VIBRATION DAMPING CHARACTERISTICS OF CANTILEVER BEAM USING PIEZOELECTRIC ACTUATOR

Transcription

1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 6, June 2017, pp , Article ID: IJMET_08_06_023 Available online at aeme.com/ijmet/issues.asp?jtype=ijmet&vtyp pe=8&itype=6 ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed VIBRATION DAMPING CHARACTERISTICS OF CANTILEVER BEAM USING PIEZOELECTRIC ACTUATOR R. Ganesh Assistant Professor, Department of Mechanical Engineering, Veltech Dr.RR & Dr.SR University, Chennai, India K. Karthik Assistant Professor, Department of Mechanical Engineering, Veltech Dr.RR & Dr.SR University, Chennai, India A. Manimaran Professor, Department of Mechanical Engineering, Veltech Dr.RR & Dr.SR University, Chennai, India M. Saleem Assistant Professor, Department of Aeronautical Engineering, Veltech Dr.RR & Dr.SR University, Chennai, India ABSTRACT Vibration is present in countless real life applications, and most of the time it is a highly undesirable phenomenon. Unwanted vibration may decrease product performance, cause economic or safety problems. Monitoring and control of vibrations has become important for the aims of many engineering systems, Advances in smart materials have shown increased interesting applications for passive and active attenuation. The advanced Technologies of smart materials lead to relatively small and light actuators and sensors with good physical integration, In general, the efficiency of passive damping materials in suppressing of mechanical vibrations is insufficient for the range of low frequencies. The resulting strong vibrations can damage or totally destroy the structure. In the case of machining devices, the undesired vibrations lead to decreased precision of products. To avoid the disadvantages of passive damping elements, piezoelectric materials have come to wider use that can be well controlled in a wide range of frequency, without adding great amount of mass to the structure. The actuators that are built in the controlled structure produce force on a given object. The signal that controls the actuator arises from the control system obtaining feedback from sensors that can be also built in the controlled structure. The research of piezoelectric materials is fast gaining attention and it is expected that this technology will upgrade the quality of production in engineeringg industry editor@iaeme.com

2 R. Ganesh, K. Karthik, A. Manimaran and M. Saleem Key words: Vibration control, Damping, Piezoelectric materials, Beam Analysis. Cite this Article: R. Ganesh, K. Karthik, A. Manimaran and M. Saleem. Vibration Damping Characteristics of Cantilever Beam Using Piezoelectric Actuator. International Journal of Mechanical Engineering and Technology, 8(6), 2017, pp INTRODUCTION Piezoelectricity was discovered by Jacques Curie and Pierre Curie in The piezoelectric effect is the generation of an electric charge as a result of a force exerted on the piezoelectric material. The Curie brothers demonstrated the first piezoelectric effect by using crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt. The reverse piezoelectric effect is the term given to the phenomenon in which an applied electric field produces a mechanical strain the piezoelectric materials. The reverse piezoelectric effect was first predicted by Gabriel Lippmann in 1881, and was demonstrated experimentally by the Curie brothers in the same year. The first serious applications work on piezoelectric devices took place during World War I, which was the sonar device. Most of the piezoelectric applications such as microphones, accelerometers, ultrasonic transducers, benders etc. were conceived after the first world war. The direct piezoelectric effect consists of the ability of certain crystalline materials (i.e. ceramics) to generate an electrical charge in proportion of an externally applied force. The direct piezoelectric effect has been widely used in transducers design (accelerometers, force and pressure transducers etc.). According to the inverse or reverse piezoelectric effect, an electric field induces a deformation of the piezoelectric material. The inverse piezoelectric effect has been applied in actuators design. Because of their light weight and high performance piezoelectric materials are widely used as actuators and sensors for noise and vibration control especially in high precision areas like space structures, airplane industries etc. There are two classes of piezoelectric materials used in vibration control: ceramics and polymers. The best known piezoceramic is the Lead Zirconate Titanate (PZT); it has a recoverable strain of 0.1% and is widely used as actuator and sensor for a wide range of frequencies, including ultrasonic applications; it is well suited for high precision as well. Piezopolymers are mainly used as sensors; the best known is the Polyvinylidene Fluoride (PVDF). For actuation and sensing purposes piezoceramic materials are usually used in the form of monolithic wafers, as single and continuous piece of piezoceramic, free from added materials. However monolithic piezoceramic wafers possess some serious disadvantages. They are brittle in nature and cannot be bonded to irregular shapes. In order to overcome these difficulties stack actuators were introduced. In PZT stack actuators, high displacement has been achieved for low voltage by staking piezoelectric laminate one above the other. The development of piezo-stacks encouraged the material scientists to develop piezoelectric fibers and actuate them axially to generate larger actuation strain. These piezoelectric fibers are then embedded inside a polymeric matrix to form composite actuator and sensor. Two types of smart composites have been developed using piezo-ceramic fibres; Active Fiber Composite (AFC) Macro Fiber Composite (MFC) The difference between AFC and MFC is in the manufacturing process of the fiber. While the AFC fibres are developed using standard sol-gel technique, the MFC fibres are essentially chopped from PZT blocks. The MFC fibres are rectangular in cross-section and hence it offers better electrical contact between the fibres. Piezoelectric composite fibres are commonly editor@iaeme.com

3 Vibration Damping Characteristics of Cantilever Beam Using Piezoelectric Actuator employed for actuation and sensing purposes, structural health monitoring and active/passive vibration damping. 2. EXPERIMENTAL POCEDURE 2.1. Smart Materials and Structures A smart structure senses environmental change and the responses to that change utilizing electronic processing. The components of a smart structure are, 1. Sensors: Sensors monitor environmental changes and generate signal proportional to the changing property that can be measured. 2. Actuators: Actuators provides the desired response by changing the properties of the smart structure. 3. Control systems: Control systems monitor the sensor s signal and applies a signal to the actuator for necessary action. The schematic view of a smart structure is shown in Fig. Figure 1 High Degree of integration 2.2. Flexural Vibration of Beams A beam is a structure member subjected to lateral loads, that is, forces or moments having their vectors perpendicular to the longitudinal axis (Liu, 2012). Beams are usually described by the manner in which they are supported. For example, the fixed boundary condition restricts both linear DOFs and the rotational DOF. No movement is allowed at the support. Flexural beams can be classified according to the combination of two mechanical boundary conditions associated with it. For example, a beam fixed at one end and free at another is conveniently referred to as a fixed-free beam, commonly called a cantilever. Actuators play a key role in all air, space and defence vehicles. Selection of actuator and actuation mechanism is more important as it directly affects the safety of the system. This paper reviews the use of electromechanical actuators (EMAs) and smart actuators for a helicopter Swash plate actuation system and an aircraft Trailing edge flap actuation system. EMAs are based on a rotary electric motor and gears to transform the motion from rotary to linear. One of the major limitation of electromechanical actuators is their positional accuracy. Smart material actuators have better nano positioning abilities and are used by space, defence and aircraft governmental agencies, such as DARPA or NASA. Smart materials are active materials that mechanically respond under a non mechanical excitation (Electric, magnetic, thermal, etc.). Smart material actuators includes Induced Strain Actuators (ISA) and Piezo motors. Induced Strain Actuators (ISA) use the strain of the smart materials to cause the actuator motion and they offer high resolution on limited stroke. Electro Active Polymers editor@iaeme.com

4 R. Ganesh, K. Karthik, A. Manimaran and M. Saleem (EAP), Shape Memory Alloys (SMA), Magnetostrictive & Magnetic Shape Memory (MSM) materials, Piezo Induced Strain Actuators (multilayer PZT piezo ceramics) are the commonly used induced strain actuators. Piezo motors are based on the accumulation of small steps produced by piezo actuators under quasi static, harmonic or transient excitation. Piezo electric actuators has been widely used in space applications now a days. Active vibration control systems has been widely employed for isolating vibrations of mechanical structures. This paper describes three systems for active vibration control designed using piezoelectric actuators. Receiver isolation with an active mounting system. Now a days the traditional piezoceramic (PZT) actuators has been replaced with piezoelectric fiber composite actuators. The major advantages of the piezoelectric fiber composite actuators over the PZT actuators are their high performance, flexibility, and durability. This paper discusses the use of macro-fiber composites (MFC), a class of piezoelectric fiber composites, for vibration suppression of an inflated object, as a sensor and actuator (self-sensing actuation) to find modal parameters of an inflatable structure and as an impedance sensor for structural health monitoring. Because of their extreme brittle nature, Monolithic PZT requires extra attention during the handling and bonding procedures. Also their conformability to curved is extremely poor. Because of these limitations the Monolithic PZTs has been replaced with Active Fiber Composite (AFC) actuator developed by MIT and Macrofiber composite (MFC) actuators constructed at NASA Langley Center. An MFC actuator consists of thin PZT fibers imbedded in Kapton film and covered with an inter digitized electrode pattern, as shown in Fig. Figrue 2 Inter digitized electrode pattern 2.3. Insatiable Structures Here the use of MFC to both sense and control the vibration of a very flexible, inflated structure has been investigated and compared with previous experiments where a PVDF sensor has been employed for the same. It has been found out that the data measured with the MFC sensors is consistent with data acquired using accelerometers or PVDF sensors. Because of their higher electromechanical coupling, the data measured with MFC have a much clearer and distinct response than does the frequency response obtained with PVDF sensors. The MFC excitation produced less interference with suspension modes of the free free torus than excitations from the shaker. Experiments were successfully performed with multiple MFC actuators/sensors positive position feedback methods. The experimental results clearly indicate that this control strategy and the MFC sensors/actuators can reduce and control the vibration in the inflatable torus. Up to 50% vibration reduction has been achieved using a single MFC actuator and up to 70% using two actuators editor@iaeme.com

5 Vibration Damping Characteristics of Cantilever Beam Using Piezoelectric Actuator 2.4. Self-Sensing MFC Actuators Piezoelectric materials are often used as a sensor and actuator simultaneously, termed as a self-sensing actuator. In this paper a self-sensing circuit for MFC patches has been designed and experimentations are carried out on a Aluminium beam with the MFC mounted at the root of the beam. After identifying the resonant frequencies of the beam using self-sensing MFC circuit, a positive position feedback control algorithm was designed to suppress the vibration of the beam. It has been found out that the MFC self sensing actuator was able to produce larger control forces on the beam than a monolithic PZT of equal size due to the MFCs higher electro-mechanical coupling. 3. RESULT AND DISCUSSION 3.1. Cantilever Beam Analysis A simple cantilever beam is modelled assuming Euler-Bernoulli beam model. The modes of vibrations of a simple cantilever beam has been extracted and compared with the results obtained from ANSYS. The maximum deflection of a cantilever beam subjected to a concentrated point load at different locations of the beam has been studied. Same studies has been carried out by replacing the concentrated point load with an uniformly distributed load. Finally steady state deflections of a simple cantilever subjected to a thermal gradient has been studied. Modal analysis has an important part in vibration analysis. In some systems, mechanical malfunction or failure can be attributed to the excitation of their preferred motion such as modal vibrations and resonances. By modal analysis, it is possible to establish the extent and location of severe vibrations in a system. The section examines the modal analysis of simple cantilever beam. The natural frequencies for five modes has been calculated using Euler- Bernoulli Beam theory. The analytical results are then compared with simulation results using FEM software of ANSYS. The cantilever beam structure is shown in the figure. The beam material selected is Stainless Steel Austenite 304. Figrue 3 Cantilever beam with one end fixed and other end free L = 0:065m - Length of beam b = 0:0015m - Cross Section Base h = 0:0005m - Cross Section Height E = 210 X 10 9 N/m 2 - Young's Modulus of Stainless Steel Austenite 304 ν= 0:28 - Poisson's Ratio of Stainless Steel Austenite 304 ρ= 7800kg/m 3 - Density of Stainless Steel Austenite 304 I = bh 3 /12m 4 - Moment of Inertia m = ρ X L X b X h kg - Mass of the Beam n = 1,2,3,. - Number of Modes (Here n=5) editor@iaeme.com

6 R. Ganesh, K. Karthik, A. Manimaran and M. Saleem Solving the Euler-Bernoulli Beam equation and applying the boundary conditions, provides the frequency in rad/s as given below, ω n = α n 2 EI/mL 3 where, α n = 1.87,4.69, 7.85,11.01, Converting to Hz, we get the natural frequency as f n = ω n /2π In ANSYS the element used for modelling is 2D Beam3. Beam3 is a uniaxial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node, translations in the nodal x and y directions and rotation about the nodal z-axis. The model is meshed with 10 elements with 11 nodes. The natural frequencies obtained for the first five modes of the cantilever beam is compared for analytical solution with the results obtained from ANSYS model. The percent error (%E) in our model can be defined as, %E = [(ft heoretical - f model )/ f theoretical ]x100 The values are tabulated as follows. Table 1 actual and theoretical frequencies Frequency Theoretical Model %E f f f f f From the results, it can be concluded that by increasing the element number or by refining the mesh the %E between theoretical values and model values can be reduced Mode Shapes The mode shapes of vibration of cantilever beam obtained from ANSYS are shown below. Figure 4 Shows vibration mode 1, Cantilever Subjected to Concentrated Point Load In this section, structural analysis of a cantilever with one end fixed and a concentrated point load at free end has been carried out. It has been found out that maximum deflection (δ max ) occurs at the free end. Analytical solutions obtained are compared with those obtained from ANSYS simulation. The beam nomenclature and structure are same as that of the one discussed for modal analysis. Here the point load is assumed as 100 N (P = 100N) applied at the free end of the beam editor@iaeme.com

7 Vibration Damping Characteristics of Cantilever Beam Using Piezoelectric Actuator The equation for maximum stress is obtained by applying the boundary conditions to Von Mises Equivalent Stress equation and Bending Stress equation. The equation for maximum stress is given as, σ max = 6PL / bh 2 By applying the boundary conditions to the Euler-Bernoulli beam equation, the relationship for maximum displacement has been obtained as, δ max = PL 3 /3EI The maximum stress is found out to be 1.04x10 11 KPa and maximum deflection has been obtained as 2.789m. The element used for ANSYS modelling is 2D Beam3. The model is meshed with 3 elements with 4 nodes. The ANSYS model is shown in below figure. From FEM simulation it has been found out that maximum deflection occurs at x = L and maximum deflection is obtained as m, which is same as that of the analytical solution of m. By increasing the number of elements close results can be achieved. The deflection of the beam and nodal deflections are shown below. Figure 5 Nodal deflections of cantilever beam subjected to a point load at free end 3.4. Cantilever Beam with Concentrated Point Load at Different Locations In this section the cantilever beam has been subjected to concentrated point load at different locations and the maximum deflection due to the point load has been calculated analytically as well as using the FEM software. By applying the boundary conditions to the Euler- Bernoulli beam equation, the relationship for maximum displacement has been obtained and is given by below equation. δ max = Pa 2 (3L-a)/6EI The beam nomenclature and structure are same as that of the one discussed in modal analysis. Here the point load is assumed as 100 N (P = 100N). The cantilever beam structure is shown below. 4. DAMPING CHARACTERISTION ANALYSIS Now the point load has been moved away from the fixed end as shown in the figure below. Fig shows Cantilever beam with a concentrated point load away from the fixed end By substituting the value a = m on the deflection equation, the maximum deflection has been calculated as, δ max = m. Now the ANSYS model is developed using the element 2D Beam3. The model is meshed with 3 elements with 4 nodes. The maximum deflection has been found out to be δ max = m editor@iaeme.com

8 R. Ganesh, K. Karthik, A. Manimaran and M. Saleem From the results it has been observed that, the maximum displacement δ max values obtained through analytical and ANSYS models are the same. Also it has been observed that maximum deflection will be highest when the point load is at the free end of the cantilever beam and the maximum deflection decreases as the point load is shifted towards the fixed end. Below figures shows the beam and nodal displacement solutions. Figure 6 Shows Nodal deflections of cantilever beam subjected to a point load away from fixed end 4.1. Cantilever Beam with Uniformly Distributed Load In this section a cantilever beam subjected to uniformly distributed load as shown in below figure has been analyzed. The maximum deflection has been calculated using the equation given below. δ max = PL 4 /8EIThe maximum deflection thus obtained is compared with ANSYS result. Here the uniformly distributed load has been assumed as 20 N/m, (i.e. P=20 N/m).From the above equation, maximum deflection has been calculated as m. Now for the ANSYS simulation, the cantilever beam has been modeled as a 2D beam using 2D SHELL181 element. The model has been meshed with 130 elements having 198 nodes. The maximum deflection obtained from ANSYS solution is m. From results, it has been observed that the analytical solution and ANSYS results are the same. The beam deflections and nodal deflections are shown below. Figure 7 Shows Nodal deflections of cantilever beam subjected to uniformly distributed load 5. CONCLUSIONS A simple cantilever beam is modelled assuming Euler-Bernoulli beam model. The modes of vibrations of a simple cantilever beam has been extracted and compared with the results obtained from ANSYS. The maximum deflection of a cantilever beam subjected to a concentrated point load at different locations of the beam has been studied. Same studies have been carried out by replacing the concentrated point load with a uniformly distributed load. Finally steady state deflections of a simple cantilever subjected to a thermal gradient has been studied.pzt sensor can be used for accurate measurement of vibration. Voltage obtained from editor@iaeme.com

9 Vibration Damping Characteristics of Cantilever Beam Using Piezoelectric Actuator the sensor can be directly amplified and used for damping. For damping purposes piezo actuators can be used. Single patch self sensing sensor+actuator used in closed loop is very effective. Accurate results were obtained even in different lading conditions. Different range of voltage were applied to actuator for checking varying conditions. Positioning of Sensor + Actuator patch is effective in maximum. REFERENCES [1] Bich D. H., Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells, Composite structures, [2] Binod P. and Yadav. Vibration Damping Using Four Layer sandwich, Journal of Sound and Vibration, Vol.317, pp. 2008, [3] Bena B. S. Benb, B. A. Adarsh,K, Damping Measurement in Composite Materials Using Combined Finite Element and Frequency Response method, International Journal of Engineering Science Invention ISSN, 2012, [4] Chronopoulos. D, A unified approach for the broadband vibroacoustic response of composite shells, Composites Part B: Engineering 43(4): 2012, [5] Cunningham.P, Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 2: Theoretical study. Journal of Sound and Vibration 264(3), 2003, [6] Cunningham. P and R. White, Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 1: Experimental study." Journal of Sound and Vibration 264(3): [7] Esmailzadeh, M. and A. Lakis, Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer. Journal of Sound and Vibration 331(2), 2012, [8] Chenson. and Ian Davies.J, Optimal Design for the Flexural Behavior of Glass and Carbon Fiber Reinforced Polymer Hybrid Composites, Materials and Design, Vol. 37, 2012, [9] Chensong Dong. and Heshan A, Flexural Properties of Hybrid Composite Reinforced by S-2glass and T700S Carbon Fibers Composites, Composites Part B, Vol. 43, 2012, [10] Darabi B, Rongong J.A, Polymeric Particle Dampers under Steady-State Vertical Vibrations, Journal of Sound and Vibration, Vol. 331, 2012, [11] Fazilati, J. and H. Ovesy. Dynamic instability analysis of composite laminated thin-walled structures using two versions of FSM, Composite structures 92(9), 2010, [12] Fazilati J. and H. Ovesy, Finite strip dynamic instability analysis of perforated cylindrical shell panels, Composite structures, 94(3), 2012, [13] Hong, Y. He, X.D. Wang, R.G, Vibration and Damping Analysis of a Composite Blade, Material and Design, Vol. 34, 2012, [14] Shafi Ullah Khan. Chi Yin Li. Naveed, A. Siddiiqui. Jang-Kyo Kim, Vibration Damping Characteristics of Carbon Fiber-Reinforced composites Containing Multi-Walled Carbon Nano Tubes, Journal of Composites Science and Technology, Vol. 71,2011, [15] Prince Kumar and Sandeep Nasier, An Analytic and Constructive Approach to Control Seismic Vibrations in Buildings. International Journal of Civil Engineering and Technology, 7(5), 2016, pp editor@iaeme.com

10 R. Ganesh, K. Karthik, A. Manimaran and M. Saleem [16] Salin, E. Liu. Y. Vippola. M, Vibration Damping Properties of Steel/Rubber/Composite Hybrid Structures, Composite Structures, Vol. 94, 2012, [17] Senthil Kumar. K, Siva. I, Jeyaraj. P, Synergy of Fiber Length and Content on Free Vibration and Damping Behavior of Natural Fiber Reinforced Polyester Composite Beams, Materials and Design, Vol. 56, 2013, [18] Ameya R. Salunke and Prof. Nishant S. Kulkarni, Analysis of Friction Induced Vibration during Engagement of Clutches. International Journal of Mechanical Engineering and Technology, 7(3), 2016, pp [19] Sridhar. I, Venkatesha. C.S, Variation of Damping Property of Polymer Composite under Saline Water Treatment, International Journal of Innovations in Engineering and Technology, Vol. 2, [20] Design and Development Methodology of Adaptive Vibration Absorber, Rushi Vyas, Rajan Zinzala and Hiren Prajapati International Journal of Design and Manufacturing Technology 7(3), 2016, pp [21] Yuvaraja. M, Senthilkumar. M, Comparative Study on Vibration Characteristics of a Flexible GFRP Composite Beam Using SMA and PZT Actuators, Manuf. and Ind. Engg, Vol. 11, 2012, editor@iaeme.com