Purdue University
Purdue e-Pubs
International Compressor Engineering Conference
School of Mechanical Engineering
1992
Calculation of Optimal Value of Taper for the Drive
Pin of the Scroll Compressor Crankshaft
D. Boyle
Copeland Corporation
Follow this and additional works at: http://docs.lib.purdue.edu/icec
Boyle, D., "Calculation of Optimal Value of Taper for the Drive Pin of the Scroll Compressor Crankshaft" (1992). International
Compressor Engineering Conference. Paper 901.
http://docs.lib.purdue.edu/icec/901
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Herrick/Events/orderlit.html
CM.COU TIOII OP Ol'Tl:KAL VALUE OJ'
TAPIR FOR TRB DR:EVI Prll OP TBB SCROLL
COMPRESSOR CblO:SH UT•
by
D. Boyle, Copelan d Co~oration
sidney, ohio
The followi ng paper calcula tes the optima l value of
cranks haft drive pin of the scroll compre ssor such taper for a
that under
severa l load conditi ons encoun tering an edge-lo
situati on is
minimi zed. Load distrib utions and forces are aded
calcula
ted using
finite elemen t analys is softwa re and the
are used with
some mathem atical analys is to arrive at results
an optima l value of
taper.
:IJITRODUCTJ:Oll
Unlike piston -type compre ssors which by compar ison
to scroll
compre ssors are well-u ndersto od, there are many invest
igative
analyse s that need to be perform ed to design scroll
compre
ssors.
In particu lar, finite element analys is is one option
that
used with much success . In the presen t instanc e, finite can be
is used to model a nonline ar drive pin contac t problem elemen t
.
Below
the problem is stated, the finite elemen t model
is outline d and
result s are discus sed. Finally the taper calcul
ation is performed and a conclus ion reached .
PROBLEM
In the presen t case with referen ce to Figure 1 under
maximum load
conditi ons, there is visible wear on the sleeve
and drive
pin.
It is postu:j. ated that the ·situat ion canbearing
be relieve d by
.taperin g the pin a certain amount, so that in the deflect
the resulti ng deform ation would be more favorab le and ed state
avoid the
edge-lo aded situati on already describ ed.
purpos e of the
presen t study is to more fully unders tand theThe
distrib ution phenom ena and then to calcula te an optimaloading
l value of taper
which will eradica te the.edg e loading and wear problem
s.
J':IID:TI!I ELBJdJIT MODEL
The problem may be viewed simpli sticall y
in·Figu re 2, that is
as two cantile vers opposin g one anothe r, as
in which the lower one
has a linear taper. Figure 3 shows the model
in more detail .
The comple te crank shaft has been modeled
the hub is modeled
as a cantile ver with a rolling suppor t in and
the Y directi on. Gap
elemen ts exist betwe~n the hub and drive
which are modeled
with beam-co lumn finite elemen ts [1). Thepin
moment of inertia of
the crank shaft and drive pin are compli cated
the fact that
there is an oil feed hole, linear ly displac ed by
the center
line in order to facilit ate centrifug~l pumping offrom
oil. This
passage way must be accoun ted for, especi ally· in the
the pin. The
force exerted on the pin is applied as shown in Figure
3. This
represe nts the maximum force require d to compre ss the
refrige rant
gas during a cycle.
*Repro duced by permis sion of swanso n Analys is System
s, Inc.,
Houston , Pennsy lvania
1069
RBSOL'l'S OJ' 'l'BJ!l PIIT.I'l'E ELEMENT MODEL
Using Ansys finite element software, the model has been run for
five values of taper, (.005, .001, .00125, .002} where the dimensions are in inches. For each value of taper there are five load
conditions, (300, 700, 1000, 1300 and 1700) where the dimensions
In particular 1000 and 1700 pounds represent
are in pounds.
important maximum load conditions, during which survivability is
an issue. Having run these load cases for all values of taper,
the results are displayed in Figures 4 through a.
Observing Figure 4, it is seen that for .0005 inches of taper,
edge loading always occurs. The situation would be worse for no
taper and agrees with observation of worn parts. At the other end
of the spectrum for .002 inches of taper it is observed that edge
loading occurs not now in the inner edge of the pin but always at
its exterior end, as illustrated in Figure 7, especially for
lower loads of 300 and 700 pounds. An observation o'f Figures 5
and 6 shows.loadings which are between these two extremes.
Figure 8 also shows the moment at the pin/shaft interface for
various loadings and tapers. It is not possible to choose any
arbitrarily large value of taper to eradicate the edge loading
problem, because the resulting high moments will cause the shaft
to become deformed and that will effect 'bearing performance. As
.would be expected the bending moment increases. with increasing
taper. Also large moments increase the likelihood of a fatigue
crack at the fillet where the pin joins the shaft.
Therefore from observation of the data, and an understanding of
the effect of taper on both edge loading and moment, the problem
then is to calculate an optimal value of taper. This 'is done.in
the next section.
CALCOU'l'IOII OF 'l'BJ!l OPriJml. VALUE OP TAPIR
It is necessary to quantify the types 'of loading in terms ?f
their desirability. Clearly it is necessary to avoid an· edge
loaded situation, where the loading is weighted to one side or
the other as indicated in Figures 4 and 7. A convenient measure
or indication of an edge loaded situation is calculated by using
standard deviation. such a value is always positive. Also low
values of standard deviation indicate progressively less onesided pressures. A standard deviation of zero could only be
achieved in fact, if the pressure was absolutely uniform across
One of our objectives then is to search for s•all
the pin.
values of the standard deviation of the gap forces obtained from
the finite element analysis. ·
Similarly it is decided to use the moment at the pin/shaft interface as another criteria for the reasons discussed above. The
loads of 1000 lbs. and 1700 lbs. are chosen for the calculation
as they are the predominant maximum load conditions and are
larger than the ·force of 300 lbs. whieh the pin would have to
withstand under normal running_ conditions.
1070
There fore for each value of taper there
tain, the standa rd devia tions of 1000 lbs,are four value s to oband 1700 lbs. and the
momen ts at the pin/s haft interf ace for
there are five value s of taper, then foureaeh of these loads . As
vecto rs are formed :
al ...
a2
~:r~!P~
56.052
88.628 8
~~:tH~l
100.90
78.31
1
~~~
944
i
M1
M2
(2)
546
634
88
~4]
(3)
66
(4)
60
al and a2
lbs. and
1000 lbs.
ize these
(1)
are the standa rd devia tions of the gap
1700 lbs. respe ctivel y. Ml and M2 are forces for 1000
and 1700 lbs. respe ctivel y, It is neces the momen t for
sary to norma lvecto rs, to give each the same impor tance.
a1
a1 ""
VlT
a2
Tm
Ml
M2 .,
(5)
a2
{6)
Hl
TM1T
(7)
H2
lM2T
(8)
The first row in each of these vecto rs
repres ents a value of the
quant ities conce rned for a certa in value
of taper ,
Looki ng at
the second row, there is anoth er combi
nation of the four varia bles for a new value of taper.
These four variab les repres ent a
four dimen sional space . We could theor
etica lly find infin itely
many point s that would be joined by a
smoot h curve , As we vary
the value of taper we trave rse this four
space along the curve .
For a certai n value of taper we will be
at any other point on an interp olate d close r to the origin than
curve conne cting these
point s.
This will repre sent small
quant ities conce rned, which is what we o; minim al value s of the
are trying to achiev e.
A
usefu l way to calcu late this minim al
distan ce from the origin to these points point is to measu re the
and
to
then
plot
this as
a functi on of taper. With this new graph
it is possib le to find
the minimu m.
1071
Calculate a new vector representing the distance from the origin
to each of the five points held in the vectors above.
(9)
At this point we have five points in the X-Y plane and a quartic
can be fit through them. It is required to determine the coefficients a, b, c, d, and e from equation 10.
f(x) - a x 4 + b xJ + c x2 + d x + e
(10)
Taking each point of the 6 vector in equation 9, with its corresponding value of taper we substitute into equation 10, and solve
the resulting set of five equations in five unknowns. This is
illustrated in equation 11.
-1
rn r
.ooo~ 2
.001
.0012~ 2
.001~
.002
.0005
.001
.00125
.0015
.002
•
&
(11)
Figure 9 shows a plot of equation 10, with the values calculated
in equation. 11. Also shown is the derivative which intersects
the Y axis at .0011 inches. This is the value of taper which is
chosen to minimize the variables discussed above.
COBCLUB:IOB
A finite element model has been developed which shows agreement
with the observed wear on the drive pin and journal bearing of
the orbiting scroll hub. By inspection of the graphs of the·gap
forces between the pin and the hub a qreater~nderstanding of the
role and magnitude of taper is obtained. The graphs suggest that
some value of taper·should be employed between .0005 and .002
inches. The optimal value of taper for this geometry is calculated. to be .0011 inches. The calculated value of taper has been
found to be similar to the experimentally determined taper.
Further studies of taper design could include oil film effects
and a more accurate hub deflection by including the flexibility
of the scroll base plate.
There is a practical limit to the amount of taper that can be
utilized. Taper helps to compensate for the drive pin.and scroll
hub flexibilities and large forces involved, however there is a
practical limit to how much taper can rectify the situation. For
too large a value of force or too flexible a drive pin, it would
be necessary to use a very large value of taper. The result of
this would mean that during normal running at lower loads·higher
bending moments would occur at the pin fillet which might cause
the origination of fatigue cracks. :It is important to take the
appropriate steps using finite element analysis and experimental
methods to investigate the fatigue strength in this area.
UI'!RDICU
1.
Ansys User Manual, Rev. 4.4, 1989.
1072
ORBITING
SCROLL
FIGURE 1 EXPLODED DRAWING OF RUNNING
GEAR ASSEMBLY
~
_ _ _ _ _ _ _ _ tape~
Hub of Q1oJIJng Scroll
Ec~Pfn
FIGURE 2 SIMPLISTIC REPRESENTATION OF PROB
LEM
1073
UG of L.w.. s-Ing
Gap element
..1.
SCRCU. CRANK SHAFT
Force
HUB CF ORBmNG SCROLL '
iii
I..1...1...1...1...1...1...1...1...1...1...1...1...1.
RCXLING SUPPORT BOUNDARY CONDmON
.
TTT TTT TTT
ECCENTRIC PIN
FIGURE 3 CLOSE-UP OF DRIVE-PIN
-300 I
1300._I
I 1000
100 .......
........I _....,.
.......
CD
....J
I
Cl)
u
~
0
LL..
a.
c
I
~..,_...,
l
1,000
(/)
1100·
.,
i
~~ I
\\ I
600
\\
i
i
800
400
\\
'\\\
.....\~\ l
··.. \;\~~
(!)
200
0
•
0
I
I
I
!i II
Ii
I
I!
I
I
~~
.2
1
:
l
I
,..:~":
.1
i
.3
.4
.5
.6
.7
.8
.9
1.0
Length along Ecc entr ic Pin - Inches
ES OF TAPER
FIGURE 4 FORCES ON PIN FOR .0005 INCH
1074
-- ...
300 11 700 11 1000 11 1300 11 1100 11
_......._..
.........
·-··········
1,000
'I
(/)
lil
....J
CD
u
~
0
LL...
a.
800
I
I
I
~\
600
\
I
l
0
200
........ ·-··:. I~--- -·--,...._
0
.1
-
-+-~
\~
... 'r.... I
··... '~
····:"!':.
0
I
I
I
\
400
0
_._
I
.2
-.3
.
.5 - .6
.4
~
I
,....~
.7
.8
.9
Length along Eccent ric Pin - Inches
1.0
FIGURE 5 FORCES ON PIN FOR .001 INCHES OF TAPER
.....
~ 700__~...........
1000 -H
G>
u
~
0
LL...
a.
600
I
Ij
I
0
(!)
200
0
'
I I I
: I
i
I
l l1
I
i
~-~
....
..
······
.......
~
I .
0
.1
~·
!
.2
..
~
~<o-·
.3
r
I
I
I
I
I
..··"'
I
j
I I
~:,.,;
i
I
!
I
!".
I .,
I
.I
j
i
I
400
.!Z£~-
!
I
:I
r
(/)
BOO
.l
13~0
'
1,000
ro
_J
-
I
I
~-
.4
I
.5
.6
I
/.
~
.lr
.7
v
.8
.9
1.0
Length along Eccent ric Pin - Inches
FIGURE 6 FORCES ON PIN FOR .0015 INCHES OF TAPER
1075
300
1100 11
11 .........
II 700 11 1000 11 -1300
.........
- -
. _ _ .........
(/)
(D
•••<~•••••••·•
1,000
_J
BOO
1::
.~
.....
600
:9
.....I..rn
400
~
0
/
"'0
0
0
200
_J
0
-.
;'_ ,.
a
J
:.-.....
,. ,.
.2
.1
~ ...,_,
..... ·····
.. -·....
·..3
.s
.4
~·
.6 ·
.7
.a
If
.9
1.0
Length along Eccentric Pin - Inches
FIGURE 7 FORCES ON PIN FOR .0021NCHES OF TAPER
1,000
r-r-----r------r----.,..-----~
VI
"'0
c
~·
0
---...
.
.
;
.
.
.
.
.
___
v----.. ...........
/
800
Q._
I
..c.
u
.........-··
600
.
c
400
.+J
1::
~
E
0
:::2:
~--
~•••••••• ~······
.........
~
........~~··· ...............................
............
.... _,. ....
~~~~~
...........................
~ ~ ~
_..
... . .
.. - - -
200H- --=---= r--=--- --+---- --t---- H
1--'---
~
a~-----~-----~-----._---1700
JOO
1300
. 1000
700
FIVE SPECIFIC LOAD CONDITIONS - LBS
FIGURE 8 MOMENT AT PIN/SHAFT INTERFACE
1076
1.6~----~------~------~----~-------,r
1.55
---T---~----r---T---
1
1.5
~
1.45
...J
~
I
- - - T - - - -, - - - -
1
I
------ ---I
1.4
z
~ 1.35
<
N
~
i=
1.3
~ 1.25
1.2
1.15
1.1
+---~~--r-.--r~-.--+-.-~-+--~~4
0.0005
0.0008
0.0011
0.0014
TAPER -INCH
0.0017
0.002
FIGURE 9 GRAPH OF EQUATION 10 AND ITS DERIVATIVE.
1077