Sensors & Actuators Velocity and acceleration 014-015 Sensors & Actuators - H.Sarmento
Outline Velocity sensors Gyroscopes Accelerometers 014-015 Sensors & Actuators - H.Sarmento 1
Velocity and acceleration Position, velocity, and acceleration are all related. Velocity is how fast an object is moving: the first derivative of the position. dy d v y dt dt Acceleration is how fast an object's speed is changing: the second derivative of the position. dv d y d d y ay a dt dt dt dt In a noisy environment, taking derivatives may result in extremely high errors. 014-015 Sensors & Actuators - H.Sarmento
Velocity measurement Velocity is a vector that consists of a magnitude (speed) and a direction. Many velocity or acceleration sensors contain components that are sensitive to a displacement. However, velocity can also be measured by direct sensors. 014-015 Sensors & Actuators - H.Sarmento 3
Linear velocity sensors Linear velocity of solids: Linear velocity transducers (LVT) Doppler radar sensors. Linear velocity of fluids: Particle image Laser Doppler Thermal anemometer Pitot probes 014-015 Sensors & Actuators - H.Sarmento 4
LVT (1) LVT consists of: A core (a permanent magnet). Two electrical coils. coil 1 coil N S V T The two coils are wrapped with opposite polarity. The south pole of the magnet induces a voltage primarily in coil, and the north pole primarily in coil 1. Moving a magnet through a coil of wire will induce a DC voltage (emf) in the coil according to Faraday's Law: d emf N dt 014-015 Sensors & Actuators - H.Sarmento 5
LVT () The induced DC voltage is proportional to the magnet's velocity and field strength. coil 1 coil N S V T B l v V T [Source: Trans-tek] B - component of the flux density normal to the velocity l - length of the conductor v - velocity 014-015 Sensors & Actuators - H.Sarmento 6
LVT (3) [Source: Trans-tek] Working range: detection of velocity along a distance limited by the size of the sensor The DC voltage is relatively independent of position within some limited range near the center. 014-015 Sensors & Actuators - H.Sarmento 7
Commercial LVTs [Source: Trans-tek] The core slides inside a hollow cylindrical tube. 014-015 Sensors & Actuators - H.Sarmento 8
LVT applications Shock Absorber Testing Machine LVTs used to rate damper performance, which leads to a better shock absorber design. Injection Molding Machine LVTs used to monitor the injection rate of molten plastic flow. Glass Pipette Pulling LVTs used to control the pull rate of molten glass to form pipettes used in most laboratories. PC Board Drilling LVTs used to control velocity in PC Board drilling applications. 014-015 Sensors & Actuators - H.Sarmento 9
Doppler radar velocity measurement When radio waves strike a moving object, the frequency of the reflected radio waves is altered. f D v cos [Source: J. M. Cimbala] v f D cos wavelength of RF incident waves in a moving object. v velocity of the moving object at angle relative to the radar unit. f d shift in frequency of the reflected wave relative to the transmitted wave. 014-015 Sensors & Actuators - H.Sarmento 10
Particle image velocimetry (1) Velocity measured following tiny particles that move with the fluid. PIV (Particle Image Velocimetry) [Source: J. M. Cimbala] 014-015 Sensors & Actuators - H.Sarmento 11
Particle image velocimetry () A double-pulse laser illuminates a region of flow under study, and a digital camera records two images timed with the two pulses of laser light. Illuminated particles appear as bright spots on the photographs 014-015 Sensors & Actuators - H.Sarmento 1
Particle image velocimetry (3) With a double pulse two bright spots appear on the photograph. The distance (displacement) d between the two bright spots is measured. Speed is determined by t - time interval between laser pulses. v d The direction of the particle movement is determined by image processing. t 014-015 Sensors & Actuators - H.Sarmento 13
Laser Doppler velocimetry (1) Velocity is measured at a fixed point in the flow, for tiny particles that move with the fluid. LDV (Laser Doppler Velocimetry) [Source: J. M. Cimbala] The laser beam is split into two parallel laser beams of equal intensity. 014-015 Sensors & Actuators - H.Sarmento 14
Laser Doppler velocimetry () Beams pass through a converging lens that focuses the beams at a point in the flow. 014-015 Sensors & Actuators - H.Sarmento 15
Laser Doppler velocimetry () At the convergence point, the waves interfere, creating a bright and dark fringe pattern due to constructive and destructive interference. 014-015 Sensors & Actuators - H.Sarmento 16
Laser Doppler velocimetry (3) Bright and dark fringe pattern : [Source: J. M. Cimbala] Tiny particles that pass through the measurement volume scatter laser light. The scattered light intensity is bright, then dark, then bright, etc. as particle moves through the fringe pattern. 014-015 Sensors & Actuators - H.Sarmento 17
Laser Doppler velocimetry (4) The scattered laser light is collected by a receiving lens and photodetector. Fluctuations in light intensity are converted to a fluctuating voltage signal. 014-015 Sensors & Actuators - H.Sarmento 18
Laser Doppler velocimetry (5) The spacing between fringe lines d λ sin - wavelength of the laser light - angle between the two beams The speed of the moving particle is linearly proportional to the frequency of the fluctuating light intensity: fλ fd sin 014-015 Sensors & Actuators - H.Sarmento 19
Laser Doppler velocimetry (6) The Bragg cell permits to shift slightly the beam frequency, causing the fringe pattern to move. This permits to detect direction. 014-015 Sensors & Actuators - H.Sarmento 0
Thermal anemometer (1) The rate of convective heat transfer from a hot object to the surrounding fluid increases as the speed of the fluid flowing around the object increases. Thermal anemometers consist of a heated (by electric current) temperature sensor. The sensor tends to cool down as fluid velocity increases, but electronic control maintains it to a constant temperature, increasing the current. 014-015 Sensors & Actuators - H.Sarmento 1
Thermal anemometer () E is the voltage across the sensor. P I Rsensor R E sensor [Source: J. M. Cimbala] Speed can measured by E E a n bv a, b, and n are constants (calibrated for a given sensor). 014-015 Sensors & Actuators - H.Sarmento
Pitot tube (1) Velocity measurement based on pressure measurement. Pitot-static probe is a tube with stagnation pressure tap and several circumferential static pressure taps. [Source: J. M. Cimbala] 014-015 Sensors & Actuators - H.Sarmento 3
Pitot tube () v P P 1 - fluid density [Source: J. M. Cimbala] 014-015 Sensors & Actuators - H.Sarmento 4
Angular velocity measurement Angular velocity sensors to measure shaft speed are many times called tachometers (tacho means speed in greek). Gyroscopes (or gyros) can also be used to measure angular velocity. Types of gyroscopes: Rotary: based on the principle of the conservation of angular momentum. Vibratory: based on Coriolis acceleration. Optical gyroscope: based on Sagnac effect. 014-015 Sensors & Actuators - H.Sarmento 5
Rotary gyroscopes (1) Rotary gyroscopes are navigational tools. They are used in the stabilization devices, where a stable directional reference is required, such as satellites, smart weapons and robotics. The basic principle involved is the principle of conservation of angular momentum. 014-015 Sensors & Actuators - H.Sarmento 6
Rotary gyroscopes () spin axis platform input axis [Source: J. Fraden, 010] output axis A rotor (heavy disk/wheel). A platform with an inner and an outer gimbal that is free to rotate about two axes. 014-015 Sensors & Actuators - H.Sarmento 7
Rotary gyroscopes (3) spin axis platform input axis [Source: J. Fraden, 010] output axis When the rotor freely rotates, it tends to preserve its axial position 014-015 Sensors & Actuators - H.Sarmento 8
Rotary gyroscopes (4) spin axis platform applied torque input axis [Source: J. Fraden, 010] output torque output axis If a torque is applied to the frame around one axis (input), the platform develops a torque around a perpendicular axis (output). 014-015 Sensors & Actuators - H.Sarmento 9
Rotary gyroscopes (5) spin axis platform applied torque input axis [Source: J. Fraden, 010] output axis precession The spin axis turns around the output axis. This phenomenon is called precession of a gyro. 014-015 Sensors & Actuators - H.Sarmento 30
Rotary gyroscopes (6) spin axis platform applied torque input axis [Source: J. Fraden, 010] output axis precession The precession becomes a measure of the applied torque and can be used as an output to, for example, correct the direction of a device. 014-015 Sensors & Actuators - H.Sarmento 31
Rotary gyroscopes (7) spin axis applied torque input axis [Source: J. Fraden, 010] output axis precession Application of torque in the opposite direction reverses the direction of precession. 014-015 Sensors & Actuators - H.Sarmento 3
Rotary gyroscopes (7) The relation between the applied torque and the angular velocity of precession is: T I T is the applied torque the angular velocity of the spin axis I moment of inertia of the rotating mass is the angular velocity of precession. 014-015 Sensors & Actuators - H.Sarmento 33
Mass Moment of Inertia Moment of Inertia of a rotating mass (I) is a measure of an object's resistance to changes in a rotation direction Moment of Inertia of a rotating mass depends: on the mass of the object its shape and its relative point of rotation. For a circular disk is T Mr M - mass of the disk r - distance between axis and outside disk 014-015 Sensors & Actuators - H.Sarmento 34
Rotary gyroscopes (8) When the wheel (rotor) freely rotates, it tends to preserve its axial position. If the gyro platform rotates around the input axis, the gyro will develop a torque around a perpendicular (output) axis, thus turning its spin axis around the output axis. This phenomenon is called precession of a gyro. 014-015 Sensors & Actuators - H.Sarmento 35
Vibratory gyroscopes In MEMS gyroscopes the rotating mass is replaced with a vibrating element: the mass moves linearly in simple harmonic motion. Vibrating gyroscopes rely on the phenomenon of the Coriolis acceleration. The resulting Coriolis acceleration can be detected and related to the angular velocity. 014-015 Sensors & Actuators - H.Sarmento 36
Coriolis acceleration (1) rotation a Coriolis acceleration x The Coriolis acceleration appears, whenever a body moves linearly in a frame of reference that is rotating about an axis perpendicular to that of the linear motion. v linear motion 014-015 Sensors & Actuators - H.Sarmento 37
Coriolis acceleration rotation a Coriolis Coriolis acceleration v a Coriolis v a Coriolis v If the sensor is rotated in the plane perpendicular to the linear vibration, an acceleration is obtained, proportional to the angular velocity. 014-015 Sensors & Actuators - H.Sarmento 38
MEMS vibratory gyroscope (1) [Source: Mems Mechanical Sensors, 004] MEMS gyroscopes rely on a mechanical structure that is driven into resonance and excites a secondary oscillation, due to the Coriolis force. 014-015 Sensors & Actuators - H.Sarmento 39
MEMS vibratory gyroscope (1) [Source: Mems Mechanical Sensors, 004] Inertial mass (gyro element). Two-gimbal (inner and outer gimbals) platform supported by torsional flexures. 014-015 Sensors & Actuators - H.Sarmento 40
MEMS vibratory gyroscope () The external gimbal is driven into oscillatory motion with a constant amplitude. This oscillatory motion is transferred to the inner gimbal, setting up an oscillating in the gyro element. 014-015 Sensors & Actuators - H.Sarmento 41
MEMS vibratory gyroscope () In the presence of an angular rotational rate normal to the plane of the device, the Coriolis force will cause the inner gimbal to oscillate about the secondary axis. The frequency is equal to the drive frequency and with an amplitude proportional to the inertial input rate. 014-015 Sensors & Actuators - H.Sarmento 4
MEMS vibratory gyroscope () Frequency in the secondary axis is sensed by two pairs of electrodes making up a (differential capacitor.) 014-015 Sensors & Actuators - H.Sarmento 43
Optical Gyroscopes Used extensively for guidance and control. No moving components. Based on the Sagnac effect: based on propagation of light in optical fibers. There are different types of optical gyros. Example: coil fiber gyroscope. 014-015 Sensors & Actuators - H.Sarmento 44
Sagnac effect (1) Two beams of light generated by a laser propagate within an optical ring in opposite directions. The two beams are received by the receiver at the same time. 014-015 Sensors & Actuators - H.Sarmento 45
Sagnac effect () If the optical ring is rotating, the beam travelling against the rotation experiences a slightly earlier than the other beam. 014-015 Sensors & Actuators - H.Sarmento 46
Sagnac effect (3) t 1 time the beam travel in the direction of rotation before being detected. t time the beam travel in the direction opposite to rotation before being detected. n is the refraction index. R l c v v n R l v 1 t1 t 014-015 Sensors & Actuators - H.Sarmento 47
014-015 Sensors & Actuators - H.Sarmento 48 Sagnac effect (4) 1 t 1 R l 1 1 v l R t 1 1 R t R v t v R v R t 1 v R v R R v R t 1 1
014-015 Sensors & Actuators - H.Sarmento 49 Sagnac effect (5) Angular velocity determined measuring l difference. 1 1 1 4 v R v R t t v R t R v 4 1 4 v R t t 1 4 4 t t v R v t R v l R v 4
Accelerometers (1) An accelerometer is a sensor that measures the linear acceleration experienced by an object. Accelerometers employ a moving mass in one form or another. Modern accelerometers are often small implemented as MEMS. 014-015 Sensors & Actuators - H.Sarmento 50
Working principle (1) Conceptually, an accelerometer behaves as a seismic mass (or proof mass) connected to a spring of stiffness (k) attached to the housing.. [Source: Fraden, 010] When the accelerometer is subjected to acceleration a, a relative displacement x of the seismic mass is produced by inertia. 014-015 Sensors & Actuators - H.Sarmento 51
Working principle () Considering the: acceleration of the accelerometer body horizontal acceleration of the mass d a dt x The equation of the movement is given by equation M Damper force d dt x b dx dt kx Ma Spring force 014-015 Sensors & Actuators - H.Sarmento 5
Working principle (3) Laplace transform X A s M 0 s k s s 0 0 k 0 0 M, b M b M 0 b km 014-015 Sensors & Actuators - H.Sarmento 53
Working principle (4) The accelerometer output signal may have an oscillating shape. < 1 = 1 >1 014-015 Sensors & Actuators - H.Sarmento 54
Working principle (5) Flat frequency response where the most accurate measurement can be made. Care shall be taken not to use the accelerometer close to its natural frequency. 014-015 Sensors & Actuators - H.Sarmento 55
Working principle (8) X A s M 0 s k s s 0 0 0 k M b M 0 b km A large mass increases the sensitivity (M/k), but reduces the natural frequency and the damping ratio. Stiffness (k) increases the natural frequency but reduces the sensitivity and the damping ratio. MEMS accelerometers are very stiff and have small mass: they have a large natural frequency, but small sensitivity and damping ratio. 014-015 Sensors & Actuators - H.Sarmento 56
Types of accelerometers (1) Acceleration sensors can be classified according to the physical principle they use: a direct measurement of a force: (force strain) a F m an indirect measurement, by means of displacement or deformation of a sensing element. (force displacement) a kx m 014-015 Sensors & Actuators - H.Sarmento 57
Types of accelerometers () F ma a F m a kx m Piezoresistive F x Capacitive Thermal Piezoelectric Other: Potentiometric, Optical, Inductive, hall effect 014-015 Sensors & Actuators - H.Sarmento 58
Piezoelectric accelerometers (1) In a piezoelectric accelerometer the seismic mass is directly connected to the piezoelectric crystal. When the accelerometer is subjected to an acceleration, the mass moves on the crystal and the compression of the crystal produces a proportional electric signal. 014-015 Sensors & Actuators - H.Sarmento 59
Piezoelectric accelerometers () The mass is enclosed between two piezoelectric crystals. Q V const coef piezo F a F m [Source: Halit Eren] The measured electric signal (Q) is equal to the force (F) applied on a crystal, due to the acceleration of the mass, multiplied for the piezoelectric coefficient. 014-015 Sensors & Actuators - H.Sarmento 60
Piezoelectric accelerometers (3) Single ended compression accelerometer: the piezoelectric crystal is sandwiched between the case and the proof mass. a F m [Source: J. Fraden, 010] 014-015 Sensors & Actuators - H.Sarmento 61
Piezoresistive accelerometer (1) In piezoresistive accelerometers the seismic mass is supported by elastic elements, which incorporates semiconductor straingauge as sensing elements. The measured strain is related to the magnitude and rate of mass displacement and, subsequently, with the acceleration. F R 1 E E A R G a F m Most piezoresistive accelerometers use two or four active gauges arranged in a Wheatstone bridge 014-015 Sensors & Actuators - H.Sarmento 6
Piezoresistive accelerometer () Cantilever design: proof-mass suspended by a spring, which in MEMS is usually a cantilever or beam. [Source: A. Albarbar] [Source: Chang Liu] 014-015 Sensors & Actuators - H.Sarmento 63
Piezoresistive accelerometer (3) Bulk-micromachined silicon accelerometer: motion perpendicular to the wafer plane. [Source: Chang Liu] [Source: R.P. vankampe, 1995] When the accelerometer is subjected to an acceleration, the mass moves up and down, causing the piezoresistances to change. 014-015 Sensors & Actuators - H.Sarmento 64
Capacitive accelerometer (1) [Source: Nathan Ida] 014-015 Sensors & Actuators - H.Sarmento 65
Capacitive accelerometer () An internal mass, supported by four silicon springs, is sandwiched between the upper cap and the base: The upper plate and the mass, at distance d 1, define a capacitance C 1. The base and the mass, at distance d, define a capacitance C. upper plate d 1 C 1 d C base [Source: J. Fraden, 010] 014-015 Sensors & Actuators - H.Sarmento 66
Capacitive accelerometer (3) upper plate d1 d C 1 d d C base x C te C a kx m [Source: J. Fraden, 010] 014-015 Sensors & Actuators - H.Sarmento 67
Capacitive accelerometer (4) When the accelerometer is subjected to an acceleration, the mass moves and the distance d 1 and d and capacitances C 1 and C change.. upper plate d1 d C 1 d d C base A A C1 C1 C C C0 C d x d x 014-015 Sensors & Actuators - H.Sarmento 68
014-015 Sensors & Actuators - H.Sarmento 69 Capacitive accelerometer (5) For small displacements: x d A x d A C C C 1 x d x A C x d A d C x
Capacitive accelerometer (6) ADXL78 (MEMS): single-axis accelerometer with signal conditioned voltage outputs that are on a single monolithic IC. [Source: Analog devices] 014-015 Sensors & Actuators - H.Sarmento 70
Thermal accelerometers (1) sealed chamber Heater detector 1 detector Substrate [Source: Yu ZHANG] Gas is the seismic mass. A resistive heating element at the centre heats gas molecules. When subjected to acceleration, the less dense (heat) gas molecules move in the direction of acceleration and denser molecules (cool) move in the opposite direction, creating a temperature difference. Acceleration lead to a forced convection of the gas within sealed chamber, creating a temperature difference. 014-015 Sensors & Actuators - H.Sarmento 71
Thermal accelerometers () sealed chamber Heater detector 1 detector Substrate Temperature sensors (detector 1 and detector ) measure the temperature difference. The difference of temperature is proportional to acceleration. 014-015 Sensors & Actuators - H.Sarmento 7
Thermal accelerometers (3) Under zero acceleration, a temperature distribution across the gas cavity is symmetrical about the heat source. acceleration [Source: MEMSIC] 014-015 Sensors & Actuators - H.Sarmento 73
Thermal accelerometers (4) MX15 dual axis accelerometer: a chamber of gas with a heating element in the center and four temperature sensors around its edge. [Source: MEMSIC] 014-015 Sensors & Actuators - H.Sarmento 74
Other types of accelerometers (1) Other accelerometers: inductive (LVDT), Hall effect, optical, etc. 014-015 Sensors & Actuators - H.Sarmento 75
Other types of accelerometers () A rod connected and moving with the mass links to a coil. The inductance of the coil is proportional to the position of the mass An LVDT may be used [Source: Nathan Ida] 014-015 Sensors & Actuators - H.Sarmento 76
Other types of accelerometers (3) Acceleration changes distance to hall element Hall element output is calibrated as acceleration The magnet may be on the hall element side (biased hall element) [Source: Nathan Ida] 014-015 Sensors & Actuators - H.Sarmento 77
Other types of accelerometers (4) Optical accelerometers use fiber optics. 014-015 Sensors & Actuators - H.Sarmento 78
Bibliography (1) Jacob Fraden, Handbook of modern sensors: physics, designs, and applications, Springer, third edition, 010 John M. Cimbala, Linear Velocity Measurement, Penn State University. Available at: https://www.mne.psu.edu/me345/lectures/velocity_measurement.pdf Charles P. Pinney, William E. Baker, Velocity Measurement, Measurement, Instrumentation, and Sensors Handbook, CRC Press, 1999 Chang Liu, Foundations of MEMS, Prentice Hall, 01 Stephen Beeby, Graham Ensell, Michael Kraft and Neil White, Mems Mechanical Sensors, Artech House, 004. Linear Velocity Transducer Technology, Trans-tek Inc. Available at: http://www.transtekinc.com/assets/files/catalog_pdfs_04c/lvts/lvt_tech04c.pdf John M. Cimbala, Linear Velocity Measurement,Penn State University. Available at: http://www.mne.psu.edu/me345/lectures/velocity_measurement.pdf Fabien Napolitano, Fiber-Optic Gyroscope key tchnological advanatges, IXSEA, 010. Available at: http://www.ixsea.com/pdf/fog-key-advantages.pdf Greg Chase, Sagnac Interferometer, Phys 517 Qunatum Mechanics. Available at: http://einstein.drexel.edu/~bob/term_reports/chase_01.pdf 014-015 Sensors & Actuators - H.Sarmento 79
Bibliography () Steps to selecting the right accelerometer, Meggitt s Endevco Corporation. Available at: https://www.endevco.com/news/newsletters/01_07/tp37.pdf National Instruments, Accelerometer Principles. Available at: http://zone.ni.com/devzone/cda/ph/p/id/1 Craig, Kevin C., Mechatronics in Design: That fictitious force, EDN Europe, Issue 11, p17, November 01. Available at: http://www.edn.com/electronics-blogs/mechatronics-indesign/4397081/that-fictitious-force 014-015 Sensors & Actuators - H.Sarmento 80