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Mechanical impedance of the sitting human body in single-axis compared to multi-axis whole-body vibration exposure
Clinical Biomechanics 16 Supplement No. 1 (2001) S101±S110
www.elsevier.com/locate/clinbiomech
Mechanical impedance of the sitting human body in single-axis compared to multi-axis whole-body vibration exposure Patrik Holmlund *, Ronnie Lundstr om National Institute of Working Life, Technical Risk Factors, PO Box 7654, Ume a S-907 13, Sweden
Abstract Objective. The study was aimed to investigate the mechanical impedance of the sitting human body and to compare data obtained in laboratory single-axis investigations with multi-axis data from in vehicle measurements. Design. The experiments were performed in a laboratory for single-axis measurements. The multi-axis exposure was generated with an eight-seat minibus where the rear seats had been replaced with a rigid one. The subjects in the multi-axis experiment all participated in the single-axis experiments. Background. There are quite a few investigations in the literature describing the human response to single-axis exposure. The response from the human body can be expected to be aected by multi-axis input in a dierent way than from a single-axis exposure. The present knowledge of the eect of multiple axis exposure is very limited. Methods. The measurements were performed using a specially designed force and accelerometer plate. This plate was placed between the subject and the hard seat. Results. Outcome shows a clear dierence between mechanical impedance for multi-axis exposure compared to single-axis. This is especially clear in the x-direction where the dierence is very large. Conclusion. The conclusion is that it seems unlikely that single-axis mechanical impedance data can be directly transferred to a multi-axis environment. This is due to the force cross-talk between dierent directions. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Whole-body; Vibration; Multi-axis; Mechanical impedance
1. Introduction Knowledge of how vibration is transmitted to and through the human body can provide an important input to our understanding of human response to wholebody vibration (WBV). For instance, biodynamic studies have identi®ed critical frequency ranges, i.e., resonant frequencies, for dierent parts of the body, such as the eyes, head, shoulders, neck and spine (e.g., [1±3]). It is possible that some types of detrimental eects are closely related to WBV exposures that contain frequencies leading to a resonant behaviour of the body or parts of the body. It has for instance been shown that the spine has a resonant frequency of about 5 Hz [1,2,4], i.e., a frequency which is produced in many types of vehicles and earth-moving machinery [5]. This might be a causal or a contributing factor for the development of
*
Corresponding author. E-mail address: [email protected] (P. Holmlund).
low back pain among professional drivers [6]. Understanding of whole-body dynamics is also necessary for proper design of protective measures, such as suspension seats. The mechanical driving point impedance can be used to describe the biodynamical properties of the human body. It speci®es the complex ratio between the dynamic force to which the subject is exposed and the resulting body motion in terms of velocity. The international standard, ISO/CD 5982 [7], presents diagrams showing the modulus and phase of the driving point impedance of the human body in the z-direction for an upright sitting posture. The diagrams cover about 80% of the range of experimental values obtained from available literature, predominantly published before 1970 (for references, see ISO/CD 5982 [7]). It is clearly stated in the standard that presented information is aicted with certain restrictions, among which the most important are the limited number of included subjects (39 males), frequency range (0.5±30 Hz), input acceleration amplitudes 1±2 m s 2 , z-direction only, whole-body weights
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 0 ) 0 0 1 0 2 - 9
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P. Holmlund, R. Lundstrom / Clinical Biomechanics 16 Suppl. No. 1 (2001) S101±S110
(51±94 kg), posture of the body and body restrains. In some cases the author does not give the input acceleration and the subject posture is usually poorly de®ned. Due to all these restrictions it is clearly stated in the standard that the information needs to be revised, as further experimental data are available. The international standard ISO/CD 5982 standard is restricted to males [7]. The question of gender dierences is getting more and more relevant, since the number of female drivers is steadily increasing. As there are differences in average anthropometric measures and muscle strength capacity between males and females it seems plausible to assume dierences in biodynamic behaviour. These dierences have to be considered when trying to understand the risk of injury. Impedance data for females are not easily found in the literature, therefore studies directed towards this matter are needed. Against this background the purpose of this paper was threefold. Firstly, to present results from a laboratory study showing data for the mechanical impedance of the human body in the three orthogonal directions fore-aft (x), lateral (y) and vertical (z), for dierent conditions. Secondly to present some corresponding data obtained during driving of a vehicle. Thirdly, to compare laboratory and ®eld data. 2. Method 2.1. Subjects The study groups for vertical and horizontal singleaxis laboratory experiments consisted of 15 females and 15 males, of which some participated in both. Vehicle
measurements were done on three subjects who had participated in both laboratory studies. Basic information about their anthropometric measures, age, work assignment, years at work, general state of health, previous or present exposure to whole-body vibration, etc., were asked for in a questionnaire. All subjects were considered to be healthy and with no signs or symptoms of musculo-skeletal disorders, such as low back pain or lumbago. Averaged anthropometric data for the subjects are shown in Table 1. 2.2. Experimental setup 2.2.1. Single-axis laboratory experiments With a signal generator (Br uel & Kjñr 1049), an electrodynamic shaker (Ling Dynamic System, Mod. 712 + ILS 712) and a power ampli®er (Ling Dynamic System, MPA 1) sinusoidal vibrations were generated. For the z-direction experiments 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 a 30 mm thick wooden board (230 300 mm2 ), and the girder four force transducers (Kistler 9251) were mounted. An accelerometer (Br uel & Kjñr 4231) was centrally attached underneath the seat plate. For the x- and y-direction experiments acceleration and force were measured with a specially designed seat plate, consisting of two aluminium plates with a tri-axial accelerometer (Br uel & Kjñr 4231) and four tri-axial force cells (Kistler 9251) mounted in between them. All transducers were of piezo-electric type.
Table 1 Mean (M), standard deviation (SD) maximum (max) and minimum (min) values for the subjects' age (years), body weight (kg) and height (cm) in the two laboratory studies and the corresponding data for the three subjects from the in vehicle study Female M (SD, max, min)
Male M (SD, max, min)
All M (SD, max, min)
Laboratory experiments z-direction n Age Weight Height
15 24 (2, 30, 32) 66 (10, 93, 54) 168 (6, 180, 157)
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)
x-, y-direction n Age Weight Height
15 34 (11, 511, 22) 63 (7, 76, 54) 167 (4, 173, 160)
15 39 (12, 59, 24) 75 (10, 93, 55) 177 (6, 188, 167)
30 37 (11, 59, 2) 69 (10, 93, 54) 172 (7, 188, 160)
Subject
Age (years)
Height (cm)
Weight (kg)
In vehicle experiments A B C
48 44 35
175 174 176
74 74 74
P. Holmlund, R. Lundstrom / Clinical Biomechanics 16 Suppl. No. 1 (2001) S101±S110
The signals from the transducers were ampli®ed and low-pass ®ltered by identical charge ampli®ers (vertically: Br uel & Kjñr 2635, horizontally: RION UV6) and Bessel-®lters (cut-o frequency: 300 Hz). By using the signal feedback function (i.e., compressor) in the signal generator, the vibration level could be kept constant independent of the frequency and load. After A/Dconversion (fs 1000 Hz) of the force and acceleration signals, the values were continuously stored on disk for later analysis. 2.2.2. In vehicle experiments The passenger seats at the back of the eight-seat minibus were removed and a semi-rigid seat was mounted between the rear wheels. The centre of the seat was approximately 20 cm in front of the rear axle. No back support or elbowrests were used in this investigation. Acceleration and force were measured with the same seat plate as in the horizontal laboratory study. The signals from these transducers were fed to six identical charge ampli®ers (Br uel & Kjñr 2635) set for bandpass in the frequency range of 0.2 to 100 Hz. Time histories were stored using a digital tape recorder (SONY PC208Ax). The sampling rate was set to 12 kHz. A digital system was used to transfer measurements to a computer (SONY PCIF250NI). Data were down sampled to 1024 Hz and analysed. 2.3. Experimental procedure Prior to the ®rst 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 Ume a, Dnr 94-255) and their right to either interrupt an on-going test run or refrain from further tests. Each subject signed informed prior consent. The experimental procedure for all test runs in the laboratory followed a predetermined protocol. After weighing in a standing position the subjects sat down on the seat plate and positioned their feet on an adjustable footrest. At each occasion the subject was exposed to one of the four (six in horizontal direction) acceleration levels (0.25, 0.35) 0.5, 0.7, 1.0 or 1:4 m s 2 r.m.s. in both erect (E) and relaxed (R) upper body posture. In vehicle experiments used the same postures as the laboratory studies, sitting erect (E) and relaxed (R). The former was de®ned as sitting upright with the hands resting on the knees, the later originated from the erect posture where the subject was asked to relax and adopt a more comfortable sitting posture. The experimenter visually checked the posture during each test run. If a correction of the posture was required this was done during measurement pauses. For laboratory studies measurement period for each frequency was followed by a 5 s pause. The sinusoidal signal was increased in frequency from 2
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to 100 Hz in steps of 1/3 octaves, except in the range 2.5± 20 Hz where the steps were 1/6 octaves, for vertical direction. For the horizontal directions frequency was increased from 1.13±2.5 to 31.5±80 Hz, depending on exposure level, in steps of 1/6 octaves, except in the range 25±80 Hz where the steps were 1/3 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 (six in each horizontal direction) occasions, all on dierent days, one for each of the dierent acceleration levels. The in vehicle measurements, lasting for at least 5 min, were recorded after the subjects had adopted the erect posture. The driving surface was a snow covered gravel road, and the speed was maintained at approximately 50 km h 1 . After the run the minibus turned around and travelled in the opposite direction, repeating the procedure for the relaxed posture. 2.4. Analysis The collected data were processed and analysed with LabViewe 3.1.1 (Macintosh version). For each test frequency, in the laboratory studies, the collected acceleration signal was integrated to get the velocity. A root mean square (r.m.s.) value for the measured time period was then calculated. The r.m.s. value for the force was determined after vector compensation for the load produced by the internal mass of the seat plate i.e., a procedure usually denoted as ``mass cancellation''. On the basis of these results, the absolute mechanical impedance was calculated. In the laboratory study the phase dierence between the force and the acceleration was calculated by measuring the time dierence between zero crossings for the force and velocity signals. The in vehicle measurements calculation of the mechanical impedance (Z) was performed by power spectral density method. Acceleration was integrated to obtain the velocity. The cross-power spectral density was calculated for the force (F) and velocity (v) and then divided by the power spectral density of the velocity [8]. The frequency range of the data were 1±20 Hz, chosen because this is the most interesting area for WBV. 3. Results A general ®nding in vertical direction laboratory experiments was that the impedance increased with the frequency up to a ®rst maximum in the range 4±6 Hz (Fig. 1). For most test subjects a second and third maximum in the ranges of 8±12 and 50±70 Hz, respectively, were also observed. At frequencies around 10 Hz, females showed a more distinct second peak. In many cases the magnitude for this peak exceeded the ®rst. Fig. 1 is separated to show the dierences between male and
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Fig. 1. Mechanical impedance and phase data for the z-direction laboratory study.
female subjects. It is clear from the ®gure that the mechanical impedance in the vertical direction was nonlinear with respect to the acceleration. It can also be noted that the peaks were shifted towards lower frequencies as the acceleration was increased. A general ®nding for both x- and y-direction laboratory experiments, was that the mechanical impedance increased with frequency up to a ®rst peak in the range 2±5 Hz dependent upon each subject (Figs. 2 and 3, respectively). For most test subjects a second peak in the range 5±7 Hz was also observed in the y-direction. Dierences between the female and male groups in mechanical impedance peak frequency and magnitude were also observed. The mean mechanical impedance spectra for the xdirection showed in principal one peak at about 3±5 Hz for both females and males (Fig. 2). At low vibration levels there was an indication of two defuse peaks at about 3 and 6±7 Hz. At higher vibration levels only one peak was discernible. The phase spectra for the six levels of acceleration were similar for both females and males in the x-direction while some dierences were discernible in the y-direction. Generally, the phase decreased from
about 80° at 1.6 Hz to between )60° and )40° at 10 Hz, after which it increased. Mean mechanical impedance in y-direction for female and male subjects are shown in Fig. 3. The spectra for the y-direction showed two peaks at about 2 and 6 Hz at low vibration levels. However, the second peak diminished with increasing vibration level. As the vibration level increased the mechanical impedance decreased over the whole frequency range. The phase is shown as a function of frequency below each mechanical impedance spectrum (Fig. 3). In the phase angle spectra for the six levels of acceleration some dierences were discernible in the y-direction. The clear dip between the male subjects mechanical impedance peaks correspond to a more concentrated phase variation than for the female subjects. Generally, the phase decreased from about 80° at 1.6 Hz to between )60° and )40° at 10 Hz, after which it increased. To visualise the range of the mechanical impedance, data for males and females, erect and relaxed posture and all vibration levels are pooled in Fig. 4. From this ®gure the mean, maximum and minimum values can be found at dierent frequencies.
P. Holmlund, R. Lundstrom / Clinical Biomechanics 16 Suppl. No. 1 (2001) S101±S110
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Fig. 2. Mechanical impedance and phase data for the x-direction laboratory study.
In vehicle measurements results showed similarities with the laboratory studies (see Fig. 5). However, results in x-direction were in general clearly dierent. Results in z-direction showed good resemblance between the studies, while y-direction results showed magnitudes in the same range as laboratory studies. These dierences can to some extent be explained by the dierent vibration magnitudes obtained in the three directions. The vertical direction showed the highest magnitude and the horizontal directions had about one®fth of the magnitude in the frequency range 1±15 Hz. For both x- and y-directions an acceleration peak was located in the range 15±20 Hz. Coherency functions between force and acceleration for the three directions showed that there was a good coherence in the z-direction, while the coherency in the x- and y-directions was low, in the range 2±12 Hz. Individual results for mechanical impedance in the zdirection, in both the minibus and the laboratory studies, are shown in Fig. 5. Even if some dierences are evident, the mechanical impedance shown had in general a good agreement with the laboratory data. The most
obvious dierences were that the second peak is located at a lower frequency. The results for the x- and y-directions are also shown in Fig. 5. The mechanical impedance shows a complex behaviour. In most cases the results from the ®eld measurement show two peaks, at about the same frequencies as y-direction laboratory data. However, the level of the mechanical impedance diers, the ®eld results show up to 50% lower levels. Interestingly, the mechanical impedance for subject C shows about the same level as in the laboratory for y-direction. In the xdirection mechanical impedance show greater dierences between laboratory and ®eld measurements. Mechanical impedance for all subjects shows high magnitudes for both postures, which is not consistent with x-direction laboratory data. 4. Discussion The results from the two laboratory studies show that the single-axis mechanical impedance of the human
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Fig. 3. Mechanical impedance and phase data for the y-direction laboratory study.
Fig. 4. Pooled data for dierent experimental conditions (described in the text) showing the mean, maximum and minimum mechanical impedance and phase.
P. Holmlund, R. Lundstrom / Clinical Biomechanics 16 Suppl. No. 1 (2001) S101±S110
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Fig. 5. Results from the in vehicle and laboratory measurements. Thick lines indicate in vehicle measurements, for subjects A, B and C (see Table 1).
body is dependent on a number of factors, such as frequency, vibration level and gender. Generally, it applies for the horizontal directions that the mechanical impedance increases with frequency up to a ®rst peak around 2±4 Hz. For the y-direction one additional peak, in the range 5±7 Hz was in most cases discernible. The ®rst peak was found to be more distinct for male subjects than for females, who have their highest impedance magnitude at the second peak. This was also the case for the vertical direction. The results from the in vehicle multi-axis measurements of the mechanical impedance clearly indicate a quite dierent outcome compared to the single-axis measurements as shown in Fig. 5. The most obvious dierence is that the mechanical impedance is higher at lower frequencies in the x-direction than would be expected. This ®nding raises some important questions. Firstly, will the biomechanical behaviour of the human
body for a certain direction be altered when exposure in other directions is present? If so, as indicated in this presentation, is then all single-axis mechanical impedance data reported so far either misleading or useless for multi-axis modelling, risk assessment or preventative purposes? Since the human body is such a complex biomechanical system its behaviour cannot easily be described by a simple model. Single-axis exposure, by using simple and easy to control stimulus, has been the way to collect data for modelling purposes. This is partly due to technical limitations such as lack of multi-axis exposure systems, limitations regarding software and hardware for calculations of multi-dimensional models. The systems and models describing the human body behaviour to vibration in single-axis have been helpful, for the understanding of human body biomechanics. However, besides the results from this study, recently reported
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work also shows results that indicate that motion applied to the human body in one direction will cause motion also in another direction. This observation is of course of outer most importance for all kinds of modelling related to human response to vibration, including biomechanical modelling and health risk assessment. The phase information between the motion transferred through the human body and the external motion is extremely important. Since the force component at the contact point between the body and the seat can be doubled or cancelled, and as a consequence show completely dierent results than single-axis experiments, one can only speculate how this could aect the health risk assessment as de®ned in ISO 2631 [9]. This standard does not mention the importance of the phase information, and that the frequency weighting ®lters de®ned in the standard destroys this information. A goal with the in vehicle experiments in the vehicle was to investigate if it is possible to quantify mechanical impedance by measurement in a real vehicle environment. The discussion will onward focus on the possible explanations of the dierences found between the laboratory studies and the in vehicle measurements. The vibration magnitudes were very dierent in the three directions measured, and the z-direction dominated the vibration at frequencies below 15 Hz. This, however, does not limit the possibilities to compare these results with earlier laboratory results. For mechanical impedance, a good resemblance with the laboratory data was found for the z-direction. Corresponding results for the horizontal directions did not show the same similarities. The impedance in the y-direction showed a better resemblance with laboratory results than the x-direction. For the x-direction, mechanical impedance with too high values at low frequencies and with too low values at high frequencies was found. One reason, however, could be the low vibration magnitudes present in the horizontal directions, but this is unlikely. As the laboratory studies showed, an increase in vibration magnitude resulted in decreased mechanical impedance magnitude. For the in vehicle results, the mechanical impedance magnitude was lower than in the laboratory study, where a higher vibration level was used. Furthermore, unreasonably high mechanical impedance was found in the frequency range 2± 6 Hz for the x-direction. The observations mentioned above can be caused by three things; either a defected or aected force and acceleration component, with respect to magnitude and phase, or any combination of them. One can, with good reason, assume that the acceleration component is not the cause. This is because acceleration is the input that eects the human body to produce a force. Thus a change in acceleration results in a change in force. A force component could induce a movement but it is not probable that it could actually move the whole vehicle.
Since the path from the seat plate, which includes the accelerometer, through the seat, seat base frame and chassis is almost rigid, the force has to be so high that it can move the minibus's suspension. Ruling out acceleration, leaves force signal and/or phase for explanation. Studying the formulae for calculating mechanical impedance provides some clues; Z f
F f v f
Ns=m:
The mechanical impedance magnitude is not eected by a change in phase, but by a change in force. Excluding acceleration, the only component that can change the magnitude of the mechanical impedance is force. Consequently, in the x-direction a too high force component is probably present for all subjects at low frequencies. A possible source for this extra force could be contribution originating from acceleration in any of the other directions. In building a model of upper body movement due to vertical whole-body vibration, Kitazaki and Grin [10] showed that a fore-and-aft movement of the spine and rotation of the pelvis were generated. This movement could be the source of the force transferred to the x-direction. The force components in the x- and y-directions have consequently been aected by a force component generated by acceleration in the z-direction. The eect of this force is probably highly dependent on their phase relationship. Since the results show a good resemblance between the laboratory and ®eld measurements in the zdirection, it is probable that the force component in that direction has been only slightly, if at all, aected by force components originating from acceleration in horizontal directions. This is also supported when acceleration levels for dierent directions are taken into consideration. This reasoning is also supported by results from another laboratory study (Holmlund, 1998 not published). The same three subjects were exposed to vibration in either x- or y-direction, while force and acceleration were measured in all three directions simultaneously. A ¯at spectra random acceleration (1±20 Hz, 0:25 m s 2 r.m.s.) was used with a rigid seat. The results are shown in Fig. 6. As can be seen, exposure in the x-direction generated a force component in the z-direction. For the y-direction, both x- and z-direction forces are generated, but they are lower than the forces generated by the xdirection vibration. These observations support the reasoning above. Even though these results do not show that there are forces in the x- and y-directions originating from vibration in the z-direction, one can assume that the reverse is likely. However, this eect needs further investigation. A good understanding of the underlying mechanisms is of utmost importance in order to be able to measure and explain human response to multi-axis vibration.
P. Holmlund, R. Lundstrom / Clinical Biomechanics 16 Suppl. No. 1 (2001) S101±S110
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2 Fig. 6. Force components obtained during single-axis random excitation (1±20 Hz, 0:25 m sr:m:s: ) and simultaneous measurements in x-, y- and zdirection.
In order to evaluate fully the biomechanical properties of the human body in an actual vibration environment, more studies of the eect of force components originating from other directions are needed. For instance, the magnitude, phase and non-linearity of force cross-talk need to be determined. Experiments with multi-axis vibration where one or two directions are kept constant and one or two directions could be varied, would, in this context be of great interest.
Design of preventative equipment is another area where multi-axis models are needed. The main conclusion is that it seems unlikely that single axis data can be simply transferred to a multi-axis environment. This is an aspect that needs further investigation in order to truly evaluate the eects of whole-body vibration on the seated human.
Acknowledgements 5. Conclusions The data presented in this paper show dierent for the seated human mechanical impedance when measured in a single-axis compared with a multi-axis wholebody vibration environment. The reason for this dierence is most likely that a single-axis vibration exposure results in motion and dynamic forces also in other directions. The consequence of this is that biomechanical models as well as guidelines for health risk assessment must be multi-axis sensitive to be useful in most areas.
The ®nancial support by the Swedish Council for Work Life Research is gratefully acknowledged (project: 94-0026).This research was supported by the European Commission under the BIOMED 2 concerted action BMH4-CT98-3251 (Vibration Injury Network). References [1] Grin MJ. Handbook of human vibration. London: Academic Press; 1990.
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[2] Dupuis H, Zerlett G. The eects of whole-body vibration. Berlin: Springer; 1986. [3] Sandover J. Behaviour of the spine under shock and vibration: a review. Clin Biomech 1988;3:249±56. [4] Pope MH, Novotny JE. Spinal biomechanics. J Biomech Eng 1993;115(4B):569±74. [5] Christ E, Brusl H, Donati P, Grin M, Hohmann B, Lundstr om R, et al. Vibration at work. Paris: International Section ``Research'', Institut National de Recherche et de Securite (INRS); 1989. [6] Bovenzi M, Hulshof CTJ. An updated review of epidemiological studies on the relationship between exposure to whole-body vibration and low back pain. Int Arch Occup Environ Health 1999;72:351±65.
[7] ISO/CD 5982. Mechanical vibration and shock ± Mechanical driving point impedance and transmissibility of the human body (revision of ISO 5982:1981 and ISO 7962:1987): International Organization for Standardization; 1991 1991-08-30. Report No. ISO 5982:1991(E). [8] Bendat JS, Piersol AG. Random data: analysis and measurement procedures, 2nd ed. New York: Wiley; 1986. [9] ISO 2631-1. Mechanical vibration and shock ± Evaluation of human exposure to whole body vibration-Part 1: General requirements: International Organization for Standardization; 1997 1997-05-01. Report No. ISO 2631-1:1997(E). [10] Kitazaki S, Grin MJ. A modal analysis of whole-body vibration, using a ®nite element model of the human body. J Sound Vib 1997;200(1):83±103.
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Mechanical impedance of the sitting human body in single-axis compared to multi-axis whole-body vibration exposure Patrik Holmlund *, Ronnie Lundstr om National Institute of Working Life, Technical Risk Factors, PO Box 7654, Ume a S-907 13, Sweden
Abstract Objective. The study was aimed to investigate the mechanical impedance of the sitting human body and to compare data obtained in laboratory single-axis investigations with multi-axis data from in vehicle measurements. Design. The experiments were performed in a laboratory for single-axis measurements. The multi-axis exposure was generated with an eight-seat minibus where the rear seats had been replaced with a rigid one. The subjects in the multi-axis experiment all participated in the single-axis experiments. Background. There are quite a few investigations in the literature describing the human response to single-axis exposure. The response from the human body can be expected to be aected by multi-axis input in a dierent way than from a single-axis exposure. The present knowledge of the eect of multiple axis exposure is very limited. Methods. The measurements were performed using a specially designed force and accelerometer plate. This plate was placed between the subject and the hard seat. Results. Outcome shows a clear dierence between mechanical impedance for multi-axis exposure compared to single-axis. This is especially clear in the x-direction where the dierence is very large. Conclusion. The conclusion is that it seems unlikely that single-axis mechanical impedance data can be directly transferred to a multi-axis environment. This is due to the force cross-talk between dierent directions. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Whole-body; Vibration; Multi-axis; Mechanical impedance
1. Introduction Knowledge of how vibration is transmitted to and through the human body can provide an important input to our understanding of human response to wholebody vibration (WBV). For instance, biodynamic studies have identi®ed critical frequency ranges, i.e., resonant frequencies, for dierent parts of the body, such as the eyes, head, shoulders, neck and spine (e.g., [1±3]). It is possible that some types of detrimental eects are closely related to WBV exposures that contain frequencies leading to a resonant behaviour of the body or parts of the body. It has for instance been shown that the spine has a resonant frequency of about 5 Hz [1,2,4], i.e., a frequency which is produced in many types of vehicles and earth-moving machinery [5]. This might be a causal or a contributing factor for the development of
*
Corresponding author. E-mail address: [email protected] (P. Holmlund).
low back pain among professional drivers [6]. Understanding of whole-body dynamics is also necessary for proper design of protective measures, such as suspension seats. The mechanical driving point impedance can be used to describe the biodynamical properties of the human body. It speci®es the complex ratio between the dynamic force to which the subject is exposed and the resulting body motion in terms of velocity. The international standard, ISO/CD 5982 [7], presents diagrams showing the modulus and phase of the driving point impedance of the human body in the z-direction for an upright sitting posture. The diagrams cover about 80% of the range of experimental values obtained from available literature, predominantly published before 1970 (for references, see ISO/CD 5982 [7]). It is clearly stated in the standard that presented information is aicted with certain restrictions, among which the most important are the limited number of included subjects (39 males), frequency range (0.5±30 Hz), input acceleration amplitudes 1±2 m s 2 , z-direction only, whole-body weights
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 0 ) 0 0 1 0 2 - 9
S102
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(51±94 kg), posture of the body and body restrains. In some cases the author does not give the input acceleration and the subject posture is usually poorly de®ned. Due to all these restrictions it is clearly stated in the standard that the information needs to be revised, as further experimental data are available. The international standard ISO/CD 5982 standard is restricted to males [7]. The question of gender dierences is getting more and more relevant, since the number of female drivers is steadily increasing. As there are differences in average anthropometric measures and muscle strength capacity between males and females it seems plausible to assume dierences in biodynamic behaviour. These dierences have to be considered when trying to understand the risk of injury. Impedance data for females are not easily found in the literature, therefore studies directed towards this matter are needed. Against this background the purpose of this paper was threefold. Firstly, to present results from a laboratory study showing data for the mechanical impedance of the human body in the three orthogonal directions fore-aft (x), lateral (y) and vertical (z), for dierent conditions. Secondly to present some corresponding data obtained during driving of a vehicle. Thirdly, to compare laboratory and ®eld data. 2. Method 2.1. Subjects The study groups for vertical and horizontal singleaxis laboratory experiments consisted of 15 females and 15 males, of which some participated in both. Vehicle
measurements were done on three subjects who had participated in both laboratory studies. Basic information about their anthropometric measures, age, work assignment, years at work, general state of health, previous or present exposure to whole-body vibration, etc., were asked for in a questionnaire. All subjects were considered to be healthy and with no signs or symptoms of musculo-skeletal disorders, such as low back pain or lumbago. Averaged anthropometric data for the subjects are shown in Table 1. 2.2. Experimental setup 2.2.1. Single-axis laboratory experiments With a signal generator (Br uel & Kjñr 1049), an electrodynamic shaker (Ling Dynamic System, Mod. 712 + ILS 712) and a power ampli®er (Ling Dynamic System, MPA 1) sinusoidal vibrations were generated. For the z-direction experiments 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 a 30 mm thick wooden board (230 300 mm2 ), and the girder four force transducers (Kistler 9251) were mounted. An accelerometer (Br uel & Kjñr 4231) was centrally attached underneath the seat plate. For the x- and y-direction experiments acceleration and force were measured with a specially designed seat plate, consisting of two aluminium plates with a tri-axial accelerometer (Br uel & Kjñr 4231) and four tri-axial force cells (Kistler 9251) mounted in between them. All transducers were of piezo-electric type.
Table 1 Mean (M), standard deviation (SD) maximum (max) and minimum (min) values for the subjects' age (years), body weight (kg) and height (cm) in the two laboratory studies and the corresponding data for the three subjects from the in vehicle study Female M (SD, max, min)
Male M (SD, max, min)
All M (SD, max, min)
Laboratory experiments z-direction n Age Weight Height
15 24 (2, 30, 32) 66 (10, 93, 54) 168 (6, 180, 157)
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)
x-, y-direction n Age Weight Height
15 34 (11, 511, 22) 63 (7, 76, 54) 167 (4, 173, 160)
15 39 (12, 59, 24) 75 (10, 93, 55) 177 (6, 188, 167)
30 37 (11, 59, 2) 69 (10, 93, 54) 172 (7, 188, 160)
Subject
Age (years)
Height (cm)
Weight (kg)
In vehicle experiments A B C
48 44 35
175 174 176
74 74 74
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The signals from the transducers were ampli®ed and low-pass ®ltered by identical charge ampli®ers (vertically: Br uel & Kjñr 2635, horizontally: RION UV6) and Bessel-®lters (cut-o frequency: 300 Hz). By using the signal feedback function (i.e., compressor) in the signal generator, the vibration level could be kept constant independent of the frequency and load. After A/Dconversion (fs 1000 Hz) of the force and acceleration signals, the values were continuously stored on disk for later analysis. 2.2.2. In vehicle experiments The passenger seats at the back of the eight-seat minibus were removed and a semi-rigid seat was mounted between the rear wheels. The centre of the seat was approximately 20 cm in front of the rear axle. No back support or elbowrests were used in this investigation. Acceleration and force were measured with the same seat plate as in the horizontal laboratory study. The signals from these transducers were fed to six identical charge ampli®ers (Br uel & Kjñr 2635) set for bandpass in the frequency range of 0.2 to 100 Hz. Time histories were stored using a digital tape recorder (SONY PC208Ax). The sampling rate was set to 12 kHz. A digital system was used to transfer measurements to a computer (SONY PCIF250NI). Data were down sampled to 1024 Hz and analysed. 2.3. Experimental procedure Prior to the ®rst 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 Ume a, Dnr 94-255) and their right to either interrupt an on-going test run or refrain from further tests. Each subject signed informed prior consent. The experimental procedure for all test runs in the laboratory followed a predetermined protocol. After weighing in a standing position the subjects sat down on the seat plate and positioned their feet on an adjustable footrest. At each occasion the subject was exposed to one of the four (six in horizontal direction) acceleration levels (0.25, 0.35) 0.5, 0.7, 1.0 or 1:4 m s 2 r.m.s. in both erect (E) and relaxed (R) upper body posture. In vehicle experiments used the same postures as the laboratory studies, sitting erect (E) and relaxed (R). The former was de®ned as sitting upright with the hands resting on the knees, the later originated from the erect posture where the subject was asked to relax and adopt a more comfortable sitting posture. The experimenter visually checked the posture during each test run. If a correction of the posture was required this was done during measurement pauses. For laboratory studies measurement period for each frequency was followed by a 5 s pause. The sinusoidal signal was increased in frequency from 2
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to 100 Hz in steps of 1/3 octaves, except in the range 2.5± 20 Hz where the steps were 1/6 octaves, for vertical direction. For the horizontal directions frequency was increased from 1.13±2.5 to 31.5±80 Hz, depending on exposure level, in steps of 1/6 octaves, except in the range 25±80 Hz where the steps were 1/3 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 (six in each horizontal direction) occasions, all on dierent days, one for each of the dierent acceleration levels. The in vehicle measurements, lasting for at least 5 min, were recorded after the subjects had adopted the erect posture. The driving surface was a snow covered gravel road, and the speed was maintained at approximately 50 km h 1 . After the run the minibus turned around and travelled in the opposite direction, repeating the procedure for the relaxed posture. 2.4. Analysis The collected data were processed and analysed with LabViewe 3.1.1 (Macintosh version). For each test frequency, in the laboratory studies, the collected acceleration signal was integrated to get the velocity. A root mean square (r.m.s.) value for the measured time period was then calculated. The r.m.s. value for the force was determined after vector compensation for the load produced by the internal mass of the seat plate i.e., a procedure usually denoted as ``mass cancellation''. On the basis of these results, the absolute mechanical impedance was calculated. In the laboratory study the phase dierence between the force and the acceleration was calculated by measuring the time dierence between zero crossings for the force and velocity signals. The in vehicle measurements calculation of the mechanical impedance (Z) was performed by power spectral density method. Acceleration was integrated to obtain the velocity. The cross-power spectral density was calculated for the force (F) and velocity (v) and then divided by the power spectral density of the velocity [8]. The frequency range of the data were 1±20 Hz, chosen because this is the most interesting area for WBV. 3. Results A general ®nding in vertical direction laboratory experiments was that the impedance increased with the frequency up to a ®rst maximum in the range 4±6 Hz (Fig. 1). For most test subjects a second and third maximum in the ranges of 8±12 and 50±70 Hz, respectively, were also observed. At frequencies around 10 Hz, females showed a more distinct second peak. In many cases the magnitude for this peak exceeded the ®rst. Fig. 1 is separated to show the dierences between male and
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Fig. 1. Mechanical impedance and phase data for the z-direction laboratory study.
female subjects. It is clear from the ®gure that the mechanical impedance in the vertical direction was nonlinear with respect to the acceleration. It can also be noted that the peaks were shifted towards lower frequencies as the acceleration was increased. A general ®nding for both x- and y-direction laboratory experiments, was that the mechanical impedance increased with frequency up to a ®rst peak in the range 2±5 Hz dependent upon each subject (Figs. 2 and 3, respectively). For most test subjects a second peak in the range 5±7 Hz was also observed in the y-direction. Dierences between the female and male groups in mechanical impedance peak frequency and magnitude were also observed. The mean mechanical impedance spectra for the xdirection showed in principal one peak at about 3±5 Hz for both females and males (Fig. 2). At low vibration levels there was an indication of two defuse peaks at about 3 and 6±7 Hz. At higher vibration levels only one peak was discernible. The phase spectra for the six levels of acceleration were similar for both females and males in the x-direction while some dierences were discernible in the y-direction. Generally, the phase decreased from
about 80° at 1.6 Hz to between )60° and )40° at 10 Hz, after which it increased. Mean mechanical impedance in y-direction for female and male subjects are shown in Fig. 3. The spectra for the y-direction showed two peaks at about 2 and 6 Hz at low vibration levels. However, the second peak diminished with increasing vibration level. As the vibration level increased the mechanical impedance decreased over the whole frequency range. The phase is shown as a function of frequency below each mechanical impedance spectrum (Fig. 3). In the phase angle spectra for the six levels of acceleration some dierences were discernible in the y-direction. The clear dip between the male subjects mechanical impedance peaks correspond to a more concentrated phase variation than for the female subjects. Generally, the phase decreased from about 80° at 1.6 Hz to between )60° and )40° at 10 Hz, after which it increased. To visualise the range of the mechanical impedance, data for males and females, erect and relaxed posture and all vibration levels are pooled in Fig. 4. From this ®gure the mean, maximum and minimum values can be found at dierent frequencies.
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Fig. 2. Mechanical impedance and phase data for the x-direction laboratory study.
In vehicle measurements results showed similarities with the laboratory studies (see Fig. 5). However, results in x-direction were in general clearly dierent. Results in z-direction showed good resemblance between the studies, while y-direction results showed magnitudes in the same range as laboratory studies. These dierences can to some extent be explained by the dierent vibration magnitudes obtained in the three directions. The vertical direction showed the highest magnitude and the horizontal directions had about one®fth of the magnitude in the frequency range 1±15 Hz. For both x- and y-directions an acceleration peak was located in the range 15±20 Hz. Coherency functions between force and acceleration for the three directions showed that there was a good coherence in the z-direction, while the coherency in the x- and y-directions was low, in the range 2±12 Hz. Individual results for mechanical impedance in the zdirection, in both the minibus and the laboratory studies, are shown in Fig. 5. Even if some dierences are evident, the mechanical impedance shown had in general a good agreement with the laboratory data. The most
obvious dierences were that the second peak is located at a lower frequency. The results for the x- and y-directions are also shown in Fig. 5. The mechanical impedance shows a complex behaviour. In most cases the results from the ®eld measurement show two peaks, at about the same frequencies as y-direction laboratory data. However, the level of the mechanical impedance diers, the ®eld results show up to 50% lower levels. Interestingly, the mechanical impedance for subject C shows about the same level as in the laboratory for y-direction. In the xdirection mechanical impedance show greater dierences between laboratory and ®eld measurements. Mechanical impedance for all subjects shows high magnitudes for both postures, which is not consistent with x-direction laboratory data. 4. Discussion The results from the two laboratory studies show that the single-axis mechanical impedance of the human
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Fig. 3. Mechanical impedance and phase data for the y-direction laboratory study.
Fig. 4. Pooled data for dierent experimental conditions (described in the text) showing the mean, maximum and minimum mechanical impedance and phase.
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Fig. 5. Results from the in vehicle and laboratory measurements. Thick lines indicate in vehicle measurements, for subjects A, B and C (see Table 1).
body is dependent on a number of factors, such as frequency, vibration level and gender. Generally, it applies for the horizontal directions that the mechanical impedance increases with frequency up to a ®rst peak around 2±4 Hz. For the y-direction one additional peak, in the range 5±7 Hz was in most cases discernible. The ®rst peak was found to be more distinct for male subjects than for females, who have their highest impedance magnitude at the second peak. This was also the case for the vertical direction. The results from the in vehicle multi-axis measurements of the mechanical impedance clearly indicate a quite dierent outcome compared to the single-axis measurements as shown in Fig. 5. The most obvious dierence is that the mechanical impedance is higher at lower frequencies in the x-direction than would be expected. This ®nding raises some important questions. Firstly, will the biomechanical behaviour of the human
body for a certain direction be altered when exposure in other directions is present? If so, as indicated in this presentation, is then all single-axis mechanical impedance data reported so far either misleading or useless for multi-axis modelling, risk assessment or preventative purposes? Since the human body is such a complex biomechanical system its behaviour cannot easily be described by a simple model. Single-axis exposure, by using simple and easy to control stimulus, has been the way to collect data for modelling purposes. This is partly due to technical limitations such as lack of multi-axis exposure systems, limitations regarding software and hardware for calculations of multi-dimensional models. The systems and models describing the human body behaviour to vibration in single-axis have been helpful, for the understanding of human body biomechanics. However, besides the results from this study, recently reported
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work also shows results that indicate that motion applied to the human body in one direction will cause motion also in another direction. This observation is of course of outer most importance for all kinds of modelling related to human response to vibration, including biomechanical modelling and health risk assessment. The phase information between the motion transferred through the human body and the external motion is extremely important. Since the force component at the contact point between the body and the seat can be doubled or cancelled, and as a consequence show completely dierent results than single-axis experiments, one can only speculate how this could aect the health risk assessment as de®ned in ISO 2631 [9]. This standard does not mention the importance of the phase information, and that the frequency weighting ®lters de®ned in the standard destroys this information. A goal with the in vehicle experiments in the vehicle was to investigate if it is possible to quantify mechanical impedance by measurement in a real vehicle environment. The discussion will onward focus on the possible explanations of the dierences found between the laboratory studies and the in vehicle measurements. The vibration magnitudes were very dierent in the three directions measured, and the z-direction dominated the vibration at frequencies below 15 Hz. This, however, does not limit the possibilities to compare these results with earlier laboratory results. For mechanical impedance, a good resemblance with the laboratory data was found for the z-direction. Corresponding results for the horizontal directions did not show the same similarities. The impedance in the y-direction showed a better resemblance with laboratory results than the x-direction. For the x-direction, mechanical impedance with too high values at low frequencies and with too low values at high frequencies was found. One reason, however, could be the low vibration magnitudes present in the horizontal directions, but this is unlikely. As the laboratory studies showed, an increase in vibration magnitude resulted in decreased mechanical impedance magnitude. For the in vehicle results, the mechanical impedance magnitude was lower than in the laboratory study, where a higher vibration level was used. Furthermore, unreasonably high mechanical impedance was found in the frequency range 2± 6 Hz for the x-direction. The observations mentioned above can be caused by three things; either a defected or aected force and acceleration component, with respect to magnitude and phase, or any combination of them. One can, with good reason, assume that the acceleration component is not the cause. This is because acceleration is the input that eects the human body to produce a force. Thus a change in acceleration results in a change in force. A force component could induce a movement but it is not probable that it could actually move the whole vehicle.
Since the path from the seat plate, which includes the accelerometer, through the seat, seat base frame and chassis is almost rigid, the force has to be so high that it can move the minibus's suspension. Ruling out acceleration, leaves force signal and/or phase for explanation. Studying the formulae for calculating mechanical impedance provides some clues; Z f
F f v f
Ns=m:
The mechanical impedance magnitude is not eected by a change in phase, but by a change in force. Excluding acceleration, the only component that can change the magnitude of the mechanical impedance is force. Consequently, in the x-direction a too high force component is probably present for all subjects at low frequencies. A possible source for this extra force could be contribution originating from acceleration in any of the other directions. In building a model of upper body movement due to vertical whole-body vibration, Kitazaki and Grin [10] showed that a fore-and-aft movement of the spine and rotation of the pelvis were generated. This movement could be the source of the force transferred to the x-direction. The force components in the x- and y-directions have consequently been aected by a force component generated by acceleration in the z-direction. The eect of this force is probably highly dependent on their phase relationship. Since the results show a good resemblance between the laboratory and ®eld measurements in the zdirection, it is probable that the force component in that direction has been only slightly, if at all, aected by force components originating from acceleration in horizontal directions. This is also supported when acceleration levels for dierent directions are taken into consideration. This reasoning is also supported by results from another laboratory study (Holmlund, 1998 not published). The same three subjects were exposed to vibration in either x- or y-direction, while force and acceleration were measured in all three directions simultaneously. A ¯at spectra random acceleration (1±20 Hz, 0:25 m s 2 r.m.s.) was used with a rigid seat. The results are shown in Fig. 6. As can be seen, exposure in the x-direction generated a force component in the z-direction. For the y-direction, both x- and z-direction forces are generated, but they are lower than the forces generated by the xdirection vibration. These observations support the reasoning above. Even though these results do not show that there are forces in the x- and y-directions originating from vibration in the z-direction, one can assume that the reverse is likely. However, this eect needs further investigation. A good understanding of the underlying mechanisms is of utmost importance in order to be able to measure and explain human response to multi-axis vibration.
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2 Fig. 6. Force components obtained during single-axis random excitation (1±20 Hz, 0:25 m sr:m:s: ) and simultaneous measurements in x-, y- and zdirection.
In order to evaluate fully the biomechanical properties of the human body in an actual vibration environment, more studies of the eect of force components originating from other directions are needed. For instance, the magnitude, phase and non-linearity of force cross-talk need to be determined. Experiments with multi-axis vibration where one or two directions are kept constant and one or two directions could be varied, would, in this context be of great interest.
Design of preventative equipment is another area where multi-axis models are needed. The main conclusion is that it seems unlikely that single axis data can be simply transferred to a multi-axis environment. This is an aspect that needs further investigation in order to truly evaluate the eects of whole-body vibration on the seated human.
Acknowledgements 5. Conclusions The data presented in this paper show dierent for the seated human mechanical impedance when measured in a single-axis compared with a multi-axis wholebody vibration environment. The reason for this dierence is most likely that a single-axis vibration exposure results in motion and dynamic forces also in other directions. The consequence of this is that biomechanical models as well as guidelines for health risk assessment must be multi-axis sensitive to be useful in most areas.
The ®nancial support by the Swedish Council for Work Life Research is gratefully acknowledged (project: 94-0026).This research was supported by the European Commission under the BIOMED 2 concerted action BMH4-CT98-3251 (Vibration Injury Network). References [1] Grin MJ. Handbook of human vibration. London: Academic Press; 1990.
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[2] Dupuis H, Zerlett G. The eects of whole-body vibration. Berlin: Springer; 1986. [3] Sandover J. Behaviour of the spine under shock and vibration: a review. Clin Biomech 1988;3:249±56. [4] Pope MH, Novotny JE. Spinal biomechanics. J Biomech Eng 1993;115(4B):569±74. [5] Christ E, Brusl H, Donati P, Grin M, Hohmann B, Lundstr om R, et al. Vibration at work. Paris: International Section ``Research'', Institut National de Recherche et de Securite (INRS); 1989. [6] Bovenzi M, Hulshof CTJ. An updated review of epidemiological studies on the relationship between exposure to whole-body vibration and low back pain. Int Arch Occup Environ Health 1999;72:351±65.
[7] ISO/CD 5982. Mechanical vibration and shock ± Mechanical driving point impedance and transmissibility of the human body (revision of ISO 5982:1981 and ISO 7962:1987): International Organization for Standardization; 1991 1991-08-30. Report No. ISO 5982:1991(E). [8] Bendat JS, Piersol AG. Random data: analysis and measurement procedures, 2nd ed. New York: Wiley; 1986. [9] ISO 2631-1. Mechanical vibration and shock ± Evaluation of human exposure to whole body vibration-Part 1: General requirements: International Organization for Standardization; 1997 1997-05-01. Report No. ISO 2631-1:1997(E). [10] Kitazaki S, Grin MJ. A modal analysis of whole-body vibration, using a ®nite element model of the human body. J Sound Vib 1997;200(1):83±103.