*5.2.2. Comparison and analysis*

To show the comparison between the experimental result and the theoretical prediction, anisotropic MRE with graphite weight fraction 21.95% is considered. Comparison between experimental and theoretical result is provided in Fig. 26.

Figure 26 shows that the experimental and theoretical result do not match each other perfectly. However, the trends of both experimental result and theoretical result are the same.

Similarly some other comparison can be made from the data. At the fixed external force (which is expressed as load) when the magnetic field intensity increases the resistance of the sample decreases. The data under three external loads such as 1 N, 5 N and 10 N were chosen to compare the experimental and theoretical result in Fig. 27.

**Figure 25.** *λg* \* *λi* versus graphite weight fraction

276 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

shows the volume fractions of all the ingredients for this sample.

**Table 3.** Volume fractions of all the ingredients (anisotropic MRE Gr 21.95%)

φ

φ

from the ratio of experimental result and theoretical prediction.

 and exp( ) *i i* λ= ⋅ *b*

*Rg* of the anisotropic MRE with graphite weight fraction 20%.

experimental and theoretical result is provided in Fig. 26.

as -65 and 250, respectively. So the relationship of *λg* and *λi* to *<sup>g</sup>*

particles volume fraction *<sup>i</sup>*

If we set exp( ) *<sup>g</sup> <sup>g</sup>* λ= ⋅ *a*

250 *<sup>i</sup> <sup>i</sup> e*

Iron particle (

Graphite powder(

φ

*5.2.2. Comparison and analysis* 

φ

λ=

same.

ϕ

The anisotropic MRE with graphite weight fraction 21.95% (contains 10g iron particles, 3g silicone rubber, 3g silicone oil and 4.5g graphite powder) can be used as an example. Table 3

Mass(g) Density(g/cm3) volume(cm3) Volume fraction

The factors showing the efforts of graphite and iron particles to the resistance in Gr-MREs

shows the product of *λg* and *λi* versus Gr-MREs (Gr 20%, 21.95% and 23.81%). The data is

and *λi*, the parameters *λg* and *λi* can be obtained and so the parameter *a* and *b* were derived

*i )* 17.09% 16.5% 15.96%

After having determined all parameters, Equation 10 is ready to calculate the final resistance

To show the comparison between the experimental result and the theoretical prediction, anisotropic MRE with graphite weight fraction 21.95% is considered. Comparison between

Figure 26 shows that the experimental and theoretical result do not match each other perfectly. However, the trends of both experimental result and theoretical result are the

Similarly some other comparison can be made from the data. At the fixed external force (which is expressed as load) when the magnetic field intensity increases the resistance of the

*g )* 28.27% 30.7% 33.01%

Gr 20% Gr 21.95% Gr 23.81%

. For each sample there are different values for *λg* and *λi*. Fig. 25

and substitute the data in Table 4 and Fig. 8 to *λ<sup>g</sup>*

φ and *<sup>i</sup>* φare φ

and iron

65\* *<sup>g</sup>*

<sup>−</sup> = ,

ϕ

*<sup>g</sup> e*

λ

Iron particle 10 7.86 1.272265 16.50% Silicone rubber 3 3.18 0.943396 12.24% Silicone oil 3 0.96 3.125 40.54% Graphite powder 4.5 1.9 2.368421 30.72%

are *λg* and *λi* respectively and *λg* and *λi* depend on the graphite volume fraction *<sup>g</sup>*

φ

**Table 4.** Volume fractions of iron and graphite (anisotropic MRE Gr 20%, 21.95% & 23.81%)

**Figure 26.** Comparison between experimental result and theoretical result (anisotropic MRE Gr 21.95%)

**Figure 27.** Resistance changing at a fixed load (anisotropic MRE Gr 21.95%)

The Fig. 27 shows the change in the resistance for given external forces. Along with the raising of magnetic field intensity, the sample's resistance decreases. The higher external load applied leads to lower resistance of Gr-MREs.

The next two figures Fig. 28 and 29 show the resistance variation between anisotropic MREs with graphite weight fraction 20%, 21.95%, and 23.81%. The magnetic field is fixed in Fig. 28 and the external load is fixed in Fig. 29.

**Figure 28.** Resistance between different sample at 117.8mT magnetic field (anisotropic MRE with graphite weight fraction 20%, 21.95% & 23.81%

**Figure 29.** Resistance between different samples at 5.1N external load (anisotropic MRE with graphite weight fraction 20%, 21.95% & 23.81%)

Because of the order of values for the three samples it is easy to see from the Fig. 28 and 29 that theoretical and experimental results can match each other very well. This again provides a proof of the theory and when either external load or magnetic field intensity increases the resistance decrease.

Therefore when the magnetic field intensity and resistance are measured, Equation 10 can be used to calculate the value of the external load which means the Gr-MREs have the potential to work as the key component in a force sensor.
