Speed, Velocity, and Acceleration Instrumentation

• Speed - Scalar quantity equal to the magnitude of velocity» frequently inferred from rotational measurements,

simply because of the machine’s design, with rotating shafts, gears, etc

– Analog-type sensors were used exclusively until the mid-1950s, where digital speed sensors were developed.

– Digital sensors were preferred for easy integration with digital-based systems.

Definition of Terms

• Velocity – Time rate of change of position.• Linear Velocity (or simply velocity) – a vector quantity

– Must specify both speed and direction– Can be treated as scalar if the line of motion is clearly

understood, with proper algebraic signs.• Angular Velocity – time rate of change of the angle ϴ rotated

through– Average angular velocity – ration of the angular

displacement divided by the time. This is not a vector, since a finite angular displacement is not a vector. Hence the instantaneous angular velocity is widely used.

Definition of Terms

• Acceleration – Rate of change of velocity with respect to time.– Expressed mathematically by dv/dt, the vector derivative

of velocity v with respect to time t.– If the motion is of a straight line whose position is clearly

understood, it is convenient to treat the velocity v and the acceleration dv/dt as scalars with appropriate algebraic signs.

– Maybe curvilinear or rectilinear.– Acceleration due to gravity is 9.82 m/s2 or 32.2 ft/s2

Definition of Terms

• Tachometers - an instrument measuring the rotational speed of a shaft or disk, as in a motor, or other machine.– Known also as: revolution-counter, tach, rev-counter, or RPM

gauge.

Definition of Terms

In some servo-controlled motion systems, feedback is required in terms of position. In other situation, the feedback must be in terms of velocity.

Tachometers

In contemporary system, apermanent-magnet dc motormay be used as a tachometer,because it generates an outputvoltage which is proportional toshaft speed.

Desirable output characteristic of tachometer

Schematic of a DC tachometer coupled to a DC generator

Tachometers

Small permanent-magnet dc motors are:• Frequently used as speed-sensing devices• Use silver commutator and silver loaded brushes

– Improves commutation at low speeds and low currents

Tachometers

To combine high performanceand low-cost, dc servomotorsare now designed to have atachometer mounted on themotor shaft incorporated withinthe housing.

Two types of DC tachometers:1. Brush-type

1. Iron core2. Moving coil

2. Brushless

The AC tachometer is fundamentally a three-phase electric generator with a three-phase rectifier on the output.

DC Tachometers

DC Tachometers

DC tachometers depends on the relative perpendicular motion between a magnetic field and a conductor, which results in voltage generation in the conductor.

The magnitude of the voltageproduced is a direct function ofthe strength of the magnetic fieldand the speed with which theconductor moves perpendicularlyto it.

• Moving-coil brush type– Winding is in the form of a shell or cup– There is a magnet on one side and and iron slug on the other– The magnetic field passes through the cup shaped winding– Only the winding is rotating– Electrical inductance is greatly reduced

Brush-type dc tachometer are usually limited to clean environments because:1. Brush life is shortened due to particulates and erosive contaminants2. Some airborne contaminants might build-up on the commutator

DC Tachometers

This can solved by placing it in sealed enclosures, but will lead to thermal problems because of trapped heat. Such problems are:

1. The heat might damage the tachometer; this heat is not generated by the tachometer since only low currents are involved. This heat is from the equipment that travels through the shaft.

2. The permanent magnets are sensitive to temperature (estimated at 0.01 to 0.05% / °C). If output stability is critical, thermal compensation may be required.

DC Tachometers

• Speed-Ratio Systems with dc tachometers - By using two dctachometer generators (Fig. 7) connected to a ratio metermechanism, measurements that are depend on differentialprocessing speed, such as percent stretch and ratio of draw,can be taken and controlled through additional elements in thesystem.

DC Tachometers

AC Tachometers, two types:1. Voltage-responsive tachometer systems2. Frequency- responsive systems

AC Tachometers

1. Voltage-responsive systems – consisting of an AC generator and a rectifier-type

indicator.– Used in installation where the generator speed for full-

scale is between 500-5000 rpm.– Conventional generators maybe used up to 10 000 rpm,

provided, special attention is given to the bearings.– The AC tachometer embodies a stator surrounding a

rotating permanent magnet– The output of the generator for V-R systems is

temperature-compensated, and proportional to speed

AC Tachometers

Schematic circuit of AC voltage-responsive tachometer system

AC Tachometers

2. Frequency-Responsive Tachometer Systems– Consisted of:

» DC indicator/recorder» Frequency-responsive network(either contained

in the recorder or a separate transformer box)» AC tachometer (conventional or bearing-less

form)

AC Tachometers

Bearing-less Tachometer Generators– AC generators of the most basic form– Consists only of a permanent magnet rotor and stator– No bearings or brushes– Impervious to oil, grease, relatively high temperature– Maybe installed in inaccessible areas (e.g. gearboxes)– Low torque burden– Capable of speeds up to 100 000 rpm

AC Tachometers

When bearing less generators are used, the frequency-responsiveapproach is employed. The reason is the system is solelydependent on the frequency output of the generator, thus voltagevariation caused by reduction of flux due to rotor handling, pooralignment of stator and rotor, or axial travel of the rotor withrespect to the stator will not affect the overall accuracy.

AC Tachometers

Magnetic Speed Sensors – essentially, a coil wound around a permanently magnetized probe.

a. Sectional Viewb. Placement of probe, allowing a small air gap between pickup and gear teethc. Output waveform, a function of rotational speed and gear-tooth dimension,

spacing, pole-piece diameter, and air gap.

Magnetic Speed Sensors

Magnetic Speed Sensors works by modulating the flux density of the probe. This occurs when discrete ferromagnetic objects are passed through the probe’s magnetic field. Example of such discrete ferromagnetic objects include, but not limited to:

• Gear teeth• Turbine rotor blades• Slotted diskes• Shafts with keyways

Magnetic Speed Sensors

Magnetic pickups are also used as timing or synchronization device. Such as:

• Ignition timing of gasoline engines• Angular position of rotating parts• Stroboscopic triggering of mechanical motion

One commercially available device is a passive or self-generatingdevice. It requires no external excitation. It produces anapproximately sinusoidal ac voltage when place in close proximityto the teeth/blades of a conventional rotating device.

Magnetic Speed Sensors

The amplitude of the ac voltage output of a self-generating device is, generally, proportional to the speed of rotation.

Magnetic Speed Sensors

The magnetic pickup circuit below contains its own signal-conditioning circuitry for generating a clean square wave outputfor each ferrous discontinuity passing the head of the pickup. Theoutput is either on or off, depending on the presence or absenceof ferrous material.

Magnetic Speed Sensors

Impulse Tachometers – uses chargingcurrent of a capacitor. The pickup headusually has a reversing switch operated by aspindle which reverses direction twice forevery revolution. Battery potential is appliedto the capacitor in each direction, and witheach impulse, current is passing through themilliammeter. The indicator responds to theaverage value of these pulses. Theindication is proportional to the rates ofpulses, which in turn are proportional to therates of spindle rotation.

Impulse Tachometers

Impulse Tachometers:• Dependent of battery, needs regular checking.• The oscillating switch can be used for speeds 200 – 10

000 rpm. Above or below these speed require suitable gears.

• If properly standardized instrument is used, the readings are not affected by temperature, humidity, vibration, or magnetic fields.

• Indicator and head can be separated up to 300 meters.

Impulse Tachometers

Optical Encoders– takes advantage of microprocessors, the impulses from an

optical encoder can be converted to velocity measurement.– Wide dynamic range. Such as 10 000, to 20 000, to 1– Accuracies are claimed better than 0.01% per revolution

Stroboscopic Tachometers– Permits intermittent observation of a cyclically moving

object in such a way as to produce and optical illusion of stopped or slowed motion.

Optical Encoders & Stroboscopic Tachometers

a.) The first part is a schematic representation of the circuit. b.) Images obtained at harmonic and subharmonic flashing rates of a stroboscope.

Optical Encoders & Stroboscopic Tachometers

Variable-Reluctance Tachometers– Produces pulses that are proportional to speed– The pulses are amplified and rectified, and control the direct current to

a milli-ammeter– Rated at 10 000 to 50 000 rpm– Accuracy of ±1/2 of full scale reading– Can withstand temperatures from -51 to 260°C

Variable-Reluctance Tachometers

Photoelectric Tachometers– Designed to measure speed of up to 3 million rpm– The movable part is arranged to provide reflecting and absorbing

areas– The reflected light is picked up by a photocell that produces

electric impulses– The impulses are applied to a frequency meter that generates

square-waves applied to a discriminating circuit that produces a fixed current at each half-cycle which are further rectified and applied to a dc milliammeter

– Meter readings are proportional to the number of pulses per second, or simply, the frequency

Photoelectric Tachometers

Eddy-Current Tachometers– Also know as drag-type– Commonly used in automobile speedometers by the use of a flexible

shaft arrangement– Has a permanent magnet spun by the revolving source to be measured– Close to it is an aluminum disk, pivoted to turn against a spring– As the permanent revolves, eddy-currents are generated on the disk– The disk turns in the direction of the rotating magnetic field and turns

until the torque developed equals the spring– The torque is directly proportional to the speed of the rotating magnet.

Eddy-Current Tachometers

Velocity Head or Hydraulic Tachometers– Takes advantage of the fact that pumps or blowers produce a

velocity which can be converted into a static pressure– incorporates a rotary pump as the transmitter and a piston as the

receiver– The pump is driven by a flexible shaft and a gear train– Pump displacement raises or lowers a counterweight piston– The piston is connected to a pointer through a rack and gear

Velocity Head or Hydraulic Tachometers

Tachometerless Regulation of Servo-speed

Within the last few years, an interesting approach to regulating thespeed of a motor without a tachometer has emerged. Basically,the arrangement consists of allowing a motor to coast for a veryshort interval, during which the back electromotive force (EMF) ismeasured.

TACHOMETERLESS REGULATION OF SERVO SPEED

• Governors - an automatic controller used to maintain the rotative speed of a machine at a desired value. – Measures speed and compares it to a desired value, then

acts to correct any error between the two– Usually corrects the values by varying the flow of energy to

the machine• Two main types:

– devices in which the speed-sensing element operates the energy metering device directly

– devices that use one or more stages of power amplification between the speed-sensing element and the energy control device

TACHOMETERLESS REGULATION OF SERVO SPEED

1) devices in which the speed-sensing element operates the energy metering device directly

– Gives more stable control on an engine or other prime mover

2) devices that use one or more stages of power amplification between the speed-sensing element and the energy control device

– Requires stabilizing factors to prevent continual oscillation of the speed (hunting)

TACHOMETERLESS REGULATION OF SERVO SPEED

• Pitot Tube Air-Speed Indicators –– consists of two elements: (1) a

dynamic tube, which points upstream and determines the dynamic pressure, and (2) a static tube, which points normal to the air stream and determines the static pressure at the same point

• Venturi Air-Speed Indicators– Limitations of the Pitot tube led to the

design of a venturi air-speed indicator in which a greater differential pressure is created

– requires individual calibration for best accuracy. Parts are not readily interchangeable.

Air and Gas Velocity Measurement

Revolving-Vane Anemometers– comprises a paddle wheel which is

revolved by the moving air stream– wheel is attached to a counter, and by

selection of the proper gear ratios and vane pitch the counter can be calibrated to read directly in feet of air

– air velocity can be determined by measuring the time interval

– measurement tends toward the average air speed. The range of the device usually is 300 to 3000 ft/min (91.5 to 915 m/min).

Air and Gas Velocity Measurement

• Propeller-Type Electric Anemometers– This is a version of the basic

rotating-vane device– the propeller type in which the

blades are fastened to the shaft of an electric generator which develops an EMF or frequency proportional to speed

– The EMF or frequency signal is fed to an indicator

– The device reads average air velocity. The direction of airflow can also be indicated mechanically or electrically.

Air and Gas Velocity Measurement

Revolving-Cup ElectricAnemometers

– The generator is mounted on avertical axis, and, like thepropeller type, its EMF orfrequency output isproportional to the speed ofthe revolving cups. The speedreadings are average, but thedevice is not directional.

Air and Gas Velocity Measurement

Constant-Temperature Thermal Anemometers– the sensor element contains a heated

wire– An electronic control circuit maintains the

sensor element at a constant temperature regardless of the air velocity

– An electronic control circuit maintains the sensor element at a constant temperature regardless of the air velocity

– An uncompensated constant-temperature hot-wire anemometer will measure accurately only if the

– temperature of the air flowing past the sensor remains constant

Air and Gas Velocity Measurement