TORQUE SENSOR IDEA

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Force II

Dynamometers

Accelerometers


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Measurement Lab21 Feb 2003

Note: this material may be copyright protected and may only be used for personal use. 1

Dynamometers

A dynamometer is an instrument for measuring the power exerted by asource or the amount of power consumed by a load.

The following two types of dynamometers are considered:

1 Absorption typeThis type of dynamometer measures torque (and power) by dissipatingmechanical energy and are suitable for power measurement of engines(such as internal combustion and gas turbine engines) and electrical

motors (ac and dc motors). A Prony brake, water brake, and cradledelectric motor are of this type.

2 Driving type

This type of dynamometer measures torque (and power) and supplyenergy to operate the device being tested. This is convenient for testingsuch devices as pumps and compressors, which require a drivingsource. A rotating electric machine can be used as a drivingdynamometer.


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Dynamometer Absorption Type

Prony Friction Brake (Absorption Type)

Historically, a device called a Prony brake was used to measure shaftpower. Consider, for example, an engine.

The Prony brake serves to provide a well-defined load for the engine, withthe output power of the engine dissipated as thermal energy in thebraking material. By adjusting the load, the output power over a range of

speeds and throttle settings can be realized.

The power P is measured by recording the torque FL acting on the torque

arm and the angular speed R of the engine which can be measured byusing a tachometer.

Hence, P=2RFL.


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The dry friction induced between the surfaces in contact will tend torotate the arm in the same direction as the shaft rotation. The entiredriving power of the shaft is expended in producing the friction at R rps(revolution per second, or Hz). This driving power is equal to themechanical effect of the shaft when running at the same R rps in theperformance of useful work. The engine torque is equal to the friction (orbrake) torque, , at this rps, which in turn is equal to the balancing torqueFL

(when arm is not rotating). Thus the engine torque is given byLoad adjusting nuts

Brake materialRotating wheel(connected to driver)Angular speed: R rps (Hz)

Load cellF

Arm length: L

Stationary arm

r

Fr

T F L= (Nm, ft- lbf)

The power at this rps is given

by

745.70W)=ft.lbf/s550=HPNm/s,=(W

2 TRP ==


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Water-brake dynamometer is similar to a Prony brake but employs fluidfriction (rather than dry friction) to dissipate energy.

When testing engines using a water-brake dynamometer, the brakingaction (or load) is developed by the principle of direct momentum

exchange between the rotor(s) and stator(s) of the dynamometer. Thedynamometer rotor(s) directs the water against the water-brake housingor stator. The stator in turn, redirects the water back against the rotor sothat it opposes the movement of the rotor(s). It is this turbulence and

back pressure which causes the braking action or load. The greater theflow of water through the dynamometer, the greater the braking action orload.

The stator is held in position by a strain gauge (torque link) which willmeasure the force acting on the stator. With proper calibration, this forceis a measure for the torque produced by the engine when it moves therotor in the water.


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Cradled Dynamometers


A cradled dynamometer is supported in bearings with a moment armconnected to a force measurement device.

1. Absorption Type

When a source (motor, engine, etc.) is connected, this dynamometeracts as a generator and dissipates the power in the form of thermal

energy in a resistive load connected to it. The mechanical powergenerated by the source can be found by measuring the rotationalspeed of the shaft using an RPM sensor (to be discussed later in thecourse) and the steady-state force required to prevent rotation of the

dynamometer.


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2. Driving Type

The torque and power of a dc motor can be measured by itself, bysupplying the electrical power to the motor, in which case a separate

load is required to dissipate the power and adjust the rotational speed.

F

r

Moment arm

Cradleddynamometer

(generator ormotor)

Shaft supportedby bearings

Base

F

To a resistive loador a power source


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Accelerometers

Vibrations and shocks are often measured using an accelerometer.Although a variety of accelerometers are available, strain gage andpiezoelectric transducers are the most widely used devices for suchmeasurements.

1. Strain Gage Accelerometer

In many strain gage accelerometers, SGs are bonded on a flexiblemember which supports a mass and senses the strain which results

from an acceleration of the mass. This device can be calibrated easily,but has relatively low sensitivity, compared with the piezoelectricaccelerometer.

Mass (M)

Cantileverspring (K)

Mounting base

Viscous fluid (D)

Strain gagesSmalldisplacement (x)


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Accelerometers

If the accelerometer frame is accelerated upward at a constant rate, themass will deflect the cantilever spring down, until the spring exert a forcelarge enough to accelerate the mass at the same rate as the frame. Atsuch a condition, Newtons law of motion gives ma = Kx(ignoring theviscous fluid damping), so we get,

where Kis the spring constant (N/m) and x the displacement (m), M themass (kg) and a the acceleration (m/s2), of the mass. (The displacementis proportional to the acceleration, when a is constant; i.e., x is constant.)

Most accelerometers are used to measure changing acceleration, andthe accuracy of this device depends on the frequency of accelerationchanges.

aK

Mx=


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Piezoelectric Accelerometer

A piezoelectric accelerometer uses a piezoelectric element (a certaincrystal), which produces voltage across the crystal when stressed.(Piezoelectric elements will be covered later in the course.) Up- or down-ward motion of the housing changes the compressive forces to thepiezoelectric element, causing a stress in the piezoelectric material and,thus, voltage. This instrument can be used to measure only varyingmeasurands (0.03 to 10kHz) and not steady accelerations. Theadvantages of this instruments are high sensitivity (1mV/g to 100mV/g),and small size.

Tightening Nut

Mass

Piezoelectricelement withelectrodes

Post

Mounting base

Viscous fluid


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Calibration of Accelerometers

One of the ways to calibrate accelerometers is the free-fall method,where a 1g stepped acceleration can be created by suspending anaccelerometer with a string which is suddenly cut. For high g case, animpact pulse can be applied to the accelerometer using a ballisticpendulum or drop tester. Using the output voltage of the accelerometerand the velocity change measured using a velocity sensor, thesensitivity (in V/g) can be found as follows:

The velocity change V2 V1 is related to the acceleration a by .and the sensitivity Kof the accelerometer is its output voltage eover the

applied acceleration, ie. K = e/a

A ccelerometer

A ballistic pendulum

=2

1

12

t

t

dtaVV


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Calibration of Accelerometers

Therefore, the sensitivity of the accelerometer can be found from

where is obtained from the accelerometer output data (byintegrating enumerically or graphically) and V2-V1 is obtained from thevelocity measurement.

http://bits.me.berkeley.edu/beam/acc_10.html

2

1

t

t

dte

( )=

2

1

12

1t

t

dteVV

K

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