Page 32 - EngineerIT March 2022

MEASUREMENT

Table 7 presents the simulation results, with some interesting
findings:
• For smaller sensor heights, and where the height is equal to the
length/ width, the epoxy resin boosts the first significant natural
frequency in the cantilevered axis (z) by up to 75%.
• Where the sensor height of 80 mm is 2× the length/width, the
first significant natural frequency in the cantilevered axis (z)
increases by 16% when using an epoxy resin fill. However, the x
and y radial axes reduce by 10%.
• As the height increases to 3× of the length/width, the epoxy
resin reduces the first significant natural frequency.

As height increases, the mass increases and the stiffness decreases.
At a certain point, the mass increase has a greater influence than
the added epoxy stiffness. For the given simulation example, this
inflection point is at greater than 80 mm. However, most sensors
are usually less than 80 mm in height. So, it can be concluded that,
for most cases, adding epoxy resin will aid the natural frequency
performance for a vibration sensor enclosure solution.
Figure 27. Cable and sensor model with material properties and 0.15 m
cable length
External cable simulation
After mounting a vibration sensor on a machine surface, the cable model is supported with a fixed constraint on the sensor attach,
should be anchored to reduce stress at cable terminations and to and the 0.15 m cable is free to vibrate along its length. The 0.15 m
prevent false signals due to cable vibration. When securing the cable, cable length can be increased to 1 m for simulation.
leave enough slack to allow free movement of the accelerometer. 7
This section simulates the effect of a vibrating cable on system Table 8 provides the simulation results, with some key findings:
response and provides guidance as to where the cable should be • If the cable is clamped at less than 0.15 m length, then the cable
clamped (at what cable length). effect on the vibration sensor frequency response is minimal.
A simulation model was created, with the material properties Both with and without a 0.15 m cable, the frequency response of
as shown in Figure 27. TE provides connector and cable models, the sensor enclosure is above 11 kHz.
such as the TAA545B1411-002, which can be used as a baseline. • If 1 m of cable is attached to the sensor and allowed to move
The cable connector is made from nylon (Nylon 6/6), with copper freely and vibrate along its entire length, then the added cable
cable wire and PVC insulation. The attached sensor is designed mass will dominate the system frequency response. The cable
using stainless steel and filled with epoxy resin. The simulation frequency response of 500 Hz will become the dominant mode.

In reality, it is unlikely that an entire 1m cable will vibrate, as the
Table 7. Height (mm), epoxy fill (Yes/No), and first significant natural
frequency for a 2 mm wall Thickness of a 40 mm (Length) × 40 mm vibration will be dampened with increased cable length. However,
(Width) stainless steel cube this simulation example shows that anchoring at around 0.15 m is a

Height (mm) Epoxy Fill? X Freq. (Hz) Y Freq. (Hz) Z Freq. (Hz) good idea for accurate system response.
40 No 8547 8450 9291
Vibration sensor mounting
40 Yes 8586 8585 16,259
Figure 28 shows the effect on mounting resonance and typical
80 No 3943 3943 9716
usable frequency range for the stud, adhesive, adhesive mounting
80 Yes 3567 3530 11,272 pad and flat magnet techniques shown in Figure 29. Stud and
120 No 2208 2208 9293 adhesive mounting places the sensor as close as possible to the
120 Yes 1906 1906 8045 machine, with best coupling of vibration signal from machine
to MEMS sensor. Using a fixture with an adhesive mounting
Table 8. Cable length (m) and first significant natural frequency (Hz), pad places additional metal material between the machine and
with and without a connected vibration sensor enclosure sensor. This additional material dampens the frequency response

Cable Length (m) Sensor Used in Simulation? Z Frequency (Hz) of the sensor solution. The flat magnet mount also dampens
1 Yes 464 the frequency response and does not provide as good a fixed
attachment to the equipment as the other methods.
1 No 508
Figure 28 provides typical guidelines only, and each sensor
0.15 Yes 11,272
should be characterised via lab measurement or simulation.
0.15 No 11,568
Simulation of stud mounting with ANSYS modal analysis is

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