the root-sums-of-squares of the weighted values obtained in each axis. The purpose is to develop the comparison between the vector sums and acceleration of different motions. The text of ISO 2631 is ambiguous because the vector sum should be used to compare measurements with the exposure limits for health and safety, indicated in the International Standard ISO 2631.
International Standard ISO 2631 affirms that
The vibration total value or vector sum have also been proposed for evaluation with respect to health and safety if no dominant axis of vibration exists.
The evaluations for health and safety is developed by the comparison between acceleration of dominant axis and acceleration of the exposure limits.
If measurements in the x- and y-axes are multiplied by a factor of 1.4, measurements in the different axes could be compared with each other. However, the International Standard ISO 2631 does not offer any notation or justification about the multiplying factor 1.4.
The International Standard ISO 2631, in Section 7.2.3, addresses partial attention to x-axis on backrest:
… Measurements in the x-axis on the backrest … are encouraged. However, … not included in the assessment of the vibration severity …
On one hand we are encouraged to acquire accelerations in the x-axis on the backrest, on the other hand the measurements are not considered in the assessment of the vibration.
The International Standard ISO 2631 is equivocal on the axes to be assessed, how they may be combined and what relationship should be chosen. In the Section 7.2.2 the International Standard ISO 2631 asseverates that
…. The assessment of the effect of a vibration on health shall be made independently along each axis. The assessment of the vibration shall be made with respect to the highest frequency-weighted acceleration determined in any axis on the seat pan…..
In Section 7.2.2 Note, the International Standard adds:
… When vibration in two or more axes is comparable, the vector sum is sometimes used to estimate health risk…..
The term sometimes can not be a criterion to evaluate human exposure to whole-body vibration.
Vibration evaluation
The standard proposes a basic evaluation method or the calculation of the r.m.s. value. The basic evaluation method is suitable for vibration with crest factors below or equal to 9.
… If the basic evaluation method may underestimate the effects of vibration (high crest factors, occasional shocks, transient vibration, …..
the standard defines the following additional or alternative methods: the running r.m.s. method and the fourth power vibration dose method.
a_{w} (t) is the instantaneous frequency weighted acceleration;
t is the integration time for running averaging;
t is the time integration variable;
t_{0} is the time of observation.
The exponential averaging is the the following relation of running r.m.s. at t=t_{0}
The exponential function Eq.2 of time, of a specified time constant, weights the square of the instantaneous weighted accelerations. The standard affirms that the difference between the two methods, defined by Eqs.1-2, may be up to 30 % for some motions. The standard recommends the use of the integration time t=1 s. If other integration times are used to calculate the running r.m.s. values, different values of running r.m.s. can be obtained. It follows that the vibration total value of weighted r.m.s. acceleration, determined from vibration in orthogonal coordinates is calculated by following relation where
a_{wx}, a_{wy} and a_{wz} are the weighted r.m.s. accelerations with respect to the orthogonal axes x, y, z;
k_{x}, k_{y} and k_{z} are multiplying factors.
Vibration dose values. The VDV gives a measure of the total exposure to vibration, taking account of the magnitude, frequency and exposure duration. VDVs are estimated using apposite frequency weightings and axis multiplying factors: where a_{w}(t) is the frequency-weighted acceleration time history, in m/s^{2}, at the input to the body; T is the duration of measurement.
According to International Standard ISO 2631, the total vibration dose value VDV_{total} is the fourth root of the sum of the fourth powers of the VDVs in each axis of vibration. VDV_{total} is calculated over the measurement period, t seconds (e.g., 60 s)
where
VDV_{xs }is vibration dose value computed in the x-axis on the seat;
VDV_{ys} is vibration dose value computed in the y-axis on the seat;
VDV_{zs} is vibration dose value computed in the z-axis on the seat.
Estimated vibration dose value. The vibration dose value can be calculated from the r.m.s. acceleration using the estimated vibration dose value, eVDV, where a_{rms} is the frequency-weighted r.m.s. value, and t is the duration (in s). There are two important remarks: ……
…This estimate is only valid for signals with low crest factors (i.e., < 6) [Mansfield, 2005, p.129].
….. The empirically determined correction factor of 1.4 is said to be obtained from typical vibration environments having low crest factors (below about 6.0) but, of course, will not work when the crest factor is high (or very low). The standard says that where there is any doubt or difference between true and estimated vibration dose values the true values according to equation 4 should be used [Griffin, 2004, p.897].
Maximum transient vibration value. A quantity called the maximum transient vibration value, MTVV is defined as the highest magnitude of the running r.m.s. . The section 6.3.3 of the standard affirms that:
Experience suggests that the use of the additional methods will be important for the judgement of the effects of vibration on human beings when the following ratios are exceeded (depending on which additional method is being used) for evaluating health or comfort:
The basic evaluation method shall be used for the evaluation of the vibration. In cases where one of the additional methods is also used, both the basic evaluation value and the additional value shall be reported.
Criteria in time domain for evaluating duration in exceed
The health guidance zones, quoted in International Standard ISO 2631, are represented in Fig.\ref{Fig:Comparison between action level and exposure limit}. Two zones are provided as they are derived from r.m.s. and VDV approaches.
The standard states that
For exposures below the zone, health effects have not been clearly documented and/or objectively observed; in the zone, caution with respect to potential health risks is indicated and above the zone health risks are likely.
Dashed and solid red lines are the rating line that define the phase of the exposure level of health warning from 2.8 ms^{-2} to 5.6 ms^{-2}. In International Standard ISO 2631 the maximum exposure is more than 10 minutes as defined by following equation:
with t_{0} =10 min and t exposure time. Eq.8 approximately corresponds to the so-called fatigue-decreased proficiency limit in the old ISO 2631 for exposures between 1 and 10 minutes [Griffin, 1998, p.904].
Dashed and solid blue lines represent the VDV assessment and define warning level between 8.5 ms^{-1.75} (lower VDV level) and 17 ms^{-1.75} (upper VDV level). An estimated vibration dose values eVDV has been used
The estimated vibration dose values correspond to 8.5 ms^{-1.75} (lower VDV level) and 17 ms^{-1.75} (upper VDV level). VDV assessment 17 ms^{-1.75} is similar to time-dependency for z-axis, proposed in International Standard ISO 2631 (1974, 1978, 1985a-c).
Above the top line health risk is likely. We distinguish caution with respect to health risks between upper and lower VDV level. Below the bottom line health effects are not been observed.
The zones coincide for duration of about 4 to 8 h (Fig.2). The standard states that
…. The health guidance caution zones for Eqs.8-9 are the same for duration from 4 h to 8 h for which most occupational observation exist….
In the caution zone, potential health risks are very likely. The standard attests that an increment of vibration dose and of risk can be provoked by two factors: the increased duration, within the working day or daily over years, and the increased vibration intensity. Periods of rest can decrease the risk.
Criteria in frequency domain for evaluating duration in exceed
International Standard ISO 2631 proposes different methods to evaluate comfort for seat vibration. The guide ISO 2631 introduces limits of exposure to vertical and lateral vibration by following criteria:
We consider the 1 min and 24 exposure limits, fatigue-decreased proficiency boundaries and reduced comfort boundaries (Fig. 3). If we consider the disturbance of activities, the fatigue decreased proficiency limits would be recommended for drivers and operators, the reduced-comfort boundaries for passengers.
The vibration limit appropriate to a system is not entirely determined by the frequency, magnitude, direction and duration of the vibration. The vibration limit for preserving performance must depend on the activities to be performed. The limit for preserving health depends on degree of allowable risk.
The relationship of limits corresponding to the three criteria for any vibration frequency, axis or duration is the following relation
Comfort reactions to vibration environments
The International Standard ISO 2631 propose 5 vibration environments and 5 comfort reactions. The International Standard ISO 2631 affirms that
…. Acceptable values of vibration magnitude for comfort depend on many factors which vary with each application. Therefore, a limit is not defined in this part of ISO 2631. The following values give approximate indications of likely reactions to various magnitudes of overall vibration total values in public transport.
…. However, as stated before, the reactions at various magnitudes depend on passengers expectations with regard to trip duration and the type of activities passengers expect to accomplish (e.g. reading, eating, writing, etc.) and many other factors.
The scale, proposed in International Standard ISO 2631, evaluates the discomfort for seat vibration (Table \ref{tab:Comfort reactions to vibration environments}), but the ISO 2631 declares that there is no definitive demonstration to sustain a universal time dependence of vibration effects on comfort.
The International Standard ISO 2631 considers continued exposure to vibration and it affirms that
…. It generally takes several years for health changes caused by whole-body vibration to occur. It is therefore important that exposure measurements are representative of the whole exposure period.
Discussion
The performance of a driver might be compromised by vibrations at seat backrest, at head and at footrests.
….. If a person is exposed to a sinusoidal signal that gradually increases in frequency (swept sine), then different parts of the body will resonate in turn. Many body parts will resonate at about 5 Hz (e.g., the head and abdomen,…. ) [Mansfield, 2005, p.170]
The International Standard ISO 2631 encourages the measurement of fore-and-aft vibration on a backrest. The measurement on seat backrest, on head and on footrests are not included in the assessment of vibration severity. A complete frequency weighting should provide a model of the response of a person to all kinds of vibration.
The International Standard ISO 2631 warns against using the zones for shorter durations. If exposure time is between about 5 and 30 min (Fig.\ref{Fig:Comparison between action level and exposure limit}), it is possible to exceed the limits of the zone according to one method and not reach the zone for the other [Mansfield, 2005, p.170].
With reference to Fig.\ref{Fig:Comparison between action level and exposure limit}, a doubling of r.m.s. acceleration magnitude originates a reduction of exposure time:
There are doubts about the use of MTVV [Griffin, 2004, p.905].
…. ISO 2631 (1997) does not indicate what measures should be compared against the r.m.s. health guidance caution zone. Users might use either of the two caution zones to assess the significance of overall r.m.s. measures. Vibration dose values will normally be compared with the vibration dose value caution zone. It is not clear how MTVV values can be compared with either health guidance caution zone without yielding unlikely conclusions.
Criteria in frequency domain are articulated in relation to measured effective accelerations (r.m.s.). Three different levels of human discomfort are proposed:
Figure 4 shows the flow chart the measurement, evaluation and assessment method defined in ISO 2631. The flow chart remarks the complex procedure for International Standard ISO 2631.
Conclusions
The International Standard ISO 2631 proposes methods to analyze the complex reality of human responses to whole-body vibration. A series of frequency weightings are defined in the International Standard ISO 2631. It is used to quantify horizontal and vertical vibration with respect to its effects on activities. Weighted values of r.m.s. acceleration in the x- y- and z-axes determined with respect to the fatigue-decreased proficiency limits in ISO 2631. The analysis is restricted to quantifying vibration between 1 and 80 Hz. Some aspects of International Standard ISO 2631 are not satisfactory.
References
Mechanical vibration and shock evaluation of human exposure to whole-body vibration. part 1: General requirements. iso 2631-1., 1997.
M. Griffin. A comparison of standadized methods for predicting the hazards of wholebody vibration and repeated shocks. Journal of Sound and Vibration, 215(4):893914, 1998.
M. Griffin. Elsevier, 2004. ISBN 0123030412.
N. Mansfield. CRC Press, 2005. ISBN 9780415282390.
Abstract
Vibration serviceability of footbridges under human induced dynamic loading attracted a lot of attention of the research community. It is proposed an analysis of dynamic load factors proposed in the scientific literature. [DOI:10.12866/J.PIVAA.2016.20]
Keywords: Pedestrian action, Force Model, Serviceability, Cycle loading
Introduction
The pedestrian-induced load and the response of pedestrians to vibration is governed by changeability and depends on biological, mechanical and psychological parameters. The main effects of this changeability are that (i) each pedestrian within a group will induce different load and each pedestrian reacts differently to a vibratory environment (inter-subject variability); (ii) small variations in the walking pattern of each pedestrian (intra-subject variability) causes narrow-band random process rather than a perfectly periodic load and (iii) the pedestrian walking force is connected to accelerating and decelerating of the mass of human body (intra-subject variability). In addition, the intra-subject variability can cause the same pedestrian to operate differently in two nominally equal circumstances. In this research it is proposed an analysis of dynamic load factors proposed in the scientific literature.
Review of the published data on modelling of human walking
Bachmann and Ammann reported the first five harmonics for vertical walking force and also harmonics for the lateral and longitudinal direction. Bachmann and Ammann declared that the first and third harmonics of the lateral and the first and second harmonics of the longitudinal force are dominant. It is interesting that in the latter case some sub-harmonics appeared. Bachmann and Ammann explained it as a consequence of more pronounced footfall on one side [Bachmann et al., 1977]. The response can be, for vertical direction, divided into five harmonics: 2, 4, 6, 8 and 10 Hz. The first harmonic corresponds to the primary walking frequency. The five harmonics of the walking load offer the higher percentage contribution of static weight (Fig.1). Bachmann and Ammann considered the walking load along lateral (Fig.2) and along longitudinal direction (Fig.3). The response can be divided into two harmonics (2, 4 Hz) and three sub-harmonics (1, 3 and 5 Hz).
The relationship between α_{n} and step frequency was studied for walking rates from 1.0 to 3.0 Hz [Rainer et al., 1988]. Figure 4 shows that for walking, the dynamic load factor of the first harmonic α_{1} is the largest, at 2.4 Hz, and reaches an averaged maximum of 0.52. Magnitude of the dynamic force, induced by different people, is also an inter-subject variable and depends on walking frequency.
The results of first harmonic data [Kerr, 1998] had a trend that tended to follow a third order polynomial function:
where f_{p} is pacing frequency in Hz. The maximum value of the third order polynomial function assumed 0.48 and it was reached at about 2.4 Hz. Second harmonic values were considerably lower than the first harmonic. The average amplitude of second harmonic data was approximately 0.07. The remaining third and fourth harmonic values were even smaller (< 0.06).
Pernica evaluated the variation of the dynamic load factors respect to footstep rate and group size [Pernica, 1990]. Pernica proposed load factors suitable for floors subjected to pedestrian movements. Pernica evaluated the relationship between dynamic load factors and group size (Fig.6-7). The addition of people to the group reduced overall group coordination in performing the activity on the platform. The partecipants found more difficult to maintain the walking rate and the distance between themselves and other group members. If partecipants wish to walk in unison with and be part of a large group of walkers, members are forced to adjust their walking characteristics. In the range 0-10 Hz, maximum value of α_{1} decreased with group size, falling from 0.56 for one person to 0.46 for two people and to 0.36 for four people. Load factors α_{2} increased rapidly with footstep rate for one person. Load factors α_{2} increased slightly with footstep rate for four people. The footstep rate of the maximum value of α_{2} changed location with group size, moving from location above 3.0 Hz for one and two people to below 3.0 Hz for four people. Dynamic load factors for the third and fourth harmonics were relatively constant over the measured frequency range irrespective of group size. Amplitudes of the two harmonics dropped slightly as group size increased. The third harmonic fell from about 0.07 for one and two people to 0.04 for four people. The fourth harmonic from 0.05 for one and two people to 0.02 for four people.
Periodic Load Models
Periodic load models are based on an assumption that all pedestrians produce exactly the same force and that the pedestrian load is periodic force [Kala et al., 2012]. It is also assumed that the force produced by a single pedestrian is constant in time. Dynamic loading F(t), caused by a moving pedestrian can be represented as a Fourier series in which the fundamental harmonic f presents a frequency equal to the pacing rate:
where G is the pedestrian’s weight, α_{n} is the load factor of the nth harmonic, f is the frequency of the force, j_{n } is the phase shift of the nth harmonic, n is the number of the harmonic and N is the total number of contributing harmonics. The dynamic component of the activity force in Eq.\eqref{fouriermodel1} is represented by the summation term, which is a Fourier series with Fourier coefficients α_{n} , at the discrete frequencies (n f). The Fourier coefficients α_{n} and the footstep frequency f represent the key parameters in Eq.\eqref{fouriermodel1}, that describe the dynamic forces. The Fourier coefficients α_{n} , called dynamic load factors (DLFs), are defined as the ratio of the force amplitude of each harmonic to the weight of the person.
Discussion
A person will never produce exactly the same force-time history during repeated experiments. In the case of two persons it is even more so. In the case of a single person, the force is assumed to be periodic, but the distribution of person’s weight, pacing rate and different postures can provoke random effects [Setra, 2006]. In the case of several people, the probability distribution of time delay between people who perform a particular activity can be added. Therefore, inter-subject variability and intra-subject variability influence the trend of DLFs [Zivanovic, 2006].
As before mentioned, a group of design procedures is based on an assumption that human-induced forces are perfectly periodic loads. Therefore human-induced forces can be decomposed into harmonics by means of Fourier decomposition as given in Eq.\eqref{fouriermodel1}. Under this assumptions, only a single force harmonic can excite a resonance frequency of a footbridge. Usually, the first three or four excitation harmonics can provoke resonant. So serviceability should be checked in footbridges with fundamental natural frequencies f from 0 up to 5 Hz.
There are some sub-harmonics appearing at frequencies between the main harmonics. It has been widely accepted in the literature that the fundamental period of the walking load is equal to the time required to make two successive steps, rather than one. In this way, the fundamental period is actually approximately two times higher than when analyzing one step only. Consequently the fundamental frequency of the walking force is approximately two times lower than that for a single step. The reason for this aspect is that walking process for two legs can be described by slightly different parameters (walking frequency/period and step length). It is deduced that one leg is stronger than another.
Respect to vertical component, the horizontal component of the load presents less intensity. However, horizontal component can be a source of vibrations and it cannot be neglected. People are very sensitive to being moved sideways. The transverse component corresponds to changing from one foot to the other. The longitudinal component is mainly linked to the frequency of walking. When walking, transverse component occurs at a frequency of half that of the frequency of walking (1 [Hz] for f_{walking} = 2 [Hz]).
A comparison among Millenium bridge, steel bridges, concrete deck bridges, composite bridges, wooden bridges shows the lateral natural frequencies as a function of span (Fig.8) in frequency field 0-4.5 Hz. A comparison between concrete deck bridges and steel bridges illustrates vertical natural frequencies of bridges (Fig.9) in frequency field 0-8.0 Hz [Dallard et al., 2001].
In both vertical and horizontal directions, there are four frequency ranges, corresponding to a decreasing risk of resonance. Table 1 defines the frequency ranges for vertical vibrations and for longitudinal horizontal vibrations. Table 2 concerns transverse horizontal vibrations.
Critical range is related to first harmonic. The dominant contribution of the first harmonic leads to the following critical range for natural frequencies f_{i} : for vertical and longitudinal vibrations 1.7 [Hz] < f_{i} < 2.1 [Hz]; for lateral vibrations 0.5[Hz] < f_{i} < 1.1 [Hz]. There are situations in which natural frequencies lie in an interval susceptible of excitation by the second harmonic of pedestrian excitation. Under these circumstances, if it is considered relevant to investigate the effects associated with the second harmonic of pedestrian loads, the critical range becomes for vertical and longitudinal vibrations: 1.25 [Hz] < f_{i} < 4.6 [Hz]. Footbridges, which have natural frequencies f_{i} in the critical range, should be object of a dynamic assessment to pedestrian excitation. Lateral vibrations are not effected by the 2nd harmonic of pedestrian loads. Table 3 summarizes DLFs for single person force models after different authors in vertical walking.
Conclusions
Several modelling process proposed a walking force models moving across the bridge. A considerable improvement of design procedures was obtained with model of walking force that considered the effect of DLFs, dependent on step frequency, harmonic and duration time, limited by the length of the bridge.
References
H. Bachmann and W. Ammann. Vibration Problems in Structures. 1977. ISBN 3-7643-5148-9.
P. Charles and H. Wasoodev. Footbridges Assessment of vibrational behaviour of footbridges under pedestrian loading. Technical report, Setra, October 2006.
P. Dallard, T. Fitzpatrick, A. Flint, A. Low, R. Smith, M. Willford, and M. Roche. London Millenium Bridge: Pedestrian-Induced Lateral Vibration. 6:412–417, 2001.
J. Kala, V. Salajka, and P. Hradil. Dynamic Action Induced By Walking Pedestrian. World Academy of Science, Engineering and Technology International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering V, 6(10):827–830, 2012.
S. Kerr. Human induced loading on staircases. PhD thesis, University of London, 1998.
G. Pernica. Dynamic load factors for pedestrian movements and rhythmic exercises. Canadian Acoustics / Acoustique Canadienne, 18(2):3–18, 1990.
J. Rainer, G. Pernica, and D. Allen. Dynamic loading and response of footbridges. Canadian Journal of Civil Engineering, 15(1):66–71, 1988.
S. Zivanovic. Probability-Based Estimation of Vibration for Pedestrian Structures due to Walking. Master’s thesis, February 2006.
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