I. Mechanical Measurands: 1. Classification of main types: EE 5344 Introduction MEMS CHAPTER 6 Mechanical Sensors 1. Position Displacement x, θ. Velocity, speed Kinematic dx dθ v =, = ω 3. Acceleration (Linear, angular) v v v v 4. Force, rque F, T = rxf 5. Stress, pressure F/A force/unit area 6. Strain L/L Deflection/unit length 7. Stiffness, compliance detection subject force. 8. Mass, density 9. Flow-rate 10. Shape, roughness (friction) 11. Viscosity (fluid friction) 1. Other (acoustic, ultrasonic) d x dv a =, d θ dω α = =. Principles of Mechanical Microsensors: Mechanical quantity Sensing Element Mechanical quantity Electrical signal 1 / Mechanical Sensors I
We sense by utilizing special properties of materials. Ex: piezoelectric material Deformation PE Material Sensor mode Charge Actuar mode See table 7.4 Capacitive charge II. Mechanical Properties of Silicon Microstuctures Most commonly used building material for microsensors. Also, it is also used for microelectronics => widely available for manufacturing technologies. 1. Mechanical Structures Key mechanical parameters and properties in design: 1. Physical dimensions: wih, height, thickness, radius. Material properties: Elastic Modulus, Yield Strength, Poisson s ratio, Density, viscosity 3. Calculable parameters: mass, spring constant, damping coefficient, strain, Natural frequency, Moment of inertia 4. Load Parameters: Applied (external) force, Applied (external) rque, stress, pressure, Impulse 5. Response parameters: Lateral deflection, Angular deflection, Sensitivity, resonance, Band-wih Hooke s Law: Linear elastic theory: F km x distributed loads: σ m = Emεm F: force, k m : spring constant, x: linear displacement, σ m : stress, E m ; Young s modulus, ε m : strain / Mechanical Sensors I
3. Micromechanical Scaling: Does size affect the physical laws/parameters? We may perform dimensional analysis get our answer! Macro L Micro KL Scale Facr Cantilever beam: m, Mass ~ Volume => Facr K 3 x, Displacement => Facr K F, Beam Force => Facr K σ m, stress ~ F/A ~ Facr K /K =1 k m, Spring constant F/ x, ~ K 3 3 L L Deflection y = F = F ~ K, Here I is the moment of inertia in kg/m 3EmI 3Em ( m L ) ω 0, Natural frequency ~ k m m ~ K K 3 = 1 K So K => m y k m ω 0 lower less stiller cost sensitive Frictional Phenomena Viscous damping (K ) Mass Coulomb damping (K 3 ) Elastic Coulomb damping (K ) Surface adhesion (K ) In amic scale, the theories of scaling break-down, decreased viscous damping, increased surface adhesion etc. 4. Silicon Micromechanical Structures Single crystal silicon =>steel, iron in Young s modulus. But more brittle => no elastic deformation, snaps! 3 / Mechanical Sensors I
Polishing Silicon or coating with SiN x improves its mechanical endurance. Polycrystalline Silicon is also used. Typical grain size should be much smaller than smallest structure dimension. (>about 80 nm) *Microflexural Structures: These are mechanical structures that deflect under force, => sensing elements. Motion => electricity Ex: Cantilever beam cantilever beam. F, y electrodes You can drive the system electrostatically Electricity Motion Characteristic Differential Equation: d y dy m + bm + km y = F( t) Here, m: mass; b m : damping coefficient; k m : spring constant. Go over Figure 7.5 and Table 7.10 General Outline: Displacement microsensors; Velocity and Flow Microsensors; Acceleration Microsensors; Force, Pressure and Strain Microsensors, Mass Microsensors, Other Microsensors (Acoustic, viscosity etc.) III. Displacement Microsensors To measure the position at an item of interest. Displacement sensor Proximity sensor Contacting (the sensor is in contact with the item of interest), potentiometers, piezo-accelerometer) {capacitive, resistive, inductive, magnetic, optical} Non-contacting (the sensor is remote) {capacitive, inductive, magnetic, infrared, ultrasonic, optical) 4 / Mechanical Sensors I
1. Capacitive and inductive displacement sensors The cantilever example We may measure the gap. We may use this indirectly measure force/rque, pressure/stress, deflection force. Optical displacement sensors They are based on: i) Interruption of a direct beam ii) Specular reflection off a surface iii) Diffuse scattering off a surface Ex: Diffuse Sensor 1. I d Drive Current V s Sense Voltage LED Object d = f (V s, I d ) non-linear Better for detecting the presence of an object Pho transisr d= 1mm Ex. Array of detecrs Light Source 5 / Mechanical Sensors I
3. Ultrasonic displacement sensors Send a wave υ in the medium is known. t is known Receive a wave υ t => s = Commonly piezo-ceramics (Lead titanate or lead zirconate) are used generate and capture the wave. Applications: measure proximity, distance, level of liquids etc. Advantages: can be used on conducting as well as non-conducting materials. Ultrasound is high frequency 50KHz, so low interference and less susceptible dirty environments. Can be used up 5m. Go over Figure 7.7. LVDT Another common type of is the linear Variable Differential Transformer, also known as the LVDT. The LVDT is basically a series of inducrs in a hollow cylindrical shaft and a solid cylindrical core, See figure below. The LVDT produces an electrical output proportional the position of the core. The physical position an electrical output. The lack of friction between the hollow shaft and the core prolong the life of the LVDT and enable very good resolution. In addition, the small mass of the core allows for good sensitivity in dynamic tests. Primary Coil Core Secondary Coils CROSS SECTION OF A LVDT The LVDT is constructed with two secondary coils placed symmetrically on either side of a primary coil contained within the hollow cylindrical shaft. Movement of the 6 / Mechanical Sensors I
magnetic core causes the mutual inductance of each secondary coil vary relative the primary, and thus the relative voltage induced from the primary coil the secondary coil as well. These LVDT s may also be calibrated by varying the position of the core and measuring the corresponding output voltages. Then Calibration curve or calibration constant may be determined and applied arrive at the engineering units of position. III. Velocity & Flow Microsensors: Basic Relationships Quantity Linear Angular displacement x θ velocity v ω acceleration a α dx ν = dθ ω = x = v θ = ω t t dv a = = d x dω d θ α = = v = t a t ω = α 7 / Mechanical Sensors I