Measurements

1 Experimental conditions

Measurement made in a metrology lab
The granite is not glued to the floor
The Y-Translation stage is powered and in closed-loop
The spindle is not powered
Mass is placed on top of the Hexapod (how much?) (figure 1).
Made by Marc Lesourd on the 17th of November 2017

Figure 1: Accelerometers position

Figure 2: Instrumented Hammer used

2 Measurements procedure

3-axis Accelerometers (specifications table 1) are glued on (see figure 1):

Marble
Y-Translation stage
Tilt stage
top of Hexapod

Table 1: Pieozoelectric acc. 356b18 - 3 axis
Sensitivity	0.102 V/(m/s2)
Measurement Range	4.9 m/s2 pk
Frequency Range	0.5 to 3000 Hz
resonant frequency	>20000 Hz
broadband resolution	0.0005 m/s2 rms

The structure is excited using an instrumented hammer with impacts on (see figure 2):

Marble
Hexapod

3 Measurement Files

Two measurements files are:

id31_microstation_2017_11_17_frf.mat that contains:
- freq_frf the frequency vector in Hz
- Computed frequency response functions (see table 2)
id31_microstation_2017_11_17_coh.mat
- Computed coherence

For each of the measurement, the measured channels are shown on table 3.

Table 2: Description of the location of direction of the excitation for each measurement
Object name	Location	Direction
frf_hexa_x	Hexapod	X
frf_hexa_y	Hexapod	Y
frf_hexa_z	Hexapod	Z
frf_marble_x	Marble	X
frf_marble_y	Marble	Y
frf_marble_z	Marble	Z

Table 3: Description of each measurement channel
Ch. nb	Element	Location	Direction
1	Not wired	na	na
2	Accelerometer	Marble	X
3	Accelerometer	Marble	Y
4	Accelerometer	Marble	Z
5	Accelerometer	Ty	X
6	Accelerometer	Ty	Y
7	Accelerometer	Ty	Z
8	Accelerometer	Tilt	X
9	Accelerometer	Tilt	Y
10	Accelerometer	Tilt	Z
11	Accelerometer	Hexapod	X
12	Accelerometer	Hexapod	Y
13	Accelerometer	Hexapod	Z

4 Data Analysis

4.1 Loading of the data

load('./raw_data/id31_microstation_2017_11_17_coh.mat',...
     'coh_hexa_x',...
     'coh_hexa_y',...
     'coh_hexa_z',...
     'coh_marble_x',...
     'coh_marble_y',...
     'coh_marble_z');

load('./raw_data/id31_microstation_2017_11_17_frf.mat',...
     'freq_frf',...
     'frf_hexa_x',...
     'frf_hexa_y',...
     'frf_hexa_z',...
     'frf_marble_x',...
     'frf_marble_y',...
     'frf_marble_z');

4.2 Pre-processing of the data

The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.

accel_sensitivity = 0.102; % [V/(m/s2)]
w = j*2*pi*freq_frf; % j.omega in [rad/s]

frf_hexa_x =  1/accel_sensitivity*frf_hexa_x./(w.^2);
frf_hexa_y = -1/accel_sensitivity*frf_hexa_y./(w.^2);
frf_hexa_z = -1/accel_sensitivity*frf_hexa_z./(w.^2);

frf_marble_x =  1/accel_sensitivity*frf_marble_x./(w.^2);
frf_marble_y =  1/accel_sensitivity*frf_marble_y./(w.^2);
frf_marble_z = -1/accel_sensitivity*frf_marble_z./(w.^2);