A Non Resonant Piezoelectric Sensor for Mass, Force and Stiffness Measurements

Abstract

The word piezo in greek means \to compress". Piezoelectric sensors work on the principle of direct piezoelectric effect, where a mechanical input generates a corresponding electric charge. The advantages of these sensors are wide fre-quency range of operation, high stiffness and small size. The main limitation of a piezoelectric sensor is that it cannot be used in measurements that are truly static. When a piezoelectric sensor is subjected to a static force, a fixed amount of charge is developed which would eventually decay at a rate dependent on the external impedance of the sensor circuitry. Operating sensors at resonance have been one of the methods to overcome the limitation of using piezoelectric sensors for static measurements. However, since both actuation and sensing are done by the same piezoelectric element, this results in a cross-talk of input and output signals. The drawback of using single piezoelectric element for actuation and sensing is overcome in this work by using two identical elements|one for actuation and one for sensing. The operating frequency is about 10 % of the natural frequency of the sensor, thus enabling to operate the sensor in non resonant mode. Since the actuation and sensing mechanisms are separated, static measurement can be carried out. The output signal from the sensing element is monitored by a Lock-in amplifier which works on the principle of phase sensitive detection. The advantage of this sensor design is high sensitivity along with narrow band detection. It can be shown that the voltage output of the sensor Vout / a1 + m(b1 + b2F + b3K) + c1F + d1K, where m and K are the external mass and interaction stiffness, respectively, F is the force acting on it. By maintaining any two of these three quantities constant, the remaining one can be measured without any difficulty. The non resonant mode of operation makes it possible to explore the potential of this sensor in investigating mechanics of solid-liquid (viscous), solid-solid (inelastic) and solid-tissue(viscoelastic) interactions. High sensitivity, wide range of measurement (1 g{1 g) and high resolutio(0.1 g) of the non resonant mass sensor makes it possible to use it in measure-ment of very small masses of the order 1 g. Typically, resonant sensors such as quartz crystal microbalance (QCM) are used for mass measurements at that range. However, since the performance of resonant sensors is controlled by damp-ing, a phenomenon known as `missing mass effect' arises. Operating a sensor in non resonant mode (stiffness controlled mode) is a way to overcome this problem, especially when the mass is viscous and/or viscoelastic in nature. Drosophila fly, egg and larvae are the viscoelastic masses that are measured using this non res-onant sensor. Evaporating sessile drops of water and Cetyl trimethylammonium bromide (CTAB) surfactant solution from nominally flat surfaces are monitored to characterize the sensor for viscous mass measurement. Evaporation rate per unit surface area remains more or less constant, during the initial stages of evap-oration. When the surfactant concentration is varied, evaporation rate per unit surface area is highest for solutions around critical miscelle concentration (CMC). A study is carried out to understand the effect of concentrations on spreading of ink over inkjet printing paper. It is found that the spreading is least around CMC, since spreading is dependent on the rate of evaporation. The non resonant piezoelectric sensor which has high stiffness and quick re-sponse is also capable of measuring very small frictional forces. This sensor is configured to work as an inertial slider. Friction measurement at micro scales is important for designing microsystems such as stick-slip actuators. At such length scales, experiments have to performed at low loads and high excitation frequencies. The support stiffness of such systems should be high and the force of friction generated during slipping, when displacements are smaller than the contact radius, are of the order of few N. The displacement during slipping (S) is dependent on the amplitude of the input voltage to the actuation element. The frictional force measured during slipping by the sensor element indicates that the co-efficient of friction ( ) is independent of the sliding velocity. The developed non resonant sensor in this work under small amplitude exci-tation, can measure force gradient (i.e. stiffness). The total force generated when a needle is inserted into a viscoelastic material is a sum of force due to stiffness of the material, friction and the cutting force at the tip. The force due to stiffness is dominant when the needle is bending the tissue before the puncture occurs. Use of the non resonant sensor in tandem with strain gauge force sensor enables distinguishing the three components of the total force. The slope of the force-displacement (F -d) curve during the initial stages of needle penetration into the viscoelastic material, before puncture, is indicative of the stiffness of the mate-rial. The peak force measured during penetration is higher for needles with larger diameters and lower insertion velocities. The viscoelastic response (relaxation) of the material remains independent of the insertion velocity, for a given thickness of the material and a constant needle diameter. In summary, the sensor designed and developed in this work operates in stiffness controlled mode to eliminate the `missing mass effect' encountered dur-ing resonant mode of operation, has been clearly highlighted. Mass, force and stiffness measurements are possible over a wide range just by varying the ampli-tude of the input signal to the actuator element. The advantages such as high stiffness, small size and high response makes it advantageous to carry out in-situ micro scale studies in scanning electron microscopy (SEM) and transmission electron microscopy (TEM).