Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral and vertical whole-body vibration

It is currently assumed that the same frequency weightings, derived from studies of vibration discomfort, can be used to evaluate the severity of vibration at all vibration magnitudes from the threshold of vibration perception to the vibration magnitudes associated with risks to health. This experimental study determined equivalent comfort contours for the whole-body vibration of seated subjects over the frequency range 2-315 Hz in each of the three orthogonal axes (fore-and-aft, lateral and vertical). The contours were determined at vibration magnitudes from the threshold of perception to levels associated with severe discomfort and risks to health.At frequencies greater than 10 Hz, thresholds for the perception of vertical vibration were lower than thresholds for fore-and-aft and lateral vibration. At frequencies less than 4 Hz, thresholds for vertical vibration were higher than thresholds for fore-and-aft and lateral vibration. The rate of growth of sensation with increasing vibration magnitude was highly dependent on the frequency and axis of vibration. Consequently, the shapes of the equivalent comfort contours depended on vibration magnitude. At medium and high vibration magnitudes, the equivalent comfort contours were reasonably consistent with the frequency weightings for vibration discomfort in current standards (i.e. W_b and W_d). At low vibration magnitudes, the contours indicate that relative to lower frequencies the standards underestimate sensitivity at frequencies greater than about 30 Hz. The results imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of whole-body vibration.     

Uncertainty in the evaluation of occupational exposure to whole-body vibration

Uncertainties associated with field assessments of daily exposure to whole-body vibration (WBV) have been investigated in four categories of work vehicles (fork lift trucks, wheel loaders, garbage trucks, buses) in different working conditions. A total of 50 vehicles were included in the study. WBV exposures were measured in different field conditions in marble quarries, marble laboratories, dockyards, paper mills, transportation and public utilities: over 700 individual vibration measurements were analysed to quantify relevant uncertainty components due to changes in the operators’ working methods, variations in the characteristics and conditions of the machines, changes in the characteristics of the travelling surface, uncertainty in the evaluation of exposure duration, and systematic errors due to measurement equipment. The methods used in the study to calculate measurement uncertainties are in accordance with the ISO publication “Guide to the Expression of Uncertainty in Measurement”. The study made it possible to isolate major sources of uncertainty in field assessment of daily exposures to WBV. The investigation revealed that, in all the field conditions, differences in the characteristics of the machines and/or in working cycles were the most relevant uncertainty components. The overall relative uncertainty p in WBV field assessment was in the range 14% <p<32%, whereas the relative uncertainty caused by transducer and measurement equipment in a correctly calibrated system is less than 4%.     

Assessing the discomfort of dual-axis whole-body vibration

This paper reports on an experiment designed to provide information fundamental to the prediction of the discomfort of multi-axis vibration. Seated subjects were exposed to various level and phase combinations of 3·15 Hz vertical (a_z) and 3·15 Hz lateral (a_y) sinusoidal vibration. One part of the experiment determined the levels of two single-axis vibrations (a_zanda_y separately) which produced similar discomfort to a selection of dual-axis vibrations. In another part of the experiment subjects adjusted the level of a 3·15 Hz motion in one of the two axes to produced similar discomfort to each of seven levels of the same frequency in the other axis.It was concluded that for dual-axis motions of the type investigated the discomfort is not greatly influenced by the phase between the two single-axis components producing the motion. Thus, the discomfort caused by the circular motion given by the combinations of the two sinusoidal components differing in phase by 90 degrees is similar to that caused by the translational motion produced by the same components combined with zero phase shift. The results confirm that a meaningful estimate of the relative discomfort produced by dual-axis stimuli can be determined from the levels of a single-axis reference motion appropriately adjusted by subjects. The level of a single-axis motion giving similar discomfort to each of the dual-axis conditions in the experiment was well approximated by the root-mean-square of the two levels of this single-axis motion equivalent to the two separate components of each dual-axis motion.     

Difference thresholds for intensity perception of whole-body vertical vibration: effect of frequency and magnitude

Difference thresholds for seated subjects exposed to whole-body vertical sinusoidal vibration have been determined at two vibration magnitudes [0.1 and 0.5 ms(-2) root mean square (r.m.s.)] and at two frequencies (5 and 20 Hz). For 12 subjects, difference thresholds were determined using the up-and-down transformed response method based on two-interval forced-choice tracking. At both frequencies, the difference thresholds increased by a factor of five when the magnitude of the vibration increased from 0.1 to 0.5 ms(-2) r.m.s. The median relative difference thresholds, Weber fractions (deltaI/I), expressed as percentages, were about 10% and did not differ significantly between the two vibration magnitudes or the two frequencies. It is concluded that for the conditions investigated the difference thresholds for whole-body vibration are approximately consistent with Weber's Law. A vibration magnitude will need to be reduced by more than about 10% for the change to be detectable by human subjects; vibration measurements will be required to detect reductions of less than 10%.     

Non-linear dual-axis biodynamic response to vertical whole-body vibration

Seated human subjects have been exposed to vertical whole-body vibration so as to investigate the non-linearity in their biodynamic responses and quantify the response in directions other than the direction of excitation. Twelve males were exposed to random vertical vibration in the frequency range 0.25-25 Hz at four vibration magnitudes (0.125, 0.25, 0.625, and 1.25 m s⁻² r.m.s.). The subjects sat in four sitting postures having varying foot heights so as to produce differing thigh contact with the seat (feet hanging, feet supported with maximum thigh contact, feet supported with average thigh contact, and feet supported with minimum thigh contact). Forces were measured in the vertical, fore-and-aft, and lateral directions on the seat and in the vertical direction at the footrest.The characteristic non-linear response of the human body with reducing resonance frequency at increasing vibration magnitudes was seen in all postures, but to a lesser extent with minimum thigh contact. Appreciable forces in the fore-and-aft direction also showed non-linearity, while forces in the lateral direction were low and showed no consistent trend. Forces at the feet were non-linear with a multi-resonant behaviour and were affected by the position of the legs.The decreased non-linearity with the minimum thigh contact posture suggests the tissues of the buttocks affect the non-linearity of the body more than the tissues of the thighs. The forces in the fore-and-aft direction are consistent with the body moving in two directions when exposed to vertical vibration. The non-linear behaviour of the body, and the considerable forces in the fore-aft direction should be taken into account when optimizing vibration isolation devices.     

Development of noise and vibration ride comfort criteria.

A laboratory investigation was directed at the development of criteria for the prediction of ride quality in a noise-vibration environment. The stimuli for the study consisted of octave bands of noise centered at 500 and 2000 Hz and vertical floor vibrations composed of either 5 Hz sinusoidal vibration, or random vibrations centered at 5 Hz and with a 5 Hz bandwidth. The noise stimuli were presented at A-weighted sound pressure levels ranging from ambient to 95 dB and the vibration and acceleration levels ranging from 0.02--0.13 grms. Results indicated that the total subjective discomfort response could be divided into two subjective components. One component consisted of subjective discomfort to vibration and was found to be a linear function of vibration acceleration level. The other component consisted of discomfort due to noise which varied logarithmically with noise level (power relationship). However, the magnitude of the noise discomfort component was dependent upon the level of vibration present in the combined environment. Based on the experimental results, a model of subjective discomfort that accounted for the interdependence of noise and vibration was developed. The model was then used to develop a set of criteria (constant discomfort) curves that illustrate the basic design tradeoffs available between noise and vibration.     

Subjective ratings of whole-body vibration for single- and multi-axis motion

Real-world whole-body vibration exposures comprise motion in fore-aft, lateral, and vertical directions simultaneously. There can also be components of roll, pitch, and yaw. If evaluating vibration with respect to human response, most investigators will use methods defined in ISO 2631-1. This uses frequency weightings that were originally derived from laboratory studies of the subjective responses to vibration in one direction at a time. This paper describes experiments that were carried out using a 6 degree-of-freedom vibration simulator to validate the applicability of ISO 2631-1 in multi-axis environments. Fifteen subjects were exposed to 87 stimuli comprising single-axis, dual-axis, and tri-axial random vibration, to which they were required to produce subjective ratings. It is shown that in this study the root-sum-of-squares method of summation of subjective ratings in individual axes was an adequate technique for prediction of subjective rating of multi-axis vibration. Better agreement between objective and subjective measures of vibration was obtained for unweighted vibration than for frequency weighted signals. The best agreement for this study was achieved when axis multiplying factors were set at 2.2 and 2.4 for x- and y-axis vibration, respectively. Different values could be appropriate for other postures, seats, and vibration conditions and should be determined in future studies.     

Effect of phase on discomfort caused by vertical whole-body vibration and shock--experimental investigation

An experimental study has investigated the effect of "phase" on the subjective responses of human subjects exposed to vertical whole-body vibration and shock. The stimuli were formed from two frequency components: 3 and 9 Hz for continuous vibrations and 3 and 12 Hz for shocks. The two frequency components, each having 1.0 ms(-2) peak acceleration, were combined to form various waveforms. The effects of the vibration magnitude on the discomfort caused by the input stimuli were also investigated with both the continuous vibrations and the shocks. Various objective measurements of acceleration and force at the seat surface, the effects of different frequency weightings and second and fourth power evaluations were compared with judgments of the discomfort of the stimuli. It was found that a 6% to 12% increase in magnitude produced a statistically significant increase in discomfort with both the continuous vibrations and the shocks. Judgments of discomfort caused by changes in vibration magnitude were highly correlated with all of the objective measurements used in the study. The effects on discomfort of the phase between components in the continuous vibrations were not statistically significant, as predicted using evaluation methods with a power of 2. However, small changes in discomfort were correlated with the vibration dose value (VDV) of the Wb frequency-weighted acceleration. The effect of phase between frequency components within the shocks was statistically significant, although no objective measurement method used in the study was correlated with the subjective judgments.     

A study of the subjective equivalence of noise and whole-body vibration

An experiment has been conducted to determine the subjective equivalence of 1000 Hz pure tone noise and 10 Hz sinusoidal whole-body vertical vibration. Each of 20 male subjects was exposed to all 64 possible combinations of 8 levels of noise (65 dB to 100 dB SPL) and 8 levels of vibration (0·20 m/s² r.m.s. to 1·2 m/s² r.m.s.). The noise was presented via circumaural headphones and the vibration exposure was by means of a flat hard seat. The method of constant stimuli was used. Both stimuli were presented simultaneously for a period of ten seconds and subjects were asked to indicate whether, if they were to be presented with the combination again, they would prefer that the noise or the vibration should be reduced.It was concluded that the subjects were relatively self-consistent and that the major source of variability was due to intersubject differences. The conditions for equivalence for 50% of the subjects ranged from about 0·2 m/s² r.m.s. at 69 dB to 1·2 m/s² r.m.s. at 94 dB. The results are presented in a form that enables an estimate to be made of the percentage of subjects who prefer reduced noise or vibration at any of the given combinations of the two stimuli. Further studies to extend the range and establish the general applicability of these results are suggested. It is considered that such results could be employed as a guide to reducing either the noise or the vibration in some environments.     

Inter-cycle variation in whole-body vibration exposures of operators driving track-type loader machines

Whole-body vibration (WBV) measurements are an important aspect of performing risk assessments for those exposed to vibration. A large array of variables affect the outcome of a vibration measurement and its extrapolation to a daily dose measure: e.g. variability in driving style, road surface roughness, loading. The variability in vibration emission is an inherent property for most vibrating environments and there is a risk that a vibration measurement might not be representative of the long-term exposures. It is important to acknowledge the variation inherent to WBV exposure to help understand how this variation will affect health risk assessments. A field investigation was conducted in order to characterise the variation of WBV magnitudes between work cycles of track-type loaders. Six different track-type loaders were measured at four different work sites. The vibrations were measured at the operators seat in three translational axes (x-, y-, and z-axis) in accordance with ISO 2631-1 (1997). The findings indicate the worst axis of vibration for the track-type loaders was predominantly the fore-and-aft (x-axis), for most operations. The most severe emission values were measured for machine C at site 2 (1.12 ms⁻² rms) and machine D at site 2 (1.03 ms⁻² rms). These machines would exceed the action value of the Physical Agents (Vibration) Directive within 2 h of exposure. All of the machines measured would exceed the exposure action value of the Directive within an 8 h working period. The lateral (y-axis) produced the greatest amount of variability between work cycles (coefficient of variation up to 20%). It is concluded that the inherent variability between work cycles and tasks reinforces the requirement to perform a full task analysis prior to measuring WBV exposures to ensure that all tasks are measured and that adequate cycles are measured to obtain a reliable indication of the vibration emission.     

Equal comfort contours for whole body vertical,pulsed sinusoidal vibration

A method by which subjects equate stimuli by active adjustment (the method of adjustment), has been used to construct a set of equal comfort curves for both men and women in an unrestrained sitting position, covering the frequency range of 4 to 80 Hz. Comparisons are made between the responses of men and women and the results of this study are compared with those of previous investigations where a form of comparative judgement was used. The present recommendations of the International Standards Organization on human vibration exposure are critically compared with the results of this study.     

Evaluation of human exposure to hand-transmitted vibration

The relative importance of some of the parameters instrumental in the production of Vibration Induced White Finger have been identified. Difficulties encountered in the measurement of the vibration signal are mentioned, and possible means of overcoming them discussed. The problems of setting up a damage risk criteria are looked at and reference is made to a number of proposed criteria.Particular reference has been paid to the relevance of a new draft British Standard and the way in which it deals with a number of spectra relating to different processes known to cause Vibration Induced White Finger.     

Equal sensation curves for whole-body vibration expressed as a function of driving force

Previous studies have shown that the seated human is most sensitive to whole-body vertical vibration at about 5 Hz. Similarly, the body shows an apparent mass resonance at about 5 Hz. Considering these similarities between the biomechanical and subjective responses, it was hypothesized that, at low frequencies, subjective ratings of whole-body vibration might be directly proportional to the driving force. Twelve male subjects participated in a laboratory experiment where subjects sat on a rigid seat mounted on a shaker. The magnitude of a test stimulus was adjusted such that the subjective intensity could be matched to a reference stimulus, using a modified Bruceton test protocol. The sinusoidal reference stimulus was 8-Hz vibration with a magnitude of 0.5 m/s2 rms (or 0.25 m/s2 rms for the 1-Hz test); the sinusoidal test stimuli had frequencies of 1, 2, 4, 16, and 32 Hz. Equal sensation contours in terms of seat acceleration showed data similar to those in the literature. Equal sensation contours in terms of force showed a nominally linear response at 1, 2, and 4 Hz, but an increasing sensitivity at higher frequencies. This is in agreement with a model derived from published subjective and objective fitted data.     

Effective seat-to-head transmissibility in whole-body vibration: Effects of posture and arm position

Seat-to-head transmissibility is a biomechanical measure that has been widely used for many decades to evaluate seat dynamics and human response to vibration. Traditionally, transmissibility has been used to correlate single-input or multiple-input with single-output motion; it has not been effectively used for multiple-input and multiple-output scenarios due to the complexity of dealing with the coupled motions caused by the cross-axis effect. This work presents a novel approach to use transmissibility effectively for single- and multiple-input and multiple-output whole-body vibrations. In this regard, the full transmissibility matrix is transformed into a single graph, such as those for single-input and single-output motions. Singular value decomposition and maximum distortion energy theory were used to achieve the latter goal. Seat-to-head transmissibility matrices for single-input/multiple-output in the fore-aft direction, single-input/multiple-output in the vertical direction, and multiple-input/multiple-output directions are investigated in this work. A total of ten subjects participated in this study. Discrete frequencies of 0.5-16 Hz were used for the fore-aft direction using supported and unsupported back postures. Random ride files from a dozer machine were used for the vertical and multiple-axis scenarios considering two arm postures: using the armrests or grasping the steering wheel. For single-input/multiple-output, the results showed that the proposed method was very effective in showing the frequencies where the transmissibility is mostly sensitive for the two sitting postures and two arm positions. For multiple-input/multiple-output, the results showed that the proposed effective transmissibility indicated higher values for the armrest-supported posture than for the steering-wheel-supported posture.     

Analyses of biodynamic responses of seated occupants to uncorrelated fore-aft and vertical whole-body vibration

The apparent mass and seat-to-head-transmissibility response functions of the seated human body were investigated under exposures to fore-aft (x), vertical (z), and combined fore-aft and vertical (x and z) axis whole-body vibration. The coupling effects of dual-axis vibration were investigated using two different frequency response function estimators based upon the cross- and auto-spectral densities of the response and excitation signals, denoted as H₁ and H_v estimators, respectively. The experiments were performed to measure the biodynamic responses to single and uncorrelated dual-axis vibration, and to study the effects of hands support, back support and vibration magnitude on the body interactions with the seatpan and the backrest, characterized in terms of apparent masses and the vibration transmitted to the head. The data were acquired with 9 subjects exposed to two different magnitudes of vibration applied along the individual x- and z-axis (0.25 and 0.4 m/s² rms), and along both the axis (0.28 and 0.4 m/s² rms along each axis) in the 0.5-20 Hz frequency range. The two methods resulted in identical single-axis responses but considerably different dual-axis responses. The dual-axis responses derived from the H_v estimator revealed notable effects of dual-axis vibration, as they comprised both the direct and cross-axis responses observed under single axis vibration. Such effect, termed as the coupling effect, was not evident in the dual-axis responses derived using the commonly used H₁ estimator. The results also revealed significant effects of hands and back support conditions on the coupling effects and the measured responses. The back support constrained the upper body movements and thus showed relatively weaker coupling compared to that observed in the responses without the back support. The effect of hand support was also pronounced under the fore-aft vibration. The results suggest that a better understanding of the seated human body responses to uncorrelated multi-axis whole-body vibration could be developed using the power-spectral-density based H_v estimator.     

Numerical assessment of fore-and-aft suspension performance to reduce whole-body vibration of wheel loader drivers

While driving off-road vehicles, operators are exposed to whole-body vibration acting in the fore-and-aft direction. Seat manufacturers supply products equipped with fore-and-aft suspension but only a few studies report on their performance. This work proposes a computational approach to design fore-and-aft suspensions for wheel loader seats. Field tests were conducted in a quarry to analyse the nature of vibration to which the driver was exposed. Typical input signals were recorded to be reproduced in the laboratory. Technical specifications are defined for the suspension. In order to evaluate the suspension vibration attenuation performance, a model of a sitting human body was developed and coupled to a seat model. The seat model combines the models of each suspension component. A linear two-degree-of-freedom model is used to describe the dynamic behaviour of the sitting driver. Model parameters are identified by fitting the computed apparent mass frequency response functions to the measured values. Model extensions are proposed to investigate postural effects involving variations in hands and feet positions and interaction of the driver's back with the backrest. Suspension design parameters are firstly optimized by computing the seat/man model response to sinusoidal acceleration. Four criteria including transmissibility, interaction force between the driver's back and the backrest and relative maximal displacement of the suspension are computed. A new suspension design with optimized features is proposed. Its performance is checked from calculations of the response of the seat/man model subjected to acceleration measured on the wheel loader during real work conditions. On the basis of the computed values of the SEAT factors, it is found possible to design a suspension that would increase the attenuation provided by the seat by a factor of two.     

Cross-modality determination of the subjective growth function for whole-body vertical,sinusoidal, vibration

A cross-modality matching technique with both noise and vibration stimuli has been used to establish the subjective growth of whole body vertical sinusoidal vibration intensity. The results show that in the frequency range 5–80 Hz the growth functions are of the Stevens' power law form, ψ = kφ^m where ψ represents the subjective magnitude of the stimulus and φ the objective magnitude. The value of the important growth parameter m is found to be greatly influenced by the choice of which stimulus (noise or vibration) serves as the dependent variable. The results of the study suggest that the concept of a vibration growth function should be regarded with a certain amount of caution.     

Factors affecting perception thresholds of vertical whole-body vibration in recumbent subjects: Gender and age of subjects, and vibration duration

Some factors that may affect human perception thresholds of the vertical whole-body vibrations were investigated in two laboratory experiments with recumbent subjects. In the first experiment, the effects of gender and age of subjects on perception were investigated with three groups of 12 subjects, i.e., young males, young females and old males. For continuous sinusoidal vibrations at 2, 4, 8, 16, 31.5 and 63 Hz, there were no significant differences in the perception thresholds between male and female subjects, while the thresholds of young subjects tended to be significantly lower than the thresholds of old subjects. In the second experiment, the effect of vibration duration was investigated by using sinusoidal vibrations, at the same frequencies as above, modulated by the Hanning windows with different lengths (i.e., 0.5, 1.0, 2.0 and 4.0 s) for 12 subjects. It was found that the peak acceleration at the threshold tended to decrease with increasing duration of vibration. The perception thresholds were also evaluated by the running root-mean-square (rms) acceleration and the fourth power acceleration method defined in the current standards. The differences in the threshold of the transient vibrations for different durations were less with the fourth power acceleration method. Additionally, the effect of the integration time on the threshold was investigated for the running rms acceleration and the fourth power acceleration. It was found that the integration time that yielded less differences in the threshold of vibrations for different durations depended on the frequency of vibration.