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REPORT ON THE NMSD PROJECT 2.3.1 (DTI ref. no. GBBK/1/13c)



A.V.I. LTD.,




8 TH JULY 2004 .

A.V.I. Ltd.
E-mail: sales@avi.f2s.com



Instrumentation for measuring human vibration is used for assessing risk to personal health and safety from vibrating machines. It is clear the uncertainty in such measurement should be minimised so as to provide useful and just assessment. Quantifying this uncertainty has become the subject of considerable interest. Uncertainties associated with the process of field assessment of daily exposure to hand-transmitted vibration have been investigated in detail (1) and the DTI has established a program within the National Measurement System intended to provide “definitive guidance regarding . .measurement uncertainties .. in the instrumentation of machines causing hand-arm vibration and whole-body vibration” (2). This report describes experiments performed to illustrate and quantify such measurement uncertainties.

The equipment used to instrument sources of human exposure to vibration should conform to the requirements of international standard ISO 8041 3. Pitts (1) notes that the margin of error acceptable within the standard leaves a typical uncertainty of order ± 4% in a correctly calibrated system, rising to perhaps ± 10% at the extremes of the frequency range (where the standard’s weighting filter tolerances are wider). This source of uncertainty, whilst a factor of those results presented later in this report, is not the object of the present work. Rather than the uncertainty native to the instrument, it is the uncertainty associated with its use “in the instrumentation of machines” which is of interest.

When field measurements of vibration exposure are conducted, a range of aspects totally unrelated to the instrumentation influence overall measurement uncertainty. These include temporal patterns of measurement and use, condition and operating load of the vibration source, etc. (1,4). In laboratory testing of vibration emission (5) many of these uncertainties are removed by operating the source in a controlled environment. There remains, however, an important source of variation whenever human exposure is instrumented – the human!

Human participation as operator and/or mechanical load for a source of vibration introduces a source of variability often capable of swamping all other factors. In the case of Hand-Arm vibration, changes in the grip with which the source is held influence the vibration of the source (assuming it to have anything other than infinite mechanical source impedance). In Whole-Body exposure, shifts in position of the human load have a similar consequence. This observation motivated the design of a pair of experiments in which representative sources of human exposure to vibration were measured in realistic load conditions without the presence of a human operator or load. The uncertainties observed in these experiments would include factors associated with the instruments and their use alone.

It was intended that measurements should be made in each experiment, which would return answers distributed according to uncertainties associated with:

During the early phases of experimentation it became apparent that data from repeated measurements with no replacement of the transducer or other disturbances would provide useful reference information.

To perform the tests, a range of measurement systems was assembled. Manufacturers represented were Bruel & Kjaer, 01 dB, Larson Davis, Svantek, Castle, Norsonic and AVI. Some systems provided were available in more than one configuration and not all available configurations were used in the tests reported below. Those systems used were fully calibrated by AV Calibration Ltd, using sources traceable to national standards for frequency response and linearity accuracy over the range of measurement used.


The first experiment used an electric angle grinder as a source of hand-arm vibration. A newly purchased, widely available electric grinder was operated in a test rig as specified in ISO 8662:4 (6) in which the tool is run with an imbalanced wheel. Rather than the normal load speed specified in the standard, the tool was run at full (no load) speed, for simplicity. In normal use a human operator holds the tool in the test rig, applying a steady feed force. The details of the grip forces will change from one operator to the next and will change over time for a single operator, such that the tool experiences different boundary conditions. These changes in boundary conditions are sufficient to change the resulting vibration levels, particularly on those areas of the tool having low mechanical source impedance (such as the rather flimsy support handle). To avoid these sources of uncertainty associated with grip, a pair of “artificial hands” was constructed for the rig. These hands were designed with reference to expressions of the mechanical impedance of the hand-arm system published in international standard ISO 10068 (7).

The artificial hand-arm systems, which hold the grinder in the operating position, are built within sub-frames, capable of rigid mounting on the test rig using a system of clamps. It originally had been envisaged that each hand-arm system should include a single mass, capable of small amplitude movement in three perpendicular directions. Movement on each axis would be opposed by independent stiffness and damping.

To support the design of these artificial hands, a numerical model of the three and four degree-of-freedom hand-arm impedance models (7) was developed using “two-port” methods. This numerical model was used to validate the simpler system proposed for the artificial hands. Listings of the relevant sections of the numerical model, which was coded in MATLAB, are appended.

Initial work with this model revealed that it is not possible to use the envisaged single mass solution (since the ratios of the xh axis equivalent moving mass to the equivalent moving mass on the other two axes are too high). Accordingly, two moving masses were used in each hand-arm system, with one mass active on all three axes and another only active on the xh axis. Rigid pivoted couplings were used between the masses and to restrain the second mass with respect to the y h and z h axes as the system is only designed to operate for small displacements. Each hand was equipped with a “Jubilee” hose clip, which gripped the tool.

The mechanical parameters of the hands were chosen to be:

xh axis

y h axis

z h axis

m (kg)

0.105 + 0.035



K (N/m)




C (Ns/m)




which gave a good fit within the envelope of mechanical impedance magnitudes (7), as shown by Figure 1 below. These figures report the range of the magnitude impedances specified in ISO 10068 and the mechanical impedance implied by the parameters in the table above (blue trace).

image 4

image 4

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Figures 1 Magnitude Driving Point Impedance of the Hand (upper and lower limits) and the Artificial Hand (blue trace)

The practical embodiment of the artificial hands used identical springs on each axis and omitted the damping elements, for simplicity. The hands are shown holding an angle grinder in the test rig in Plate 1.


Plate 1: Artificial Hands holding the Grinder

image 4

Transducers were mounted on the support and throttle handle of the grinder, using “cable ties”, as shown in Plates 2, below. Tri-axial measurements allowed instrumentation of the weighted equivalent acceleration, calculated either directly within the instrument or by hand, using the expression:

image 4

Plates 2 Accelerometer mountings on the throttle (left) and support (right) handles

image 4image 4

In those instruments having only a single measurement channel, the accelerometer mounting block was fixed to the measurement point and the accelerometer moved between the three orthogonal positions without disturbing the block, ensuring accurate sampling of the three component vector accelerations. The mounting block was removed from the tool once all of the three component vectors had been measured.

In practice, it was found difficult to operate with the 40N feed-force specified in the angle grinder test standard (6), as this placed the artificial hands in a position of conditional stability from which one of the suspension springs was prone to buckling deformation. It was decided to limit the feed-force to 20N to avoid this problem.


image 4 The whole-body experiment was motivated by the measurement of vibration transmission through a vehicle seat. Measures of seat transmission using a human subject would include inevitable variations associated with shifts of the occupant’s position on the seat during and between measurement runs. Thus, the human subject was replaced by a 75 kg metal mass, which could be lowered onto the seat using a crane.

The seat, intended for use on an agricultural vehicle, was mounted on a flat steel plate atop a vertical hydraulic shaker. The shaker was driven by a pink noise source, resulting in significant accelerations of the mounting plate from 5 Hz to 500 Hz. A reference transducer on the steel plate continuously monitored the acceleration.

The whole-body experiment is shown in Plate 3.



Plate 3: The Whole-body Experimental Rig


The acceleration at the reference position was continuously monitored and both linear and (Wk) weighted reference levels were recorded for each measurement. Although the shaker rig was operated by an open-loop control system, weighted reference accelerations remained within a ± 0.5 dB(Wk) range over two days of measurement. A typical power spectrum of the reference acceleration is shown as Figure 1

image 4

Figure 1 Typical Reference Acceleration Spectrum for Whole-Body Experiment

image 4 The acceleration of the top of the seat, loaded by the metal mass, was instrumented by accelerometers in “whoopee cushions”. Repeat positioning of the “whoopee cushion” on the seat was assisted by a reference circle, drawn on the seat top. It is estimated that the accelerometer could be replaced to accuracy better than ±2mm. The base of the metal mass loading the seat was flat and extended over an area greater than that of the accelerometer mounting cushions. Re-positioning of the mass was referenced to the seat back and to stitched seams on the seat cushion, shown in Plate 4.



Plate 4 Seat Cushion, showing reference markings


In each experiment, groups of ten repeated measurements were made with a range of commercial instrumentation systems all claiming conformance to the relevant standard (3). Six measuring systems were used in the hand-arm experiment whilst another six systems were investigated in the whole-body work. Absolute calibration and frequency response of the appropriate weighting filters was checked for all instruments.

4.1 Repeat Measurement with No Repositioning

The results of repeating measurements with no disturbance of the transducer or the experimental rig are shown below.

Ten typical repeat measurements with no transducer re-positioning from the Hand-Arm experiment are shown in Figure 2a whilst ten from the Whole-Body experiment are shown in Figure 2b. The data of Figures 2 is presented in dB relative to the mean of the ten measurements, all from one measurement set-up, frequency weighted by the HA and Wk filters, respectively.

image 4

Fig2a – Hand-Arm

image 4

Fig. 2b – Whole-Body

Figures 2 Ten Typical Repeat Measurements – no transducer re-positioning

The distributions of repeat measurements returned by different instruments are reported in Figure 3. The data sets in Figure 3 were collected from only four instruments in the hand-arm experiment and five instruments in the whole-body work. Data sets 2 and 3 were gathered from the same instrument, measured on different days.

image 4

Figure 3 Distributions of results with no transducer re-positioning

It is seen that the distributions of results for repeat measurements of whole-body or hand-arm vibration exposure are distributed with ratio σ/μ < 2%.

4.2 Repeat Measurements with Transducer Re-Positioning

The results of repeating measurements following complete removal and replacement of the transducer system are shown below.

Ten typical repeat measurements with transducer re-positioning from the Hand-Arm experiment are shown in Figure 4a whilst ten from the Whole-Body experiment are shown in Figure 4b. The data of Figures 4 is presented in dB relative to the mean of the ten measurements, all from one measurement system, frequency weighted by the HA and Wk filters, respectively.

Fig 4a – Hand-Arm Fig. 4b – Whole-Body

image 4image 4

Figures 4 Ten Typical Repeat Measurements – with transducer re-positioning

The distributions of repeat measurements returned by different instruments are reported in Figure 5. The results are presented as ratio of standard deviation to mean for each data set of ten measurements.

image 4

Figure 5 Distributions of results with transducer re-positioning

Data sets 2 and 3 were gathered from one instrument and data sets 5 and 6 from another. It is seen that the whole-body results generally are more widely distributed than the hand-arm results. For the whole-body experiment, σ/μ < 7%, whilst σ/μ < 4% for the hand-arm results.

4.3 Variations between Instruments

The means of ten measurements of weighted acceleration are compared in the figures below.

image 4

Figure 6 Mean Hand-arm weighted accelerations in ms -2

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Figure 7 Mean Whole-body Wk weighted accelerations in ms-2

Only five of the available instruments were used to gather the data in Figure 7. Data sets 3 and 4 were collected from the same instrument used in different configurations (see discussion, below),

Whilst the different systems in the whole-body experiment and the throttle handle returned reasonably consistent results, the data for the support handle shows alarming variations.


Figure 3 confirms that commercial human vibration meters, conforming to international standard (3) and correctly calibrated, are capable of producing reasonably consistent measures of the weighted accelerations which constitute human exposure to vibration. The results, obtained in stable and representative experimental conditions, are distributed about a mean, with σ/μ < 2%. When, however, the transducer is removed and re-positioned, the distribution of results broadens, as shown in Figure 5.

The act of removing and re-positioning the transducer can introduce a placement error in re-positioning the transducer. In the case of both the whole-body and the hand-arm experiments, transducer re-positioning was estimated to be accurate to better than ±2 mm.

In the case of the hand-arm experiment, re-positioning the transducer involved re-fitting the “cable tie” strap used to hold the mounting block to the angle grinder handle. Experience revealed the tension of this strap to be critical and both “running in” and ageing effects were observed. When tightening a new cable tie by hand, it was found to be difficult to tension the strap past elastic deformations to a stable, repeatable state. This meant that a new cable tie had to be “run-in” by tightening and re-tightening. Alternatively, satisfactory performance could be achieved by the use of a cable tie tool to tighten the strap – even on first use.

Whether tightened by hand or by a custom tool, it was noted that conventional reusable cable ties with the ratchet lock mechanism were subject to ageing when used on the same tool for more than 15 re-mounts. This was caused by mechanical wear of the strap at the point of repeated locking. In the light of this finding, new cable ties were used for each group of ten measurements on the Hand-Arm experiment, all tightened by a cable tie tool.

The superior performance seen in Figure 5, measurement set-up 9, is in part due to the use of the single-use “Kabelrap” system, a product of HellermannTyton, visible in Plates 2.

Re-positioning the “whoopee cushion” in the Whole-body experiments necessitated removal of the mass from the seat and re-fitting. Although the mass could be accurately positioned with reference to stitched seams on the uncompressed seat cushion (Plate 4), deformation of the seat under the weight of the mass meant that repositioning of the mass in the equilibrium could be the subject of significant error, partially explaining the poorer repeatability seen in the Whole-Body data of Figure 5.

Five of the measurement systems used to instrument the Whole-body experiment returned a range of mean weighted (vertical) accelerations, as reported in Figure 7. Data sets 3 & 4 of Figure 7 are associated with one instrument, although in set-up 3 the “whoopee cushion” was inverted. The 14 % difference between the mean accelerations with the same accelerometer in these two orientations appeared to reflect a stable and repeatable error. The ratio of largest to smallest mean weighted acceleration was 1.40 (1.26 if measurement set-up 3 is excluded).

The six measurement systems used to instrument the Hand-arm experiment returned a range of mean weighted equivalent accelerations as reported in Figure 6. The results for the throttle handle were most consistent, with a ratio of largest to smallest mean weighted acceleration of 1.855. However, the range of mean accelerations reported for the support handle were very widely distributed, with ratio of largest to smallest mean weighted acceleration of 3.449. Neither of these ratios is acceptable when considered against ordinary expectations of the validity of measurement of hand-arm vibration (e.g. the ISO test 6 accepts a test sequence to be valid when ratio of maxima to minima is less than 1.4). If data sets 4 & 5 are rejected, the ratio of largest to smallest mean weighted accelerations is 1.42 for the throttle handle and 1.34 for the support handle.

The high values of mean acceleration indicated by data sets 4 & 5 are conspicuous in Figure 6 and both these data sets were derived from instruments using transducers with common features. They both used high-mass accelerometers, when the other measurement set-ups included lighter and smaller accelerometers. They also shared an accelerometer mounting block which was significantly larger than the other set-ups.

The unusually high results were returned during measurement of vibration of the support handle. It was conjectured that the movement of this rather flimsy structure constitutes a vibration source of lower source impedance than that of the throttle handle. This lower source impedance would make measurement of vibration of the support handle more sensitive to mass loading effects from the transducer than measurement at the throttle handle. The following analysis was performed to test that conjecture.

An equivalent circuit of the observation problem is shown below, Figure 8, in which the vibration source is seen as having explicit source impedance, Zs. The transducer, being firmly fixed to the tool in the same manner as the hand load, has equal velocity. This means that the transducer impedance and the hand load appear in series in the equivalent circuit model (which is cast as an impedance analogy).

The input impedance of the hand-arm shall be treated in three orthogonal directions, x, y, and z by three separate solutions of the equations arising from analysis of the circuit. Rotational motions are ignored. The input impedances of the hand, which loads the equivalent circuit of Figure 8, shall be those impedances defined in ISO1066 (7) or the impedance of the AVI artificial hands (above).

image 4

Figure 8 Equivalent circuit used to Analyse the Mass Loading Effect

The masses of the transducer assemblies used during Hand-Arm experiment are shown in the table below…

System #

Accel. Mass

Mount Mass

Total Mass

High results ?












Tri-axial accel.


























Not used in tests

X : data not available at time of writing

Y : not independently specified

The impedance of the transducer system shall be modelled as that of a mass equal to the total mass of the accelerometer(s) and mount, as shown in the “Total Mass” column above. This gives impedance of the form:

image 4

in which m is the total mass, ω is the angular velocity and j is the imaginary unit vector.

Given Zload (from ISO10068) and Zducer (above), it is possible to study the effects of different source impedances Zs. Given that the actual source impedance of the power tool used in the tests is unknown, the limiting cases of Zs= ∞ and Zs= 0 will be considered.

When Z s = 0 (i.e. the tool behaves as a constant force source), the velocity in the equivalent circuit of Figure 8 is proportional to the inverse of the impedance Zload+ Z xducer. In this case, the transducer has a loading effect on the vibration. When Z s = ∞ (i.e. the tool behaves as a constant velocity source) the vibration is independent of the transducer.

Thus, the effect of the transducer impedance is to introduce an observation error of magnitude:

image 4

in the context of constant force excitation. Note that the error disappears when there is no transducer present (Obs_error = 0dB for Z xducer =0) and increases with increasing mass – so the maximal total mass used in the previous experiments (m=33.2g) shall be used in subsequent analysis. (Note that a transducer system having higher total mass = 38.5g is commercially available, but this was not used in the Hand-Arm experiment for other technical reasons).

The equivalent circuit was analysed using two port techniques, as described in the MATLAB code appended to this document.

The observation error introduced by a transducer, having mass = 33.2g, instrumenting a constant force source loaded by the driving point impedance of the human hand-arm system is plotted as a function of frequency in the figures below. Figure 9 shows the observation error as a function of frequency with the three degree-of-freedom impedance defined in ISO10068. Figure 10 shows the observation error with the simpler artificial hand load. In both cases the blue trace represents the x direction, the black trace the y direction and the red trace the z direction.

image 4

Figure 9 Observation errors (in three orthogonal directions) caused by a 33.2g mass load added to a ISO10068 (3 dof) hand load

image 4

Figure 10 Observation errors (in three orthogonal directions) caused by a 33.2g mass load added to an artificial hand load

Figures 9 and 10 reveal that the magnitude of the observation error introduced by a 33.2 gram transducer system in the context of constant force excitation of a representative model of the driving point impedance of the human hand-arm generally is small and particularly is small at those frequencies where the hand-arm weighting network has greatest response (0 – 100 Hz). The vibration energy emitted from the power tool used in the Hand-Arm experiment had peak value at approximately 155Hz, associated with the no-load rotational speed of the tool. At this frequency, the worst case (Zs= 0) absolute observation error is of order 1 dB for the ISO10068 load and of order 2 dB for the artificial hands’ load. This is much smaller than the absolute observation error seen when measurement systems 4 and 5 instrumented vibration emissions from the grinder support handle. More significantly, the observation errors are of different sign.

The loading effects described in the model above cause, in most cases, a reduction in vibration (there is a slight amplification effect in the y direction in the ISO 10068 model around 100 Hz). At other source impedances, 0 < |Zs| < ∞, it is possible for resonant interaction between the total mass and the source impedance to introduce amplification effects, although this is seen as pathological. The errors noted in the experimentation were additive; measurement systems 4 & 5 in Figure 6 appeared to over estimate the support handle vibration emission by factors of approximately 6dB and 10 dB respectively (with respect to the mean result from the other instruments).

Although the analysis above suggests that the exaggerated readings in Figure 6 are not due to mass loading effects, it was made under the assumption that the hand load, artificial or real, contacts the tool at the same point as the transducer. This was not the case in the experiment, making the model of observation errors introduced by mass loading only useful as an approximation.

If mass loading is discounted as an explanation for the exaggerated readings in Figure 6, a second aspect of the large transducer assemblies used to gather data sets 4 & 5 may be significant. The larger accelerometer mounting block moves the accelerometers further from the point of contact with the handle, making the transducers more sensitive to rotational motion.




Experimentation has revealed that, whilst individual instruments are capable of producing repeatable measures of vibration, the disturbance to the total system caused by the removal and re-fitting of transducers introduces a significant measure of uncertainty. Without disturbing the transducer, repeat measurements are distributed with σ/μ < 2%, whereas the disturbance caused by transducer re-fitting broadens the distribution such that σ/μ < 7% in the Whole-Body experiment and σ/μ < 4% in the Hand-Arm experiment.

The mean weighted accelerations reported by different instruments in the same environment differ considerably. The instruments all claimed conformance to international standard, were all correctly calibrated and were used within their intended operating envelope. The experiments placed the instruments in representative, controlled, stable environments in which the greater number of the factors imposing uncertainty on practical assessment of human exposure to vibration had been removed or minimised. It would appear that the instrumentation of machines causing hand-arm vibration and whole-body vibration is subject to considerable uncertainty, in which commercially available instrumentation systems can return results differing by 25%.



The findings of this report have been presented at a Meeting of the Measurement and Instrumentation Group of the Institute of Acoustics (8). A further paper is to be presented to the September 2004 meeting of the UK Group for Human Response to Vibration.



This work was supported by the National Measurement System Directorate (NMSD) of the DTI, under Project ref. no. GBBK/1/13c, granted to AVI Ltd, Shefford, Beds., The cooperation of manufacturers and their UK agents for the loan of measuring equipment is gratefully acknowledged.



1 Pitts P (2003) Uncertainty in evaluating exposure to hand-transmitted vibration. Acoustics Bulletin Vol 28, No 5, Sep/Oct 2003

2 National Physical Laboratory: Acoustics (2004). Retrieved 2 June, 2004, from http://www.npl.co.uk/acoustics/research/theme2/hv.html

3 International Organisation for Standardisation ISO 8041:1990. Human response to vibration -- Measuring instrumentation

4 Tyler RG, A good practice guide to the use of instrumentation to measure vibration affecting people, Published by the Institute of Acoustics, July 2004

5 International Organisation for Standardisation ISO 8662-1:1988 Hand-held portable power tools -- Measurement of vibrations at the handle -- Part 1: General

6 International Organisation for Standardisation ISO 8662-4:1994 Hand-held portable power tools -- Measurement of vibrations at the handle -- Part 4: Grinders

7 International Organisation for Standardisation ISO 10068 (1998) Mechanical vibration and shock – Free, mechanical impedance of the human hand-arm system at t he driving point

8 Darlington P Measurement Uncertainty In Human Exposure To Vibration, Proceedings of “Shake, Rattle and (the) Role…”, Institute of Acoustics, 7th July 2004


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