Page 27 - EngineerIT March 2022

MEASUREMENT

Table 6. Area moment of inertia (IYY), shear modulus (G), density (ρ),
and cross-sectional area (A) for 1 mm and 2 mm wall thickness of a
40 mm height cylinder
Shape IYY (m4) G (N/m ) ρ (kg/m ) A (m ) 2
3
2
Cylinder, 2 mm wall 6.24E-8 7.7E10 7850 1.03E-3
Cylinder, 1 mm wall 3.12E-8 7.7E10 7850 5.28E-4

What is the effect of reducing enclosure wall thickness or
diameter?
Reducing enclosure wall thickness
Table 6 shows the geometric and material properties if the cylinder
in Figure 6 is reduced from a 2 mm to a 1 mm wall thickness but
keeps the 40 mm height and 43 mm outer diameter.
Using the Table 6 values and equation 5, the critical frequency
is 60.74 kHz for the 2 mm wall thickness cylinder and 61.48 kHz for
the 1 mm wall thickness cylinder. With both I YY and A parameters
decreasing by about 50%, the numerator and denominator in
equation 5 are equally affected for the 1 mm wall thickness
cylinder. From this calculation it is assumed that both cylinders will
perform similarly in FEM modal analysis.
In Figure 11, the FEM results of first natural frequency with
significant MPF (greater than 0.1 for the ratio of effective mass to Figure 12. Enclosure diameter study.
total mass of the system) is plotted vs. cylinder wall thickness. The
effect of reducing the cylinder wall thickness compared to natural the x and y axes’ first natural frequencies reduce by about 1.5 kHz,
frequency is very small. while the z-axis first natural frequency increases by 1.9 kHz. In
changing the cylinder diameter, both the area moment of inertia
Reducing enclosure diameter (I YY) and the cross-sectional area (A) decrease. The I YY parameter
The examples presented so far have all focused on cylindrical will decrease more than the A parameter.
enclosures with a 43 mm outer diameter. Some designs may only In reducing the diameter from 43 mm to 30 mm, the I YY will
require 30 mm or 26 mm outer diameters. Figure 12 illustrates the reduce by 2/3, while the A will reduce by 1/3. Again, referencing
simulation model, and Figure 13 shows the effect of varying the Equation 5, the net effect is a gradual decrease in first natural
outer diameter of the enclosure. frequency. Intuitively, reducing the cylinder diameter will make the
When reducing the cylinder diameter from 43 mm to 26 mm,

Figure 11. First significant natural frequency (Hz) for a cylinder with 1 mm
or 2 mm wall thickness Figure 13. First significant natural frequency vs. cylinder outer diameter

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