Calculation of Loss-Factor

Modeling and Evaluation of Dehydration Effect on Tip Position and Bending Response of IPMC Actuator

3.2 Calculation of Loss-Factor

A new term ‘loss-factor’ is introduced in this work for estimating the loss of moisture/water content from IPMC. Experiment is conducted with an IPMC actuator of size 20 5 0.2× × (mm³) (Figure 3.1) with varying input voltage. The IPMC used in the experiment is based on silver electrode with Nafion-117 as the base polymer (fabricated at Mechatronics laboratory, IIT Guwahati) as shown in Figure 3.1(a) while Figure 3.1(b) shows the experimental setup (which is same as Figure 2.15) to obtain the bending characteristics of the IPMC actuator subjected to input voltage (V).

(a) (b)

Figure 3.1 (a) Silver electroded IPMC fabricated at IIT Guwahati (b) Experimental setup.

Figure 3.2 Schematic diagram of the experimental setup and bending configuration of an IPMC actuator for an input voltage V.

Figure 3.2 shows the schematic diagram for bending configuration. Experiment is conducted in hydrated state in fixed-free configuration by applying voltage quasi- statically from a DC power supply (0-32V DC, 0-2 A) through copper strips at the fixed end. Subsequently, the tip deflection of IPMC is measured and the bending characteristics are obtained. Experimentally dehydration loss is studied for the same IPMC sample subjected to input voltage from 0.2V to 1.2V with an increment of 0.2V. For each input voltage after 30s (sufficient time is allowed to settle any back relaxation effect and to attain the steady-state) the tip position (p_xd,p_yd) of the IPMC has been measured which are given in Table 3.1. The experiment is carried out for five samples and it is observed that the variation is negligible. The average value is given in Table 3.1.

Table 3.1 Tip position and angle of IPMC actuator with ‘positive’ and ‘zero’

dehydration.

X- Coordinate

( )

px (mm)

Y-Coordinate

( )

py (mm)

Tip angle (rad) Input

voltage (V)

Time (s)

pxd p_x0 p_yd p_y0 ϕ_d ϕ₀

0.2 30 19.7 19.8 1.0 1.1 0.10142 0.11098

0.4 60 19.5 19.6 2.1 2.3 0.21454 0.23362

0.6 90 18.9 19.0 4.7 5.1 0.48746 0.52446

0.8 120 17.8 18.0 7.2 8.0 0.76874 0.82714

1.0 150 16.1 16.0 9.4 10.8 1.0569 1.20238

1.2 180 13.4 12.8 12.5 14.5 1.50128 1.69516

Similar way, a fully hydrated IPMC sample has been taken for each time and experimentally the tip position (p_x0,p_y0) (zero dehydration), for each input voltage is obtained. After each experiment IPMC is retrieved and allowed to hydrate in aqueous deionized water and used for another set of experiment. At the starting of the experiment, the IPMC is considered fully hydrated i.e., moisture content is

considered 100% (reference value), while dehydration is zero. The obtained tip positions for ‘zero dehydration’ are given in Table 3.1. Following Bandopadhya et al., (2009) the tip angle

( )

^ϕ as shown in Figure 3.2 can be obtained as:

2 tan (1 p_y/ p_x)

ϕ= ⁻ . The tip angle with ‘zero dehydration’ (ϕ₀) and ‘positive dehydration’ (ϕ_d) are calculated using the above formula and are given in Table 3.1 for various input voltages.

A term ‘loss factor’ (λ) is introduced by correlating loss in bending moment due to dehydration. As there is loss in bending moment due to dehydration during working, the bending moment at any instant (t) for an input voltage (V ) can be expressed as:

0 0

Md =M −M λ (3.1)

where,M_d,M₀ are the bending moment of the actuator for ‘positive’ and ‘zero’

dehydration respectively.

Assuming pure bending, i.e.,

c

EI EI EI

M R l l

ϕ

= ϕ

= = , equation (3.1) reduces to

0(1 )

EI d EI

l l

ϕ ϕ

= −λ (3.2)

Simplifying the equation (3.2), one can rewrite the equation as:

0

1 ϕ^d

λ ^{= −}ϕ ^(3.3)

where, EI is the flexural rigidity of IPMC and R_cis the radius of curvature;

and 0

ϕd ϕ are the measurable parameters. As the IPMC dehydrates continuously in working condition, the primary goal is to develop an empirical model satisfying the working condition which can predict the loss of dehydration for any instant (t) and input voltage (V ). Experimentally it is observed that the tip position and hence the tip angle depends on the applied voltage and actuation time while assuming temperature remains constant during the experiment. Therefore, the loss-factor also depends on these parameters and hence a power fit correlation is proposed as:

( , )V t V t^{a b}

λ = ϒ (3.4)

where,ϒ,a,bare the constants and depend on the material properties. Equation 3.4 also can be written as

( ) ( ) ( ) ( )

ln λ( , )V t =ln ϒ +aln V +bln t (3.5) The goal is to develop a power fit correlation using Cobb-Douglas production method which correlates the loss-factor

( )

^λ in terms of input voltage

( )

^{V and}

actuation time (t). Using equation 3.5 and the experimental data given in Table 3.1, a set of equations have been developed which are solved by the Cobb-Douglas production method. The resulting expression for the loss-factor is obtained as:

0.7184 0.681

( , )V t 0.9626V t , V 0 ,t 0

λ = ⁻ ≥ > (3.6)

Loss-factor for various voltages with time has been calculated subsequently and is given in Table 3.2. It is observed that with constant input voltage, loss-factor decreases continuously with time, although, it increases as the input voltage increases.

Table 3.2 Loss-factor for various input voltages and time.

Volt Loss-factor

( )

^λ with time (t)

10s 20s 30s 40s 50s 60s 70s 80s 90s 100s

0.2 V 0.0631 0.0394 0.0299 0.0246 0.0211 0.0186 0.0168 0.0153 0.0141 0.0132 0.4 V 0.1039 0.0648 0.0492 0.0404 0.0347 0.0307 0.0276 0.0252 0.0233 0.0217 0.6 V 0.1390 0.0867 0.0658 0.0541 0.0465 0.0410 0.0369 0.0337 0.0311 0.0290 0.8 V 0.1709 0.1066 0.0809 0.0665 0.0571 0.0505 0.0454 0.0415 0.0383 0.0356 1.0 V 0.2007 0.1252 0.0950 0.0781 0.0671 0.0592 0.0533 0.0487 0.0449 0.0418 1.2 V 0.2287 0.1427 0.1082 0.0890 0.0764 0.0675 0.0608 0.0555 0.0512 0.0477

Figures 3.3(a) and (b) show the variation of loss-factor with actuation time and applied voltage, respectively. These results are in good agreement with the observation that initial water content decreases with time, Enikov and Seo, (2005).

Further, it is also observed that larger electric potential enhances more water loss Yeh and Shih, (2010). Further, it is observed that for a given input voltage, as the loss-factor decreases with time there is gradual reduction of actual bending moment and the tip deflection of the actuator. Table 3.3 shows both the estimated data (using equation (3.6)) and the observed data at zero dehydration for 30s.

Figure 3.3 (a)

Figure 3.3 (b)

Figure 3.3 Variation of loss-factor with (a) time (b) input voltage.

Table 3.3 Comparison between the estimated data (using equation (3.3)) and the observed data (zero dehydration).

Observed data (mm)

Estimated data (mm) Voltage

(V)

px p_y p_x p_y

% difference in X-Coordinate

% difference in Y-Coordinate

0.2 19.8 1.1 18.1096 1.0308 8.53 6.29

0.4 19.6 2.3 18.2748 2.2087 6.76 3.96

0.6 19.0 5.1 17.9479 5.0310 5.53 1.35

0.8 18.0 8.0 17.0362 7.8338 5.35 2.07

1.0 16.0 10.8 15.4272 10.3867 3.58 3.82

1.2 12.8 14.5 12.5206 14.0166 2.18 3.33