Mechanical Engineering (ME)- 4201
Machine Design Laboratory
Patrick F. Taylor Hall (CEBA)- 2209
Laboratory Manual
Compiled/Prepared by
Department of Mechanical Engineering
Louisiana State University
Fall -2007
PART-ONE
FIRST CYCLE EXPERIMENTS
Table of Contents
Page Number
REPORT WRITING GUIDE ............................................................................................ 3
FIRST CYCLE LABORATORY EXPERIMENTS
I.
Gyroscope Experiment ............................................................................ 11
II.
Cam - Follower Experiment ..................................................................... 17
III.
Journal Bearing Lubrication Experiment .................................................. 23
IV.
Static & Dynamic Balancing Experiment .................................................. 32
REPORT WRITING GUIDE
Introduction
The importance of good report writing and data presentation cannot be
overemphasized. No matters how good an experiment, or how brilliant a discovery; it is
worthless, unless the information is communicated to other people. As you complete
each laboratory report, you will be gaining experience in writing technical reports and
will be developing skills that you will find invaluable throughout your career. There are a
great many books available on report writing. However, the purpose of this document is
to provide some basic pointers in the writing of laboratory reports. In particular, a major
objective of this work is to provide the format for laboratory report writing, and to provide
hints and tips to improve your reports. Each of these topics is discussed at length in the
appropriate sections that follow.
General Guidelines for Report Writing
All of the reports you submit during your career at Louisiana State University
should follow one of two basic formats. There may be small differences due to
individual preferences of the instructor, but for the most part, all of the components of
the report will be identical.
Style:
Third-person past tense is generally accepted as the most formal grammatical
style for technical reports. However, in some isolated instances, it may be most
effective to stress a point or to emphasize that a particular statement is primarily the
opinion of the writer. An example of each of these styles is shown below.
Third person: Equation (6) is recommended for the final calculation procedure as
a result of the limitations of the data as discussed above.
2
First-person: We recommend Eq. (6) for the final calculation procedure as a
result of the limitations of the data as discussed above.
As you can see, in the first-person statement, the writer is making the recommendation
on a much more personal basis than in the third-person statement. The selection of the
proper statement often depends on many factors, including the consideration of the
people who will eventually read the report. In most cases, the third-person statement
will be most preferable; however, if you have completed an engineering study for a
particular individual, the first-person usage may be more appropriate. As most of the
work that you will be completing will require a formal report, the third-person style is
to be used.
Format:
All reports must be typed or near-letter-quality (NLQ) printed. All work should be
double- spaced, one side only. All pages must be trimmed or neatly folded to 8.5" - 11".
Reports should be bound, such that the back of a page is on left and the front of the
page is on the right (no binder, paper clips). Block format with separated side headings
or an indented format with center of side heading may be used. This is an individual
choice for the writer. Paragraphs may or may not be numbered, but all pages must be
numbered. All pages should have identical margins. A reasonable set of margins is 1.0
inch at the top and the bottom, and 1.5 inches at the left, and 1.0 inch on the right.
These margins allow for ease of binding, as well as clarity of reading.
Rules for the Plotting of Data:
One of the more common tasks in completing engineering reports is plotting
data. This section contains some rules to follow when making graphs. Automated
graph-making programs such as Excel, Lotus, or SigmaPlot often take care of many of
these details for you, but you are responsible for checking that these guidelines are
followed.
All axes must be drawn in a location on the page, which will allow the numbering,
and labeling of the scales to occur without entering the margin. Each axis must be
labeled and the proper units given. The lettering on the page must be oriented such
that it is readable from either the bottom or the right-hand side of the page. This
becomes important if the plot is drawn in landscape mode (i.e., sideways) on the page.
The independent variable is always plotted along the abscissa (x-axis), and the
dependent variable on the ordinate (y-axis).
Choose convenient scale factors for each of the scales, generally using multiples
of 1, 2 or 5. An axis, with divisions of 2.5 or 3.33, is very troublesome when it is desired
to read intermediate values from the curve, to say nothing of the difficulty you will
experience in plotting the data. The plotted data points should be clearly marked by
drawing a small circle about each point. These should be drawn with a template for
neatness and usually are not more than 3/32 of an inch in diameter. Normally, this
formality is automatically done when commercial computer graphing packages are
used. If points for more than one curve are to be plotted on a single graph, or the data
of different observers is to be indicated, a differentiation can be made by using small
3
squares, triangles or other symbols in addition to the circles. On the other hand, the
calculated points used in plotting a curve representing theoretical results should not be
marked with such symbols. Only the curve itself (and not the points used to plot it)
should be shown.
In most cases you will be required to draw a best-fit curve (with a French curve,
not freehand!!) through the data points. It is not necessary that the curves intersect all
data points or even the first and last data points. It should, however, be a smooth curve
which best represents (in some average sense) the data. The curve should not be
allowed to pass through the circles or other symbols surrounding the points. The
purpose of this is to leave the points visible so they may be checked at any time.
Calibration curves and correction curves are drawn with small sections of straight line
joining the points. This is done because the errors are mostly random and do not
conform to a mathematical law.
Curves are drawn to as large a scale as is consistent with the precision with
which the measurements are made. That is, the scale should not be so large that the
curve can be read to a precision greater than that of the measured data, nor should the
scale be so small that the curve cannot be read to as great a precision as that to which
the measurements are made.
Do not place too many curves on one sheet of paper, particularly if the curves
cross one another. Typically, this leads to confusion and a cluttered appearance.
Prepare all plots on ruled graph paper, however, for computer-generated plots this is
not necessary. Do not use quad paper or engineering paper. If more than one curve is
present, label each curve as close to the curve as possible. Do not use colors to
distinguish curves, as this distinction disappears upon reproduction. (Use full, dashed,
or dotted lines instead). Each curve should have a figure number and a descriptive title
such as “Frequency Response of a R-C circuit.” Non-descriptive titles such as “Voltage
versus Frequency,” which are evident from axes labels, should be avoided. In
calibration experiments, your name, the date on which the experiment was performed,
the instruments manufacturer, model number, and serial or identification number should
appear on the figure.
Full-page graphs in landscape mode (printed sideways on the page) must have
the top of the graph at the left-hand side of the page. As in the text, any bibliographical
references may be enclosed in brackets [xx].
Application of Probability and Statistics
Probability and statistics play an important role in experimental work, especially
in industry. When presented without consideration of probability and statistical analysis,
data can be misleading because measurement error prevents an engineer from
determining the true value of measured quantities at any given time. Engineering
measurements, repeatedly taken under seemingly identical conditions will normally
show variations in measured values. The use of statistics in mechanical measurements
provides a method of dealing with characteristics that have variability. Because the
topic of probability and statistical analysis is presented in standard engineering texts, it
4
is not necessary to present the full theory here. However, reports for this class may
require some of the following analysis techniques.
(1)
If more than one measurement is taken for a given value, your report should
include calculation of mean and standard deviation. This information should be
included whenever the data is reported. If data is reported in tabular form, one
column each should be devoted to mean and standard deviation. If data is
reported in a graph, error bars should be used to indicate the standard deviation
for each mean value.
(2)
If a curve-fit or regression is used, the correlation factor should be reported along
with the equation of the curve. In some cases, the two curves representing 95%
confidence intervals (or other specified intervals) may also be required to
demonstrate the goodness of fit.
(3)
When specified in the manual, uncertainty analysis should be performed to
account for the effects of measurement uncertainties on calculated values.
For this specific class, always conduct analysis (1) and (2) whenever applicable.
Conduct analysis (3) ONLY when specified in the individual experiment.
CONTENT
A good laboratory report answers the questions: What was done?, How was it
done?, and What were the results?. There are standard sections to each lab report
which help answer these questions, and allow the reader the opportunity to move right
to the section most appropriate to his or her interest. Basically, any formal lab report
consists of the following sections:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Title Page & Abstract
Table of Contents
Introduction
Background and Theory
Equipment
Procedure
Results and Analysis
Conclusions and Recommendations
Bibliography
Appendix/Appendices.
A short description of each of these topics follows.
Title Page & Abstract:
This is one of the most important sections of your report, and will probably be the
most carefully scrutinized section of any report you write. Basically, this section tells a
short story about your lab, and very concisely answers the three questions posed
above: What was done?, How was it done?, and What were the results?. The abstract
5
is included as part of the title page, so that anyone reading the report can very quickly
see who wrote the report, the subject of, and the procedure followed for the lab, and
what results were obtained. This section should probably be the last section written,
and will summarize all of the work done for the lab. A common mistake is to write this
section first, and then force the rest of the report to fit with the abstract.
Table of Contents:
Obviously, the table of contents is nothing more than a listing of headings with
the page numbers. However, the table of contents is often a good indicator of the
organization of the report, and can be a good tool for the development of the lab report.
When figures and tables are used in the report, an independent List of Figures and List
of Tables is also required.
Introduction:
An introduction sets the context of the experiment, and gives the relevant
background to the experiment. This section is very important for the individual who
wishes to read the entire report. The introduction should include a concise description
of what you were trying to discover, as well as describe what is going to follow in the
remainder of the report. It is not appropriate to include results in this section; rather,
you are trying to set the stage for what follows in the rest of the report.
Background and Theory:
This section is used to lay the technical and theoretical groundwork for the
process being studied. It is in this section that the technical basis for the work that you
did is explained. In other words, why are the results that you obtained valid? Discuss
the technical fundamentals, which lie behind the experiment. This includes describing
(and laying the technical groundwork for) the analysis process for the data. This section
does not have to be a master’s level thesis, but should demonstrate your understanding
of the process and the sources of error in measuring it. A well-written background
section greatly simplifies discussion of the results.
Equipment:
This segment of the report, along with the section that immediately follows (the
procedure section), allows the reader to duplicate your experiment should the need
arise. Any equipment used in the experiment should be listed along with identifying
marks (serial numbers, model numbers, ...). Any particular settings of the instruments
should be denoted in the procedure section. It is especially useful in this segment to
include a sketch of the experimental setup. This sketch is especially helpful to avoid
any ambiguities that might exist when the experiment is re-run, or when attempts are
made to duplicate your results.
Procedure:
A procedure section simply lists what was done in the lab, and the order in which
it was done. As previously mentioned, it is this section, along with the equipment
section, that allows the reader to reconstruct your experiment, if necessary. This
section is most effective if it is written in the form of a list, following a chronological order
as shown below.
6
1. A beaker was filled with 500 ml of water, and placed on a hot plate.
2. A thermocouple was placed in the beaker, and the temperature of the water
sampled once every 8 seconds.
3. The recording ...
Elements in the list are either all complete sentences, or all short phrases but not
both. Overhanging paragraph format is good for lists. The procedure section is also the
appropriate place to discuss any deviations from the intended procedure. For example,
if you originally intended to monitor the temperature of two beakers of water, you might
note that only one thermometer was available, and that this was not possible.
Results and Analysis:
This section may be the most crucial for your report. The results and the
analysis to obtain these results should be presented here. This section is most effective
if written in the past tense. “The data were taken ...”; “the curve was generated...”
However, it is appropriate to say such things as ‘the data are well represented by a
second order polynomial’ since this is a fact that extends into present. Additionally,
estimate the error in measuring whatever your objective was to measure. Be
particularly careful when referring to ‘human’ or ‘round-off’ errors that these errors are
significant in terms of the discrepancies observed.
Plots and figures tend to be the most effective ways to present data. It is
extremely useful to include figures in the text at the point where they are being
discussed (a helpful tool is to use the graphic import feature available with many word
processors to import figures right into the text).
When graphs or tables will present the ideas clearly, use them, but also include a
concise discussion of the graphs and tables focusing the reader’s attention on the
salient features of data. Do not simply recite numbers or parameters that should be
obvious upon simple inspection of the figures. Moreover, never forget to indicate units.
The location of figures and tables should be included in the List of Figures/Tables in the
Table of Contents section of the report.
Probability and statistical analysis should be included with your calculations in
this section, if applicable. Please follow the requirements given above.
Conclusions and Recommendations:
By the time the reader reaches this section of the report, most of the conclusions
regarding the work should have already been presented. The object of the conclusion
section is to gather all of the important results and interpretations in clear summary
form. Recommend cost-effective feasible ways to improve the performance of the
laboratory. Also remember, there will be many readers who focus only on the
conclusion and abstract sections, so it is especially important that they be well written.
7
Bibliography:
This section should include all references (including the lab manual), which were
cited in the report. Citations should include all information that is not developed by the
authors. A standard format should be used such as
“... Smith [1] discusses the effects of temperature...” which would refer to the
following citation in the bibliography.
1.
Smith, R., Turbulent Natural Convection for a Vertical Plane Surface,
Journal of Heat Transfer, Vol.76, p.234, 1979.
Your work will often require you to reference other contributions, not only in this
particular course, but in others as well. Learn to do so.
Appendices:
A laboratory report should be a complete, concise, self-contained document
without appendices. These sections contain information not appropriate to any other
section. For example, raw data, sample calculations, detailed derivations, etc. may be
included in the appendices. This is the most ‘free’ space in the report. For example,
you might include a sketch of an improved way to complete the experiment, or to
present the data. An appendix can be a very valuable addition to the report.
Hints to Writing
Before You Begin:
It is very difficult to write good lab reports if you don’t understand what you were
doing when you carried out the experiment. Therefore, before coming into the
laboratory, you are urged to carefully read both the experiment sheet and the partially
completed laboratory report for that week’s experiment.
Take advantage of
opportunities to discuss with your instructor any questions you may have regarding the
experiment. The experiment tends to run a little smoother if you designate one member
of your group as the data taker. He or she is responsible for recording information
pertinent to any device calibrated during the experiment. At the end of the lab, each
member of the group should then copy this information directly onto their data sheets. It
is this type of information, which should appear in your appendices.
Writing the Report:
It is important to write your report as soon as possible after the experiment is
completed. This will save you time since the experiment is still fresh in your mind.
Remember, as always, that each section of the report should answer one of the three
basic questions: What did you do? How did you do it?, or What did you find out?
In terms of these, think carefully about what you did in the experiment. Think
about what figures you want to include that help clarify the information. Decide the flow
of information before actually sitting down to write. As you write, keep in mind the
common rules of English grammar and punctuation. Proofread your report, and keep in
mind that your report speaks for you. Does your report give the impression that you
would want to make if you were in person?
8
Write a sketchy outline itemizing the basic sections of the report and listing the
primary points to be made in each section. With the available text processors this
should be relatively straightforward. The outline will help organize the report, help
establish the flow of information, and can help indicate where figures and graphs are
needed.
Once the content of the report is established with a multilevel of detail outline, it
is much easier to begin writing. It should be much simpler to concentrate on rules of
grammar and punctuation when not having to think about what to say also.
After Getting Back your Report:
After your report has been graded and returned to you, take the time to read and
understand the comments that have been made. Consider these comments when
writing your next lab report. Work with the instructor to improve the quality of your lab
reports, and always keep in mind that the ability to write a good lab report is an
excellent talent, that will be extremely useful throughout your educational and
professional careers.
______________________________________________________________________
I. GYROSCOPE EXPERIMENT
Introduction
The study of gyroscopic action is particularly important in the field of vehicle
engineering. The gyroscopic couple produced by rotating components can often lead to
undesirable effects, which affect the stability of vehicles. For example, when a road
vehicle travels around a bend, the gyroscopic couple produced by turning the axis of the
wheels tends to overturn the vehicle. In the case of an aircraft changing direction, the
gyroscopic couple due to the rotating components of the engine causes the aircraft to
pitch up or down. Gyroscopic effects can also be used to ones advantage, as in the
case of gyrostabilizers and gyroscopic instruments. If mounted in a suitable position, a
gyroscope consisting of a rotating disc can be used to resist undesirable motion and so
provide a means of stabilization. Gyroscopic action occurs whenever the axis of a
rotating body causes the axis of rotation to remain in the same direction so long as no
external couple acts on the system. However, if a turning couple is applied to the axis,
a torque reaction is produced which tends to turn the axis in a plane at right angles to
the plane in which the applied couple acts. This torque reaction, or gyroscopic couple
as it is called, results from attempting to alter the direction of angular momentum of the
body.
If we have a stationary fly wheel, of moment of inertia I, on a shaft mounted in a
trunnion frame such that it is supported but free to rotate about any axis, then the
couple applied to the system will cause the shaft to move in the plane of application of
the couple. Now consider Figure 1, where the flywheel disk is spinning with angular
9
velocity ω, and the axis of spin is simultaneously rotating in the horizontal plane XOZ
Gyroscopic Couple = Iω ω p
……………………….
Equation 1
……………………….
Equation 2
with angular velocity ωp. Then:
mgL = I ω ω p
A couple is applied, to balance the gyroscopic couple, by adding a mass (m) to
keep the axis of the disc
from rotating in the horizontal plane. Therefore, the applied couple equals the
gyroscopic couple or:
In order to investigate the validity of equation (1) it is necessary to determine the
moment of inertia of the gyroscope rotor. In the experiment, this is done by suspending
the rotor and disk on two wires as shown in Figure 2 and observing its torsional
oscillation. This represents simple harmonic motion in which the periodic time τ (for
small oscillation angle θ such that sin θ is essentially equal to θ) is given by:
τ = 2π
4Il
2
M rd g d
…………………………
Equation 3
Where, Mrd is the mass of the rotor-disk (1100 gms) combination, d is diameter of the
disk (or the distance between the suspended strings), I is the mass moment of inertia
about the centroidal axis of the rotor and disk, l is the length of the suspended string,
and g is the acceleration constant due to gravity (9.81 m/sec2 or 386.4 in/sec2).
Figure 1. Fly Wheel Disk Spinning About
About Disk Axis and Precessing
About Y-Axis
10
Figure 2. Experiment Used to Determine Rotor-Disk Period
and Moment of Inertia
Figure 3.
Examples of the Gyroscopic Couples Produced with Different Rotor-Disk
Rotation (ω) and Precession (ωp) Combinations
Objective
The purpose of this experiment is to:
•
Study the direction of gyroscopic couple, angular velocity of the rotor (ω), and the
precession velocity (ωp).
•
Determine the mass moment of inertia of the rotor-disk experimentally by use of
Eq. (3), which is based on small oscillation theory.
•
Investigate the validity of the gyroscopic couple relation, Eq. (1), by comparing
the I value based on Eqs. (1) and (3).
Necessary Equipment and Materials
•
Stop watch (determines precession speed)
•
E64 electronic tachometer (determines rotor speed)
•
Additional gyroscope rotor and armature assembly
•
Fold-out bifilar suspension arm mount to base of gyroscope apparatus
•
Gyroscope apparatus (see Figure 4)
-
Small variable speed motor (B) carried in a gimbal frame (this
frame not shown in Figure 4).
Rotor disc (A) mounted on motor (B)’s shaft.
11
-
-
-
Second variable speed motor housed inside apparatus base (not
shown in Figure 4).
Torque arm (G) carrying a mass (D) at its end to balance the motor
and rotor disc.
Retaining plate (E) fitted over the torque arm to limit the angular
movement of the motor assembly.
Additional masses (F) attached to the end of the torque arm to
balance the gyroscopic couple (add mass as directed in
Procedure).
Removable electrically interlocked transparent safety cover (or
dome) fitting completely over rotating assembly (cover not shown in
Figure 4). (Note: Removing this cover automatically stops both
motors.)
Slip ring at the base of the gimbal frame supplying power to rotor
motor (B).
E66 Mains Transformer Unit.
TecQuipment E91 dual speed control units for both motors.
Figure 4. Gyroscope Apparatus
Procedure
1.
Make sure the following connections are completed before operating the
gyroscope apparatus.
a.
The 12V input terminals on the E91 Dual speed control unit to the 12V
D.C. power supply.
b.
One pair of the output terminals on the E91 unit to the rotor input terminals
on the apparatus, and the other pair to the precession input terminals.
c.
The E64 tachometer input to the output socket on the apparatus using the
signal lead provided.
12
d.
If all of the preceding connections are made, the apparatus is ready for
operation. Switch on all the units.
2.
Check that the gyroscope rotor assembly is adjusted so that with no weight
added, the line scribed on the end of the torque arm lies in the plane of the line
scribed around the safety cover. If the arm does not lie in the plane, slacken the
screws holding the rotor on the motor shaft, then adjust the rotor position until the
rotor assembly balances. Replace the cover, check the alignment and when
satisfactory, re-tighten the screws to clamp the rotor in position.
3.
Check that the cover is correctly in position, then set the rotor and precession
motors running. Note the direction of rotation of the rotor, the direction of
precession of the gyroscope and whether the torque arm rises of falls. By
interchanging the motor input connection on the front panel, determine the
direction of the gyroscope couple for each combination of rotor and precession
directions.
4.
Screw a 150g mass onto the end of the torque arm and replace the safety dome.
Connect the rotor and precession motor’s supplies so that the gyroscopic couple
will raise the torque arm.
5.
Set the rotor speed to approximately 1000 RPM using the speed control unit.
Vary the precession velocity until the torque arm rises to a level at which the
scribed line lies in the same plane as the line on the safety cover. This is the
point of balance at which the gyroscopic couple is just equal to the moment
produced by the mass on the torque arm.
6.
At this point, measure the precession speed by timing a suitable number of
revolutions of the assembly using a stopwatch. The number of revolutions you
will need to time depends on the test conditions. To obtain high accuracy always
use a time period of at least 1 minute.
7.
Decrease the rotor speed in order to get 4 more measurement points (for
example, 1500 RPM, 2000 RPM, 2500 RPM.) and determine the precession
speed at the balance point for each different rotor speed.
8.
Add additional masses to the torque arm and obtain similar sets of results for
each value of mass as for the 150g mass. Use 150g, 200g, 250g, and 300g
masses. (Please look in to the NOTE for the required weights and speeds to be
carried out for the experiment)
9.
Calculate the moment using T = mgL, where: L = Torque arm = 15 cm, m = mass
added, and g = 9.81 m/s2
10.
Plot the reciprocal of the precession velocity (1/ωp) against the rotor velocity for
each mass. Obtain the linear regression and indicate its coefficient of
correlation. Find the moment of inertia (I) using the slope of each graph.
13
11.
The second method to obtain the moment of inertia, I, is based on vibration
theory as described in the manual. Measure the vibration period, τ, for at least
five times using various sampling time. Obtain the average τ and its standard
deviation. Calculate the moment of inertia using Eq. (3).
12.
Compare the moment of inertia obtained through steps #10 and 11. Discuss the
results.
Note : Carry out the Experiments for the following weights and speed combination
Speed (rpm) 150 (gm) 200(gm) 250 (gm) 300 (gm)
1000
1500
2000
2500
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II. CAM-FOLLOWER EXPERIMENT
Introduction
A cam-follower system (sometimes referred to as a direct contact mechanism) is
one of the simplest mechanisms used for control and conversion of one type of motion
to another. However, the accuracy of output, which is generally the motion of follower,
depends on the cam and follower being in contact at all times.
The forces acting on a follower may be shown to consist of:
P = W cos β + F s +
W 2 d2 Z
ωc
g
dθ2
…………………
Equation 1
where,
W
β
=
=
ωc
Fs
Z
θ
=
=
=
=
Weight of the follower, retainer and applied weight (lb or N),
Angle between the line of motion of the follower and the vertical
(direction of gravitational acceleration),
Angular velocity of the cam (rad/s),
Spring force behind the follower (lb or N),
Vertical displacement of the follower (in or mm),
Angular displacement of the cam (radians)
The spring force behind may be broken up into two components where:
F s = F so + kZ
F so = k[Initial (free length)-Final (Compressed length)] ………. Equation 2
where:
Fso
=
k
=
Spring force behind the follower when the follower is at its
closest position the center of rotation of the cam (lb or N),
Spring constant (lb/in or N/mm).
In Eq. (1), P must always be positive in order for the follower to remain in contact
with the cam. The combination of the first two terms is always positive, however a large
negative d2Z/dθ2 term may cause P to be negative. For a given cam profile, the RPM of
the camshaft that results in separation of the follower from the cam may be calculated
from Eqs. (1) and (2) as:
N
RPM
⎡
⎢
60 ⎢ - (W cos
=
2π ⎢
(W
⎢
⎣⎢
⎤
⎥
β + F so + kZ ) ⎥
⎥
⎛ d 2Z ⎞
⎥
g )⎜
⎜ d 2 θ ⎟⎟
⎝
⎠
⎦⎥
1/2
………
Equation 3
where, d2Z/dθ2 is the maximum negative value. Note that in Equation 3 , β = 0 since the
follower and cam are in line.
Obviously, the RPM at which the follower separates from the cam is a function of
the weight of the follower, the spring force behind the follower, as well as the cam
profile. Furthermore, if the cam-follower separation is going to take place, it will occur
15
first at the point where d 2 Z/dθ 2 has its maximum negative value during the cycle.
Once the follower loses contact with the cam, in reestablishing contact a fairly large
impact force is generated which may eventually result in fatigue failure of the surfaces
of the cam as well as the follower.
Objective
The objective of this experiment is to:
•
Observe the follower behavior and determine the effect of weight of the follower
on the critical speed Ncr of the cam shaft (i.e., the speed at which the follower
and cam temporarily lose contact),
•
Determine the effect of spring force on the critical speed of the camshaft.
Necessary Equipment And Material
•
Cams with different profiles
•
A roller and flat follower
•
Springs with different stiffness values
•
Variable speed drive motor
•
Necessary instrumentation and recording devices
•
Experimental apparatus frame and assembly
(see Fig. 1)
Equipment Specifications
See the following tables:
16
Cam-Follower Experiment Spring Dimensions
Spring
Weight
(lb)
Nomina
l
Stiffnes
s
(lb/in)
Retaine
r
Weight
(lb)
Color
Dimensions
Red
1.12" MD* x 1/8' Dia. x 2.99"
Long
0.138
31.4
0.156
White
1.85" MD* x 1/8" Dia. x 3.02"
Long
0.294
22.5
0.300
Black
1.37" MD* x 1/8" Dia. x 2.95"
Long
0.156
19.7
0.144#
_______________________
#
: Steel retainer
Cams
Quantity
Profile
2
1
1
Convex
Concave
Tangent
Followers
Quantity
Type
1
1
Roller
Flat Face
* = Mean Diameter
Miscellaneous
Weight of
attachment
roller
follower
and 3.78 lb (excluding spring, spring
retainers, and additional weights).
Weight of
attachments
flat
follower
and
4.30 lb (excluding spring, spring
retainers, and additional weights)
17
Diameter of roller follower
1-1/8" Dia.
Diameter of paper recording drum
3.673" Dia
Procedure
1.
Select the direction of rotation of the cam by turning the switch provided for this
purpose. Do not change the direction of rotation while the motor is running.
2.
Select a cam and obtain a trace of its profile on paper and then assemble it on
the camshaft. (The cam you select may depend upon the discretion of your
instructor.)
3.
Select one of the followers and assemble that also on the machine (note that if
the cam has any concave section the follower must be a roller follower).
4.
Select one of the springs and place it in the machine with some preload (if
desired).
5.
Wrap a piece of Teledeltos paper around the recording drum and secure its ends
with scotch tape. Obtain, with the motor off, a trace of displacement of the
follower and then remove the paper from the drum.
6.
Increase the speed of the motor slowly until you detect the tapping noise,
indicating the impact between cam and follower. Decrease and then increase
the speed several times to make sure that you are detecting the tapping noise
the very moment that it starts. Read the speed of the camshaft on the
tachometer and record it. This is the experimental value of the speed, Ncr, at
which P in Eq. (1) becomes zero. Because the collection of data is dependent on
each individual’s hearing sensitivity, each person needs to obtain his/her own
data and record them without getting influence from others.
7.
Repeat step 6 five times, each time adding a weight of 400 grams to the follower.
8.
Change the spring force Fs by either a) replacing the spring or b) increasing the
initial compression. Then repeat steps 6 and 7 for one other level of spring force.
9.
Calculate the critical speed (Ncr) analytically by differentiating twice, the Z-θ curve
and plotting dZ/dθ and d2Z/dθ2 verses θ, obtaining the maximum negative value
of d2Z/dθ2 from the plot and substituting this maximum negative value into Eq.
(3). Because a curve-fit is required to approximate the cam surface in this step,
95% confidence intervals should also be shown on the Z-θ plot.
10.
Plot the variation of Ncr versus the weight of the follower as well as the spring
force (either Fso or k if the spring was replaced). Be sure to indicate the mean
and standard deviation of each data point on graphs containing measured
values.
18
11.
Compare the theoretical Ncr with the experimental Ncr values obtained and
comment on the results.
Cam-Follower Experiment
Name:
Section:
Group:
Date:
Cam Profile:
Spring(s) Used:
Critical Speeds (RPM)
Data Sheet (Preload #1)
Extra Weight
(grams)
Person#1
0
400
800
1200
1600
2000
19
Person # 2
Person #3
Critical Speeds (RPM)
Data Sheet (Preload #2)
Extra Weight
(grams)
Person#1
0
400
800
1200
1600
2000
20
Person # 2
Person #3
III. JOURNAL BEARING LUBRICATION EXPERIMENT
Introduction
The major objective of lubrication of journal bearings is to induce and maintain a
film of lubricant between the journal and the bearing. The purpose of this film of
lubricant is to keep the two surfaces separate at all times and thus prevent metal to
metal or dry contact which otherwise will create bearing failure.
Hydrodynamic lubrication is the
most common method of lubrication of
journal bearings. In this method, as the
shaft rotates it will, due to the load applied
to it (as well as its own weight), take a
slightly eccentric position relative to the
bearing. The eccentric rotation of the shaft
in the bearing, as shown in Fig. 1, acts
some-what like a rotary pump and
generates a relatively high hydrodynamic
pressure in the con-verging zone. The
hydrodynamic pressure for a properly
designed bearing is responsible for
supporting the shaft without allowing it to
come in contact with the bearing.
It can be shown, analytically, that the
hydrodynamic pressure distribution around the bearing is related to other parameters
by:
⎡ 12πμε r 2 N ⎤ ⎡ (2 + ε cosθ ) sin θ ⎤
(P - P0 ) = ⎢⎥ ⎢ (2 + 2 ) (1 + ε cosθ 2 ⎥ ……….. Equation 1
2
)⎦
c
ε
⎣
⎦⎣
and that
⎡ (2 + ε cosθ 1) sin θ 1 ⎤
(P - P0 )max = (- K) ⎢
⎥ ……….. Equation 2
2
⎣ (1 + ε cosθ 1 ) ⎦
where
21
The remaining terms in the above equations are defined as,
K=
r
c
μ
ε
θ1
N
P0
P
=
=
=
=
=
=
=
=
12πμε r 2 N
……………….. Equation 3
2
2
c (2 + ε )
Journal radius, (in)
Radial clearance, (in)
Oil viscosity at operating temperature, (reyn)
Eccentricity ratio (= e/c)
Location of maximum film pressure
Journal speed (RPS)1
Ambient or oil supply pressure (psi)
Hydrodynamic pressure at position θ
A dimensionless number called the Sommerfeld Number or Characteristic
Number defined by relates the bearing performance to the design parameters:
2
⎛ r ⎞ ⎛ N ⎞
S =⎜ ⎟ ⎜μ
⎟ ……………… Equation 4
⎝ c ⎠ ⎝ P ⎠
and
P=
W
……………… Equation 5
2rL
where,
P =
L =
W=
Load per projected area of the bearing (psi),
Bearing length (in),
Load carried by the bearing (lb).
Other relationships that can be obtained analytically are as follows:
cosθ 1 =
1 RPS denotes revolutions per second or rev/sec
22
- 3ε
…………… Equation 6
2+ε2
and
h0
= 1 - ε ……………. Equation 7
c
Where, cosθ1 is the location of maximum pressure relative to the line of centers and h0
is the minimum oil film thickness. The h0/c ratio and the friction coefficient are plotted
vs. the Sommerfeld No. in Figs. 2 and 3.
Objective
The purpose of this experiment is to:
•
Measure hydrodynamic pressure variation in a journal bearing at different
speeds,
•
Calculate load carrying capacity of the journal bearing and compare it with
theory;
•
Measure the location of maximum film pressure,
•
Measure the friction loss in the bearing and compare it with theory.
Necessary Equipment and Material
•
Journal bearing with adjustable speed journal
•
Instrumentation to measure the pressure around the bearings
(manometer tube equipment)
•
Instrumentation to measure journal RPM (stroboscope)
•
Dead weights to adjust the load on the bearing
Equipment Specifications
•
Bearing diameter = 2.166 in
•
Journal diameter = 1.984 in
•
Effective bearing length = 2.766 in
•
Bearing weight with attachments = 1.43 lb
•
Weight of each movable load = 0.22 lb
•
Lubricant = SAE 15 W 50
•
Lubricant’s density = 0.0282 lb/in3
Procedure
1.
Select the direction of rotation of the motor by turning the switch provided for this
purpose. Do not change the direction of rotation while the motor is running.
2.
Start the motor and let it run for about half and hour for the temperature and the
oil viscosity to reach the steady state condition.
3.
Apply about a one-pound load on the bearing, using the dead weights.
23
4.
Increase the shaft speed gradually until you observe instability and vibration of
the bearing. Measure the speed of rotation ω of the shaft. Observe and
comment about the pressure distribution around the bearing.
5.
Using the strobe light set the journal speed to 1200 RPM. (Make sure to
periodically check this speed as it may increase during the course of the
experiment.) Allow enough time for the oil to level in the barometer tubes to
stabilize (about 3 min.)
6.
Read the pressures for locations 1 through 16 and convert the readings to psi.
7.
Change the shaft speed to 1400 and 1600 and repeat steps 5 through 7 for the
new RPM’s.
For Each RPM Setting
8.
Plot the variation of pressure along the bearing axis (pressure taps 1 through 5)
and obtain the average pressure along the axis as well as the ratio (R) of
average pressure to the maximum pressure along the axis (pressure tap No. 3).
9.
Multiply the reading of pressure tap 3 by the ratio R obtained in Step 8 to obtain
the axially averaged pressure. Repeat the same multiplication procedure for the
readings of pressure taps 6 through 16. Plot the axially averaged pressure vs.
theta in Cartesian as well as polar coordinates.
10.
Find 2 points A and B on the experimental pressure curve that are 180o apart but
having equal pressure. Note that for any pressure curve there will be only one
such pair of points possible. These two points, A and B, form the axis P - P0 = 0
for the Sommerfeld curve.
11.
Of these two points choose as the origin the point with a larger thickness of oil
film and take the axis θ = 0 to pass through this point.
12.
13.
From your pressure distribution graph determine the location (θ1) of maximum
pressure and then from Eq. (6) find the eccentricity ratio.
Using Eq. (2) to calculate the constant K, and then plot the Sommerfeld curve
(theoretical pressure distribution), using Eq. (1). A typical curve is shown in Fig.
4.
14.
Calculate the load carrying capacity of the bearing from:
12
⎛ πLd ⎞
W =∑⎜
⎟ (P - P0 )i cos β i
i=1 ⎝ 12 ⎠
Where, (P-P0)i is the pressure at the midpoint between any two consecutive
pressure tap points and βi is the angle between that mid-point and the line of
24
action of load (pressure tap point no. 3). Compare this load with the actual load
on the bearing.
15.
Calculate the Sommerfeld number from:
⎛r⎞
S=⎜ ⎟
⎝c⎠
2
⎛ N ⎞ K (2 + ε 2 )
⎜ μ ⎟=
12πεP
⎝ P⎠
and then the friction coefficient from Fig. 3.
16.
Calculate and plot theoretical HP lost in the bearing based on the friction
coefficient obtained in the previous step.
17.
Discuss your results and comment on them.
25
Figure 2. Variation of ho/c with Sommerfeld No.
Figure 3. Variation of (r/c)f with Sommerfeld No.
26
Figure 4. Comparison of Theoretical & Experimental Pressure Curves.
27
Figure 5. Polar Pressure Diagram.
28
Journal Bearing Lubrication Experiment
Name:
Date:
Section:
Group:
h0:
Rotation Speed (ω)
of Shaft when Oil
Whirl
Instability RPM
Occurs:
Tap Pressure1 (lb/in2)
Tap Number
RPM
RPM
RPM
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
Computation of the tap pressure in psi: P = ρ(h - h0)
29
RPM
IV. STATIC AND DYNAMIC BALANCING EXPERIMENT
Objective
The purpose of this experiment is to understand the principles of static and
dynamic balancing of rotating machinery.
Necessary Equipment
• Machinery fault simulator.
• Two rotating disc with 2 set of ¼ ” threaded holes spread circumferentially
around the rotating disc.
• One dozen ¼ ”-18 screw/nuts, weight of 1 g each
Procedure
Part 1
1. With the computer powered up, enter the data acquisition software.
Select “SET UP DAQ “. In that set channel numbers and ICP power for
channels 1,2, 3 & 4
“ON”. Rest of the channels should be off as we are using only
accelerometers, 2 on each bearing.
2. Let the couple be AC, volts/unit = 0.1, units = “g” for acceleration
measurements. Set REPLICATE channel # = 0, TACHOMETER channel #
= 0. Press OK to come out of DAQ
3. Go to ACQUIRE, and set number of scans =1, frequency range = 500,
number of spectral lines = 400.
4. In the same ACQUIRE window, on right hand side in signal processing
select the following parameters:
Velocity
Magnitude
Vrms
Degree
DB
No averaging
Linear
Hanning
5. Set the motor speed to 15 Hz, at this speed note down the V21 and V43 .
i.e, relative rms velocity of channel 2 with respect to channel 1 and
relative rms velocity of channel 4 with respect to channel 3. For V21 set
“1=accel 1” as reference and “2 = accel2” as channel in signal
processing window. Similarly for V43 change reference to “3=accel 3”
and “4 = accel4” as channel.
30
6. To measure the rms velocity at a given frequency (Hz), use the markers 1
or 2 to reach the set frequency of the rotor. By looking at the window of
M1 or M2 at the given frequency (Hz), the velocity is noted. This gives the
base data of vibration without any unbalance.
7. Add weight of say 10 g on the any one of the holes at the outer radius (r =
69.91mm). Note down the values of V21 and V43. By looking at the data
one can make out that there is an unbalance in the rotor.
8. To nullify the effect of the unbalance we need to add a counter weight of
10 g at the same radius and at an angle of 1800 apart. Now note down V21
and V43. Remove both the weights.
9. To see the effect of radius, add weight of say 10 g on the any one of the
holes at inner radius (r = 57.21mm). Note down the values of V21 and V43.
Again add the counter weight of same mass on same radius at an angle
1800 apart to balance the rotor. Note down the values of V21 and V43.
10. Repeat the steps 5-10 for speeds 30 Hz and 45 Hz.
Part 2
1. Set the motor speed to 25 Hz. Remove all the weights from the system.
2. Run the motor and note down the values of V21 and V43. This would be the
base data.
3. Add a weight of 10 g at 300 from reference and 10 g at 1300 from the
reference.
Run the motor and note down the values of V21 and V43. This would give
the results for the unbalance.
4. To balance the rotor, we need to add counter weight, whose mass and
position has to be calculated. The procedure is given at the end of the
section.
5. Add the calculated mass at the position determined in step 4.
6. Run the motor and note down the values of V21 and V43, this would give
the results for balanced rotor.
7. Repeat steps 3-6 with weights of 9.37 g @ 2100 and 10 g @ 1700
The magnitude and direction of the balancing mass may be obtained analytically
and graphically as discussed below.
Analytical method
1. Find out the centrifugal force (Product of the mass and its radius of
rotation) exerted by each mass on the rotating shaft.
2. Resolve the centrifugal forces horizontally and vertically and find their
sums, i.e. Σ H and Σ V.
Σ H = m1 r1 cosθ1 + m2 r2 cosθ2 + ….
31
Σ V = m1 r1 sinθ1 + m2 r2 sinθ2 + ….
3. Magnitude of the resultant centrifugal force, FC =
∑H
2
+ ∑V 2
4. If θ is the angle, the resultant force makes with the horizontal or the
reference, then
Tan θ = Σ V / Σ H
5. The balancing force is then equal to the resultant force but in opposite
direction, hence add 180 to the θ obtained.
6. Now find the magnitude of the balancing mass, such that
FC = m r
Where m = Balancing mass, r = radius of rotation (57.21 mm or 69.91 mm,
depending on the location).
7. Knowing FC, r, determine m, the magnitude of the balancing mass.
8. Verify the above results using Graphical method.
Tabular column
Part 1
Base
Data
15 Hz
30 Hz
45 Hz
R = 69.91 mm
R = 57.21 mm
Unbalance Balanced
Unbalance Balanced
V21 in/s
V43 in/s
V21 in/s
V43 in/s
V21 in/s
V43 in/s
32
Part 2
Speed = 25 Hz
Case 1,
…………
Case 2,
…………
m1 = 10 g , θ1 = 300 , m2 = 10 g , θ2 = 1300 , m = ……….., θ =
m1 = 9.37 g , θ1 = 2100 , m2 = 10 g , θ2 = 1700 , m = …… ., θ =
Base Data
Case 1
Case 2
Unbalance
Balanced
V21 in/s
V43 in/s
33
Unbalance
Balanced