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Development of a simulator for use in the measurement of chain saw vibration
Applied Ergonomics 1977, 8.3, 130- 134
Development of a simulator for use in the measurement of chain saw vibration C.F. Abrams, Jr, and C.W. Suggs Department of Biological and Agricultural Engineering, North Carolina State University, USA
The measurement of vibration production of light, hand held power tools is important in the assessment of the potential for elicitation of vibration injury to the operators of these tools. The manner in which these measurements are made can greatly affect the results. The measured vibration production of the tool becomes a function of the operator holding the saw during the measurement and his physical characteristics. The objective of the work reported here was to develop a simulator of the operator which might be used in the vibration production analysis of chain saws. The operator was modelled in terms of the driving point mechanical impedance characteristics of humans for input to the hands. A simulator was developed based on the driving point impedance characterization of the operator and evaluated with chain saw vibration measurements.
Introduction Vibration-induced sicknesses are of concern for those persons who are regularly exposed to vibration in the course of their work activities. Of particular interest are the disorders of the peripheral circulation due to the exposure of the hands to vibration from power tools. The chain saw is an example of such a tool. Criteria are being proposed which set forth the vibration tolerance for input to the hands. Successful application of such criteria to the vibration production rating of tools such as chain saws will require an objective, repeatable means of measuring the vibration production of the tool in a working configuration. Vibration production is generally measured by affixing acceleration transducers near the hand/tool interface and observing the vibration production while the tool is used by the operator. This approach has the inherent problem of lack of general applicability since the same operator cannot be used at every test installation. The objective of the work reported here was to develop a physical simulator of the human operator in which a chain saw could be mounted for vibration measurement. The concept of driving point mechanical impedance was to be used to define the parameters of such a simulator. Such a
Paper No 5021 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, NC. The use of trade names in this publication does not imply endorsement by the North Carolina Agricultural Experiment Station of the products named, nor criticism of similar ones not mentioned. The authors are, respectively, assistant professor and professor, Department of Biological and Agricultural Engineering, NC State University, Raleigh, NC 27607, USA.
130
Applied Ergonomics September 1977
simulator could be described by engineering specifications, produced and used for the meaningful measurement of chain saw vibration production.
Review of literature Other researchers have used impedance methods to determine parameters for modelling the human hand as a vibrational energy receiver. Dieckmann (1958) studied driving point mechanical impedance in the 5 to 70 Hz frequency range for subjects in normal working configurations and developed lumped parameter models. Miwa (1964) investigated impedance characteristics over the 20-800 Hz range in a configuration which did not simulate the actual working configuration and thus there is a difficulty in directly applying his results to the design of a simulator. Reynolds and Soedal (1972) measured the apparent mass characteristics of subjects in normal operating configurations over the 20 to 500 Hz range. They proposed an analytical model employing a Kelvin body driven through a point mass for which the parameters m, c, and k take on different values, depending upon the portion of the frequency range involved. Mishoe and Suggs (1975) in a later study measured the mechanical impedance of human subjects in a normal operating configuration and proposed rather complex multi-mass analytical models for the hand arm system. These studies contribute greatly to the basic knowledge regarding the mechanism of vibration entry and dissipation into the hand. The refinements presented in these studies, however, offerlittle which can be practically applied to the design of a simulator for saw testing. Franke (1951) studied the mechanical impedance of the surface of the human thigh over the 50 to 1500 I-Iz range. He proposed a Kelvin body driven through a point mass as sufficient to model the system over the frequency range indicated.
Mechanical impedance testing has long been useful in the characterization of mechanical systems which are to be interfaced with others. This quantity is generally obtained using some modification of a sweep-sinusoidal test. The mechanical impedance Z (']co)is (Harris and Crede, 1961):
Z (/co)
Vo(~)
= ~
e jO(w) ,
the acceleration signal from the force signal. The acceleration and corrected force signals were then monitored by a phase meter (Dranetz Model 301) and dual beam oscilloscope (Tektronix Type 549). For each input frequency, the phase angle between the force and acceleration and the amplitude of the force and acceleration were recorded. The impedance can be shown to be:
. . . . (1)
Z(jco)
vo(co)
-
where
/ = x/-1 co = frequency of excitation F o = force amplitude I1o= velocity amplitude 0 = angle by which force leads velocity. Experimental arrangement An electromagnetic vibrator (AGAC Derritron AV 50) was utilized to provide a controllable source of sinusoidal vibration. An associated power amplifier (AGAC Derritron N-300) was used to amplify a sine wave signal to drive the shaker coil. The usable frequency range of the system was 5 Hz to 10 kHz. Handles were fabricated to be mounted on the shaker table so that the human hand could be excited in a manner similar to chain saw usage. One type of handle allowed the subject to grip a cylindrical bar executing transverse vibration; the other type provided an axially vibrating bar for gripping. The sensing transducer was a piezoelectirc impedance head (Wilcoxon Research Z 602) which served as the connecting link between the handle and the vibrating platform. The outputs of the impedance head were analogue voltages, one proportional to the force transmitted to the handle and the other proportional to the acceleration of the handle. Fig. 1 shows a subject undergoing impedance measurement. Correction of the force signal for the mass of the handle was necessary since the desired measurement was the force transmitted to the hand. Since the handle was rigid over the frequency range of interest, this correction was effected electronically by subtracting a proportion of
Fo coe - j (a + 90) Ao
. . . (2)
where A o = acceleration amplitude and a = phase angle (in degrees) of the acceleration relative to the force. The tests were conducted at a constant acceleration amplitude so that only the force and phase angle measurements were required in order to compute impedance. The gripping force exercised by the subjects during a measurement was indirectly controlled by conditioning the subjects with a grip tester. They were trained to grip at about 17 N squeezing force, simulating typical working conditions. It was found, by checking after each run, that the subjects were capable of rather accurately judging the intensity of their grip. Three subjects were employed. They were of normal stature and were accustomed to chain saw usage. The impedance characteristics were measured contiguously over the frequency range of 70 to 1670 Hz at constant peak to peak acceleration of 92 m/s 2 . Several viscoelastic materials were investigated to determine their applicability in the fabrication of a simulator to model the hand and to be utilized in monitoring the vibration of chain saws. The materials were evaluated by mechanical impedance measurement in a manner similar to that used for the human subjects. The physical model was then evaluated by comparing vibration measurements obtained with an operator to those obtained with the saw mounted in the apparatus. These measurements were taken using a Bruel and Kjar 4335 piezoelectric accelerometer and 2203 Sound Level Meter equipped with a 1613 Octave Band Filter.
Operator impedance characteristics The measured impedance characteristics, an example of which is shown in Fig. 2, indicated that for any single direction of excitation, the hand could be described as a one degree of freedom system consisting of a foundationcoupled Kelvin body driven through a point mass. Such a response was anticipated based upon previous work (Abrams and Suggs, 1969; Abrams, 1971 ; Dieckmann, 1958; Miwa, 1964) and it was hypothesised that the system could be modelled by the relation: Z(jco)
=
c+j(mw-
k/co)
...(4)
where Z = mechanical impedance, N.s/m, c = damping coefficient, N.s/m, m = mass, kg, k = stiffness, N/m, and
Fig. 1
Subjectundergoing right hand-driving point impedance measurement
co = angular frequency, rads
The impedance decreased with frequency from 70 to about 120 Hz and then increased rather uniformly with frequency.
Applied Ergonomics September 1977
131
Values were obtained for each subject tot the model parameters m, c and k in Equation (3) by fitting the data covering the 70 to 1670 Hz range to the model equation. Table 2 shows the parameters obtained for one subject. The mass values for all subjects ranged from 14 to 50 g, the damping values from 3.9 to 175 N.s/m, and the stiffness from 4000 to 27 000 N/m. An acceptable fit to the model equation was obtained for each of the subjects and a one degree of freedom mass-spring-damper system thus appeared a suitable model of the operator characteristics.
400 300 z
-
200
E
E
I00 8o
Model impedance characteristics z~ Subject impedance magnitude data O Subject impedance phase angle data
_E 6o 50 40
8o 0
. . , ~ 0 / 0
40
o
o
-40 r
I 810 I
70
Fig. 2
I00
I 200
L 300
i I L S I 500 800 400 60O I000 Excitation frequency, Hz
a. -80
Driving point impedance, subject BD, 92 m/s 2 peak to peak, right hand, vertical excitation
The near 90 ° phase angle and linear increase of impedance magnitude with frequency in the high frequency range is indicative of a mass-like behaviour. The near zero phase angle at about 100 Hz and the relatively constant magnitude in that vicinity is indicative of a resonant condition. The gradual change of phase angle over the entire frequency range indicates that the system is highly damped.
The principle motivation for a simulator was the variability associated with otherwise making vibration measurements while the saw is held by a live human operator. It was therefore not as important that a population be represented by the simulator as it was that the simulator be specifiable and known to be a good simulation of a typical operator. Accordingly, it was decided to attempt to model one of the subjects with the physical simulator and to compare the saw vibration measurements made with that simulator with those made with that operator. Subject BD, whose physical characteristics are given in Table 1 and whose model impedance data are shown in Table 2, was chosen because his physical characteristics were typical of chain saw operators and because he was an experienced chain saw user. Also, for the sake of symplicity the model was constructed to have the same impedance for both 'hands' in both directions. The data for the right hand, vertical direction was used. Simulator design
The basic approach in the design of the simulator was one of providing a rigid, movable base from which to suspend the saw under test with the appropriate coupling medium.
Table 1." Physical description of subject (BD) for whom simulator was developed Characteristic
Value
Height Weight Right hand width (widest point) Left hand width (widest point) Right hand thickness (thenar eminence) Left hand thickness (thenar eminence) Right hand length (wrist to 2nd finger tip) Left hand length (wrist to 2nd finger tip) Right forearm length Left forearm length Right forearm circumference (max) Left forearm circumference (max)
1.68m 72"5 kg 9"5 cm 9"5cm 4"4 cm 4"0 cm 19"1 cm 19"1 cm 23"5 cm 23"5 cm 27"9 cm 27'3 cm
-Reaction moss
.............
I~Excitation
Direction
Front foundation ~ block ~
Left
Vertical Longitudinal Lateral Vertical Longitudinal Lateral
Right
132
m gram
c N's/m
k N/mm
39 39 18 50 16 50
100 114 51 121 68 140
13"1 14"9 5-5 11 '4 10.5 8"8
Applied Ergonomics September 1977
~ 3 t i ° n ~ ~ - ~ _ V i b r a t o r
a
Table 2: Model parameters obtained for subject BD (acceleration level - 92 m/s 2 ) Hand
_
~
~
~ I
I
~Reaction moss
~
I
I ~ X..~
~
foundation
block
Sow under test
b Fig. 3
Schematic of the physical model showing: (a) impedance testing (showing schematic of model); (b) the mounting arrangement for the saw
400 300 Z
Model impedonce chorocteristics Subjectimpedonce mognitude dolo
A 0 S
u
b
j
e
c
t
magnitude curve and the comparatively abrupt change in phase is indicative of low damping as compared with the operator curve for which the resonance was not as pronounced. While this condition was not wholly desirable, this material responded considerably better than others (.polyethelene foams) available and tested. Furthermore, it was dimensionally stable, taking no noticeable permanent set upon repetitive loading. Basically, then, the choice of viscoelastic material was based mainly on its elastic characteristics.
A A J
~
- 200
g
o
A
80
-~ 6o 50 40
A A 0
0 0
8O 4o 0
40
O
(~
i
°
70 80 I00
Fig. 4
i
200
i
t
i
I
-80 1
a_
I
500 800 400 600 1000 Excilotion frequency, Hz 300
Comparison of simulator and operator driving point impedance characteristics
That coupling medium served mainly to represent the damping and spring characteristics of the human operator. The appropriate aluminium weight to represent the mass obtained in the curve fit on the subject impedance data was attached rigidly to the saw handle and represented the inertial characteristics of the operator as viewed through the hand in a working configuration.
The simulator was evaluated by testing a chain saw in the fashion shown in Fig. 5 and Fig. 3b. The saw was operated at 9200 rev/min under no load. The no load condition was used because of the difficulty of loading the saw by cutting while mounted in the simulator and is justified since preliminary tests showed that vibration levels measured with the saw cutting and not cutting at 9200 rev/min were not different (Abrams, 1971). It was postulated that the excitation arising from the cutting action would be essentially damped out by the surrounding wood. Reynolds and Soedel (1974) have concluded, based upon experimentation, that analysing the vibration response of chain saws under no cutting load would be fairly indicative of the response under load. The speed was monitored by an electro-tachometer and controlled by means of a remote throttle. Octave band analyses were performed on three orthogonal accelerations measured on each of the front and rear handles. These analyses were compared with the same analyses made with the saw held by the operator. This comparison shown is in Fig. 6. While the 70 - 1670 Hz range contains the frequencies
The two steel foundation blocks were specially constructed, one for the front and one for the rear handle. The front' foundation block was 60 c m x 6.0 cm x 7-6 cm with a 3"8 cm diameter hole centre bored along the 7.6 cm dimensionl to accept the tubular front handle of the saw. Means for mounting the saw handle were provided by cutting away a face plate and providing for bolting it in place. The rear foundation block was similarly constructed except that the cavity for accepting the rear handle was rectangular in shape to accept the rectangular cast rear handle of the saw. The block was 7.1 cm x 7.5 cm x 6.7 cm with the cavity extending along the 6-7 cm dimension Each block was designed in such a way as to allow a 0.6 cm radial clearance within the cavity between the saw handle and the block. This clearance was provided for placement of the viscoelastic material used in modelling the stiffness and damping characteristics of the operator. The simulator was developed by testing various viscoelastic materials in the fashion shown in Fig. 3a. Here one can also see the basic structure of the simulator. The internal surfaces of the cavities in the foundation blocks were lined with a 13 mm thickness of the material (Rubatex*). Impedance data were obtained and compared with operator (model) curves, Fig. 4. In the 100 to 400 Hz range there was poor agreement between the operator and the model impedance characteristics. The pronounced trough in the
*Trade name for material generally used for insulation of water pipes, Density = 166 kg/m 3, static stiffness for configuration used = 42 000 N/m.
Fig. 5
Chain saw mounted in simulator as used for vibration measurement
Applied Ergonomics September1977
133
Vertical
2O E
Lo~Jitudinol
Lateral
0
~ -IO co
-u ,',Simulator
//
V///~Y//,
//,////~S/
20
<
saws was developed based upon this analytical model, the parameters for which were derived from measured driving point impedance characteristics of a human operator. Such a device offers the advantage of not requiring use of live operators to obtain measurements of chain saw vibration production having direct meaning with respect to operator exposure. The simulator was based on driving point impedance data obtained over the 70 - 1670 Hz frequency range and the response of the simulator in terms of octave band analyses chain saw vibration was satisfactory.
0 -I0
References ,
51 5
125
4 000 500
,I.5 125 4 000 31.5 125 4000 31500 500 31500 ,500 31500 Frequency, Hz
Abrams, C.F. Jr, and Suggs, C.W. 1969 Transactions of ASAE 12. 4,423. Chain saw vibration isolation and transmission through the human arm.
Abrams, C.F. Jr. Fig. 6
Octave band analysis of chain saw vibration production comparing the operator to the simulator
most important based on current knowledge and is the frequency range over which the model parameters were determined, from a human comfort and injury standpoint, saw vibration data have traditionally been taken over a wider range (30 - 30 000 Hz). Fig. 6 shows the unshaded octave band analyses over this wider frequency range with the unshaded areas identifying the frequency range covered by the impedance modelling work. The responses indicated by these analyses tend to show that the simulator provides a reasonable approximation to the operator. However, it should be noted that octave band analysis may not have revealed some possible high Q peaks in the model response curve caused by the lack of impedance operator/model match in the 100 - 400 Hz range. It is also possible that the impedance characteristics of the operator in the 100 400 Hz range do not greatly affect the vibration production markedly; if this is in fact the case then accurate impedance modelling in this range would be unnecessary. A narrow band analysis would possibly be revealing in this regard and such is recommended for further work. Also, testing and evaluation should be extended to lower frequencies. Conclusions The suitability of an analytical model of chain saw operator characteristics of a one degree of freedom system consisting of a foundation-coupled Kelvin body driven through a point mass was demonstrated. A simulator useable for the measurement of the vibration production of chain
134
Applied Ergonomics September 1977
1971 Modelling the vibrational characteristics of the human hand by the driving point mechanical impedance method. Ph D dissertion, Department of Biological and Agricultural Engineering, North Carolina State University, Raleigh, North Carolina, USA. Dieekmann, D. 1958 Internat Z angew physiol einschl Arbeitsphysiol 17, 127. Ein mechanisches Model fuer das schwengungserregra hand-arm System des Menschen. Franke, E.E. 1951 JApplPhysiol. 3, 582. Mechanical impedance of the surface of the human body. Harris, C.M., and Crede, C.E. eds 1961 Shock and Vibration Handbook (three volumes). New York: McGraw-Hill Book Company, Inc.
Mishoe, J.W., and Suggs, C.W. 1975 American Society of Agricultural Engineers, t975 Winter Meeting Paper No 75-1515. American Society of Agricultural Engineers, St Joseph, Michigan 49085.
Miwa, T. 1964 Ind Health (Japan), 2, 95. Studies of hand protectors for portable vibrating tools 1. Measurements of the attenuation effect of porous elastic materials.
Reynolds, D.D., and Soedd, W. 1972 Journal of Sound and Vibration 21.3,339. Dynmaic response of the hand-arm system to a sinusoidal input.
Reynolds, D.D., and Soedel, W. 1974 Journal of Sound and Vibration 32.3,371. Vibration characteristics of non-isolated chain saws.
Development of a simulator for use in the measurement of chain saw vibration C.F. Abrams, Jr, and C.W. Suggs Department of Biological and Agricultural Engineering, North Carolina State University, USA
The measurement of vibration production of light, hand held power tools is important in the assessment of the potential for elicitation of vibration injury to the operators of these tools. The manner in which these measurements are made can greatly affect the results. The measured vibration production of the tool becomes a function of the operator holding the saw during the measurement and his physical characteristics. The objective of the work reported here was to develop a simulator of the operator which might be used in the vibration production analysis of chain saws. The operator was modelled in terms of the driving point mechanical impedance characteristics of humans for input to the hands. A simulator was developed based on the driving point impedance characterization of the operator and evaluated with chain saw vibration measurements.
Introduction Vibration-induced sicknesses are of concern for those persons who are regularly exposed to vibration in the course of their work activities. Of particular interest are the disorders of the peripheral circulation due to the exposure of the hands to vibration from power tools. The chain saw is an example of such a tool. Criteria are being proposed which set forth the vibration tolerance for input to the hands. Successful application of such criteria to the vibration production rating of tools such as chain saws will require an objective, repeatable means of measuring the vibration production of the tool in a working configuration. Vibration production is generally measured by affixing acceleration transducers near the hand/tool interface and observing the vibration production while the tool is used by the operator. This approach has the inherent problem of lack of general applicability since the same operator cannot be used at every test installation. The objective of the work reported here was to develop a physical simulator of the human operator in which a chain saw could be mounted for vibration measurement. The concept of driving point mechanical impedance was to be used to define the parameters of such a simulator. Such a
Paper No 5021 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, NC. The use of trade names in this publication does not imply endorsement by the North Carolina Agricultural Experiment Station of the products named, nor criticism of similar ones not mentioned. The authors are, respectively, assistant professor and professor, Department of Biological and Agricultural Engineering, NC State University, Raleigh, NC 27607, USA.
130
Applied Ergonomics September 1977
simulator could be described by engineering specifications, produced and used for the meaningful measurement of chain saw vibration production.
Review of literature Other researchers have used impedance methods to determine parameters for modelling the human hand as a vibrational energy receiver. Dieckmann (1958) studied driving point mechanical impedance in the 5 to 70 Hz frequency range for subjects in normal working configurations and developed lumped parameter models. Miwa (1964) investigated impedance characteristics over the 20-800 Hz range in a configuration which did not simulate the actual working configuration and thus there is a difficulty in directly applying his results to the design of a simulator. Reynolds and Soedal (1972) measured the apparent mass characteristics of subjects in normal operating configurations over the 20 to 500 Hz range. They proposed an analytical model employing a Kelvin body driven through a point mass for which the parameters m, c, and k take on different values, depending upon the portion of the frequency range involved. Mishoe and Suggs (1975) in a later study measured the mechanical impedance of human subjects in a normal operating configuration and proposed rather complex multi-mass analytical models for the hand arm system. These studies contribute greatly to the basic knowledge regarding the mechanism of vibration entry and dissipation into the hand. The refinements presented in these studies, however, offerlittle which can be practically applied to the design of a simulator for saw testing. Franke (1951) studied the mechanical impedance of the surface of the human thigh over the 50 to 1500 I-Iz range. He proposed a Kelvin body driven through a point mass as sufficient to model the system over the frequency range indicated.
Mechanical impedance testing has long been useful in the characterization of mechanical systems which are to be interfaced with others. This quantity is generally obtained using some modification of a sweep-sinusoidal test. The mechanical impedance Z (']co)is (Harris and Crede, 1961):
Z (/co)
Vo(~)
= ~
e jO(w) ,
the acceleration signal from the force signal. The acceleration and corrected force signals were then monitored by a phase meter (Dranetz Model 301) and dual beam oscilloscope (Tektronix Type 549). For each input frequency, the phase angle between the force and acceleration and the amplitude of the force and acceleration were recorded. The impedance can be shown to be:
. . . . (1)
Z(jco)
vo(co)
-
where
/ = x/-1 co = frequency of excitation F o = force amplitude I1o= velocity amplitude 0 = angle by which force leads velocity. Experimental arrangement An electromagnetic vibrator (AGAC Derritron AV 50) was utilized to provide a controllable source of sinusoidal vibration. An associated power amplifier (AGAC Derritron N-300) was used to amplify a sine wave signal to drive the shaker coil. The usable frequency range of the system was 5 Hz to 10 kHz. Handles were fabricated to be mounted on the shaker table so that the human hand could be excited in a manner similar to chain saw usage. One type of handle allowed the subject to grip a cylindrical bar executing transverse vibration; the other type provided an axially vibrating bar for gripping. The sensing transducer was a piezoelectirc impedance head (Wilcoxon Research Z 602) which served as the connecting link between the handle and the vibrating platform. The outputs of the impedance head were analogue voltages, one proportional to the force transmitted to the handle and the other proportional to the acceleration of the handle. Fig. 1 shows a subject undergoing impedance measurement. Correction of the force signal for the mass of the handle was necessary since the desired measurement was the force transmitted to the hand. Since the handle was rigid over the frequency range of interest, this correction was effected electronically by subtracting a proportion of
Fo coe - j (a + 90) Ao
. . . (2)
where A o = acceleration amplitude and a = phase angle (in degrees) of the acceleration relative to the force. The tests were conducted at a constant acceleration amplitude so that only the force and phase angle measurements were required in order to compute impedance. The gripping force exercised by the subjects during a measurement was indirectly controlled by conditioning the subjects with a grip tester. They were trained to grip at about 17 N squeezing force, simulating typical working conditions. It was found, by checking after each run, that the subjects were capable of rather accurately judging the intensity of their grip. Three subjects were employed. They were of normal stature and were accustomed to chain saw usage. The impedance characteristics were measured contiguously over the frequency range of 70 to 1670 Hz at constant peak to peak acceleration of 92 m/s 2 . Several viscoelastic materials were investigated to determine their applicability in the fabrication of a simulator to model the hand and to be utilized in monitoring the vibration of chain saws. The materials were evaluated by mechanical impedance measurement in a manner similar to that used for the human subjects. The physical model was then evaluated by comparing vibration measurements obtained with an operator to those obtained with the saw mounted in the apparatus. These measurements were taken using a Bruel and Kjar 4335 piezoelectric accelerometer and 2203 Sound Level Meter equipped with a 1613 Octave Band Filter.
Operator impedance characteristics The measured impedance characteristics, an example of which is shown in Fig. 2, indicated that for any single direction of excitation, the hand could be described as a one degree of freedom system consisting of a foundationcoupled Kelvin body driven through a point mass. Such a response was anticipated based upon previous work (Abrams and Suggs, 1969; Abrams, 1971 ; Dieckmann, 1958; Miwa, 1964) and it was hypothesised that the system could be modelled by the relation: Z(jco)
=
c+j(mw-
k/co)
...(4)
where Z = mechanical impedance, N.s/m, c = damping coefficient, N.s/m, m = mass, kg, k = stiffness, N/m, and
Fig. 1
Subjectundergoing right hand-driving point impedance measurement
co = angular frequency, rads
The impedance decreased with frequency from 70 to about 120 Hz and then increased rather uniformly with frequency.
Applied Ergonomics September 1977
131
Values were obtained for each subject tot the model parameters m, c and k in Equation (3) by fitting the data covering the 70 to 1670 Hz range to the model equation. Table 2 shows the parameters obtained for one subject. The mass values for all subjects ranged from 14 to 50 g, the damping values from 3.9 to 175 N.s/m, and the stiffness from 4000 to 27 000 N/m. An acceptable fit to the model equation was obtained for each of the subjects and a one degree of freedom mass-spring-damper system thus appeared a suitable model of the operator characteristics.
400 300 z
-
200
E
E
I00 8o
Model impedance characteristics z~ Subject impedance magnitude data O Subject impedance phase angle data
_E 6o 50 40
8o 0
. . , ~ 0 / 0
40
o
o
-40 r
I 810 I
70
Fig. 2
I00
I 200
L 300
i I L S I 500 800 400 60O I000 Excitation frequency, Hz
a. -80
Driving point impedance, subject BD, 92 m/s 2 peak to peak, right hand, vertical excitation
The near 90 ° phase angle and linear increase of impedance magnitude with frequency in the high frequency range is indicative of a mass-like behaviour. The near zero phase angle at about 100 Hz and the relatively constant magnitude in that vicinity is indicative of a resonant condition. The gradual change of phase angle over the entire frequency range indicates that the system is highly damped.
The principle motivation for a simulator was the variability associated with otherwise making vibration measurements while the saw is held by a live human operator. It was therefore not as important that a population be represented by the simulator as it was that the simulator be specifiable and known to be a good simulation of a typical operator. Accordingly, it was decided to attempt to model one of the subjects with the physical simulator and to compare the saw vibration measurements made with that simulator with those made with that operator. Subject BD, whose physical characteristics are given in Table 1 and whose model impedance data are shown in Table 2, was chosen because his physical characteristics were typical of chain saw operators and because he was an experienced chain saw user. Also, for the sake of symplicity the model was constructed to have the same impedance for both 'hands' in both directions. The data for the right hand, vertical direction was used. Simulator design
The basic approach in the design of the simulator was one of providing a rigid, movable base from which to suspend the saw under test with the appropriate coupling medium.
Table 1." Physical description of subject (BD) for whom simulator was developed Characteristic
Value
Height Weight Right hand width (widest point) Left hand width (widest point) Right hand thickness (thenar eminence) Left hand thickness (thenar eminence) Right hand length (wrist to 2nd finger tip) Left hand length (wrist to 2nd finger tip) Right forearm length Left forearm length Right forearm circumference (max) Left forearm circumference (max)
1.68m 72"5 kg 9"5 cm 9"5cm 4"4 cm 4"0 cm 19"1 cm 19"1 cm 23"5 cm 23"5 cm 27"9 cm 27'3 cm
-Reaction moss
.............
I~Excitation
Direction
Front foundation ~ block ~
Left
Vertical Longitudinal Lateral Vertical Longitudinal Lateral
Right
132
m gram
c N's/m
k N/mm
39 39 18 50 16 50
100 114 51 121 68 140
13"1 14"9 5-5 11 '4 10.5 8"8
Applied Ergonomics September 1977
~ 3 t i ° n ~ ~ - ~ _ V i b r a t o r
a
Table 2: Model parameters obtained for subject BD (acceleration level - 92 m/s 2 ) Hand
_
~
~
~ I
I
~Reaction moss
~
I
I ~ X..~
~
foundation
block
Sow under test
b Fig. 3
Schematic of the physical model showing: (a) impedance testing (showing schematic of model); (b) the mounting arrangement for the saw
400 300 Z
Model impedonce chorocteristics Subjectimpedonce mognitude dolo
A 0 S
u
b
j
e
c
t
magnitude curve and the comparatively abrupt change in phase is indicative of low damping as compared with the operator curve for which the resonance was not as pronounced. While this condition was not wholly desirable, this material responded considerably better than others (.polyethelene foams) available and tested. Furthermore, it was dimensionally stable, taking no noticeable permanent set upon repetitive loading. Basically, then, the choice of viscoelastic material was based mainly on its elastic characteristics.
A A J
~
- 200
g
o
A
80
-~ 6o 50 40
A A 0
0 0
8O 4o 0
40
O
(~
i
°
70 80 I00
Fig. 4
i
200
i
t
i
I
-80 1
a_
I
500 800 400 600 1000 Excilotion frequency, Hz 300
Comparison of simulator and operator driving point impedance characteristics
That coupling medium served mainly to represent the damping and spring characteristics of the human operator. The appropriate aluminium weight to represent the mass obtained in the curve fit on the subject impedance data was attached rigidly to the saw handle and represented the inertial characteristics of the operator as viewed through the hand in a working configuration.
The simulator was evaluated by testing a chain saw in the fashion shown in Fig. 5 and Fig. 3b. The saw was operated at 9200 rev/min under no load. The no load condition was used because of the difficulty of loading the saw by cutting while mounted in the simulator and is justified since preliminary tests showed that vibration levels measured with the saw cutting and not cutting at 9200 rev/min were not different (Abrams, 1971). It was postulated that the excitation arising from the cutting action would be essentially damped out by the surrounding wood. Reynolds and Soedel (1974) have concluded, based upon experimentation, that analysing the vibration response of chain saws under no cutting load would be fairly indicative of the response under load. The speed was monitored by an electro-tachometer and controlled by means of a remote throttle. Octave band analyses were performed on three orthogonal accelerations measured on each of the front and rear handles. These analyses were compared with the same analyses made with the saw held by the operator. This comparison shown is in Fig. 6. While the 70 - 1670 Hz range contains the frequencies
The two steel foundation blocks were specially constructed, one for the front and one for the rear handle. The front' foundation block was 60 c m x 6.0 cm x 7-6 cm with a 3"8 cm diameter hole centre bored along the 7.6 cm dimensionl to accept the tubular front handle of the saw. Means for mounting the saw handle were provided by cutting away a face plate and providing for bolting it in place. The rear foundation block was similarly constructed except that the cavity for accepting the rear handle was rectangular in shape to accept the rectangular cast rear handle of the saw. The block was 7.1 cm x 7.5 cm x 6.7 cm with the cavity extending along the 6-7 cm dimension Each block was designed in such a way as to allow a 0.6 cm radial clearance within the cavity between the saw handle and the block. This clearance was provided for placement of the viscoelastic material used in modelling the stiffness and damping characteristics of the operator. The simulator was developed by testing various viscoelastic materials in the fashion shown in Fig. 3a. Here one can also see the basic structure of the simulator. The internal surfaces of the cavities in the foundation blocks were lined with a 13 mm thickness of the material (Rubatex*). Impedance data were obtained and compared with operator (model) curves, Fig. 4. In the 100 to 400 Hz range there was poor agreement between the operator and the model impedance characteristics. The pronounced trough in the
*Trade name for material generally used for insulation of water pipes, Density = 166 kg/m 3, static stiffness for configuration used = 42 000 N/m.
Fig. 5
Chain saw mounted in simulator as used for vibration measurement
Applied Ergonomics September1977
133
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saws was developed based upon this analytical model, the parameters for which were derived from measured driving point impedance characteristics of a human operator. Such a device offers the advantage of not requiring use of live operators to obtain measurements of chain saw vibration production having direct meaning with respect to operator exposure. The simulator was based on driving point impedance data obtained over the 70 - 1670 Hz frequency range and the response of the simulator in terms of octave band analyses chain saw vibration was satisfactory.
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References ,
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Abrams, C.F. Jr, and Suggs, C.W. 1969 Transactions of ASAE 12. 4,423. Chain saw vibration isolation and transmission through the human arm.
Abrams, C.F. Jr. Fig. 6
Octave band analysis of chain saw vibration production comparing the operator to the simulator
most important based on current knowledge and is the frequency range over which the model parameters were determined, from a human comfort and injury standpoint, saw vibration data have traditionally been taken over a wider range (30 - 30 000 Hz). Fig. 6 shows the unshaded octave band analyses over this wider frequency range with the unshaded areas identifying the frequency range covered by the impedance modelling work. The responses indicated by these analyses tend to show that the simulator provides a reasonable approximation to the operator. However, it should be noted that octave band analysis may not have revealed some possible high Q peaks in the model response curve caused by the lack of impedance operator/model match in the 100 - 400 Hz range. It is also possible that the impedance characteristics of the operator in the 100 400 Hz range do not greatly affect the vibration production markedly; if this is in fact the case then accurate impedance modelling in this range would be unnecessary. A narrow band analysis would possibly be revealing in this regard and such is recommended for further work. Also, testing and evaluation should be extended to lower frequencies. Conclusions The suitability of an analytical model of chain saw operator characteristics of a one degree of freedom system consisting of a foundation-coupled Kelvin body driven through a point mass was demonstrated. A simulator useable for the measurement of the vibration production of chain
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Applied Ergonomics September 1977
1971 Modelling the vibrational characteristics of the human hand by the driving point mechanical impedance method. Ph D dissertion, Department of Biological and Agricultural Engineering, North Carolina State University, Raleigh, North Carolina, USA. Dieekmann, D. 1958 Internat Z angew physiol einschl Arbeitsphysiol 17, 127. Ein mechanisches Model fuer das schwengungserregra hand-arm System des Menschen. Franke, E.E. 1951 JApplPhysiol. 3, 582. Mechanical impedance of the surface of the human body. Harris, C.M., and Crede, C.E. eds 1961 Shock and Vibration Handbook (three volumes). New York: McGraw-Hill Book Company, Inc.
Mishoe, J.W., and Suggs, C.W. 1975 American Society of Agricultural Engineers, t975 Winter Meeting Paper No 75-1515. American Society of Agricultural Engineers, St Joseph, Michigan 49085.
Miwa, T. 1964 Ind Health (Japan), 2, 95. Studies of hand protectors for portable vibrating tools 1. Measurements of the attenuation effect of porous elastic materials.
Reynolds, D.D., and Soedd, W. 1972 Journal of Sound and Vibration 21.3,339. Dynmaic response of the hand-arm system to a sinusoidal input.
Reynolds, D.D., and Soedel, W. 1974 Journal of Sound and Vibration 32.3,371. Vibration characteristics of non-isolated chain saws.