Chap13 Mass Measurements

7/28/2019 Chap13 Mass Measurements

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Mass Measurements

1 lb = (1 lbm)(32.17ft/s2)/gc

Analytical Balance.Sensitivity increases

withL, but decreases

with the weight of

the arms.


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13.3.1 Analytical Balance

M r F


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13.4 Elastic Transducers

K=F/y

F= the applied load

y = the resulting deflection at the location ofF

K= the deflection constant

This is a broad category, but in most cases, a load is applied to a

member which bends as a result. The deflection is picked up bysome mechanical means, or by a secondary transducer such as a

strain gage.


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Force Measurements

Load Cell A transducer that generates a voltage

signal as a result of an applied force.


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1

As with pressure sensors, sensitivity trades off with frequency response


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Proving RingsThis is often used as a calibration standard for loads in the range

from 300 to 300,000 lbf.

Reed

Micrometer


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Proving Ring Load Cells

y

2 4

FnD

3

16EI

Fn

D

Very precise--used as local

standard.


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Strain Gage Load Cells

Shaped to:

1) Provide an appropriate range

of force measuring capability

2) Provide sensitivity to forces inone direction only.


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Bending beam Load Cells

Cheap


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Shear Beam Load Cell

Fast Response, low creep.


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Temperature Sensitivity

When an elastic member changes temperature, its dimensions and

stiffness both change. Youngs modulus changes by roughly2.5%/100F while the dimensions may change by 0.15%. This can be

compensated for by adding a resistor to the bridge with has a value

that changes with temperature.

The sensitivity of the

bridge is reduced by a

factorn where

n

1

1 Rs /R


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eoei

R

2/R

4 2 R2/R (7.17 in book)

eoei

k

4

RR

if 2R/R


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eoP

ei4

FRk

A

1

E R Rs

IfE(R +Rs) remains constant, then we

have accomplished compensation

If we assume that the modulus varies linearly with temperature (eq.

6.15) and we can find a resistor that also varies linearly with

temperature,

E R Rs E1 cT R Rs 1 bT

RsR

c

b cc is generally negative and b is always

positive, so b > -c

So, given the material of the member, c, we can

chooseRs and b


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Examples


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Torque Measurements

Torque Load Cell

Difficult to use on a

rotating shaft.

Slip rings, telemetry


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13.9.1 Mechanical and Hydraulic

Dynamometers1) Absorption Dynamometers

dissipate mechanical energy.

Good for power systems.

2) Driving dynamometers measure

torque as they supply power

3) Transmission dynamometers

measure torque without

dissipating or supplying energy. Prony Brakes

W B k


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Water Brakes

Power absorption goes like the cube of speed

Absorption at a given speed is controlled by water level


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T = FR

P = wT

El i l D


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Electrical Dynamometers

The eddy current dynamometer shown

generates electrical currents by rotatinga disk in a magnetic field. The

resultant currents are dissipated inside

the machine. An electrical input

allows the user to dictate the strength

of the field and thus amount ofdissipation for a given speed.

C dl d DC d


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Cradled DC dynamometers

This type can drive or absorb.

T i i D


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Transmission Dynamometers

Chap13 Mass Measurements

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