Upload
koutrgor
View
227
Download
1
Embed Size (px)
Citation preview
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 1/24
I L
L U
S
T
RAT E
D
S
O U
R C E
of ME
C
H A N I
C A L
C MP N E N
T
S
S E C T I O N
12
RETAINING
Comparisons of Retaining Rings Verses Typical Fasteners
12-2
12-4
12-6
12-8
Retaining Rings Aid Assembly, I
Retaining Rings Aid Assembly, II
Coupling Shafts with Retaining Rings
The Versatile Retaining Ring 12-12
The Multiple-Purpose Retaining Ring 12-16
More Work for Round Retaining Rings
12-18
12-20
12-22
12-24
Energy Absorber Squeezes Rings to Cushion Shocks
Defection of Perpendicularly Loaded Split Circular Rings
Improve Design with Retaining Rings
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 2/24
12-2
Comparisons of Retaining Rings
Verses
Typical
Fasteners
A
variety
of
basic applications show how these rings simplify design and cut costs.
Howard Roberts
MACHINED SHOULDERS are replaced
with savings in material, tools and time.
Grooving for ring can be done during a
ut-off, or o ther m achining operation.
WHEN COLLAR AND SETSCREW
are sub-
stituted by ring, risk of screw vibrating loose
is
avoided. Also,
no
damage to shaft
by
screw
point occurs- frequent cause
of
trouble.
RINGS
THAT
CAN REPLACE
cotter pin
and washer are economical since only one
part
is
required and pin-spreading operation
is not needed thus cutting time and costs,
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 3/24
RETA IN COMPONENTSon diecastings with
a simple-to-use grip ring. Slipped over the
end of the shaft, the ring exerts a frictional
hold against axial displacement
of
the shaft.
r---i
Retaining Rings 12-3
7
SHOULDER AND NUT are replaced by two
retaining rings.
A
flat ring replaces th e shoul-
der, while a bowed ring holds the com ponent
on shaf t f or res i l ien t end-p lay take-u p ,
THREADED INTERNAL FASTENERS
are
costly because of expensive internal thread-
ing operation. Simplify by substituting a self-
locking retaining ring-see lower drawing.
COVER-PLATE ASSEMBLY
has been re-
designed (lower drawing) to avoid use of
screws and machined cover-plate. Much thin-
ner wall ca n be used-no drilling or tapping.
w
W
HEAT-FORMED STUD provides a shoulder
against retained parts but must be scrapped
if the parts must be disassembled for serv-
ice. Self-locking ring can be easily removed.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 4/24
12-4
Retaining Rings Aid Assembly,
I
By Functioning as both a shoulder and as a locking device these versatile fasteners
reduce machining and the number and complexity of parts in an assembly.
Robert0 Parmley
Slow-moving piston of hydraulic motor is assembled to the crank throw by
two
retainers. These are held in place by two retaining rings that
fit
into
grooves in the crankthrow
Internal self-locking ring supports a
locator. Elevation of the pin may be
altered in the entry direction only; the
pin won't push down into the frame
TWO ort ring
, ~ - P c housing
Two-piece interlocking retaining ring
serves to hold a two-piece assembly on
a rotating shaft, and is more simple
than a threaded cap, a couple of
capscrews or other means of assembly
Source: American Machinists, June3, 1968 by permissionof Publisher
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 5/24
Free ring
Groove detai l
Roller
Roller axle
Heavy-duty
Two types of rin gs may be used on one assembly. Here permanent-shoulder r ings
provide a unifo rm axle step for each roller, without spotwelding or the like.
Heavy-duty rings keep the rollers in place
Reinforced circular
self- locking
r a p e r e d
-section
self- ocking
Retaining Rings 12-5
Reinforced
E - r ing
Bowed
locktnq-
prong ring
Snug assembly
of
side members to
a casting with cored hole is secured
with two rings: 1-spring-like ring has
high thrust capacity, eliminates springs,
bow washers, etc; 2-reinforced E-ring
acts as a retaining shoulder or head.
Each ring can be dismantled with a
screwdriver
~ ~ i l ~ ~ ~ ~ ~ ~ g
riangular retaining nu t eliminates the
need for tapping mounting holes and
using a large nu t and washer. Secure
mounting of small motors and devices
can be obtained in thi s manner
These three examples show self-locking retaining rings used as adjustable
,stops on suppor t members (pins made to commercial tolerances): A-external
riu g provides positive grip, and arched rim adds strength; B-ring is
adjustable i n both directions, but frict ional resistance is considerable,
and C-triangular ring with dished body and three prongs will resist extreme
thrust. Both A and
C
have one-direction adjustment only
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 6/24
12-6
Retaining Rings
Aid
Assembly, II
Here are eight thought-provoking uses for retaining rings.
R o b e r t
0. Parrnley
Heavy duty ring
\733
Retaining ring
Axial pin for lever is secured with a heavy-
duty ring, making a neat, strong assembly
Free ring Ring af te r assembly
P i n t
Belt alignment is assured by using permanent
shoulder retain ing rings. The rings are crimped
into the sha ft grooves for a permanent, clean,
and inexpensive flange. A retainer ring of
thi s type has a high capacity for thrus t loads
Bdz
Detai l
of
groove
Adjustment:
u p only
Ho
anger
hook
is
held
at desired height by
a self-locking external ring. A multitude of
adjustments can be made without troub le
Retaining rng,
Bal l
Coi
Housing
Sleeve or
valve
ball
seat
A sleeve or ball
seat
valve is safely retained
by a ring that acts like a wedge in the outer
groove. Rigid end-play take -up is provided
Source: American Machinist, Feb. 22, 1971 by permission of publisher.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 7/24
Retaining Rings 12-7
\ .Housing
\
Ring
\ f
Vacuum
released
Interna l self-locking ring supports the plastic ball valve
when the vacuum is released, thus providing a support
during the off cycle. Air or liquid is released when ball
is at rest and exits through the areas between the gr ip
points of the ring, which i s adjustable at entry position
s+em-----.m
Weight
disc,
.Ring
-Rubber stopper
w i t h internal
threaded s l eeve
Drain hole
Triangular retainer nut positions and unifies components of
the tank drain assembly. The triangular nut eliminates the
need for a large standard nut and lockwasher or spring-
type component and simplifies the design
Tamper-proof lock for a shaft in a
housing provides location of the
shaft and a t the same time retains
the key. Heavy axial loading and
permanent retention of the key are
double values in thi s application
Ring hal f \
Observation
lid .
I*
ing half
Observation lid on tubing makes it
possible to inspect wiring at will.
The two-part balanced retainer ring
has identical semicircular halves,
which are held together by the
interlocking prongs at the free ends
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 8/24
12-8
Coupling
Shafts with Retaining
Rings
These simple fasteners can provide an original way around certain design snags.
For example here are eight ways they’re used
to
solve shaft-coupling problems.
Robert 0. Parmley
S l e e v e
Pin,
Sleeve, and Ri ng 1 ,
Pre-assembly position
1
I
A
/ ’
This
inexpensive connection
i s
for light torques and moderate
loads where accurate positioning
i s
not required. A heavy-duty ring
i s used to resist high-impact and
thrust loads.
Sleeve
Key, and Ring
Retaining ring
S h a f i
Crimping the retaining ring into
the groove produces a permanent,
simple, and clean connection.
This
method i s used to avoid machining
shoulders in expensive materials,
and
to
permit use of smaller-diarn-
eter shafts. When the ring i s com-
pressed into a V-shaped groove on
the shaft, the notches permanently
deform into small triangles, caus-
ing a reduction of the inner and
Sie‘eve outer diameters of the ring. Thus,
the fastener tightly grips the
groove, and provides a
360-deg
shoulder around the shaft. Good
torsional strength and high thrust-
load capacity
i s
provided by this
connection.
I
Retaining ring
Crimped afier
assembly
Reprintedwith Permission rom Machine Design, Jan.
19,
1967. A Penton Publication
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 9/24
Retaining Rings
Shaft h a l f
etaining r ing
A
balanced two-part ring provides an attractive appearance in addition to with-
The one-piece ring, b,
tanding high rotational speeds and heavy thrust loads,
a.
secures the shafts in
a
high-torque capacity design.
12-9
This
assembly for heavy-duty service requires minimum machining.
Ring thickness
should be substantial, and extra ring-section height i s desirable.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 10/24
12-10
self-locking ring
ha f t
VA ----_____I14
I I
r
For a connection tha t requires ax ia l shaft adjustment, the self-locking ring requires
An alternate solution, b, uses an inverted-lug ring seated in an internal
The ring i s uniformly
no groove, a.
groove.
concentric with housing and shaft.
Extra ring-section height provides a good shoulder.
Coupler and
Coup1;ng hal f
Retaining
r i ng
Ring groove I Couplings locked to shafts
with s ei screw and k e y s
Where attractive appearance i s desired in a dependable locking device, this
connector and ring can be used.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 11/24
Retaining Rings 12-11
/Tapered threadse t c i n i n g r in g eeve
/
S h a f t
-
f l a t washer for bet ter contad
A slotted sleeve with tapered threads connects shafts which cannot be machined.
Prongs on the retaining ring provide positive shaft gripping to stop collar movement.
The arched rim add s extra strength.
Seam
Coup l i ng
half
An alte rnat e solution for coupling unmachined shafts uses bossed coup ling halves
with locking retaining rings.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 12/24
12- 12
The Versatile Retaining Ring
A
design roundup of some unusual applications
of
retaining rings.
Robert
0
Parrnley
\
RETAINING RING
I
Fig 1
The assembly
of
a hubless gear and
threaded shaft may be accomplished by
using a triangular nut retaining component
which eliminates the need for a large stan-
dard nut and
lock
washer
or
other spring
type part. The dished body of the triangular
nut flattens under torque to lock the gear
to t h e shaft.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 13/24
Retaining Rings 12-13
E v c r y enginecr is famil iar wi th the
uye of ietai ning rings in produ ct as-
scmbly. Applications for this type of
fastening device range from minia-
ture clectronic asscmblics to heavy
cluty eq uipm ent.
In
spite
of
this wide-
spread use, many opportunities for
taking advantage of these versatile
fastening components oftcn arc ovcr-
looked. However, when
a
value en-
ginecring approach is talccn and thc
basic function of retaining rings as
easily assemblccl locating and locking
devices is lccpt clearly in mind it
will
be found tha t
these
simple fasteners
can provide
a
unique solution to dif-
f icult assembly problems.
This roundup of 8 unusual appli-
cations il lustrates how different types
of retaining rings
have
been used to
simplify assembly and reduce manu-
facturing costs . Thc captions under
thc drawings givc the details involved
in each case.
The author wishes to acknowledge
with appreciation the cooperation he
received froin the Tivarc Retaining
Ring5
Division of Waldes Kohinoor,
Inc. in developing these assembly
designs.
Fig 2 This heavy duty hubless gear and
shaft is designed for high torque and end
thrusts. The reta ining ring seated
in
a square
groove and the key In slot provide a tamper-
proof lock. This design is recommended for
permanent assemblies in which th e ri ng may
be subjected to heavy loads from either or
both axial directions An angled groove can
be provided which has one wall cut: at a
40
angle to the sh aft axis. This wil l p ermit
the ring to be removed without damage.
@
S H A F T
IN iAT
URE YIGH-STRENCTH
RETAINING RING
/
/
Fig 3 Two different types of retaining rings
are used in this application involving a leaf
sprin g and shackle assembly. A locking -pro ng
retaining ring is bowed for tension while the
prongs act as fastening elements to secure
the pivot bolt. A fiat or standard external
ring is used as a flange or bolt head.
LEAF
RING
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 14/24
12-14
Fig 4 The self-locking retaining r ings used
in this application provide stops for a float.
The rings are adjustable on he guide rod and
yet the friction force produced by the heavy
spring pressure makes axial displacement
from the light weight hollow float impossible.
FREE
RING
I
Fig
5
Retaining rings provide a uniform ciT-
cular shoulder for small diameter parts such
as the pipe nipple shown
here. In thi s case
the retaining r ing shoulder
s
used as a
stop fo r the plastic tube. The wall thickness
of the n ipple should be at least three times
as thick as the depth of the groove. When
assembling the ring in the groove, the nipple
should be supported by inserting a mandrel
or rod.
SEC. A-A -
R ING
RING
AFTER
ASS'M.
I
\
PERMANENT-SHOULDER RETAIN ING RING
MOISTURE
JAR
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 15/24
CONNECTING ROD
\
/
i
PISTON
PISTON AS5 M.
/
'CONNECTING. ROD
I
F R R;NG -
Retaining Rings
Fig 6 This internal retaining ring is a key part
in
the
assembly of a connecting rod and piston for a hy-
draulic motor. The ring's lu g holes make rapid assembly
and disassembly possible when the proper pliers are
used. The piston assembly in this case is slow moving
and is not subject to heavy cycle loading.
Fig 7 Internal self-locking rings can act as a su pport
carrier when the
I.D.
of a sleeve or housing cylinder
is too larg e to center and stabilize small rods or con-
duit. The rings are adjustable in the entry direction
only, however, and a sufficie nt nu mber should be used
to secure the rod.
l
I
I
ADJUSTMENT'
DIRECT I 0 N
CYCLINDER
12-15
A
INTERNAL
SELF-LOCKING
RETAINING RING
Fig
8
The heavy duty external reta ining rin g shown
here controls the elevation or position of a support
post in a holding clamp. This type of ring
is
ideal for
heavy duty applications where extreme loading condi-
tions are encountered. By adding washers under the
ring the elevation of th e support post can be adjusted
as required.
NL
ARG
EME
T
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 16/24
12-16
The
Multiple-Purpose
Retaining Ring
A
roundup
of
ten unusual ways for putting retaining rings to work in assembly jobs.
Robert
0
Parmley
7
Standard e x t e r na I. y p e
ring
serves as adjustable stop or
shoulder for positioning sleeve
members on post or shaft.
T h e
post i tsel f is locked to t he base
by a retaining ring.
Adjustment
Platform
Radius Arm
Hub
Retaining
Ring
1
Special iugless
ring
of external
type is used
to
offset center.
l ine of shaft which i s station-
ary or roteting slowly in hub or
journal.
Shaft Centerline
4
Retaining Rine
-
F l a t Washer
Tape
Coil S
Movable Head
Sel f- lock ing e x t e r na l ring i 5
used with flat washer to pro.
vide adjustable shoulder for
control of spring action.
Supported Plate Load
\ L
etaining Ring
Retair
Heavy duty self-locking ring
acts as adjustable stop on pin
used as support me mber for
plate section.
Excerpted from Assembly Engineering, July, 1966 by permission of Publisher 0 1966. Hitchcock Publishing
Co.
All rights reserved
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 17/24
Retaining Rings
12-17
Retaining Ring
Panel Section
Contact
h n t
Retaining R I ~ E
Bowed ring with locking prcngs
act: as fast ening element and
sprin g fcr clectrical pu;h but -
tcn.
Retaining Ring
5
Self-locking external rin g con.
trols position
of
eye rod
in
an
adjustab le ca b l e h an ge r ar.
rangement.
Retaining Ring
Clamp
t
S t a n d a r d externabtype ring;
with holes in
lugs
for plier as-
sembly prov ide a pr ac t i c a l
hanger or supp ort. for hose,
rods,
and
wires.
Ring
Work Piece
Retaining Ring
Retaining Ring
Retaining Ring Retaining Ring Retaining Ring
(seat
in
housing groove)
G
‘_ _otating ShaH
9 10
In ter lock ing extern a
I r i n g
serves as a loc king element for
a coupling that joins glass tub-
in g sections.
Interlocking external
ring
locks
two.piece h o u s i n g t h a t f i t s
around a rota ting shaft.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 18/24
12- 18
More
Work for Round
Retaining Rings
Try
this
low-cost fastener for locking shafts and other parts. It will also
work as a shaft step for bearings and an actuating ring for switches.
Dominic J. Lalera
Conical wedge
Spring- fingered cage,
\
Unfocked
position
\Locked position
Piston
Rod\ r
ing
PISTON tS LOCKED in place on the rod
when drawn into place by means of
B
setscrew.
To
remove, slide the piston
aw ay f ro m the ring, then remove the ring,
LOCK A SHAFT by forcing
a
retaining
ring ov er the groove in the shaft. In
luck-
ing position, the springfingered cage
is
actuated by the conical wedge.
THIS SHAFT
STEP
for
a
rotating
bear-
ing i s quickly and simpla made hp groov-
ing the shaft t o acccpt
B
spring ring.
Countcrbore the shaft step to mare.
FLANGE ASSEMBLY
is
permanentlj
fastened by threading the n i r e into the
mating grooves through the Hangc. 1 h 1 g c
can rotate if wire doesn't protrude.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 19/24
Retaining Rings 12-19
ASSEMBLE CYLINDER HEADS
and
siniilar parts to thin walls by means of
a
retaining ring and a locking block. 'i'ight-
ening the screws expands the ring.
THIS
SPRING-HELD shaft lock is a
basic application for retaining rings. Th e
best groove dimensions for round spring
rings are readily available from suppliers.
wifch
mounfing-bar
Male fhreaded
wedqe
\fnlemal
wedge\
THREE-P1ECE WEDGE lets the
shaft
i n n ~ e reelj unt i l the wedge i c lighfen d
by wrewing it
in.
I he round
rclnirring
ridg is
then forced into the groove.
SWITCH ACTUATORS of rnund refain-
ing rings offer
a simple solution
when
lmnianent sliaft steps
would
pr e m i t
assenibly problenls. Close the ring
gap.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 20/24
12-20
Energy Absorber Squeezes Rings
to Cushion Shocks
A
novel shock absorber based on an easily demonstrated but li ttle-known
principle handles strains up to
1,000,OO Ib.
and performs through
100
cycles.
ake a metal clothes hanger and
T ull it apart until it breaks (as-
suming you have the super strength
needed for this feat). The hanger
elongates slightly until it fractures
and thus absorbs energy; the amo unt
of energy absorbed is a function of
the Eorce exerted and the amount of
stretch.
Now, take another hanger and
flex it back and forth. During each
flex, the metal deforms slightly; it
fatigues and eventually breaks.
Although the am ount of force ap-
plied at any one time during flexing
is not much, the total amount of en-
ergy absorbed far exceeds that ab-
sorbed when the hanger is ruptured
by a pure tensile force.
Principle rediscovered. This lit-
tle-known principle in energy ab-
sorption has been applied success-
fully and with dram atic results to the
development of a new shock ab-
sorber by Mechanics Research, Inc.
(MRI), El Segundo, Calif.
In a recent demonstration (left),
MRI sandwiched two soda crackers
between weights, each in its own
test fixture, and dropped them si-
multaneously. Baseballs on top of
each carriage provided added crack-
er load.
The left carriage struck a plain
rigid rod. The cracker, smashed un-
der im pact, was sprayed in all direc-
tions. The baseball rebounded,
springing into th e air.
The right carriage, however,
struck a novel shock absorber that
s effectively absorbs the impact en-
ergy that the carriage comes to a
smooth stop. The cracker remained
intact with narv a crumble. and the
baseball did
io t
rebound.’
Trapped
rings. The new absorb-
ers trap rolling rings (or sometimes
tube segments) between concentric
tubes under enough interference to
strain the metal in the rings beyond
its yield point. The interference
fit
may be
only
a few thousandths of a n
An internal wire ring aligns the
small rolling rings at each station.
Increasing either the ring wall thick-
ness or the interference increases
the energy absorber force. The unit
can be designed as either a otary
or
linear absorber.
The absorber cannot reset by it-
self. It needs springs to do
so.
But
it
Working ring
elements
Retainer
r ing
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 21/24
Retaining Rings 12-2
1
Unidirectional Cyclic straining
to
failure to failure
strain range
-
c straining with
5
cycles
Plastic
Cyclic straining
Cyclic plastic straining absorbs more energy than unidirectional straining.
1
OFHC
Copper annealed
.- Nickel
A
annealed
0.1 1
10
100
1000 10,00
Cycles
t o failure
The
amount of plastic strain determines the number of cycles to failure.
24
ST
Aluminum,
347
Stainless steel
1
Cycles
to
failure
The number of cycles to failure influences total amount of energy absorption.
can be recycled if required and thu s
fills a need between one-shot sys-
tems, such as crushable honeycombs
and frangible tubes, an d the infinitely
reusable devices, such as hydraulic
shock absorbers.
Heavyweight capacity.
The ab-
sorbers can handle forces ranging
from 0.01 Ib. to
1,000,000
Ib., with
possible application in automotive
safety, spacecraft landers, aircraft
seats, and protection from blasts an d
earthquakes.
All-metal construction avoids the
undesirable features of fluids, seals,
and elastomers and permits long use
in difficult temperature and corro-
sion environments. Moreover, the
load-stroke behavior is relatively in-
sensitive to the effects of temp eratur e
and rate.
Cyclic strains. The underlying
principle is the cyclic straining
of
metal in the plastic range. This pro-
duces a hysteresis loop (left, top
drawing) that stabilizes after a
few
cycles. Repeated cycling results in
almost constant energy absorption
per cycle there is eventually fatigue
failure.
The specific energy absorption
(SEA) for
N
cycles to failure is
about N times the SE A for the o ne-
shot unidirectional straining to fail-
ure (middle, top drawing). Thus, a n
absorber designed to last, say, five
cycles to failure (right, top draw ing)
will be able to absorb
5
times
(roughly 2.24) the SEA for a uni-
directional straining.
Fo r example: Suppose the device
must handle 1000 cycles (strain cy-
cles) before failure. To do
so the
interference fit should cause a plas-
tic strain range
of
1.3
(0.013
in./
in., left middle chart) to obtain
maximum energy absorption of the
device.
The amount of SEA for
1000
cy-
cles is abou t
800,000
ft.-lb./lb. (bot-
tom ch art) . With a factor
of
one-half
to account for the n onuniform strain-
ing in the rings (th.e curv e is for
uniform straining), the average SEA
would be 4 00,00 0 ft.-lb./lb.
Thus, if the rolling rings in the
absorber add up t o 1 lb., they will ab-
sorb the energy
of
a 4000-lb. force
traveling through a foot of stroke
100
times.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 22/24
12-22
Deflections of Perpendicularly
Loaded Split Circular Rings
M. M.
Lerncoe
FORMULAS FOR THE D E F L E C T I O N Of a Split uniform CirCu-
lar ring perpendicular to the plane of the r ing are given
for various positions of the load. Meth ods
of
developing
those formulas are demonstrated.
In Fig. 1
is
shown a split uniform circular ring of radius
R, loaded with a force P applied perpendicular to the plane
of the ring at the point B. At the po in t Q, the bending
moment
M
and the twisting moment T due to the load
P are respectively:
111
=
P
R
sin
p
-
0 )
(1)
T = P R [ l OS p
e) j (2)
Also, if there were a unit load at the point A, there
would be at point Q a bending moment m and a twisting
moment t du e to that unit load. These are given by the
following formula
nz =
R
sin a - )
t =
R
11- os
a-
e)]
3 )
(4)
From strain energy considerations, the deflection A
of
the point
A
can be formulated. If E is the modulus
of
elasticity and G is the shear modulus and if I is the moment
of inertia about the neutral axis of a cross-section, and
Fig. 1-Split circular ring loaded
by
a force
perpendicular to the
ring
at point B. The
deflection A at point A is
to
be catculated.
is the polar moment of inertia of a cross-section, the
formula is
A=j;:de j@
______
t R d 0
5)
Sub-
0 C J
Th e an g le
4
equals the smaller of angles a
or 8.
stituting
Eqs
I), 2 ) ,
( 3 )
and 4 ) in to
Eq
5 ) gives:
[I
-
OS a
-
]
[ l
-
OS
I
G
J p
-
]
From the trigonometric identities
sin a
-
e) sin
p
-
e =
4 cos a - B )
-
os
a
+ p
-
e)l
cos a e)
cos
p - = [COS a 8 ) + cos a+ 8 - e)l
The formula for A becomes:
1
s:
cos
a+
6
-
8 ) d
0
+
[1' os
a
- e)
d
B
2 G . I
0
-
/:
os a+ e) d 0
-
Integrating
Eq
6 ) gives
P
R3
E l
+ c o s a- 8 )
2
= -
[
1
in a
+ 8 -
4)
-
in a-
8)
4
I
P
R3
6 os a- )
-[ I
2
sin a+ 8 - 4) - in a
+
8)
4
-
+
4
+
in
( K
- 4) - in a
+ in 8 -
)
- in
8
(7)
From Eq
( 7 ) formulas can be developed for h for
Formulas for various positions
of
points A and B are
1
various positions of points A and B.
given below.
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 23/24
Retaining Rings 12-23
A
= Deflection at Point
A
P
=
Load at Point B
R
= Radius of Ring
= Modulus of Elasticity
G
= Shear Modulus
J = Cross-Section Polar Moment
of
Inertia
I = Cross-Section Polar Moment of Inertia About Neutral Axis
A
A-- R3 ( +g)
2
A 0
8/11/2019 86174_12
http://slidepdf.com/reader/full/8617412 24/24
12-24
Improve Design
with
Retaining Rings
Waldes
Kohinoor
supplied the retaining
ri n s
for the assembly illustrated here.
Look
at the old
design,
look at the new design. What did retaining
rings
do? Well, by changing
the design to ret*
rings
these advantages are achieved:
1)
Six beveled r i n g w n e at each end of the three shaft bores-replace
24
hex-head bolts and eliminate drilling and tapping
24
holes in the cast housing.
2
Special gaskets’ needed to provide a proper seal between the end cap and
housing have been replaced by less expensive standard O-rings. Six facing o pera-
tions
on
the outside
of
the casting, required for the gasket seals, have been elimi-
nated. (O-ring grooves are an integral part of the redesigned cover plates.)
3) Twelve external ring s-& bowed, six flat-secure the h e r races of the
bearings
The rings are assembled
in
grooves machined simultaneously with the
sha ft cut-off and chamfering operations. They replace six threaded ring
nuts
and
six
lock washers and eliminate
12
ground diameters, six threading operations and
six
keyways
on
the
shaft.
4) Six basic internal rings, installed in grooves machined
in
the housing, elimi-
nate
six
machined shoulders and the need f or holding close axial tolerances
on
the
bearing bore and end cap.
Reusable following disassembly, the rings are assembled with special pliers,
and can be removed for field service.
0 LO
DESIGN
Lack
washer
i n
keywoy
NEW
DESIGN