ME314 - Mechanical Measurements Fall 2015
Project #2
Due November 6, 2015
Using Microsoft Excel, develop a spreadsheet program to calculate the
practical frequency range for a second order system. Your inputs
should include the mass, stiffness, damping co

Wheatstone Bridge Circuit
B
R2
R1
A
D
Eo
R4
R3
C
Ei
1
The voltage drop across R1 is denoted by EB and is given by
R1
EB =
Ei
R 1 R 2
Voltage divider theorem yields
Ei = IR1 + IR2 = I(R1 + R2 )
2
Ohm's Law
Georg Simon Ohm, a German
schoolmaster, showed tha

Definition of temperature: ?
Temperature is a measure of the relative heat intensity of an object.
Where there is heat transfer there occurs a change in temperature.
Along with this change in temperature there are certain effects.
1.
2.
3.
4.
5.
Change in

Dynamic characteristics of measuring systems
Most measuring systems will consist of first and/or second order
mechanical and electrical components.
Consider a simple spring-mass-damper mechanical system.
Spring
Damper
k
c
Single degree of freedom
m
y(t)
M

Unknown
Quantitative Comparison
Predefined
St andard
Measurement
(numerical result )
1
Reference: Omega Engineering, Inc.
2
Reference: Omega Engineering, Inc.
3
Generalized Measuring System
Most measurement systems consist of three stages:
Measurand
STAGE

Jean Baptiste Joseph Fourier
(1768-1830) was a French
mathematician and a professor at
the Ecole Polytechnique in Paris.
His works on heat flow, published
in 1822, and on trigonometric
series are well known. The
expansion of a periodic function
in terms o

Experimental Error
Error = True Value Measured Value
1
Omega PX209 and PX219 Series
Solid State Pressure Transducer
SPECIFICATIONS
Voltage Output
Excitation: 24 Vdc @ 15 mA (7 to 35 Vdc for 5 V output, 12 to 35 for 10 V output )
Output: 0 to 5 Vdc or 0 to

[0 WC
ME414 - Mechanical Measurements
Quiz #12 December 4, 2015
A farmer decides to build a crude weighting device to weigh bags of grain up to 120 lb. -
He has available a 1 inch steel pipe (1.5 in OD, 1.0 in ID) and intends to measure the
deection of th

Second-Order System Response
Since most moving bodies involve a mass, let's now consider
a spring-damper-mass system (i.e. second-order system)
Recall the general equation of motion:
d 2 y
dy
F(t) = m 2 + c + ks
dt
dt
1
First we apply a step fun

Vibration Measurement
Seismic
instrument
1
ym
yhs
M
c
yr
k
If we apply Newton's second law to the mass m, we
obtain the equation of motion:
mm c ym yhs k ym yhs
y
2
Let the relative displacement of the mass and the case be
given by:
yr = (ym - yhs )
subs

ME414 - Mechanical Measurements Fall 2015
Project #1
Due: September 25, 2015
Determine the steady-state output of temperature measuring systems,
with time constants of 0.01, 0.05, and 0.5 seconds, for the input shown
in Figure 1. You must use Excel to det

Force and Torque Measurements
Force;
Torque;
F = ma
W = mg
T = Fd
Applications?
1
Basic Methods of Force Measurement (Unknown Force)
1. Balancing it against the known gravitational force on a
standard mass.
Example is typical balance scale.
2
2. Measuring

Sound Measurement
Sound - a disturbance that propagates through an elastic
material at a speed characteristic of that medium.
Types of sound:
(a)
Atmospheric sound (air-borne sound,
aeroacoustics)
(b)
Underwater sound (hydroacoustics)
(c)
Structure-borne

Data Acquisition
Components of a DAQ System
1
Types of Signals
2
Signal Conditioning
3
Amplification
4
5
Signal Grounding
6
7
8
Measuring Grounded Signal Sources
A grounded signal source is best measured with a differential or non-referenced
measurement s

Usually, dynamic motion is not simple harmonic but complex (i.e., consists of
many different frequencies and amplitudes).
Fourier showed that any periodic motion can be represented by a series of
sines and cosines which are harmonically related.
A
y t o
2

Operational Amplifiers (Op-Amp)
An operational amplifier (op-amp) is a complete amplifier
circuit (an IC with transistors, diodes, resistors, etc.) that can
be employed in a number of different ways by adding a small
number of external passive components

Electrical Systems and Filters
Consider a first-order electrical system. (RC)
Q
E=
C
E = IR
C
R
E
1
Now if we apply voltage E to the circuit it behaves as step input.
E = 0,
E = Eo ,
t<0
t 0
Using Kirchoff's law of potentials (the algebraic sum of all
vol

A system changes an input signal into an output signal by:
The input signal is decomposed into a set of impulses, each a
scaled and shifted delta function.
The output resulting from each impulse is a scaled and
shifted version of the impulse response.

Linear Systems
The Superpostion Principle Applies to Linear Systems
Requires two mathematical properties:
Homogeneity
Additivity
Not required but essential for most DSP techniques:
Shift invariance
427
Homogeneity
2
Additivity
3
Shift invariance
x[n-6]
S=

Data Reduction Methods
Uniaxial State of Stress
xx 0
In a uniaxial state of stress the stress xx is the only nonzero
component and the direction of xx is known. (Encountered
in tension members and in beams in pure bending.) In this
case a single-element

Strain Measurement
Strain - normal strain is defined as the change in length
divided by the original length.
L
=
L
Strain gage - the electrical-resistance strain gage is the most
widely used device for measuring strain. Its operation is
based on the princ

Planning an experiment
Define objective
Identify key variables (factors)
Create model if applicable
Define experimental method
Conduct experiment
Data analysis
Write report or paper
1
Define objective
Determine what information you need and why?
2
Identif

PROBLEM 3.4
KNOWN: System model equation
K = 1 unit/unit
F(t) = 100U(t)
y(0) = 75 units
FIND: y(t)
SOLUTION
(a) The solution to the system model was shown to be given by the general form,
y(t) = y + (y(0) - y )e-t/
Where here,
y(0) = 75 units
y = 100 unit

PROBLEM 11.6
KNOWN: Aluminum having a volume of
e 2.66 10 8 m
10
5
m3, and a resistivity,
.
FIND: Resistance, R, of 2 mm and 1 mm diameter wires having the same total volume.
SOLUTION:
Volume for a cylindrical wire is
V D2 L
4
yielding
L2mm = 10 m and L