Reduction of gravity effect on the results of low-frequency accelerometer calibration


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 365 

ACTA IMEKO 
ISSN: 2221-870X 
December 2020, Volume 9, Number 5, 365 - 368 

 
 

REDUCTION OF GRAVITY EFFECT ON THE RESULTS OF LOW-

FREQUENCY ACCELEROMETER CALIBRATION  
 

G. P. Ripper1, C. D. Ferreira2, R. S. Dias2, G. B. Micheli2 

 
1 Division of Acoustics and Vibration Metrology - DIAVI, INMETRO., Brazil, gpripper@inmetro.gov.br  

2 Vibration Laboratory - LAVIB, INMETRO, Brazil, rsdias@inmetro.gov.br  

 

Abstract: 

This paper describes a study on the possible 

sources of systematic errors during the calibration 

of accelerometers at low-frequencies. This study 

was carried out on a primary calibration system that 

uses an air-bearing vibration exciter APS Dynamics 

129 and applying the sine-approximation method. 

Tests performed and actions taken to reduce the 

effect on experimental results are presented.  

Keywords: calibration; vibration; low-

frequency; accelerometer. 

1. INTRODUCTION 

The warp of the linear guide can cause a tilt with 

variable angle of the moving table when it is linearly 

translated. This might cause a variable effect of 

local gravity on dc-responsive accelerometers as for 

instance servo-accelerometers. In the key 

comparison EURAMET.AUV.V-K3 a larger 

dispersion among the results of participants was 

evidenced at the lowest frequencies [1]. For the key 

comparison CCAUV.V-K3 [2], INMETRO have 

reported results down to 0.2 Hz. Later on, some 

efforts were made to extend the lower limit range to 

0.1 Hz but the systematic effect was high compared 

to the desired uncertainty for the service. This was 

confirmed during a measurement audit carried out 

during the peer review of Lavib. In this opportunity 

(June 2019) we could calibrate a servo-

accelerometer from PTB and quantify the problem. 

The application of a mathematical correction of 

the systematic error caused by gravity had been 

proposed by T. Bruns and S Gazioch in 2016 [3]. 

We preferred to attack the problem following a 

different approach. Instead of dealing with the effect, 

we decided to try to identify and reduce the cause.  

Therefore, we searched the responses for the 

basic questions: Can we clearly identify the cause 

and consider it is exclusively generated by the warp? 

Can we minimize the cause of the problem to reduce 

or even exclude the need of a mathematical 

correction? 

Some experiments were carried out to respond to 

these questions and the results obtained will be 

presented in the following sections. 

2. DESCRIPTION OF THE WORK  

The study started with the establishment of a 

reference condition that was nothing else than the 

result of sensitivity obtained for a servo-

accelerometer Q-Flex QA-3000.   

The calibration of accelerometers is usually carried 

out using two mountings (0° and 180°). The final 

sensitivity is the mean of the results obtained at 2 

mountings. This basic condition was used as 

parameter to evaluate the results obtained in our 

subsequent tests. 
 
2.1 INITIAL TESTS  

The influence of gravity on the accelerometer was 

first tested using different orthogonal mounting 

position (90° and 270°). Despite of the servo-

accelerometer Q-Flex being a based on a cantilever 

beam design no significant difference was observed. 

The influence of the distance of the accelerometer 

from the centre of gravity of the moving table was 

also tested. A calibration was carried out placing the 

accelerometer below the mounting plate of the 

moving table. No significant difference was 

observed. 

The influence of tilt on the measuring points used 

for calibration was evaluated by using different 

measuring distances between the laser measuring 

point and the centre axis of the accelerometer. 

Tests after loosening the screws of one end of the 

guide bar were performed and later after loosening 

the screws of both ends of the guide bar. Change on 

the behavior of sensitivity magnitude at low 

frequencies could be observed at these times. 

 

2.2 CORRECTION PROPOSED BY PTB 

The correction procedure proposed by PTB have 

also been tested by INMETRO.  Figure 1 presents 

corrected sensitivity results obtained according to 

the method proposed by Bruns and Gazioch using 

http://www.imeko.org/
mailto:gpripper@inmetro.gov.br
mailto:rsdias@inmetro.gov.br


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 366 

the same coefficient published by PTB in [3]; using 

the coefficient determined by INMETRO for its 

system; original certificate results obtained in 2018 

and in 2019; and results with 3 screws loosened at 

one side the linear guide. 

 
Figure 1: Experimental and corrected results according to 

method proposed by Bruns and Gazioch. 

Figure 1 demonstrates that the repeatability of 

the results from year to year is good, but the 

systematic error is too high at 0.1 Hz. The 

mathematical correction improves the final result 

obtained but this can be dependent on specific 

characteristics of the accelerometer under test. The 

simple test of just loosening the three screws at one 

side of the linear guide have shown the possibility 

of achieving an improvement of the sensitivity 

response measured with the interferometric system 

by mechanical means.  

Therefore, it was decided to quantify the effect 

caused by this process and take actions in order to 

improve the straightness of the guide. 

 

2.3 STRAIGTHNESS MEASUREMENTS 

The procedure applied by INMETRO to measure 

the straightness comprised the use of an 

Autocollimator Taylor Robson mounted on an 

independent seismic block, which is usually used to 

position a breadboard with the interferometer. The 

setup is shown in Figure 2. 

 

 
Figure 2: Setup used to measure the straightness of the 

linear guide of shaker APS 129. 

A plane mirror stand was positioned on the top 

of the moving table and the angle of inclination of 

this mirror was measured at different positions of 

the moving table. The zero position was taken as the 

equilibrium static point with no voltage input to the 

shaker. This is close to the mid-point of the linear 

translation guide. 

A dc-voltage source was used to provide a 

voltage of approximately 200 mV to the power 

amplifier. The gain knob of the amplifier was 

manually set to place the moving table at different 

x-positions. The measurement of the x-position was 

made with a laser distance measurer placed on the 

top of the table, which was pointed to a fixed 

reference stand on the same seismic block used to 

support the autocollimator.  

Initially, straightness measurements were made 

at the mid-point and close to the positive and 

negative limits of motion used for accelerometer 

calibrations. Absolute angles measured were -14, -

12,6 and -11,5 seconds. Normalizing these values in 

relation to the mid-point angle gives us a better view 

of the difference of the angle  measured at different 

positions of the linear guide.  This is shown in 

Figure 3. 

 
Figure 3: Difference of the angle measured at different 

positions of the moving table. 

New straightness measurements were made 

while changing the mechanical system as follows: 

1. Original measurement conditions 

2. Measurements after release of the 3 screws that 

fix the linear guide to the base 

3. Measurements after release of the 6 screws that 

fix the linear guide to the base 

4. Measurements after release of the 6 screws that 

fix the linear guide to the base and release of the 

4 screws that hold the base of the shaker to the 

seismic block 

5. Measurements after re-fixture of the 4 screws 

that hold the base of the shaker to the seismic 

block 

6. Measurements after re-fixture of the 6 screws 

that fix the linear guide to the base 

 

After applying the step 6 above, we considered 

that any stress due to mounting and assembly of the 

shaker to the seismic block have been released.  

A more refined straightness evaluation was 

made using a positioning resolution of 

approximately 10 mm. The results obtained are 

presented in Figure 4. This graph shows that the 

http://www.imeko.org/


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 367 

straightness of the system was highly improved. All 

measurement values were within ±0.2 sec relative to 

the angle at the reference point. 

 
Figure 4: Difference of the angle measured at different 

positions of the moving table after reassembly of shaker 

and linear guide. 

2.4 DYNAMIC CALIBRATION OF SERVO-

ACCELEROMETER  

Primary calibrations of a high quality dc-

response accelerometer were then carried out to 

determine the influence of the improvement 

obtained on the straightness of the linear guide. 

After the reassembly of the system, with all its 

screws retightened, calibrations of a servo-

accelerometer Allied Signal QA-3000 was 

calibrated in the frequency range 0.1 Hz to 80 Hz.  

The effect to be considered here is the deviation 

of the sensitivity magnitude response below 0.4 Hz.  

The changes are caused by the combination of 

longer displacements and change of gravity effect 

due to different angle of the accelerometer while it 

moves along the linear guide. 

The results obtained in the range 0.1 Hz to 10 Hz for 

the accelerometer QA-3000 have shown that the 

frequency response is now almost flat. Figure 5 

presents the magnitude and phase of sensitivity.  

 

 

(a) Sensitivity magnitude 

 

(b) Phase shift 

Figure 5: Sensitivity results measured after reassembly of 

the shaker APS 129 

The relative difference of sensitivity magnitude 

results are now all within 0,1 % taking as reference 

the value measured at 1 Hz. 

 

Figure 6: Relative difference of magnitude results 

relative to the sensitivity value at 1 Hz - results obtained 

after reassembly of the shaker APS 129 

2.5 STATIC CALIBRATION OF SERVO-

ACCELEROMETER  

As a final check, the calibration of the 

accelerometer sensitivity at 0 Hz was carried out by 

static rotating the accelerometer in the gravity field. 

The main sensitivity axis of the accelerometer was 

positioned at different angles relative to the local 

gravity field and the electrical output was measured. 

The range of angles from 0o to 360o was covered 

using 20o steps. Then a sine fit was applied to 

measured data to obtain the sine amplitude and 

determine the accelerometer static sensitivity. This 

was carried out using both a voltmeter Agilent 

3458A and the DAQ board NI PCI-6115 used in 

actual low-frequency accelerometer calibrations 

applying the sine-approximation method. Due to the 

difference of input impedance between these two 

measuring instruments (voltmeter: 10 GΩ and DAQ: 

1 MΩ), the voltmeter measurement results were 

corrected by approximately 0.5% to reflect the same 

impedance available at the DAQ input channel.  

Figure 7 shows that the results obtained statically 

are in close conformity with the ones obtained 

http://www.imeko.org/


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 368 

dynamically, being all within ±0.1%. This 

demonstrates the improvement obtained in the low-

frequency calibration system. 

 
Figure 7: Relative deviation of magnitude results to the 

sensitivity value at 0.1 Hz: green square - dc calibration 

with DAQ, red square - dc calibration with HP3458A 

(corrected), blue diamond - dynamic calibration results 

obtained after reassembly of the shaker APS 129. 

3. SUMMARY 

Small deviations from a purely straight linear 

motion can cause systematic errors on the 

calibration of dc-responsive accelerometers at low-

frequencies due to the effect of local gravity. This 

problem was studied at INMETRO, where 

differences as large as 0.85% were observed on 

primary calibration of accelerometers at 0.1 Hz. The 

cause identified was a warp of the linear guide, 

which cause a variable tilting angle of the moving 

table while it was translated. A procedure was 

applied to release any possible mechanical stresses 

that could occur during the mounting of the shaker 

on the inertial block and try to improve the 

straightness of the linear guide. This action was 

successful and allowed us to eliminate the main 

source of error in calibration below 0.4 Hz. 

Significant improvement of the calibration results 

was achieved and eliminated the need of further data 

correction. The estimated expanded uncertainty of 

sensitivity is 0.3% for magnitude and 0.3° for phase 

shift in the frequency range from 0.1 Hz to 10 Hz. 

4. REFERENCES 

[1] Bartoli et al, “Final Report of EURAMET.AUV.V-
K3”, Metrologia 52 09003, 2015. 

[2] Sun Qiao et al, “Final report of CCAUV.V-K3: key 
comparison in the field of acceleration on the 

complex charge sensitivity”, Metrologia 54 09001, 

2017. 

[3] Th Bruns and S Gazioch, “Correction of shaker 
flatness deviations in very low frequency primary 

accelerometer calibration”, Metrologia 53, 986, 

2016. 

 
 

http://www.imeko.org/