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Whole-body vibration: A comparison of different methods for the evaluation of mechanical shocks
International Journal of Industrial Ergonomics. 7 (1991) 41-52 Elsevier
41
Whole-body vibration: A comparison of different methods for the evaluation of mechanical shocks Bengt-O. WikstrSm, Anders Kjellberg and Margareta Dallner National Institute for Occupational Health, S-171 84, Solna, Sweden
(Received February 28, 1990; accepted in revised form August 16, 1990)
Abstract Two studies were performed in order to compare different technical methods for assessing the effect of mechanical shocks on discomfort. The studies were carried out in the field with a forest machine and a harbour tractor. These were driven by professional drivers on test tracks consisting of different sections with obstacles producing shocks. The discomfort of each section was rated with magnitude estimation. Vibrations on the seat were recorded. Each vibration record was analysed with different technical assessment methods. These included acceleration peak values, time-mean values, dose values, impulse values, acceleration response and displacement response methods. Regression analyses were applied to the drivers' ratings and each of the assessment methods to find the strength of the relationship. The study showed that a dose value based on an Rms or Rmq calculation gave the best prediction of discomfort from the shocks. The integration time should be long enough (several seconds) to let significant parts of the shock give contribution to the dose value. In many vehicles and working-machines shocks occur, which can be harmful to the driver. Knowledge of how to evaluate these shocks should therefore be of interest for manufacturers of vehicles and also for health service groups in industry. Relevance to industry In many vehicles and working-machines shocks occur, which can be harmful to the driver. Knowledge of how to evaluate these shocks should therefore be of interest for manufacturers of vehicles and also for health service groups in industry. Keywords Whole-body vibration, shock, technical evaluation methods, discomfort, field-study.
Introduction Several m e t h o d s have b e e n used over the years for the e v a l u a t i o n of discomfort from w h o l e - b o d y v i b r a t i o n (ISO, 1974; VDI, 1963). Miwa's work formed the basis of the i n t e r n a t i o n a l s t a n d a r d , ISO 2631 (Miwa, 1967). I n the s t a n d a r d the ' s i n g l e - a x i s 1 / 3 - o c t a v e b a n d a n a l y s i s ' is the favoured method, b u t other m e t h o d s are also included as secondary, like the 'single-axis frequency weighted r m s - v a l u e ' a n d ' t h e sum of vector frequency weighted rms-value'. T h e s t a n d a r d has been used b y researchers a n d others, e.g. health executive organizations, for the last fifteen years. 0169-1936/91/$03.50 © 1991 - Elsevier Science Publishers B.V.
Several l a b o r a t o r y studies a n d some field studies have shown that it works r e a s o n a b l y well for the assessment of discomfort d u r i n g exposure to stat i o n a r y v i b r a t i o n s (Shoenberger, 1978; H a n s s o n a n d Wikstr~Sm, 1979; G r i f f i n et al., 1982). However, its applicability to v i b r a t i o n s which c o n t a i n shocks has repeatedly b e e n q u e s t i o n e d b y several parties a n d has been of m a j o r c o n c e r n in the o n - g o i n g revision of ISO 2631 (ISO, 1988). This p a p e r reports a n investigation designed to evaluate which m e t h o d s should be used for the e v a l u a t i o n of discomfort in the driver's work env i r o n m e n t from v i b r a t i o n c o n t a i n i n g shocks. T h e investigation was set up as two e x p e r i m e n t a l stud-
42
B.-O. Wikstrrm et al. / Whole-body vibration
ies in the field with ordinary machines and experienced drivers. It was judged important to make the discomfort assessment under realistic driving conditions since many possibly critical aspects of the driver's situation are more or less impossible to simulate in the laboratory. To lessen the risk that the conclusions become valid for only a special class of shocks, two studies with different types of vehicles were performed. Parallel to the present investigation, a laboratory investigation was conducted with the same aim. Results from this study are presented in Sp~ng et al. (1985). The comparison was based on three assessment methods of shocks discussed during the last few years: response measures especially the Shock Response Spectrum analysis, dose measures especially the Vibration Dose Value and impulse methods especially the Impulse Extended Dose. Time-mean measures, e.g. the Rms value, as well as peak measures, e.g. the simple Peak value, were also included.
Methods
Two studies were performed, the Harbour Study and the Forest Study. In both studies experienced drivers drove without stopping three times around a closed test track, which contained a number of obstacles producing shocks of different intensities. The driver rated the discomfort at the end of each shock. Vibrations on the seat were recorded on tape and analyzed with different assessment methods. The power of the different technical methods of analysis as predictors of the discomfort ratings was determined by regression analyses.
Fig. 1. The terminal tractor used in the Harbour study. without load on a closed track 390 meters long (figure 1). The seat, which had a maximum spring displacement of 100 mm, was adjusted to minimize the risk of bottoming. Fourteen obstacles were placed at even distances on the track. They were made by steel-plates and wooden planks with heights between 10-70 mm. All produced shocks of about 3.5 s duration. Both tyres passed the obstacle at the same time. The speed was held constant at 70 m / m i n . The drivers gave their ratings over the radio communication system. For every driver measurements of 42 shocks were made and in total, data from 630 shocks were collected. Test procedure - the Forest S t u d y
A large forwarder (Kockum 85-35), with a conventional springed seat (BeGe Nord Forest),
Subjects Fifteen drivers participated in the Harbour Study. Their mean age was 37.9 years and they had 4.5 to 20 ( M = 8.2) years of experience as industrial truck drivers. The eleven drivers in the Forest Study had 5 to 30 ( M = 16.7) years of experience as forest machine drivers and their mean age was 41.4 years. Test procedure - the H a r b o u r S t u d y
A terminal tractor (BoUn~is PT20), with a conventional springed seat (BeGe Pluto), was driven
Fig. 2. The forwarder used in the Forest study.
43
B.-O. WikstriJm et aL / Whole-body t'ibration
placed in the X-, Y- and Z-directions (see ISO 2631) on a flat, round aluminium plate (diam. = 200 mm), upon which the driver sat. The signals were recorded on a PCM tape-recorder (Stellavox, Johne & Reilhofer Mini-Din). The shock portions of the tape-recorded vibration were selected with, edited by and stored on a PC. Anti-aliasing was made with 48 d B / o c t a v e filters with a cut-off frequency of 80 Hz. Analyses were performed with an IBM P C / A T connected via a Gpib-bus to a two-channel FFT-analyzer (Briiel & Kjaer 2032), which was used to simulate the weighting filters and the response functions demanded by the analysis. The different analyses were performed in the FFT-analyzer using an internal processing language SPL. The methods of analysis described below resulted in 52 measures in each direction for each shock.
was driven without load on a track in forest terrain 453 meters long (figure 2). The seat, which had a m a x i m u m spring deflection of 100 mm, was adjusted to minimize the risk of bottoming. Of the naturally occurring obstacles fifteen were chosen. These were smooth rocks with a height between 0.2-0.6 m and one pit with a depth of 0.5 m. Thirteen of the obstacles gave shocks lasting 4 - 9 s; two gave series of shocks lasting 12 s and 16 s, respectively. The machine was driven with a constant speed of 45 m / m i n on the first rougher part of the track and 63 m / r a i n on the smoother second part. The test procedure was the same as in the Harbour Study except that the test leader stood behind the driver and noted the ratings. Data from 495 shocks were collected in this study.
Subjective ratings of discomfort
Description of the technical measures used for evaluation
The driver made magnitude estimations of the ride discomfort basing the rating on the whole shock event. The first shock of a lap served as reference shock and was always given a rating of 10. If the second shock event was experienced as twice as discomforting as the first, it got a rating of 20, if half as discomforting a rating of 5 and so on. The start of the three laps was done at different obstacles evenly distributed over the track. Therefore the reference shock and the subjective scale varied between the laps. The order between starting points was counterbalanced.
Separate analyses were made in the X, Y and Z directions for all measures. Four different types of analysis were used (see below). For the Peak-value measures, the Weighting measures and the Impulse measures the signal was weighted with three different filters (figure 3): linear weighting (A), weighting according to ISO 2631 (B) and a weighting proposed by Griffin (C) in the new draft proposal of ISO 2631 (ISO, 1988) with the background presented in Corbridge and Griffin (1986). In addition to this, in the Forest Study a weighting filter for the Y direction was tested, which was equal to the ISO-filter except for a breakpoint at 4 Hz instead of at 2 Hz (D).
Equipment Vibration measurements were accomplished with three accelerometers (Endevco 2265-20)
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Fig. 3. Characteristics of the weighting filters in the X-. Y- and Z-directions.
4
8
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64
Hz
44
B.-0. WikstriSrn et a L / Whole-body vibration
Peak-value measures
Response measures
The maximum positive (Posmax) and negative acceleration values ( N e g m a x ) and the sum of their absolute values (Posmax + Negmax) were calculated for the signals weighted with the different filters (A, B, C, D).
The analyses were performed in two ways. In the first method the acceleration response of the mass of a one degree of freedom model (figure 4) was calculated, whereas in the second, the relative displacement between the mass and the base was calculated. The measured acceleration signal on the driver's seat, from the test track runs, was applied to the base of the model. Acceleration response. The model was given a Q-value (figure 4) of 5, which was considered narrow enough to discriminate between different responses in the body. The resonance frequency was varied in 1/3-octave band steps between 0.5 and 50 Hz. For each resonance frequency the absolute value of the m a x i m u m positive part (Maximax) and that of the m a x i m u m negative part (Minimin) was determined for the mass of the model during the shock event. The two response spectra were compared to the sensitivity curves for human response to vibration corresponding to three of the weighting methods (A, B, C). The response measure was obtained by moving the sensitivity curve downwards until it touched the response curve (figure 5). The acceleration level for the horizontal part of the sensitivity curve at that level was used as a response measure. This method has been proposed by Sphng in the ISO committee for human vibration (Sphng et al., 1985). Displacement response. The model was given a Q-value (figure 4) of 2. The resonance frequency was set at either 1 or 2 Hz for vibration in the X and Y direction and to 5 or 8 Hz for vibration in the Z direction. Two response measures were
Weighting measures Analyses of the weighted signals were made with two methods, Time-mean measures and Dose measures. In both, analyses were made of separate directions and of the Sum of vectors (S~y:). Hereby two methods were used; one in which X- and Y-direction were given a higher weight (as recommended by ISO 2631) and one in which the three vibration directions were weighted equally. Time-mean measures. The calculation was based on the following formula:
(1/Tfora~(t)dt) t/" where T is the integration time, corresponding to the duration of the shock event, aw(t ) is the momentary acceleration value weighted with one of the weighting filters (A, B, C, D). Five values of n were tested (2, 4, 6, 8 and 10), resulting in measures labeled Rm2 (i.e. rms), Rm4 (i.e. rmq), Rm6, Rm8 and RmlO. Of these analyses the Rm2-analysis is used with the ISO-filters (B) in ISO 2631. The Rm4-method has been proposed by Griffin (Griffin and Whitham, 1980). In a complementary analysis the integration time ( T ) was set to 1, 2 or 4 seconds. The time window was moved in small steps over the shock event. The biggest resulting time-mean value was evaluated for each shock event. Dose measures. The calculation was based on the following formula: T .
y(t) m
..... Acceleration response:
fo a,.( t )d t
Max of ~;(t)
Disl~lacement response: Max of y(t) - x(t)
where T is the integration time, corresponding to the duration of the shock event, aw(t) is the momentary acceleration value weighted with one of the weighting filters (A, B, C, D). The value of n was varied as above, thus giving the following five measures: Dose2, Dose4, Dose 6, Dose8 and DoselO. Of these measures the Dose4 measure has been proposed by Griffin under the name 'Vibration Dose Value'.
? ~
x(t)
Fig. 4. Description o f the model and equations for acceleration and displacement response. Response was evaluated with the base of the model (X) subjected to the acceleration signal measured on the seat of the vehicle. The Q-value of the model is a measure of the sharpness of the resonance and equals cc/2c, where c is the da mpi ng coefficient and c c is the d a m p i n g coefficient at critical damping. K and m in the model are spring coefficient and mass.
45
B.-O. Wikstr6m et aL / Whole-body vibration m/$ 2
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Fig. 5. E x a m p l e of critical frequency b a n d a n d level used in the a c c e l e r a t i o n r e s p o n s e m e a s u r e (in this case Z - d i r e c t i o n a n d ISO-filter).
IO
-IO
calculated for each shock event: Maximax displacement response (corresponding to tension of the model) and Minimin displacement response (corresponding to compression of the model). This method has been proposed under the name of DRI by Payne for assessment of the risk of lower back injuries at ejection of an aviator. It has also been proposed as a possible method for the assessment of shocks occurring in the work environment (Payne, 1978).
0
I
2
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Fig. 6. T i m e records for o n e of the s h o c k events m e a s u r e d on the seat of the t e r m i n a l tractor. H a r b o u r study.
A similar method has been proposed by a German group for the assessment of the influence of shocks on man in the ISO committee for human vibration (ISO, 1984). Statistical analyses
Impulse measures The squared value of the weighted time-signal was calculated. This signal passed a low-pass filter with a time-constant of 0.125 s. The maximum positive value ( M a x ) of this signal was calculated. The following formula was used:
Separate regression analyses were made for each lap between each technical measure and the discomfort ratings of the shock events. The correlation coefficients shown in the tables are means (after transformation to Fisher's z) of the correlations obtained in these analyses. The correlation coefficients of linear regressions of log-log scales are presented since these were the highest throughout.
where T = 0.125 s. nVs 2 mls 2.0 ~
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Fig. 7. T y p i c a l l / 3 - o c t a v e b a n d spectra m e a s u r e d o n the seat of the t e r m i n a l t r a c t o r in the X-, Y- a n d Z-directions. = 8-hour curve for ' m a x i m u m e x p o s u r e - health or safety" a c c o r d i n g to ISO 2631. * * 8-hour c u r v e for ' f a t i g u e - d e c r e a s e d p r o f i c i e n c y ' a c c o r d i n g to ISO 2631.
46
B.-O. 14/ikstrSm et a L / Whole.body cibration Rating
Results 100
The Harbour Stud), One of the shock events is shown in figure 6. Typical spectra for the machine are shown in figure 7. The highest frequency weighted acceleration levels were obtained in the Z-direction for 91% of the shocks (the mean Rm2 level with weighting B was 1.4 m / s 2 with a range of 0.247.0). With weighting A the signals in the X direction were critical for the majority of shocks. The critical frequency band in the Acceleration response analyses of the Z direction was in most cases either 3.15, 6.3 or 8 Hz. Due to failures in the data collection, the regression analyses involving the Z direction were based upon 551 shocks, and those involving the X and Y directions upon 580 shocks. In table 1 the mean correlations between ratings and different technical measures for the 42 laps are given. The Dose measures are not included since they gave virtually the same correlations as the corresponding Rm measures (all shock events in this case had about the same duration, 3.5 s). From the table it is evident that the discomfort ratings had the highest correlation with the measures of the Z-direction and that the R m measures gave higher correlations than the other measures. Rating 300
100
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Fig. 9. M e a n s o f rated d i s c o m f o r t
3
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as a f u n c t i o n o f the R m 2
level of the shocks in figure 8. The shocks were divided into 20 classes from the Rm2 value.
The Rm2 measure gave the highest correlation and it was gradually reduced for bigger exponents. Rm2 gave significantly higher correlations than R m 6 - R m l 0 ( p < 0.01), the Peak, Response and Impulse measures; the difference between Rm2 and Rm4 was, however, nonsignificant. The relative strength of the correlations was unaffected by the exclusion of the 50 weakest or the 50 strongest shocks. As shown in figures 8 and 9 there was no apparent deviation from linearity within the investigated range of shock levels. Figures 8 - 9 and 12-13 were made possible by standardizing both vibration and discomfort data giving them the same mean (the grand mean of all shocks) and standard deviation in all laps. Lower correlations were obtained for the Sum of vectors (Sx, :, table 1) calculated as recommended in ISO 2631 than for the critical Z direction. The correlations were strengthened by giving the directions equal weight in the calculation, but they never exceeded those for the Z direction. Weighting C of the Z-axis values gave overall somewhat lower correlations than weighting A and B. The differences, however, were not significant.
Rm2 0.3
0.1
i 0.3
= 1
= 3
= 10
30
m/s2
Fig. 8. Rated discomfort as a function o f the R m 2 level f o r all shocks in the H a r b o u r study. A normalisation was made such that b o t h ratings and R m 2 values were transformed to the same mean and standard d e v i a t i o n for each lap.
The Forest Study One of the shock events is shown in figure 10. Typical spectra for the forwarder are shown in figure 11. The highest frequency weighted acceler-
B.-(9. Wikstri~m et aL / Whole-body vibration
47
Table 1 Pearson's correlation coefficients for linear regressions between technical vibration measures for different directions (X. Y, Z) and rated discomfort (log-log), the Harbour Study. A, B and C stands for different weighting functions (see Methods). S~y:: Sum of vectors. X (n = 580)
Y (n = 580)
Z (n = 551)
Sx,: (n = 545)
Peak measures Posmax, A Negmax, A Posmax + Negrnax, A Posmax, B Negmax, B Posmax + Negmax, B Posmax, C " Negmax, C Posmax + Negmax, C
0.674 0.668 0.682 0.721 0.695 0.729 0.721 0.695 0.729
0.702 0.712 0.719 0.667 0.691 0.708 0.667 0.691 0.708
0.825 0.809 0.833 0.805 0.809 0.828 0.801 0.793 0.815
0.699
Time-mean measures Rm2, A Rm4, A Rm6, A RmS, A Rml0, A Rm2, B Rm4, B R,m6, B Rm8, B Rml0, B Rm2,C a Rm4, C ~ Rm6, C " Rm8, C a Rml0 C a
0.735 0.708 0.699 0.694 0.692 0.797 0.761 0.745 0.737 0.733 0.797 0.761 0.745 0.737 0.733
0.771 0.740 0.727 0.720 0.716 0.750 0.723 0.712 0.708 0.706 0.750 0.723 0.712 0.708 0.706
0.866 0.852 0.839 0.832 0.827 0.866 0.850 0.835 0.827 0.823 0.851 0.834 0.820 0.813 0.809
Acceleration response measures Maximax, A Minimin, A Maximax, B Minimin, B Maximax, C Minimin, C
0.622 0.623 0.668 0.664 0.668 0.664
0.704 0.699 0.658 0.656 0.658 0.656
0.812 0.810 0.821 0.819 0.788 0.795
Displacement response measures Maximax (X, Y:I Hz; Z:5 Hz) Minimin (X, Y:I Hz; Z:5 Hz) Maximax (X, Y:2 Hz; Z:8 Hz) Miaimin (X, Y:2 Hz; Z:8 Hz)
0.635 0.644 0.667 0.663
0.648 0.623 0.696 0.681
0.824 0.822 0.819 0.803
Impulse measures Max, A Max, B Max, C
0.663 0.712 0.712
0.697 0.691 0.691
0.828 0.818 0.799
0.800
0.789
0.818 0.772 0.741 0.726 0.717 0.842 0.832 0.819 0.812 0.808 0.833 0.821 0.808 0.801 0.796
"s~yz: Z weighted according to filter C; X & Y according to B.
a t i o n levels w e r e o b t a i n e d i n t h e Y d i r e c t i o n ( R m 2 w e i g h t i n g B: m e a n = 1.7 m / s 2 , r a n g e = 0 . 2 8 - 3 . 4 ) ,
shocks. T h e critical f r e q u e n c y b a n d in the Acceleration response measures was for the majority of
w h i c h w a s t h e c r i t i c a l d i r e c t i o n f o r 92% o f t h e
s h o c k s b e l o w 1 H z , i.e. c o n s i d e r a b l y l o w e r t h a n
B.-0. H"ikstr~m et al. / H/hole-body cibration
48 m s2
Rating x
1000
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R2 = 0.606
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=
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Fig. 10. Time records for one of the shock events measured on the seat in the forwarder. Forest study.
Fig. 12. Rated discomfort as a function of the Dose2 level for all shocks in the Forest study. A normatisation was made such that both ratings and Dose2 values were transformed to the same mean and standard deviation for each lap.
those o f the H a r b o u r Study. Fifty-six r e c o r d i n g s h a d to be d i s c a r d e d due to d a t a collection failures. Thus, the analyses were b a s e d u p o n 447 shocks in this study. C o r r e l a t i o n s are given in tables 2 a n d 3. T h e highest c o r r e l a t i o n s o c c u r r e d for a l m o s t all m e a sures in the Y d i r e c t i o n with weighting A. D o s e measures ( t a b l e 3) y i e l d e d significantly ( p < 0.01) higher c o r r e l a t i o n s with d i s c o m f o r t than the corres p o n d i n g T i m e - m e a n m e a s u r e s (table 2). A p a r t from the D o s e measures, the highest c o r r e l a t i o n s were o b t a i n e d with the Peak m e a s u r e P o s m a x + Negmax. A m o n g the D o s e m e a s u r e s the c o r r e l a t i o n was lowered as the e x p o n e n t was raised f r o m 2 to 10,
except for the measures with weighting A in the Y direction in which R m 4 gave h i g h e r c o r r e l a t i o n s t h a n Rm2. T h e r a n k i n g o f the c o r r e l a t i o n s was u n a l t e r e d b y the exclusion o f the w e a k e s t 10% o f the shocks. In no case, however, was the d i f f e r e n c e b e t w e e n R m 2 a n d R m 4 significant. T w o o f the shock events were e x t r e m e l y long, 12 s a n d 16 s, respectively. A n exclusion of these two shocks f r o m the analyses d i d not affect the r a n k i n g o f the correlations. Figures 12 a n d 13 show the s t a n d a r d ized ratings p l o t t e d a g a i n s t the s t a n d a r d i z e d D o s e 2 levels. T h e results of the T i m e - m e a n m e a s u r e s were o p p o s i t e to that o f the D o s e measures, i.e. the c o r r e l a t i o n s were a u g m e n t e d as the e x p o n e n t was
2
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Direction
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64
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loo 0.5
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Hz
Fig. 11. Typical l/3-octave band spectra measured on the seat of the forwarder in the X-. Y- and Z-directions. * 8-hour curve for "maximum exposure - health or safety' according to ISO 2631. * * 8-hour curve for 'fatigue-decreased proficiency" according to ISO 2631.
B.-O. Wikstr~m et al. / Whole-body vtbration
49
Table 2
Table 3
Pearson's correlation coefficients for linear regressions between technical measures for different directions (X, Y. Z) and rated discomfort (log-log), the Forest Study (n z 447). A, B and C stand for different weighting functions (see Methods). S~y.: Sum of vectors.
Pearson's correlation coefficients for linear regressions between Dose measures for different directions (X. Y, Z) and rated discomfort (log-log). the Forest Study (n ,~ 447). A, B and C stand for different weighting functions (see Methods). Sxy.: Sum of vectors.
X
Y
Z
Sxy..
Peak values Posmax, A Negmax, A Posmax + Negmax, A Posmax, B Negmax, B Posmax + Negmax, B Posmax, air a Negrnax, alt a Posmax + Negmax, alt a
0.715 0.678 0.743 0.661 0.619 0.704 _
0.737 0.669 0.792 0.710 0.600 0.769 0.726 0.628 0.797
0.721 0.692 0.731 0.727 0.691 0.734 0.726 0.705 0.740
0.760 0.756 0.757 -
0.679 0.712 0.717 0.718 0.718 0.606 0.640 0.654 0.661 0.665 -
0.708 0.744 0.748 0.749 0.751 0.662 0.703 0.716 0.722 0.726 0.718 0.748 0.753 0.755 0.756
0.651 0.696 0.709 0.714 0.716 0.644 0.695 0.708 0.713 0.716 0.664 0.706 0.716 0.720 0.722
0.739 0.753 0.752 0.751 0.752 0.710 0.727 0.732 0.735 0.738 0.703 0.723 0.730 0.735 0.738
0.714 0.688 0.681 0.672 -
0.756 0.724 0.706 0.694 -
0.664 0.671 0.692 0.682 0.721 0.697
-
Hz; Z:5 Hz)
0.586
0.534
0.673
-
Hz; Z:5 Hz)
0.615
0.665
0.728
-
Hz; Z:8 Hz)
0.619
0.612
0.657
-
Hz; Z:8 Hz)
0.662
0.728
0.728
0.724 0.668 0.668
0.750 0.728 0.728
0.734 0.730 0.734
Time-mean measures Rm2, A Rm4, A Rrn6, A Rm8, A Rml0, A Rm2, B Rm4, B Rm6, B Rm8, B Rml0, B Rm2, air a Rm4, alt a Rm6, air a Rm8, alt a Rml0, alt a
Acceleration response measures Maximax, A Minimin, A Maximax, B Minimin, B Maximax, C Minimin, C
Displacement measures Maximax (X, Y:I Minimin (X, Y:I Maximax (X, Y:2 Minimin (X, Y:2
Impulse measures Max, A Max, B Max, C
X
Y
Z
Sx~.-
0.798 0.799 0.784 0.775 0.771
0.748 0.743 0.737 0.734 0.732
0.808 0.797 0.780 0.771 0.776
0.779 0.777 0.766 0.759 0.754
0.743 0.741 0.736 0.733 0.731
0.799 0.786 0.771 0.763 0.759
0.808 0.808 0.793 0.784 0.779
0.755 0.748 0.741 0.738 0.736
0.795 0.783 0.769 0.762 0.759
Frequency weighting A
-
Z: weighted according to filter C; Y according to filter D. Sxw: Z according to filter C; X & Y according to filter B.
Dose 2 Dose 4 Dose 6 Dose 8 Dose 10
0.760 0.757 0.745 0.738 0.734
Frequency weighting B Dose Dose Dose Dose Dose
2 4 6 8 10
0.721 0.708 0.698 0.693 0.690
Alt. frequency weightings " Dose Dose Dose Dose Dose
2 4 6 8 10
-
a Z: weighted according to filter C; Y according to filter D. Sxy..: Z weighted according to filter C; X & Y according to filter B.
raised from 2 to 10. A comparable subset of 164 shocks from the Forest Study with a similar range of duration (4-5 s) was analyzed. Correlations were considerably lower in this shock sample due to the restriction of the acceleration range. The ranking of the correlations in this sample, however, was the same as in the Harbour Study, i.e. Rm2 gave the highest and R m l 0 the lowest correlations. The only significant difference occurred between Rm2 and Rml0. The Sum of vectors calculated as recommended by ISO 2631 was significantly more highly correlated with discomfort than was the critical direction. This increase was most pronounced for the Dose2 measure. The Sum of vectors was also calculated with equal weight given to all directions. This measure gave somewhat lower correlations throughout than the ISO procedure. In the Y direction the Dose measures with weighting A gave higher correlations than those with weighting B. This indicated that filter B did not give sufficient weight to the higher frequency
B.-O. Wikstrrm et aL / Whole-body vibration
50 Rating
Table 4
100
Pearson's correlation coefficients for linear regression between technical vibration measures with different integration times and rated discomfort (log-log).
30
lii/B
1 sec
n2 - 0.969
10
= m
Dose2 1
I
I
I
I
3
10
30
100
300
m ")'/s3
Fig. 13. Means of rated discomfort as a function of the Dose2
level of the shocks in figure 12. The shocks were divided into 20 classes from the Dose2 value.
components. An alternative weighting filter D was therefore tested in which the break-point was set to 4 Hz instead of 2 Hz as in filter B. This weighting yielded slightly higher correlations than weighting A and significantly higher correlations than weighting B.
-
Effect of integration time for Time-mean measures both studies
In order to evaluate the effect of different integration times, these were varied in the Timemean analyses from the duration of the whole shock event down to 4, 2 or 1 seconds respectively (methods). The results from both studies indicated that the correlation increased with longer durations (table 4). This was the case also for the directions not shown in the table.
Discussion The highest correlations were found for both studies in the direction which was critical according to ISO 2631. The Time-mean and Dose measures ( R m2 - R ml0 and Dose2-Dosel0, respectively) yielded overall higher correlations with the discomfort ratings than the Peak, Impulse and Response measures. In the Harbour Study the Time-mean and Dose measures with the same
2 set:
4 sec
Harbour Study, Z-direction Rm2, A 0.856 0.865 Rm4, A 0.842 0.850 Rm6, A 0.835 0.840 Rm8, A 0.832 0.835 Rml0, A 0.830 0.833 Rm2, B 0.847 0.859 Rm4, B 0.837 0.845 Rm6, B 0.833 0.838 Rm8, B 0.831 0.834 Rml0, B 0.830 0.832 Rm2, C 0.826 0.838 Rm4, C 0.824 0.832 Rm6, C 0.821 0.827 Rm8, C 0.820 0.823 Rml0, C 0.819 0.821 Forest Study, Rm2, A Rm4, A Rm6, A Rm8, A R_ml0, A Rm2, B Rm4, B Rm6, B Rm8, B Rml0, B
Y-direction 0.748 0.766 0.757 0.768 0.757 0.764 0.756 0.761 0.756 0.759 0.723 0.733 0.735 0.744 0.739 0.745 0.739 0.744 0.740 0.743
Whole event (Dose values) 0.866 0.852 0.839 0.832 0.827 0.866 0.850 0.835 0.827 0.823 0.851 0.834 0.820 0.813 0.809
0.786 0.781 0.771 0.765 0.762 0.758 0.755 0.752 0.749 0.747
0.798 0.799 0.784 0.775 0.771 0.779 0.777 0.766 0.759 0.754
exponents got nearly the same correlations since all shocks were of approximately equal duration. This was not the case in the Forest Study, in which the durations differed, where the Dose analyses got the highest correlations. Furthermore, both studies showed that the correlations for the Dose values were lowered as the exponent was increased from 2 to 10. The results therefore indicate that a measure sensitive to the peak value of the shock is less appropriate than a measure which takes into account the whole shock event. This is in agreement with laboratory studies of short-time events of vibration and shock, which show that a time-dependency exists for discomfort, which builds up fairly quickly at the onset of vibration but grows much more slowly after a few seconds (Miwa, 1968; Griffin and Whitham, 1980; Kjellberg and Wikstr~Sm, 1985). In conclusion, a Dose
B.-O. WikstriJrn et al. / Whole-body vibration
value seems to give a better correlation with discomfort than all the other measures tested. Of the Dose measures, the Dose2 and Dose4 best reflect the discomfort experienced during a shock in both studies. The figures as well as the analyses show that an exponent of 2 or 4 was best not only for the weaker shocks but for the whole range of shock levels. Likewise, these measures gave higher correlations also after an exclusion of the longest shock events. It should, however, be emphasized that the present studies could not differentiate between Dose2 and Dose4 with respect to their correlations with rated discomfort since the correlation between the Dose2 and Dose4 measures was very high. The present results correspond to the findings of Hiramatsu and Griffin (1984). However, they differ from the results of the laboratory studies by Miwa (1968), Griffin and Whitham (1980) and Kjellberg and WikstrSm (1985), which indicated that a higher exponent than 2 was to be preferred in the assessment of shocks. One factor which may have led to this discrepancy is the fact that the drivers saw the obstacles and were thus prepared for the shocks, whereas the subjects in the laboratory experiments h a d no idea what intensity the next shock would have. It is well known that predictability and control may weaken the response to aversive stimulation (Miller and Grant, 1978). In the Harbour Study the Sum of vectors showed a weaker correlation with discomfort than the Z direction values. This indicates that the ISO standard gives too much weight to the X and Y directions in the computation of the Sum of vectors. In the Forest Study, where the Y direction was critical, the Sum of vectors was more highly correlated with discomfort than the Y direction and the ISO weighting of directions proved to be better than an equal weighting of all directions. Thus, the discomfort ratings seemed to be determined primarily by the critical direction, irrespective of which this was. Both studies included a test of different frequency weighting procedures. No significant differences could be found. However, the results in the Forest Study indicate that weighting B gives too little weight to frequencies above 2 Hz in the Y direction. Such a conclusion is supported by the results of a French experiment (Donati et al.,
51
1983). The assessment of different weighting procedures must, however, be interpreted with caution since the shock characteristics were not under experimental control. Accidental correlations between acceleration levels in different directions and frequency bands may thus have influenced the results. The points and directions of the measurements used were based on ISO 2631. Studies at e.g. ISVR have shown that additional data from the footplate and the backrest as well as data from rotational transducers on the seat can give additional information, which may be useful for evaluation of the discomfort (Parsons and Griffin, 1982; Parsons et al., 1982). Still, the main input of information is normally given by linear transducers on the seat used in the present investigation. Of the machines studied there was some roll motion in the forwarder as the machine travelled in rough terrain, which might explain some of the variance in the correlation analyses. In the terminal tractor, vibrations from the floor might have had some influence on the correlations. Considering the normal biological variation among subjects and the reliability of the ratings, the correlation between the discomfort ratings and the best vibration evaluation methods seems high enough to justify conclusions on the choice of methods from measurements on the seat only. The investigations were performed with drivers of heavy vehicles. The conclusions are therefore valid only for this population. Passengers are often subjected to much lower vibration levels and shorter exposure times and are often not prepared for sudden shock events, where other methods than the Dose2 and Dose4 measures might be more suitable. It is worth noting that an Rm-value with a fixed integration time, which is not necessarily equal to the duration of the shock, corresponds to a dose-value and thus would have given the same correlation with discomfort as the best measures, the Dose2 and Dose4 measures. With such an Rm2 value, for example, results can be given in familiar units, i.e. m / s 2 . From table 4 its seems as if the integration time must be defined long enough (i.e. 4 - 8 seconds) to let the amplitude of the shock subside completely in the body. An evaluation method for shock events must take care of the highest values, which in the work
52
B.-O. Wikstri~m et aL / Whole-body vibration
environment are in the range of 40-50 m / s 2 peak. A solution could be a distribution of Rm values (with a fixed integration time), measured over an exposure, which may be compared to a given distribution. The latter may serve as a recommended guideline for the maximum number of shocks, which may occur up to a certain level. Although statistically significant, most of the differences between the correlations in the present study were rather small and probably in m a n y cases of minor practical importance. This would have been a problem if one of the more cumbersome methods of analysis had proven to be the best (e.g. shock response analysis). The additional information might in that case not be worth the extra amount of work required for the analysis. Given the present results this conflict is less problematic.
References Corbridge. C. and Griffin, M.J., 1985. Vibration and comfort: Vertical and lateral motion in the range 0.5 to 5.0 Hz. Ergonomics. 29: 249-272. Donati. P., Grosjean, A., Mistrot, P. and Roure, L., 1983. The subjective equivalence of sinusoidal and random wholebody vibration in the sitting position. (An experimental study using the 'floating reference vibration' method). Ergonomics. 26: 251-273. Griffin. M.J. and Whitham, E.M., 1980. Discomfort produced by impulsive whole-body vibration. J. Acoust. Soc. Am., 68: 1277-1284. Griffin. M.J., Parsons, K.C. and Whitham, E.M., 1982. Vibration and comfort, IV. Ergonomics, 25: 721-739. Hansson, J.-E. and Wikstrt~m, B.-O., 1979. Comparison of some technical methods for the evaluation of whole-body vibration. Ergonomics, 24: 953-963. Hiramatsu, K and Griffin, M.J., 1984. Predicting the subjective
response to non-steady vibration based on the summation of subjective magnitude. J. Acoust. Soc. Am., 76: 10801088. ISO, 1974. Guide for the evaluation of human exposure to whole-body vibration. ISO 2631. First edition 1974, second edition 1978. International Organization for Standardization, Geneva. ISO, 1984. Description of procedures for evaluation of vibration containing events of short duration. Working draft for an ISO Technical Report. ISO TC108/SC4. International Organization for Standardization. Geneva. ISO. 1988. First draft proposal ISO/DP 2631--Guide for the evaluation of human exposure to whole-body mechanical vibration. ISO TC 1 0 8 / S C 4 / N 177. International Organization for Standardization, Geneva. Kjellberg. A. and WikstriSm. B.-O.. 1985. Subjective reactions to whole-body vibration of short duration. J. Sound. Vib., 99: 415-424. Miller. S.M. and Grant. R.P.. 1978. The blunting theory: A theory of predictability and human stress. In: P.O, SjOd~n, S. Bates and W.S. Dockens (Eds.), Trends in Behavior Therapy. Academic press, New York. Miwa, T., 1968. Evaluation methods for vibration effect, Part 7: The vibration greatness of the pulses. Ind. Health, 6: 143-164. Parsons, K.C. and Griffin, M.J., 1982. Vibration and comfort, II. Rotational seat vibration. Ergonomics. 25: 631-644. Parsons, K.C.. Griffin, M.J. and Whitham, E.M.. 1982. Vibration and comfort. III. Translational vibration of the seat and back. Ergonomics, 25: 645-720. Payne, P.R., 1978. Method to quantify ride comfort and allowable accelerations. Aviat. Space Environ. Med., 49: 262-269. Shoenberger, R.W.. 1978. Intensity judgements of nonsinusoidal vibrations: Support for the ISO weighting method. Aviat. Space Environ. Med.. 49: 1327-1330. Sp~ng, K.. Arnberg. P.W., Bennerhult, O. and Kloow, T., 1985. The influence of transient vibrations on perception. Part I. Report TR 5.339.01 from IFM Akustikbyr/m. Stockholm. VDI, 1963. Beurteilung der einwirkung mechanischer Schwingungen auf den Menschen. Verein Deutscher Ingenieure, Diisseldorf.
41
Whole-body vibration: A comparison of different methods for the evaluation of mechanical shocks Bengt-O. WikstrSm, Anders Kjellberg and Margareta Dallner National Institute for Occupational Health, S-171 84, Solna, Sweden
(Received February 28, 1990; accepted in revised form August 16, 1990)
Abstract Two studies were performed in order to compare different technical methods for assessing the effect of mechanical shocks on discomfort. The studies were carried out in the field with a forest machine and a harbour tractor. These were driven by professional drivers on test tracks consisting of different sections with obstacles producing shocks. The discomfort of each section was rated with magnitude estimation. Vibrations on the seat were recorded. Each vibration record was analysed with different technical assessment methods. These included acceleration peak values, time-mean values, dose values, impulse values, acceleration response and displacement response methods. Regression analyses were applied to the drivers' ratings and each of the assessment methods to find the strength of the relationship. The study showed that a dose value based on an Rms or Rmq calculation gave the best prediction of discomfort from the shocks. The integration time should be long enough (several seconds) to let significant parts of the shock give contribution to the dose value. In many vehicles and working-machines shocks occur, which can be harmful to the driver. Knowledge of how to evaluate these shocks should therefore be of interest for manufacturers of vehicles and also for health service groups in industry. Relevance to industry In many vehicles and working-machines shocks occur, which can be harmful to the driver. Knowledge of how to evaluate these shocks should therefore be of interest for manufacturers of vehicles and also for health service groups in industry. Keywords Whole-body vibration, shock, technical evaluation methods, discomfort, field-study.
Introduction Several m e t h o d s have b e e n used over the years for the e v a l u a t i o n of discomfort from w h o l e - b o d y v i b r a t i o n (ISO, 1974; VDI, 1963). Miwa's work formed the basis of the i n t e r n a t i o n a l s t a n d a r d , ISO 2631 (Miwa, 1967). I n the s t a n d a r d the ' s i n g l e - a x i s 1 / 3 - o c t a v e b a n d a n a l y s i s ' is the favoured method, b u t other m e t h o d s are also included as secondary, like the 'single-axis frequency weighted r m s - v a l u e ' a n d ' t h e sum of vector frequency weighted rms-value'. T h e s t a n d a r d has been used b y researchers a n d others, e.g. health executive organizations, for the last fifteen years. 0169-1936/91/$03.50 © 1991 - Elsevier Science Publishers B.V.
Several l a b o r a t o r y studies a n d some field studies have shown that it works r e a s o n a b l y well for the assessment of discomfort d u r i n g exposure to stat i o n a r y v i b r a t i o n s (Shoenberger, 1978; H a n s s o n a n d Wikstr~Sm, 1979; G r i f f i n et al., 1982). However, its applicability to v i b r a t i o n s which c o n t a i n shocks has repeatedly b e e n q u e s t i o n e d b y several parties a n d has been of m a j o r c o n c e r n in the o n - g o i n g revision of ISO 2631 (ISO, 1988). This p a p e r reports a n investigation designed to evaluate which m e t h o d s should be used for the e v a l u a t i o n of discomfort in the driver's work env i r o n m e n t from v i b r a t i o n c o n t a i n i n g shocks. T h e investigation was set up as two e x p e r i m e n t a l stud-
42
B.-O. Wikstrrm et al. / Whole-body vibration
ies in the field with ordinary machines and experienced drivers. It was judged important to make the discomfort assessment under realistic driving conditions since many possibly critical aspects of the driver's situation are more or less impossible to simulate in the laboratory. To lessen the risk that the conclusions become valid for only a special class of shocks, two studies with different types of vehicles were performed. Parallel to the present investigation, a laboratory investigation was conducted with the same aim. Results from this study are presented in Sp~ng et al. (1985). The comparison was based on three assessment methods of shocks discussed during the last few years: response measures especially the Shock Response Spectrum analysis, dose measures especially the Vibration Dose Value and impulse methods especially the Impulse Extended Dose. Time-mean measures, e.g. the Rms value, as well as peak measures, e.g. the simple Peak value, were also included.
Methods
Two studies were performed, the Harbour Study and the Forest Study. In both studies experienced drivers drove without stopping three times around a closed test track, which contained a number of obstacles producing shocks of different intensities. The driver rated the discomfort at the end of each shock. Vibrations on the seat were recorded on tape and analyzed with different assessment methods. The power of the different technical methods of analysis as predictors of the discomfort ratings was determined by regression analyses.
Fig. 1. The terminal tractor used in the Harbour study. without load on a closed track 390 meters long (figure 1). The seat, which had a maximum spring displacement of 100 mm, was adjusted to minimize the risk of bottoming. Fourteen obstacles were placed at even distances on the track. They were made by steel-plates and wooden planks with heights between 10-70 mm. All produced shocks of about 3.5 s duration. Both tyres passed the obstacle at the same time. The speed was held constant at 70 m / m i n . The drivers gave their ratings over the radio communication system. For every driver measurements of 42 shocks were made and in total, data from 630 shocks were collected. Test procedure - the Forest S t u d y
A large forwarder (Kockum 85-35), with a conventional springed seat (BeGe Nord Forest),
Subjects Fifteen drivers participated in the Harbour Study. Their mean age was 37.9 years and they had 4.5 to 20 ( M = 8.2) years of experience as industrial truck drivers. The eleven drivers in the Forest Study had 5 to 30 ( M = 16.7) years of experience as forest machine drivers and their mean age was 41.4 years. Test procedure - the H a r b o u r S t u d y
A terminal tractor (BoUn~is PT20), with a conventional springed seat (BeGe Pluto), was driven
Fig. 2. The forwarder used in the Forest study.
43
B.-O. WikstriJm et aL / Whole-body t'ibration
placed in the X-, Y- and Z-directions (see ISO 2631) on a flat, round aluminium plate (diam. = 200 mm), upon which the driver sat. The signals were recorded on a PCM tape-recorder (Stellavox, Johne & Reilhofer Mini-Din). The shock portions of the tape-recorded vibration were selected with, edited by and stored on a PC. Anti-aliasing was made with 48 d B / o c t a v e filters with a cut-off frequency of 80 Hz. Analyses were performed with an IBM P C / A T connected via a Gpib-bus to a two-channel FFT-analyzer (Briiel & Kjaer 2032), which was used to simulate the weighting filters and the response functions demanded by the analysis. The different analyses were performed in the FFT-analyzer using an internal processing language SPL. The methods of analysis described below resulted in 52 measures in each direction for each shock.
was driven without load on a track in forest terrain 453 meters long (figure 2). The seat, which had a m a x i m u m spring deflection of 100 mm, was adjusted to minimize the risk of bottoming. Of the naturally occurring obstacles fifteen were chosen. These were smooth rocks with a height between 0.2-0.6 m and one pit with a depth of 0.5 m. Thirteen of the obstacles gave shocks lasting 4 - 9 s; two gave series of shocks lasting 12 s and 16 s, respectively. The machine was driven with a constant speed of 45 m / m i n on the first rougher part of the track and 63 m / r a i n on the smoother second part. The test procedure was the same as in the Harbour Study except that the test leader stood behind the driver and noted the ratings. Data from 495 shocks were collected in this study.
Subjective ratings of discomfort
Description of the technical measures used for evaluation
The driver made magnitude estimations of the ride discomfort basing the rating on the whole shock event. The first shock of a lap served as reference shock and was always given a rating of 10. If the second shock event was experienced as twice as discomforting as the first, it got a rating of 20, if half as discomforting a rating of 5 and so on. The start of the three laps was done at different obstacles evenly distributed over the track. Therefore the reference shock and the subjective scale varied between the laps. The order between starting points was counterbalanced.
Separate analyses were made in the X, Y and Z directions for all measures. Four different types of analysis were used (see below). For the Peak-value measures, the Weighting measures and the Impulse measures the signal was weighted with three different filters (figure 3): linear weighting (A), weighting according to ISO 2631 (B) and a weighting proposed by Griffin (C) in the new draft proposal of ISO 2631 (ISO, 1988) with the background presented in Corbridge and Griffin (1986). In addition to this, in the Forest Study a weighting filter for the Y direction was tested, which was equal to the ISO-filter except for a breakpoint at 4 Hz instead of at 2 Hz (D).
Equipment Vibration measurements were accomplished with three accelerometers (Endevco 2265-20)
dB i
10
Direc~on Y
t
!
_. L.
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\
-10
~. . . . .
1 ~
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i
-20
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1
2
4
8
16
32
64
0.5
1
2
4
,
8
16
32
64
0.5
1
2
Fig. 3. Characteristics of the weighting filters in the X-. Y- and Z-directions.
4
8
16
32
64
Hz
44
B.-0. WikstriSrn et a L / Whole-body vibration
Peak-value measures
Response measures
The maximum positive (Posmax) and negative acceleration values ( N e g m a x ) and the sum of their absolute values (Posmax + Negmax) were calculated for the signals weighted with the different filters (A, B, C, D).
The analyses were performed in two ways. In the first method the acceleration response of the mass of a one degree of freedom model (figure 4) was calculated, whereas in the second, the relative displacement between the mass and the base was calculated. The measured acceleration signal on the driver's seat, from the test track runs, was applied to the base of the model. Acceleration response. The model was given a Q-value (figure 4) of 5, which was considered narrow enough to discriminate between different responses in the body. The resonance frequency was varied in 1/3-octave band steps between 0.5 and 50 Hz. For each resonance frequency the absolute value of the m a x i m u m positive part (Maximax) and that of the m a x i m u m negative part (Minimin) was determined for the mass of the model during the shock event. The two response spectra were compared to the sensitivity curves for human response to vibration corresponding to three of the weighting methods (A, B, C). The response measure was obtained by moving the sensitivity curve downwards until it touched the response curve (figure 5). The acceleration level for the horizontal part of the sensitivity curve at that level was used as a response measure. This method has been proposed by Sphng in the ISO committee for human vibration (Sphng et al., 1985). Displacement response. The model was given a Q-value (figure 4) of 2. The resonance frequency was set at either 1 or 2 Hz for vibration in the X and Y direction and to 5 or 8 Hz for vibration in the Z direction. Two response measures were
Weighting measures Analyses of the weighted signals were made with two methods, Time-mean measures and Dose measures. In both, analyses were made of separate directions and of the Sum of vectors (S~y:). Hereby two methods were used; one in which X- and Y-direction were given a higher weight (as recommended by ISO 2631) and one in which the three vibration directions were weighted equally. Time-mean measures. The calculation was based on the following formula:
(1/Tfora~(t)dt) t/" where T is the integration time, corresponding to the duration of the shock event, aw(t ) is the momentary acceleration value weighted with one of the weighting filters (A, B, C, D). Five values of n were tested (2, 4, 6, 8 and 10), resulting in measures labeled Rm2 (i.e. rms), Rm4 (i.e. rmq), Rm6, Rm8 and RmlO. Of these analyses the Rm2-analysis is used with the ISO-filters (B) in ISO 2631. The Rm4-method has been proposed by Griffin (Griffin and Whitham, 1980). In a complementary analysis the integration time ( T ) was set to 1, 2 or 4 seconds. The time window was moved in small steps over the shock event. The biggest resulting time-mean value was evaluated for each shock event. Dose measures. The calculation was based on the following formula: T .
y(t) m
..... Acceleration response:
fo a,.( t )d t
Max of ~;(t)
Disl~lacement response: Max of y(t) - x(t)
where T is the integration time, corresponding to the duration of the shock event, aw(t) is the momentary acceleration value weighted with one of the weighting filters (A, B, C, D). The value of n was varied as above, thus giving the following five measures: Dose2, Dose4, Dose 6, Dose8 and DoselO. Of these measures the Dose4 measure has been proposed by Griffin under the name 'Vibration Dose Value'.
? ~
x(t)
Fig. 4. Description o f the model and equations for acceleration and displacement response. Response was evaluated with the base of the model (X) subjected to the acceleration signal measured on the seat of the vehicle. The Q-value of the model is a measure of the sharpness of the resonance and equals cc/2c, where c is the da mpi ng coefficient and c c is the d a m p i n g coefficient at critical damping. K and m in the model are spring coefficient and mass.
45
B.-O. Wikstr6m et aL / Whole-body vibration m/$ 2
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IO
-IO
calculated for each shock event: Maximax displacement response (corresponding to tension of the model) and Minimin displacement response (corresponding to compression of the model). This method has been proposed under the name of DRI by Payne for assessment of the risk of lower back injuries at ejection of an aviator. It has also been proposed as a possible method for the assessment of shocks occurring in the work environment (Payne, 1978).
0
I
2
3
Fig. 6. T i m e records for o n e of the s h o c k events m e a s u r e d on the seat of the t e r m i n a l tractor. H a r b o u r study.
A similar method has been proposed by a German group for the assessment of the influence of shocks on man in the ISO committee for human vibration (ISO, 1984). Statistical analyses
Impulse measures The squared value of the weighted time-signal was calculated. This signal passed a low-pass filter with a time-constant of 0.125 s. The maximum positive value ( M a x ) of this signal was calculated. The following formula was used:
Separate regression analyses were made for each lap between each technical measure and the discomfort ratings of the shock events. The correlation coefficients shown in the tables are means (after transformation to Fisher's z) of the correlations obtained in these analyses. The correlation coefficients of linear regressions of log-log scales are presented since these were the highest throughout.
where T = 0.125 s. nVs 2 mls 2.0 ~
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: D i ~
/,/
!!ii!/^/I
32
64
'JI 0.5
1
2
4
8
16
32
64
0.5
i i ,
2
,
8
~6
"~ 32
64
Fig. 7. T y p i c a l l / 3 - o c t a v e b a n d spectra m e a s u r e d o n the seat of the t e r m i n a l t r a c t o r in the X-, Y- a n d Z-directions. = 8-hour curve for ' m a x i m u m e x p o s u r e - health or safety" a c c o r d i n g to ISO 2631. * * 8-hour c u r v e for ' f a t i g u e - d e c r e a s e d p r o f i c i e n c y ' a c c o r d i n g to ISO 2631.
46
B.-O. 14/ikstrSm et a L / Whole.body cibration Rating
Results 100
The Harbour Stud), One of the shock events is shown in figure 6. Typical spectra for the machine are shown in figure 7. The highest frequency weighted acceleration levels were obtained in the Z-direction for 91% of the shocks (the mean Rm2 level with weighting B was 1.4 m / s 2 with a range of 0.247.0). With weighting A the signals in the X direction were critical for the majority of shocks. The critical frequency band in the Acceleration response analyses of the Z direction was in most cases either 3.15, 6.3 or 8 Hz. Due to failures in the data collection, the regression analyses involving the Z direction were based upon 551 shocks, and those involving the X and Y directions upon 580 shocks. In table 1 the mean correlations between ratings and different technical measures for the 42 laps are given. The Dose measures are not included since they gave virtually the same correlations as the corresponding Rm measures (all shock events in this case had about the same duration, 3.5 s). From the table it is evident that the discomfort ratings had the highest correlation with the measures of the Z-direction and that the R m measures gave higher correlations than the other measures. Rating 300
100
• . ' ~=. 30
'. -,'f't ' " :
S
R2 = 0.746
=
~..o~
•.. ,~ ~,~," •
10
.
3
f
1
;r:~.:;'
"-,, •
30
=
0990 .
10
Rm2
1 0.3
~
Fig. 9. M e a n s o f rated d i s c o m f o r t
3
10 m/s 2
as a f u n c t i o n o f the R m 2
level of the shocks in figure 8. The shocks were divided into 20 classes from the Rm2 value.
The Rm2 measure gave the highest correlation and it was gradually reduced for bigger exponents. Rm2 gave significantly higher correlations than R m 6 - R m l 0 ( p < 0.01), the Peak, Response and Impulse measures; the difference between Rm2 and Rm4 was, however, nonsignificant. The relative strength of the correlations was unaffected by the exclusion of the 50 weakest or the 50 strongest shocks. As shown in figures 8 and 9 there was no apparent deviation from linearity within the investigated range of shock levels. Figures 8 - 9 and 12-13 were made possible by standardizing both vibration and discomfort data giving them the same mean (the grand mean of all shocks) and standard deviation in all laps. Lower correlations were obtained for the Sum of vectors (Sx, :, table 1) calculated as recommended in ISO 2631 than for the critical Z direction. The correlations were strengthened by giving the directions equal weight in the calculation, but they never exceeded those for the Z direction. Weighting C of the Z-axis values gave overall somewhat lower correlations than weighting A and B. The differences, however, were not significant.
Rm2 0.3
0.1
i 0.3
= 1
= 3
= 10
30
m/s2
Fig. 8. Rated discomfort as a function o f the R m 2 level f o r all shocks in the H a r b o u r study. A normalisation was made such that b o t h ratings and R m 2 values were transformed to the same mean and standard d e v i a t i o n for each lap.
The Forest Study One of the shock events is shown in figure 10. Typical spectra for the forwarder are shown in figure 11. The highest frequency weighted acceler-
B.-(9. Wikstri~m et aL / Whole-body vibration
47
Table 1 Pearson's correlation coefficients for linear regressions between technical vibration measures for different directions (X. Y, Z) and rated discomfort (log-log), the Harbour Study. A, B and C stands for different weighting functions (see Methods). S~y:: Sum of vectors. X (n = 580)
Y (n = 580)
Z (n = 551)
Sx,: (n = 545)
Peak measures Posmax, A Negmax, A Posmax + Negrnax, A Posmax, B Negmax, B Posmax + Negmax, B Posmax, C " Negmax, C Posmax + Negmax, C
0.674 0.668 0.682 0.721 0.695 0.729 0.721 0.695 0.729
0.702 0.712 0.719 0.667 0.691 0.708 0.667 0.691 0.708
0.825 0.809 0.833 0.805 0.809 0.828 0.801 0.793 0.815
0.699
Time-mean measures Rm2, A Rm4, A Rm6, A RmS, A Rml0, A Rm2, B Rm4, B R,m6, B Rm8, B Rml0, B Rm2,C a Rm4, C ~ Rm6, C " Rm8, C a Rml0 C a
0.735 0.708 0.699 0.694 0.692 0.797 0.761 0.745 0.737 0.733 0.797 0.761 0.745 0.737 0.733
0.771 0.740 0.727 0.720 0.716 0.750 0.723 0.712 0.708 0.706 0.750 0.723 0.712 0.708 0.706
0.866 0.852 0.839 0.832 0.827 0.866 0.850 0.835 0.827 0.823 0.851 0.834 0.820 0.813 0.809
Acceleration response measures Maximax, A Minimin, A Maximax, B Minimin, B Maximax, C Minimin, C
0.622 0.623 0.668 0.664 0.668 0.664
0.704 0.699 0.658 0.656 0.658 0.656
0.812 0.810 0.821 0.819 0.788 0.795
Displacement response measures Maximax (X, Y:I Hz; Z:5 Hz) Minimin (X, Y:I Hz; Z:5 Hz) Maximax (X, Y:2 Hz; Z:8 Hz) Miaimin (X, Y:2 Hz; Z:8 Hz)
0.635 0.644 0.667 0.663
0.648 0.623 0.696 0.681
0.824 0.822 0.819 0.803
Impulse measures Max, A Max, B Max, C
0.663 0.712 0.712
0.697 0.691 0.691
0.828 0.818 0.799
0.800
0.789
0.818 0.772 0.741 0.726 0.717 0.842 0.832 0.819 0.812 0.808 0.833 0.821 0.808 0.801 0.796
"s~yz: Z weighted according to filter C; X & Y according to B.
a t i o n levels w e r e o b t a i n e d i n t h e Y d i r e c t i o n ( R m 2 w e i g h t i n g B: m e a n = 1.7 m / s 2 , r a n g e = 0 . 2 8 - 3 . 4 ) ,
shocks. T h e critical f r e q u e n c y b a n d in the Acceleration response measures was for the majority of
w h i c h w a s t h e c r i t i c a l d i r e c t i o n f o r 92% o f t h e
s h o c k s b e l o w 1 H z , i.e. c o n s i d e r a b l y l o w e r t h a n
B.-0. H"ikstr~m et al. / H/hole-body cibration
48 m s2
Rating x
1000
j
R2 = 0.606
I0 0 -I0i
i
lOO
I0
:
. t - . . : ' . - ~:,
=
I
.-
-I0
I Z
I0
Dose2 0
0.1
I
1
-I0
I
10
=
I
1 O0
1000
m 9./S3
Fig. 10. Time records for one of the shock events measured on the seat in the forwarder. Forest study.
Fig. 12. Rated discomfort as a function of the Dose2 level for all shocks in the Forest study. A normatisation was made such that both ratings and Dose2 values were transformed to the same mean and standard deviation for each lap.
those o f the H a r b o u r Study. Fifty-six r e c o r d i n g s h a d to be d i s c a r d e d due to d a t a collection failures. Thus, the analyses were b a s e d u p o n 447 shocks in this study. C o r r e l a t i o n s are given in tables 2 a n d 3. T h e highest c o r r e l a t i o n s o c c u r r e d for a l m o s t all m e a sures in the Y d i r e c t i o n with weighting A. D o s e measures ( t a b l e 3) y i e l d e d significantly ( p < 0.01) higher c o r r e l a t i o n s with d i s c o m f o r t than the corres p o n d i n g T i m e - m e a n m e a s u r e s (table 2). A p a r t from the D o s e measures, the highest c o r r e l a t i o n s were o b t a i n e d with the Peak m e a s u r e P o s m a x + Negmax. A m o n g the D o s e m e a s u r e s the c o r r e l a t i o n was lowered as the e x p o n e n t was raised f r o m 2 to 10,
except for the measures with weighting A in the Y direction in which R m 4 gave h i g h e r c o r r e l a t i o n s t h a n Rm2. T h e r a n k i n g o f the c o r r e l a t i o n s was u n a l t e r e d b y the exclusion o f the w e a k e s t 10% o f the shocks. In no case, however, was the d i f f e r e n c e b e t w e e n R m 2 a n d R m 4 significant. T w o o f the shock events were e x t r e m e l y long, 12 s a n d 16 s, respectively. A n exclusion of these two shocks f r o m the analyses d i d not affect the r a n k i n g o f the correlations. Figures 12 a n d 13 show the s t a n d a r d ized ratings p l o t t e d a g a i n s t the s t a n d a r d i z e d D o s e 2 levels. T h e results of the T i m e - m e a n m e a s u r e s were o p p o s i t e to that o f the D o s e measures, i.e. the c o r r e l a t i o n s were a u g m e n t e d as the e x p o n e n t was
2
4
6
s
m/s 2 n ~
~
Direction
X
j/
/
_._+'_
/i ~rec~n Y
I
/
iJ
i
,/
i
120
L
//~/
•. ~ 8 "
da
i
I
11o
' I o.1
F ! ! 0.5
1
2
! il
/'7"\
4
16
8
\/ 32
64
0.5
1
2
4
8
! 16
32
64
loo 0.5
1
2
4
8
16
32
64
Hz
Fig. 11. Typical l/3-octave band spectra measured on the seat of the forwarder in the X-. Y- and Z-directions. * 8-hour curve for "maximum exposure - health or safety' according to ISO 2631. * * 8-hour curve for 'fatigue-decreased proficiency" according to ISO 2631.
B.-O. Wikstr~m et al. / Whole-body vtbration
49
Table 2
Table 3
Pearson's correlation coefficients for linear regressions between technical measures for different directions (X, Y. Z) and rated discomfort (log-log), the Forest Study (n z 447). A, B and C stand for different weighting functions (see Methods). S~y.: Sum of vectors.
Pearson's correlation coefficients for linear regressions between Dose measures for different directions (X. Y, Z) and rated discomfort (log-log). the Forest Study (n ,~ 447). A, B and C stand for different weighting functions (see Methods). Sxy.: Sum of vectors.
X
Y
Z
Sxy..
Peak values Posmax, A Negmax, A Posmax + Negmax, A Posmax, B Negmax, B Posmax + Negmax, B Posmax, air a Negrnax, alt a Posmax + Negmax, alt a
0.715 0.678 0.743 0.661 0.619 0.704 _
0.737 0.669 0.792 0.710 0.600 0.769 0.726 0.628 0.797
0.721 0.692 0.731 0.727 0.691 0.734 0.726 0.705 0.740
0.760 0.756 0.757 -
0.679 0.712 0.717 0.718 0.718 0.606 0.640 0.654 0.661 0.665 -
0.708 0.744 0.748 0.749 0.751 0.662 0.703 0.716 0.722 0.726 0.718 0.748 0.753 0.755 0.756
0.651 0.696 0.709 0.714 0.716 0.644 0.695 0.708 0.713 0.716 0.664 0.706 0.716 0.720 0.722
0.739 0.753 0.752 0.751 0.752 0.710 0.727 0.732 0.735 0.738 0.703 0.723 0.730 0.735 0.738
0.714 0.688 0.681 0.672 -
0.756 0.724 0.706 0.694 -
0.664 0.671 0.692 0.682 0.721 0.697
-
Hz; Z:5 Hz)
0.586
0.534
0.673
-
Hz; Z:5 Hz)
0.615
0.665
0.728
-
Hz; Z:8 Hz)
0.619
0.612
0.657
-
Hz; Z:8 Hz)
0.662
0.728
0.728
0.724 0.668 0.668
0.750 0.728 0.728
0.734 0.730 0.734
Time-mean measures Rm2, A Rm4, A Rrn6, A Rm8, A Rml0, A Rm2, B Rm4, B Rm6, B Rm8, B Rml0, B Rm2, air a Rm4, alt a Rm6, air a Rm8, alt a Rml0, alt a
Acceleration response measures Maximax, A Minimin, A Maximax, B Minimin, B Maximax, C Minimin, C
Displacement measures Maximax (X, Y:I Minimin (X, Y:I Maximax (X, Y:2 Minimin (X, Y:2
Impulse measures Max, A Max, B Max, C
X
Y
Z
Sx~.-
0.798 0.799 0.784 0.775 0.771
0.748 0.743 0.737 0.734 0.732
0.808 0.797 0.780 0.771 0.776
0.779 0.777 0.766 0.759 0.754
0.743 0.741 0.736 0.733 0.731
0.799 0.786 0.771 0.763 0.759
0.808 0.808 0.793 0.784 0.779
0.755 0.748 0.741 0.738 0.736
0.795 0.783 0.769 0.762 0.759
Frequency weighting A
-
Z: weighted according to filter C; Y according to filter D. Sxw: Z according to filter C; X & Y according to filter B.
Dose 2 Dose 4 Dose 6 Dose 8 Dose 10
0.760 0.757 0.745 0.738 0.734
Frequency weighting B Dose Dose Dose Dose Dose
2 4 6 8 10
0.721 0.708 0.698 0.693 0.690
Alt. frequency weightings " Dose Dose Dose Dose Dose
2 4 6 8 10
-
a Z: weighted according to filter C; Y according to filter D. Sxy..: Z weighted according to filter C; X & Y according to filter B.
raised from 2 to 10. A comparable subset of 164 shocks from the Forest Study with a similar range of duration (4-5 s) was analyzed. Correlations were considerably lower in this shock sample due to the restriction of the acceleration range. The ranking of the correlations in this sample, however, was the same as in the Harbour Study, i.e. Rm2 gave the highest and R m l 0 the lowest correlations. The only significant difference occurred between Rm2 and Rml0. The Sum of vectors calculated as recommended by ISO 2631 was significantly more highly correlated with discomfort than was the critical direction. This increase was most pronounced for the Dose2 measure. The Sum of vectors was also calculated with equal weight given to all directions. This measure gave somewhat lower correlations throughout than the ISO procedure. In the Y direction the Dose measures with weighting A gave higher correlations than those with weighting B. This indicated that filter B did not give sufficient weight to the higher frequency
B.-O. Wikstrrm et aL / Whole-body vibration
50 Rating
Table 4
100
Pearson's correlation coefficients for linear regression between technical vibration measures with different integration times and rated discomfort (log-log).
30
lii/B
1 sec
n2 - 0.969
10
= m
Dose2 1
I
I
I
I
3
10
30
100
300
m ")'/s3
Fig. 13. Means of rated discomfort as a function of the Dose2
level of the shocks in figure 12. The shocks were divided into 20 classes from the Dose2 value.
components. An alternative weighting filter D was therefore tested in which the break-point was set to 4 Hz instead of 2 Hz as in filter B. This weighting yielded slightly higher correlations than weighting A and significantly higher correlations than weighting B.
-
Effect of integration time for Time-mean measures both studies
In order to evaluate the effect of different integration times, these were varied in the Timemean analyses from the duration of the whole shock event down to 4, 2 or 1 seconds respectively (methods). The results from both studies indicated that the correlation increased with longer durations (table 4). This was the case also for the directions not shown in the table.
Discussion The highest correlations were found for both studies in the direction which was critical according to ISO 2631. The Time-mean and Dose measures ( R m2 - R ml0 and Dose2-Dosel0, respectively) yielded overall higher correlations with the discomfort ratings than the Peak, Impulse and Response measures. In the Harbour Study the Time-mean and Dose measures with the same
2 set:
4 sec
Harbour Study, Z-direction Rm2, A 0.856 0.865 Rm4, A 0.842 0.850 Rm6, A 0.835 0.840 Rm8, A 0.832 0.835 Rml0, A 0.830 0.833 Rm2, B 0.847 0.859 Rm4, B 0.837 0.845 Rm6, B 0.833 0.838 Rm8, B 0.831 0.834 Rml0, B 0.830 0.832 Rm2, C 0.826 0.838 Rm4, C 0.824 0.832 Rm6, C 0.821 0.827 Rm8, C 0.820 0.823 Rml0, C 0.819 0.821 Forest Study, Rm2, A Rm4, A Rm6, A Rm8, A R_ml0, A Rm2, B Rm4, B Rm6, B Rm8, B Rml0, B
Y-direction 0.748 0.766 0.757 0.768 0.757 0.764 0.756 0.761 0.756 0.759 0.723 0.733 0.735 0.744 0.739 0.745 0.739 0.744 0.740 0.743
Whole event (Dose values) 0.866 0.852 0.839 0.832 0.827 0.866 0.850 0.835 0.827 0.823 0.851 0.834 0.820 0.813 0.809
0.786 0.781 0.771 0.765 0.762 0.758 0.755 0.752 0.749 0.747
0.798 0.799 0.784 0.775 0.771 0.779 0.777 0.766 0.759 0.754
exponents got nearly the same correlations since all shocks were of approximately equal duration. This was not the case in the Forest Study, in which the durations differed, where the Dose analyses got the highest correlations. Furthermore, both studies showed that the correlations for the Dose values were lowered as the exponent was increased from 2 to 10. The results therefore indicate that a measure sensitive to the peak value of the shock is less appropriate than a measure which takes into account the whole shock event. This is in agreement with laboratory studies of short-time events of vibration and shock, which show that a time-dependency exists for discomfort, which builds up fairly quickly at the onset of vibration but grows much more slowly after a few seconds (Miwa, 1968; Griffin and Whitham, 1980; Kjellberg and Wikstr~Sm, 1985). In conclusion, a Dose
B.-O. WikstriJrn et al. / Whole-body vibration
value seems to give a better correlation with discomfort than all the other measures tested. Of the Dose measures, the Dose2 and Dose4 best reflect the discomfort experienced during a shock in both studies. The figures as well as the analyses show that an exponent of 2 or 4 was best not only for the weaker shocks but for the whole range of shock levels. Likewise, these measures gave higher correlations also after an exclusion of the longest shock events. It should, however, be emphasized that the present studies could not differentiate between Dose2 and Dose4 with respect to their correlations with rated discomfort since the correlation between the Dose2 and Dose4 measures was very high. The present results correspond to the findings of Hiramatsu and Griffin (1984). However, they differ from the results of the laboratory studies by Miwa (1968), Griffin and Whitham (1980) and Kjellberg and WikstrSm (1985), which indicated that a higher exponent than 2 was to be preferred in the assessment of shocks. One factor which may have led to this discrepancy is the fact that the drivers saw the obstacles and were thus prepared for the shocks, whereas the subjects in the laboratory experiments h a d no idea what intensity the next shock would have. It is well known that predictability and control may weaken the response to aversive stimulation (Miller and Grant, 1978). In the Harbour Study the Sum of vectors showed a weaker correlation with discomfort than the Z direction values. This indicates that the ISO standard gives too much weight to the X and Y directions in the computation of the Sum of vectors. In the Forest Study, where the Y direction was critical, the Sum of vectors was more highly correlated with discomfort than the Y direction and the ISO weighting of directions proved to be better than an equal weighting of all directions. Thus, the discomfort ratings seemed to be determined primarily by the critical direction, irrespective of which this was. Both studies included a test of different frequency weighting procedures. No significant differences could be found. However, the results in the Forest Study indicate that weighting B gives too little weight to frequencies above 2 Hz in the Y direction. Such a conclusion is supported by the results of a French experiment (Donati et al.,
51
1983). The assessment of different weighting procedures must, however, be interpreted with caution since the shock characteristics were not under experimental control. Accidental correlations between acceleration levels in different directions and frequency bands may thus have influenced the results. The points and directions of the measurements used were based on ISO 2631. Studies at e.g. ISVR have shown that additional data from the footplate and the backrest as well as data from rotational transducers on the seat can give additional information, which may be useful for evaluation of the discomfort (Parsons and Griffin, 1982; Parsons et al., 1982). Still, the main input of information is normally given by linear transducers on the seat used in the present investigation. Of the machines studied there was some roll motion in the forwarder as the machine travelled in rough terrain, which might explain some of the variance in the correlation analyses. In the terminal tractor, vibrations from the floor might have had some influence on the correlations. Considering the normal biological variation among subjects and the reliability of the ratings, the correlation between the discomfort ratings and the best vibration evaluation methods seems high enough to justify conclusions on the choice of methods from measurements on the seat only. The investigations were performed with drivers of heavy vehicles. The conclusions are therefore valid only for this population. Passengers are often subjected to much lower vibration levels and shorter exposure times and are often not prepared for sudden shock events, where other methods than the Dose2 and Dose4 measures might be more suitable. It is worth noting that an Rm-value with a fixed integration time, which is not necessarily equal to the duration of the shock, corresponds to a dose-value and thus would have given the same correlation with discomfort as the best measures, the Dose2 and Dose4 measures. With such an Rm2 value, for example, results can be given in familiar units, i.e. m / s 2 . From table 4 its seems as if the integration time must be defined long enough (i.e. 4 - 8 seconds) to let the amplitude of the shock subside completely in the body. An evaluation method for shock events must take care of the highest values, which in the work
52
B.-O. Wikstri~m et aL / Whole-body vibration
environment are in the range of 40-50 m / s 2 peak. A solution could be a distribution of Rm values (with a fixed integration time), measured over an exposure, which may be compared to a given distribution. The latter may serve as a recommended guideline for the maximum number of shocks, which may occur up to a certain level. Although statistically significant, most of the differences between the correlations in the present study were rather small and probably in m a n y cases of minor practical importance. This would have been a problem if one of the more cumbersome methods of analysis had proven to be the best (e.g. shock response analysis). The additional information might in that case not be worth the extra amount of work required for the analysis. Given the present results this conflict is less problematic.
References Corbridge. C. and Griffin, M.J., 1985. Vibration and comfort: Vertical and lateral motion in the range 0.5 to 5.0 Hz. Ergonomics. 29: 249-272. Donati. P., Grosjean, A., Mistrot, P. and Roure, L., 1983. The subjective equivalence of sinusoidal and random wholebody vibration in the sitting position. (An experimental study using the 'floating reference vibration' method). Ergonomics. 26: 251-273. Griffin. M.J. and Whitham, E.M., 1980. Discomfort produced by impulsive whole-body vibration. J. Acoust. Soc. Am., 68: 1277-1284. Griffin. M.J., Parsons, K.C. and Whitham, E.M., 1982. Vibration and comfort, IV. Ergonomics, 25: 721-739. Hansson, J.-E. and Wikstrt~m, B.-O., 1979. Comparison of some technical methods for the evaluation of whole-body vibration. Ergonomics, 24: 953-963. Hiramatsu, K and Griffin, M.J., 1984. Predicting the subjective
response to non-steady vibration based on the summation of subjective magnitude. J. Acoust. Soc. Am., 76: 10801088. ISO, 1974. Guide for the evaluation of human exposure to whole-body vibration. ISO 2631. First edition 1974, second edition 1978. International Organization for Standardization, Geneva. ISO, 1984. Description of procedures for evaluation of vibration containing events of short duration. Working draft for an ISO Technical Report. ISO TC108/SC4. International Organization for Standardization. Geneva. ISO. 1988. First draft proposal ISO/DP 2631--Guide for the evaluation of human exposure to whole-body mechanical vibration. ISO TC 1 0 8 / S C 4 / N 177. International Organization for Standardization, Geneva. Kjellberg. A. and WikstriSm. B.-O.. 1985. Subjective reactions to whole-body vibration of short duration. J. Sound. Vib., 99: 415-424. Miller. S.M. and Grant. R.P.. 1978. The blunting theory: A theory of predictability and human stress. In: P.O, SjOd~n, S. Bates and W.S. Dockens (Eds.), Trends in Behavior Therapy. Academic press, New York. Miwa, T., 1968. Evaluation methods for vibration effect, Part 7: The vibration greatness of the pulses. Ind. Health, 6: 143-164. Parsons, K.C. and Griffin, M.J., 1982. Vibration and comfort, II. Rotational seat vibration. Ergonomics. 25: 631-644. Parsons, K.C.. Griffin, M.J. and Whitham, E.M.. 1982. Vibration and comfort. III. Translational vibration of the seat and back. Ergonomics, 25: 645-720. Payne, P.R., 1978. Method to quantify ride comfort and allowable accelerations. Aviat. Space Environ. Med., 49: 262-269. Shoenberger, R.W.. 1978. Intensity judgements of nonsinusoidal vibrations: Support for the ISO weighting method. Aviat. Space Environ. Med.. 49: 1327-1330. Sp~ng, K.. Arnberg. P.W., Bennerhult, O. and Kloow, T., 1985. The influence of transient vibrations on perception. Part I. Report TR 5.339.01 from IFM Akustikbyr/m. Stockholm. VDI, 1963. Beurteilung der einwirkung mechanischer Schwingungen auf den Menschen. Verein Deutscher Ingenieure, Diisseldorf.