Energy dissipation in human hand-arm exposed to random vibration* J. S. Cundiff Universityof GeorgiaCoastalPlain ExperimentStation, Tifton, Georgia31794 (Received 3 April 1974) The problem of correlatingthe incidenceof Raynaud'sphenomenonwith exposureto a given vibration environmentis well known. It is hypothesizedthat energyabsorbedand dissipatedin the hand is energy which can changehand tissuein somemanner,and thus may causeinjury. Absorbedpower is therefore suggestedas a parameterwhich has potentialfor evaluationof individual worker susceptibilityto vibration injury. The arm is representedas a foundation with finite mechanicalimpedancefor the hand model. The hand model parameters,obtainablefrom experimentalimpedancemeasurements on individual subjects,are assumedto be, in general,frequencydependent.The total impedanceexpressionfor the systemis generalizedfor the casewhere the hand is grippinga vibratinghandle coveredwith a layer of viscoelastic material. An expressionfor absorbedpower in this compositesystemexposedto random vibration is presented.
SubjectClassification:[43]40.45.
INTRODUCTION
The effects of vibrating hand tooIs upon human opera-
tors have been studied by many investigators, and a solid cause and effect relationship has been established between vibration and a disease known as Raynaud's phe-
nomenon.As early as 1911, Lorigaz from Rome, and in the UnitedStates, Cottingham •' in 1916reportedhand abnormalities in quarry workers using pneumatic drills. With the great swell of industrial production in the 1940s and early 1950s, Raynaud's phenomenonbecame almost epidemic in certain industrial occupations. Citing some of the more definitive of the early studies
for long periods of time and have not been injured, whereas others develop Raynaud's phenomenon after only a short exposure to similar vibration. Clearly, there
must be differences
in hand characteristics
which
figure prominently in susceptibility. The investigation then of physical differences in the hand is of fundamental importance.
Abrams? andReynoldset al. 8 havemeasuredthe impedance of the human body at the gripped hand, and used these measurements to derive an analytical model of the human hand. Model parameters differed between
test subjects. One subject's left hand had a natural fre-
availablein the literature: Agate et al. 3 foundthat 32 of
quencyof 71.8 Hz, while another's hand in the same
37 workers using a particular hand grinder developed Raynaud's phenomenon within 21 months of beginning
test configuration showed a natural frequency of 130 Hz.
work, andJepson 4foundthatthe diseasedeveloped in 23 of 38 clinchers and flangers of rail car doors within one year of starting work. In a later paper, Agate
et al. 5 found184 of 278 workers scuffingandpolishing metal castings with rotary hand tools to be affected. Medical researchers have conducted extensive physiological examinations of exposed workers in an attempt to evaluate neurological damage, and lesions to other
tissue causedby vibration. WassermenandBadger6 have prepared an exhaustive bibliography of world literature
on vibration
ences the latest
and its effect
of this work.
on man which
Review
refer-
of these refer-
ences reveals that there is still great disagreement as to the type of injury caused by vibration.
Engineering researchers have typically recorded and carefully analyzed the vibration environment where workers have developed Raynaud's phenomenon. This is certainly useful and necessary information; however, between
this
information
and the medical
research
there
is an unknown area which must be explored before all that is known can be brought together to promulgate a
safety standard for hand-held tools, which will insure an acceptably low probability of the incidence of vibration injury. It is interesting to consider references in the literature to individuals who have been exposed to vibration 212
J. Acoust.Soc. Am., Vol. 59, No. 1, January1976
Would these two men have equal susceptibility when exposed to the same vibration environment ?
Intuitively it seems there should be a correlation between susceptibility to vibration injury and the hand model. It would be interesting to see if the hand model of workers with Raynaud's phenomenon had a parameter
that differs significantly from a population"norm." Screening tests for this characteristic could then be used to divert sensitive individuals into occupations with low vibration exposure.
The parameter proposed here is the mean power dissipation in the hand. Dissipated or absorbed power has been used in other
studies
of the effect
of vibration
on
man. Pradko½!al. 9 has correlated absorbedpower with subjective evaluations of ride comfort. Whole body vibration with greater absorbed power was judged to be progressively more uncomfortable. Medical
research
has searched
for
some lesion
modification to tissue caused by vibration.
or
Theoreti-
cally, the energy absorbedand dissipated in the handis energy which has been used to change hand tissue in some manner. It is thus reasonable to expect dissipated power to be related to injury.
The dissipated power expression derived herein is appropriate for a general vibration input. Since essentially all tools have a broad-band spectra, it is particuCopyright¸ 1976 by the AcousticalSocietyof America
212
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 84.88.136.149 On: Mon, 15 Dec 2014 11:48:51
213
Letters to the Editor
213
larly important to be able to evaluate the contribution from random vibration. The computation of dissipated
' m[
E;'1f uh--Uhejet
power in a specific individual's hand requires knowledge of his hand model parameters. It is necessary then to begin with a general derivation of the Abrams' dynamic model of the human hand. I. MODELING
THE HAND-ARM
f u=UeJmt
I mhI
SYSTEM
The fixed parameter model can be generalized by utiliz•ing the concept of a complex elastic modulus, as
?Z•/ / / FIG.
1.
Model
with viscoelastic
material
on handle.
shownby Snowdon. •0 This parameteris, in general, frequency dependent, and this makes it particularly appropriate to model a system which is known to change
materials.
with frequency.
elastic material and the hand, respectively. Values for Zm and m h are obtainable from experimental imped-
From observation of the hand-arm
system excited by
a shaker input, it is knownthat lower frequencies excite the entire arm, whereas higher frequencies are confined
to the hand.
The tissue
between
the hand sur-
face and the arm is not stiff enough to drive the arm except at low frequencies. Cadaver measurements by
Abrams n verify thetransmission lossalongthe length
The geometric constants, Kv and Kh, are
simply the grip area divided by thickness for the visco-
ance measurementson a given subject. (Notethat, in general, m• is frequencydependent). III.
ENERGY
DISSIPATION
IN THE
HUMAN
HAND
The total energy in the one dimensional system (Fig. 1) is given by
of the arm at higher frequencies.
For the analysis here, that portion of the hand-arm system which responds in the frequency range of Abrams'
model will be considered
and be denoted by the subscript h.
the "effective
hand"
The remaining por-
tion of the system will be consideredthe "effective arm" arm" and will be denoted by the subscript a.
MECHANICAL
IMPEDANCE
MODEL
Manufacturers of powered hand implements often cover the handle grip with a piece of viscoelastic mate-
rial. The hand-arm system (Fig. l) with arm impedance Za, hand mass mh, and hand elastic modulus is then isolated from the vibrating handle mass m, by a grip with complex elastic modulus E•*.
Snowdon •' has analyzedthe responseof a structure
(2)
where R• and X• are the real and imaginary parts of Zoo. The mean, or time average, energy dissipated can be expressed as absorbed power,
Ph
Abrams' model assumes a rigid foundation which means actually, that the effective arm has infinite impedance. This is a correct assumption except at the lower frequencies where the arm becomes part of the system. For a general model it is necessary then to consider the case where the model foundation, or effective arm, has finite mechanical impedance. II.
E=fR,u•'dt+j/X,u•'dt,
G(f )R,t(f )df ,
(3)
where
the mean-square spectra density of the velocity func-
tion. The determination of R•(f) from a hand model has been previously discussed, and G(f) can be measured with spectrum analysis equipment. Numerical integration of Eq. 3 then gives the mean power dissi-
pated in a subject'shandsubjectedto velocity, u(t).
*This analysis was originally presented in Paper No. 73-526 at the 1973 Annual Meeting, American Society of Agricultural Engineers, University of Kentucky, Lexington, Kentucky, 17-30
June, 1973.
with finite mechanical impedance when isolated from a
1G.Loriga,Encyclopedia ofHygiene, Pathology andSocial
vibratingbodywith a viscoelasticmounting. It is a
2 Welfa•'e, Vol. 2, p. 161 (1934).
simple matter to tailor his analysis to obtain an expres-
sion for the effective impedanceZof, seen by the excitation force.
If it is assumed that U•
SubjectClassification:[43]40.45.
INTRODUCTION
The effects of vibrating hand tooIs upon human opera-
tors have been studied by many investigators, and a solid cause and effect relationship has been established between vibration and a disease known as Raynaud's phe-
nomenon.As early as 1911, Lorigaz from Rome, and in the UnitedStates, Cottingham •' in 1916reportedhand abnormalities in quarry workers using pneumatic drills. With the great swell of industrial production in the 1940s and early 1950s, Raynaud's phenomenonbecame almost epidemic in certain industrial occupations. Citing some of the more definitive of the early studies
for long periods of time and have not been injured, whereas others develop Raynaud's phenomenon after only a short exposure to similar vibration. Clearly, there
must be differences
in hand characteristics
which
figure prominently in susceptibility. The investigation then of physical differences in the hand is of fundamental importance.
Abrams? andReynoldset al. 8 havemeasuredthe impedance of the human body at the gripped hand, and used these measurements to derive an analytical model of the human hand. Model parameters differed between
test subjects. One subject's left hand had a natural fre-
availablein the literature: Agate et al. 3 foundthat 32 of
quencyof 71.8 Hz, while another's hand in the same
37 workers using a particular hand grinder developed Raynaud's phenomenon within 21 months of beginning
test configuration showed a natural frequency of 130 Hz.
work, andJepson 4foundthatthe diseasedeveloped in 23 of 38 clinchers and flangers of rail car doors within one year of starting work. In a later paper, Agate
et al. 5 found184 of 278 workers scuffingandpolishing metal castings with rotary hand tools to be affected. Medical researchers have conducted extensive physiological examinations of exposed workers in an attempt to evaluate neurological damage, and lesions to other
tissue causedby vibration. WassermenandBadger6 have prepared an exhaustive bibliography of world literature
on vibration
ences the latest
and its effect
of this work.
on man which
Review
refer-
of these refer-
ences reveals that there is still great disagreement as to the type of injury caused by vibration.
Engineering researchers have typically recorded and carefully analyzed the vibration environment where workers have developed Raynaud's phenomenon. This is certainly useful and necessary information; however, between
this
information
and the medical
research
there
is an unknown area which must be explored before all that is known can be brought together to promulgate a
safety standard for hand-held tools, which will insure an acceptably low probability of the incidence of vibration injury. It is interesting to consider references in the literature to individuals who have been exposed to vibration 212
J. Acoust.Soc. Am., Vol. 59, No. 1, January1976
Would these two men have equal susceptibility when exposed to the same vibration environment ?
Intuitively it seems there should be a correlation between susceptibility to vibration injury and the hand model. It would be interesting to see if the hand model of workers with Raynaud's phenomenon had a parameter
that differs significantly from a population"norm." Screening tests for this characteristic could then be used to divert sensitive individuals into occupations with low vibration exposure.
The parameter proposed here is the mean power dissipation in the hand. Dissipated or absorbed power has been used in other
studies
of the effect
of vibration
on
man. Pradko½!al. 9 has correlated absorbedpower with subjective evaluations of ride comfort. Whole body vibration with greater absorbed power was judged to be progressively more uncomfortable. Medical
research
has searched
for
some lesion
modification to tissue caused by vibration.
or
Theoreti-
cally, the energy absorbedand dissipated in the handis energy which has been used to change hand tissue in some manner. It is thus reasonable to expect dissipated power to be related to injury.
The dissipated power expression derived herein is appropriate for a general vibration input. Since essentially all tools have a broad-band spectra, it is particuCopyright¸ 1976 by the AcousticalSocietyof America
212
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 84.88.136.149 On: Mon, 15 Dec 2014 11:48:51
213
Letters to the Editor
213
larly important to be able to evaluate the contribution from random vibration. The computation of dissipated
' m[
E;'1f uh--Uhejet
power in a specific individual's hand requires knowledge of his hand model parameters. It is necessary then to begin with a general derivation of the Abrams' dynamic model of the human hand. I. MODELING
THE HAND-ARM
f u=UeJmt
I mhI
SYSTEM
The fixed parameter model can be generalized by utiliz•ing the concept of a complex elastic modulus, as
?Z•/ / / FIG.
1.
Model
with viscoelastic
material
on handle.
shownby Snowdon. •0 This parameteris, in general, frequency dependent, and this makes it particularly appropriate to model a system which is known to change
materials.
with frequency.
elastic material and the hand, respectively. Values for Zm and m h are obtainable from experimental imped-
From observation of the hand-arm
system excited by
a shaker input, it is knownthat lower frequencies excite the entire arm, whereas higher frequencies are confined
to the hand.
The tissue
between
the hand sur-
face and the arm is not stiff enough to drive the arm except at low frequencies. Cadaver measurements by
Abrams n verify thetransmission lossalongthe length
The geometric constants, Kv and Kh, are
simply the grip area divided by thickness for the visco-
ance measurementson a given subject. (Notethat, in general, m• is frequencydependent). III.
ENERGY
DISSIPATION
IN THE
HUMAN
HAND
The total energy in the one dimensional system (Fig. 1) is given by
of the arm at higher frequencies.
For the analysis here, that portion of the hand-arm system which responds in the frequency range of Abrams'
model will be considered
and be denoted by the subscript h.
the "effective
hand"
The remaining por-
tion of the system will be consideredthe "effective arm" arm" and will be denoted by the subscript a.
MECHANICAL
IMPEDANCE
MODEL
Manufacturers of powered hand implements often cover the handle grip with a piece of viscoelastic mate-
rial. The hand-arm system (Fig. l) with arm impedance Za, hand mass mh, and hand elastic modulus is then isolated from the vibrating handle mass m, by a grip with complex elastic modulus E•*.
Snowdon •' has analyzedthe responseof a structure
(2)
where R• and X• are the real and imaginary parts of Zoo. The mean, or time average, energy dissipated can be expressed as absorbed power,
Ph
Abrams' model assumes a rigid foundation which means actually, that the effective arm has infinite impedance. This is a correct assumption except at the lower frequencies where the arm becomes part of the system. For a general model it is necessary then to consider the case where the model foundation, or effective arm, has finite mechanical impedance. II.
E=fR,u•'dt+j/X,u•'dt,
G(f )R,t(f )df ,
(3)
where
the mean-square spectra density of the velocity func-
tion. The determination of R•(f) from a hand model has been previously discussed, and G(f) can be measured with spectrum analysis equipment. Numerical integration of Eq. 3 then gives the mean power dissi-
pated in a subject'shandsubjectedto velocity, u(t).
*This analysis was originally presented in Paper No. 73-526 at the 1973 Annual Meeting, American Society of Agricultural Engineers, University of Kentucky, Lexington, Kentucky, 17-30
June, 1973.
with finite mechanical impedance when isolated from a
1G.Loriga,Encyclopedia ofHygiene, Pathology andSocial
vibratingbodywith a viscoelasticmounting. It is a
2 Welfa•'e, Vol. 2, p. 161 (1934).
simple matter to tailor his analysis to obtain an expres-
sion for the effective impedanceZof, seen by the excitation force.
If it is assumed that U•
