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The vibration transmissibility and driving-point biodynamic response of the hand exposed to vibration normal to the palm
International Journal of Industrial Ergonomics 41 (2011) 418e427
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The vibration transmissibility and driving-point biodynamic response of the hand exposed to vibration normal to the palm Xueyan S. Xu*, Daniel E. Welcome, Thomas W. McDowell, John Z. Wu, Bryan Wimer, Christopher Warren, Ren G. Dong Engineering & Control Technology Branch, National Institute for Occupational Safety and Health, 1095 Willowdale Road, Morgantown, WV 26505, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 August 2009 Received in revised form 3 May 2011 Accepted 27 May 2011 Available online 28 June 2011
Prolonged, intensive exposure to vibrations from palm and orbital sanders could cause finger disorders. They are likely to be associated with the biodynamic responses of the fingers. Although the biodynamic responses of the hand-arm system have been studied by many researchers, the detailed biodynamic responses distributed in the hand substructures have not been sufficiently understood. To advance the knowledge in this aspect and to aid in the development of improved finite element models of the substructures, this study simultaneously measured the overall driving-point biodynamic response and the distribution of vibration transmissibility at the fingers and back of the hand exposed to a flat plate vibration (as an approximate simulation of the operations of the palm and orbital sanders) and examined the relationship between these two measures of biodynamic responses. Ten subjects (five males and five females) participated in the experiment. A scanning laser vibrometer was used to measure the distributed vibration. This study confirmed that the distributed hand responses generally varied with locations on each finger, vibration frequencies, and applied hand force. Two major resonances were observed in the vibration transmissibility. At the first resonance, the transmitted vibrations at different locations were more or less in phase; hence, this resonance was also observed in the driving-point biodynamic response that measures the overall biodynamic response of the system. The second resonance was observed at the fingers. Because this resonant frequency varied greatly among the fingers and the specific segments of each finger, it is difficult to identify this resonance in the driving-point biodynamic response. The implications of the findings for further model developments and applications are discussed. Relevance to industry: This study enhanced the understanding of the biodynamic responses of the fingers and hand exposed to vibrations on a contact surface with a large effective radius such as that found on palm and orbital sanders. The results can also be used to develop and/or validate models of the substructures of the hand-arm system, which can be further used to help design and analyze these tools and associated anti-vibration devices. The results may also be applicable to help develop location-specific frequency weightings to assess the risks of the finger vibration exposure. Published by Elsevier B.V.
Keywords: Hand-arm vibration Hand-transmitted vibration Driving-point biodynamic response Hand vibration transmissibility Palm sander Orbital sander
1. Introduction Palm sanders and orbital sanders are widely used in the furniture manufacturing. Such tools usually generate fairly highfrequency vibrations (Griffin, 1997), which are largely absorbed by the hand, especially the fingers (Dong et al., 2005c; Dong et al., 2008a). Prolonged, intensive exposure to such vibrations could cause symptoms of hand-arm vibration syndrome such as
* Corresponding author. Tel.: þ1 304 285 5840; fax: þ1 304 285 6265. E-mail address: [email protected] (X.S. Xu). 0169-8141/$ e see front matter Published by Elsevier B.V. doi:10.1016/j.ergon.2011.05.007
vibration-induced white finger. The risk assessment of the syndrome is currently based on International Standard ISO 5349-1, 2001. Although vibration-induced white finger is a unique and important component of the hand-arm vibration syndrome, epidemiological studies have not shown reasonable agreement between the observed risk of vibration-induced white finger and that predicted by the ISO-5349 model (Lidström, 1977; Bovenzi et al., 1980; Bovenzi, 1998; Griffin, 1997, 2008; Griffin et al., 2003). One of the possible reasons is that the current ISO frequency weighting may be inappropriate for the assessment of vibration-induced white finger. An effective approach to develop an improved frequency weighting for such an assessment is to study
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the vibration-induced biodynamic responses of the fingers and hand (Dong et al., 2005a, 2006a; Dong et al., 2008a). The biodynamic response has been primarily studied using the following three measures: vibration transmissibility (VT) measured on the skin or surface of the hand and/or arm (Miwa, 1968; Pyykkö et al., 1976; Reynolds, 1977; Sörensson and Lundström, 1992; Gurram et al., 1994; Scalise et al., 2007); driving-point biodynamic response functions (DPBR) such as apparent mass or mechanical impedance (Burström, 1990; Kihlberg, 1995; Marcotte et al., 2005); and vibration-induced stresses, strains, and power absorption density in the tissues of the hand-arm system (Wu et al., 2004, 2008; 2010; Dong et al., 2007). These measures of responses reflect different aspects of the vibration-induced biodynamic response but must be associated with each other in some respects because they are measured from the same system. A feasible method has not been developed to directly measure the vibration-induced stress, strain, power absorption density on tissues in a living subject. It is also technically demanding to simulate the detailed responses of the system tissues. Therefore, previous studies have been mostly focused on either vibration transmissibility or driving-point biodynamic response functions and the detailed tissue responses have been far from sufficiently understood. Considering that the detailed responses are likely to be more directly associated with vibrationinduced psychophysical, physiological, and pathological responses (Wu et al., 2004; Dong et al., 2005a), it is very important to conduct further studies on these detailed responses. Similar to the estimations of the dynamic loads and motions in the human body using an inverse dynamic approach, the quantifications of the detailed biodynamic responses to vibration primarily depends on the inverse dynamic simulation of the handarm system. Similar to the forces measured at the feet and the motions measured on the body in biomechanics studies, the DPBR and the transmitted vibration are vital inputs for the development of a validated model for the predictions of detailed biodynamic responses. To avoid the mass effect of conventional accelerometers (Griffin et al., 1982), several studies have employed advanced laser vibrometers to accurately measure the vibration transmitted to the surface of the hand-arm system (Sörensson and Lundström, 1992; Rossi and Tomasini, 1995; Deboli et al., 1999; Nataletti et al., 2005; Scalise et al., 2007). However, a review of literature for the current study found only one study that reported simultaneously measured DPBR and surface VT using a laser vibrometer (Concettoni and Griffin, 2009). For a sufficient understanding of the biodynamic response and to perform any modeling of the fingers and hand, both the magnitude and phase angle of the responses are generally required but the phase information was not reported in
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the vast majority of the reported studies. Further studies are also required to verify the reported data and to interpret them. In light of these noted shortcomings, the specific aims of this study are (a) to simultaneously measure the DPBR of the hand-arm system and the VT distributed at the fingers and back of the hand using a laser vibrometer for further modeling studies; and (b) to enhance the understanding of the vibration transmitted to the fingers and to examine the relationship between the DPBR and VT. The applications of these different measures of the biodynamic response are also discussed in this study. 2. Method 2.1. Experimental setup Ten healthy adults (five males and five females) participated in this study. Their major anthropometrics are listed in Table 1. The study protocol was reviewed and approved by the NIOSH Human Subjects Review Board. As shown in Fig. 1, the vibration testing system and the basic test setup used in this study are similar to those used for standardized glove testing (ISO 10819, 1996). However, a different interface between the hand and the vibration source was considered in this study. The vibration velocity transmitted to the surface or skin of the hand was measured using a scanning laser vibrometer (Polytec PSV-300eH). The specific measurement locations are identified in Fig. 2. As observed in a previous study (Dong et al., 2006b), it is very difficult to use the laser vibrometer to reliably measure the vibration on a surface that is largely non-perpendicular to the laser beam. As an initial investigation, this study considered an openhand pushing action on a flat rectangular aluminum platform (21.6 12.7 cm, 1.09 kg), as shown in Fig. 1. While it is expensive and time-consuming to replicate the exact contact geometries of palm sanders or orbital sanders, such a test setup can be considered as an approximate simulation of the hand vibration exposure in the operations of these tools. Although the transmitted vibration and driving-point biodynamic response measured in such a test setup may be different from those in power grip on cylindrical handles equipped on many other tools, this approach can be used to establish a baseline for understanding the major features of the vibration transmitted to the fingers and back of the hand and the basic relationship between the DPBR and hand-transmitted vibration exposure. Probably for this reason, the newly reported study also used such an approach (Concettoni and Griffin, 2009). In the present study, the platform was fixed on a 1-D Vibration Test System (Unholtz-Dickie, TA250-S032-PB) through three force sensors (Kistler 9212), which were used to measure both the
Table 1 Subject anthropometry. Subject Height (cm) Weight (N) Hand length (mm) Hand breadth (mm) Hand circumference (mm) Finger length (mm) Hand volume (ml) Finger volume (ml) L Z X V Y U B C G F
180.3 175.3 188.0 195.6 175.3 167.6 162.6 161.3 160.0 171.5
867.9 978.7 925.7 889.5 733.5 511.9 600.2 533.5 645.3 645.3
194 184 192 191 193 166 168 175 180 182
88 85 96 88 86 72 76 74 77 80
215 200 225 210 220 180 195 185 190 194
82 79 82 78 85 71 72 75 78 78
435 400 450 393 380 210 285 235 280 290
65 70 80 55 65 50 50 40 55 45
Mean SD
173.7 11.73
733.1 170.6
182.5 10.29
82.2 7.61
201.4 15.33
78 4.42
335.8 85.64
57.5 12.30
hand length ¼ tip of middle finger to crease at the wrist; hand breadth ¼ the width measured at metacarpal of the hand; hand circumference ¼ the circumference measured at metacarpal of the hand; finger length ¼ tip of middle finger to crease at the base of the finger; hand volume ¼ water displaced by hand submerged to crease at wrist; finger volume ¼ water displaced by fingers submerged to crease at the base of the middle finger.
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Fig. 1. Subject posture and experiment setup.
applied push force and the dynamic responding force. The applied hand push force was taken as 15 and 30 N in the experiment, which is likely to be within the range of the hand force applied on these sanders in wood sanding and polishing. The platform was angled at 45 from the horizontal plane so that the subjects could apply a more natural and steady pushing action on the platform in a standing posture as shown in Fig. 1. The arm posture was selected so that the laser beam for measuring the vibration was not blocked during the exposure measurement. An accelerometer (Endevco, Model 65e100) was rigidly fixed on the back of the platform to measure the input vibration and to control the excitation. A constant-velocity (8 mm/s) broad-band random vibration from 16 to 1250 Hz was used as the excitation. The summation of the three force signals, the signal of the accelerometer fixed on the platform, and the vibration signal measured with the laser vibrometer were input into a data acquisition system (B&K Model 3032A) to simultaneously evaluate the DPBR and the VT using the cross-spectral function built into the B&K Pulse software. The data were expressed in one-third octave bands with center frequencies from 16 to 1000 Hz. Both the real and imaginary parts of the responses were recorded.
graphical display was developed in-house using LabVIEWÔ software to display the real-time push force along with the target force. Twenty points on the hand were defined for the measurement, as shown in Fig. 2. There were four measurement locations/points (P1-P4) on each digit. Fingertip measurements (P1) were collected at the base of each fingernail. Inter-phalangeal joint measurements (P2 and P3) were also collected for each digit. Measurements on the back of the hand (P4) were also collected for each digit. To ensure stable push forces and to prevent fatigue, test trials were limited to the measurement of vibrations at the four points for a selected digit. Once the subject’s push force stabilized at the target force, the four measurement points were scanned with the laser vibrometer. Each of the four measurement points was scanned for 20 s; each trial took about 90 s. The subjects rested for at least 2 min between trials. Two trials were performed for each point at each force level. The testing order of the five digits and two push force levels were independently randomized among the subjects. 2.3. Evaluations of measurement systems, vibration transmissibility, and driving-point biodynamic response To assure the accuracy and reliability of the measurement, this study conducted a series of tests to evaluate the measurement systems before subject testing. In one evaluation, the platform vibration was measured with the laser vibrometer at 20 points corresponding to the locations of the hand measurement points. The results indicated that the fundamental resonance of the platform fixed on the shaker is 1085 Hz. The resonance resulted in nonunity transmissibility (>1.05) and some phase shift (>10 deg.) at high frequencies (>500 Hz). Some bending motion of the platform was also observed, which made some significant differences (>5%) between the vibrations at the different measuring points at the higher frequencies. Therefore, the non-uniform distribution should be corrected by normalizing the measured data. Specifically, corrections of the measured subject transmissibility at each measuring point were made based on the corresponding platform transmissibility using the following formulas:
TrCorrected
Skin ðuÞ
¼
TrMeasured Skin ðuÞ TrPlatform ðuÞ
(1)
TrMeasured
Skin ðuÞ
¼
ASkin Laser ðuÞ APlatform Accelerometer ðuÞ
(2)
2.2. Subject testing procedures The study and testing procedures were explained to each subject upon arrival. After signing the required consent form, the subject was instructed to practice the pushing action on the platform with the opened right hand, as shown in Fig. 1. A custom
Fig. 2. Laser scanning points on five fingers and back of hand.
TrPlatform ðuÞ ¼
APlatform Laser ðuÞ APlatform Accelerometer ðuÞ
(3)
where ASkin_Laser and APlatform_Laser are the accelerations measured with the laser vibrometer on the skin at the measuring points and at the corresponding points on the platform, respectively, APlatform_Accelerometer is the acceleration measured on the platform using the accelerometer fixed on the platform, and u is the center frequency of each one-third octave band. Acceleration from the laser vibrometer was calculated via the B&K Pulse program by taking the first derivative of the directly-measured velocity. In another evaluation, the reliability of the laser measurement on the skin was examined. In the test, the motions of the hand on the platform with and without vibration input were separately measured with a subject. The signal measured on the hand without vibration exposure was divided by the signal measured during the hand exposure to vibration, which was termed as the noise/signal ratio of the measurement in this study. The driving-point biodynamic response functions evaluated in this study were expressed as apparent mass and mechanical
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impedance. Similarly to the evaluation of the vibration transmissibility, the apparent mass (MA) and mechanical impedance (Z) were evaluated using the following formula:
MA ðuÞ ¼
FH ðuÞ APlatform
Accelerometer ðuÞ
ZðuÞ ¼ MA ðuÞ,ju
(4)
(5)
pffiffiffiffiffiffiffi where FH is the measured dynamic force and j ¼ 1. The directly-measured impedance is the total response that includes that of the plate tare mass and that of the hand-arm system. A frequency domain method was used to cancel the tare mass effect (Dong et al., 2006b). Due to the platform resonance bending motions, the biodynamic response of the hand at frequencies above 250 Hz may not be reliable. This is also because the tare mass of the platform is much larger than the apparent mass of the hand. Therefore, only the mechanical impedances from 16 to 250 Hz were analyzed in this study. 2.4. Statistical analyses The two repetitive measures under each condition were utilized for the statistical analysis. Mixed Model Analysis of Variance (ANOVA) tests of vibration transmissibility were performed to identify the significance of the following fixed factors: frequency, push force, and measuring point. Subject was treated as a random factor. Further stratified ANOVAs were performed to examine the distribution signficance of the transmissibility on each digit/finger. The ANOVAs were performed using SPSS statistical software (SPSS, version 16.0). Differences were considered significant at the p < 0.05 level. 3. Results
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measurement points (P3 and P4) at frequencies above 160 Hz. These observations, together with the above-mentioned measurement system problems, suggest that the transmissibility data at frequencies above 400 Hz at P2, 250 Hz at P3 and 160 Hz at P4 may include significant errors. 3.2. General characteristics of the transmissibility Fig. 4 shows typical examples of the transmissibility (magnitude and phase) at the four measurement points of the middle finger of Subject Z measured with the 30 N push force. Two peaks were generally observed in the transmissibility measured for each individual, which can be considered as the resonances at the measured points or locations. The first peak was more obvious at P2eP4 than that at P1. Also as an example, Fig. 5 shows the magnitudes of the transmissibility measured at the four measuring points (P1eP4) on the middle fingers of the ten subjects, together with the mean transmissibility. Because of the arithmetical averaging effect (Dong et al., 2009), the peak magnitudes, especially in the second peak, were somewhat suppressed; however, the averaging process does not change the basic trends. The majority of the frequencies for the first peak fell in the range of 30e60 Hz. The phase angles were close to each other below 40 Hz, as shown in Fig. 4. In the first peak frequency range, the magnitude of the transmissibility generally increases from the fingertip (P1) to the back of the hand (P4). The highest second peak was observed at the fingertip (P1), as shown in Figs. 4 and 5. It is also obvious in the response measured at the second phalange (P2). The second peak frequency is generally in the range of 80e300 Hz, which is much more spread out than the first peak frequency. The transmissibility magnitudes at the third and four phalanges (P3 and P4) at frequencies above 200 Hz, especially over 300 Hz, are very small. As above-mentioned, the transmissibility at P2, P3, and P4 at the high frequencies may include some significant errors. Also because of the low
3.1. Evaluation of the laser vibrometer measurement Fig. 3 shows typical examples of the noise/signal ratios measured on the four points of the middle finger of a subject, which is an indication of the potential measurement errors at these locations. The noise/signal ratio is generally less than 5% at frequencies below 160 Hz, but it becomes significant at higher frequencies, depending on the location of the measurement. This result, shown in Fig. 3, indicates that the potential error generally increases as the measurement point moves from the fingertip toward the back of the hand. While the potential error on the nail (P1) is negligible (<5%) in the entire frequency range of concern, it could become significantly high at the third and forth
Fig. 3. A typical example of noise/signal ratios (NSR) of the laser measurement at the four measurement points (P1eP4) for the middle finger.
Fig. 4. Typical examples of the transmissibility (magnitude and phase) at the four measurement points (P1eP4) of the middle finger at a 30 N push force.
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3
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Fig. 5. Transmissibility functions of the ten subjects measured at the four measuring points (P1eP4) on the middle finger measured with 30 N push force, together with their of the subjects. corresponding mean responses
transmissibility at these locations at the high frequencies, the corresponding phase angles are not reliable; hence, they are not presented or further analyzed. 3.3. Statistical results of the vibration transmissibility The results of the ANOVA for vibration transmissibility are listed in Table 2. As indicated, each of the three fixed factors (force, measurement location, and frequency) analyzed was significant. While the two-way interactions between the frequency and each of the other two factors were significant, the interaction between the force and location is not significant. As also shown in Fig. 5, the vibration transmissibility functions varied substantially among subjects. Figs. 6 and 7 illustrate the mean transmissibility functions of all the subjects at each measurement point of the five digits/fingers under the 15 N and 30 N push force, respectively. Increasing the push force increased the first peak or resonance frequency (F ¼ 31.5, p < 0.001). The second peak was also shifted toward a higher frequency as the push force increased (F ¼ 39.6, p < 0.001). The second peak frequencies also varied significantly with the measurement point on each finger (F 3.246, p 0.022). As also shown in Figs. 6 and 7, the transmissibility functions at the same location on the five fingers have some similarities at some frequencies, especially those on the index, middle, and ring fingers. Table 2 Results of ANOVA for vibration transmissibility data. Source of variance
Sum of squares
Degrees of freedom
Mean square
F-value
p -value
Frequency (Freq) Applied Force (Force) Measurement Point (Point) Freq Force Freq Point Force Point
2910.39 15.40
19 1
153.18 15.40
261.54 276.72
< 0.001 < 0.001
163.12
3
54.37
120.92
< 0.001
17.98 544.55 0.24
19 57 3
0.95 9.55 0.08
17.01 171.69 1.44
< 0.001 < 0.001 0.229
However, the transmissibility functions are generally significantly different, as confirmed from the measurement point-stratified ANOVAs (F 11.32, p < 0.001). This study also performed a finger-stratified ANOVA. The results further confirmed that the effects of the force, measurement location, and frequency were significant for the responses on each finger (F 43.45, p < 0.001). The interactions between the frequency and the other two factors were also significant (F 6.79, p < 0.001). Consistent with that observed in Table 2, the interaction between the force and measurement point was not significant (F 2.25, p 0.08). This means that the variation of the push force did not significantly change the basic distribution features of the vibration transmissions at the four measurement locations, which can also be observed by comparing the data presented in Figs. 6 and 7. 3.4. Driving-point biodynamic response The apparent mass and mechanical impedance responses of the ten subjects and their mean values for the 15 N and 30 N push forces are shown in Figs. 8 and 9, respectively. The apparent mass of the hand-arm system at frequencies above 250 Hz is generally less than 0.1 kg, which is much less than the platform mass (1.09 kg). This, together with the platform bending effect, makes it very difficult to reliably measure the driving-point biodynamic response above 250 Hz. For this reason, only the BR data up to 250 Hz are presented, which is sufficient for the purposes of this study. The impedance magnitudes and phase angles shown in Figs. 8 and 9 indicate that there are at least two resonances reflected in the response. The first peak occurs at about 20 Hz for the 15 N push and 25 Hz for the 30 N push. Such a peak frequency could not be identified in the vibration transmissibility measured on the fingers or back of the hand, probably because this peak could be mainly associated with the resonance of the palm-wrist-arm substructure under the specific arm posture used in this study, but the transmissibility of the wrist and arm was not measured. The second impedance peak occurs at about 45 Hz for the 15 N push and 60 Hz for the 30 N push; these peak frequencies are generally higher than
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427 P1
423 P2
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0 100
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Fig. 6. Mean transmissibility functions of all the subjects at each point of the five fingers under 15 N push force.
the first peak frequency (30e50 Hz) observed in the transmissibility measurements. Similar to transmissibility, inter-subject differences in the driving-point biodynamic responses were obvious, as also shown in Figs. 8 and 9. Because this study only measured the overall biodynamic responses of the hand-arm system, the effect of the measurement point could not be examined. Therefore, the fixed factors in this case are the push force and frequency. The results of the ANOVA indicate that they were significant factors (F 2698.69, p < 0.001) and their interaction was also significant (F ¼ 22.22, p < 0.001). The peak frequencies for mechanical impedance with the 30 N forces were significantly higher than those with the 15 N forces (F 8.6, p 0.015). 4. Discussions As an approximate simulation of the hand vibration exposure on a contact surface with a large effective radius, this study measured
the vibration transmissibility and biodynamic response of an openhand pushing against a flat platform. The experimental results provide some useful information for the understanding of the basic features of the vibration transmission to the hand, especially the fingers, which is further elaborated and discussed in this section. 4.1. Vibration measurement on the hand using the laser vibrometer The results of this study suggest the irregularity of the skin surface could play an important role in the measurement using the laser vibrometer, and its accuracy depends on the frequency, as shown Fig. 3. The most reliable measurement was found on the nail, probably because the nail has no hair and is smooth and reflective. The irregularity of the skin surface and the density of the hair generally increase with the measurement location moving from the fingertip to the back of the hand, which explains why the noise/ signal ratios presented in Fig. 3 also show the same trend. Therefore, the reliability of the measurement may be improved by
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Fig. 7. Mean transmissibility functions of all the subjects at each point of the five fingers under 30 N push force.
increasing the smoothness and reflection of the skin surface. This supports the practice used by Concettoni and Griffin (2009), who applied some reflective paint on the skin, and by Sörensson and Lundström (1992), who attached a piece of adhesive lightweight retro-reflecting tape on the skin without shaving the hairs on the skin, which should be considered in further studies. 4.2. Comparisons with published data and findings The hand posture and position on the flat platform in the current study is very similar to those in position #1 used in the study reported by Concettoni and Griffin (2009). Although the reported study used different measuring locations (close to the finger joints or on the knuckles), arm posture (with forearm parallel to the vibrating platform surface), and hand push force (25 N), the basic features of the finger transmissibility functions at each corresponding location in both studies are similar. For example, the
average resonance frequencies at the four fingernails (P1 on index, middle, ring, and small finger) shown in Figs. 6 and 7 are generally in the range of 100e250 Hz, and they are very similar to those measured at the first knuckles of the four fingers reported by Concettoni and Griffin (2009) (see position 1 data at Pt.#3, #6, #9, and #12 in Fig. 6 of their report). Their magnitudes of the transmissibility are also similar. The locations and direction of the transmissibility measurement reported by Sörensson and Lundström (1992) are similar to those considered in the current study, but the hand grasped a nearcylindrical handle in their experiment. While the resonances at the fingernails in their study were generally at higher frequencies (>300 Hz) than those observed in the current study, the vibration transmissibility functions and resonance frequencies measured at other locations on the fingers are similar to those on the fingernail and the first phalange area measured in the current study. This may be partially because the second and third phalange areas of the
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427
a
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Fig. 8. Apparent mass and mechanical impedance responses (magnitude and phase) of the ten subjects at 15 N push force, together with their corresponding mean responses of the subjects.
fingers were better adapted or coupled to the near-cylindrical handle than those on the flat plate, which could result in a large difference between the effective contact pressures in these two test setups. This observation suggests that the geometrical features of the handetool interface could affect the vibration transmissibility. However, both studies showed that the resonance frequencies increase with the increase in the applied hand force, and they decrease as the measurement point moves from the fingertip to the palm of the hand.
2
4.3. Vibration exposure and reduction of the fingers As above-mentioned, the hand vibration exposure on the flat platform can be considered as an approximate simulation of that in
b Magnitude (Ns/m)
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The magnitude and damping characteristic of the finger transmissibility at P2 and P3 are very comparable with those of rat tail transmissibility (Welcome et al., 2008). This further supports the use of the rat model for studying finger vibration exposure.
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Fig. 9. Apparent mass and mechanical impedance responses (magnitude and phase) of the ten subjects at 30 N push force, together with their corresponding mean responses of the subjects.
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the operations of some tools such as palm and orbital sanders. The dominant vibration frequencies of these tools are usually in the neighborhood of 100 Hz (Griffin, 1997), which are within the range of the observed finger resonance frequencies. Hence, it is important to reduce the vibration from these tools. The results of this study also imply that it is difficult to reduce the vibration transmitted to the fingers, especially the fingertips, using any anti-vibration glove. In principle, the vibration reduction of the glove depends on both the mechanical properties of the glove and the effective mass of the fingers. Whereas it is not practical to make the fingers of the glove very thick to achieve the required low stiffness and high damping value, the mass of the fingers is small, as reflected from the high resonance frequencies (80e300 Hz) of the fingers. An anti-vibration cap may be developed to reduce the vibration exposure on these tools. 4.4. Relationships between vibration transmissibility and drivingpoint biodynamic response Theoretically, the driving-point biodynamic response depends on the overall dynamic force of the hand-arm system induced by the vibration input to the hand, as dictated in Eq.(4). Because the dynamic force is directly associated with the acceleration on the hand and arm, the DPBR should also be associated with vibration transmissibility. If the hand-arm system would be considered as a rigid mass (m) on a spring-damper system connected to the plate, the apparent mass (M1-D) of such a 1-D model is directly associated with the transmissibility (Tr1-D) of the mass as follows:
M1D ðuÞ ¼ m,Tr1D ðuÞ
(6)
As observed from the phase angles measured in this study and from the corresponding patterns reported by Concettoni and Griffin (2009), the majority of the substructures in the hand-arm system move approximately in phase under low-frequency vibration exposures. Therefore, as a crude approximation, it is reasonable to consider the hand-arm system as a rigid mass on a spring-damper system that simulates the palm elasticity and damping property. This justifies the use of a 1-D model to simulate the hand-arm system if only the low frequencies are of concern. In fact, the 1-D model (including the 2-D model with a lumped mass at its end) can provide a reasonable simulation of the overall response along the forearm direction at frequencies up to 100 Hz (Dong et al., 2008b). Eq.(6) indicates that the low-frequency transmissibility measured at the back of hand or wrist can also be used to approximately represent the basic trend of the apparent mass in this frequency range. Because the vibration-induced biodynamic force acting on the palm and wrist can be estimated from the apparent mass (Dong et al., 2005b), it seems reasonable to use the transmissibility measured at the back of the hand and wrist as a frequency weighting for assessing the risk of vibration-induced injuries and disorders in the palm-wrist-forearm substructure. These theoretical analyses provide an additional justification for the wrist vibration measurement method (Thomas and Beauchamp, 1998; Xu et al., 2009). Similarly, the apparent mass of the fingers should also be closely correlated with the vibration transmissibility measured at the fingers. The second peak observed in the impedance should be closely associated with the first finger resonance observed in the transmissibility. As presented above, however, their peak frequencies are different because the impedance peak frequency is generally higher than that of the apparent mass directly associated with the transmissibility. This can be understood from the relationship between the apparent mass (M) and the mechanical impedance (Z) shown in Eq.(5) (Dong et al., 2006a). The second peak frequency identified in the transmissibility functions of the fingertip (P1) and
middle phalange (P2) is associated with the local structure resonance. The local resonance is largely independent of the responses and conditions of the remaining structures of the hand-arm system (Dong et al., 2005c). Because the local resonances could occur at very different frequencies, and their motions may be largely out-ofphase, the vector summation of the biodynamic forces could not reflect the specific features of the local responses. This explains why such a peak was practically undetectable in the measured DPBR, which suggests that it is necessary to use a local biodynamic response (BR) measurement method to quantify the local dynamic forces. The independence of the response at high frequencies also suggests that it is not necessary to simulate the entire hand-arm system to predict the local high-frequency responses of the fingers, which justifies the use of a finger model for the prediction of the biodynamic response in the finger (Wu et al., 2008). The skin surfaces may vibrate differently from those of the bones of the hand-arm system. While it is practically very difficult to measure the vibrations distributed on the bones of a human subject, the reliability of the model can be increased by considering the skin as a separate component in the model structure, as used in some reported studies (Wu et al., 2008, 2010). Besides the structural consideration, the model may become more realistic if both the VT and the DPBR are simultaneously measured and used to construct the model. As a step toward the model development, this study simultaneously measured the DPBR and the VT distributed at the fingers and back of the hand. The experimental data may not be sufficient for simulating the response of the hand coupled to a cylindrical handle, but they should be sufficient to simulate the responses of the fingers in contact with surfaces with large effective diameters such as those on the palm sanders and orbital sanders. 5. Conclusions This study simultaneously measured the overall driving-point biodynamic response (DPBR) and the vibration transmissibility (VT) distributed at the fingers and the back of the hand. The relationship between these two measures was also examined. The results confirm that the distributed hand biodynamic response is a function of frequency, and it generally varies with locations or substructures, individuals, and applied hand forces. The major parts of the hand move more or less in phase in the first major resonance of the hand. Therefore, the VT resonance was well-correlated with the DPBR. A second major VT resonance was observed at the fingers. Because this resonant frequency varies greatly among the fingers and the specific locations on each finger, it is very difficult to clearly identify this resonance in the DPBR that reflects the overall response of the entire system. These observations suggest that the models developed based solely on the DPBR may be sufficient for designing and analyzing some tools and anti-vibration devices, but they may not be reliable for predicting the detailed location-specific responses in the hand-arm system, especially in the fingers. Better models for predicting detailed biodynamic responses may be built based on both the transmissibility and the biodynamic response. The results of this study also suggest that the dominant vibrations of palm sanders and orbital sanders are likely to be within the range of the finger resonance frequencies, and available antivibration gloves are unlikely to be effective at reducing such vibrations. The developments of low-vibration tools and/or more effective anti-vibration devices are required to reduce the vibration transmitted to the fingers in the operations of these tools. 5.1. Disclaimers The content of this publication does not necessarily reflect the views or policies of the National Institute for Occupational
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427
Safety and Health (NIOSH), nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government. References Bovenzi, M., Petronio, L., Marino, F.D., 1980. Epidemiological survey of shipyard workers exposed to hand-arm vibration. International Archives of Occupational and Environmental Health 46 (3), 251e266. Bovenzi, M., 1998. Exposure-response relationship in the hand-arm vibration syndrome: an overview of current epidemiology research. International Archives of Occupational and Environmental Health 71, 509e519. Burström, L., 1990. Measurement of the impedance of the hand and arm. International Archives of Occupational and Environmental Health 62 (6), 431e439. Concettoni, E., Griffin, M., 2009. The apparent mass and mechanical impedance of the hand and the transmission of vibration to the fingers, hand, and arm. Journal of Sound and Vibration 325 (3), 664e678. Deboli, R., Miccoli, G., Rossi, G.L., 1999. Human hand-transmitted vibration measurements on pedestrian controlled tractor operators by a laser scanning vibrometer. Ergonomics 42 (6), 880e888. Dong, R.G., Wu, J.Z., Welcome, D.E., 2005a. Recent advances in biodynamics of hand-arm system. Industrial Health 43, 449e471. Dong, R.G., Welcome, D.E., Wu, J.Z., 2005b. Estimation of the biodynamic force acting at the interface between hand and vibrating surface. Industrial Health 43, 516e526. Dong, R.G., Wu, J.Z., McDowell, T.W., Welcome, D.E., Schopper, A.W., 2005c. Distribution of mechanical impedance at the fingers and the palm of the human hand. Journal of Biomechanics 38, 1165e1175. Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z., Schopper, A.W., 2006a. Frequency weighting derived from power absorption of fingers-hand-arm system under zh-axis. Journal of Biomechanics 39, 2311e2324. Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z., 2006b. Measurement of biodynamic response of human hand-arm system. Journal of Sound and Vibration 294 (4e5), 807e827. Dong, R.G., Welcome, D.E., Wu, J.Z., 2007. A method to quantify hand-transmitted vibration exposure based on biodynamic stress concept. Journal of Engineering in Medicine. Proceedings of the Institution of Mechanical Engineers Part H 221, 847e861. Dong, J.H., Dong, R.G., Rakheja, S., Welcome, D.E., McDowell, T.W., Wu, J.Z., 2008a. A method for analyzing absorbed power distribution in the hand and arm substructures when operating vibrating tools. Journal of Sound and Vibration 311, 1286e1309. Dong, R.G., Welcome, D.E., Wu, J.Z., McDowell, T.W., 2008b. Development of handarm system models for vibrating tool analysis and test rig construction. Noise Control Engineering Journal 56 (1), 35e44. Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z., 2009. Methods for deriving representative biodynamic response of hand-arm system to vibration. Journal of Sound and Vibration 325, 1047e1061. Griffin, M.J., Macfarlane, C.R., Norman, C.D., 1982. In: Brammer, A.J., Taylor, W. (Eds.), The Transmission of Vibration to the Hand and the Influence of Gloves. Vibration Effects on the Hand and Arm in Industry. John Wiley & Sons, New York, pp. 103e116. Griffin, M.J., 1997. Measurement, evaluation, and assessment of occupational exposures to hand-transmitted vibration. Occupational and Environmental Medicine 54 (2), 73e89. Griffin, M.J., Bovenzi, M., Nelson, C.M., 2003. Dose-response patterns for vibrationinduced white finger. Occupational and Environmental Medicine 60 (1), 16e26. Griffin, M.J., 2008. Measurement, evaluation, and assessment of peripheral neurological disorders caused by hand-transmitted vibration. International Archives of Occupational and Environmental Health 81 (5), 559e573.
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Gurram, R., Rakheja, S., Gouw, G.J., 1994. Vibration transmission characteristics of the human hand-arm system and gloves. International Journal of Industrial Ergonomics 13 (3), 217e234. ISO 10819, 1996. Mechanical Vibration and Shock e Hand-arm Vibration e Method for the Measurement and Evaluation of the Vibration Transmissibility of Gloves at the Palm of the Hand. International Organization of Standard, Geneva, Switzerland. ISO 5349-1, 2001. Mechanical Vibration- Measurement and Evaluation of Human Exposure to Hand-transmitted Vibration e Part 1: General Guidelines. International Organization of Standard, Geneva, Switzerland. Kihlberg, S., 1995. Biodynamic response of the hand-arm system to vibration from an impact hammer and a grinder. International Journal of Industrial Ergonomics 16, 1e8. Lidström, I.M., 1977. Vibration injury in rock drillers, chiselers, and grinders. Some views on the relationship between the quantity of energy absorbed and the risk of occurrence of vibration injury. Proceeding of the 2nd International Conference on Hand-Arm Vibration, Cincinnati, OH, USA, 77e83. Marcotte, P., Aldien, Y., Boileau, P.E., Rakheja, S., Boutin, J., 2005. Effect of handle size and hand-handle contact force on the biodynamic response of the hand-arm system under zh-axis vibration. Journal of Sound and Vibration 283 (3e5), 1071e1091. Miwa, T., 1968. Evaluation methods for vibration effects. Part 4: measurement of vibration greatness for whole-body and hand in vertical and horizontal vibration. Industrial Health 6, 1e10. Nataletti, P., Paone, N., Scalise, L., 2005. Measurement of Hand-vibration Transmissibility by Non-contact Measurement Techniques. International Conference on Environmental Health Risk, Bologna, Italy. 315e324. Pyykkö, I., Färkkilä, M., Toivanen, J., Korhonen, O., Hyvärinen, J., 1976. Transmission of vibration in the hand-arm system with special reference to changes in compression force and acceleration. Scandinavian Journal of Work. Environment & Health 2, 87e95. Reynolds, D.D., 1977. A review of 3 years’ research. In: Wasserman, D.E., Taylor (Eds.), Proceedings of the International Occupational Hand-arm Vibration Conference. National Institute for Occupational Safety and Health, Cincinnati, Ohio, USA, pp. 99e128. Hand-Arm Vibration. Rossi, G.L., Tomasini, E.P., 1995. Handearm vibration measurement by a laser scanning vibrometer. Measurement 16 (22), 113e124. Scalise, L., Rossetti, F., Paone, N., 2007. Hand vibration: non-contact measurement of local transmissibility. International Archives of Occupational and Environmental Health 81, 31e40. Sörensson, A., Lundström, R., 1992. Transmission of vibration to the hand. Journal of Low Frequency Noise and Vibration 11, 14e22. Thomas, M., Beauchamp, Y., 1998. Development of a new frequency weighting filter for the assessment of grinder exposure to wrist transmitted vibration. Computers & Industrial Engineering 35 (3e4), 651e654. Welcome, D.E., Krajnak, K., Kashon, M.L., Dong, R.G., 2008. An investigation on the biodynamic foundation of a rat tail vibration model. Journal of Engineering in Medicine. Proceedings of the Institution of Mechanical Engineers (Part H) 222, 1127e1141. Wu, J.Z., Dong, R.G., Schopper, A.W., Smutz, W.P., 2004. A structural fingertip model for simulating of the biomechanics of tactile sensation. Medical Engineering and Physics 26 (2), 165e175. Wu, J.Z., Krajnak, K., Welcome, D.E., Dong, R.G., 2008. Three-dimensional finite element simulations of the dynamic response of a fingertip to vibration. ASME Journal of Biomechanical Engineering 130 (5), 054501. Wu, J.Z., Dong, R.G., Welcome, D.E., Xu, S.X., 2010. A method for analyzing vibration power absorption density in human fingertip. Journal of Sound and Vibration 329, 5600e5614. Xu, X.S., Welcome, D.E., McDowell, T.W., Warren, C., Dong, R.G., 2009. An investigation on characteristics of the vibration transmitted to wrist and Elbow in the operation of impact Wrenches. International Journal of Industrial Ergonomics 39 (1), 174e184.
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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon
The vibration transmissibility and driving-point biodynamic response of the hand exposed to vibration normal to the palm Xueyan S. Xu*, Daniel E. Welcome, Thomas W. McDowell, John Z. Wu, Bryan Wimer, Christopher Warren, Ren G. Dong Engineering & Control Technology Branch, National Institute for Occupational Safety and Health, 1095 Willowdale Road, Morgantown, WV 26505, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 August 2009 Received in revised form 3 May 2011 Accepted 27 May 2011 Available online 28 June 2011
Prolonged, intensive exposure to vibrations from palm and orbital sanders could cause finger disorders. They are likely to be associated with the biodynamic responses of the fingers. Although the biodynamic responses of the hand-arm system have been studied by many researchers, the detailed biodynamic responses distributed in the hand substructures have not been sufficiently understood. To advance the knowledge in this aspect and to aid in the development of improved finite element models of the substructures, this study simultaneously measured the overall driving-point biodynamic response and the distribution of vibration transmissibility at the fingers and back of the hand exposed to a flat plate vibration (as an approximate simulation of the operations of the palm and orbital sanders) and examined the relationship between these two measures of biodynamic responses. Ten subjects (five males and five females) participated in the experiment. A scanning laser vibrometer was used to measure the distributed vibration. This study confirmed that the distributed hand responses generally varied with locations on each finger, vibration frequencies, and applied hand force. Two major resonances were observed in the vibration transmissibility. At the first resonance, the transmitted vibrations at different locations were more or less in phase; hence, this resonance was also observed in the driving-point biodynamic response that measures the overall biodynamic response of the system. The second resonance was observed at the fingers. Because this resonant frequency varied greatly among the fingers and the specific segments of each finger, it is difficult to identify this resonance in the driving-point biodynamic response. The implications of the findings for further model developments and applications are discussed. Relevance to industry: This study enhanced the understanding of the biodynamic responses of the fingers and hand exposed to vibrations on a contact surface with a large effective radius such as that found on palm and orbital sanders. The results can also be used to develop and/or validate models of the substructures of the hand-arm system, which can be further used to help design and analyze these tools and associated anti-vibration devices. The results may also be applicable to help develop location-specific frequency weightings to assess the risks of the finger vibration exposure. Published by Elsevier B.V.
Keywords: Hand-arm vibration Hand-transmitted vibration Driving-point biodynamic response Hand vibration transmissibility Palm sander Orbital sander
1. Introduction Palm sanders and orbital sanders are widely used in the furniture manufacturing. Such tools usually generate fairly highfrequency vibrations (Griffin, 1997), which are largely absorbed by the hand, especially the fingers (Dong et al., 2005c; Dong et al., 2008a). Prolonged, intensive exposure to such vibrations could cause symptoms of hand-arm vibration syndrome such as
* Corresponding author. Tel.: þ1 304 285 5840; fax: þ1 304 285 6265. E-mail address: [email protected] (X.S. Xu). 0169-8141/$ e see front matter Published by Elsevier B.V. doi:10.1016/j.ergon.2011.05.007
vibration-induced white finger. The risk assessment of the syndrome is currently based on International Standard ISO 5349-1, 2001. Although vibration-induced white finger is a unique and important component of the hand-arm vibration syndrome, epidemiological studies have not shown reasonable agreement between the observed risk of vibration-induced white finger and that predicted by the ISO-5349 model (Lidström, 1977; Bovenzi et al., 1980; Bovenzi, 1998; Griffin, 1997, 2008; Griffin et al., 2003). One of the possible reasons is that the current ISO frequency weighting may be inappropriate for the assessment of vibration-induced white finger. An effective approach to develop an improved frequency weighting for such an assessment is to study
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427
the vibration-induced biodynamic responses of the fingers and hand (Dong et al., 2005a, 2006a; Dong et al., 2008a). The biodynamic response has been primarily studied using the following three measures: vibration transmissibility (VT) measured on the skin or surface of the hand and/or arm (Miwa, 1968; Pyykkö et al., 1976; Reynolds, 1977; Sörensson and Lundström, 1992; Gurram et al., 1994; Scalise et al., 2007); driving-point biodynamic response functions (DPBR) such as apparent mass or mechanical impedance (Burström, 1990; Kihlberg, 1995; Marcotte et al., 2005); and vibration-induced stresses, strains, and power absorption density in the tissues of the hand-arm system (Wu et al., 2004, 2008; 2010; Dong et al., 2007). These measures of responses reflect different aspects of the vibration-induced biodynamic response but must be associated with each other in some respects because they are measured from the same system. A feasible method has not been developed to directly measure the vibration-induced stress, strain, power absorption density on tissues in a living subject. It is also technically demanding to simulate the detailed responses of the system tissues. Therefore, previous studies have been mostly focused on either vibration transmissibility or driving-point biodynamic response functions and the detailed tissue responses have been far from sufficiently understood. Considering that the detailed responses are likely to be more directly associated with vibrationinduced psychophysical, physiological, and pathological responses (Wu et al., 2004; Dong et al., 2005a), it is very important to conduct further studies on these detailed responses. Similar to the estimations of the dynamic loads and motions in the human body using an inverse dynamic approach, the quantifications of the detailed biodynamic responses to vibration primarily depends on the inverse dynamic simulation of the handarm system. Similar to the forces measured at the feet and the motions measured on the body in biomechanics studies, the DPBR and the transmitted vibration are vital inputs for the development of a validated model for the predictions of detailed biodynamic responses. To avoid the mass effect of conventional accelerometers (Griffin et al., 1982), several studies have employed advanced laser vibrometers to accurately measure the vibration transmitted to the surface of the hand-arm system (Sörensson and Lundström, 1992; Rossi and Tomasini, 1995; Deboli et al., 1999; Nataletti et al., 2005; Scalise et al., 2007). However, a review of literature for the current study found only one study that reported simultaneously measured DPBR and surface VT using a laser vibrometer (Concettoni and Griffin, 2009). For a sufficient understanding of the biodynamic response and to perform any modeling of the fingers and hand, both the magnitude and phase angle of the responses are generally required but the phase information was not reported in
419
the vast majority of the reported studies. Further studies are also required to verify the reported data and to interpret them. In light of these noted shortcomings, the specific aims of this study are (a) to simultaneously measure the DPBR of the hand-arm system and the VT distributed at the fingers and back of the hand using a laser vibrometer for further modeling studies; and (b) to enhance the understanding of the vibration transmitted to the fingers and to examine the relationship between the DPBR and VT. The applications of these different measures of the biodynamic response are also discussed in this study. 2. Method 2.1. Experimental setup Ten healthy adults (five males and five females) participated in this study. Their major anthropometrics are listed in Table 1. The study protocol was reviewed and approved by the NIOSH Human Subjects Review Board. As shown in Fig. 1, the vibration testing system and the basic test setup used in this study are similar to those used for standardized glove testing (ISO 10819, 1996). However, a different interface between the hand and the vibration source was considered in this study. The vibration velocity transmitted to the surface or skin of the hand was measured using a scanning laser vibrometer (Polytec PSV-300eH). The specific measurement locations are identified in Fig. 2. As observed in a previous study (Dong et al., 2006b), it is very difficult to use the laser vibrometer to reliably measure the vibration on a surface that is largely non-perpendicular to the laser beam. As an initial investigation, this study considered an openhand pushing action on a flat rectangular aluminum platform (21.6 12.7 cm, 1.09 kg), as shown in Fig. 1. While it is expensive and time-consuming to replicate the exact contact geometries of palm sanders or orbital sanders, such a test setup can be considered as an approximate simulation of the hand vibration exposure in the operations of these tools. Although the transmitted vibration and driving-point biodynamic response measured in such a test setup may be different from those in power grip on cylindrical handles equipped on many other tools, this approach can be used to establish a baseline for understanding the major features of the vibration transmitted to the fingers and back of the hand and the basic relationship between the DPBR and hand-transmitted vibration exposure. Probably for this reason, the newly reported study also used such an approach (Concettoni and Griffin, 2009). In the present study, the platform was fixed on a 1-D Vibration Test System (Unholtz-Dickie, TA250-S032-PB) through three force sensors (Kistler 9212), which were used to measure both the
Table 1 Subject anthropometry. Subject Height (cm) Weight (N) Hand length (mm) Hand breadth (mm) Hand circumference (mm) Finger length (mm) Hand volume (ml) Finger volume (ml) L Z X V Y U B C G F
180.3 175.3 188.0 195.6 175.3 167.6 162.6 161.3 160.0 171.5
867.9 978.7 925.7 889.5 733.5 511.9 600.2 533.5 645.3 645.3
194 184 192 191 193 166 168 175 180 182
88 85 96 88 86 72 76 74 77 80
215 200 225 210 220 180 195 185 190 194
82 79 82 78 85 71 72 75 78 78
435 400 450 393 380 210 285 235 280 290
65 70 80 55 65 50 50 40 55 45
Mean SD
173.7 11.73
733.1 170.6
182.5 10.29
82.2 7.61
201.4 15.33
78 4.42
335.8 85.64
57.5 12.30
hand length ¼ tip of middle finger to crease at the wrist; hand breadth ¼ the width measured at metacarpal of the hand; hand circumference ¼ the circumference measured at metacarpal of the hand; finger length ¼ tip of middle finger to crease at the base of the finger; hand volume ¼ water displaced by hand submerged to crease at wrist; finger volume ¼ water displaced by fingers submerged to crease at the base of the middle finger.
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Fig. 1. Subject posture and experiment setup.
applied push force and the dynamic responding force. The applied hand push force was taken as 15 and 30 N in the experiment, which is likely to be within the range of the hand force applied on these sanders in wood sanding and polishing. The platform was angled at 45 from the horizontal plane so that the subjects could apply a more natural and steady pushing action on the platform in a standing posture as shown in Fig. 1. The arm posture was selected so that the laser beam for measuring the vibration was not blocked during the exposure measurement. An accelerometer (Endevco, Model 65e100) was rigidly fixed on the back of the platform to measure the input vibration and to control the excitation. A constant-velocity (8 mm/s) broad-band random vibration from 16 to 1250 Hz was used as the excitation. The summation of the three force signals, the signal of the accelerometer fixed on the platform, and the vibration signal measured with the laser vibrometer were input into a data acquisition system (B&K Model 3032A) to simultaneously evaluate the DPBR and the VT using the cross-spectral function built into the B&K Pulse software. The data were expressed in one-third octave bands with center frequencies from 16 to 1000 Hz. Both the real and imaginary parts of the responses were recorded.
graphical display was developed in-house using LabVIEWÔ software to display the real-time push force along with the target force. Twenty points on the hand were defined for the measurement, as shown in Fig. 2. There were four measurement locations/points (P1-P4) on each digit. Fingertip measurements (P1) were collected at the base of each fingernail. Inter-phalangeal joint measurements (P2 and P3) were also collected for each digit. Measurements on the back of the hand (P4) were also collected for each digit. To ensure stable push forces and to prevent fatigue, test trials were limited to the measurement of vibrations at the four points for a selected digit. Once the subject’s push force stabilized at the target force, the four measurement points were scanned with the laser vibrometer. Each of the four measurement points was scanned for 20 s; each trial took about 90 s. The subjects rested for at least 2 min between trials. Two trials were performed for each point at each force level. The testing order of the five digits and two push force levels were independently randomized among the subjects. 2.3. Evaluations of measurement systems, vibration transmissibility, and driving-point biodynamic response To assure the accuracy and reliability of the measurement, this study conducted a series of tests to evaluate the measurement systems before subject testing. In one evaluation, the platform vibration was measured with the laser vibrometer at 20 points corresponding to the locations of the hand measurement points. The results indicated that the fundamental resonance of the platform fixed on the shaker is 1085 Hz. The resonance resulted in nonunity transmissibility (>1.05) and some phase shift (>10 deg.) at high frequencies (>500 Hz). Some bending motion of the platform was also observed, which made some significant differences (>5%) between the vibrations at the different measuring points at the higher frequencies. Therefore, the non-uniform distribution should be corrected by normalizing the measured data. Specifically, corrections of the measured subject transmissibility at each measuring point were made based on the corresponding platform transmissibility using the following formulas:
TrCorrected
Skin ðuÞ
¼
TrMeasured Skin ðuÞ TrPlatform ðuÞ
(1)
TrMeasured
Skin ðuÞ
¼
ASkin Laser ðuÞ APlatform Accelerometer ðuÞ
(2)
2.2. Subject testing procedures The study and testing procedures were explained to each subject upon arrival. After signing the required consent form, the subject was instructed to practice the pushing action on the platform with the opened right hand, as shown in Fig. 1. A custom
Fig. 2. Laser scanning points on five fingers and back of hand.
TrPlatform ðuÞ ¼
APlatform Laser ðuÞ APlatform Accelerometer ðuÞ
(3)
where ASkin_Laser and APlatform_Laser are the accelerations measured with the laser vibrometer on the skin at the measuring points and at the corresponding points on the platform, respectively, APlatform_Accelerometer is the acceleration measured on the platform using the accelerometer fixed on the platform, and u is the center frequency of each one-third octave band. Acceleration from the laser vibrometer was calculated via the B&K Pulse program by taking the first derivative of the directly-measured velocity. In another evaluation, the reliability of the laser measurement on the skin was examined. In the test, the motions of the hand on the platform with and without vibration input were separately measured with a subject. The signal measured on the hand without vibration exposure was divided by the signal measured during the hand exposure to vibration, which was termed as the noise/signal ratio of the measurement in this study. The driving-point biodynamic response functions evaluated in this study were expressed as apparent mass and mechanical
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427
impedance. Similarly to the evaluation of the vibration transmissibility, the apparent mass (MA) and mechanical impedance (Z) were evaluated using the following formula:
MA ðuÞ ¼
FH ðuÞ APlatform
Accelerometer ðuÞ
ZðuÞ ¼ MA ðuÞ,ju
(4)
(5)
pffiffiffiffiffiffiffi where FH is the measured dynamic force and j ¼ 1. The directly-measured impedance is the total response that includes that of the plate tare mass and that of the hand-arm system. A frequency domain method was used to cancel the tare mass effect (Dong et al., 2006b). Due to the platform resonance bending motions, the biodynamic response of the hand at frequencies above 250 Hz may not be reliable. This is also because the tare mass of the platform is much larger than the apparent mass of the hand. Therefore, only the mechanical impedances from 16 to 250 Hz were analyzed in this study. 2.4. Statistical analyses The two repetitive measures under each condition were utilized for the statistical analysis. Mixed Model Analysis of Variance (ANOVA) tests of vibration transmissibility were performed to identify the significance of the following fixed factors: frequency, push force, and measuring point. Subject was treated as a random factor. Further stratified ANOVAs were performed to examine the distribution signficance of the transmissibility on each digit/finger. The ANOVAs were performed using SPSS statistical software (SPSS, version 16.0). Differences were considered significant at the p < 0.05 level. 3. Results
421
measurement points (P3 and P4) at frequencies above 160 Hz. These observations, together with the above-mentioned measurement system problems, suggest that the transmissibility data at frequencies above 400 Hz at P2, 250 Hz at P3 and 160 Hz at P4 may include significant errors. 3.2. General characteristics of the transmissibility Fig. 4 shows typical examples of the transmissibility (magnitude and phase) at the four measurement points of the middle finger of Subject Z measured with the 30 N push force. Two peaks were generally observed in the transmissibility measured for each individual, which can be considered as the resonances at the measured points or locations. The first peak was more obvious at P2eP4 than that at P1. Also as an example, Fig. 5 shows the magnitudes of the transmissibility measured at the four measuring points (P1eP4) on the middle fingers of the ten subjects, together with the mean transmissibility. Because of the arithmetical averaging effect (Dong et al., 2009), the peak magnitudes, especially in the second peak, were somewhat suppressed; however, the averaging process does not change the basic trends. The majority of the frequencies for the first peak fell in the range of 30e60 Hz. The phase angles were close to each other below 40 Hz, as shown in Fig. 4. In the first peak frequency range, the magnitude of the transmissibility generally increases from the fingertip (P1) to the back of the hand (P4). The highest second peak was observed at the fingertip (P1), as shown in Figs. 4 and 5. It is also obvious in the response measured at the second phalange (P2). The second peak frequency is generally in the range of 80e300 Hz, which is much more spread out than the first peak frequency. The transmissibility magnitudes at the third and four phalanges (P3 and P4) at frequencies above 200 Hz, especially over 300 Hz, are very small. As above-mentioned, the transmissibility at P2, P3, and P4 at the high frequencies may include some significant errors. Also because of the low
3.1. Evaluation of the laser vibrometer measurement Fig. 3 shows typical examples of the noise/signal ratios measured on the four points of the middle finger of a subject, which is an indication of the potential measurement errors at these locations. The noise/signal ratio is generally less than 5% at frequencies below 160 Hz, but it becomes significant at higher frequencies, depending on the location of the measurement. This result, shown in Fig. 3, indicates that the potential error generally increases as the measurement point moves from the fingertip toward the back of the hand. While the potential error on the nail (P1) is negligible (<5%) in the entire frequency range of concern, it could become significantly high at the third and forth
Fig. 3. A typical example of noise/signal ratios (NSR) of the laser measurement at the four measurement points (P1eP4) for the middle finger.
Fig. 4. Typical examples of the transmissibility (magnitude and phase) at the four measurement points (P1eP4) of the middle finger at a 30 N push force.
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3
3
Magnitude
P1
P2
2
2
1
1
0
0
10
100
1000
10
100
3
3
P4
P3 Magnitude
1000
2
2
1
1
0
0 10
100
1000
Frequency (Hz)
10
100
1000
Frequency (Hz)
Fig. 5. Transmissibility functions of the ten subjects measured at the four measuring points (P1eP4) on the middle finger measured with 30 N push force, together with their of the subjects. corresponding mean responses
transmissibility at these locations at the high frequencies, the corresponding phase angles are not reliable; hence, they are not presented or further analyzed. 3.3. Statistical results of the vibration transmissibility The results of the ANOVA for vibration transmissibility are listed in Table 2. As indicated, each of the three fixed factors (force, measurement location, and frequency) analyzed was significant. While the two-way interactions between the frequency and each of the other two factors were significant, the interaction between the force and location is not significant. As also shown in Fig. 5, the vibration transmissibility functions varied substantially among subjects. Figs. 6 and 7 illustrate the mean transmissibility functions of all the subjects at each measurement point of the five digits/fingers under the 15 N and 30 N push force, respectively. Increasing the push force increased the first peak or resonance frequency (F ¼ 31.5, p < 0.001). The second peak was also shifted toward a higher frequency as the push force increased (F ¼ 39.6, p < 0.001). The second peak frequencies also varied significantly with the measurement point on each finger (F 3.246, p 0.022). As also shown in Figs. 6 and 7, the transmissibility functions at the same location on the five fingers have some similarities at some frequencies, especially those on the index, middle, and ring fingers. Table 2 Results of ANOVA for vibration transmissibility data. Source of variance
Sum of squares
Degrees of freedom
Mean square
F-value
p -value
Frequency (Freq) Applied Force (Force) Measurement Point (Point) Freq Force Freq Point Force Point
2910.39 15.40
19 1
153.18 15.40
261.54 276.72
< 0.001 < 0.001
163.12
3
54.37
120.92
< 0.001
17.98 544.55 0.24
19 57 3
0.95 9.55 0.08
17.01 171.69 1.44
< 0.001 < 0.001 0.229
However, the transmissibility functions are generally significantly different, as confirmed from the measurement point-stratified ANOVAs (F 11.32, p < 0.001). This study also performed a finger-stratified ANOVA. The results further confirmed that the effects of the force, measurement location, and frequency were significant for the responses on each finger (F 43.45, p < 0.001). The interactions between the frequency and the other two factors were also significant (F 6.79, p < 0.001). Consistent with that observed in Table 2, the interaction between the force and measurement point was not significant (F 2.25, p 0.08). This means that the variation of the push force did not significantly change the basic distribution features of the vibration transmissions at the four measurement locations, which can also be observed by comparing the data presented in Figs. 6 and 7. 3.4. Driving-point biodynamic response The apparent mass and mechanical impedance responses of the ten subjects and their mean values for the 15 N and 30 N push forces are shown in Figs. 8 and 9, respectively. The apparent mass of the hand-arm system at frequencies above 250 Hz is generally less than 0.1 kg, which is much less than the platform mass (1.09 kg). This, together with the platform bending effect, makes it very difficult to reliably measure the driving-point biodynamic response above 250 Hz. For this reason, only the BR data up to 250 Hz are presented, which is sufficient for the purposes of this study. The impedance magnitudes and phase angles shown in Figs. 8 and 9 indicate that there are at least two resonances reflected in the response. The first peak occurs at about 20 Hz for the 15 N push and 25 Hz for the 30 N push. Such a peak frequency could not be identified in the vibration transmissibility measured on the fingers or back of the hand, probably because this peak could be mainly associated with the resonance of the palm-wrist-arm substructure under the specific arm posture used in this study, but the transmissibility of the wrist and arm was not measured. The second impedance peak occurs at about 45 Hz for the 15 N push and 60 Hz for the 30 N push; these peak frequencies are generally higher than
X.S. Xu et al. / International Journal of Industrial Ergonomics 41 (2011) 418e427 P1
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Fig. 6. Mean transmissibility functions of all the subjects at each point of the five fingers under 15 N push force.
the first peak frequency (30e50 Hz) observed in the transmissibility measurements. Similar to transmissibility, inter-subject differences in the driving-point biodynamic responses were obvious, as also shown in Figs. 8 and 9. Because this study only measured the overall biodynamic responses of the hand-arm system, the effect of the measurement point could not be examined. Therefore, the fixed factors in this case are the push force and frequency. The results of the ANOVA indicate that they were significant factors (F 2698.69, p < 0.001) and their interaction was also significant (F ¼ 22.22, p < 0.001). The peak frequencies for mechanical impedance with the 30 N forces were significantly higher than those with the 15 N forces (F 8.6, p 0.015). 4. Discussions As an approximate simulation of the hand vibration exposure on a contact surface with a large effective radius, this study measured
the vibration transmissibility and biodynamic response of an openhand pushing against a flat platform. The experimental results provide some useful information for the understanding of the basic features of the vibration transmission to the hand, especially the fingers, which is further elaborated and discussed in this section. 4.1. Vibration measurement on the hand using the laser vibrometer The results of this study suggest the irregularity of the skin surface could play an important role in the measurement using the laser vibrometer, and its accuracy depends on the frequency, as shown Fig. 3. The most reliable measurement was found on the nail, probably because the nail has no hair and is smooth and reflective. The irregularity of the skin surface and the density of the hair generally increase with the measurement location moving from the fingertip to the back of the hand, which explains why the noise/ signal ratios presented in Fig. 3 also show the same trend. Therefore, the reliability of the measurement may be improved by
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Fig. 7. Mean transmissibility functions of all the subjects at each point of the five fingers under 30 N push force.
increasing the smoothness and reflection of the skin surface. This supports the practice used by Concettoni and Griffin (2009), who applied some reflective paint on the skin, and by Sörensson and Lundström (1992), who attached a piece of adhesive lightweight retro-reflecting tape on the skin without shaving the hairs on the skin, which should be considered in further studies. 4.2. Comparisons with published data and findings The hand posture and position on the flat platform in the current study is very similar to those in position #1 used in the study reported by Concettoni and Griffin (2009). Although the reported study used different measuring locations (close to the finger joints or on the knuckles), arm posture (with forearm parallel to the vibrating platform surface), and hand push force (25 N), the basic features of the finger transmissibility functions at each corresponding location in both studies are similar. For example, the
average resonance frequencies at the four fingernails (P1 on index, middle, ring, and small finger) shown in Figs. 6 and 7 are generally in the range of 100e250 Hz, and they are very similar to those measured at the first knuckles of the four fingers reported by Concettoni and Griffin (2009) (see position 1 data at Pt.#3, #6, #9, and #12 in Fig. 6 of their report). Their magnitudes of the transmissibility are also similar. The locations and direction of the transmissibility measurement reported by Sörensson and Lundström (1992) are similar to those considered in the current study, but the hand grasped a nearcylindrical handle in their experiment. While the resonances at the fingernails in their study were generally at higher frequencies (>300 Hz) than those observed in the current study, the vibration transmissibility functions and resonance frequencies measured at other locations on the fingers are similar to those on the fingernail and the first phalange area measured in the current study. This may be partially because the second and third phalange areas of the
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fingers were better adapted or coupled to the near-cylindrical handle than those on the flat plate, which could result in a large difference between the effective contact pressures in these two test setups. This observation suggests that the geometrical features of the handetool interface could affect the vibration transmissibility. However, both studies showed that the resonance frequencies increase with the increase in the applied hand force, and they decrease as the measurement point moves from the fingertip to the palm of the hand.
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the operations of some tools such as palm and orbital sanders. The dominant vibration frequencies of these tools are usually in the neighborhood of 100 Hz (Griffin, 1997), which are within the range of the observed finger resonance frequencies. Hence, it is important to reduce the vibration from these tools. The results of this study also imply that it is difficult to reduce the vibration transmitted to the fingers, especially the fingertips, using any anti-vibration glove. In principle, the vibration reduction of the glove depends on both the mechanical properties of the glove and the effective mass of the fingers. Whereas it is not practical to make the fingers of the glove very thick to achieve the required low stiffness and high damping value, the mass of the fingers is small, as reflected from the high resonance frequencies (80e300 Hz) of the fingers. An anti-vibration cap may be developed to reduce the vibration exposure on these tools. 4.4. Relationships between vibration transmissibility and drivingpoint biodynamic response Theoretically, the driving-point biodynamic response depends on the overall dynamic force of the hand-arm system induced by the vibration input to the hand, as dictated in Eq.(4). Because the dynamic force is directly associated with the acceleration on the hand and arm, the DPBR should also be associated with vibration transmissibility. If the hand-arm system would be considered as a rigid mass (m) on a spring-damper system connected to the plate, the apparent mass (M1-D) of such a 1-D model is directly associated with the transmissibility (Tr1-D) of the mass as follows:
M1D ðuÞ ¼ m,Tr1D ðuÞ
(6)
As observed from the phase angles measured in this study and from the corresponding patterns reported by Concettoni and Griffin (2009), the majority of the substructures in the hand-arm system move approximately in phase under low-frequency vibration exposures. Therefore, as a crude approximation, it is reasonable to consider the hand-arm system as a rigid mass on a spring-damper system that simulates the palm elasticity and damping property. This justifies the use of a 1-D model to simulate the hand-arm system if only the low frequencies are of concern. In fact, the 1-D model (including the 2-D model with a lumped mass at its end) can provide a reasonable simulation of the overall response along the forearm direction at frequencies up to 100 Hz (Dong et al., 2008b). Eq.(6) indicates that the low-frequency transmissibility measured at the back of hand or wrist can also be used to approximately represent the basic trend of the apparent mass in this frequency range. Because the vibration-induced biodynamic force acting on the palm and wrist can be estimated from the apparent mass (Dong et al., 2005b), it seems reasonable to use the transmissibility measured at the back of the hand and wrist as a frequency weighting for assessing the risk of vibration-induced injuries and disorders in the palm-wrist-forearm substructure. These theoretical analyses provide an additional justification for the wrist vibration measurement method (Thomas and Beauchamp, 1998; Xu et al., 2009). Similarly, the apparent mass of the fingers should also be closely correlated with the vibration transmissibility measured at the fingers. The second peak observed in the impedance should be closely associated with the first finger resonance observed in the transmissibility. As presented above, however, their peak frequencies are different because the impedance peak frequency is generally higher than that of the apparent mass directly associated with the transmissibility. This can be understood from the relationship between the apparent mass (M) and the mechanical impedance (Z) shown in Eq.(5) (Dong et al., 2006a). The second peak frequency identified in the transmissibility functions of the fingertip (P1) and
middle phalange (P2) is associated with the local structure resonance. The local resonance is largely independent of the responses and conditions of the remaining structures of the hand-arm system (Dong et al., 2005c). Because the local resonances could occur at very different frequencies, and their motions may be largely out-ofphase, the vector summation of the biodynamic forces could not reflect the specific features of the local responses. This explains why such a peak was practically undetectable in the measured DPBR, which suggests that it is necessary to use a local biodynamic response (BR) measurement method to quantify the local dynamic forces. The independence of the response at high frequencies also suggests that it is not necessary to simulate the entire hand-arm system to predict the local high-frequency responses of the fingers, which justifies the use of a finger model for the prediction of the biodynamic response in the finger (Wu et al., 2008). The skin surfaces may vibrate differently from those of the bones of the hand-arm system. While it is practically very difficult to measure the vibrations distributed on the bones of a human subject, the reliability of the model can be increased by considering the skin as a separate component in the model structure, as used in some reported studies (Wu et al., 2008, 2010). Besides the structural consideration, the model may become more realistic if both the VT and the DPBR are simultaneously measured and used to construct the model. As a step toward the model development, this study simultaneously measured the DPBR and the VT distributed at the fingers and back of the hand. The experimental data may not be sufficient for simulating the response of the hand coupled to a cylindrical handle, but they should be sufficient to simulate the responses of the fingers in contact with surfaces with large effective diameters such as those on the palm sanders and orbital sanders. 5. Conclusions This study simultaneously measured the overall driving-point biodynamic response (DPBR) and the vibration transmissibility (VT) distributed at the fingers and the back of the hand. The relationship between these two measures was also examined. The results confirm that the distributed hand biodynamic response is a function of frequency, and it generally varies with locations or substructures, individuals, and applied hand forces. The major parts of the hand move more or less in phase in the first major resonance of the hand. Therefore, the VT resonance was well-correlated with the DPBR. A second major VT resonance was observed at the fingers. Because this resonant frequency varies greatly among the fingers and the specific locations on each finger, it is very difficult to clearly identify this resonance in the DPBR that reflects the overall response of the entire system. These observations suggest that the models developed based solely on the DPBR may be sufficient for designing and analyzing some tools and anti-vibration devices, but they may not be reliable for predicting the detailed location-specific responses in the hand-arm system, especially in the fingers. Better models for predicting detailed biodynamic responses may be built based on both the transmissibility and the biodynamic response. The results of this study also suggest that the dominant vibrations of palm sanders and orbital sanders are likely to be within the range of the finger resonance frequencies, and available antivibration gloves are unlikely to be effective at reducing such vibrations. The developments of low-vibration tools and/or more effective anti-vibration devices are required to reduce the vibration transmitted to the fingers in the operations of these tools. 5.1. Disclaimers The content of this publication does not necessarily reflect the views or policies of the National Institute for Occupational
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