Recent Advances in MEMS Sensor Technology—Mechanical Applications
This is the second of a three-part series on micro-electromechanical systems (MEMS) sensor technology. In the first part, a general introduction to MEMS sensing was given, including its underlying principles . Biomedical MEMS sensors were also described by reviewing the principles of bio-sensing and describing a typical set of biologically inspired sensors. In this part, mechanical sensors for displacement, acceleration, impact, vibration, force and torque, and stress and strain are discussed. Various applications of these sensors include high-g measurement, study of golf swing dynamics, vibration control of space inflatable structures, force and torque measurement in micro-robots, bone stress monitoring, metrology, and characterization of nano-scale structures. Some related technologies of MEMS sensors are discussed including compensation for environmental effects, the Casimir effect, and harvesting of energy for self-powered sensors. Also, the subject of sensor selection is addressed. Part 3 of the series will present MEMS sensing in the thermo-fluid and electromagnetic domains.
Micro-electromechanical systems (MEMS) technology benefits from small size, low weight, high performance, easy mass-production and low cost. Sensing techniques are typically based on piezoelectric, capacitive, electromagnetic and piezoresistive principles. Sensing of mechanical variables such as motion (displacement, velocity, and acceleration), force (and other forms of loading such as moment and torque), deformation, stress, and strain are considered below. Applications that use sensors in this category are indicated.
Adaptive optics are used to correct wave aberrations in various fields including astronomical observation, retina imaging and laser shaping. Adaptive optic systems are typically deformable mirrors (DM) integrated with wavefront sensors. Resolution of imaging quality with deformable mirrors is associated with high-actuator density. For instance, a deformable mirror may consist of a 64×64 actuator array with actuators placed 400 μm apart. Micro-fabricated deformable mirrors (MEMS DM) can provide high-actuator density with better performance compared with DM. Electrostatic-actuated MEMS DMs with a 32×32 piezoelectric actuator array integrated with displacement sensors are fabricated for high resolution monitoring .
A PZT thick film actuator is able to measure its own displacement. This multi-function device consists of a central top electrode for actuation and a sensor electrode for measuring the piezoelectric displacements. The piezoelectric charge induced on the PZT due to motion is proportional to the stress acting on the PZT, which is translated into displacement. The sensor displacement sensitivity is approximately 4 pC/nm. In view of the piezo-electric characteristic of the functional element, the integration of the sensor into the actuator does not require an additional fabrication process and does not have any effect on the actuator performance.
Multimode Micro-Displacement Sensor
Fiber optic technology is commonly used in applications with fiber lasers and sensors. Optical fiber-based sensor technology makes it possible to develop sensors for the detection of a wide range of physical parameters. Optical fiber sensors allow measurement of physical parameters such as displacement, pressure, temperature and electric field with high sensitivity for various industrial and medical applications. Characteristics of these sensors include simplicity, small size, mobility, wide frequency capability, extremely low detection limit and non-contact properties. Although the interferometer technique provides high sensitivity measurements, it is relatively complex. An intensity modulation technique in conjunction with a multimode fiber probe offers coupling ability, large core radius and high numerical aperture. A fiber optic displacement sensor with a sensitivity of 0.56 mV/mm that makes use of a concave mirror is available .
Linear and Angular Position Sensor
Probe-based storage systems in various portable electronic devices such as digital cameras and camcorders, handheld telephones, and palmtop computers require positioning
a storage medium relative to an array of probes at nanometer
scale. MEMS capacitive position sensors have been
employed in nanopositioning applications to develop a high precision
X–Y linear and angular (rotational) position sensor
. This sensor is capable of sensing a large range of movements
at high speed in an electromagnetic scanner. Such
capacitive sensors are relatively easy to fabricate and offer
high-resolution capability at low cost.
Metrology for High Aspect Ratio Micro-Holes
Slender piezoresistive micro-cantilever sensors are exploited for tactile (touch) metrology in deep and narrow micro holes. There is a linear strain–displacement relationship associated with transversal and axial loading in these sensors. The resolution and uncertainty of the cantilever sensors are in the ranges of nanometers and tens of nanometers, respectively . A set of 3 mm long cantilevers are used for displacements above 200 μm. This sensor has been used to obtain the form and roughness of diesel injector nozzle spray holes.
Angular Rate Gyroscope Sensor
Rate gyros use the gyroscopic principle to measure angular velocities in which a torque is required to change the direction of an angular momentum, the product of moment of inertia and angular velocity. An angular rate MEMS gyro in a vacuum has exhibited improved robustness and stability of sensing against drive–mode oscillations with minimized mechanical crosstalk between the drive and sense modes . This is achieved by a special arrangement of capacitive sense-mode frame and flexures and reduces double-frequency mechanical crosstalk and quadrature signals.
The mechanical noise due to Brownian motion of the air surrounding capacitor plates in accelerometers is a main factor that reduces the sensitivity and resolution in these sensors. In a MEMS inertial sensor with enhanced sensing capacitors, the mass of the proof mass is increased to reduce the mechanical noise . The associated capacitance sensing may be improved by an innovative structural design. The sensor is composed of a single seismic mass, a supporting beam, grid strips, combs, and fingers. In this design, a set of sensing capacitances are built in various configurations such as grid strip capacitances, comb capacitances, finger capacitances, and capacitances between the combs and the fingers. The area of a capacitor is the facing area of the two capacitor plates (electrodes) and the capacitance is proportional to this area. It can be improved by these various capacitance sensing configurations. This design lowers the air damping between the capacitor plates and consequently reduces the electronic noise.
In structural health monitoring, dynamic characteristics of structures such as natural frequencies, mode shapes, and damping ratios are monitored using modal analysis. Deformations or changes in orientation of structure due to applied loads can also be monitored by comparing the current status of the structure with reference models. Piezoelectric transducers are commonly used for structural health monitoring. However, conventional piezoelectric transducers are bulky, require high power actuation, and exhibit narrow frequency bandwidths, which reduce their efficiency and applicability to miniature structures. Active MEMS inertial sensors have wide frequency bandwidths and high accuracies.
Traditional accelerometers that use a proof mass as a detectable motion element of the sensors have the drawbacks of low shock resistance and a complex fabrication process. A thermal convective micro-accelerometer, developed by Dao et al., in 1996 and described in , uses a thermal bubble instead of a seismic mass. It is based on the movement of a small hot air bubble created around the heater in a chamber. The thermal heater is placed in between two thermistors, microminiature temperature sensors made of semiconductor material whose resistance changes with temperature. Applied acceleration to the sensor forces the thermal bubble to move. When the thermal bubble approaches one of the thermistors, it increases the thermistor ‘s temperature and causes the opposing thermistor to exhibit a lower temperature (Fig. 1). This temperature variation is reflected in the changes in the resistances of the thermistors and is converted to a voltage using Wheatstone bridges. The measured voltage is translated into an acceleration.
Keeping the heater at a high temperature offers high sensitivity for the sensor . The sensor sensitivity also depends on the position of the thermistors. If the thermistors are placed at a position with a factor of x/D = 0.2, maximum sensitivity will be achieved. Here, D is the distance between the heater and the cavity wall, and x is the distance between the heater and the temperature sensor. Using carbon dioxide as the filling gas in the sensor leads to a more sensitive sensor than using air, nitrogen and hydrogen. Air and nitrogen provide the same sensitivity but less than carbondioxide. The sensor’s sensitivity is very low when hydrogen is used. The frequency response of the sensor and the behavior of its transient response depend on the density of the fluid in the sensor and the thermal diffusivity of the sensor. Conduction of the heat in the sensor will balance the energy between the heater and the enthalpy carried away by the buoyant layer. This decreases the response time. Moreover, lower gas density allows faster convection. Therefore, large thermal diffusivity and low gas density provide faster response. Hydrogen has low density and large thermal diffusivity, providing a high frequency response, although it has low sensitivity. A self-mixing laser displacement sensor coupled with a MEMS accelerometer enables reliable displacement measurements with a resolution of 300 nm.
Wireless MEMS Inertial Sensor
MEMS inertial sensors are attractive in sports training systems where the sensor is embedded in the sports equipment. A six degrees-of-freedom wireless sensor measures the dynamics of a golf club used in putting, using accelerometers and angular rate gyros with an integrated microprocessor and RF transceiver . The sensors measure the position, velocity, and orientation of the club head at the opposite end of the shaft during the entire putting stroke.
MEMS technology integrated with optical detection techniques allows sub-angstrom scale sensitivity and nano-g acceleration measurement (1 g = 1 unit of acceleration due to gravity ≈ 9.81 m/s2) and performance close to the Brownian noise limits of the mechanical structure . This sensitivity cannot be achieved by capacitive or piezoresistive methods. Adding mass to the accelerometer will allow sensing at lower frequencies.
High-g Smart Sensor
Conventional g sensors fail when there are high-g ( >300 g) impacts. MEMS-based high-g smart sensors are able to measure very high-g (3,000–21,000 g) impacts and identify the material when a projectile makes an impact on a hard object . The sensor is composed of a cantilever and a spring structure made of silicon with Young’s modulus of about 190 GPa (1 Pa = 1 N/m2) and does not exhibit mechanical hysteresis. This is one of the reasons why silicon is suitable for building sensors and actuators. A MEMS-based acceleration sensor is effectively used in seatbelt systems for emergency locking during vehicle rollover.
Force and Torque Sensing of a Micro-Robot
Measuring force at the micro/milli-newton scale has been exploited in atomic force microscopes, microsystem characterization, micro-assembly, biomaterial characterization and biological research. These measurement systems generally
only operate in one direction for single-axis measurements.
When using such sensors, multi-axis measurements are carried
out using multiple single-axis force sensors in various
orientations. Design of capacitive MEMS sensors has been reported
for two-axis force measurement, and three-axis force measurements have been reported for piezoresistive sensors.
A magnetically actuated micro-robot can deliver a drug inside the human body . This robot is driven by external magnetic fields. The magnetic force aligns and drives the robot along its long axis due to the shape anisotropy effect. This is analogous to a needle becoming magnetized along its long axis. This micro-robot is fabricated from electroplated nickel parts. The dimensions of the robot are 2 mm in length and 1 mm in width, and the thickness of the nickel parts is 0.045 mm with a mass of 2.26 mg. The sensing system of the robot is a multi-axis micro-sensor. This sensor measures two force components and one torque component using capacitive comb drives with sensitivity levels of microNewtons (μN) for forces and nano-Newton-meters (nNm) for torques. The forces and torques acting on the micro-robot are in the range of microNewtons and nano-Newton-meters, respectively. Precise sensing of force and torque is essential for magnetic position control of the robot for medical applications such as drug injection into organ systems.
The Casimir Effect
The Casimir effect is a quantum effect in which boundaries at a sub-micron distances relative to each other interact. The effect is a direct manifestation of the zero-point energy fluctuations. This interaction does not exist within the field of classical electrodynamics. Micro-force sensors whose design is based on the Casimir effect combine a novel micro- machined torsional oscillator with an interferometric position-sensing mechanism. This sensor allows precision control of vertical scans. The exper imental setup for measuring the Casimir force includes a sphere and a plate (as it is difficult to maintain and align two parallel planes relative to each other at sub-micron scales). In dynamic force measurement, the force gradient (the variation of force relative to displacement) is measured, unlike static force measurements where only the force is measured. The force gradient can be measured by the Casimir oscillator by monitoring the change in the resonant frequency of the oscillator as the sphere-plate separation changes. The sensor resolution can be improved by changing the dimensions of the torsional springs of the oscillator.
Multi-dimensional force measurement in micro-robotic manipulations can be attained by strain gauges which offer precise force measurement in the submicro-newton scale.
Piezoelectric sensors for force measurement in micro-robotic
manipulation are usually more costly than strain gauges, and
their design is not as straightforward.
Stress and Stain Sensors
Biomechanical properties of living bones are studied for clinical management of skeletal trauma and disease. The commonly used radiodensitometric imaging techniques for assessing bone quality measure mineral density to infer mechanical strength. This technique does not necessarily lead to values that correlate well with bone strength. Dual energy x-ray absorptimetry for two-dimensional imaging is a more accurate approach, but it requires higher radiation doses. In the ultrasound technique , ultrasound waves are passed through the bone, and the resulting signals are processed to estimate bone density and some structural information. The use of low-frequency vibration to measure bone biomechanical properties does not necessarily provide precise data for bone strength, due to interaction with soft tissues surrounding the bone. Direct stress measurement using strain gauges implanted in internal fixators, prosthetics or bone surfaces requires surgical procedure which are costly. A multi-axis implantable MEMS sensor can measure bone stress directly and accurately, with applications in bone healing such as spinal fusion monitoring . The device is permanently implanted within open fractures,
embedded in bone grafts, or placed on implants at the interfaces between bone and prosthetics. The sensor stress resolution is 100 Pa in 1 s averaging by an array of piezoresistive pixels. The sensor is suitable for integration with wireless RF telemetry, for power and data retrieval, with a 3 mm × 3 mm × 0.3 mm footprint. The piezoresistive elements are designed with a textured surface which helps when integrating with the bone.
An improved piezoresistive MEMS strain sensor which enhances the geometric characteristics of the sensor in the vicinity of the sensing elements has been fabricated. It provides stress concentration regions and therefore improves the sensitivity.
Sometimes when procedures are carried out on the spine, instrumentation is implanted across the affected vertebrae for stability and formation of fusion. Grafted bone applied during surgery is expected to fuse with adjacent vertebrae in six to twelve months. Strain applied to the instrumentation is monitored to assess fusion development. A MEMS capacitive bending strain sensor utilizing a comb drive (Fig. 2) is designed to monitor bending strain . This sensor allows orthopedic surgeons to monitor spinal fusion. The sensor size is 10 mm by 4 mm, and it measures capacitance and strain values up to 100 pF and 1000 μԐ, respectively.
Unwanted vibration may generate noise, reduce stability, or decrease positioning accuracy of sensors. Fiberoptic strain sensors sense the change in wavelength or phase of light which is a measure of strain. They generally provide high resolution (in microstrain and nanostrain per Hz range). However, they are bulky. Piezoresistive strain gauges are generally used for static to low frequency strain detection. Smaller sensors are influenced less by the structural dynamic behavior (due to their smaller mass) and detect local strains, not the average strains in the neighborhood of the sensor. Strain-based MEMS sensors such as pressure sensors, accelerometers, and atomic force microscopy sensors have been developed. In piezoelectric sensors, response strength is proportional to piezoelectric material thickness of lead (Pb) zirconate titanate (PZT), zinc oxide (ZnO), or aluminum nitride (AlN) materials.
Although piezoelectric materials have good signal-tonoise
ratios (SNR) over a large frequency range and are
suitable for vibration monitoring, they lose sensitivity at the micro-scale. Unlike piezoelectrics, piezoresistive materials are less sensitive to smaller size. However, they have
lower SNR relative to piezoelectrics. ZnO MEMS piezoelectric
strain sensors for dynamic strain are sensitive to thermal
noise and parasitic capacitance. However, if the sensing
signal is properly handled, these piezoelectric sensors are
superior to the laser-Doppler-vibrometer (LDV) in dynamic
signal sensing. A high-performance dynamic strain MEMS
sensor measures structural vibration without placing an extra
burden on the host. The sensing element is composed of
micro-ZnO piezoelectric. The sensor is capable of sensing a
40.0 nanostrain, time domain signal at frequencies above 2
Resonant sensors are favored in precision measurements due to their high sensitivity. The frequency output of the sensors can be measured with high accuracy. Silicon comb-driven double-ended tuning fork resonators are used for measuring acceleration, gyroscopic motion and strain. These can sense force for feedback control in robotic grippers and strain in structural monitoring. Silicon materials degrade at temperatures above 500 ºC, and their electronic properties fail beyond 150 ºC. Therefore, Si is not appropriate for applications in harsh environments such as high radiation exposure, operation in high temperature and corrosive media and ultrahigh g-shock. Silicon carbide (SiC) has a higher stiffness and fracture strength and is more resistant to wear, oxidation, high temperatures and corrosion relative to Si.
A poly-SiC balanced-mass, double-ended tuning fork resonant strain sensor is used for structural monitoring of components in high temperature or otherwise harsh environments. Poly-SiC resonant strain sensors exhibit similar resolution to silicon sensors (0.11 microstrain resolution in a bandwidth of 10–20 kHz). These sensors have been used in environments with temperatures beyond 300 ºC and successfully subjected to 10,000 g-shock .
Transmission Electron Microscope
Transmission electron microscope-atomic force microscopy (TEM-AFM) combines TEM and scanning probe microscopy (SPM). Integrating SPM into TEM provides the local probe and manipulator for in situ measurements and obtains properties not measured in standard TEM. Because of the limited space available inside the TEM pole gap, MEMS is a suitable candidate when combining the SPM with TEM. Measuring forces using nano-newton scales is typically performed by a standard AFM cantilever with a known spring constant, which is fitted inside the TEM. The deflection of the cantilever is determined using the TEM images and is translated into force values (through Hooke’s law). An alternative approach is to reconstruct a TEM to incorporate a standard AFM instrument with optical detection. A MEMS atomic force microscope enables in situ transmission electron microscope force measurements in the nano-newton range and obtains characteristics of nano-scale structures . The compact design of the device allows the sensor to be fitted in the pole gap inside the TEM. The piezoresistive detection principle integrated with a Wheatstone bridge is employed in the sensor design.
MEMS-Based Flexible Sensor and Actuator Systems
Inflatable and membrane structures are favored in space exploration because of their light weight, low stored volume, high deployment reliability and low cost. The materials used for these structures are typically realized from flexible polymers. These structures require internal pressure during operation. Inflatable structures may experience catastrophic failure in harsh space environments particularly due to unwanted structural vibration. Potential applications of lightweight inflatable space structures include very large aperture optics and antennas, light (or micro) sails, sunshields, solar concentrators, deployable solar arrays, landing systems and habitable structures. These structures are built in various sizes ranging from a few cm (in the case of micro- craft) to several km for sails and space solar power systems. To monitor the dynamic behavior of these structures, a MEMS device which is lightweight and flexible is attached to the external surface of the inflatable structure. It is useful in health monitoring and controlling vibrations in structures. A combined health monitoring and control system consists of a sensor layer at the top, a polyimide substrate in the middle and an actuator layer at the bottom which operates in three dimensions. The sensor system is designed as a network of MEMS sensors for monitoring the environmental conditions and structural vibrations.
Piezoelectric polyvinylidene fluoride (PVDF) actuators provide precision surface control of an inflatable antenna. However, they require high activation voltages and produce small displacements. Electroactive polymers (EAP) convert electrical energy into mechanical energy due to their electromechanical properties and offer better performance in terms of stress and strain when compared to other smart materials like PVDF . EAP requires a low activation voltage and is flexible and lightweight. It is suitable for health monitoring and control of inflatable and membrane structures. Therefore, the actuator layer is constructed from EAPs which control the structural behaviour by using the strain and vibration data obtained from the MEMS sensors.
Tissue elasticity provides information in various medical applications such as ligament tension measurement during knee implant surgery, detection of compartment syndrome, and cartilage hardness measurement. A MEMS stiffness sensor can measure both contact force and stiffness of the object under contact. The sensor consists of multiple membranes with varying stiffness values. The deflection of the sensing membrane is measured to obtain the stiffness or elasticity of an object. The capacitive principle is employed in these sensors.
Swing Monitoring of Large-Scale Structures
Vibration of large scale and heavy barges at sea should be monitored and controlled particularly under intense wind conditions and wave loads. A wireless MEMS inclination sensor system is developed in the framework of structural health monitoring of large-scale hook structures. A tuned mass damper control module has been integrated with MEMS sensors for the swing monitoring of a hook. This wireless sensor system provides a new way of swing monitoring. Other applications include vibration monitoring of TV towers and large cranes.
MEMS Tactile Sensor for a Robotic Finger
Lifting and grasping tasks by robots are controlled based on sensor signals. Piezoelectric and piezoresistive sensors allow robotic fingers to characterize different surface textures. Requirements for effective sensing include obtaining a rich data set by spatial distribution of contact forces on the robotic finger at high sensitivity. MEMS can meet these requirements due to their small size which allows distribution of a large number of sensors on the finger and provides high resolution and high sensitivity. Integrating the sensors on a robotic finger is enabled by a layer of elastomeric skin-like material on the finger surface . Employing the capacitive sensing principle in the sensors (Fig. 3) offers increased sensitivity, long term drift stability, lower temperature sensitivity and lower power consumption, which is advantageous compared to piezoresistive, strain gauge, and piezoelectric sensing approaches.
Polymer-Based MEMS Tactile Sensor
Biological tactile sensors can provide information about an object’s shape, force, hardness, motion, temperature, and so on. Tactile sensors are fabricated mainly from silicon, polymer or metal using the piezoresistive or capacitive principles (Fig. 4). Other techniques under investigation include ultrasonic, pneumatic, and hybrid resistive principles. Because of the brittle characteristic of silicon materials, polymers are better suited for this use, and they offer greater robustness. Biological sensors provide excellent electrical and mechanical transduction characteristics. A polymerbased MEMS tactile sensor array on a polyimide substrate has been used to classify surface textures. These sensors are flexible and their sensing capabilities resemble those of biological skin . The texture classification is done by maximum likelihood decision making and using arrays of mechanical strain gauges. The sensor has demonstrated classification accuracy levels of about 70%. Techniques developed for satellite photography and RADAR imagery data processing, such as probability density function (pdf) estimation and neural networks (NNs), are utilized in tactile sensor data analysis. Among image-based texture classification approaches, the maximum likelihood (ML) estimation technique can correctly identify the texture 98% of the time, which is far better than the results from the autocorrelation method (76%), pdf estimation (83–97%), and NN identification (81–88%). The success of the ML identification is limited to Gaussian texture distributions.
MEMS circular diaphragms measure added mass to the 9 pg scale . The diaphragm characterization is obtained by electrostatic actuation of the diaphragm and detecting its response using optical surface profilometry and laser Doppler vibrometry.
Related Technologies to MEMS Sensors
There are useful topics and applications related to MEMS sensors such as multi-functional multi-sensors, micro-resonator and nano-resonator sensors, and self-powered sensors. These are briefly addressed next.
Nanoindentation is used to determine material properties by pressing a sharp, hard tip into a sample while performing forcedisplacement measurements. Nanoindentation techniques in conjunction with TEM are employed in real-time, high-resolution imaging. A MEMS capacitive force sensor with an electrically conducting tip measures force and current simultaneously for in situ transmission electron microscope nanoindentation . This enables the investigation of electromechanical properties of materials.
Micro- and Nano-Resonator Sensors
Microresonators and nanoresonators are utilized in chemical and biological sensing, environmental control, monitoring of viscosity and magnetic fields, and inertial force measurement. Applications include detection of chemical species and gases, proteins, viruses, magnetic fields, acceleration, pressure, viscosity, and mechanical properties of thin-film materials. For the purpose of increasing the quality factor (Q-factor), a resonator commonly operates at its first natural frequency in the bending or torsional mode. Resonators have complex designs and include beam and plate arrays with different cross-sections and load types. Deflection response of the beams and plates with various cross sections excited by external stimuli (e.g., mass, force, and magnetic field) corresponds to the sensor output .
Self-sustained or passive sensors harvest their own energy to generate sufficient power for the operation of the sensor system. Such sensors are particularly practical in remote sensing and condition monitoring in hostile or inaccessible environments that permit little or no maintenance. Various schemes are employed to harvest low level vibrations of the energy harvesting unit as power sources for wireless sensor nodes, including piezoelectric, electrostatic and electromagnetic techniques. Piezoelectric energy convertors do not need a voltage source. However, their integration into micro-systems can be relatively difficult. Electrostatic systems can be more easily integrated into micro-systems, but a separate voltage source is needed to operate the systems. Electro-magnetic convertors do not need a voltage source. However, the output voltage of electro-magnetic systems is limited.
As an example, energy harvesting from vibration is presented next. A sensor can be powered by the same vibration that is being measured. A transducer which converts the mechanical energy of structural vibration or vibration of a machine into electrical energy powers the system. The transducer which represents the energy supply component in the system is considered as an electro-magnetic device with a moving magnet and a coil. The power obtained from the harvested energy is supplied to a nano-electromechanical capacitive sensor. Fig. 5 shows a schema ticdiagram o f a mass-spring–damper system. This system represents a proof mass mounted on a spring and a damper setup in a structure subjected to a harmonic base excitation y= Y sinωt. The sensor base motion is transmitted to the mass through the spring and the damper. The corresponding harmonic absolute oscillation of the mass is given by z= Zsin(ωt-ψ). Vibration of the mass relative to the structure is x=z-y or x= Xsin(ωt-Φ). To harvest the mechanical energy of the structural vibration, the mass is designed as a permanent magnet moving relative to a coil. Electrical energy is generated through electromagnetic transduction.
Motion of the magnet relative to the coil dampens the vibration of the mass due to mechanical-to-electrical energy conversion. The behavior of this oscillator in harvesting electrical energy is addressed now. The equation of motion of the mass-spring-damper system is given by
where k = spring stiffness, c = damping constant, and m = mass. For harmonic base excitation, the equation of motion of the system can be written as`
For x= Xsin(ωt-Φ) we obtain
The power absorbed by the damper, the energy-harvesting element, is P=cω2X2cos2(ωt-Φ). The harvested energy in one cycle is given by
The average power in one period (τ=π/2) is determined as Paverage=cω2X2/2. By substituting the value for X, we have
where Xmax= maximum amplitude of the mass response when ω=ωn for a maximum power of . Denoting the frequency ratio as r=ω/ωn , and with the damping ratio of , the dimensionless power is plotted in Fig. 6 and is given in  as
The following is clear from Fig. 6: If the sensor is employed for vibration monitoring of a structure with a known fixed operational or ambient vibration frequency, the transducer should be designed for that particular resonant frequency to achieve maximum power by the generator. If the frequency of the ambient vibration of the system is not confined to a small range and varies over a wide frequency range or the source of vibration is random, then an electrical transducer with a higher damping ratio can supply greater maximum power.
Transducer damping also consists of unwanted damping due to undesirable effects such as air resistance. When designing the system, the damping factor (damping constant) can be modified to account for such effects. If the mechanical damping factor is cmec and the force due to electromechanical coupling of the generator is F=Ki, where K is the generator coefficient and i is the current (Fig. 7) , then the governing equation of the system may be written as
The transducer voltage is proportional to the velocity of the seismic mass moving relative to the coil. From Kirchhoff’s voltage law, the electrical relation of the circuit in Fig. 7 is given by
By substituting i from this equation into the former, we obtain
Hence, the total damping due to mechanical damping and the electrical transducer is given by c=cmec+K2/Rload.
The power from the harvested energy is supplied to a wireless nano-electromechanical capacitive sensor. In this sensor, vibration sensing is carried out by detecting the oscillations of a forest of carbon nanotubes (CNTs). The CNTs are excited when they are subjected to a base motion corresponding to the measured vibration. Acquisition of the sensor signal is performed by a capacitive circuit using the electric charge generated in the CNT bundle. Modulation of the charge in the CNTs due to the change in capacitance leads to a modulation in the bundle’s conductance and is used in measuring the input vibration. A schematic representation of the sensor is given in Fig. 8.
The equivalent electrical circuit of the device is shown in Fig. 9 where the contact is modeled as resistance Rs and the capacitance from the contact pad is denoted by Cs. The capacitance between the tube and the gate (or base) is Cg , and the gate ac and dc voltages are and , respectively. VCNT is the CNT voltage and Iω is the corresponding current. The gate material is Si.
The current in this sensor in  is given by
then the electromechanical relation is
where dGdc/dVg denotes the transconductance.
Sensor performance can be affected by changes in environmental conditions. Compensation for environmental effects (e.g., temperature) may be achieved by means of a bridge circuit where the active sensor is placed in one of its arms and a reference sensor in another arm . The bridge circuit will also function as the frontend signal acquisition circuit of the sensor. Fig. 10 shows a bridge circuit for this sensor. In a capacitive sensing scenario,
where the active sensor capacitance is Cg and the compensator capacitance is C1 . Z2 and Z3 are bridge completing impedances, vref=va sinωt is the excitation ac voltage, and is the bridge output with a phase lag of Φ with respect to the excitation.
Since the potentials at the negative and positive leads of the operational amplifier are equal (due to the high gain of an opamp) and the current in these leads is zero (due to the high input impedance of an op-amp), the current balance equations are given by
By eliminating v, the common voltage at the op-amp, in these equations, we have
In this equation, if Zg/Z1=Z3/Z2.
then the bridge will be balanced, and V0=0 . Therefore, if a bridge circuit is used in the measurement system, the changes in the sensor capacitance will come from the changes in the measurand only. When the ambient conditions change, all of the capacitors are affected similarly and are compensated for.
The Casimir Effect Revisited
The Casimir effect is an attractive pressure that can influence the performance of a MEMS device. The effect of this phenomenon has to be accounted for in the design and analysis of micro/nano/multi-scale electromechanical systems . For instance, the study of the Casimir effect is beneficial in performance improvement of a capacitive vibration sensor
when the gap distance between the two capacitive plates of the
sensor is at a submicron scale. It is desired to avoid this effect
or calibrate the sensor giving consideration to the existence of
the Casimir effect to achieve accurate measurements. This effect
can also be employed in the design of novel and efficient
systems at nano- and micro-scales  which is not feasible at
When considering the general subject of sensors, the identification of sensors should be addressed with respect to function, operation and interaction, as well as the proper selection and interfacing of these components for various applications . Parameter selection (including system tuning) is an important step as well. The great majority of sensor ratings provided by manufacturers are in the form of static parameters. In engineering applications, however, dynamic performance specifications are also very important.
The Perfect Sensor
A perfect sensor can be defined as one that possesses the following characteristics:
Sensor output instantly reaches the sensed value or measurand (fast response).
Transducer output is sufficiently large (high gain, low output impedance, high sensitivity).
Device output remains at the measured value (without drifting or being affected by environmental effects and other undesirable disturbances and noise) unless the measurand itself changes (stability and robustness).
The output signal level of the transducer varies linearly in proportion to the signal level of the measurand (static linearity).
Connection of a measuring device does not distort the measurand itself (loading effects are absent and impedances are matched).
Power consumption is small (high input impedance).
All of these properties are based on dynamic characteristics and, therefore, can be explained in terms of dynamic behavior of the measuring device. In particular, items 1 through 4 can be specified in terms of the device response, either in the time domain or in the frequency domain. Items 2, 5, and 6 can be specified using the impedance characteristics of the device. Even though real sensors and transducers can behave quite differently in practice, when developing a practical system, we may use the ideal behaviour as a reference for the design specifications.
Accelerometer Selection Guide
Many MEMS sensors are designed to perform various forms of vibration detection. We now present a basic guide for selecting an accelerometer. In what follows, we consider the following categories:
◗◗Analog or digital: Depending on whether the interface hardware for the accelerometer is analog or digital, an analog or a digital accelerometer is used.
◗◗Category of g value:
◗◗ Steady acceleration or transient vibration/shock:
◗◗Acceleration, displacement, and velocity:
Acceleration can be converted to velocity and displacement using analog integrator circuits. MEMS can be used in machinery vibration monitoring applications that exhibit frequencies in the range of 0.5 Hz to 50 Hz, velocities in the range of 0.005 in/s to 2 in/s (0.13 mm/s to 51 mm/s), and displacements from 0.001 in to 0.010 in (0.25 mm to 2.5 mm). Displacement sensors are suitable for measuring low frequency and low amplitude magnitudes. Velocity sensors have lower sensitivity for high frequency vibrations. Velocity sensors are used in low to medium frequency measurements. Accelerometers are applicable to most vibration monitoring applications in low to very high frequency scenarios. Low cost MEMS accelerometers are commercially available for a wide variety of applications.
It is often advantageous to use mechanical sensors at the micro/nano scale rather than conventional macro-scale sensors. This article addressed the recent advances in MEMS sensor technology and presented their impact in technological innovation and progress. A variety of application scenarios and practical considerations were presented in this paper. This is the second of a three-part series. In the first part, a general introduction to MEMS sensing was given including the main underlying principles . Also, biomedical MEMS sensors were studied by describing the principles of bio-sensing and a typical set of biologically inspired sensors. Part 3 of the series will cover MEMS sensing in the thermo-fluid and electro-magnetic domains.
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