Week 6. Lecture 1 Velocity Measurement. Velocity (Speed) Measurement

Transcription

1 Week 6 Lecture 1: Velocity Measurement Lecture 2: Acceleration Measurement Activity: Module 6 Tutorial: Solving ODEs with Simulink and MATLAB solvers (ode45, ode23, etc.) Lecture 1 Velocity Measurement State velocities (linear and angular) and units for velocities List velocity measurement methods Describe mechanical and electrical tacho State the Doppler effect and principle State the principle of ship speed log Velocity (Speed) Measurement Linear velocity is a vector quantity and is the rage of change of linear displacement in a direction. Linear speed is a scalar quantity, which gives the magnitude of the linear velocity. Angular velocity is a vector quantity and is the rate of change of angular displacement about an axis. Angular speed is a scalar quantity, which gives the magnitude of the angular velocity. Frequency is the number of cycles, oscillations, or vibrations of a wave motion or oscillation in one second. Velocity: v = dx/dt, ω = dθ/dt, f = 1/T, ω = 2πf 1

2 Velocity Measurement Units: Linear velocity: m/s, km/h, Knots (NM/h) Rotational (angular) velocity: rad/s, deg/s (speed: r.p.m, r.p.s) Frequency: Hz, khz, MHz Methods: Mechanical, pressure, Electrical & Electronic Electrical/Electronic Doppler method Marine Doppler Speed Log Speed: Mechanic Tachometer Principle: Centrifugal force causes the sliding collar to move, then moves pointer. Reading of speed can be read by a scale. Speed: Drag Cup Tachometer Principle: Output voltage is proportional to the speed of the driven shaft. 2

3 Tachogenerators: Pick-up tachometer: (a) inductive; (b) capacitive Ship Speed Measurement Methods Speed measurement using water pressure Speed measurement using electromagnetic induction Speed measurement using acoustic correlation techniques (piezoelectric ceramic transducer) Speed measurement using Doppler principle Reference: Electronic Navigation Systems by Laurie Tetley & David Calcutt, Butterworth Heinemann, GB, Pressure Tube Speed Logging System Principle P= Kv 2 3

4 Ultrasonic Wave Propagation of Ultrasonic Waves c = f λ 1 f = T ω = 2πf Units: m/s, Hz and m respectively Units: Hz, second Units: rad/s, Hz c: velocity of propagation (m/s 2 ), f: frequency (>20kHz), λ: wave length (m), and ω: angular frequency (rad/s) Ultrasonic Wave Velocity of propagation depends on temperature of liquid (decrease as temp increases except for water) Velocity of propagation in solutions and suspension depends on the concentration of individual components Influence of hydrostatic pressure is 0.1% per Mpa, therefore is negligible Velocity of propagation is expressed by adiabatic and isothermal coefficients of compressibility. Ultrasonic wave reflects and refracts when going through a surface at an angle Applications of Ultrasonic Waves Level Measurement, Velocity Measurement, Flow Measurement, Viscosity Measurement, Depth Measurement, Medical Science,etc. Two techniques: Doppler: measure Doppler frequency shift Transit-time: measure the difference in travel time between pulses (travel and reflection) 4

5 What Is Doppler Effect? Christian Andreas Doppler ( ) born on 29 Nov 1803 in Salzburg Austria died on 17 March 1853 in Venice Italy. To discover the speed of the corpuscular elements in blood and the principle is named as Doppler principle/doppler effect: Doppler shift f (Hz) is proportional to both the flow velocity, v (cm/s) and the transmission frequency of the ultrasound f (MHz) Doppler Effect The Doppler effect, named after Christian Andreas Doppler, is the apparent change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the waves. A source of waves moving to the left. The frequency is higher on the left, and lower on the right. Examples of Doppler Effect Doppler phenomenon with sound and relative movement The whistle from a moving train: as the train approaches a stationary listener, the pitch (frequency) of the whistle sounds higher than when the train passes by (recedes), at which time the pitch sound the same as if the train were stationary. As the train recedes from the listener, the pitch decreases. The car horn (noise from a car) exhibits the same phenomenon 5

6 Illustration of Doppler Effect Principles of Doppler Speed Radar/Log Traffic Radar: Radar (wave transmitter and receiver) is stationary, target car is moving Radar (wave transmitter and receiver) is moving, target car is moving Ship s Doppler Speed Log: Wave transmitter and receiver are installed on board the ship whose velocities are measured. Doppler Effect Doppler Shift Stationary source Approaching Receding Frequency of Transmit Signal: f t (Hz) Velocity of Transmit Signal: c (m/s 2 ) Frequency of Reflection Signal f r (Hz) Velocity of Target: v Relationship between f t, f r, c, and v? 6

7 Doppler Effect Doppler Shift Approaching (moving towards) target: f r = f t + f d Receding (moving away) target: f r = f t f d where f d is Doppler shift the difference between the frequency of transmit signal and reflection frequency of reflection signal (echo) Doppler Effect Doppler Shift Doppler Shift (Hz): f d = ± v = ± 2vf c cfd 2f t t + for targets that are moving towards - for targets that are moving away Java Simulation of Doppler Effect: Doppler Effect Doppler Shift Both the source and target are moving: Source and target moving in the opposite direction Source and target moving in the same direction vr = vs ± v where v is velocity of moving target, v s is velocity of moving source, and v r is the relative velocity between the source and the target + opposite direction - same direction 7

8 Examples 1. You are driving your car at speed of 90km/h and approaching a police officer who is using a speed radar (stationary) with frequency of 200kHz, and wave velocity of 300*10 6 m/s to measure your car speed. Calculate the Doppler shift f d? 2. What is Doppler shift f d if you are driving at 130km/h and the police officer car (140km/h, 300kHz) is chasing your car? Applications of Doppler effect Speed logging systems (ship, police radar) Depth logging systems Astronomy Medical imaging Temperature measurement Laser Doppler velocimeters Acoustic Doppler velocimeters Doppler Effect Speed Log Principle Doppler shift: f d f d 2vft = c v 2vft = c f d = Doppler frequency shift (Hz) f t = transmitted frequency c = velocity of propagation v = relative speed 8

9 Speed: Doppler Speed Log f d = 2vft cosθ c Speed: Doppler Speed Log Speed: Doppler Speed Log f d 2vft = cos c ( cosθ + θ ) 0 θ = θ = 60 f d 2vf = c t 9

10 Speed: Doppler Speed Log Dual axis Doppler speed log DSL in market Sperry Marine SRD-500 Performance: Sperry Marine SRD-500 Sperry SRD- 500 Dual Axis Doppler Speed Log System 10

11 Sperry Marine Furuno Doppler Sonar DS-30 Ref: Summary of Lecture 1 There are several methods to measure speed. Doppler frequency shift is a natural phenomenon that has been used for many years to measure velocity. Doppler speed logging system: Transmits a frequency (typical 100kHz) towards the ocean floor and calculates the vessel s speed from the frequency shift detected The arrangement of transducer reduces errors 11

12 Any Questions? Lecture 2 Acceleration Measurement Lecture 2: Acceleration Measurement State acceleration and units State the Newton s 2 nd Law the basic principle to measure acceleration State general principles of accelerometers: force - displacement - acceleration Describe 4 types of accelerometer: potentiometric, l.v.d.t., variable reluctance, piezoelectric 12

13 Acceleration Measurement Acceleration: is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity. Units: m/s 2 (free fall - g, ft/s 2, in/s 2, Gal = 1cm/s 2 ) Angular motion: rad/s 2, deg/s 2 Newton s 2nd Law: F = ma x v Gal = Galileo Galilei ( ) F (N) m (kg) Accelerometer Using Simple Pendulum Consists of seismic mass and spring Principle of Mass-Spring Accelerometer Applying Newton s and Hooke s laws: k ma = k x a = x m 13

14 Types of Accelerometer Potentiometric accelerometers Capacitive accelerometers Inductive (L.V.D.F, variable reluctance) accelerometers Piezoelectric accelerometers micro electro-mechanical system (MEMS) accelerometers Inertial measurement units (IMU) Potentiometric, Capacitive and Inductive Accelerometers Accelerometers: a through e = one-direction accelerometers with various transduction mechanisms, f = triaxial accelerometer; a = acceleration, ax, ay, and az = triaxial accelerations, 1 = seismic mass, 2 = spring, 3 = damper, 4 = potentiometric element, 5 = capacitive element, 6 = inductive element with moving armature, 7 = inductive element with moving core, 8 = differentialtransformer element (LVDT), 9 = case, 10 = one-directional accelerometer. Inertial Measurement Units (IMU) Coordinate System 3 Linear motions 3 Angular motions 14

15 Accelerometers in market PCB Products: Model 307B Product Type: Accelerometer, Vibration Sensor High sensitivity, quartz shear ICP accel., 100 mv/g, 2.5 to 10k Hz, top conn., ground isolation Honeywell Sensotec: Uses of Accelerometer Uses of accelerometer: Indication and control Motion detection Process monitoring Vibration measurement application Automotive: automotive electronics, vehicle control systems General industries: equipment vibration detection, inertial navigation Summary of Lecture 2 Acceleration Measurement Acceleration and Units Newton s 2nd law basic principle Simple Accelerometer using Pendulum Accelerometer using Mass-Spring System Types of Accelerometer Applications of Accelerometers 15

16 Any Questions? Activity Module 6 16