Keys & Splines

Suez Canal University Faculty of engineering – Port-Said Production Engineering and mechanical Design Department

Keys and Keyways Keyways Prepared By Dr. Eng. Mohammed A. Soliman Associate Prof. Of Machine Design And Tribology

Fundamental Problem in Shaft Design How do I connect stuff to the shaft? Interference Fits

Keys & Keyseats

Integral Shaft

Pins

Hubs/Collars

Splines/Polygons

Interference Fits Interference Fits± s +ROHLVXQGHUVL]HGDQGSDUWLVKHDWHGWR DOORZLWWRVOLGHRYHUVKDIW&RPSUHVVLYHLQWHUIDFHSUHVVXUH GHYHORSVZKHQSDUWFRROVR eference Lecture 15 N otes

K eys and K eyseats

K eyseat .H\VDUHXVHGWRWUDQVPLWWRUTXH IURPDFRPSRQHQWWRWKHVKDIW

M ott,Figure 11-1

Types ofK eyseats

K eyseats are classified according to the process by w hich they are m ade. O livo,Fig.40-3

K eyw ay Fabrication M ethods

End M illon V ertical M illing M achine

K ey C utter on H orizontal M illing M achine C hang,Fig.5.8,M ott,Fig.12-6

FilletR adiiand K ey C ham fers

45o cham fer

N otto Scale

Better Practice

G eneralPractice:Zero rootfilletand cham fer

Standard contains recom m ended fillet radiiand key cham fer com binationsto provide low er stress concentration factors.

“K eys and K eyseats,” A N SI Standard B17.1-1967 1967

FilletR adiiFabrication 5

$µ%XOO¶HQGPLOOFDQEHXVHGWR PDFKLQHILOOHWUDGLLLQNH\ZD\V

%XOO(QG0LOO M SC C atalog,Fanfara,Figure 3-6

Square and R ectangular ParallelK eys

7KHKXELVVOLJKWO\ODUJHUWKDQWKHVKDIWDQGNH\WRDOORZLWWR VOLGHRYHUWKHVKDIWGXULQJDVVHPEO\7KHVHWVFUHZLVXVHGWR WDNHXSWKHVODFN7KHUHVXOWLQJIULFWLRQLVXVHGWRSURYLGH UHVLVWDQFHWRD[LDOPRWLRQ7KUHDGDGKHVLYHPD\EHUHTXLUHGWR HQVXUHWKDWYLEUDWLRQGRHVQ¶WFDXVHWKHVHWVFUHZWRORRVHQ M ott,Figure 11-1

Square and R ectangular K ey G eom etry “K eys and K eyseats,” A N SI Standard B17.1-1967 1967 :LGWKLVDSSUR[LPDWHO\ó WKHGLDPHWHURIWKHVKDIW 6WDQGDUGFRQWDLQVWDEOHVRI UHFRPPHQGHGNH\VL]HVYHUVXV VKDIWGLDPHWHU

SetScrew s

FlatPoint

O valPoint

C up Point

C one Point

H olding Pow er± er 5HVLVWDQFHWRD[LDORU URWDU\PRWLRQRIWKHKXERU FROODUUHODWLYHWRWKHVKDIW +ROGLQJSRZHULVD IXQFWLRQRIIULFWLRQ EHWZHHQFRQWDFWLQJ SRUWLRQVRIKXERUFROODU DQGVKDIWDQGDQ\ SHQHWUDWLRQRIWKHVHWVFUHZ LQWRWKHNH\ZD\RUVKDIW

H alf-dog Point Shigley,Fig.8-26

R epresentative H olding Pow er V alues %DVHGRQDOOR\VWHHOVFUHZ DJDLQVWVWHHOVKDIWFODVV $FRDUVHRUILQHWKUHDGV LQFODVV%KROHVDQGFXS SRLQWVRFNHWVHWVFUHZV

Shigley,Table 8-13

Tapered K eys

'HVLJQHGWREHLQVHUWHGIURPWKHHQGRIWKHVKDIWDIWHUWKHKXE LVLQSRVLWLRQ7KHWDSHUZLOOLPSDUWDFRPSUHVVLYHFRQWDFW SUHVVXUHEHWZHHQWKHKXEDQGWKHVKDIW)ULFWLRQZLOOKHOS WUDQVPLWWRUTXHDQGSURYLGHUHVLVWDQFHWRD[LDOPRWLRQRIWKH KXEUHODWLYHWRWKHVKDIW7DSHUHGNH\VGRQRWUHTXLUHVHW VFUHZV$FFHVVWRERWKHQGVRIWDSHUHGNH\VDUHUHTXLUHGVR WKDWWKHNH\FDQEHLQVHUWHGDQGGULYHQRXWZKHQWKHNH\LV EHLQJUHPRYHG M ott,Figure 11-3

G ib H ead K eys

,QVWDOODWLRQLVVLPLODUWRVWDQGDUGWDSHUHGNH\V 7KHH[WHQGHGKHDGSURYLGHVDKROGLQJPHWKRGIRU UHPRYLQJWKHNH\E\SXOOLQJLQVWHDGRIGULYLQJLW RXW

M ott,Figure 11-3,Shigley,Fig.8-28

W oodruffK eys

&LUFXODUJURRYHLQVKDIWKROGVWKHNH\LQSODFHZKLOHWKHKXE LVVOLGRYHUWKHVKDIW7KH:RRGUXIINH\ZLOOKDYHOHVVVKHDU VWUHQJWKWKDQDUHFWDQJXODURUVTXDUHNH\ A N SI Standard B17.2-1967 lists recom m ended dim ensions for W oodruffK eys. M ott,Figure 11-3

C ircular (Pin)K eys

6LJQLILFDQWO\ORZHUVWUHVVFRQFHQWUDWLRQIDFWRUVUHVXOWIURP WKLVW\SHRINH\DVFRPSDUHGWRSDUDOOHORUWDSHUHGNH\V$ EDOOHQGPLOOFDQEHXVHGWRPDNHWKHFLUFXODUNH\VHDW

Fanfara,Figure 3-6,M ott,Figure 11-3

Tapered Bushings 7DSHUHGKXEFDXVHVVSOLWEXVKLQJWREHGUDZQGRZQRQ VKDIW+LJKHUVWUHQJWKDOWHUQDWLYHWRVHWVFUHZV

.H\LVXVHGWRWUDQVPLWWRUTXH IULFWLRQNHHSVV\VWHPIURP VOLGLQJD[LDOO\DORQJVKDIW

M ott,Fig.11-10,w w w .em erson-ept.com

Stress A nalysis of ParallelK eys $NH\KDVWZRIDLOXUHPHFKDQLVPV LWFDQEH VKHDUHGRIIDQG LWFDQEHFUXVKHGGXHWRWKH FRPSUHVVLYHEHDULQJIRUFHV Bearing Surface Shear Plane ) )

7

Shear Stress A nalysis ofSquare and R ectangular ParallelK eys )=

7 ' 

$ V = :/ IJ DYH =

7 ) = ' (:/ ) $V 

IJ DYH =

7 ':/

( )

M ott,Fig.11-4(b)

R equired K ey Length (Shear) )URP0D[LPXP6KHDU 6WUHVV)DLOXUH7KHRU\ WKHVKHDU\LHOGVWUHQJWK LVJLYHQE\

7KHPLQLPXPOHQJWKRIWKH NH\FDQEHIRXQGE\VHWWLQJ WKHDYHUDJHVKHDUVWUHVVHTXDO WRWKHDOORZDEOHVKHDUVWUHVV

6\V = 6\W

IJ DYH IJ DOO =

6\W 1 VI

6 \W 7 = = ':/ 1 IV

71 IV /V = 6\W ':

Bearing Stress:Square and R ectangular ParallelK eys

) ıE = $E

ı EDOO =

7 )= '  $ E = +/

.6\F 1 IV

71 IV /E = .6\F '+

TriaxialStress Factor

 ≤ . ≤  

M ott,Fig.11-4(a)

C om parison ofShear and Bearing Length Equations M inim um R equired Length to Prevent Shear Failure

M inim um R equired Length to Prevent Bearing Failure

71 IV /V = 6 \W ':

71 IV /E = .6\F '+

,I. WKHVHHTXDWLRQVJLYHWKHVDPHUHVXOWIRUDVTXDUHNH\,Q JHQHUDO.ZLOOEHJUHDWHUWKDQDQGPRUHVKHDUIDLOXUHVZLOOEH REVHUYHGLQWKHILHOG.H\VDUHJHQHUDOO\GHVLJQHGWRIDLOEHIRUH RYHUORDGVFDQFDXVHGDPDJHWRWKHVKDIWRUDWWDFKHGFRPSRQHQW ,QWKLVUHVSHFWWKH\DFWOLNHDPHFKDQLFDOIXVH

Stress A nalysis of W oodruffK eys % % − GV 



$ 6KHDU$UHD

GV 



æ %ö æ % ö  ç ÷ = ç − GV ÷ + $ èø è ø

Shear A nalysis of W oodruffK eys 

% % − GV 





ö æ %ö æ %  ç ÷ = ç − GV ÷ + $ ø èø è $ = G V (% − G V )

$ GV

$ V ≡ 6KHDU$UHD=: G V (% − G V ) IJ DYH

7 = '$ V

IJ VDOO =

6 \W 1 IV

Shear Pins

7KHVWUHQJWKDQDO\VLVRIVKHDUSLQVLVVLPLODUWRWKDW XVHGWRILQGWKHVWUHQJWKRIDIDVWHQHU:H¶OOGHIHUWKH VWUHQJWKDQDO\VLVXQWLOZHFRYHUIDVWHQHUV M ott,Fig.11-9

Stress C oncentration Factors .H\VHDWVFUHDWHVWUHVVFRQFHQWUDWLRQVLQWKHVKDIW7KHUHDUH GLIIHUHQWVWUHVVFRQFHQWUDWLRQIDFWRUVIRUEHQGLQJDQGWRUVLRQDO ORDGV3HWHUVRQFRQWDLQVDFRPSLODWLRQRIVWUHVVFRQFHQWUDWLRQ IDFWRUVWKDWLQFOXGHVNH\VHDWJHRPHWULHV)RUIODWHQGPLOOV 3HWHUVRQJLYHV.W IRUEHQGLQJDQG.W IRUWRUVLRQ 7KHVHPD\EHUHGXFHGE\XVLQJNH\VHDWVPDGHZLWKEXOOHQG PLOOV7KHVWUHVVFRQFHQWUDWLRQIDFWRUIRUDVOHGUXQQHUNH\VHDW LVVLJQLILFDQWO\ORZHUWKDQIRUDSURILOHNH\VHDW$FLUFXODUNH\ DQGNH\VHDWZLOOKDYHORZHUVWUHVVFRQFHQWUDWLRQIDFWRUVDQ\ RWKHUNH\JHRPHWU\ R .E.Peterson,Stress C oncentration Factors,W iley,N ew Y ork,1974.

A ssignm ent  'HWHUPLQHWKHOHQJWKRIDSDUDOOHONH\IRUDJHDUWREH PRXQWHGRQDVKDIWZLWKDLQGLDPHWHUVKDIW7KH NH\LVPDGHIURP$,6,FROGGUDZQVWHHO7KHJHDU WUDQVPLWVOELQRIWRUTXHDQGKDVDKXEOHQJWKRI LQFK  $9EHOWVKHDYHWUDQVPLWVOELQRIWRUTXHWRD LQGLDPHWHUVKDIW7KHVKHDYHLVPDGHIRUP$670FODVV FDVWLURQDQGKDVDKXEOHQJWKRILQ'HVLJQD SDUDOOHONH\DQGNH\VHDW7KHNH\PDWHULDOLV$,6, FROGGUDZQVWHHO&UHDWHDQ$XWR&$'GUDZLQJWKDW ZRXOGHQDEOHDPDFKLQLVWWRPDNHWKHNH\VHDW

Splines

Fundamental Problem in Shaft Design How do I connect stuff to the shaft? Interference Fits

Keys & Keyseats

Integral Shaft

Pins

Hubs/Collars

Splines/Polygons

Splines G Splines can be thought of as a series of axial keyways with mating keys machined onto a shaft. G There are two major types of splines used in industry: 1) straight-sided splines, and 2) involute splines. G Splines provide a more uniform circumferential transfer of torque to the shaft than a key. Mott, Fig. 11-6

Splined Shaft and Hub

External Spline

Internal Spline www.advanceadapters.com

Spline Standards G ANSI B92.1-1970 (R1982), Involute Splines, American National Standards Institute. G ANSI B92.2-1980, Metric Module Involute Splines, American National Standards Institute. G SAE Straight Tooth Splines

Straight-Tooth Spline Geometry G SAE straight-tooth splines usually contain 4,6,10, or 16 splines. G Parameter dimensions are controlled by the fit needed for a particular application.

Mott, Fig. 11-4

Straight-Tooth Spline Strength G The torque capacity per unit length of an SAE spline is based on a 1,000 psi bearing stress on the sides. G Depending on the class of fit, a spline is able to accommodate axial movement along the shaft and still transmit torque. Splines have the same failure mechanisms as keys: 1) shear or 2) bearing.

Straight-Tooth Spline Strength (Continued) T = 1,000 ⋅ N ⋅ R ⋅ h 1æD dö D+d R= ç + ÷= 2è 2 2ø 4 1 h = (D − d ) 2 D+d 1 T = 1,000 ⋅ N ⋅ ⋅ (D − d ) 4 2

T = Torque per unit length N = Number of teeth D = Major spline diameter d = Minor spine diameter d = f (D)

æ D2 − d 2 ö ÷÷ T = 1,000 ⋅ N ⋅ çç è 8 ø

Torque Capacity Curves (SAE Straight-Tooth Splines)

Note that an involute spline has a higher torque capacity than does a straight-tooth spline of the same major diameter.

Mott, Fig. 11-7

Involute Splines

Involute splines generally have a 30o pressure angle. Mott, Fig. 11-8

Standard Diametral Pitches and Lengths Diametral Pitches There are seventeen diametral pitches in common use: 2.5 3 4 5 6 8 10 12 16 20 24 32 40 48 64 80 128 Standard Lengths Common designs use spline lengths of 0.75 D to 1.25 D, where D is the pitch diameter of the spline. When these standard lengths are used, the shear strength of the splines will exceed that of the shaft from which they are made.

Spline Manufacturing Methods Splines are either “cut” (machined) or rolled. Rolled splines are stronger than cut splines due to the cold working of the metal. Nitriding is common to achieve very hard surfaces which reduce wear. Rolled Spline Process Forged blank is rolled under tons of pressure prior to heat treating. The finished spline is more accurate and stronger (35%) than cut spines. www.drivetraindirect.com

Spline Failure Example

Note the yielding of the shaft outside of the engagement area due to a torsional load. The mating internal spline forced the external slines to remain parallel. In this case the spline is stronger than the shaft. www.4wdonline.com

Splined Linear Bearing

Circular shaped splines have been combined with ball bearings to create linear bearings that can resist a torsional load. www.tsubaki.com

Polygons An alternative to splines that has significantly lower stress concentration is the polygon. Four and three lobed polygons are shown. Design information on polygons is available from General Polygon.

www.generalpolygon.com

Retaining Rings G Retaining rings are used on shafts to maintain the axial position of components. G There are many types of retaining rings. In general, they may be classified as: 1) External internal and 2) external. Internal

www.rotorclip.com

Different Types of Retaining Rings

www.mdmetric.com

Spring Loaded Retaining Rings G“Bowed” retaining rings provide restoring forces to the components being held. GFlat retaining rings allow small amounts of axial motion of the held component.

Bowed Internal Retaining Ring

Bowed External Retaining Ring www.rotorclip.com

Smalley Compression Spring Retaining System

Higher restoring forces can be obtained using compression rings manufactured by Smalley. www.smalley.com

Retaining Ring Stress Concentrations G External retaining rings used on shafts require that grooves be cut into the shaft. G The grooves generally have sharp corners or very small fillet radii which result in significant stress concentration factors.

Mott, Fig. 11-5

Retaining Ring Stress Concentration Factors G The high stresses at the root of the retaining ring groove will be highly localized and will not significantly effect the static strength of a shaft made from a ductile material. G The stress concentration factors will be important in determining the life of the shaft and must be included in life calculations.

Shigley, Fig. A15-14 & 15

Retaining Ring Design Dimensions and design guidelines for retaining rings are contained in catalogs and literature published by retaining ring manufacturers.

Rotoclip, Inc.

Smalley

Waldes Truarc, Inc.

Designs that use retaining rings must take into account how the rings will be installed and make sure that sufficient assembly clearance is provided.

Integral Shafts G An alternative to attaching components to shafts is to machine the components directly onto the shaft. G This higher priced approach is often the only approach available when tight space constraints exist. G Complex combinations of components can be obtained using modern CNC turning centers. www.astas.co.za/shafts.html

Assignment 1) Make a drawing of an SAE straight-tooth- 4-spline connection having a major diameter of 1.5000 in and a class A fit. Show all critical dimensions. What is the torque capacity of the spline?

2) Identify two applications of retaining rings used in mechanical equipment. Describe the applications and discuss why you think retaining rings of the type used were chosen by the designer.