The Lecture Contains: Piezoelectric Sensors and Actuators Magnetostrictive Sensors and Actuators file:///d /chitra/vibration_upload/lecture33/33_1.htm[6/25/2012 12:42:09 PM]
Piezoelectric Sensors and Actuators PZT based actuators can normally generate a maximum strain of about 0.2% (about 2000 µ-strain ). Though, single crystals of PZN and PMN are known to generate strains of the range of 8000 µ-strain, the use of such crystals as actuators are limited due to their high cost and difficulty of integrating in a structure. Even with the maximum available active strain, it is quite difficult to control machine-vibration using the smart materials directly. Various forms of displacement and force amplification techniques have been recently developed towards the use of piezo-electric actuators in industrial scale. These systems are classified into three major groups : Internally Leveraged System: In this system, the actuators contain multiple piezoelectric elements to get an amplified effect. The simplest example is a Piezo-stack where many piezoelectric wafers are stacked in such a way that a comparatively larger deformation is obtained in the d 33 mode by applying a smaller voltage. More advanced systems include various configurations such as Rainbow, C-block, and Crescent etc. Externally Leveraged System: In these actuators mechanical systems are utilized to amplify the output of a piezoelectric actuator these include actuators like unimorph, bimorph, flexure based actuator, moonie, cymbal etc. Frequency Leveraged System: This type of system is based on alternating current supply to a piezo-actuator. Typical examples are piezoelectric inchworm motors, ultrasonic motors, etc. Even though different designs of actuators achieve different degrees of efficiencies in terms of energy conversion, displacement and force amplification, the basic principle used for strain generation is quite similar. file:///d /chitra/vibration_upload/lecture33/33_2.html[6/25/2012 12:42:09 PM]
Magnetostrictive Sensors and Actuators We have noted that for smart structural applications magnetostrictive materials, like Terfenol-D, are as good as piezoelectric materials. The free-strain or the maximum strain under no-load condition in Terfenol-D is about 2000 µ-strain, which is comparable to free-strain of polycrystalline piezoelectric material; the band-width of the material is up to MHz level indicating it's superiority over SMA. Also, because of higher modulus of elasticity, the energy density of Terfenol-D is maximum among all the smart materials. Here, we will discuss how one can utilize these properties in developing actuators and sensors. Many researchers have developed mini and micro-actuators using Terfenol-D. Consider for example, the mini-actuator developed by Anjannappa et al. A typical magnetostrictive mini-actuator is shown in Fig. 33.1. Figure 33.1: A magnetostrictive mini actuator file:///d /chitra/vibration_upload/lecture33/33_3.html[6/25/2012 12:42:09 PM]
It may be noted that the Terfenol-D rods work very much similar to Piezo-stacks. Unlike piezoactuators, the effect of thickness of a Magnetostrictive Mini Actuator (MMA) is not negligible. Hence, the induced (constrained) strain is related to the free-strain by the following relationship: (33.1) where b and t are, respectively, the width and thickness of the host beam, A m and t m are the crosssectional area and thickness of the MMA. E -denotes the modulus of elasticity of the host-beam and E m denotes the modulus of elasticity of the magnetostrictive material. The expression for the free-strain Λ, contains an additional term - the thermal effect due to current passing through the solenoid and hence Λ is expressed as (33.2) where G is the coil-constant,a / is the coefficient of equivalent thermal expansion, K and C 2 are two thermal constants which are obtained experimentally and i is the current passed through the magnetizing coil. file:///d /chitra/vibration_upload/lecture33/33_4.htm[6/25/2012 12:42:09 PM]
Example Consider the same MEMS beam similar to that discussed in the Example of Lecture 30. However, instead of piezoelectric layers on top and bottom the host beam is excited by a magnetostrictive mini-actuator of same length as that of the host beam. The MMA has a cross-sectional area of 4x10-8 m 2 and thickness 100 µ-m. The elastic modulus of the magnetostrictive actuator is 50 GPa, the magneto-mechanical constant is 15 nm/a and a current of 750 ma is passed through the coil. Considering the coil-constant G to be 10,000 and neglecting the thermal effect, find out the strain induced at the host beam. Solution Neglecting the thermal effect, the free-strain that could be developed by the MMA could be obtained using eqn. (33.2) as Using eqn. (33.1), the strain induced on the host beam is Magnetostrictive sensors are developed based on three phenomena: 1. The Villari effect, which refers to the changes in magnetization when a magnetostrictive material is subjected to applied uniaxial stress. 2. The Matteuci effect, referring to the changes in axial magnetization of a current carrying amorphous wire when it is twisted. 3. The change in permeability of these materials when subjected to applied stress. Magnetostrictive delay line sensors are based on this phenomenon. file:///d /chitra/vibration_upload/lecture33/33_5.htm[6/25/2012 12:42:09 PM]