fsBN97S9n2A-&0
PROSIDING Nasional Tahunan TeknikMesin($NTTM) V $eminar Indonesla, 21-23 Nopember Unlrcrsltas flXF
EDITOR: HARINALDI YULIANTO S. NUGROHO GANDJAR KISWANTO JOS ISTIYANTO
Prosiding Seminar f\lasional Tahunan TeknikMesin$NffW V Editor: Harinaldi YuliantoS. Nugroho GandjarKiswanto Jos lstiyanto
Penyelenggara: Departemen TeknikMesin TeknikUniversitas Indonesia Fakultas
SeminarNasionalTahunanTeknikMesin(SNTTM) V Editor: Harinaldi,YuliantoS. Nugroho,GandjarKiswanto,Jos lstiyanto ISBN: 979-97726-8-0
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SeminarNasionalTahunanTeknikMesinV (SNTTMV) bertempat di Depok,Indonesia pada 2l-23 November2006 denganDepartemenTeknik Mesin FakultasTeknik UniversitasIndonesiasebagaituan rumah. Seminar ini diadakansebagaiajang bertemunyapara peneliti dan praktisi teknik mesin di seluruh Indonesiauntuk menyajikan,berdiskusian mempromosikan perkembangan teknik mesindi Indonesia. Seminar diharapkanmelingkupi para ilmuan dan insinyur mesin dalam tema "MeningkatkanSinergi Perguruan Tinggi dan Industri Melalui Pendidikan dan Riset yang Berkelanjutan". Bukuelektronikprosidingini adalahkompilasidarisemuapaperyangdipresentasikan dalamSNTTMV dengankelompokdibawahini: r Rekayasa DesainsistemdanKomponenMesin(Ml) meliputiDesaindan Pengembangan Produk,vibrasi, Teknikotomotif, cAE, FEM, danBEM, Fatique & Fracture,Tribology. r KonversiEnergi(M2)meliputiTermodinamika, MekanikaFluida,Aerodinamika, Perpindahan PanasdanMassa,TeknologidanMotor pembakaran, optimasi Energi,EnergidanLingkungan, TeknologiRefrigasidanAC. o TeknologiPengembangan MaterialdanProsesManufaktur(M3) yangmeliputi Pengujian Material,Korosi,TeknologiLas& cor, Polimer& Komposit,Fairure Analyis,ProsesPermesinan, Pembentukan, Mekatronika, FabrikasidanOtomasi Industri,Manajemen danTeknologiInformasi,CAD/CAIWCIM r Pendidikan TeknikMesin(M4). Panitia SNTTM V mengucapkan terimakasihkepada para pembicarakunci, para pemakalahyang berkontribusidalambuku ini, dan semuapartisanyang menghadiri seminar.Karni juga berterimakasih atasnasihat,dukungannyatadan partisipasiaktif yangdiberikanparasponsor demiterselenggaranya acaraini.
Editor: . Harinaldi YuliantoS.Nugroho GandjarKiswanto JosIstiyanto
]ITAKALAU ITNLOMPOK M3 M3-001 Analisis Kegagalan Bahan PorosGearBoxKilnPabrik Semen: Pendekatan DariSisiSifat Mekanik danKomposisi Kimia HairulAbral Perlakuan Annealing Terhadap StrukrurMikrodanSifatMekanik Tembaga " M3-002Pengaruh Komersialyang Diproses dengan ECAP RUTE Bc JonAffi,Gunawarman M3-003 StudiPengaruh Rapat ArusdanWaktuPadaProses Pemasukan Hidrogen terhadap Kekuatan Tarik, Struktur Mikro danMode Patahan Baja Assab 705 Alian Helmy M3-004 Keefektifan KondisiPemotongan Terhadap Getaran danKekasaran Permukaan Dalam Proses Gurdi Ahmad Yusran Aminy, llyas R.,Yohanes BY,Hammada Abbas M3-005 Effects ofOverload-Affected ZoneonFatigue CrackPropagation Behavior afterApplying a Single Overload under Negative Stress Ratio Anindito Purnowidodo, Chobin, Makabe M3-006 Circumferential TIGWelding ofAluminum PipeUsing Neural Network ArloSunar Easkoro, Yasuo Suga M3-007 Pengaruh KadarAirTerhadap Kekuatan TarikdanKekuatan GeserInterfacial SeratRami yangDiberi Perlakuan Alkali kistomus Boimau, Heru, S.B,Rochardjo M3-008 AnalisaPertumbuhan RetakPadaAl 7075-TO Dengan Menggunakan MesinUjiLentur3 Titik Hendri Chandra M3-009 Mechanical Characteristics of Nano-structured ToolSteelby Ulkasonic ColdForging Technology Chang-Min Suh,Gi#oSongMrn-Soo Suh,Young-Shik Pyoun, Seong-Yun Km M3-010 Pengaruh Kemiringan Sumbu PutarCetakan Sentrifugal Terhadap Distribusi SifatMekanik HasilCoran Djarot B.Darmadi M3-011 StudiPemilihan JenisSkinStruktur PanelSandwich CarBodyMonorail Berdasarkan Analisis Kekuatan lmpak Diharjo Kuncoro padaDinding M3-012 Penggunaan Refraktori Monolitik MgO-C Pelapis Tungku Pengolahan Logam Hady Efendy, Cynthia L.Radiman, Bambang Ariwahjoedi, Aditianto Ramelan
)
M3-013 Kontribusi ProsesECAPdengan VariasiRutedanJumlahLaluan Terhadap Penguatan Alumunium Tanpa Paduan Komersil Gunawarman M3'014Pengaruh KorosiRetakTegang Terhadap FaktorIntensitas padaLogam Tegangan Paduan Al-Cu diLingkungan 0.2MNaOH QomarulHadi M3-015 padaKatalis Pemrosesan Material Otomotif Si Harjanto M3-016 Penentuan LetakSaluran danPenambah untukMemprediksi Kemungkinan Cacatpada Pengecoran Logam AbdulHay M. M3-017 Perancangan Sistem Servo Elektrohidraulik dengan Teknik Variable Speed Pumping Indraw anto,IeguhSefiarsq ElvinSubhianto M3-018 Tinjauan lnvestigasi Penyebab JalurPerambatan Retak-Lelah UnikMode-Campuran l+ll padaPelat Aluminum Murni Komersial YudySurya lrawan M3'019 Analisa UnjukKerjaMesinGerinda Berbasis MesinBubutpadaProses Pemesinan Rotor Aidock Joslstiyanto, AliRidho M3-020Effectof SurfaceTreatment onFatigue Strength lmprovement of Martensitic Stainless Steel PriyoTi lswanto M3-021 Anelastic-Plastic Contact Model ofa Sphere Against a HardFlat Jamail
M3'022StudiPengaruh FraksiVolume SeratTerhadap Serapan PanasRadiasi BahanKomposit Berpenguat Limbah Sawit Dengan Serat Matrik Poliester Jamasfi, Kuncoro Dihaio M3-023 Analisa Kegagalan PipaPVCPada Sistem Pemanas AirRumah Tangga Hermawan Judawisastra, Permonowidi M3'024 Peningkatan Kualitas Produk CorAluminium Paduan Untuk Komponen Otomotif I Nyoman Jujur M3-025Optimasi JumlahCutter-Contact PointPadaPembuatan Lintasan PahatProses Pemesinan Milling Berbasis Model Faset 3D Gandjar Kswanto M3-026 Pengembangan Metode Penentu JarakAntarLintasan yangAkurat Pahat(step-over) padaPembuatan Lintasan Pahat Proses Pemesinan Milling Berbasis Model Faset 3D Gandjar Kiswanto
M3'027 Pengembangan Metode Simulasi Pergerakan PahatMenggunakan VTKpadaSistemCAMBerbasis (Development Model Faset 3D oftoolmovement simulation module using VTKforCAM-'system based onfaceted models) Gandjar Kiswanto, A.Mujahid M3-028 Pengembangan Algoritma CepatPenentuan Titik-Kontak Pahat(CutterContact Point) padaSistem-CAM Berbasis ModelFaset3D untukPemesinan (Roughing) Awal dan Akhir(Finishing) Gandjar Kswanto, AMujahid M3-029 StressConcentration Factors of Stepped-Shafts of Circular-to-Square CrossSection Under PureBending Asnawi Lubis, JamiatulAkmal M3'030Karakterisasi HasilPerlakuan KimiaAlkaliX%NaOH terhadap Topografi Permukaan, Kekuatan Tarik danModel Patahan (Boehmeria Serat Tunggal Rami nivea) E.Marsyahyo, R.Soekrisno, HeruS.B.Rochardjo, Jamasri M3-031 Optimisasi ProsesPemesinan Nonkonvensional EDMWireCutMenggunakan Algoritma Genetik Sigit Yoewono Martowibowo, VinaSariYosephine, Adriansyah M3'032 NumericalAnalysis ofBuckling ofSandwich Plates withAluminum Foam Core N.T.Nama, l. S.Putra, T,Dirgantara, D.Widagdo, H.Homma M3-033 Pemecahan padaBajaHipereutektoid Sementit Proeutektoid Andi Prastiawan, Akhmad Saufan, Agung Premono M3'034 Pengaruh JenisPenguat Terhadap SifatMekanik Komposit Bermatrik KeramikPada Beberapa FraksiVolume DiahKusuma Pratiwi M3-035 padaProses RekondisiDies Diamond Drawing Gatot Prayogo M3-036 Analisis (RBB) Rasio Batas Bentuk Logam Lembaran DediPriadi M3-037 Pengukuran ProfilCelah(Gap)Berbentuk StepMiringpadaBagian Dalam TubeSilinder dengan Metode Prisma Kontak Yongky Permana Ramlan M3-038TheEffectof Machinery PowerBecouse of CuttingDepthVariation at Manufacturing Process ofConventional Milling HaiRarindo M3-039 TheWelding Ergonomic Position toProductivity ofWelding Process HariRarindo M3-040 Plastic Collapse of PipeBends Under Combined External Pressure andinPlaneBending IGNWratmaja Puja, l(hamtanh SANI/SOUK
Seminsr Nasional TahunanTeknikMesin (SNTTM V UniversitasIndonesia.2l-23 November2006
StressConcentrationFactorsof Stepped-Shafts of Circular-to-SquareCrossSection underPureBending AsnawiLubisr& JamiatutAkmal Jurusan TeknikMesin,Universitas Lampung Sumantri Brojonegoro GedungH Fakultas Teknik,JalanProfessor Gedongmeneng, BandarLampung, 35145 T elp: (62-72l) 7479221,70I 609 ext.22 l, Fax:(62-72l) 704947 rE-mail :
[email protected]
Abstract Shaft is a mschine element whose main function for power transmission,Shaft is often neededin steppedform (changein cross-section).For a non-smoothshaft (steppedshqft), the elementary stress equationsare no longer holdfor calculating the actual stressas the stresswould be higher than the nominal slresses.To relate the ma"rimumslressqt the discontinuitywith the nominal stresscalculated using the elementary stressequation, a fector is neededwhich is called stressconcentrationfactor (SCF). This paper presentsa graphfor designpurpose ofstress concentrationfactor ofstepped shaft of circular-to-square cross-sectionunder pure bending. The graph was derivedfrotn an exlensive linier fnite elementparametric study and presentedin line of the well-knownPeterson'sgraphfor steppedshaft of uniform circular cross-section.Finite elementparametric study was carried out for every combination of diameter to diagonal ratio, D/d and radius of fillet to diagonal ratio, r/d. For geometry with particular D/d value, six analyseswere done by varying the r/d value. Stress distribulion showsthat maximumaxial (bending)stresslocatedat the root of squi*e, exactlyat the corner. In general graphical designsimilar to the vell known Petersongraph wasproduced, but with small range of parameter becauseof geometryrestriction. elementanalysis Keyvords: stepped-shafts, stress-concentrationfactors,Jinite
Introduction Shaftis often neededin Shaftis a machineelementwhosefunctionfor powertransmission. (change is rotated with Example a shaft squareshoulderfor the seatof steppedform in cross-section). loading to combined ofaxial, bending,andtorsion. bearing.In such,the shaftcouldbe subjected If a shaft is smooth,the resultingstressdue to loadingcan be computedusing the elementary stressequations.This stressis called nominal stress.For a non-smoothshaft (steppedshaft), the elementarystressequationsare no longerhold for calculatingthe actualstressas the stresswould be higher than the nominal stresses.To relatethe maximumstressat the discontinuitywith the nominal stresscalculatedusing the elementarystressequation,a factor is neededwhich is called stress concentrationfactor (SCF).The magnitudeof this factor dependson diameterratio, shapeand areaof cross-section, radiusof fillet andtypesof loading(axial,bending,torsion,or their combination). can be foundin many factorfor a steppedshaftofuniforrn cross-section Stressconcentration standardtextbooksof mechanicsof materials.Until now, the most completesourceof graphof stress concentrationfactorsfor variousgeometryof shaft,bar,and plat is a compendiaby Peterson[974]. In this compendia,stressconcentrationfactor (K,) for steppedshaft of uniform cross-sectionare plotted as function of non-dimensionalgeometry.Today stateof the art modernliteratureare also still using seefor example,Kang, the Peterson'sgraph for analyzingthe steppedshaftof uniform cross-section, graphto analyzethe torsionalvibrationofstepped et al [2005].Pan,et al [2000]usedthe Peterson's shaft.Kim and Kim [995] usedthe samegraphto analyzethe stressesat the steppedshaft subjected to axialtension.
M3-02911
SeminarNasionalTqhunanTeknikMesin(SNTTM V Universitqs Indonesia. 2l-23 November 2006
In the compendiaof stressconcentrationfactorsby Peterson,it cannotbe found a graph for stepped shaftof circular-to-square cross-section. Baker[999] canied out a finite elementstudyusingALGOR version3.18to obtainthe characteristic ofsteppedshaftofcircularto squarecross-section subjected to combinedloadingof staticbendingand torsion.In his MSc thesis,Baker investigatedthreevaluesof diameterratio, but did not makethe radiusof filled varied so that graphsthat can be usedfor design purposewere not produced.To analyzea steppedshaft of circular-to-squarecross-section,it was common to apply the graph for steppedshaft of uniform circular cross-sectionof equivalentcrosssectionalareato square[Yusron,2004].This is usuallydonebecausesimilar graphfor steppedshaftof circular-to-squarecross-sectionwas not available either in textbooks or in today state of the art modern literature.This paper presentsa graph for design purposeof stressconcentrationfactor of steppedshaft of circular-to-squarecross-sectionunder static pure bending.The graph was derived from an extensivelinier finite elementparametricstudy and presentedin line of the well-known Peterson's graphfor steppedshaftofuniform circularcross-section.
Stress-Concentration Factors Shaft is an importantelementin mechanicalconstruction. Shaft is usuallyhas functionfor power transmission.Shaft can be found as squarecross-section as well as circular cross section, however,majority of shaft are circular cross-sectionas its main function is for power transmission. Whereas, shaftof squarecross-section is usuallyonly usedfor supportingload. Circular shaft is a rotating element where other elementssuch as gears and pulley are mounted.Sucha shaftcouldbe subjected to axial (tensionor compression), bending,torsion,or their combinationasshownin FieureL
f \* Figure1 A circularshaftsubjectedto combinedloadingof axial,bendingand torsion In particularapplication,a shaftofnon-unifoffnareaof crosssection(steppedshaft)might be used. Changein areaofcross-section ofsteppedshaftresultsin stressconcentration at the discontinuity.In order to reducethe effect of stressconcentration at the regionof changein cross-section, fillet of radiusr is usuallyappliedasshownin Figure2. ! I
/--+\ /t\
- -.-{-i- -l- \il
\.i_/ i
Figure2 Circular stepped shaftwithshoulder or radiusr
M3-029t2
SeminarNasionalTahunanTeknikMesin (SNTTM)V UniversitasIndonesia,2l-23 November2006
The ratio of maximum stressat a critical point to the nominal stressis called stressconcentration factor (,SCF).Stressconcentrationfactor ofcircular steppedshaft hasbeengiven by Peterson11974]. The magnitudeof this factor is a function of non-dimensionalparameterDzlDr and r/D1. Stress concentrationfactornK, canbe written as: K, =
o**
; for normalstress
(la)
oron
K ,, = " ^* ' for shearstress
(1b)
T no,
Where,for circularcrosssectionthe nominalstressis givenby:
4P
6,u, = =; ztu, o * non
foraxial load
(2)
32M 1D'3
Trur =
t6 T ^ lUJl
r ; for torsionload
(4)
Figure3 and 4 are typical graphof stressconcentration factor for squareand ,ir.ulu, stepped-shaft respectively underpurebendingload.Thesegraphsweretakenfrom a book of"stress Concentration Factor" by Peterson11974).Similar graph for axial and torsion load can be obtainedfrom the same book.
3.S ? fi 1 .-
t^s|*"
*--,,*t**;** { t
0.10
0,15 rld
0.?s
Figure3 Stress-concentration factorsforsquarestepped-shaft underpurebending 1974] [Peterson, M3-029t3
SeminarNasional TahunanTeknikMesin (SNTTM V UniversitasIndonesia.2l-23 November2006
3.('
afr 1
t
Iw
i ,**1,,,,.,."
L [\
\\ \
f.a
"{ t,
#ld* *
\'
-3 f
\ \\
*I-$* p 1"10-
\\
l-ft
\
ahffi nff" Iffi
L4
0.0$
'$.10
0.1* rld
s*ff
0ss
fi,as
Figure4 Stress-concentration factorsfor circularstepped-shaft underpurebending[Peterson,1974] In the book ofPeterson,it cannotbe found a graphofstress-concentration factor for a steppedshaftof (Figure5). In fact, steppedshaftofthis form can be found in practice, circular-to-square cross-section such as, the output low speedreducerat mill and diffuser station in sugar cane industry [Yusron, 20041.This paperaimsto providea graphof stressconcentrationfactorsof steppedshaftsof circular to squarecross-section underpurebendingthatcanbe useddirectlyfor designpurpose.
! I
i
,..-_.-.i....r_ /"1'ri f
|
i
i
\;
\l
-.-.-1.-.-.-.-Ll.-.-.-.-.1.ll!l
\\'
'.
i i t
"*-i---'
li ,ri
:
I
i i
! I
Leftview
'
Frontview
Rightview
Figure5 Steppedshaftof circularto squarecross-section
M3-02914
SeminarNasionalTahunanTeknikMesin6NffM V Universitas Indonesia. 2l-23 November 2006 FiniteElementAnalysis Figure 5 showsa steppedshaftofcircular crosssectionofdiameter D to squarecross-section of diagonald. Finite elementparametricstudywas canied out for everycombinationof pararneter D/d andr/d. For geometrywith particularD/d value, six analyseswere done by varying-ther/d value. TableI givesthe geometryconfigurationfor parametricfinite elementstudyperformed. TableI Geometricconfiguration for parametric study(seeFigure2)
D/d
r/d
l .l
0,0s
0.l0
0.15
0.20
0.2s
0.30
t.2
0.05
0.l0
0 .r5
0.20
0.25
0.30
1.5
0.05
0.10 0.15
0.20
0.25
0.30
2.0
0.05
0.10 0.15
0.20
0.25
0.30
2.5
0.05
0.10 0.15
0.20
0.25
0.30
3.0
0.05
0.10 0.15
0.20
a.2s 0 . 3 0
Figure6 showsa typical finite elementmodelof the shaft.The elementtype usedhasten nodeswith three degreeof freedomat eachnode:translationin the -X, -y, and-z direction.All nodesat the circularendwerefixed andpurebendingloadwasappliedat the squarecrosssectionend.
Fixedend Loadedend
---l-t---ti
ii r!
+ l------' -c
Figure6 Typicalfiniteelementmodelof steppedshaftof circularto squarecross-section
Figure 7 showsthe normal bendingstressdistributionalong the shaft due to pure bending.The maximumbendingstresscan be read from the graph.This maximumstresswas then recordedfor everycombinationof parameter D/d andr/d anddividedby the nominalstressfor purebending[see equation(3)]. From this, a graphin line of Peterson's for uniformcircularsteppedshaftcan then be plotted.
SeminarNasional TahunanTeknikMesin (SNTTM) V UniversilasIndonesia,2l-23 November2006
.l
t a a
l
t(t
Figure7 bendingstressdistribution in circular-to-square stepped-shaft duetb purebending R.esults& Discussion As can be seenfrom Figure7, the maximumstresslocatedat the regionof changein crosssection.The stressploftedin Figure7 is the von Mises stress.In fact, this stressis almostthe sameas the normalbendingstress,as the load was only pure bending.A small differentbetweenvon Mises and normal bending stressesresults from the effect of Poisson'sratio. The maximum von Mises stresseswerethenrecordedasshownin TableII: Tablell Maximumvon Misesstressfor variusgeometryof steppedshaftunderaxialtension(MPa)
Md: t.r
r/d = 0.A5 r/d = 0.10 0.013856
r/d = 0.15
r/d:0.20
r/d:0.25
r/d = 0.30
M d :1.2
0.014880 0.0r24t6
Nd: t.s
0.015768 0.013144 0 . 0 1 8 8 8
0.010688 0.01096
Md =2.0
0.015208 0.013216 0 . 0 1 5 9 2
0 . 0 1 l2 t 6
0 . 0 1 0 8 7 2 0.010744
R/d=2,5
0.016256 0.012864 0 . 0 1 8 0 0
0 . 0 11I 2 8
0 . 0 1 0 5 8 4 0.010768
M d=3 .A
0.015704 0 .0 1 3 3 28 0.011600 0.01II 12
0.01I160 0.010632
Stressconcentrationfactor can be obtainedfrom Table II by dividing the stressesby the nominal stress.Becausethe maximum stresseslocatedat the shoulder.exactly at the corner of the squarepart,thenthe nominalstresscanbe obtainedas:
M3-029/6
SeminarNasional TahunanTeknikMesin (SNTTM) V UniversitasIndonesia.2l-23 November2006
M 6,on
(6)
s
Where M: appliedpurebending,N.mm = mm'. ^S sectionmodulusof square-shaft, The sectionmodulus,S,of the square-shaft of diagonald is given by:
.
J
r-
bh'
bh.h A.h
=-=_____==
A.d
d'J'
6 666J 2
(7)
24
In this analysis,the areaof square-shaftwas constantby settingthe value of diagonalof the square constant,i,e,d :50 mm,therefore:
_ s0'Jt=7365.7mm3
L)= -
24
The appliedmomentbendingMwas 58.9N.mm.Fromequation(6), the nominalbendingstressis:
58'? N'mm-= o o.oo8 MPa. - nom -^*7365.7mm3
By dividing the maximum stressesin Table II with this nominal stress,stressconcentrationfactors were obtainedas shown in Table IIL A graphof stressconcentrationfactorscan then be plottedfrom TableIII asshownin Figure8.
ablelll: Stressconcentration factorforvarious r/d = 0.05 r/d= 0.10 r/d = 0.15
r/d = 0.20
shaftunderaxialt ension r/d = 0.25 r/d = 0.30
Nd - l.l
t.732
Nd = 1 .2
1.860
t.552
Nd = 1.5
t.971
t.643
1.486
1.336
1.370
Nd :2.0
1.901
t.652
t.449
t.402
1.359
1.343
Nd=2.5
2.032
1.608
|. 4 7 5
1.391
1.323
l.346
R/d= 2.0
t.963
r.666
1.450
1.389
1.395
t.329
As can be seenfrom Figure 8, stressconcentrationfactorsdecreaseas the radiusof filled to diagonalratio increase.The graphshowsa similar trendto the well-knownPeterson'sgraphfor stressconcentrationfbctor for steppedshaft of uniform circular of squarecross-section. By comparing Figure 8 with Figure 3 and 4, it seemsthat the effect of diameterto diagonal ratio, D/d, is not significant.It shouldbe noted,however,that the spectrumof this ratio is smallcomparedwith Figure 3 and 4. A wide rangeof D/d valuesshouldbe includedandthis is the subjectof furtherpublication elsewhere.
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SeminarNasionqlTahunanTeknikMesin (SNTTM)V UniversitasIndonesia,2l-23 November2006
1 .9
ad=1.5
I
1A
\.2'="'
1.7
\ \
E i.s
D/d=3.o
\ \*
o
1 .4
\. \
It
1.2 1.1 1.0 0.00
Figure8 Stressconcentration factorof stepped-shaft of circular-to-square crosssectionunderpure bending
Conclusion A graphfor stressconcentration factorsofsteppedshaftofcircular to squarecrosssectionunderpure bendingload was produced.This graphwas derivedfrom parametricfinite elementstudy and can be directlyusedfor designpurpose.This graphshowsa similartrendto the well knownPeterson's graph for stressconcentrationfactorsofuniform circularor squaresteppedshaft.
Acknowledgement The authorswould like to acknowledgeDIKTI of the National EducationDepartmentfor providing fund throughfundamentalresearchgrantundercontractNo. 010/SP3lPPlDPZMllll2006.
References
tll t2) t3l t4l t5l
Baker, D.A., A Finite Element Study of Stressesin SteppedSplined Shafts and Partially Splinned Shafts under Bending, Torsion, and CombinedLoadings. MSc Thesis, Virginia PolytechnicInstituteand StateUniversity, 1999. Benham,P.P.' R.J. Crawford, and C.G. Armstrong, Mechanicsof EngineeringMaterisls, secondedition.LongmanGroupLimited,UK, 1996 Cook, RD., and W.C. Young, AdvancedMechanicsof Materials,secondedition.PrenticeHall IntemationalInc., 1999. Den Hartog, J,P.oAdvancedStrengthof Materials.McGraw-HillBook Company,New York, t952. Feese, T., and C. Hill, Guidelinesfor Preventing Torsional Vibration Promlems in ReciprocatingMachinery. Proceedingsof Gas Machinery Conference,Nashville, Tennesseeo
usA,2002.
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Kang, M.K., R. Huang, and T. Knowless,TorsionalVibrationof Circular Elastic Plateswith ThiclmessSteps.IEEE Transactionson Ultrasonics,Fenoelectric,andFrequencyControl,2005. Kim, Y.Y., and J.H. Kim, J.H., StressAnalysis of a SteppedShaft under RemoteTension. I7l Vol. 48, pp. 517- 530, 1995. QuarterlyJoumalof AppliedMathematics, Pan, J.Q., et. al., Three-Dimensional Response and Intensity of Torsional Vibration in a t8] SteppedShaft JournalofSoundandVibration,Vol. 236,pp.115- 128,2000. Concentration Factors.JohnWiley & Sons,lnc.,1974. t9] Pcterson,R.8., ^S/ress Popov, 8.P, Mechanics of Materials, secondedition.Prentice-HallInc., New Jersey,USA, [10] 1978. Ul] Roark, R.J., and W.C. Young, Formulafor Stressand Strain, fifth edition.McGraw-Hill Book Company,New York, 1975. [lzJ Saeed,M, Finite ElementAnalysis (Theory and Application with ANSYS).MinnesotaState University,Mankato,USA, 1987. [13] Timoshenko, S.P., Mechanicsof Materials, third SI edition. StanleyThornes(Publisher) Limited,1998. tl4l Timoshenko,S.P.,and J.N. Goodier, Theoryof Elasticity,third edition.McGraw-Hill Book Company,New York, 1970. ll5] Yusron, N, Fracture Analysis of a Square Shaft Output Low SpeedReducer of Milt and Difuser Stationof SugarCaneIndustryof PT BungaMayangof North Lampung(In Indonesia). StudentJob TrainingReport,Departmentof MechanicalEngineering, Universityof Lampung, 2004. t6]
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