Force – II
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Dynamometers
Accelerometers
Dynamometers
A dynamometer is an instrument for measuring the power exerted by a
source or the amount of power consumed by a load.
The following two types of dynamometers are considered:
1
Absorption type
This type of dynamometer measures torque (and power) by dissipating
mechanical 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 cradled
electric motor are of this type.
2
Driving type
This type of dynamometer measures torque (and power) and
energy to operate the device being tested. This is convenient for
such devices as pumps and compressors, which require a
source. A rotating electric machine can be used as a
dynamometer.
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supply
testing
driving
driving
Dynamometer – Absorption Type
Prony Friction Brake (Absorption Type)
Historically, a device called a Prony brake was used to measure shaft
power. Consider, for example, an engine.
The Prony brake serves to provide a well-defined load for the engine, with
the output power of the engine dissipated as thermal energy in the
braking 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 by
using a tachometer.
Hence,
P=2πRFL.
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Dynamometer – Absorption Type
• The dry friction induced between the surfaces in contact will tend to
rotate the arm in the same direction as the shaft rotation. The entire
driving power of the shaft is expended in producing the friction at R rps
(revolution per second, or Hz). This driving power is equal to the
mechanical effect of the shaft when running at the same R rps in the
performance of useful work. The engine torque is equal to the friction (or
brake) torque, , at this rps, which in turn is equal to the balancing torque
FL (when arm is not rotating). Thus the engine torque is given by
T = F × L (Nm, ft - lbf)
The power at this rps is given
by
Load adjusting nuts
Arm length: L
Fr
r
Stationary arm
P = 2
πR × T
F
=ω
(W = Nm/s, HP = 550 ft.lbf/s = 745.70W)
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Rotating wheel
(connected to driver)
Angular speed: R rps (Hz)
Brake material
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Load cell
Dynamometer – Absorption Type
Water-brake dynamometer is similar to a Prony brake but employs fluid
friction (rather than dry friction) to dissipate energy.
• When testing engines using a water-brake dynamometer, the braking
action (or load) is developed by the principle of direct momentum
exchange between the rotor(s) and stator(s) of the dynamometer. The
dynamometer rotor(s) directs the water against the water-brake housing
or stator. The stator in turn, redirects the water back against the rotor so
that it opposes the movement of the rotor(s). It is this turbulence and
back pressure which causes the braking action or load. The greater the
flow of water through the dynamometer, the greater the braking action or
load.
• The stator is held in position by a strain gauge (torque link) which will
measure the force acting on the stator. With proper calibration, this force
is a measure for the torque produced by the engine when it moves the
rotor in the water.
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Cradled Dynamometers
Cradled Dynamometers
• A cradled dynamometer is supported in bearings with a moment arm
connected to a force measurement device.
1. Absorption Type
When a source (motor, engine, etc.) is connected, this dynamometer
acts as a generator and dissipates the power in the form of thermal
energy in a resistive load connected to it. The mechanical power
generated by the source can be found by measuring the rotational
speed of the shaft using an RPM sensor (to be discussed later in the
course) and the steady-state force required to prevent rotation of the
dynamometer.
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Cradled Dynamometers
2. Driving Type
The torque and power of a dc motor can be measured by itself, by
supplying the electrical power to the motor, in which case a separate
load is required to dissipate the power and adjust the rotational speed.
r
Cradled
dynamometer
(generator or
motor)
To a resistive load
or a power source
F
Shaft supported
by bearings
F
Moment arm
Base
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Accelerometers
•
Vibrations and shocks are often measured using an accelerometer.
Although a variety of accelerometers are available, strain gage and
piezoelectric transducers are the most widely used devices for such
measurements.
1. Strain Gage Accelerometer
In many strain gage accelerometers, SGs are bonded on a flexible
member 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 piezoelectric
accelerometer.
Viscous fluid (D)
Mass (M)
Strain gages
Cantilever
spring (K)
Small
displacement (x)
Mounting base
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Accelerometers
• If the accelerometer frame is accelerated upward at a constant rate, the
mass will deflect the cantilever spring down, until the spring exert a force
large enough to accelerate the mass at the same rate as the frame. At
such a condition, Newton’s law of motion gives ma = Kx (ignoring the
viscous fluid damping), so we get,
a =
K
x
M
• where K is the spring constant (N/m) and x the displacement (m), M the
mass (kg) and a the acceleration (m/s2), of the mass. (The displacement
is proportional to the acceleration, when a is constant; i.e., x is constant.)
• Most accelerometers are used to measure changing acceleration, and
the accuracy of this device depends on the frequency of acceleration
changes.
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Piezoelectric Accelerometer
• A piezoelectric accelerometer uses a piezoelectric element (a certain
crystal), which produces voltage across the crystal when stressed.
(Piezoelectric elements will be covered later in the course.) Up- or downward motion of the housing changes the compressive forces to the
piezoelectric element, causing a stress in the piezoelectric material and,
thus, voltage. This instrument can be used to measure only varying
measurands (0.03 to 10kHz) and not steady accelerations. The
advantages of this instruments are high sensitivity (1mV/g to 100mV/g),
and small size.
Viscous fluid
Tightening Nut
Mass
Piezoelectric
element with
electrodes
Post
Mounting base
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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 an
accelerometer with a string which is suddenly cut. For high g case, an
impact pulse can be applied to the accelerometer using a ballistic
pendulum or drop tester. Using the output voltage of the accelerometer
and the velocity change measured using a velocity sensor, the
sensitivity (in V/g) can be found as follows:
A b a l l is t ic p e n d u l u m
A c c e l e r o m e te r
t2
• The velocity change V2 – V1 is related to the acceleration a by V2 − V1 = t∫ a dt.
and the sensitivity K of the accelerometer is its output voltage e over the
applied acceleration, ie. K = e/a
1
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Calibration of Accelerometers
• Therefore, the sensitivity of the accelerometer can be found from
K=
t2
1
t2
(V2 − V1 )∫ edt
t1
• where ∫ edt is obtained from the accelerometer output data (by
t
integrating e numerically or graphically) and V2-V1 is obtained from the
velocity measurement.
1
• http://bits.me.berkeley.edu/beam/acc_10.html
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