r
STRBSS CONCEiTRATION INO,TLE
I2EYE SECTION OF A
CON~EC••mTNi,
T
OD
BY
BAL
B.E.,
D. KALELKAR
University of Bombay
1940
Submitted in Partial Fulfillment of the
Requirements for the Degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
from the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
1941
SIgnature of Author
Department of Mechanical Engineering,
Signature of Professor
in Charge of Research
Signature of Chairman of Department
Coonittee on Graduate Students
R
~Blla~-
July 31, 1941
:
Graduate House, M.I.T.
Cambridge, Mass.
July 31, 1941
Prof. GJ.W.Swett
Secretary of the Faculty
Mass Institute of Technology
Cambridge, Mass.
Dear Sir,
In partial fulfillment of the requirements
for the Degree of Master of Science, I hereby submit this
thesis entitled, 'STRESS CONCENTRATION IN THE EYE SECTION
OF A CONNECTING ROD.'
Respectfully yours
Bal D. Kalelkar
I
Table of Contents
I
II
III
IV
Acknowledgement
3
Purpose of the Investigation
4
Previous Work
8
The Procedure
15
i) The Method of Attack
17
ii) Three Dimensional Treatment
17
iii) Two-Dimensional Treatment
17
V
Experimental Results
40
VI
Mathematical Results
57
VII
Mathematical Symbols
61
VIII The Mathematical Theory
62
IX
Calculated Results
82
X
Discussion ot the Results
92
XI
General Discussion
95
XII
Comparison of the Experimental Results-103
XIII A Few Words to the Future Investigator-l07
XIV
Suggestion to the Designer
108
XV
Bibliography
113
AC KNO WLEDGEMENT
The author of this thesis would like to express his
deen aopreciation
•o
Prof. W:M: Murray and Prof. E.S.Taylor
for the invaluable assistance and guidance in the work and
for sug~esting the problem.
The author would also like to take this opportunity
of thanking with gratitude Dr. Durelli for his assistance
received during the experimental and mathematical work on
the subject.
The author is also thankful to Mr. R.A.Frigon for
his assistance in photographic work, and Mr. R.P. Misra
for his invaluable help in dding the most tedious work of
writing the formulas and other eleventh hour work.
L
J
NINT
~
cpns.-·
-
Puroose of the Investigation
As is known to every engineer, the inertia force
produced by the reciprocating piston in an engine, is
directly proportional to the square of the speed of the
engine, and is maximum at the dead centers, where the
piston changes its direction of motion.
Due to this force
at the top dead center, the connecting rod is subjected
to a momentary tensile stress of considerable magnitude.
With the development of the high speed engines, the
problem of the stress concentration in the eye-section
of the connecting rod due to this tensile stress, became
more and more importanty-the increase in the importance
being directly proportional to the square of the piston
speed.
If the reader traces the motion of the connectirg
rod of an engine; he
rill see that the latter is subjected
to the following kinds of loading:
Suction Stroke and Compression Stroke
During this stroke, the piston tries to lag behind the piston pin and consequently, the tensile stress
is
produced in the connecting rod, rrhich is
solely re-
sponsible for opposing the lagging tendency of the piston.
At the end of the suction stroke, due to tho'inertia of the
piston, the piston tries to continue its motion in the
direction of the shaft, while the connecting rod changes
its direction, and so a compressive stress is exerted on
the connecting rod, during this change of the direction
of the piston, and also during the next compression stroke.
Power Stroke and the Exhaust Stroke
Somewhere near the next top dead center position,
the explosion takes place, and the piston continues to
exert a compressive force on the connecting rod during this
power stroke and the next exhaust stroke.
At the end of the exhaust stroke the pressure
on the top of the piston being only that of the atmosphere,
the inertia force of the piston produces a tension on the
connecting rod and hence the latter is subjected to a
considerablAO amount of tensile stress.
The oresent oaper
is concerned with the investigation of the stress concentration due to this tensile stress.
The author would like to warn, however,
that
this is not the only critical condition under which a connecting rod is subjected.
Due to the sideway motion of
the connecting rod, and due to the bending and buckling,
the various kinds of complicated stresses are produced
in the body of the connecting rod; but as far as the eyesection of the rod is concerned, the tensile stress described above is perhaps the most critical of all.
This leads the designer to the question of investigating the stress concentration in the eye-section
of a connecting rod and the author of the present paper
has tried to investigate that concentration in an actual
connecting rod.
Next the question arises why should one worry
so much about this stress concentration when it is possible
to increase the thickness of the eye-ring without any appreciable difficulty with regard to the working of the
engine?
But the problem becomes more important in the
design of the connecting rod for an aero engine, where the
reduction of even an ounce of metal would be welcomed by
the designers and where the use of the high speed engines
has become quite common.
In the case of the high speed
engines thqtheavy connecting rods would give a headache
to the engineers when the latter tries to compensate the
out of balance forces of the engine.
All these difficulties make the problem of the
stress concentration very important and very interesting.
As the reader would see from the above discussion,
the problem of the stress concentration is more important
in the case of the aero engines than any other kind.
Be-
cause of this reason, the author has particularly made his
test model of the same type as that used in an aero engine
of the radial type.
F
The only change that the author has
made in the model is that the thickness of the eye-section
was kept the same as that of the I section of the connecting rod, while in the case of the actual rod, that thickness was 1/16" more on both sides.
This change was made
on the assumption that it would produce no effect whatsoever on the stress concentration except the increase
in stress that would be produced due to the change in the
actual cross-sectional area of the eye.
The author was
convinced about the correctness of this assumption from
the results that he obtained during his treatment of the
subject, by the three dimensional method.
The writer would like to state here, however,
that the work done in this thesis is just one of the
series of experiments that the designer must perform to
get sufficient data for the connecting rod design.
As
the reader would see from the discussion on the result of
this investigation, one must also find out the stress
variations in other cross-sections of the rod, besides
the two sections treated in this paper.
Again, we must
treat the whole problem anew, by changing the inside and
outside radii of the eye-sdction (ri and ra), and from
all these results, one must find out, a general empirical
formula for the design of the eye section.
So, the reader
S•Twould see that the work done here is just a drop in the
vast ocean of the data on the connecting rod design.
Previous Wiork
Before the vriter starts giving in detail his
method of attack, the results and mathematical calculations, he would like to give in short, the review of the
mathematical and experimental work done by the other investigators.
The writer would like to divide the articles
into three catagories:
a).
Experimental investigation,
b). Descriptive treatment,
c). Mathematical treatment.
a). Exnerimental Investigation:
As far as the writer is
able to find out, the only photo-elastic analysis that
has been done on the subject is by Kango Takemura
Kogakuhakusi and Yehei Hosokawas,
from the Aeronautical
Research Institute, Tokyo Imperial University, in 1928.
But as the writer of the present paper has expressed in
the above section of this work, done by Kango and his
colleague, is also just another drop in the ocean of the
knowledge about the stress concentration in the eye
section; and tbholgh this work is
is complete in itself.
good for guidance,
as it
Of course. it is true, that in
those days the photoelasticity ;,as not so much developed
as it is today and so one cannot expect a better treatment
than that we find in this paper.
In their paper the authors give the (p-q) curves
at the critical sections for the four different kinds of
eye bars and compares them with the p-q curves obtained
for the critical section of a circular ring and an infinite
plate with a circular discontinuity. They also give the
Isoclinics and the Stress Trajectories for those forms of
the eye bars though the author of the present paper has
his doubts about the correctness of some of those stress
trajectories.
On the whole the article is very good and gives
a general idea about the effect of the change of shape on
the stress distribution and the stress concentration in an
eye bar.
Coming to the second article which appeared in
Forschungsarbeiten Heft 306, and which was written by
Dr. Mathar,,in 1928, the article deals with the results
of the experimental determination of the stress variation
in the different kinds of eye bars.
In his experiments,
Dr. Mathat has used the strain method for finding the
stresses. He also gives the stress curves for the different
sections of the connecting rods.
Unfortunately, however,
the writer of the present paper cannot read German and so
is unable to give a better and more detailed review of
Dr. Mathar's work.
The results obtained in the present
paper tally somewhat with the results of Dr. Mathar.
Dr, Mathar's paper seems to be very interesting and important too.
Descriptive Treatment
Coming to the second category the author is
able to find only two articles which give in detail the
different shapes of the connecting rods.
The article by Mr. Volk in V.D.I.Ziet. Oct.22,
1938, gives in detail the different forms of connecting
rods used and proposed for different kinds of engines.
The other article written by Mr. Angle,
(Automotive Industries, March 1935) gives much information
regarding the ratios of different dimensions of the connecting rods used in present day practice.
He also gives a
general empirical formula for the design of the eye section
but he does not give any proof pofthe same.
c). Mathematical Treatment
Coming to the mathematical treatment, one article has appeared in "Machine Design" of September 1939.
In this article, Mr. K.E.Bisshopp treats the eye section
as a curved beam and uses the method suggested by 44P.
2--6
in "Machine Design" of August 1937. Mr. Bisshopp gives a
series of curves obtained by the mathematical treatment
for different ratios of the inside and outside radii of
the eye bars.
In his article he shows how the stress
concentration can be read directly from those curves.
The author first tried to apply this new method
r
of calculations for his model of the connecting rod, but
FPOW
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Connac±ina Rod
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found out at the end that although the method is easier
to follow, the results, in case of an actual connecting
rod, were quite absurd.
The author is of the opinion
that the consideration of the eye section as a curved
beam is not justified in the cases where the width of
the eye ring (ra - ri) is very small and where the curvature of the section is too great compared to that width.
In an actual connecting rod the width is small and the
curvature is large.
Coming to the last article by Mr. H.Reissner
of Berlin, .the article treats the eye section of an
connecting rod by the application of the Theory of
Elasticity.
The article is a thorough treatment on the
su4cn+
his4
"k'r" ncl%11
teathonr hasC bkee
+'ud
compelled~ in common with the other investigators, to
make a number of assumptions, not only to simplify the
mathematical work but also to make it possible.
In his
article, Mr. Reissner has treated the problem for four
different sets of conditions, i.e., the four different
kinds of conditions at the inside and outside edges of
the eve ring.
The article is excellent as far as the mathematical treatment of the subject is concerned, and the
writer of the present paper has used his method for the
calculations of the stresses for his connecting rod.
Mr. Reissner, in his paper, calculates the stress varia-
EM
/,5
tion for two eye bars having the ratios of r
= 2 and 4.
Though these ratios make the calculations
easier to
work,
the ratios are not used in actual practice and so
the work done by Mr. Reissner is useful only for comparisona piuroses.
As stated above, the author has followed the
method given in this article and so the details of the
method will be given at a later stage.
The Procedure
A connecting rod was machined from the Bakelite
BT 61-893 and the dimensions were made three fourths of
the dimensions of an actual connecting rod of a radial
aero engine. (Fig. 1).
This connecting rod was tested
by the two dimensional method as well as by the three
dimensional method.
The appnaratus used in these experiments were:
(a) A standard type of polariscope w.,hich is shown
in Fig. 2.
(b) The loading arrangement was also 'of just the
standard type as that shown in Figure 3.
(c). For finding out the values of (p + q),
the
author used an interferometer strain gage, developed at
M.I.T.
All these instruments are of the standard type
and so the author does not find it necessary to describe
i
3.l.ile
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M124d!½
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them in detail and thinks that the photographs given in
Figvires 2 and 3 will explain everything,
the
without any
difficultry.
0?
The Method Attack:
In case of a problem in Photoelasticity, the
first question that arises is whether the three-dimensional
treatment is necessary for the particular problem.
In the present case of the connecting rod, after
a thorough study of the case by the three dimensional
method, the author of this paper has come to the conclusion
that though the problem does appear to be in the three
dimensions, the Three Dimensional attack is absolutely
unnecessary from the point of view of the stress concentration.
The' region, at which the effect of the three dimen-
sions takes place, is subjected to such low stress, and
the effect of the stresses at this region on the stress
concentration in the ring are so negligible, that the
three dimensional attack becomes unnecessary.
How Three Dimensional Treatment is Unnecgessarv
The model of the connecting rod was loaded with
a load of 7.5 lbs. (though the author must confess that
to keep this load constant was very difficult at high
temperatures as the material became plastic and that the
author has only tried to keep the load constant, as far
~ci
. ·S-
20
as was possible.) under a temperature of 1150C.
This tem-
nerature was obtained gradually within 3 hours.
The model
was kept at that temperature only for 14 hours.
The tem-
perature was then gradually reduced to 700 C in 8 hours.
Again this temperature was maintained for the next 14 hours
and then the temperature was brought to the normal room
temperature in about 6 hours.
The model was then cut into
three pieces as shown in Figure 4 and the fringe photographs
were taken.
(Figs. 5 and 6)
Now from these photographs one sees that if one
superimposes the fringe photograph of the middle-strip on
that of the side-strip, the position of the concentration of
the fringe pattern is the same in both the cases.
Again,
if one calculates the value of (p-q) stresses at these
points of the maximum concentrations, one sees that the
stresses in both the cases are almost the same.
(The reader
is warned here not to get misled from the actual photographs,
where the number of lines are not the same, due to the fact
that
The
i
the
calculations
thicknesses
of
for
this
the
two
follow.
strips
are
not
the
same.)
The data obtained from the Fringe photographs of the
two strips (the middle and the side strips).
The Middle Strip:thickness = .087"?
maximum fringe order = 1.5
Fringe order in the shank (I section) = .75
The Side Strip:Thickness = .165"
Maximum fringe order = 3
Fringe order in the shank (I section) = 1.5
Now say, K is the fringe constant for the material
at this elevated temperature; then, maximum value of the
(p-q) curve for both the cases will be as follows:
For the middle strip:-
(p-q) = -. 5x K = 17.3 K
.087
For the side strip:(p-q)
= 3 x K
.165
= 18.18 K
Again (p-q) = value for the shank (I section) will be
For the middle strip
(p-q) = .75 x K = 8.61 K
.087
For the side strip
(p-q)
1.5
.165
x K = 9.09 K
In all the above cases, the value of q is 0; and
so the p-q gives directly the stresses at these points.
22.
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From these results we see that the stress variation
in the middle strip will not be very different from that
in the side strip.
If we study the stress trajectories for these
sections (Fig.
7 and 8),
we see that the direction of the
principal stresses in the eye-ring section of the connecting
rod are the same in both the strips, Fig. 7 and 8. The only
change that takes place is in the region just below the
lower part of the inside edge.
Fig. 7 and 8.
After the study of the p-q curves and the stress
trajectories and the isoclinics for these two strips, the
author has come to the conclusion that the only variation
that must be taking place must be somewhere in the region
shown by the dotted line in figure 9.
Now from the lacquer
experiment and also from the two dimensional results, it
was found that this region is subjected to a very low stress.
In his experiment in lacquer, the author painted the model
with a lacquer layer and allowed it to dry.
After the lacquer
was completely dry, the author loaded the model with a load
of 3490 lbs.
It
was observed that no cracks appeared in the
region shown by the dotted lines in Fig. 9.
The author
:-anted to confirm whether the absence of cracks was due to a
compressive stress or was due to the fact that the region
was not subjected to an appreciable stress at all, so he
kept the model loaded for 6 hours and then unloaded the model.
It
wvas observed that not a single crack appeared even after
/·
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r--I-
The cracks obaied dur.n
the
LaCour Expe-r :iment.
Fig. 10
~.
/2
t/4. /3
/4
that treatment and so the author concluded that the absence
of the cracks was due to the fact that the region concerned
was subjected to a stress -whichwas very low in value.
The photographs obtained in the lacquer experiment
are given on Figs. 11 to 15 and Fig. 10 gives a general view
of the cracks that appeared on the lacquer due to loading.
The model of the connecting rod was very small and
it was very difficult to get a better picture of the cracks.
The author hopes that Fig. 10 will give a clear idea about
the cracks which were quite visible on the model.
From the above discussion the reader will understand how in the three dimensional treatment the stress concentration in the eye ring portion will remain the same for
both the strips.
The author came to the conclusion that,
for the three dimensional treatment Twas not necessary in
the case of a connecting rod.
Two-Dimensional Method
In his experiments, in two dimensions, the author
studied the sections AA and BB (Fig. 1) and found out the
actual values of the principal stresses
for these two
sections, thinking that the maximum stress concentration
would occur somewhere on these two cross-sections.
The
complete stress analysis of these two sections was obtained
from the p-q and p+q curves for these two sections.
The
detail analysis and the results will be given on the next pages.
After the mathematical study of the subject, the
author has realized that his assumption that the maximum
stress would occur on the section AA was not correct.
The
position of the e section on which the maximum stress would
occur depends on many variables, which will be discussed in
detail at the end of this paper.
So it will be seen that,
though the author has studied the stresses in two of the
principals sections, the work is still incomplete even from
the point of view of maximum stress concentration, and there
is a vast field for the other investigators.
Before giving the results of the experiments and
tables, the author would like to describe in short, the
method of his experiments and the precautions that he had
to take during the experiment.
Of course, the reader is
here supposed to have a general knowledge of the apparatus
of the photoelasticity and the strain gages.
The author fitted a pin inside the eye, the former
being made of the same material as that used in the construction of the connecting rod. (Bakelite BT 61-893).
A steel
rod was inserted through the middle of this pin to help hold
the whole structure in the loading machine.
This precaution of keeping the pin of the same
material as that used in the connecting rod body is very
essential, because as the reader would see, from the photographs taken during the three dimensional treatment, (Fig.5,6)
the eye-hole of the connecting rod becomes elliptical v-hen
the rod is loaded.
Though the deformation obtained in this
way, in the three dimensional treatment, is much more exaggerated of form, it gives a very good idea of the way in
which the eye of an actual connecting rod would deform.
Now
in the case of a Bakelite model of the connecting rod, if we
use a steel pin while loading, the manner in which the eye
section deforms would be completely changed, and consequently,
the stress distribution also will be changed, therefore, the
author is of the opinion that the pin used must be made of
the same material.
(b) The loading arrangement must be such that the conneeting rod is loaded exactly vertically and has no bending
moment whatsoever.
This was obtained in the present case by
using two universal joints, one at each end.
(c)
The 4mount of load that one should put depends on
the material used, and also on the size of the enlargement
of the fringe photograph.
In the pzsent case, the author
obtained a fairly good pattern with a load of 152.5 lbs.
(d) The pin was introduced inside the eye, with a
slight force.
This question of "fit"
is
a debatable one,
and as will be seen later, from the discussion of the results,
the manner of "fit" plays a very important part in the
position of the stress concentration.
In case of an actual connecting rod, one knows,
that the pin is a "slide fit"and not the"force fit."
So,
one may argue, that during the experiments, one must not use
a "force fit".
The author thinks that, as the eye-holes aret
fitted generally with a bushing made of some kind of bearing
material, the manner of "fit" depends on the manner of fit
46 . / S
A
. /.
.
--
T37
TABLE 1
Distance from the
Fringe
(p-q)
outside edge
order
Lbs/4!
11
1290
.029
9
1050
.051
.062
.076
.094
.113
8
7
6
5
4
935
820
700
534
467
.130
4.145
3
2
350
234
.159
1
117
.174
0
0
.188
1
117
0
0~
4I
Table 2
THE VALUES OF p AND q OBTAINED
FROM
THE(p-q) and (p+q) CURVES :
Stations
(p-q,
Lbs/o
0
.5
1350
1140
1.0
1005
1.5
880
2.0
760
635
2.5
3.0
3.5
4.0
4.5
5.0
Edge
510
380
260
130
117
(p+q)
Lbs/)"
235
290
340
385
430
470
498
480
430
355
250
117
p
Lbs/D
792.5
715
672.5
632.5
595
552.5
504
430
345
242.5
125
117
-q
Lbs/ "
557.5
425
332.5
247.5
165
82.5
- 50
-85
-112.5
-125
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of this bushing, and not on that of the pin itself.
Because
of this reason, the author has used a "force fit" and not a
"slide fit" in this experiment.
(e) It was observed by the experiments that a slight
oil film on the pin gives a much better uniform loading and
consequently a better fringe picture.
Results:- (t- .-
raQQ
The Figs. 15A and 15B shows the fringe photographs
obtained during the experiment, the latter being taken on
the light field.
The Tables 1 and 2 gives the p-q~alues
for the section AA (Fig. 1) obtained from the fringe photographs.
The graph in Fig. 16 shows this curve.
Note: Here the reader is asked to note the two
different wajys of plotting the (p-q) curves. (one shown by
the dotted curve).
The question in this case is about the
existence of a singular point on the section AA.
From the lacquer pattern that the author obtained,
it was quite obvious that the section was not subjected to
a compressive stress and consequently, there could not be
a singular point on the section.
The mathematical treatment
showed that the section concerned is subjected to a compressive force and so the author has drawn two alternative curves.
The curves in Figs. 18 and 19 for p and q
are also shown in the two different ways, each representing
;the corresponding p-q curve.
TABLE 3
READINGS 'OF THE INTERFEROMETER
FOR THE SECTION AA:
STATION 1
Load in Lbs
116
128
140
Lines
0
1
2
3
4
150
157.5
169
STATION 2
Load in Lbs
69
94
3
4
Lines
0
1
2
77
3
104
5
84
Lines
67
1
75
85
2
STATION 4
Load in Lbs
Lines
65
STATION 5
Load in Lbs
72.5
74
88
83*.5
10o2.5
92*.5
117
128
182.5
STATION 3
Load in Lbs
55
62
Lines
0
1
2
3
4
TABLE 3,
(o+q)
_
__
Station
I
section AA
for the
values
__
______
I~__
A- bands
(p+q)
14.3
336
16.5
388
20.9
491
16.5
388
10.5
246.
Ah x E
where (p+q)=-
q
_ý,
___
_ _
.4,ý
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144
For finding the (p + q) value for this section,
five stations were located on this section and the interferometer strain gage was used to determine the change in the
strain for each point.
The change in load required for the
change in every interference line was noted.
gives these values).
These values give an almost straight
line curve for each point.
for each point and the
(the Table 3 a-
A separate graph was plotted
bands for a load of 152.5 lbs. was
calculated from the slope of this graph.
The graphs in
Fig. 17 show the curves for this station.
From these values of bands for each point, the
p+q value for that point was calculated by the use of
Lateral Constant (Note: the Lateral Constant for the material
was found by the usual experiments, but for the sake of
brevity the author does not propose to give in detail the
experimental results and graphs obtained in this experiment.
The Lateral Constant was found to be 17.3)
The curve of p+q for this section AA is drawn in
Fig. 16.
From these two curves of p-q and p+q, the separate
curves of p and q were plotted as shown in Figs. 18 and 19.
Now the lacquer pattern obtained to get the stress
trajectories show that the direction of the principal stresses
(p and q) at the section AA are exactly tangential and radial
(Fig. 10), so in this case, the load obtained by integrating
the p curve must give the value = P , where P is the total
load applied on the model.This was checked and found that the
3c
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Table --- 4
The values oI (p+q)
for the
Section BB
Stations
-
-
Distance from the
Bands for
outside-edge.
a load= 152.5Lbs.
--
(p+q)
Lb s/a"
.03
17.95
421
.0925
15.25
358
.155
7.75
182
.2175
3.72
87.5
* 8
3.6
84.6
.3425
5. 5
123.5
.405
4.36
102.5
.4675
3.99
93.8
.53
4.8
--
The -values of
--
(p-q) LI- for the
|
Section BB
Points
Distance from the
Number of order
(p-q)
outside-edge
.00444
.0178
.0488
700
.0666
089
467
.115
350
.151
234
*195
117
.32
117
!L
Table---5
p and q values for the
Section BB--
Distance from the
outside edge.
(p+q)
-4FV.
-q
(p-q)
(cI
0.060
520
520
520
.025
465
715
590
125
.050
410
700
555
145
.100
305
410
357.5
.150
200
230
.200
100
115
107.5
7.5
.250
85
100
92.5
7.5
.300
87
115
101
125
107.5
17.5
112.5
17.5
.350
52.5
15
.4c C
95
.450
97
132
114.5
17.5
.500
102
15
138.5
16.5
error was only 10.8%j of the correct load, which is
a quite
satisfactory result for the photoelastic work.
Calculations:-
Area under the p curve = 26.125 sq. in.(Not
the dotted
curve)
The scale for the abscissa ----1" = .035"
The scale for the ordinate --- l" = 100 lbs.
So 1 square inch = 3.5 lbs/inch thickness of the model.
Total load = 2x(26.125 x 3.5x .744)
= 136 lbs.
%error = 152.5
- 136
152.5
= .108 i.e.
10.8%
The stress concentration for this section, compared with the mean stress across this section will be as
follows:
Actual maximum stress obtained by experiments =
Pmax.
=
792.5 lbs. per sq. in.
pmean =
mean
152.5
2 x .188 x .744
So the stress concentration-
792.5
546
=
546 lbs/per sq. in.
= 1.45
Section BB (Fig. 1)
The Table 4 gives the p-q values and the distances
of those points for the section BB.
Here the curve is drawn
only for half the section, the remaining half being the duplicate of this curve.
F
1
St~I~nS e
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TABLE 6
STRESS- VARIATION ALONG THE
EDGE OF THE CONNECTING ROD.
Distance from4he
head of the eyesection in inches
Order of
Number
Stress
p
Lbs/a"
.0889
4
468
.311
3
*506
.58
2
1
2
350
234
117
234
3
2
1
2
350
234
117
234
1.091
3
4
350
468
1.155
1.215
5
4
585
.666
*.835
. 940
. 995
1.o40
1.065
1.28
1.350
1.44
2
2
2
468
350
234
117
TABLE
READINGS OF THE INT.RFEROMETER
FOR THE SECTION BB
STATION 1
STATION 2
Load in Lbs
Lines
Load in Lbs
Lines
55
0
36
0
65
72.5
80
87.5
1
2
45
1
2
STATION 4
Load in Lbs
35
75
115
157.5
STATION 7
Load in Lbs
3
4
Lines
0
1
2
S3
Lines
55
65
77.5
3
4
STATION 5
Lines
Load in Lbs
0
30
115
1
2
162.5
3
72.5
STATION 8
Load in Lbs Lines
STATION 3
Load in Lbs
155
135
Lines
0
115
1
2
96
3
STATION 6
Load in Lbs
Lines
38.5
0
72.5
1
2
96.5
125
3
152.5
4
STATION 9
Load in Lbs
Lines
160
3
18
26
0
125
2
55.25
53
1
90o
86
1
2
o0
132.5
87.5
55
123.5
3
159
4
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Distance from. the outside edge in inches.
I
The Tables 4 and 5 give similarly the values of
p+q obtained exactly in the same manner as described above.
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8 sections were located on this section.
The curves in
Fig. 20 show the 4 banýs against the load for each station. A-^
7" •--L&5
VT-" Iýý
w.-The values of p-q and p+q were plotted as usual
in Fig. 21 and from that the p and q stresses were evaluated
and plotted on a separate graph, Fig. 22.
For this section too, one sees from the lacquer
pattern that the direction of the principal stresses is
almost horizontal and vertical (considering the main axis
of the connecting rod as vertical).
4
So in this case too,
the load obtained from the area of the p curve must be
=
'
2
BB)*
(because our curve is only for half the section across
Calculations:-
Scale for abscissa = 1" = .1"
"
"
ordinate = l" = 100 lbs/ sq. in.
Area under the curve = 10.625 sq. in.
One square inch = .1 x 100 = 10 lbs/inch width
of the model.
Thickness of the model = .744
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Load =.10.625 x .744 x 10 x 2 = 158 lbs.
.'.
Error = 158 - 152.5 x 100 = 3.4%
152.5
X
Here, the error is very small and the results are
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amazingly accurate.
Coming to the third curve in our experiment, the
author calculated the stress variation across the outside
boundary of the connecting rod from the fringe photographs
of the model.
(Fig. 15A and 15B).
As is well known - one
of the principal stresses at the boundary is zero and the
fringe pattern gives directly the stresses at those points.
The value of these stresses and the distance of the points
were tabulated (Table 6) and plotted as shown in Fig. 23.
This curve gives a very good idea about the stress variation
along the outside boundary of the connecting rod.
Coming to the last experimental curve in this
paper, Fig. 24 shows a curve across the section CC (1).
Here too, the load being vertical and one of the principal
stresses being vertical too, the stress q will be 0, and
so the fringe photographs will give directly, the value of
the other principal stress, i.e., p.
in Fig.
This curve is drawn
24.
Mathematical Calculations:For his problem, the author of this paper studied
the mathematical treatment discussed by Mr. H.Reissner of
Berlin, in "?Jahrbuch, der Wissenschaftlichen, Gesellschaft
fur Luftfahrt e.V.(WGL) 1928, and has used the same method
to calculate the stresses for his connecting rod.
So the
reader would see that the method given below is just copied
s$
I...;.T-
[
i
C
4~-.
L
i~~
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14..r
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4~V~s.
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K
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Lb
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1J
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from the above paper.
The author of the present paper has
given the theory in detail on the fond hope that some other
investigator would take up the problem in future and would
be benefited by it.
Fig. 25 gives the curve obtained from the mathematical calculations:
In this case the integration of the p curve must
give a total load which will be equal to R.
2
lations are as follow:
The calcu-
Data:The area of the curve (mathematical curve) in
Fig. 25
= 7 - 2.25 =
4.75 sq.in.
Scale of the abscissa = 1" = .0376"
"
"
"i ordinate = 1" = 600 lbs/sq.in.
.*. 1 square inch = .0376 x 600 = 22.56 lbs/inch width
..
..
Total load = 2 x 22.56 x 4.75 x .744
= 159 lbs.
Error = 159 - 152.5 x 100 = 4.27
152.5
The Fig. 25 gives the curve obtained from the
mathematical calculations.
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6l
MATHEIMATICAL SYMBOLS
t
= Radial or Tangential Displacement
or
= Normal Stress (Positive when in Tension)
= Radial Stress (Ring Stress)
S= Tangential Stress
= Shear Stress
=
=
=
=
Unit Elongation
Radial Elongation
Tangential Elongation
Change in Angle
= Modulus of Elasticity
S= Poisson's Ratio
a
<
3
= Thickness ofthe plate of the Ring
= Outside and Inside Radii of the Ring
= Coefficient of the development of the series for
obtaining u and v shown by the constants
and similarly for /1
a'_2~
= Coefficients for the development of a series for
the stresses and shown by
= Tool resultant force
Mean Stress
SAverage Ring Stress =
AI_
77 /
17F
/
-
"
62.
The Me l
r
Y%%
, - c7•i
0
-A
The well-known fundamental equations for the
plane problem of a ring-shaped plate are given below in
the cylindrical polar coordinate form.
The equations are
obtained from the equilibrium condition for the normal
stresses
r and Yg and shear stress
9
(Fig. Mc ).
Here
it is assumed that the body forces are absent.
Ic631.
-0
From these equations, the relation between the
stress and strain follows as given below:
1~,s
-
_
p
Finally, the relation between strain and displacement is given by the following equations:
One knows that these equations hold good for
even so called quase plane, if one takes ),
V,
and u and
v as the average quantities, the average being taken over
the thickness of the body concerned.
Now, under the assumptions of the boundary conditions, (which will be given later) these equations are to
be integrated.
The Method Integration:
Since we know that the displacements are monovalent
periodic functions of the angle 9, we develop the values of
u and v in the following trigonometric series:
u =
cos
0Un n 9
v = *Vn
sin n 9
Where V,
2.
and Uf, are functions of the radial co-
ordinates r, which will be determined later on.
So now, if we substitute the equation 2 in equations
1 b and 1 c, we get the following expression for the stresses
641
E
LL
UAA,
Vj
LL
j~L
r
Lk
V,
I
aC~,
Where primes represent the differentiation with
respect to r,
Introducing this equation 3 into the equation of
i.e., la, which gives the following
equilibrium conditions,
total differential equation which will help determine Un
and Vn.
_ k
,,-
V
VV
.
--
-
1:_
_
--
A.
.
2 2-.
O
+
2.
+ V'A, - '
2.-i
The index 'Y has been omitted in these equations
for the present and they are of equal dimensionality so they
can be integrated by the simple power of r and so we get
the following series.
A
O
y=x
01;-
Now this gives a very simple algebraic equation
for the value of each
equation 4.
when on is introduced in the
r,
The roots of each of these equations are
t
L-
CI± -)
--.....
Also
$L C+%
I -+
-6=+'
L4
While between the constants aoand #•,
the
following lelations hold good.
(NAY u
("
=
0(1-
Where q and S are the abbreviated forms, the
value of which is given below.
ly
r2
Fora= 0 and
.9
• = 1, the case is
especially simple.
If we substitute - = 0 in equation 4 it gives two equations
for U0 and V0 and
1= 1 yields a two-fold root po = + 0.
Hence we get the following particular integral of logarithmic
type:
MJ
Lkc,_
_
_
6__
6c-,
_
Here, the coefficient,* gives a state of pure
normal stress with purely radial displacement while coefficient
gives purely tangential stress with purely tangen-
tial displacement.
'^AIi
4-
U"
=Q(.
%.
-A*
-,+
d, --, "T_-tt
2.
ýC 4 -+ A -1
+
,
-
&6s.
V4L-
4
4-
~-
c~
4
2
A-l
-_
' - .+ +X
Z _
-
'
6c.
G7
From these equations, the displacements U
and V
are obtained immediately by the help of equation 2.
In order to derive the stresses from the equation
I
3, it is now necessary to introduce some abbreviations and
different constants, in the above theory.
For this purpose
a new constant 5 will be introduced in place ofe>
Y~and Z
certain reduced dimensionless stresses
place of the original stresses
and
and a
in
'.
Further, the dimensionless coordinates and their
reciprocals, which are in terms of external and internal
radii, will also be used.
These reciprocals are always < 1
due to their definition, and so, the equation 2 reduces to
a convergent series, which is quite apparent.
The above mentioned reduced stresses will be as
follows:
S
=
_
P
S
S
and
Where
P
stands for the total force on the circumF
ference of the circle. b is the thickness of the eye and
Ye and
are the assumed new values.
The reduced radial coordinates and their recip-
rocals will be as follows.
1
9L
:252.
40
To derive the coefficient we get the following equations:
When
?v = 0
•_(
SCS•
i7LPL,6
E
r2 E
-
2.-
7c
<
>1
when
z= 1
SI
~44=
For
o(
'L
1-i L
6E
,~ 0(,IE
&~4
~r>1
If-A
& A|
,
,,
-
k-1
4 1
_._
P~c
(n-i) (v+-L)
7FZ
S> 3
( I441)
'9'
1]
d?
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1
____
VZ
II-·)
2.
IT
The magnitude •
which appears in all the above
equations is intimately tied up with the mean stress
P
*?
61*ý'
_
.
eL
-
Or also with the mean pressure on the inside
surface of the ring.
So one can define the reduced stresses
by the following expressions:
I
3s
I'
7'..
= the rate of the internal and external
Where
radii, or
ri
ra
Now with these reduced coordinates of Yi and Ya
and with the help of the new constants in Ss, the reduced
stresses
Y and
S. can be obtained as follows:
For
e
7
ý
7o
- \
For
iib x.
4C
3~s
J
tab I
2
For
'
>
i
*~&*
2
~'
I;
yvt'L~ 6
*\i.* 1..
-I
lv'
-Ki .
The Problem of the Eye-Ring:
The above is given a general theory.
Coming to-
the application of that theory to the problem of the eyering, it is quite possible that we can assume the several
kinds of boundary conditions, the latter being dependent
on the construction of the eye bar and on the manner of
loading.
If one wishes to determine the distribution of
stresses on the inside or outside surface of the eye and
and
7 then one has to develop the series shown in 6(a,b,c)
and 8(a,b,c)
In our problem, we assume that the boundary conditions are as shown in the Fig.
i.e, at the inner
surface.
(When 9
-
i
-
)
q%
=.0,t -I-I%
-ti:
c4,L
->,,,I
42".
z.--
Similarly, for the outside surface:
=s-, jý=
9, 1ý = ýx--'
tz -2-7%
2.
____·___i~iLS=_____rr___lT~
I
I
_ha. Ma-
PFi'.
Mb
Fig. Mb represents this surface condition in a
graph form where, the angle 9 is plotted on a straight line.
This distribution, fulfills the requirements that the resulting force in the direction of the radius, for which
9 = 0 or 7is
= P, at both inner and outer surface of the
ring.
Now we have to develop the stresses
and
each in a trigonometric series, in such a way that they
correspond to the above mentioned boundary conditions.
According to the well-known Fourier's method of
determining the coefficient by means of definite integrals,
one obtains the equation given below in 12, where only even
values of-n exist.
-~~
v~rz Pe
~~+
CI .
&I%, .
-
-
-
-
f
*
11
Y4ieC
I
1'
Now, if one determines the coefficient
I
, he
has to satisfy, besides the above mentioned conditions for
the normal stresses at the outside, inside surfaces, also
the condition that the 7', the shearing stress in zero.
So this condition also should satisfy that equation.
Now, for mathematical simplification, if one in-
troduces 7min place of
7
(which is its reciprocal) and
after the comparison of the coefficient
9
of the equations 8
(a,b,c) at the location of r = r i and r = ra, with the coefficients cni and cna of the equation 12, he gets the following
relations
= 0
When
4
=
from which we get
Whe (A-1
W7hen 'A
1
i.t,
44 'Z
7S
m
For which we get
'r"f
"A24
77Here one of the equations is derived from the other
because of the fact that the resultant force at both inside
and outside the boundaries, must he equal, because, the
rod is in equilibrium condition.
Now when
"'
/
'i/i.
-
/IL
-M-+'&LI
I
~
-I
t1 -
~&i.
.~'~
-
ACA A I R -
I
C2.
0
-
-~t
S,
IVA
A"
-I
4L
IV%
AA'
And from that we get the equations
••-
_v •-)' " -4
( ' "2i•
• 3
VH
+
)(,,-,
)A't'A.
)ýA3
k ') "•
A
5
]e:'
".
-L*VA-l
Ail
120
76
Shi.
=
l)
s,
--
44
-
eI4L
4
ý;
"At
~aa
~t/24
I
i
Now,
before we evaluate the above mentioned coef-
ficients, let us put down the resulting general expression
for the most important stress, i.e., the ring stress Y,
which is obtained from the equations 8 (a,b,c)
c'.
8P
=S -+S,t ýý- 4 &9[.CS
90
ý_;
i5-~Z~2jJ
6
I
L
%I
1.~\
'YI
LA) A
. / S
1
ýC:t- ýa
(
' .L
Now,we are merely interested in the sections where
9
O or cos
W78
= 1,i.e., on the straight vertical line of
the resultant force P, and either the head or tail of the eye.
j~CI
77
and also where 9
±I
i.e., at the flanks of the eye.
Again in these sections too, only three points on
the cross-sections may be taken to find out the stress curve
for the section.
So the following theory follows:
From the equation 14 we get:
When
9 = 0
42 LLA4
/-S
- :v I42
Now for the inner edge, i.e., then A
S_
I
we get the equation
y1I-I
Similarly, for the outside edge
i .,
~.
~M4
71
For the point which is halfway between the inner
and outer edges the equation will be as follows:
(i.e., when
%.--
j
-
X.2.I
"7_~
"bf
+
I/-___
1
_• S•
-
4
So from these three equations (15, a.b.c.)the
stress curve for this section can be calculated.
(The method
of finding the constants in these equations will be given at
a later stage).
Now for the section which is horizontal and passes
through the center of the ring (AA in fig. 1), we get the
following equations
Here
1
I-
Z.)
So for this section we get the relation
So for this section we must multiply the constants
obtained from the equation 13 (c), by the term
0-)
and
, -¾ "
this way we must get
a s for each 'n'.
So now the equations for this section are as
follows:-
I
L
+(
Applying this equation to the points at which
we want to find the stress, we get the following equations.
The point on the inner surface:1
4%
A .7
+
-~
-•
i~~\
'-A
4. L
For a point on thehutside edge:-
I
-fXt <
.4_
...
.51 0_t V ic _4
ý LAý
(3
-i
A4f.
-
--ý
4 -tI.)
Similarly for the point at half way,the equation will be:-
'I
Cw~
(IA
t
UA
-t <ý -A
C
I4~A
--
||W"-
J
'%-
rL
Now,
in all thesO six equations--15 a b c and 16 a b c7 the
constants are found out from the following equations:-
I
A-
t S'LAV
CtY
And also,
Similarly,
U.
I
A
And
values of
I#1h
.---. etc. means the corresponding
and
f r each value of n.
So from these equations we xxone can evaluate the
value of stesses at any poimt on these crossections.
Here,
it
is
interesting to note that, thLe :XizMx*X
Poisson's ratio has the effect on the xxxtI
xhae
stress
curve
for the section where
G = 0 i.e. where the pin has a contact
with the main ring. This shows how it
is
essential to make
the pin, of the same material as that of the main body.
The author has used the equations 16 a b c to
determine the stress curve for the section AA (Fig.
1)
The
results of his calculations and the values of the constants
are given on the next pages.
The curve is
Fiý-'25.
shown2in the
ra
The author's ratios of ri being very small,
author
the
had to work out the series upto fifteen places.
AlL the 0alculations were done on a calculating
machine and &
are very accurate.
The tables of the constants
Wt -etc. can be
for the stress curve
used for the calculations/for any other section,by this method.
(C MR C.J dA
7-ezlolte
__
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2
4.378
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12.01875000
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7.05245000
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20
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30
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14
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28
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30
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7.33297225
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05245000
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18.70858516
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ry\
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3.46260187
13.14450720
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18
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30
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']yr.kapedEnd of Bar imnestliamdby Plhto-lodatic A•ltod.
135
lyc-shap.d End of Bar invcstý al t /9
-:•'t . 7, 7
t'o-/lasti .1/
,/.
92.
Discussion of the Results:The main point that arises in this case is that
the authorts mathematical calculations do not tally a bit
with those obtained from the experimental results.
Naturally, the question arises about the correctness of
the mathematical assumptions, because the author has taken
great pains in checking the results of the interferometer
readings and has not the slightest doubt about their
correctness, and of course the fringe photograph is already there to prove the correctness of the p-q curves.
After a thorough study of the subject, and
particularly after the study of the three articles one by Mr. Takemura, the other by Mr. Reissner, and the
third by Dr.*Mathak -- the author of the present paper has
come to the conclusion that, the assumptions made at the
beginning of the mathematical calculations do not represent exactly the conditon as is present in this case.
Of
course if the manner of fit is changed, then these assumptions may be applied in that case.
The results obtained by
the author in his mathematical work are given here in the
hope that they may be of use to other investigators who
may try the other corresponding fit.
To explain the above paragraph in detail, and to
give the author's interpretation of the results of the
present work, it is essential that the reader should have
136
K Tak•nma and Y. loasokaw~a.
~/
Eye-skapad Ad of Bar imnsigatldby PIhto-cdaloi AdftA.
Kt
139
a general idea of the problem of the connecting rod, and
for that reason, the author would like to discuss the case
in general and then would explain how the results obtained
in this paper are in tune with that discussion.
The dis-
cussion is based on the work of the above mentioned three
scientists.
General Discussion;
The stress distribution and the position of the
stress concentration in the eye section of a connecting rod
depend on many different variables.
For example, if we
change the shape of the eye end, the stress distribution
changes completely.
In this respect, the author would
like to give the results obtained by Mr. Takemura.
The
photographs in Fig. 26 to 29 show how the change in the
shape of the eye ring changes the pattern of the isoclinics
and the stress trajectories completely, so much so that the
position of the singular point* (A in each photograph) also
changes.
According to M1r. Takemurra,
"----
The lines of
the principal stresses in the eye end are generally curved,
buit there is one line which may be taken as straight or
very nearly so (KK' in our photographs).
"For the sake of simplicity, let it be called the
"Principal Lines".
The stress at the cross-section of
these "Principal Lines" with the inner edge of the eye,. was
* These photographs are reproduced from the article by Mr.
Takemura and Yahei Hosokawa. The letters A and KK are introduced by the author.
r,
Abb. i. Spannungsertellung in StangenkOpfen-Bolzei
F~.
ohnt ,litl.
'i7
found to be maximum by means of "the Comparison Test Piece".
Again, let this intersection be called the "Principal Point"
(K' in our photographs).
"The position of this 'principal point' varies
according to the shape of the contours of the eye shaped end.--"
The author of the present paper would like to call
this "Principal Line" as "The Line of the Maximum Stress".
So, according to the results obtained by Mr. Takemura, the
positions of the "Line of Maximum Stress" changes with the
shape of the eye end.
(Photographs in Figs. 26 - 29).
The second main factor that affects the position
of the Line of Maximum Stress is that of the clearance of
the pin fitted inside the eye-hole.
This is clearly seen
from the comparison of the two photographs in Figs. 28 and
29.
(In the first case the pin is loose while in the second
the pin just fits the eye).
Again the same fact is proved from the results
obtained by Dr. Matha% in 1928.
As a matter of fact, in
his article, Dr. Mathat gives in detail the effect of the
clearances on the stresses.
ones.
His results are all experimental
The author of the present paper has reproduced some
of his figures on the next page.
From these three photo-
graphs (Figs. 30 - 32) one sees that in case of a tight fit
(Fig. 30) the stress across the section horizontal to the
centre line of the connecting rod, and passing through the
centre of the eye, does not become zero as it does on the
2
.\hb. Z.
Sparniunigsverteilung in Sttangenkolifen-Bolzen
mit 1,5 mm Spiel.
-4
b
Abb. A.
Spannungenl in Augest•fibe•l.
Sz2.
c
100o
'10
same section in Fig. 31.
From this data the author of the present paper concludes
that
a) The position of the Line of Maximum Stress depends on the
shape of the eye end.
b) It also depends on the clearance of the pin.
c) It is quite possible (though the author has no
conclusive proof for this statement) that this Line of
Maximum Stress may be exactly situated at the point on the
circle from which the loading contact begins.
That is,
say, the angle of contact is represented by the angle
in
Fig. 33, then the section HH (Fig. 33) would give the Line
of Maximum Stress.
The author would like to give the
following proof in support of his statement.
In Fig. 30 obtained by experiments by Dr. Mathar,
the Maximum Stress occurs not at the section AA but at the
section ac.
This is a case of "force fit?
and it is
quite sensible to believe that in this case, the angle of
contact must be more than 1800, and possibly just ending
at the section ac.
Again, in the case of Fig. 34 where Mr. H.Reissner
has calculated the stresses mathematically, one observes
that, the maximum stress concentration occurs at the top
point of the inside edge.
Now in this case Mr. Reissner
has assumed that the load is applied at the topmost point,
(i.e., the mathematical angle of contact is zero).
The
Abb.5.
Spannun
ertoilun
t
Ah.
I PM
stress concentration in this case is maximum at this point
of contact, and is less at any other point on any other
section.
Again, if the reader studies the fringe photograph given in the present paper, he will see that the
angle of contact in this case is also more than 1800.
In
his experiments the author has used a "tight fit" and so
this case too supports the above statement.
All these facts tend to show that the above statement about the position of the "line of Maximum stress"
must be true.
Comparison of J
Experimental Results with Those of the 0the~
If the reader compares the curves obtained in this
experiment with that obtained by Dr. Mathar in his experiment
with an eye bar having a tight fit, (Fig. 30) he will observe
that both the curves are similar, i.e., they go from maximum value at the inside edge to some positive value at the
outside edge, and this positive value at the outside edge is
also very small.
In the results of this paper, the author gets
similar results.
The only difference that is observed is
that, while Dr. Matha94 gets a slight concave curve, the author
of the present paper, gets a slightly convex curve.
If the reader promises not to charge the author
with being too bold, the author would like to state that, as
far as the trend of the curve is concerned, the results ob-
I8oi
I,
.ti~i
,llti~i
iiIi
Abb 7.
Spannungsdlagrammce bel wecchrendcn Iinghr.it.l.
.
i
tained in this paper are more reliable; the reason being that,
while Dr. Mathar must have drawn his curves from the results
obtained just for the three points, the curve given in this
paper, is drawn from many points.
Mathematical Work:-
Coming to the mathematical results obtained in his
work, the author is sorry to state that, as the assumptions
that he had made in his calculations did not agree with the
stress condition that was present during his experimental
test, his mathematical curve is quite different than that
of the experimental work.
Of course the curve obtained from the mathematical
calculations is exactly like what one would expect from these
calculatione.
For example, if the reader compares this
curve with those obtained by Mr. Reissner, he will see that
the curve given in this paper is just as one would expect.
(Fig. 35).
Mr. Reissner has calculated the stresses at the
section AA for a rod having the ratio of ra
ri
=00,
4 and 2.
The author of the present paper has calculated the same curve
for the rod having that ratio = 1.365 (which was the ratio
obtained from the actual connecting rod).
The author from his experience on this problem
thinks that the stress condition that one should assume in
Fig.
36 and not as assumed in these calculations,
case of a connecting rod having "force fit".
is for the
Mr. Reissner
/06
/
/
/r
,'1
./
it
N
K'
\Aff
\
Y
\\
'~
1'~
1¾
- O)und-
~2~
K>
co i. .v
I-.
At lirrside Qd~e Y
4
At ouft51Je ec1a
T=0
Y
0
T~
-rsin6~
10~7
has also treated the problem considering the stress conditions
as shown in Fig. 37.
This case is nearer to the actual
condition of a "force fit" though the existence of shear shown
at the outside boundary is a debatable question.
The curves
in Fig. 35 are those obtained by Mr. Reissner from his mathematical work, the conditions being the same as those assumed
in the mathematical work of this paper.
A Few Words to Future Investigators:To summarize the above discussion, the author
would like to give a few suggestions to the future investigator in a nutshell form.
a) He should not bother about treating the subject by
three dimensional method.
b) He vshould first decide the manner of loading i.e.
whether he wants to keep a clearance or intends to have a
"force fit".
All the calculations depend on these conditions.
c) From the study of his fringe photograph, he should
first figure out the actual angle of contact between the pin
and the rod.
This is very essential because the position of
the Line of Maximum Stress depends on this angle, and also,
this angle is to be used in the assumptions that one has to
make in the mathematical calculations.
d) Having done this, he should select the section at the
point where the contact between the inside edge of the eye
bar and the pin just begins.
(HH in Fig. 33) and then find
out the p+q and p-q curves for this section.
This will give
the maximum stress concentration in the rod.
e) Unlike the author of this paper, he should start his
mathematical work only after finishing his experimental work
completely, and after determining the boundary stress conditbn
from his experiment.
This would enable him to assume the same
conditions at the edges that would be present in his problem
at the time of loading.
f)
If
he takes the case of a tight fit,
the stress con-
ditions at the outside and inside edges would be something
as shown in Fig. 36.
A method of integration for such an
angle of contact must be found out.
g) The different methods of attack given by Mr. Reissner
in his article will be of very much help to the investigator.
H(nust make it a point to study that article thoroughly.
The Suggestions to the Designer of a Connecting Rod
As the reader would agree, it is very hard to give
the concrete suggestions to a designer, from the experience
of the stress distribution of a single connecting rod.
nevertheless,
the author would jot domwn a few points
But,
rhich a
designer might consider and study; and which might be of some
use to him.
a) From the experimental results of Mi. Takemura and
his colleague, and from the results and curves of the experiments performed by the author of the present paper, it is
quite clear that, the radii of the curvatures at the junction
of the eye ring and the stem (I section) must be made as large
as possible.
The study of the p and q curves for the section
BB (Fig. 21) show how the peak occurs very near the edge of
this curve.
Mr.
Takemura suggests that the shape of the eye
should be as shown in Fig. 27.
article).
(which is produced from his
The author of the presentpaper endorses that state-
ment.
b) If one studies the region shown by the dotted lines
in Fig. 9 one sees that this region is not subjected to any
appreciable stress, tension or compression, during the
tension tests.
So it is quite possible that the metal in this
region may be reduced to a considerable extent.
The author
would like to go even so far as to suggest that if a hole is
drilled in this region the stress concentration due to that
hole will not be very appreciable because of the low value of
the original stress.
ting rod.
We may use this removed metal to fill in the cur-
vature at the fillet.
(Fig.
This will reduce the weight of the connec-
This will make the stress curve for BB
21) alnost uniform.
Besides the above advantage, the author of the
present paper thinks that this drilling of the hole would also
make the load on the bearing of the pin uniform, and so natural
would help the design of the bearing.
Of course all of the above suggestions are put forward
only after the study of the stress conditions in the rod during
M/O
the tensile loading, and so the reader is advised to study
the rod under compression before adopting the suggestions.
Even if
one does not agree to drill a hole in the
eye ring as suggested above, he may at least make the groove
which forms the eye section of the stem, such that, it goes
almost near the inner edge of the ring.
This will not produce
any appreciable change in the stress variation in the rod.
(of course only under tension).
This would reduce the metal
and would permit the addition of metal near the fillet.
c) The author has not been able to reason out the curve
for the cross-section of the stem (I section) Fig. 24.
Here,
unlike the expectation, the stress is not uniform, but instead,
the stress curve drooDs down at the edges.
This may possibly be explained from the curve for the
section BB (Fig. 21).
This curve means that the transferance
of the force from the eye ring to the stem may be taking place
in the same manner as the p curve for this section.
So,
naturally, the stresses in the stem will not become uniform
for a long distance.
From the p curve for this section BB one
sees that the stress at the edge of the eye is less than the
peak point (which is .05" from the edge) of the curve.
This
may be the reason why the curve for the stem is drooping at
the edges.
If
the above argument is true then it
follows that
the width of the I section in this case is more than what is
IlI
required for the tension loading.
Besides enlarging the radii
of the fillets, the width of the stem may be reduced gradually
with advantage.
d) Before adopting any of the above suggestions it is
essential that the connecting rod be tested under compression.
The studying of the rod under dynamic conditions
would also enlighten the designers to a considerable eXtennt.
e) The failure that takes place in actual connecting rods
is always at the section HH (Fig. 33).
The author thinks
that this is solely due to the fatigue of the metal at this
section.
It is quite possible that, under compression, the
section HH is subjected to a stress curve which is exactly
opposite to the stress curve under tension.
Due to this the
actual range of the stress for this section would be greater
than that of.the section AA.
This would affect the 'Natural
Elastic Range" of the material.
This problem of cyclic vari-
ation also brings in the factor of time, i.e., the connecting
rods of the high speed engines would be much more liable to
the fatigue failure of this kind than those of the slow speed
engines.
f) The study of the mathematical treatment of Mr. Reissner,
and the experimental work of Dr. MathaA show that the "force
fit"? would bring down the Line of Maximum Stress nearer to
the section HH (Fig. 33) than to the section AA. (Fig. 1).
should be avoided for the reasons given above in (e).
the following deductions follow:
This
Naturally,
/11L
i) The bushing of the bearing metal fitted inside the
eye ring should not be tight.
A stopper to stop the revolving
tendency would permit the bushing to be made of the "sliding
type."
ii) In some engines, the pin is fitted tightly inside
the connecting rod eye while the former is allowed to rock
in the piston bushings.
The above discussion in section (e)
shows that this will bring the Line of Maximum Stress nearer
to the section HH (Fig. 33) and so the practice should be
discontinued.
/i3
BIBLIOGRAPHY
1.
"Das Augenstabproblem und Verwandte Aufgaben" By H. Feisner
"Jahrbuch" Der Wissenschaftlichen Oesellschaft
1928
p. 126- 137
2. Uber die Spannungsverteilung in Stangenkopfen" by I.J.Mathar
Forschungsabbeiten Heft 306. 1928 p. 1 - 12
3. " Eye - shaped End of Bar Investigated by Photo-Elastic
Method " by Kango Takemura and Yahei Hosokawa. Reports of
the Aeronautical Research Institute, Tokyo Imperial University, Vol 11. 1928,
4.
p. 127 - 143
"Stress Analysis is Simplified by New Method" by K.E.Bisshopp
Machine Design, Aug. 1937, p.40
5.
" Computing Eye-Rod Stresses of a Connecting Rod"
by K.E.Bisshopp. Machine Design, Sept. 1939, p. 47-48.
6.
"Theory of Elasticity" by S. Timoshenko, p. 120
7.
"Design of Small End of an Aero-Engine Connecting Rod".
by Angle, Automotive Industries, March 9, 1935, p.34 9"513
8. "Entwicklung Von Triedwerksteihen" by Volk
V.D.I.Ziet, Oct. 22, 1938, p 1233-9
9.
"Theories Und Berechnung der Eisernen Bruechen" by Bleich
p. 256.
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