ME 021 Final

The following represent the relationship between temperature and length of a steel bar. Carry out a linear least-squares fit of the data of the form y = ax + b. Give the values of a and b, as well as the corresponding values of the correlation coefficient r for the fit.

Temperature (C) Length (mm)

10 1003

15 1005

20 1010

25 1011

30 1014

a = 0.56

b = 997.4

r = 0.983

What is signified if the Run icon on the LabVIEW panel has the broken shape?

There is an error in the VI

What is the name of the LabVIEW icon that carries out the basic data acquisition process?

DAQ assistant

Describe briefly the function of the Shift Registers in a LabView While loop.

It allows to retain values between loop iterations

The input to XY graph is what data type?

Two arrays

The input to the Array Size icon is an array. What is its output?

An integer that represents the number of elements in the input

The output of the DAQ assistant is what data type?

Waveform

There are many types of strain gages that measures strain. What type of strain gage did we use in all of our experiments

Foil gage

Briefly describe the construction of a foil gage

It consists of a thin, continuous, encapsulated strip of foil laid out in rows along the long axis of the gage. As the foil strip is stretched along the gage axis, its resistance changes linearly with strain.

How is execution of a LabView While loop halted?

1)If the stop button is pressed, 2) If the conditional terminal stops

How is a "bad wire" depicted on the LabVIEW diagram panel?

It is shown by a broken or dashed line along the wire.

Briefly describe the construction of a semiconductor gage.

A semiconductor gage uses a thin strip of silicon to measure strain and has a high gage factor (around 100), making it ideal for applications requiring high accuracy.

What color wire in LabVIEW is used to pass a floating point variable?

Orange

What color wire in LabVIEW is used to pass a string variable?

Pink

In a Waveform Plot, LabVIEW plots the experimentally measured variable vs ______

time

When a measurement is made, the signal that comes from the transducer is in the form of a _________ signal; while the computer can only read signals in __________ format. The device that converts the signal from the first format to the second is called a ________________

1. Analog 2. Digital 3. A/D (Analog-to-digital converter).

The following data were obtained from 10 repeated measurements of the same experimental quantity: 22.3, 23.8, 21.4, 22.1, 24.3, 22.9 24.1, 23.3, 23.2, 24.5. Give a set of limits within which you are 95% confident that the true value of the quantity lies.

23.18 ± 1.94, (21.24,25.12)

The volume of a circular cylinder is given by V=πr^2h, where r is the radius of the cylinder and h is the height. Repeated experimental measurements give r = 20 ± 0.5 mm and h = 100 ± 1.0 mm. For these data estimate the mean value of the volume V and the uncertainty in the volume δV.

V = 125664mm^3 δV = 6408mm^3

Name three different transducers that we used this semester, along with the physical quantity that each each was designed to measure.

1. Strain gage - Strain 2. Thermocouple - Temperature 3. Accelerometer - Acceleration

Name the electrical circuit that we use to convert small changes in strain gage resistance into voltage changes.

Wheatstone Bridge

The output signal of each of the transducers we used this semester are generally in what physical quantity?

Voltage

What does standard deviation measure?

Amount by which individual measurement differs from the mean

The volume of a cuboid is given by the relationship V = wbh, where w = width, b = breadth, and h = height of the cuboid. If the errors in measurements are δw, δb, and δh respectively, the expression for the error δV, in the volume is:

dV= sqrt((dV/dw dw)² + (dV/db db)² + (dV/dh dh)²)

What does the correlation coefficient r mean when you perform a linear regression?

The strength of the linear relationship between two variables

Load cells are normally constructed from an elastic body of some sort. For example, we use a circular ring for outs. What property of elastic bodies makes them useful for this application?

They can deform elastically

Load cells are normally constructed from an elastic body of some sort. For example, we use a circular ring for outs. Name the transducers glued to our circular aluminum ring for measuring loads.

Strain gage

What is the name of that instability when an Aluminum can is compressed

Buckling

The compensating gage and the active gage (the gage glued to the beam that we tested) form two of the four legs in an electrical circuit. What is that circuit called?

Wheatstone Bridge

Each of the strain gage rosettes that we have been using is composed of how many individual strain gages?

3

What is the angle between adjacent gages in the rosettes that we have been using?

45

Of the three types of accelerometers presented in class, name the type of accelerometer that can measure extremely fast changes in accelerations

Piezoelectric accelerometer

What is the method used in numerically calculating the integral of the measured signal from the accelerometer?

Digital integration

When you first get into a LabVIEW vi, that window is called __________

Front Panel

The window in a LabVIEW vi that contains the program that drives the vi is called

Block Diagram

In LabVIEW what do the letters "vi" represent?

Virtual Instrument

What is the name of that device in a data acquisition system that amplifies and linearizes the incoming signal to the computer?

Signal conditioner

Experimental error derives from what three sources?

1. Human error

2. Systematic error

3. Random error

What is the best way to combat human error?

Repeated checking of results, along with a healthy degree of skepticism.

What is the best way to combat systematic error?

Calibration

Define calibration.

Comparing the reading of a given instrument to a known standard, preferably a standard from the National Institute of Standards and Technology.

What is the best way to combat random error?

Use a sufficiently large number of measurements.

Random experimental errors, when plotted as a frequency of observation f vs. the measured value x, follow a _______________, mathematically known as a ________ or a __________________.

1. bell-shaped distribution

2. Guassian

3. normal distrubution

Then the mean value x is given by

Xbar = (1/n) ∑xi

What is the mathematical definition of sample standard deviation?

σ = sqrt((∑(xi-xbar))/(n-1))

Approximately what percentage of data falls between (x+σ, x−σ)?

68%

Approximately what percentage of data falls between (x+2σ, x−2σ)?

95%

Approximately what percentage of data falls between (x+3σ, x−3σ)?

99%

Suppose we obtain the following hand-timed values for the period of oscillation in seconds of a spring-mass system: 32.1, 31.0, 34.5, 29.4, 32.7, 32.3, 33.1, 29.8, 29.0, 33.9, 31.7, 30.3. Solve for the mean, standard deviation, and 95% confidence interval.

Mean = 31.7 s

σ = 1.8 s

31.7 ± 3.6s

Suppose that we want to calculate the uncertainty in the volume of a right circular cylinder V resulting from uncertainties in measurements in the cylinder radius and the cylinder height. We have that V = πr h 2 . Further suppose that, as a result of experimental measurements, we establish that r = 25 ± 0.5 mm and h = 200 ± 1 mm, where the quantities after the ± sign indicate the uncertainties at the 95% confidence level. Calculate the mean volume, and the fractional uncertainty.

V = 392699.817mm at 4.031%

Hardness

The resistance to penetration of an indenter under a prescribed load.

Rockwell Hardness Test

A prescribed combination of load and indenter.

What does b1 represent in the method of least squares?

slope

What does b0 represent in the method of least squares?

The y intercept

What is the mathematical equation to find b1 in the method of least squares?

b1=(n∑xy-∑x∑y)/(n∑x²-(∑x)²)

What is the mathematical equation to find b0 in the method of least squares?

b =

What is the mathematical equation to find r in the method of least squares?

r

Use the method of least squares on the following data set. x(1,2,3,4,5,6,7); y(1.5,3.8,6.7,9.0,11.2,13.6,16.0) to find an equation and the correlation coefficient r.

m = 2.4143 b = -0.8286 r=0.999

Equation for a linear fit

y = ax + b

Equation for a power-law fit

y = ax^b

Equation for an exponential fit

y = ae^(bx)

Explain the primary difference between analog and digital signals

An analog signal can take any value and changes continuously over time, while a digital signal uses only specific, discrete values.

Define transducer

A device that converts the quantity of interest into an electrical voltage.

Define sampling rate

The rate at which we sample signal

The higher the sample rate, the more ______ our representation of the analog signal will be.

accurate

Define resolution

Number of bits used by the A/D converter.

Equation for resolution, where V is voltage and N is number of bits

Resolution = V/2^N

What is an LVDT?

A device that measures linear displacement

How does an LVDT operate?

Sensing the difference in voltage induced in two adjacent coils by a moving inner rod.

Difference between for loop and while loop

A for loop performs a task for a designated number of iterations, and a while loop runs indefinitely if a specified conditions is true.

What fit is log-log?

Power

What fit is semilog?

Exponential

Most strain gages experience a change in ________________ as they are strained, and by measuring this change in resistance, we may measure the _____________.

1) electrical resistance 2) applied strain

Equation for strain, where F is the gage factor, ΔR is the change in gage resistance, and R is the original resistance.

ε = (1/F)(ΔR/R)

Do you want a higher or lower value of F (gage factor)? Why?

You want a higher value of F because this leads to a larger value of ΔR

Equation for τ (shear stress) in terms of r, T, and t

τ = T/(2πr²t)

Equation for λ (shear strain) in terms of r, L, and angle of twist

λ = (r/L)(angle of twist)

Bauschinger effect

The reduction in yield stress experienced after a reversal of loading

Cyclic hardening

When unloading and reloading for the second time, the yield stress will be higher than that experienced on initial loading.

Draw the graph that represents initial loading, unloading and reloading stage one, and unloading and reloading stage 2. Label all the yield shear stresses.

graph

Draw a Wheatstone bridge, labeling, R1, R2, R3, R4, the voltmeter, all the currents, and the fixed voltage source

Wheatstone Bridge

Define active gage

The gage which will be strained

Define compensating gage

A gage applied to an unstrained piece of the same material, to compensate for strains induced by changes in temperature.

Draw the configuration of strain gage rosettes

3 blocks that are 45 degrees apart

Define piezoelectric material

One that generates a small electric field as it is trained or deformed.

When performing a calibration of an accelerometer, we are interested in determining the constant k. This constant relates _______ to _______.

Acceleration, Voltage

What color wire is string

Pink

What color wire is floating point variable

Orange

What color wire is integer variable

Blue

What color wire is boolean

Green

What are the three palettes in labview?

1. Controls

2. Functions

3. Tools