Analysis of Time Dependent Bending Response of Ag-IPMC Actuator

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 144 (2016) 600 – 606

12th International Conference on Vibration Problems, ICOVP 2015

Analysis of Time Dependent Bending Response of Ag-IPMC Actuator Dillip Kumar Biswala*, Biswajit Nayakb a

Department of Mechanical Engineering, C.V. Raman College of Engineering and Technology, Bhubaneswar, Odisha-752054, India b Department of Mechanical Engineering, Centurion University of Technology and Management, Jatni-752050, India

Abstract In this work, time dependent bending characteristics of Silver electrode Ionic Polymer Metal Composite (IPMC) has been studied under potential gradient. Euler-Bernoulli approach has been followed for obtaining the bending moment generates taking into account of the applied voltage. Kinematic modeling is done for the Ag-IPMC actuator after constituting the homogeneous coordinate transformation. Based on the forward kinematic model, energy based dynamic model of the IPMC actuator has been formulated following the Lagrangian principle. The motion of the patches is restricted as planar in 2D. Simulation has been done for Ag-IPMC actuator based on the experimental deflection data to demonstrate the time dependent response for different sequence of input voltages. © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICOVP 2015. Peer-review under responsibility of the organizing committee of ICOVP 2015

Keywords: Ionic Polymer-Metal Composite (IPMC); Lagrangian; Homogeneous Co-ordinates; Torsional Spring Constant

1. Introduction Ionic polymer metal composites (IPMCs) are one type of electro-active polymer that is gaining lot of importance nowadays as actuator and sensor. IPMCs are active actuators that show large bending deformation with the application of low actuation voltage and it induces large bending strain, led to its consideration for various potential applications like robotics, aerospace and biomimetics [1- 4].

* Corresponding author. Tel.: +91- 904-045-0180; fax: +91- 674- 211-3593. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICOVP 2015

doi:10.1016/j.proeng.2016.05.047

Dillip Kumar Biswal and Biswajit Nayak / Procedia Engineering 144 (2016) 600 – 606

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A typical IPMC consists of a thin polyelectrolyte membrane (usually Nafion® or Flemion®) and is chemically plated on both faces of the membrane by a noble metal such as gold and platinum. An IPMC undergo a large bending deformation when an external electric potential is applied across the material. Conversely, a measurable electric potential is developed across the strip when it is subjected to a bend or twist. Thus IPMC can serve as both actuator and sensor. An IPMC offers advantages, such as compliant, lightweight, low voltage operation and capability of working in water medium. These properties make it promising for numerous applications in biomedical, naval, robotic and microelectromechanical system (MEMS) engineering [5-10]. Based on electrostatic interaction of ion transport, a model was presented by Nemat-Nasser and Li [11]. Further, micromechanics of IPMC material was investigated by Nemat-Nasser, and proposed a hybrid model considering electrostatic, osmotic and elastic effects in the actuation process [12]. A technique to minimize dehydration loss and to increase the force density of IPMCs was proposed by Shahinpoor and Kim [13]. A linear electro-mechanical-model was developed by Newbury and Leo for IPMC transducers considering the visco-elastic property [14]. Extensive experimental studies on IPMCs with different backbone ionomers and various cation forms have been conducted by Nemat-Nasser and Wu [15]. A computational micromechanics model was proposed by Weiland and Leo, to assess the impact of uniform ion distribution on spherical clusters of IPMC ionomer [16]. Here, a silver electrode IPMC has been fabricated using chemical deposition process, and modelling is done considering distributed pressure during bending motion following the Euler-Bernoulli method. Further, energy based model of the Ag IPMC actuator has been derived following the Lagrangian principle considering hydrated condition. Euler-Bernoulli approach has been followed to get the end-tip position of the Ag IPMC actuator. Simulation has been performed based on the experimental bending deformation data for different applied voltages to demonstrate time dependent response of the tip position. The results clearly demonstrate the time dependent response of the Ag IPMC actuator for various input voltages in fully hydrated condition. 2. Bending Characteristics of IPMC An IPMC actuator of silver electrode is prepared and cut into a size of 20 u 5 u 0.2 mm3 for the experimental study. For fabrication of IPMC actuator a Nafion-117 membrane with a standard thickness of 0.183 mm is used as the base polymer. The process comprises pretreatment, adsorption, reduction, and development.

Fig. 1. Photograph of the (a) Nafion-117 membrane and (b) Fabricated ionic polymer–metal composite

The detailed fabrication process is outlined in [17]. The photographs of the Nafion membrane and the fabricated Ag IPMC are shown in figure 1(a) and (b), respectively. Figure 2 shows the experimental setup to obtain the bending characteristics of the IPMC actuator subjected to input voltage ( V ). The experiment is conducted in hydrated state in a cantilever mode. Voltage is applied from a DC power supply through copper strips attached to the fixed end and the tip deflection of Ag IPMC is measured. The radius of curvature R of bent IPMC for an externally applied voltage V is obtained as R L / T . Where, L is the length of the IPMC and T is the tip angle of IPMC. From figure 2(b), tip position P( px , p y ) , tan D p y / px , further using Euler-Bernoulli equation of curvature we may write, dT ds

M (1) EI where, dT is the rate of change in angular deflection along the IPMC strip (curvature s), M is the bending moment ds generated due to input voltage V and EI is the flexural rigidity of IPMC.

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Dillip Kumar Biswal and Biswajit Nayak / Procedia Engineering 144 (2016) 600 – 606

Fig. 2. (a) Experimental setup and (b) Bending configuration of IPMC for an input voltage V

Using equation (1) and on integration one can obtain the end point coordinates as: EI EI px sin T ; p y (1  cos T ) M M

(2)

From equation (1) and (2) we can obtain,

tan D

py

1  cos T

px

sin T

tan

T

ŸT

2D

(3)

2

Using equation (2), the tip position of the IPMC actuator is plotted for various input voltages and is shown in figure 3.

Fig. 3. Tip position of the IPMC actuator following Euler-Bernoulli method

3. Modeling of IPMC Actuator Euler-Bernoulli approach has been followed to evaluate the bending response of the IPMC actuator based on forward kinematic model. It is assumed that IPMC bends with linear curvature with a tip angle T , this angle varies with input voltages as shown in figure3. Large deflection assumptions have been made in this equation, as the

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Dillip Kumar Biswal and Biswajit Nayak / Procedia Engineering 144 (2016) 600 – 606

integration is done with respect to length (curvature, s ) the distance along the strip rather than with respect to X , the horizontal distance. 3.1. Kinetic energy of IPMC Actuator Using Euler-Bernoulli equation for large deflected IPMC, dT

M

ds

EI

, the tip position of the IMPC actuator may be

obtained as: EI

px

M

EI

sin T ; p y

(1  cos T )

(4)

M

The kinetic energy of the system is the sum of the kinetic energy of IPMC actuator and the payload. As in this case payload is considered as zero, the kinetic energy of the system is the kinetic energy of the IPMC actuator only. Since the velocity at any point on the strip depends on the position and time, hence, kinetic energy of the system/strip at any time is an integral over the length of the strip. Using equation (4), EI

px

cos T .T and

EI

py

M

sin T .T

(5)

M

Therefore, velocity at the tip point is obtained as 2

v

2

2

2

px  p y

2

§ EI · ª 2 § EI · 2 2 2 ¨ ¸ ¬cos T  sin T º¼ T ¨ ¸ T M © ¹ ©M ¹

(6)

Thus, kinetic energy of the system is obtained as

KE

KElink

1

mv

2

2

v

2 l

2

³ U Ads

(7)

0

Where, m is the mass of the link, U is the mass density and A is the cross section of IPMC. Therefore, total kinetic energy is obtained as:

KElink

2

§ EI · 2 ¸ T 2 ©M ¹

1

m¨

where, m

(8)

U Al

3.2. Potential energy of IPMC Actuator Potential energy of the system is due to the gravity and torsional spring of IPMC i.e. PE PE1  PE2 . Where, PE1 is the potential energy due to gravity and PE2 is the potential energy due to torsional spring. However, the potential energy due to gravity can be neglected as the motion of the patch is restricted to two dimensional coordinates. Potential energy due to torsional spring is given by: 1 2 PE PE2 KT (9) 2 where, K is the torsional spring constant.

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Dillip Kumar Biswal and Biswajit Nayak / Procedia Engineering 144 (2016) 600 – 606

3.3. Governing equation of IPMC Actuator After getting the expression for both total potential energy and kinetic energy, the Lagrangian of the system is obtained as:

L

KE  PE

§ EI · T 2  1 KT 2 m¨ ¸ 2 ©M ¹ 2 2

1

(10)

Therefore, governing equation of the system is expressed as:

§ wL ·  wL ¨ ¸ dt © wT ¹ wT d

M (11)

§ EI · T  KT m¨ ¸ ©M ¹ 2

ŸM

Incorporating the damping into the system governing equation may be written as: 2

M

§ EI · m¨ ¸ T  CT  KT ©M ¹

(12)

where, C is the damping factor of IPMC. The state-space representation of the system is given by: 0 ª « d ªT º K « 2 « » dt ¬T ¼ « § EI · m ¨ ¸ ¬« © M ¹

º ª 0 º » « » C 1 ªT º » « » M   2 2 « » EI · » ¬T ¼ « § EI · » § m¨ m¨ ¸ ¸ ¬« © M ¹ ¼» © M ¹ ¼» 1

(13)

4. Result and Discussion In this section, results obtained from numerical simulation based on the fabricated Ag IPMC actuator properties and the experimental tip deflection data. The tip deflections data are taken for 30 seconds for each input voltage. All programs are developed in MATLAB. A function called ‘ode45’ is used to solve the differential equation in state space. Property

E l

w h

U

K m C

Table 1. Physical properties of Ag-IPMC material. Ag-IPMC

Elastic modulus Length Width Thickness Density

0.081877 GPa 0.02 m 0.005 m 0.0002 m 2125 kg/m3

Torsional spring constant Mass

1.3646 u105 Nm 5.56 u105 kg

Damping Co-efficient

5.7712 u108 Nm/rad

Fabricated Ag IPMC actuator has been analyzed and time dependent bending response has been studied based on the experimental data. Experimentally bending deflection of IPMC actuator has been observed for 30 seconds. Both tip position and rate of change of tip position has been evaluated for the time period to show the performance of the system.

Dillip Kumar Biswal and Biswajit Nayak / Procedia Engineering 144 (2016) 600 – 606

Fig. 4. Response of the IPMC for each input voltage

605

Fig. 5. Step response of the system transfer function of IPMC for each input voltage

The damping factor is calculated by using the formula C 2[Z , where, [ 0.018 is the damping coefficient of IPMC obtained experimentally. Figure 4 shows the bode diagram of the system transfer function of the IPMC for input voltage of 0.2; 0.6; and 1.0 V respectively, while figure 5 is showing the performance of the system for step disturbance applied on it. From figure 4 it can be observed that, as the input voltage increases from 0.2V to 1.0V with a step of 0.2V, its gain crossover frequency (magnitude of the system at 0 dB) and phase margin of the system shows steep changes at that frequency. All the curves showed one resonant peaks between 0.253 to 1.23 rad/s for applied voltage of 0.2 to 1.0 V, and their phase plots were almost identical Moreover, the plot also revealed that the bending angles in response to unit driving potential at different driving amplitudes were different. Figure 5 shows the change in dynamic tip displacement for input voltages 0.2 V, 0.6 V and 1.0 V. It is observed that the change in tip displacement is maximum just immediately after the input voltage has applied and gradually diminishes before reaching the steady-state. At steady-state condition, no bending response of the IPMC is observed. Form the figure it is also observed that due to moisture loss from the IPMC actuator the amplitude is also decreases as the applied voltage is increases. 5. Conclusion The paper addresses modeling and analysis of time dependent bending response of silver coated IPMC based on experimental data. Dynamic modeling of IPMC has been done after formulating the forward kinematic model of IPMC following Euler-Bernoulli approach. It is observed that as the voltage increases, the response of the IPMC diminishes in faster rate. Further, these concept of multi-segmented IPMC patches have potential application in micro-robotics and as well as in compliant mechanisms.

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