Bevel Gear: Fundamentals and Applications

358 Pages·2016·10.41 MB·English

by  Jan Klingelnberg (eds.)

Jan Klingelnberg
Editor
Bevel Gear
Fundamentals and Applications
Bevel Gear
ThiSisaFMBlankPage
Jan Klingelnberg
Editor
Bevel Gear
Fundamentals and Applications
Editor
JanKlingelnberg
KlingelnbergGmbH
Peterstraße45,42499
Hu¨ckeswagen
Germany
Editorial team:
HartmuthMu¨ller
KlingelnbergGmbH,Peterstraße45,42499Hu¨ckeswagen,Germany
JoachimThomas
ZGHypoidGmbH,Georg-Kollmannsberger-Straße3,D-85386Eching-Dietersheim,
Germany
Hans-Ju¨rgenTrapp
KlingelnbergGmbH,Peterstraße45,42499Hu¨ckeswagen,Germany
ClaudeGosselinIng.Ph.D.,InvoluteSimulationSoftwaresInc.,Quebec,Canada
ISBN978-3-662-43892-3 ISBN978-3-662-43893-0 (eBook)
DOI10.1007/978-3-662-43893-0
LibraryofCongressControlNumber:2015949639
©Springer-VerlagBerlinHeidelberg2016
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Preface
Inalltextbooksongeartechnology,cylindricalgearsusuallycometoattentionfirst
becauseoftheirwideuse,whereasbevelgearsaredealtwithsuperficially.There-
fore,readerswithadeepinterestinbevelgearsarenotsatisfied.
Although the essential differences between bevel and cylindrical gears are
always outlined, the true characteristics and features of bevel gears, and their
“three-dimensional” nature which varies along the face width, are not sufficiently
detailed.
In this book, a team of authors from academia and industry aims to provide a
comprehensivetextbookonbevelgears.
After covering the major fields of application for these machine elements, this
book presents the geometrical attributes of bevel gears and the different cutting
methodsbasedongeartheory.
Thethree-dimensionalaspectofthegearteethistreatedindetail,withchapters
on tooth flank development, load capacity, and noise behaviour. Descriptions of
production processes and necessary technologies provide a knowledge base for
sounddecision-making.
Theaimofthistextbookistointroducethereadertoallaspectsofthecomplex
worldofbevelgearsandtopresentindetailandinunderstandableformtheresults
ofrapiddevelopmentsinrecentyears
I like to thank all the co-authors for their contributions and for sharing their
knowledgegainedthroughmanyyearsofprofessionalexperience.
Hu¨ckeswagen,Germany JanKlingelnberg
2016
v
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Symbols and Units
Symbols Definition Units
A Auxiliaryfactorfordynamicfactor –
AE DistancebetweencontactpointsAandE(completepathof mm
contact)
A Areaofthehalfofellipseofcontactpressuredistributionover mm2
m
themiddlecontactline
A Areaofthehalfofellipseofcontactpressuredistributionover mm2
r
therootcontactline
A Areaofthehalfofellipseofcontactpressuredistributionover mm2
t
thetipcontactline
a Hypoidoffset mm
a Hypoidoffsetinthepitchplane mm
p
a Relativeoffset –
rel
a Centredistanceofvirtualcylindricalgears mm
v
B Accuracygradeacc.ISO17485 –
B Auxiliaryfactorfordynamicfactor –
B Thermalcontactcoefficient N
M
mm1=2m1=2s1=2K
b Minorhalf-axisofthecontactellipse mm
b Facewidth mm
b Effectivefacewidth(wheel) mm
2eff
b Facewidthfromcalculationpointtooutside mm
e
b Semi-widthofHertziancontactband mm
H
b Facewidthfromcalculationpointtoinside mm
i
b Facewidthofvirtualcylindricalgears mm
v
b Effectivefacewidthofvirtualcylindricalgears mm
veff
C Tiprelief μm
a
C Effectivetiprelief μm
eff
vii
viii SymbolsandUnits
Symbols Definition Units
C ,C ,C , Factorsfordetermininglubricantfilmfactors –
ZL ZR ZV
C ,C Experimentalweightingfactorsforcalculationofbulk –
1,2 2H
temperature
c Componentofcircumferentialspeedinplaneofcontact m/s
c Clearance mm
c Facewidthfactor –
be2
c Meanaddendumfactorofwheel –
ham
c Specificheatperunit Nm/kgK
M
cα Componentofcircumferentialspeedinplaneofcontactintooth m/s
depthdirection
cβ Componentofcircumferentialspeedinplaneofcontactin m/s
directionoffacewidth
cγ Meshstiffness N/(mm∙μm)
D Sumofdamage –
D ,D ,D Integrationconstantsoftheslidingvelocityoverthepathof –
1 2 3
contact
d Tipdiameterofvirtualcrossedaxeshelicalgear mm
a
d Outsidediameter mm
ae
d Basediameterofvirtualcrossedaxeshelicalgear mm
b
d Outerpitchdiameter mm
e
d Meanpitchdiameter mm
m
d Pitchdiameterofvirtualcrossedaxeshelicalgear mm
s
d Tolerancediameter mm
T
d Referencediameterofvirtualcylindricalgear mm
v
d Tipdiameterofvirtualcylindricalgear mm
va
d Tipdiameterofvirtualcylindricalgearinnormalsection mm
van
d Basediameterofvirtualcylindricalgear mm
vb
d Basediameterofvirtualcylindricalgearinnormalsection mm
vbn
d Referencediameterofvirtualcylindricalgearinnormalsection mm
vn
d* Pitchdiameterofvirtualcylindricalgearacc.FVA411 mm
v
E Modulusofelasticity(Young’smodulus) N/mm2
E Auxiliaryfactorfortoothformfactor –
e Toothslotwidthatthebottomofthetoothspace mm
fn
F ,F Auxiliaryfactorsformid-zonefactor –
1 2
F Axialforce N
ax
F Tangentialforceatmeandiameter N
mt
F Tangentialforceofvirtualcylindricalgears N
mtv
F Normalforce N
n
F Cumulativepitchdeviation,total μm
p
F Cumulativepitchtolerance,total μm
pT
F Frictionforce N
R
F Runoutdeviation μm
r
F Radialforce N
rad
F Runouttolerance μm
rT
SymbolsandUnits ix
Symbols Definition Units
F Tangentialforce N
t
F Indexdeviation μm
x
F’ Single-flankcompositedeviation,total μrad/μm
i
F” Double-flankcompositedeviation,total μm
i
F” Double-flankrunoutdeviation μm
r
f Distancefrommid-pointMtoanylineofcontact mm
f Distancefrommid-pointMtothemeanlineofcontact mm
m
f Maximumdistancetothemiddlelineofcontact mm
max
f Singlepitchdeviation μm
pt
f Singlepitchtolerance μm
ptT
fαlim Influencefactoroflimitpressureangle –
f Distancefrommid-pointMtotherootlineofcontact mm
r
f Distancefrommid-pointMtothetiplineofcontact mm
t
f’ Tooth-to-toothsingle-flankcompositedeviation μrad/μm
i
f’ Short-wavepartofsingle-flankdeviation μrad/μm
k
f’ Long-wavepartofsingle-flankdeviation μrad/μm
l
f” Tooth-to-toothdouble-flankcompositedeviation μm
i
f” Eccentricityofdouble-flankcompositedeviation μm
e
G Movementofaxisincaseofsliding mm
G Auxiliaryfactorfortoothformfactor N
G Auxiliaryvalueforintegrationofslidingvelocityoverpathof –
contact
g Lengthoftheaddendumpartofthepathofcontactinthe mm
an
normalsection
g Lengthofthededendumpartofthepathofcontactinthe mm
fn
normalsection
g Distanceofacontactpointtothepitchorhelixpointonthe mm
n
contactlineinthenormalplane
g Distanceofacontactpointtothepitchorhelixpointonthe mm
t
contactlineinthepitchplane
gvα Lengthofthepathofcontactofvirtualcylindricalgears mm
gvαn Lengthofthepathofcontactofvirtualcylindricalgearsinthe mm
normalsection
H Auxiliaryfactorfortoothformfactor –
HB Brinellhardness –
HRC Rockwellhardness –
HV Vickershardness –
H Toothmeshlossfactor –
V
h Outeraddendum mm
ae
h Meanaddendum mm
am
h Meanchordaladdendum mm
amc
h Tooladdendum mm
a0
h Outerdedendum mm
fe
h Innerdedendum mm
fi