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Absorption of energy during vertical whole-body vibration exposure
Journal of Biomechanics 31 (1998) 317 — 326
Absorption of energy during vertical whole-body vibration exposure Ronnie Lundstro¨m*, Patrik Holmlund, Lennart Lindberg Department of Technical Hygiene, National Institute for Working Life, P.O. Box 7654, S-907 13 Umeas , Sweden Received in Final Form 16 December 1997
Abstract Absorbed power (P ) during exposure to vertical whole-body vibration in a sitting posture was measured on 15 male and 15 A"4 female subjects. Different experimental conditions were applied, such as vibration level (0.5—1.4 m s~2) and frequency (2—100 Hz), body weight (54—93 kg) and, relaxed and erected upper body positions. Results show that P was strongly related to the frequency of A"4 the vibration, peaking within the range of 4—6 Hz. The peak was predominantly located in the lower end of this range for females and for the relaxed sitting position. P increased with acceleration level and body weight. Almost a ten-fold increase in P was observed A"4 A"4 at the critical frequency when the vibration exposure was raised from 0.5 to 1.4 m s~2. If risk assessment is based on the assumption that the amount of P , independent of the frequency of the vibration, indicates a hazard, then the ISO-standard 2631 under- and A"4 overestimates the risk at frequencies below and above about 6 Hz, respectively. The results also indicate a need for differentiated guidelines for females and males. Many types of vehicles produce whole-body vibration with frequencies which coincide with the range where the highest P was observed. P is a ‘new’ concept for measurement of whole-body vibration exposure. Although not A"4 A"4 yet thoughly evaluated, this measure may be a better quantity for risk assessment than those specified in ISO 2631 since it also takes the dynamic force applied to the human body into account. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Vibration; Whole body; Vertical; Power; Absorption
1. Introduction Several people are exposed to whole-body vibration (WBV) in their occupational life, especially drivers of various vehicles such as dumpers, excavators, scrapers, buses and trucks. The main categories of response to WBV are perception, degraded comfort, interference with activities, impaired health and occurence of motion sickness. Many scientific papers, reports and other documents have addressed these types of responses. Some publications present comprehensive surveys of current knowledge on the effects of WBV (e.g. Christ, et al., 1989; Dupuis and Zerlett, 1986; Griffin, 1990; Hulshof and Zanten, 1987; Magnusson, 1991; Pope et al., 1994; Sandover, 1988; Wikstro¨m et al., 1994). It can be concluded that human response to WBV is a very complex phenomenon. Combinations of effects may occur simultaneously but also one effect may promote the onset of another. During exposure to WBV there are many physiological,
* Corresponding author. Tel.: #46 90 786 5097; fax: #46 90 786 5027; e-mail: [email protected]. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 0 1 1 - 6
psychophysical and physical factors which are relevant for the development of unwanted effects, such as individual susceptibility, body constitution, posture together with the frequency, direction, magnitude and duration of the vibration. Guidelines given in the International standard ISO 2631-1 (1997) are most often used for risk assessment. Accordingly, measurement of WBV should be conducted on the surface transmitting vibration to the human body. Vibration should be measured within the frequency range 0.5—80 Hz in terms of frequency-weighted acceleration. A disadvantage with this measure is that it only describes the acceleration magnitude on the vibrating surface. Thus, it can be argued that it presents a poor description about the extent of vibration actually being transmitted to the body. The amount of vibration energy, either absorbed or exchanged between the source and body, may therefore be a better measure of the physical stress on the body since it takes into consideration the interplay between the vibrating structure and the body in contact with it. Moreover, energy is a scalar quantity which makes it easy to add up contributions from all three directions to a single value.
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The instantaneous power P transmitted to the strucT3 ture is:
2. Methods
P "F(¹) ) l(t),P (t)#P (t). (1) T3 A"4 EP (t) is the absorbed part of the power, accounting for A"4 the energy necessary for keeping pace with the energy dissipated through structural damping. The elastic power P (t) is continuously delivered to and removed from the Estructure during each period of excitation and averages zero for each sinusoidal cycle of motion. Thus, the timeaveraged absorbed power SP T equals the transmitted A"4 power, SP T i.e. T3 SP T"SP T"SF(t) ) l(t)T. (2) A"4 T3 The concept of absorbed energy was discussed in the mid-1960s by a group of scientists (Lee and Pradko, 1968; Pradko and Lee, 1968; 1966; Pradko et al., 1965a, b). They presented results from investigations which indicated that subjective experience of vibration is related to the amount of vibration energy absorbed by the body. A decade later, Janeway (1975) defended these observations. He pointed out several arguments which he felt supported the idea of including the concept of energy absorption in ISO 2631, at least for the comfort criteria. Since then, no further work appears to be published in this area. However, in regard to hand-arm vibration, the concept has been discussed to a larger extent. For instance, Lidstro¨m (1977) showed that the prevalence of vibration-induced injuries within different occupational groups is related to the amount of absorbed energy. The purpose of this study was to investigate WBV energy absorption during different experimental conditions. The relation between absorbed power and frequency, exposure level, direction, upper-body position, body weight and gender were focused.
2.1. Subjects The study group consisted of 15 females and 15 males (Table 1). Information about their anthropometric measures, age, work assignment, years at work, general state of health, previous or present exposure to WBV, etc., was provided by questionnaire. All subjects were healthy with no signs or symptoms of disorders of the musculo-skeletal system, such as low back pain or lumbago. 2.2. Apparatus Sinusoidal vibration was generated with the help of a signal generator (Bru¨el and Kjær 1049), an electrodynamic shaker (LDS 712#ILS 712) and a power amplifier (LDS, MPA 1) (Fig. 1). A girder was directly bolted onto the shaker table. Two linear ball bearings were mounted on the girder, one at each edge, in order to reduce momentum forces on the shaker. Between the seat plate, which was made of 3 cm thick wooden board Table 1 Mean (M), standard deviation ($SD), maximum (max) and minimum (min) values for the subjects’ age, body weight (kg) and height (cm) Females Males All subjects M M M ($SD, max, min) ($SD, max, min) ($SD, max, min) n Age Weight Height
15 24 (2, 30, 23) 66 (10, 93, 54) 168 (6, 180, 157)
Fig. 1. Chart showing the experimental set-up.
15 38 (12, 58, 22) 74 (9, 92, 57) 177 (6, 190, 167)
30 31 (11, 58, 22) 70 (11, 93, 54) 173 (7, 190, 157)
R. Lundstro( m et al. / Journal of Biomechanics 31 (1998) 317—326
(23]30 cm), and the girder, four piezo-electric force transducers (Kistler 9251) were mounted. A piezo-electric accelerometer (Bru¨el and Kjær 4231) was centrally attached to the underside of the seat plate. The signals from the transducers were amplified and low-pass filtered by identical charge amplifiers (Bru¨el and Kjær 2635) and Bessel filters (cut-off frequency: 300 Hz). The risk of adding any phase difference between the signals are thereby minimized. By using the compressor function in the signal generator, the vibration level could be kept constant independent of the frequency and load. After A/D-conversion of the force and acceleration signals, the values were continuously stored on disk for later analysis. To calibrate the force channel dynamically at 5 Hz, the seat plate was loaded with solid concrete masses weighing 53 and 85 kg. An accelerometer calibrator (Bru¨el and Kjær 4291) was used for the vibration channel. Before the experiments the measuring system was tested without load in order to secure a ‘zero-power’ result and to determine the signal-to-noise ratio. 2.2. Experimental procedure Prior to the first occasion, each subject was given written information about the experiment, which included the purpose of the study, possible risk for acute or chronic injuries, ethical committee approval (University of Umeas , Dnr. 94-255) and their right to either interrupt an ongoing test run or refrain from further tests. Informed prior consent was signed by each subject. The experimental procedure for all test runs followed a predestinated protocol. After weighing in a standing position the subjects sat on the seat plate with feet positioned on an adjustable footrest. The footrest was adjusted so that the lower legs were vertical and the upper legs horizontal. The static weight on the force plate and the footrest were then determined. At each occasion the subject was exposed to one of the four acceleration levels, 0.5, 0.7, 1.0 or 1.4 m s~2 in both erected (E) and relaxed 3.4 (R) upper-body posture. The posture was visually checked by the experimenter during each test run and if necessary corrected during measurement pauses. The measurement period for each frequency was 15 s followed by a 5 s pause. The frequency was increased from 2 to 100 Hz in steps of 1/3 octaves, except in the range 2.5—20 Hz where the steps were 1/6 octaves. The entire experiment took about 30 min to complete for which about 20 min consisted of exposure to vibration. Each subject participated at four occasions, all on different days, one for each of the different acceleration levels. 2.3. Data and statistical analysis The collected data were processed and analysed with LabViewTM. For each test frequency the collected acceler-
319
ation signal a(t) was integrated to get the velocity v(t). The total force F (t) registered by the force cells also M%!4 consist of a contribution generated by the mass of the seat plate (m ). This contribution is always in phase P-!5% with the acceleration signal and was cancelled by vectorial substraction. The force F(t) transmitted to the sitting subject was determined as F(t)"F (t)! M%!4 m a(t). The time-average absorbed power SP T was P-!5% A"4 thereafter determined according to Eq. (2). The statistical analyses consisted of the determination of the means and standard deviations plus analysis of variances (ANOVA).
3. Results Fig. 2 shows individual graphs for absorbed power at different test frequencies during vibration exposure at 1.0 m s~2. As can be seen, individual graphs have a relatively similar shape. Absorbed power increased with the frequency up to a peak in the range of 4—6 Hz after which it decreased. For females, there was an indication for an additional peak around 9 Hz. The frequency for maximal absorption was somewhat lower for the relaxed sitting position compared to erected. The inter-individual variation was quite large for both females and males, at least for frequencies up to about 10 Hz. A large amount of this variation was due to differences in body weight. Regression and correlation analysis clearly indicated that absorbed power, summed up over the entire frequency range, increased with body weight (Fig. 3, Table 2). With the intention of reducing the influence of this factor, obtained data were normalized against the individual static sitting weight, i.e in units of W kg~1. Fig. 4 shows mean values for normalized absorbed power at different frequencies for both females and males, for both sitting positions and all accelerations levels. The numerical turn out for one acceleration level (1.0 m s~2) is given in Table 3. The mean to standard deviation ratio for each test frequency was roughly the same for all acceleration levels. For a structure with a fixed mass and internal damping, absorption of power should theoretically increase quadratically with the exposure level, i.e. PJa2. Regression analysis based on this model supports this idea. The highest correlation coefficients were, however, obtained when the regression analysis was based on the model PJ0#k a#k a2. The zero intercept in the 1 2 model implies that no absorption of power occurred when acceleration was set to zero. Table 4 shows regression and correlation coefficients for both females and males, split by relaxed and erected sitting positions. By the size of the regression coefficients, k and k , it can be 1 2 stated that the amount of absorbed power predominantly depends on the square of the acceleration. An extract from statistical analysis (ANOVA) is given in Table 5. The result showed that the absorbed power
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Fig. 2. Individual graphs for absorbed power at different frequencies for males (n"15) and females (n"15) sitting relaxed and erected.
was significantly dependent on the acceleration level for all test frequencies. For most frequencies below 25 Hz there were also significant differences due to posture. In the frequency ranges of about 3—10 Hz and above 60 Hz significant differencies due to gender seemed to exist. A significant interplay between gender and acceleration (GA) as well as posture and acceleration (PA) were apparent for frequencies below 4 Hz.
4. Discussion
Fig. 3. Absorbed power-sum for the frequency range 2—100 Hz for different stimulus acceleration levels (K"0.5, £"0.7, L"1.0, n"1.4 m s~2) in relation to ‘sitting’ weight. Regression and correlation coefficients are given in Table 2.
This study showed that absorption of power depends on several factors with frequency and magnitude of vibration among the most significant. In general, the amount of absorbed power increases with the frequency up to a peak in the range of 4—6 Hz during exposure at a constant acceleration level. Above this frequency range a gradual decrease in P with increasing frequency A"4 occurred. Absorbed power at each frequency was proportional to the square of the acceleration. The frequency at which maximal absorption occurs tended to be lower for females as compared to males. Another finding was that maximal absorption tended to increase and slide towards
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321
Table 2 Regression (k) and correlation (r2) coefficients for the relation between absorbed power sum (P ) for the frequency range 2—100 Hz and sitting weight S6. (w ) at different acceleration levels (m s~2). Linear regression model: P "0#kw . Regression lines are presented in Fig. 3 4 46. 4 Acceleration (m s~2)
0.5 0.7 1.0 1.4
Males
Females
Relaxed
Erected
Relaxed
Erected
k
r2
k
r2
k
r2
k
r2
0.067 0.135 0.269 0.516
0.99 0.992 0.992 0.995
0.066 0.13 0.256 0.499
0.988 0.986 0.989 0.991
0.074 0.147 0.294 0.597
0.995 0.995 0.991 0.994
0.07 0.136 0.271 0.555
0.994 0.992 0.992 0.994
Fig. 4. Normalized mean absorbed power for females (n"15) and males (n"15) sitting erected and relaxed.
lower frequencies when the body position was changed from erected to relaxed. As shown in Table 5 significant gender differencies in P weight could be observed for some stimulus frequenA"4 cies after normalization with sitting weight. Graphs for males and females have however a very similar shape. Some other studies, however with respect to normalized apparent mass and mechanical impedance have shown a similar outcome (e.g. Fairley and Griffin, 1989;
Holmlund et al., 1995). The principal reason for observed significances, at least for frequencies lower than about 10 Hz, seems to be a slight lowering of the frequency at which maximal absorption occurs for females. This may be due to differences in the bodily structure of males and females and/or due to the higher m /m ratio which &!5 .64#-% is generally observed among females. A higher ratio causes a decrease in the stiffness-to-mass ratio which in turn lowers the resonance frequency and consequently
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Table 3 Mean (M) and standard deviation ($SD) for absorbed power at different frequencies for males (n"15) and females (n"15) during vibration exposure to an acceleration level of 1 m s~2 Frequency (Hz)
Absorbed power (10~3 W kg~1) Relaxed position Males
2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
10.8 10.8 10.7 10.9 12.2 17.6 29.2 32.6 26.8 20.7 15.5 12.1 10.2 9.0 7.4 6.1 4.4 3.4 2.6 2.1 1.3 0.8 0.6 0.4 0.2 0.1 0.05
Erected position Females
(5.5) (2.0) (2.0) (2.2) (3.2) (6.9) (14.0) (9.8) (4.5) (3.7) (3.4) (2.5) (1.9) (1.6) (1.2) (0.8) (0.6) (0.6) (0.4) (0.3) (0.1) (0.07) (0.09) (0.08) (0.05) (0.02) (0.01)
8.6 10.1 12.4 14.3 17.7 22.7 29.9 31.1 23.2 18.1 15.1 14.1 12.7 10.5 8.0 6.4 4.6 3.5 2.7 2.2 1.3 0.8 0.6 0.4 0.2 0.1 0.05
Males (3.9) (3.4) (5.5) (5.7) (5.4) (6.7) (9.7) (5.6) (4.2) (3.7) (3.3) (2.2) (1.6) (1.5) (1.2) (1.0) (0.7) (0.6) (0.4) (0.3) (0.1) (0.08) (0.06) (0.04) (0.05) (0.03) (0.01)
also the frequency for maximal power absorption. More fat also implies more damping and thus more power absorption. The effect of posture on other biomechanical measures, such as transmissibility, apparent mass and mechanical impedance, has been studied by several other investigators (e.g. Coermann, 1962; Fairley and Griffin, 1989; Griffin, 1975; Holmlund et al., 1995; Miwa, 1975; Potemkin and Frolov, 1972). For all measures it seems like a change in posture may alter the response, but not necessarily for all subjects. The effect of posture however tends to be more pronounced for transmissibility for which a larger and more consistent effect has been observed. Any corresponding data for P has to our knowA"4 ledge not been published. A general observation, as shown in this as well as other studies, is that sitting in a relaxed posture results in a softening of the biomechanical system which redu ces the resonance frequency. A possible explanation could be that relaxed sitting posture constitutes more relaxed muscles in the abdominal region which in turn reduces body stiffness and increases damping. Another explanation could be
9.4 11.7 13.0 13.4 17.4 27.0 35.8 32.4 24.2 18.3 13.8 11.1 9.1 7.9 6.5 5.2 3.8 2.9 2.3 1.9 1.2 0.8 0.6 0.4 0.2 0.1 0.04
Females (2.9) (3.8) (3.6) (3.7) (6.9) (12.1) (10.9) (5.3) (6.3) (5.0) (3.0) (1.9) (1.5) (1.2) (1.0) (0.9) (0.6) (0.4) (0.3) (0.2) (0.1) (0.1) (0.07) (0.07) (0.06) (0.03) (0.01)
9.4 12.7 16.4 19.4 24.0 34.0 37.4 29.7 19.8 15.7 13.8 13.4 12.3 10.3 7.4 5.6 3.9 3.0 2.4 1.9 1.2 0.8 0.6 0.4 0.2 0.1 0.04
(3.1) (3.2) (5.2) (5.6) (5.7) (10.0) (7.2) (5.2) (3.5) (2.8) (2.6) (1.7) (1.3) (1.3) (0.9) (0.7) (0.5) (0.4) (0.2) (0.2) (0.1) (0.07) (0.05) (0.04) (0.05) (0.03) (0.02)
that biomechanical response is affected by stretch reflexes in the paraspinal muscles shown to be evoked by vibration (e.g. Sandover, 1981; Seidel, 1988; Seroussi et al., 1989). Interestingly, evoked strech reflexes are synchronous with a sinusoidal vibration stimuli but are, at many stimulus frequencies, so far out of phase that their forces are added to those of the stimulus (Seroussi et al., 1989). Such evoked muscle activity will most certainly have an influence on all biomechanical measures as well as absorbed power. It can also be argued that the state of disc hydration is of importance since it will affect the biomechanical properties of the spine. Three subjects were tested at different times during a day as well as between days. Very small and unsystematical differences in absorbed power were observed which was taken as an indication that diurnal changes were not of significant importance in this context. There are most likely several other human or experimental factors that may influence the characteristics of absorbed power which adds to the complexibility in this context. In this report, it is assumed that it is the absorbed portion of the total power which should be considered as
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Table 4 Regression and correlation coefficients for the relation between normalized absorbed power P (W kg~1) and acceleration level a (m s~2) for A"4,N03. each frequency used. Regression model: P "0#k a#k a2 A"4,N03. 1 2 Frequency (Hz)
Absorbed power (10~3 W kg~1) Relaxed position
Erected position
Males
2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
Females
k 1
k
2.7 3.6 4.5 3.4 !0.75 !5.7 !8.3 0.38 5.8 4.9 2.1 0.59 0.21 0.14 0.50 0.80 0.76 0.50 0.36 0.24 0.12 0.058 0.069 0.015 !0.002 !0.007 !0.004
6.4 7.8 8.1 10.2 18.2 32.0 42.7 31.0 18.3 13.9 12.1 10.8 9.1 7.9 6.0 4.4 3.1 2.5 1.9 1.6 1.1 0.73 0.50 0.37 0.22 0.10 0.05
2
r2 0.892 0.948 0.962 0.940 0.866 0.853 0.934 0.971 0.932 0.930 0.959 0.976 0.980 0.981 0.976 0.973 0.972 0.977 0.984 0.988 0.986 0.985 0.986 0.977 0.946 0.927 0.909
k 1 0.26 !2.4 !1.8 !1.5 !4.8 !13.9 !4.5 5.0 4.1 1.4 !0.65 !1.8 !0.21 1.8 1.8 1.4 0.78 0.47 0.30 0.19 0.066 0.047 0.073 0.017 0.017 0.009 0.007
Males k 2
r2
8.9 15.3 18.3 21.4 30.4 50.0 42.3 24.8 16.3 15.0 15.0 15.4 12.5 8.3 5.6 4.2 3.2 2.6 2.1 1.7 1.2 0.76 0.49 0.35 0.19 0.086 0.037
0.926 0.967 0.957 0.949 0.956 0.943 0.977 0.974 0.966 0.959 0.981 0.992 0.984 0.982 0.981 0.984 0.983 0.984 0.987 0.991 0.994 0.993 0.992 0.988 0.947 0.919 0.908
most important. This assumption can of course be questioned since it can be argued that power, which is not absorbed, may also have an effect on the body. Vessels, nerves, muscles, bone, joints and other parts of the body will be subjected to compression and extension during vibration exposure. No power will be absorbed if this physical strain does not exceed the elastical range for a body structure. All this implies that organic damages occurs first after elastic limits are exceeded. This discussion presumes body structures behaving like ideal mass-spring systems without internal damping. However, most biological structures do have internal damping which means that they absorb power even when affecting dynamic forces are within the elastic range. Non absorbed power may still have an influence since vibration activates for instance different types of receptors, such as mechanoreceptors, proprioceptors, thermoceptors and nociceptors. This, and the mechanical strain itself, may have an influence on biochemical processes and interfere with blood circulation and nutrition. It is thus possible that some types of complaints or disorders
k 1 4.6 2.7 2.9 2.8 0.06 !0.97 !4.4 !1.2 0.91 0.97 0.04 !0.50 !0.15 0.51 1.1 1.3 1.1 0.70 0.44 0.26 0.097 0.42 0.065 0.024 0.004 !0.003 0.004
Females k 2
r2
5.3 7.4 7.5 8.2 13.0 18.5 32.3 33.1 26.1 20.6 16.4 13.2 10.6 8.4 6.3 4.7 3.4 2.7 2.2 1.8 1.2 0.79 0.51 0.37 0.22 0.10 0.043
0.769 0.926 0.935 0.932 0.870 0.845 0.830 0.931 0.966 0.955 0.939 0.965 0.975 0.973 0.971 0.971 0.968 0.968 0.970 0.975 0.981 0.982 0.983 0.966 0.945 0.938 0.911
k
1
0.96 !0.33 !0.39 !0.74 !1.5 !7.1 !8.5 !2.0 1.7 1.2 !0.39 !1.9 0.99 2.0 1.8 1.6 1.1 0.74 0.50 0.29 0.091 0.042 0.067 !0.001 !0.003 0.005 0.003
k 2
r2
7.4 10.4 12.5 15.1 19.9 32.3 40.5 33.4 21.8 17.2 15.7 16.2 12.4 8.3 6.1 4.7 3.4 2.7 2.1 1.8 1.2 0.78 0.50 0.37 0.21 0.093 0.041
0.810 0.908 0.890 0.936 0.937 0.875 0.944 0.971 0.964 0.954 0.977 0.987 0.981 0.983 0.982 0.979 0.980 0.982 0.986 0.988 0.990 0.992 0.991 0.983 0.946 0.918 0.896
are solely related to either power absorbed or power not absorbed while others are related to both. An example of an absorbed power-related effect might be musculo-skeletal disorders while effects on comfort and perception more likely are related to power not absorbed. This is of course purely speculative since no support for this exists in the scientific literature. Another possibility is that detrimental effects are purely related to the total amount of power affecting the body. The interindividual variation in absorbed power is relatively large, both in the magnitude and frequency plane. Differences in body weight and bodily structure are likely the most important reasons. In order to reduce the influence of at least differences in body weight we chose to individually normalize our results with respect to the sitting weight. This procedure suggests certain advantages. It not only makes the data more easy to compile and interpret but also increases the usefulness of the results. An estimation of the amount of absorbed power can thus be calculated by multiplying normalized data and sitting weight. The sitting and standing weight
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Table 5 P-values extracted from an analysis of variances ANOVA (G"gender, P"posture, A"acceleration). For more information, see text Frequency (Hz) 2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
G
0.0699 0.6045 (0.0001 (0.0001 (0.0001 (0.0001 0.2254 0.0060 (0.0001 (0.0001 0.0048 0.0002 (0.0001 0.0001 0.1841 0.6337 0.1309 0.0962 0.0977 0.0863 0.0062 0.0015 (0.0001 (0.0001 0.0002 0.0095 0.0066
P
0.9702 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 0.0001 0.2981 0.0002 0.0004 0.0008 0.0012 0.0149 0.0104 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 0.0002 0.0602 0.6214 0.6535 0.6793 0.3725 0.2622
GP
0.2207 0.0984 0.0453 0.0213 0.1934 0.6102 0.6134 0.5882 0.9068 0.4100 0.1559 0.2291 0.0968 0.1325 0.4070 0.8711 0.6858 0.4958 0.5549 0.5123 0.5279 0.2968 0.9538 0.6462 0.7000 0.9427 0.8277
ratio for subjects participating in this study was on average 0.77 (SD$0.033) and 0.76 (SD$0.030) for females and males, respectively. A normalization with respect to other measures for bodily structure, for instance length, is desirable but requires a more extensive data set before a more complete model for normalization can be outlined. An interesting aspect of the results was how absorbed power relates to the guidelines presented in ISO 2631-1 (1997). The frequency weighting procedure implies that human response to WBV is not only related to magnitude and duration but also to the frequency of the vibration. The purpose of the frequency weighting procedure is thus to compensate, or in other words to normalize, for differences in human susceptibility at different frequencies. As stated earlier, vibration quantified in terms of acceleration do not neccessarily mirror the physical strain on the body. It merely reflects the vibration level on the contact surface between the body and the vibration source. A better way to quantify the emmission i.e. the actual vibration dose, may therefore be ‘absorbed power’. Whether a frequency weighting procedure is required also for this measure cannot yet be determined. A first assumption could be that a certain amount of absorbed power is equally harmful or annoying regardless of frequency. A frequency weighting in this
A
(0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001
GA
PA
0.8995 0.0024 (0.0001 (0.0001 (0.0001 (0.0001 0.6379 0.0601 0.0007 0.0240 0.8449 (0.0001 (0.0001 0.2662 0.8843 0.6810 0.7429 0.6504 0.7371 0.7850 0.5110 0.2427 0.0519 0.0175 0.0522 0.0971 0.0513
0.8754 0.0033 0.0003 (0.0001 (0.0001 (0.0001 0.0345 0.2462 0.0007 0.0062 0.0293 0.0387 0.3727 0.5644 0.1529 0.0364 0.0149 0.0267 0.0346 0.0173 0.0596 0.4873 0.9610 0.9703 0.9682 0.9278 0.8923
GPA
0.9340 0.1677 0.1534 0.3082 0.6302 0.9665 0.6644 0.6685 0.9212 0.4980 0.3428 0.5986 0.5197 0.8115 0.9937 0.9962 0.9815 0.9364 0.8744 0.8493 0.9125 0.8809 0.9848 0.8991 0.9445 0.9849 0.9964
case would not be necessary. Fig. 5 shows acceleration levels at different frequencies corresponding to constant absorbed power. The frequency weighting curve, ¼ , in , accordance with ISO 2631-1 (1997), corresponding to an acceleration level of 0.5 m s~2 is also shown. The amount of absorbed power at 6 Hz, at which the ¼ correction , factor is 1, was calculated to be 5.4 and 4.5]10~3 W for males and females, respectively, sitting relaxed. The corresponding acceleration levels at other frequencies were thereafter determined. Interestingly, calculations based on corresponding data for males presented by Lee and Pradko (1968) show an almost identical result as ours. However, their data covers frequencies up to 12 Hz which limits the comparison to the range of 2—12 Hz. Thus, according to both theirs and our result it seems like the frequency weighting procedure underestimates the risk for unwanted effects for frequencies below 6 Hz and vice versa for frequencies above. An adjustment of the ISO-weighting in accordance with the concept of absorbed power would consequently lead to a sharpening with 2—3 dB and a reduction with 5—6 dB at low and high frequencies respectively. The basis for this discussion is of course the frequency from which the calculations originate. In this case, 6 Hz was chosen. For instance, if 5 Hz was chosen instead, the ISO- and absorbed power curves would almost meet at low frequencies but the differences
R. Lundstro( m et al. / Journal of Biomechanics 31 (1998) 317—326
325
Fig. 5. Comparisons of two concepts for risk assessments of whole-body vibration exposure, i.e. constant frequency-weighted acceleration in accordance with ISO 2631 versus constant absorbed power. Graphs for the latter concept is given for relaxed sitting posture split by gender but converted to acceleration levels. For more information, see text.
at higher frequencies would become even more obvious. It seems like females absorb a larger amount of power than males which might imply a need for differentiated guidelines for risk assessments which should be more restrictive for females. The extent of data obtained in this study is however too limited to allow any extensive conclusion in this regard. The current study consists of data only for the vertical direction. It is therefore of utmost importance to conduct similar studies for the horizontal directions, i.e. fore-and-aft and lateral direction, since these also contribute to the risk of health problems due to WBV exposure. The concept of absorbed power as a ‘new’ measure for the evaluation of WBV exposure definitely opens a new area for research. Epidemiological studies on different categories of professional drivers could be a fruitful way to compare different measures for vibration exposure in relation to health effects. Professional drivers could, for instance, be asked to rate percieved comfort on a visual analogue scale during controlled WBV excitation in a laboratory environment or while driving on a test track.
Acknowledgements The financial support by the Swedish Council for Work Life Research is gratefully acknowledged (Project: 94-0026).
References Christ, E., Brusl, H., Donati, P., Griffin, M., Hohmann, B., Lundstro¨m, R., Meyer, J., Straatsa, H., 1989. Vibration at work. International Sektion ‘‘Research’’, Institut National de Recherche et de Securite (INRS), Paris. Coermann, R.R., 1962. The mechanical impedance of the human body in sitting and standing position at low frequencies. Human Factors 4, 227—253. Dupuis, H., Zerlett, G., 1986. The Effects of Whole-Body Vibration. Springer, Berlin. Fairley, T.E., Griffin, M.J., 1989. The apparent mass of the seated human body: vertical vibration. Journal of Biomechanics 22, 81—94. Griffin, M.J., 1975. Vertical vibration of seated subjects: effects of posture, vibration level and frequency. Aviation, Space and Environmental Medicine 46, 269—276. Griffin, M.J., 1990. Handbook of Human Vibration. Academic Press, London. Holmlund, P., Lundstro¨m, R., Lindberg, L., 1995. Whole-body vibration. Mechanical impedance of human body in the vertical direction. In: Proceedings of the United Kingdom Informal Group Meeting on Human Response to Vibration, Silsoe Research Institute, West Park, Silsoe, Bedford MK45 4HS. Hulshof, C., Zanten, v.B.V., 1987. Whole-body vibration and low-back pain — a review of epidemiological studies. International Archives of Occupational and Environmental Health 59, 205—220. ISO 2631—1, 1997. Mechanical vibration and shock — evaluation of human exposure to whole-body vibration — Part 1: General requirements. International Organization for Standardization. Janeway, R.N., 1975. Human vibration tolerance criteria and application to ride evaluation. SAE Paper 750166.
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Lee, R.A., Pradko, F., 1968. Analytical analysis of human vibration. ASME Paper No. 680091. Lidstro¨m, I., 1977. Vibration injury in rock drillers, chiselers, and grinders. Some views on the relationship between the quantity of energy absorbed and the risk of occurence of vibration injury. In: Proceedings of the International Occupational Hand-Arm Vibration Conference. Cincinnati, OH, USA. Department of Health and Human Services, NIOSH Publication. p. 77—83. Magnusson, M.L., 1991. Effects of seated whole body vibrations on the spine. Ph.D. Dissertation, Division of Occupational Orthopaedics, Department of Orthopaedics, University of Go¨teborg and Sahlgrenska Hospital, Gothenburg, Sweden. Miwa, T., 1975. Mechanical impedance of human body in various postures. Industrial Health 13, 1—22. Pope, M.H., Jayson, M.I.V., Blann, A.D., Kaigle, A.M., Weinstein, J.N., Wilder, D.G., 1994. The effect of vibration on back discomfort and serum levels of von Willebrand factor antigen: a preliminary communication. European Spine Journal 3, 143—145. Potemkin, B.A., Frolov, K.V., 1972. Representation by models of the biomechanical system ‘‘man-operator’’ under the action of random vibrations. Royal Aircraft Establishment Library, Translation No. 1651. Pradko, F., Lee, R.A., 1966. Vibration comfort criteria. SAE Paper 660139.
Pradko, F., Lee, R.A., 1968. Analysis of human vibration. SAE Paper 680091. Pradko, F., Lee, R.A., Greene, J.D., 1965a. Human vibration — response theory. In: Proceedings of the the Winter Annual Meeting. Chicago, 7—11 November, 1965. The American Society of Mechanical Engineers, p. 11. Pradko, F., Orr, T.R., Lee, R.A., 1965b. Human vibration analysis. SAE Paper 650426. Sandover, J., 1981. Vibration, posture, low-back disorders of professional drivers. Report No. DHS 402, Department of Human Sciences, University of Technology, Loughborough. Sandover, J., 1988. Behaviour of the spine under shock and vibration: a review. Clinical Biomechanics 3, 249—256. Seidel, H., 1988. Myoelectric reactions to ultra-low frequency and low-frequency whole body vibration. European Journal of Applied Physiology 57, 558—562. Seroussi, R.E., Wilder, D.G., Pope, M.H., 1989. Trunk muscle electromyography and whole body vibration. Journal of Biomechanics 22, 219—229. Wikstro¨m, B.-O., Kjellberg, A., Landstro¨m, U., 1994. Health effects of long-term occupational exposure to whole-body vibration: a review. International Journal of Industrial Ergonomics 14, 273—292.
Absorption of energy during vertical whole-body vibration exposure Ronnie Lundstro¨m*, Patrik Holmlund, Lennart Lindberg Department of Technical Hygiene, National Institute for Working Life, P.O. Box 7654, S-907 13 Umeas , Sweden Received in Final Form 16 December 1997
Abstract Absorbed power (P ) during exposure to vertical whole-body vibration in a sitting posture was measured on 15 male and 15 A"4 female subjects. Different experimental conditions were applied, such as vibration level (0.5—1.4 m s~2) and frequency (2—100 Hz), body weight (54—93 kg) and, relaxed and erected upper body positions. Results show that P was strongly related to the frequency of A"4 the vibration, peaking within the range of 4—6 Hz. The peak was predominantly located in the lower end of this range for females and for the relaxed sitting position. P increased with acceleration level and body weight. Almost a ten-fold increase in P was observed A"4 A"4 at the critical frequency when the vibration exposure was raised from 0.5 to 1.4 m s~2. If risk assessment is based on the assumption that the amount of P , independent of the frequency of the vibration, indicates a hazard, then the ISO-standard 2631 under- and A"4 overestimates the risk at frequencies below and above about 6 Hz, respectively. The results also indicate a need for differentiated guidelines for females and males. Many types of vehicles produce whole-body vibration with frequencies which coincide with the range where the highest P was observed. P is a ‘new’ concept for measurement of whole-body vibration exposure. Although not A"4 A"4 yet thoughly evaluated, this measure may be a better quantity for risk assessment than those specified in ISO 2631 since it also takes the dynamic force applied to the human body into account. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Vibration; Whole body; Vertical; Power; Absorption
1. Introduction Several people are exposed to whole-body vibration (WBV) in their occupational life, especially drivers of various vehicles such as dumpers, excavators, scrapers, buses and trucks. The main categories of response to WBV are perception, degraded comfort, interference with activities, impaired health and occurence of motion sickness. Many scientific papers, reports and other documents have addressed these types of responses. Some publications present comprehensive surveys of current knowledge on the effects of WBV (e.g. Christ, et al., 1989; Dupuis and Zerlett, 1986; Griffin, 1990; Hulshof and Zanten, 1987; Magnusson, 1991; Pope et al., 1994; Sandover, 1988; Wikstro¨m et al., 1994). It can be concluded that human response to WBV is a very complex phenomenon. Combinations of effects may occur simultaneously but also one effect may promote the onset of another. During exposure to WBV there are many physiological,
* Corresponding author. Tel.: #46 90 786 5097; fax: #46 90 786 5027; e-mail: [email protected]. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 0 1 1 - 6
psychophysical and physical factors which are relevant for the development of unwanted effects, such as individual susceptibility, body constitution, posture together with the frequency, direction, magnitude and duration of the vibration. Guidelines given in the International standard ISO 2631-1 (1997) are most often used for risk assessment. Accordingly, measurement of WBV should be conducted on the surface transmitting vibration to the human body. Vibration should be measured within the frequency range 0.5—80 Hz in terms of frequency-weighted acceleration. A disadvantage with this measure is that it only describes the acceleration magnitude on the vibrating surface. Thus, it can be argued that it presents a poor description about the extent of vibration actually being transmitted to the body. The amount of vibration energy, either absorbed or exchanged between the source and body, may therefore be a better measure of the physical stress on the body since it takes into consideration the interplay between the vibrating structure and the body in contact with it. Moreover, energy is a scalar quantity which makes it easy to add up contributions from all three directions to a single value.
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The instantaneous power P transmitted to the strucT3 ture is:
2. Methods
P "F(¹) ) l(t),P (t)#P (t). (1) T3 A"4 EP (t) is the absorbed part of the power, accounting for A"4 the energy necessary for keeping pace with the energy dissipated through structural damping. The elastic power P (t) is continuously delivered to and removed from the Estructure during each period of excitation and averages zero for each sinusoidal cycle of motion. Thus, the timeaveraged absorbed power SP T equals the transmitted A"4 power, SP T i.e. T3 SP T"SP T"SF(t) ) l(t)T. (2) A"4 T3 The concept of absorbed energy was discussed in the mid-1960s by a group of scientists (Lee and Pradko, 1968; Pradko and Lee, 1968; 1966; Pradko et al., 1965a, b). They presented results from investigations which indicated that subjective experience of vibration is related to the amount of vibration energy absorbed by the body. A decade later, Janeway (1975) defended these observations. He pointed out several arguments which he felt supported the idea of including the concept of energy absorption in ISO 2631, at least for the comfort criteria. Since then, no further work appears to be published in this area. However, in regard to hand-arm vibration, the concept has been discussed to a larger extent. For instance, Lidstro¨m (1977) showed that the prevalence of vibration-induced injuries within different occupational groups is related to the amount of absorbed energy. The purpose of this study was to investigate WBV energy absorption during different experimental conditions. The relation between absorbed power and frequency, exposure level, direction, upper-body position, body weight and gender were focused.
2.1. Subjects The study group consisted of 15 females and 15 males (Table 1). Information about their anthropometric measures, age, work assignment, years at work, general state of health, previous or present exposure to WBV, etc., was provided by questionnaire. All subjects were healthy with no signs or symptoms of disorders of the musculo-skeletal system, such as low back pain or lumbago. 2.2. Apparatus Sinusoidal vibration was generated with the help of a signal generator (Bru¨el and Kjær 1049), an electrodynamic shaker (LDS 712#ILS 712) and a power amplifier (LDS, MPA 1) (Fig. 1). A girder was directly bolted onto the shaker table. Two linear ball bearings were mounted on the girder, one at each edge, in order to reduce momentum forces on the shaker. Between the seat plate, which was made of 3 cm thick wooden board Table 1 Mean (M), standard deviation ($SD), maximum (max) and minimum (min) values for the subjects’ age, body weight (kg) and height (cm) Females Males All subjects M M M ($SD, max, min) ($SD, max, min) ($SD, max, min) n Age Weight Height
15 24 (2, 30, 23) 66 (10, 93, 54) 168 (6, 180, 157)
Fig. 1. Chart showing the experimental set-up.
15 38 (12, 58, 22) 74 (9, 92, 57) 177 (6, 190, 167)
30 31 (11, 58, 22) 70 (11, 93, 54) 173 (7, 190, 157)
R. Lundstro( m et al. / Journal of Biomechanics 31 (1998) 317—326
(23]30 cm), and the girder, four piezo-electric force transducers (Kistler 9251) were mounted. A piezo-electric accelerometer (Bru¨el and Kjær 4231) was centrally attached to the underside of the seat plate. The signals from the transducers were amplified and low-pass filtered by identical charge amplifiers (Bru¨el and Kjær 2635) and Bessel filters (cut-off frequency: 300 Hz). The risk of adding any phase difference between the signals are thereby minimized. By using the compressor function in the signal generator, the vibration level could be kept constant independent of the frequency and load. After A/D-conversion of the force and acceleration signals, the values were continuously stored on disk for later analysis. To calibrate the force channel dynamically at 5 Hz, the seat plate was loaded with solid concrete masses weighing 53 and 85 kg. An accelerometer calibrator (Bru¨el and Kjær 4291) was used for the vibration channel. Before the experiments the measuring system was tested without load in order to secure a ‘zero-power’ result and to determine the signal-to-noise ratio. 2.2. Experimental procedure Prior to the first occasion, each subject was given written information about the experiment, which included the purpose of the study, possible risk for acute or chronic injuries, ethical committee approval (University of Umeas , Dnr. 94-255) and their right to either interrupt an ongoing test run or refrain from further tests. Informed prior consent was signed by each subject. The experimental procedure for all test runs followed a predestinated protocol. After weighing in a standing position the subjects sat on the seat plate with feet positioned on an adjustable footrest. The footrest was adjusted so that the lower legs were vertical and the upper legs horizontal. The static weight on the force plate and the footrest were then determined. At each occasion the subject was exposed to one of the four acceleration levels, 0.5, 0.7, 1.0 or 1.4 m s~2 in both erected (E) and relaxed 3.4 (R) upper-body posture. The posture was visually checked by the experimenter during each test run and if necessary corrected during measurement pauses. The measurement period for each frequency was 15 s followed by a 5 s pause. The frequency was increased from 2 to 100 Hz in steps of 1/3 octaves, except in the range 2.5—20 Hz where the steps were 1/6 octaves. The entire experiment took about 30 min to complete for which about 20 min consisted of exposure to vibration. Each subject participated at four occasions, all on different days, one for each of the different acceleration levels. 2.3. Data and statistical analysis The collected data were processed and analysed with LabViewTM. For each test frequency the collected acceler-
319
ation signal a(t) was integrated to get the velocity v(t). The total force F (t) registered by the force cells also M%!4 consist of a contribution generated by the mass of the seat plate (m ). This contribution is always in phase P-!5% with the acceleration signal and was cancelled by vectorial substraction. The force F(t) transmitted to the sitting subject was determined as F(t)"F (t)! M%!4 m a(t). The time-average absorbed power SP T was P-!5% A"4 thereafter determined according to Eq. (2). The statistical analyses consisted of the determination of the means and standard deviations plus analysis of variances (ANOVA).
3. Results Fig. 2 shows individual graphs for absorbed power at different test frequencies during vibration exposure at 1.0 m s~2. As can be seen, individual graphs have a relatively similar shape. Absorbed power increased with the frequency up to a peak in the range of 4—6 Hz after which it decreased. For females, there was an indication for an additional peak around 9 Hz. The frequency for maximal absorption was somewhat lower for the relaxed sitting position compared to erected. The inter-individual variation was quite large for both females and males, at least for frequencies up to about 10 Hz. A large amount of this variation was due to differences in body weight. Regression and correlation analysis clearly indicated that absorbed power, summed up over the entire frequency range, increased with body weight (Fig. 3, Table 2). With the intention of reducing the influence of this factor, obtained data were normalized against the individual static sitting weight, i.e in units of W kg~1. Fig. 4 shows mean values for normalized absorbed power at different frequencies for both females and males, for both sitting positions and all accelerations levels. The numerical turn out for one acceleration level (1.0 m s~2) is given in Table 3. The mean to standard deviation ratio for each test frequency was roughly the same for all acceleration levels. For a structure with a fixed mass and internal damping, absorption of power should theoretically increase quadratically with the exposure level, i.e. PJa2. Regression analysis based on this model supports this idea. The highest correlation coefficients were, however, obtained when the regression analysis was based on the model PJ0#k a#k a2. The zero intercept in the 1 2 model implies that no absorption of power occurred when acceleration was set to zero. Table 4 shows regression and correlation coefficients for both females and males, split by relaxed and erected sitting positions. By the size of the regression coefficients, k and k , it can be 1 2 stated that the amount of absorbed power predominantly depends on the square of the acceleration. An extract from statistical analysis (ANOVA) is given in Table 5. The result showed that the absorbed power
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Fig. 2. Individual graphs for absorbed power at different frequencies for males (n"15) and females (n"15) sitting relaxed and erected.
was significantly dependent on the acceleration level for all test frequencies. For most frequencies below 25 Hz there were also significant differences due to posture. In the frequency ranges of about 3—10 Hz and above 60 Hz significant differencies due to gender seemed to exist. A significant interplay between gender and acceleration (GA) as well as posture and acceleration (PA) were apparent for frequencies below 4 Hz.
4. Discussion
Fig. 3. Absorbed power-sum for the frequency range 2—100 Hz for different stimulus acceleration levels (K"0.5, £"0.7, L"1.0, n"1.4 m s~2) in relation to ‘sitting’ weight. Regression and correlation coefficients are given in Table 2.
This study showed that absorption of power depends on several factors with frequency and magnitude of vibration among the most significant. In general, the amount of absorbed power increases with the frequency up to a peak in the range of 4—6 Hz during exposure at a constant acceleration level. Above this frequency range a gradual decrease in P with increasing frequency A"4 occurred. Absorbed power at each frequency was proportional to the square of the acceleration. The frequency at which maximal absorption occurs tended to be lower for females as compared to males. Another finding was that maximal absorption tended to increase and slide towards
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321
Table 2 Regression (k) and correlation (r2) coefficients for the relation between absorbed power sum (P ) for the frequency range 2—100 Hz and sitting weight S6. (w ) at different acceleration levels (m s~2). Linear regression model: P "0#kw . Regression lines are presented in Fig. 3 4 46. 4 Acceleration (m s~2)
0.5 0.7 1.0 1.4
Males
Females
Relaxed
Erected
Relaxed
Erected
k
r2
k
r2
k
r2
k
r2
0.067 0.135 0.269 0.516
0.99 0.992 0.992 0.995
0.066 0.13 0.256 0.499
0.988 0.986 0.989 0.991
0.074 0.147 0.294 0.597
0.995 0.995 0.991 0.994
0.07 0.136 0.271 0.555
0.994 0.992 0.992 0.994
Fig. 4. Normalized mean absorbed power for females (n"15) and males (n"15) sitting erected and relaxed.
lower frequencies when the body position was changed from erected to relaxed. As shown in Table 5 significant gender differencies in P weight could be observed for some stimulus frequenA"4 cies after normalization with sitting weight. Graphs for males and females have however a very similar shape. Some other studies, however with respect to normalized apparent mass and mechanical impedance have shown a similar outcome (e.g. Fairley and Griffin, 1989;
Holmlund et al., 1995). The principal reason for observed significances, at least for frequencies lower than about 10 Hz, seems to be a slight lowering of the frequency at which maximal absorption occurs for females. This may be due to differences in the bodily structure of males and females and/or due to the higher m /m ratio which &!5 .64#-% is generally observed among females. A higher ratio causes a decrease in the stiffness-to-mass ratio which in turn lowers the resonance frequency and consequently
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322
Table 3 Mean (M) and standard deviation ($SD) for absorbed power at different frequencies for males (n"15) and females (n"15) during vibration exposure to an acceleration level of 1 m s~2 Frequency (Hz)
Absorbed power (10~3 W kg~1) Relaxed position Males
2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
10.8 10.8 10.7 10.9 12.2 17.6 29.2 32.6 26.8 20.7 15.5 12.1 10.2 9.0 7.4 6.1 4.4 3.4 2.6 2.1 1.3 0.8 0.6 0.4 0.2 0.1 0.05
Erected position Females
(5.5) (2.0) (2.0) (2.2) (3.2) (6.9) (14.0) (9.8) (4.5) (3.7) (3.4) (2.5) (1.9) (1.6) (1.2) (0.8) (0.6) (0.6) (0.4) (0.3) (0.1) (0.07) (0.09) (0.08) (0.05) (0.02) (0.01)
8.6 10.1 12.4 14.3 17.7 22.7 29.9 31.1 23.2 18.1 15.1 14.1 12.7 10.5 8.0 6.4 4.6 3.5 2.7 2.2 1.3 0.8 0.6 0.4 0.2 0.1 0.05
Males (3.9) (3.4) (5.5) (5.7) (5.4) (6.7) (9.7) (5.6) (4.2) (3.7) (3.3) (2.2) (1.6) (1.5) (1.2) (1.0) (0.7) (0.6) (0.4) (0.3) (0.1) (0.08) (0.06) (0.04) (0.05) (0.03) (0.01)
also the frequency for maximal power absorption. More fat also implies more damping and thus more power absorption. The effect of posture on other biomechanical measures, such as transmissibility, apparent mass and mechanical impedance, has been studied by several other investigators (e.g. Coermann, 1962; Fairley and Griffin, 1989; Griffin, 1975; Holmlund et al., 1995; Miwa, 1975; Potemkin and Frolov, 1972). For all measures it seems like a change in posture may alter the response, but not necessarily for all subjects. The effect of posture however tends to be more pronounced for transmissibility for which a larger and more consistent effect has been observed. Any corresponding data for P has to our knowA"4 ledge not been published. A general observation, as shown in this as well as other studies, is that sitting in a relaxed posture results in a softening of the biomechanical system which redu ces the resonance frequency. A possible explanation could be that relaxed sitting posture constitutes more relaxed muscles in the abdominal region which in turn reduces body stiffness and increases damping. Another explanation could be
9.4 11.7 13.0 13.4 17.4 27.0 35.8 32.4 24.2 18.3 13.8 11.1 9.1 7.9 6.5 5.2 3.8 2.9 2.3 1.9 1.2 0.8 0.6 0.4 0.2 0.1 0.04
Females (2.9) (3.8) (3.6) (3.7) (6.9) (12.1) (10.9) (5.3) (6.3) (5.0) (3.0) (1.9) (1.5) (1.2) (1.0) (0.9) (0.6) (0.4) (0.3) (0.2) (0.1) (0.1) (0.07) (0.07) (0.06) (0.03) (0.01)
9.4 12.7 16.4 19.4 24.0 34.0 37.4 29.7 19.8 15.7 13.8 13.4 12.3 10.3 7.4 5.6 3.9 3.0 2.4 1.9 1.2 0.8 0.6 0.4 0.2 0.1 0.04
(3.1) (3.2) (5.2) (5.6) (5.7) (10.0) (7.2) (5.2) (3.5) (2.8) (2.6) (1.7) (1.3) (1.3) (0.9) (0.7) (0.5) (0.4) (0.2) (0.2) (0.1) (0.07) (0.05) (0.04) (0.05) (0.03) (0.02)
that biomechanical response is affected by stretch reflexes in the paraspinal muscles shown to be evoked by vibration (e.g. Sandover, 1981; Seidel, 1988; Seroussi et al., 1989). Interestingly, evoked strech reflexes are synchronous with a sinusoidal vibration stimuli but are, at many stimulus frequencies, so far out of phase that their forces are added to those of the stimulus (Seroussi et al., 1989). Such evoked muscle activity will most certainly have an influence on all biomechanical measures as well as absorbed power. It can also be argued that the state of disc hydration is of importance since it will affect the biomechanical properties of the spine. Three subjects were tested at different times during a day as well as between days. Very small and unsystematical differences in absorbed power were observed which was taken as an indication that diurnal changes were not of significant importance in this context. There are most likely several other human or experimental factors that may influence the characteristics of absorbed power which adds to the complexibility in this context. In this report, it is assumed that it is the absorbed portion of the total power which should be considered as
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323
Table 4 Regression and correlation coefficients for the relation between normalized absorbed power P (W kg~1) and acceleration level a (m s~2) for A"4,N03. each frequency used. Regression model: P "0#k a#k a2 A"4,N03. 1 2 Frequency (Hz)
Absorbed power (10~3 W kg~1) Relaxed position
Erected position
Males
2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
Females
k 1
k
2.7 3.6 4.5 3.4 !0.75 !5.7 !8.3 0.38 5.8 4.9 2.1 0.59 0.21 0.14 0.50 0.80 0.76 0.50 0.36 0.24 0.12 0.058 0.069 0.015 !0.002 !0.007 !0.004
6.4 7.8 8.1 10.2 18.2 32.0 42.7 31.0 18.3 13.9 12.1 10.8 9.1 7.9 6.0 4.4 3.1 2.5 1.9 1.6 1.1 0.73 0.50 0.37 0.22 0.10 0.05
2
r2 0.892 0.948 0.962 0.940 0.866 0.853 0.934 0.971 0.932 0.930 0.959 0.976 0.980 0.981 0.976 0.973 0.972 0.977 0.984 0.988 0.986 0.985 0.986 0.977 0.946 0.927 0.909
k 1 0.26 !2.4 !1.8 !1.5 !4.8 !13.9 !4.5 5.0 4.1 1.4 !0.65 !1.8 !0.21 1.8 1.8 1.4 0.78 0.47 0.30 0.19 0.066 0.047 0.073 0.017 0.017 0.009 0.007
Males k 2
r2
8.9 15.3 18.3 21.4 30.4 50.0 42.3 24.8 16.3 15.0 15.0 15.4 12.5 8.3 5.6 4.2 3.2 2.6 2.1 1.7 1.2 0.76 0.49 0.35 0.19 0.086 0.037
0.926 0.967 0.957 0.949 0.956 0.943 0.977 0.974 0.966 0.959 0.981 0.992 0.984 0.982 0.981 0.984 0.983 0.984 0.987 0.991 0.994 0.993 0.992 0.988 0.947 0.919 0.908
most important. This assumption can of course be questioned since it can be argued that power, which is not absorbed, may also have an effect on the body. Vessels, nerves, muscles, bone, joints and other parts of the body will be subjected to compression and extension during vibration exposure. No power will be absorbed if this physical strain does not exceed the elastical range for a body structure. All this implies that organic damages occurs first after elastic limits are exceeded. This discussion presumes body structures behaving like ideal mass-spring systems without internal damping. However, most biological structures do have internal damping which means that they absorb power even when affecting dynamic forces are within the elastic range. Non absorbed power may still have an influence since vibration activates for instance different types of receptors, such as mechanoreceptors, proprioceptors, thermoceptors and nociceptors. This, and the mechanical strain itself, may have an influence on biochemical processes and interfere with blood circulation and nutrition. It is thus possible that some types of complaints or disorders
k 1 4.6 2.7 2.9 2.8 0.06 !0.97 !4.4 !1.2 0.91 0.97 0.04 !0.50 !0.15 0.51 1.1 1.3 1.1 0.70 0.44 0.26 0.097 0.42 0.065 0.024 0.004 !0.003 0.004
Females k 2
r2
5.3 7.4 7.5 8.2 13.0 18.5 32.3 33.1 26.1 20.6 16.4 13.2 10.6 8.4 6.3 4.7 3.4 2.7 2.2 1.8 1.2 0.79 0.51 0.37 0.22 0.10 0.043
0.769 0.926 0.935 0.932 0.870 0.845 0.830 0.931 0.966 0.955 0.939 0.965 0.975 0.973 0.971 0.971 0.968 0.968 0.970 0.975 0.981 0.982 0.983 0.966 0.945 0.938 0.911
k
1
0.96 !0.33 !0.39 !0.74 !1.5 !7.1 !8.5 !2.0 1.7 1.2 !0.39 !1.9 0.99 2.0 1.8 1.6 1.1 0.74 0.50 0.29 0.091 0.042 0.067 !0.001 !0.003 0.005 0.003
k 2
r2
7.4 10.4 12.5 15.1 19.9 32.3 40.5 33.4 21.8 17.2 15.7 16.2 12.4 8.3 6.1 4.7 3.4 2.7 2.1 1.8 1.2 0.78 0.50 0.37 0.21 0.093 0.041
0.810 0.908 0.890 0.936 0.937 0.875 0.944 0.971 0.964 0.954 0.977 0.987 0.981 0.983 0.982 0.979 0.980 0.982 0.986 0.988 0.990 0.992 0.991 0.983 0.946 0.918 0.896
are solely related to either power absorbed or power not absorbed while others are related to both. An example of an absorbed power-related effect might be musculo-skeletal disorders while effects on comfort and perception more likely are related to power not absorbed. This is of course purely speculative since no support for this exists in the scientific literature. Another possibility is that detrimental effects are purely related to the total amount of power affecting the body. The interindividual variation in absorbed power is relatively large, both in the magnitude and frequency plane. Differences in body weight and bodily structure are likely the most important reasons. In order to reduce the influence of at least differences in body weight we chose to individually normalize our results with respect to the sitting weight. This procedure suggests certain advantages. It not only makes the data more easy to compile and interpret but also increases the usefulness of the results. An estimation of the amount of absorbed power can thus be calculated by multiplying normalized data and sitting weight. The sitting and standing weight
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Table 5 P-values extracted from an analysis of variances ANOVA (G"gender, P"posture, A"acceleration). For more information, see text Frequency (Hz) 2 2.5 2.83 3.15 3.56 4 4.5 5 5.7 6.3 7.1 8 9 10 11.3 12.5 14.3 16 18 20 25 31.5 40 50 63 80 100
G
0.0699 0.6045 (0.0001 (0.0001 (0.0001 (0.0001 0.2254 0.0060 (0.0001 (0.0001 0.0048 0.0002 (0.0001 0.0001 0.1841 0.6337 0.1309 0.0962 0.0977 0.0863 0.0062 0.0015 (0.0001 (0.0001 0.0002 0.0095 0.0066
P
0.9702 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 0.0001 0.2981 0.0002 0.0004 0.0008 0.0012 0.0149 0.0104 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 0.0002 0.0602 0.6214 0.6535 0.6793 0.3725 0.2622
GP
0.2207 0.0984 0.0453 0.0213 0.1934 0.6102 0.6134 0.5882 0.9068 0.4100 0.1559 0.2291 0.0968 0.1325 0.4070 0.8711 0.6858 0.4958 0.5549 0.5123 0.5279 0.2968 0.9538 0.6462 0.7000 0.9427 0.8277
ratio for subjects participating in this study was on average 0.77 (SD$0.033) and 0.76 (SD$0.030) for females and males, respectively. A normalization with respect to other measures for bodily structure, for instance length, is desirable but requires a more extensive data set before a more complete model for normalization can be outlined. An interesting aspect of the results was how absorbed power relates to the guidelines presented in ISO 2631-1 (1997). The frequency weighting procedure implies that human response to WBV is not only related to magnitude and duration but also to the frequency of the vibration. The purpose of the frequency weighting procedure is thus to compensate, or in other words to normalize, for differences in human susceptibility at different frequencies. As stated earlier, vibration quantified in terms of acceleration do not neccessarily mirror the physical strain on the body. It merely reflects the vibration level on the contact surface between the body and the vibration source. A better way to quantify the emmission i.e. the actual vibration dose, may therefore be ‘absorbed power’. Whether a frequency weighting procedure is required also for this measure cannot yet be determined. A first assumption could be that a certain amount of absorbed power is equally harmful or annoying regardless of frequency. A frequency weighting in this
A
(0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001 (0.0001
GA
PA
0.8995 0.0024 (0.0001 (0.0001 (0.0001 (0.0001 0.6379 0.0601 0.0007 0.0240 0.8449 (0.0001 (0.0001 0.2662 0.8843 0.6810 0.7429 0.6504 0.7371 0.7850 0.5110 0.2427 0.0519 0.0175 0.0522 0.0971 0.0513
0.8754 0.0033 0.0003 (0.0001 (0.0001 (0.0001 0.0345 0.2462 0.0007 0.0062 0.0293 0.0387 0.3727 0.5644 0.1529 0.0364 0.0149 0.0267 0.0346 0.0173 0.0596 0.4873 0.9610 0.9703 0.9682 0.9278 0.8923
GPA
0.9340 0.1677 0.1534 0.3082 0.6302 0.9665 0.6644 0.6685 0.9212 0.4980 0.3428 0.5986 0.5197 0.8115 0.9937 0.9962 0.9815 0.9364 0.8744 0.8493 0.9125 0.8809 0.9848 0.8991 0.9445 0.9849 0.9964
case would not be necessary. Fig. 5 shows acceleration levels at different frequencies corresponding to constant absorbed power. The frequency weighting curve, ¼ , in , accordance with ISO 2631-1 (1997), corresponding to an acceleration level of 0.5 m s~2 is also shown. The amount of absorbed power at 6 Hz, at which the ¼ correction , factor is 1, was calculated to be 5.4 and 4.5]10~3 W for males and females, respectively, sitting relaxed. The corresponding acceleration levels at other frequencies were thereafter determined. Interestingly, calculations based on corresponding data for males presented by Lee and Pradko (1968) show an almost identical result as ours. However, their data covers frequencies up to 12 Hz which limits the comparison to the range of 2—12 Hz. Thus, according to both theirs and our result it seems like the frequency weighting procedure underestimates the risk for unwanted effects for frequencies below 6 Hz and vice versa for frequencies above. An adjustment of the ISO-weighting in accordance with the concept of absorbed power would consequently lead to a sharpening with 2—3 dB and a reduction with 5—6 dB at low and high frequencies respectively. The basis for this discussion is of course the frequency from which the calculations originate. In this case, 6 Hz was chosen. For instance, if 5 Hz was chosen instead, the ISO- and absorbed power curves would almost meet at low frequencies but the differences
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Fig. 5. Comparisons of two concepts for risk assessments of whole-body vibration exposure, i.e. constant frequency-weighted acceleration in accordance with ISO 2631 versus constant absorbed power. Graphs for the latter concept is given for relaxed sitting posture split by gender but converted to acceleration levels. For more information, see text.
at higher frequencies would become even more obvious. It seems like females absorb a larger amount of power than males which might imply a need for differentiated guidelines for risk assessments which should be more restrictive for females. The extent of data obtained in this study is however too limited to allow any extensive conclusion in this regard. The current study consists of data only for the vertical direction. It is therefore of utmost importance to conduct similar studies for the horizontal directions, i.e. fore-and-aft and lateral direction, since these also contribute to the risk of health problems due to WBV exposure. The concept of absorbed power as a ‘new’ measure for the evaluation of WBV exposure definitely opens a new area for research. Epidemiological studies on different categories of professional drivers could be a fruitful way to compare different measures for vibration exposure in relation to health effects. Professional drivers could, for instance, be asked to rate percieved comfort on a visual analogue scale during controlled WBV excitation in a laboratory environment or while driving on a test track.
Acknowledgements The financial support by the Swedish Council for Work Life Research is gratefully acknowledged (Project: 94-0026).
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