1.2.5 Straightness 1.3.1 Choice of arrangement type 1.3.2 ... · 1.3.1 CHOICE OF ARRANGEMENT TYPE...

TABLE OF CONTENTS

1.1 UNITS AND DEFINITIONS 12

1.2 PRECISION AND TOLERANCES 13

1.2.1 Qualities 131.2.2 Profiletolerances 13 1.2.3 Lengths,holedistances 131.2.4 Matching 141.2.5 Straightness 151.2.6 Rollingelements 15

1.3 APPLICATION FEATURES 16

1.3.1 Choiceofarrangementtype 161.3.2 Determinationofguidewayandcagelengths 171.3.3 Holetypesandholepatterns 181.3.4 Endpiecesandwipers 201.3.5 Loadrating,loadcarryingcapacity 21

1.3.5.1 Basicstaticloadrating 21 1.3.5.2 Staticloadcarryingcapacity 21 1.3.5.3 Basicdynamicloadrating 22 1.3.5.4 Dynamicloadcarryingcapacityandratinglife 22 1.3.5.5 Effectiveloadrating 24 1.3.5.6 Correctionfactorsforloadcarryingcapacity 25 1.3.5.7 Eccentricload 26 1.3.5.8 Calculation 27

1.4 RIGIDITY 32

1.5 PRELOAD 34

1.5.1 Settingthepreload 34

1.5.1.1 Pressurescrews 35 1.5.1.2 Guidewayswithadjustinggib 35

1.6 LUBRICATION 36

1.6.1 Lubricants 361.6.2 Lubricatingwithgrease 36

1.6.2.1 Primaryoperationandgreasequantity 36 1.6.2.2 Relubrication 37

1.6.3 Lubricatingwithoil 37

1.7 FRICTION 38

1.8 PROTECTION AGAINST SOILING 39

1.9 OPERATING LIMITS 39

1.10 INSTALLATION GUIDELINES 40

1.10.1 Precisionoftheconnectingstructure 401.10.2 Assemblyinstructions 41 1.10.2.1 Priortoinstallation 41 1.10.2.2 Closedlayout 42 1.10.2.3 Openlayout 43

PRODUCT TECHNOLOGY 11

UNITS AND DEFINITIONS

1.1 UNITS AND DEFINITIONS

B mm Guidewaywidth

B1 mm Cagewidth

b mm Distancebetweenguidance systemcentres

b1 mm Distancebetweenrear guidewaysurfaces

C N Basicdynamicloadratingforcagelengthof100mm

Cw N Effectivedynamicloadrating

Cwe N Correctedeffectivedynamic loadrating

CL N/mm Rigidityoftheflatcage guidancesystem

C0 N Basicstaticloadratingforcagelengthof100mm

C0we N Correctedeffectivestaticloadrating

C0w N Effectivestaticloadrating

Dw mm Balldiameter

e mm Eccentricityoftheload

fH - Dynamichardnessfactor

fH0 - Statichardnessfactor

f - Dynamicloaddirectionfactor

f 0 - Staticloaddirectionfactor

F N Operatingload,guideloading

Fi N Variableload

FR N Displacementresistance

FR0 N FR,lubricantfrictionpercentage

FR1 N FR,load-dependentrollingfrictionpercentage

FRA N Displacementresistance,wiperpercentage

FRV N Carriagedisplacementresistance, preloaded

Fw N Limitingloadforeffective cagelength

H mm Distancefromextreme strokepositions

kF - Dynamicloadfactor

k0F - Staticloadfactor

K - Typefactorfor determinationofrigidity

L mm Guidewaylength

L 105m Nominalratinglife

L1 mm Distancebetweenthefirsthole andthestartoftheguideway

L1 mm Distancebetweenthefirstorlastpocketcentreandtheendofthecage

L2 mm Distancebetweenthelastholeandtheendoftheguideway

L1, L2min mm MinimumvalueforL1andL2

LA mm Holedistanceinguideways

LA mm Spacingdistanceinflatcages

Lh h Nominalratinglifeinoperatinghours

LK mm Cagelength

LR mm Guidewaylengthwithrunning surfaceforthewiper

n - MaximumpossiblenumberofholedistancesLA

nosz min-1 Numberofdoublestrokesperminute

p - Ratinglifeexponent

p N/mm2 Contactpressureforslidinglayer

P N Dynamicequivalentload

P0 N Staticequivalentload

qi % Proportionoftotalduration

RS N Dampingforceindirection ofmovement

S0 - Staticloadsafetyfactor

t mm DepthofthreadinT03holes

vi m/min Variablespeed

m/min Dynamicequivalentspeed

x - Numberofholes

Z - Numberofrollingelementsperrow

° Loaddirectionangledeviatingfrommainloaddirection

µm Elasticdeformationatcontactpoints

µ - Frictioncoefficient

mm2s-1 Kinematicviscosity

Δh µm Permissibleheightvariation

12

Q10

Q6

Q2

Guideway length

Per

mis

sibl

e de

viat

ion

in µ

m

PRECISION AND TOLERANCES

1.2 PRECISION AND TOLERANCES

1.2.1 QUALITIES

Theracewaysandlocatingsurfacesareprecision-ground.

Theguidewaysaresuppliedin3qualities(parallelismtoleranceoftheracewaystothereferencesidesoftheguidewayinrelationtoadefinedlength).

Q10:normalqualityforgeneralmachineconstruction

Q6: precisequalityformachinetoolconstruction

Q2: particularlyprecisequalityforexceptionallydemandingstructures

1.2.2 PROFILE TOLERANCES

Seeproductchapter

1.2.3LENGTHS,HOLEDISTANCES

Length:thelengthtoleranceisdefinedusingtheformula ±[0.2+(0.0012*lengthL)].

Guidewayswhichexceedthemaximumlengthindicated (see“normallengths”table)aremanufacturedinseveralsections.Thesesectionsarematchedprecisely.Itisimportantnottointerchangetheguidewaysinordertomaintainthetoleranceduringassembly.

Hole distances:thetoleranceoftheholedistancesiscalculatedtoensurethatguidewayscanbeassembledonapre-drilledholepatternuptothemaximumnormallength.Thetoleranceismeasuredbetweenthefirstandlastguidewayholeandisdistributedevenlyoverthelength.

Forguidewayswhichexceedthemaximumnormallength,thesuffix“P”isrequiredinordertomaintainthecorrespondingtolerance.

13


1.2.4 MATCHING

Guidewaysofthesamedesign(sameorderreference)aremanufactured,labelledandpackedinpairs.Pairedmatch-ingisbasedonthedistancebetweenthecentreoftheprofileandthemountingsurface“A”.

Standardmatching(US1/US2)allowspartstobeexchangedwhilstmaintainingaverynarrowtolerance.Inthehighesttolerancecategoryoratthecustomer’srequest,theguidewaysarematchedandlabelledbymorenarrowtolerances.

Forguidewayswithdifferentorderreferenceswhichstillhavetobematchedinpairs,thesuffix“X”hastobeaddedtotheorderreferences,e.g.

1M+1ML=2SXor1M+1V+1J+1S=4SRXor1V…T15+1V…T03=2SX

Matchingpossibilities:

14


1.2.5 STRAIGHTNESS

Straightnessaswellasparallelismischeckedinthefactory(tolerancesaccordingtoDIN644).

Straightnessvariancescanbebalancedoutbytighteningagainstthelocatingsurfaceduringassembly.

1.2.6 ROLLING ELEMENTS

Flatcageassembliescompriseneedleorcylindricalrollerswithadiametertoleranceof2µmandageometricalaccuracyof1µm.

Forparticularlychallengingrequirements,especiallyforguidewayswithaqualitylevelof2,speciallydesignedneedleorcylindricalrollerscanbesuppliedwithadiameter toleranceof1µmandageometricalaccuracyof0.5µm.

Thediametertoleranceamountsto1µmandthegeometricalaccuracy0.13µmforballbearings.

Seetable(page76),inchapter8onflatcageassemblies.

Paired matching code Number of guideways matched together In relation to reference side

2SA 2 ReferencesideA



etc… Numberofguideways ReferencesideA

2SR 2 ReferencesideR



etc… Numberofguideways ReferencesideR

2SAR 2 ReferencesidesA+R



etc… Numberofguideways ReferencesidesA+R

15

APPLICATION FEATURES

1.3 APPLICATION FEATURES

1.3.1 CHOICE OF ARRANGEMENT TYPE

Closed layout M/V

Thislayoutcancarryloadsandmomentsinanydirec-tion,canbeadaptedtoanyoperatingpositionandcanbepreloaded(preloadingpage34).

Itisalocating/locatingbearingandconsistsoftwoM/MLandtwoVguidewayswiththecorrespondingangledflatcageassemblies.

Open layout

Thislayoutisextremelyassembly-friendlyandismainlyusedforapplicationswithloadsactingcentricallyorvertically. Itisalocating/non-locatingbearingandconsistsofMandVguidewayswiththecorrespondingangledflatcageassemblyandJandSguidewayswiththecorre-spondingflatcageassembly.

Closed layout LUE

Thislayoutcancarryloadsandmomentsinanydirec-tioninresponsetothemostdemandingprecisionsrequirements.Thesystemispreloadedbycomponentswhichhavebeenadjustedagainstoneanotherintermsofdimensions.

Thesubdivisionintolocatingandnon-locatingbearingspreventsthesystemfrombecomingdistortedbythermalexpansion.TheguidancesystemconsistsofMandVguideways,JandSguideways,LUcounterstays,angledflatandflatcageassemblies.

Figure1.ClosedlayoutM/V

Figure2.OpenlayoutM/V,J/S

Figure3.ClosedlayoutLUE

16


Guidancesystemswithwipers

B) Calculation of cage length LK Withpresetguidewaylengthsandstroke:

Guidancesystemswithoutwipers

1.3.2 DETERMINATION OF GUIDEWAY CAGE LENGTHS

Therigidityandloadcarryingcapacityoftheguidancesystemaredeterminedbythesizeandlengthoftheflatcageassembly(LK).Theloadbearingcapacityandloadcarryingcapacityincreaseformomentsalongthelongitudinalaxis(rolling)inproportiontothecagelengthwhilstthepermissiblemomentsalongtheverticalaxis(yawing)andthediagonalaxis(pitching)increaseinsquarewiththecagelength.

Layoutprinciples:

–Thecageassemblyalwaystravelshalfofthestroke ofthemovingguideway

–Theentirelengthofthecageassemblymustalwaysremainbetweenthetwoguideways

–Wipersmustalwaysremainontheraceways

Recommendationsforminimumcagelengthsdependentonthestroke:

LK≥1.5·H foropenlayoutinordertomaintaintheoperationlimit(figure12,page26)

LK≥H forclosedlayout

H mm distancefromextremestrokepositions

A) Calculation of guideway lengths L, LR Withpresetcagelengthandstroke:

Guidancesystemswithoutwipers

17

Special length ratios:

Ifthelengthsareconfiguredaccordingtotheequationsabove,theflatcageassemblywillbeineverystrokepositionbetweentheraceways.

Inordertoachievethemaximumloadcarryingcapac-ityorasignificantstroke,thelengthscanbeconfiguredundernormaloperatingconditionsinsuchawaythattheflatcageassemblyextendsbeyondtheendsoftheguideways.Racewayleadareasshouldbeprovidedinthiscase(suffixE2).

1.3.3 HOLE TYPES AND HOLE PATTERNS

Guidewaysareattachedwithscrews.EGISguidewaysaresuppliedwith4holetypes(figure4).

EGISguidewaysofstandardlengthsintheMandVrangesarehardenedandpre-groundwithT15sinkholes. ByaddingESMinsertnuts,theseguidewayscanbeattachedinthesamemanneraswithathreadedhole(T03,figure5).

Theinsertnutsmustbeorderedseparatelyandstuckintothecounterbores(T13,accessories,page91).

Figure4.Holetypes

Figure5.AttachmentwithholetypeT13

Guidancesystemswithwipers:

Thenecessarycagesizecanbeselectedonthebasisofloadandrigidityparameters.

APPLICATION FEATURES 18

Withnoparticularspecifications,theholedistancesL1andL2atbothendsoftheguidewaysareofthesamesizeanddependentontheguidewaylength(symmetri-calholepattern,figure6).Guidewayswithnon-symmetricalholepatternsmayalsobesuppliedonrequest.Inthiscasethefollowingvaluesmustapply:L1≥L1min andL2≥L2min.

ParticularattentionshouldbepaidtothepositionoftheL1distance.ForthedefinitionofthepositionofL1seefigure7.

SuffixLA(L1/L2)

Determiningtheholepatterns

Numberofspacingdistances

DistancesL1andL2

Guidewayswithsymmetricalholepattern

Numberofholes

L mm Lengthofguideway

LA mm Holedistance

L1,L2 mm Distancebetweenthestartorendoftheguidewayandthenexthole

L1min, mm MinimumvalueforL1andL2L2min (Tablesdimensions)

n - Maximumpossiblespacing distances

x - Numberofholes

Figure6.Symmetrical(a)andnon-symmetrical(b)holepatternwithaseriesofholes

Figure7.PositionofdistancebetweenfirstholeandbeginningofguidewayL1

(L-2·L1min)LA

n= wholenumber

L1+L2=L-n·LA

L1=L2=(L-n·LA)/2

x=n+1

T..R

T..L


1.3.4 END PIECES AND WIPERS

Endpiecesorendpieceswithwipersholdthecageas-semblyinplacecorrectlyinthefinalstrokepositions.Twoendpiecesneedtobemountedforeachcage.Ifthisisnotpossible,partsoftheconnectingstructureshouldbeusedtoassumethefunctionoftheendpieces.

Endpiecesorwipersmustnotbeused tolimitthestroke.

Endpiecesorwipersmustnotbeallowed tocrossover(figure8)

Inspecificapplicationscenarios,e.g.withrapidaccel-erations,extremeloadsinthefinalstrokepositionsorinthecaseofalternatingpartialstrokewhichneverthelessremainconstantoverlongperiods,thecagepositioningmaynolongerbeguaranteedwithnormalendpieces.Insuchcases,itispossiblewhenwipersareusedtoassembleadditionalendpiecesbeforethewipersortosubjectthecagetopositivecontrolbyanintegratedgear/toothedrackunitasanoptimumsolution(MVZseries,page54).

Figure8.Incorrectlyassembledendpiecesorwipers


1.3.5LOADRATING,LOADCARRYINGCAPACITY

Thedynamicandstaticloadratingsareusedasareferenceforthelayoutofaflatcageguidancesystem.Theloadratingsforlinearguidancesystemswithoutrecirculatingrollingelementsaredefinedaccording totheISO14728internationalstandard.

1.3.5.1 bASIC STATIC LOAD RATING

ThebasicstaticloadratingsC0aretheloadswhichbringapermanentdeformationoftheracewaysandrollingele-mentsinatenthousandthoftherollingelementdiameter.

Static load safety factor

ThestaticloadsafetyfactorS0isthesecurityinrelationtothepermanentdeformationintherollingcontact.

S0 Staticloadsafetyfactor

C0w N Effectivestaticloadrating(page24)

P0 N Maximumstaticequivalentload

Particularattentionshouldbepaidtotheloadsafetyfactor.

AccordingtoISO14728,thestaticsafetyS0 = C0/P0mustnotfallbelowthevalueof2.

Ifstrictrequirementsapplyintermsoftherunningaccu-racyandsmoothness,thestaticloadsafetyfactorshouldnotfallbelowS0 = 3.

1.3.5.2 STATIC LOAD CARRYING CAPACITY

Thepermissiblestaticloadforaflatcaseguidancesys-temislimitedbythefollowingcharacteristics:

– Basicstaticloadratingoftheflatcageassemblies: recommendationsforS0shouldbeobserved.

– Loadcarryingcapacityoftheraceways: requiredhardnessHRC58min.

– Loadcarryingcapacityoftheconnectingstructure:theconnectingstructureisgenerallyconfiguredwithahighdegreeofrigidityandthereforesufficientstrength.

–Loadcarryingcapacityofthescrewconnection: thelayoutoftheguidewayattachmentisbasedonthescrewstrength8.8andthecorrespondingtighteningtorquetakingthestandardmaterialsfortheconnectingstructureintoaccount.Screwsofthislevelofstrengthallowforthetransferralofloadswhilstscarcelyaffec-tingtheprecisionoftheguidancesystem.

Whenscrewsofahigherstrengthcategoryareused,thetighteningtorqueaccordingtothestrengthcategory8.8shouldnotbeexceededintheinterestofaccuracy(exception:LUEsystemcounterstay,seepage73).

Itisimportanttocheckthescrewconnectionwhere S0<3whentensileand/ormomentloadsarepredo-minant.

C0w

P0S0 =


1.3.5.4 DYNAMIC LOAD CARRYING CAPACITY AND RATING LIFE

Thedynamicloadcarryingcapacityisdeterminedbythefatiguebehaviourofthebearingcomponents.Thefatigueperiod(theratinglifeinhours)isobtainedfromtheloadandthemovementspeedoftheguidancesystemaswellasthestatisticalprobabilityofdamageoccurring.

Nominalratinglife

L 105 m Nominalratinglife

Lh h Nominalratinglifeinoperatinghours

Cw N Effectivedynamicloadrating(p.24)


p - Ratinglifeexponent

Forflatcageguidancesystemswithrollers:p=10/3 Forflatcageguidancesystemswithballs:p=3

H mm Distancefromextreme strokepositions

nosz min-1 Numberofdoublestrokesperminute


AccordingtoISO14728,thedynamicequivalentloadmustnotexceedthevalueP=0.5·CW.

1666

Cw

P

pLh =

Cw

P

pL =

8.33 105

HnoszCw

P

pLh =

1.3.5.3 bASIC DYNAMIC LOAD RATING

ThebasisforthebasicdynamicloadratingCisthenominalratinglifeof100,000mdisplacementdistanceobtainedorexceededwithareliabilityof90%.

LOADRATING,LOADCARRYINGCAPACITY


q1· v1+q2·v2+...+qz·vz100

=

Equivalentloadandspeed

Thelifecalculationequationrequireaconstantloadandspeed.Ifthisisnotthecase,equivalentoperatingvaluesmaybeusedforthecalculation. (ISO281standard)

Generaldynamicequivalentload

Generaldynamicequivalentspeed

Graduallyalternatingload

Graduallyalternatingspeed

Graduallyalternatingloadandgradually alternatingspeed


p - Ratinglifeexponent:

Forflatcageguidancesystemswithrollers:p=10/3 Forflatcageguidancesystemswithballs:p=3

qi % Proportionoftotalduration

Fi N Variableload

vi m/min Variablespeed


Operatinglife

Theoperatinglifeistheactualexpectedratinglifeofaflatcageguidancesystem.Itmaydifferfromthenominalratinglife.

Potentialcausesincludewearandtearand/orfatiguedueto:

–Soiling–Insufficientlubrication–Misalignment–Movementswithminimalstrokes–Vibrationsduringdeadtime(falsebrinelling).

Theoperatinglifeofaflatcageguidancesystemcannotbecalculatedpreciselyinadvanceduetothewiderangeofinstallationandoperatingconditions.Themostreliableinformationisobtainedfromcomparisonswithsimilarinstallations.

P=p∫ v(t)·FP(t) dt/∫ v(t) dtT T

O O

1T

q1· F1+q2·F2+...+q2·Fz100

P =

LOADRATING,LOADCARRYINGCAPACITY

q1· v1 + F1·q2v2 F2+...+q2vz Fz

q1· v1+q2v2+...+q2·vzP =


1.3.5.5 EFFECTIVE LOAD RATING

ThebasicdynamicandstaticloadratingsCandC0givenforthedifferentproductsrelatetoacagewithatheoreticallengthof100mm.Thisallowsdirectcomparisonstobemadebetweentheloadcarryingcapacitiesofflatcagesofdifferentseriesanddimensions.TheeffectivedynamicandstaticloadratingsCwandC0warecalculatedaccordingtothefollowingequationsfortheeffectivecagelengths.

Forneedlerollerflatcageassemblies:

Forballflatcageassemblies:

C N Basicdynamicloadratingforacagelengthof100mm(tabledimensions)

C0 N Basicstaticloadratingforacagelengthof100mm(tabledimensions)

Cw N Effectivedynamicloadrating


LK mm Cagelength(figure9)

L1 mm Distancebetweenthefirstandlastpocketcentreandtheendofthecage(figure9)

LA mm Spacingdistanceintheflatcage(figure9,tabledimensions)

ThevaluesforC0wandCwcorrespondtotheloadratingcalculationaccordingtoISO14728

TheequationsonlyprovidepreciseresultswhenthecagelengthLkisbasedonawholenumberofrollingelementsperrow.

EquationforverificationofZ:

Z-numberofrollingelementsperrow(figure9)

Figure9.Dimensionstodeterminetheeffectiveloadrating

Cw = C LK - 2L1 + LA100

34

1 36 LK - 2L1

100 - LA

Cw = C LK - 2L1 + LA100

23

1 36 LK - 2L1

100 - LA

C0w = C0LK - 2L1 + LA

100

C0w = C0LK - 2L1 + LA

100

Z = LK - 2L1

LA+1 = wholenumber


1

0.9

0.8

0.70 5 10 15 20 25 30 35 40 45

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

070060.1

65057.8

60055.2

55052.3

50049.1

45045.3

40040.8

35035.5

30029.8

25022.2

200-

HVHRC

hardness

fH0

fH

fH0 roller

fH0 ball

fH

Thebasicloadratingsgivenforthedifferentproductsonlyapplysubjecttothefollowingrequirements:

–Racewayhardness≥HRC58(670HV)

–Centricloaddirection

Deviatingconditionsaretobetakenintoaccountusingthefollowingcorrectionfactors:

–HardnessfactorsfH0orfH

Figure10.Hardnessfactors

–Loaddirectionfactorf orf 0 Thebasicloadratingsforthedifferentproductsonlyapplyprovidedthattheloadoperatesinsymmetrywiththecageshanks( =0°).Thecorrectionfactorforotherloaddirectionscanbeobtainedfromthefigure:

Figure11.Loaddirectionfactor

Staticloadrating

C0we N Correctedeffectivestaticloadrating

f 0 - Staticloaddirectionfactor

fH0 - Statichardnessfactor

C0w N Staticloadratingfortheeffectivecagelength

Dynamicloadrating

Cwe N Correctedeffectivedynamic loadrating

f - Dynamicloaddirectionfactor

fH - Dynamichardnessfactor

Cw N Dynamicloadratingfortheeffectivecagelength

1.3.5.6 CORRECTION FACTORS FOR LOAD CARRYING CAPACITY

C0we=f 0·fH0·C0w

Cwe=f ·fH·Cw


5

4.5

4

3.5

3

2.5

2

1.5

10 0.05 0.10

0.167

0.15 0.20 0.25 0.3 0.35 0.4

Relative load eccentricity e/LK

kOF

1.3.5.7 ECCENTRIC LOAD

Inalinearguidancesystemwithoutrecirculatingrollingelements,theflatcagealwaystravelshalfthestrokeofthemobileguidewayandthusaltersitspositioninrelationtotheload.Itthereforedoesnotgenerallycarryanequalload.However,theloadratingsgivenforthedifferentproductsonlyapplywithanequalloaddistribution.

Eccentricloadwithopenlayout

Openlayout:seeapplicationfeatures(page16,figure2)Inthecaseofaneccentricload,theloadcarryingcapac-itycanbedeterminedwiththestaticequivalentcageload(figure12).

P0 N Staticequivalentload

k0F - Staticloadfactor

F N Guideloading

Figure12.Staticloadfactorforeccentricallyloadedflatcagesandopenlayout

Ifaloadeccentricityof>0.167isexceeded,onlypartoftherollingelementisloaded.Thisisextremelydetri-mentaltotheloadcarryingcapacityandrigidityoftheguidancesystem.

P0 = k0F·F

Eccentricloadwithclosedlayout

Closedlayout:seeapplicationfeatures,(page16,figure1)

Linearguidancesystemswithaclosedlayoutcancarry additionalloadsandtiltingmoments.Inthesecases,thecalculationoftheequivalentcageloadisfairlycomplex.EGISofferssupportwithcorrespondingcalculationpro-grammesonrequest(pages28to31).


Example

Inputdata

Guideways M5025andV5025

Flatcageassembly E-HW15

Basicdynamicloadratingfora C =25960N

cagelengthof100mm

Basicstaticloadratingfora C0 =88900N

cagelengthof100mm

Operatingload,functioning F =9500N

centricallyontheguidancesystem

(factorsf ,f 0,k0F=1)

Dynamicequivalentload P =9500N

Staticequivalentload P0 =9500N

Distancefromextreme H =100mm

strokepositions

Numberofdoublestrokes nosz =50min-1

perminute

Cagelength LK =300mm

Requireddata

Staticloadsafetyfactor S0

Nominalratinglife LandLh

Calculation

Verificationofnumberofrollingelementsperrow (LA,L1,dimensiontables)

Forcalculation:

Effectivestaticloadrating

StaticloadsafetyfactorSo

EffectivedynamicloadratingCw:

NominalratinglifeL:

NominalratinglifeLh

1.3.5.8 CALCULATION

Z = +1LK - 2L1LA

C0w = C0 ·LK - 2L1 + LA

100

C0w = 88900· = 264000 N297100

S0 = C0w

P0S0 = = 27.8264000

9500

Z= +1 = 66300 - 74.5

Cw =C· ·¾ 1/36

LK - 2L1 + LA100

LK - 2L1100 - LA

L =10/3

Cw

PL = =472·105

10/3602509500

LK=(Z-1) · LA+2L1=299.5mm

Cw =25960· ·¾ 1/36

295100

28895.5

= 60250 N

Lh = ·10/3

Cw

P8.33·10H·nosz

Lh = ·472=78600h8.33·10100·50


X

Y

Z Mz

My Mx

xi

yi zi

Fzi Fxi Fyi

O

Thecalculationonpages21to27canbeusedtoestab-lishaninitiallayoutforflatcageguidancesystems.Theequationsarebasedonadefinedstaticsystem.Inpractice,however,anundefinedstaticsystemisgen-erallyused.Thisdoesnotallowforsimplecalculations;inordertoobtainaprecisecalculation,thepreloadandinternalloaddistributionhavetobetakenintoaccount.TheloadcarryingcapacityandrigidityfordifferentloadscanbecalculatedusingacorrespondingEGIScalcula-tionprogramme.

Thecalculationprogrammedeterminesthefollowingdata:

–Staticloadsafetyfactor–Displacementstemmingfromtheelasticityofthebearing.

Thenon-lineardeflectionoftherollingelementsistakenintoaccountinthiscontext.Theconnectingstructureisassumedtoberigid.

Thefollowingdetailsarerequiredforthecalculationofeveryloadscenario(figure14anddatasheet,page29):

–Sizeandpositionoftheelementsoftheguidancesystem–Positionofthedriveaxis–Positionoftheloadingpointandexternalloadcomponents–Shear-freemoments–Positionofthebalancepointsandsizeofweights–Kineticvalves–Durationofparticularsteps

Thegeometryandloadscanbedescribedsimplyusingthefollowingdatasheet.Aright-handedcoordinatesystemisusedforthede-scription.Theright-handruleappliesformoments.

Positionofco-ordinateorigin:

–Carriagesincentralstrokeposition–x:centreofbearingcagelength–y:centreplaneofguideways–z:centralbetweentheguideways

Oneormorestrokepositionsdeviatingfromthecentralpositionmaybeusedforthecalculation.

Thedataenteredinthedatasheetcorrespondtotheguidancesystempresentedinfigure15asanexample.

Calculationprogramme

Figure13.Internalloaddistributioninthecaseofloadsproducedbyloadsandmoments

Figure14.Coordinatesystem


Project : Example

Guidance system : Horizontal drilling carriage

Guidance geometry Guideway size 4020Cage length LK 200 mm

Distance between rear guideway surfaces b1 145 mm

Installation layout XIStroke H 110 mm

Position of drive axis yA -‐32 mm

zA 30 mm

Load case No./ description Nr. 1 Drilling

Carriage position(s) for the calculation xB 50 mm

Speed v 3 m/min

Duration of particular step q 50 %

xi yi zi Fxi Fyi Fzi Mxi Myi Mzi

mm mm mm N N N Nmm Nmm Nmm1 195 -90 0 -1200 -20000

2 55 -40 0 800

3

4

5

6

7

8

9

10

11

12

13

14

15

Moments Point i

Description Coordinates Loads, components

Drilling tool: drilling pressure, torque

Carriage + shaft weight

Datasheet


x z

Y

A

1

2

Antrieb

x

z Y

Fx1

Mx1

1

X1

zA

//

//

Lk

2

x z

Y

X2 y2

Fy2

Y1 Fx1

Mx1 1

Antrieb

YA

x z

Y

A

1

2

Antrieb

x

z Y

Fx1

Mx1

1

X1

zA

//

//

Lk

Example:horizontaldrillingcarriage

Figure15.Geometryandloaddetails

Xlayout,internalcarriage Xlayout,externalcarriage

XI XA

OI OA

Olayout,internalcarriage Olayout,externalcarriage

Installationlayout


Drive

Drive

30

Example:horizontaldrillingcarriage

Results

Poweroncarriagedrive Fx = -1200 NResultingloadonguidancesystem: Fy = 800 N Fz = 0 N Mx = -20000 Nmm My = -36000 Nmm Mz = -82400 Nmm

Requiredpreloadpower Pv = 3050 N

Percentagerateofstaticloadcarryingcapacity C0: 2.54%

Displacementoftheguidancesystem: del y = 0.13992 µm del z = -0.00719 µm phi x = -0.00152 mrad phi y = -0.00389 mrad phi z = -0.00863 mrad

Staticloadsafetyfactor: S0 = 31.6

Displacementatpointi(µm) Nr. del ix del iy del iz

1 -0.27622 0.18561 0.04155 2 -0.77686 -1.54327 0.88915 3 -0.34527 -0.33483 0.26788

Thecalculateddisplacementsonlyincludetheeffectofthedeflectionofrollingelementsandraceways.Thedeformationoftheconnectingstructureisnottakenintoaccount.


100

90

80

70

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50

40

30

20

10

0

0

1000

2000

3000

4000

5000

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8000

9000

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00

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17'0

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Load F (N)

BallØ 9

RollerØ 9 x 9

3 needle rollersØ 3 x 9

Def

lect

ion

δ (µ

m)

F

F

F

Flatcageguidancesystemsuseneedlerollers,cylindri-calrollersorballsasload-bearingrollingelements.Needlerollersandcylindricalrollerspossessalinecontactintherollingcontactwhilstballspossessapointcontact.TheoperatingloadFcreatesanelasticdefor-mationatthecontactpointsandthereforecausestheracewaystoconvergearoundthedeflection .

Rigidityistherelationshipbetweentheload anddeformation:

Guidancesystemswithneedlerollersaresignificantlymorerigidthanthosewithcylindricalrollersgiventhesamespacerequirementduetothelargenumberofcontactlines.Therigidityofguidancesystemswithballsisconsider-ablyloweronaccountofthepointcontact(figure16).

Deformationsoftheconnectingstructure,settlementphenomena,etc.arenottakenintoaccount.Deformationcanthereforebemoresignificantinpractice.

InguidancesystemswithMandVguidewaysinaclosedlayout,therigiditycanbeincreasedbypre-loading(preloading,page34).

1.4 RIGIDITY

CL = F

Figure16.Comparisonbetweenrollingelementtypeswiththesamespacerequirement

RIGIDITY 32

Therigidityisdependentontheloadand thenumberandgeometryoftherollingelements.

Flatcageguidancesystemswithlinecontact

Flatcageguidancesystemswithpointcontact

µm Elasticdeformationatthecontactpoints,convergenceofthetworacewaylevels

K - Factorforthedeterminationof elasticdeformationdependent ofthetype(table17)

F N Operatingload

Z - Numberofrollingelementsperrow

Lw mm Rollingelementlength

CL N/µm Rigidityoftheflatcageguidancesystem

DW mm Balldiameter.

Table17:factorKforthedetermination ofelasticdeformation

CL =1/K·F0.1·Z0.9 · Lw0.8

CL =1/K·F1∕3 ·Z2∕3 · Dw1∕3

=K·(F/Z)0.9/ Lw0.8

=K·(F/Z) 2∕3 / Dw1∕3

Calculationexample

Guideway M5025andV5025Flatcageassembly E-HW15x300Operatingload F=9500NNumberofrollingelementsperrow Z=66Rollingelementlength Lw=6.8mmTypefactor(table) K=0.0822

Elasticdeformationcalculation:

=0.0822·(9500/66)0.9/6.8 0.8=1.6µm

Rigiditycalculation:

CL=1/0.0822·95000.1·660.9·6.80.8=6100N/µm

=K·(F/Z)0.9/Lw0.8

CL=1/K·F0.1·Z0.9·Lw0.8

GuidewayType FactorK GuidewayType FactorK

0.0822

0.0794

0.0426

0.8776

RIGIDITY 33

Thepreloadofflatcageguidancesystemscanbeusefulforthefollowingreasons:

–Increaseofrigidity–Improvementofrunningaccuracy–Improvementofloaddistributionandreduction ofmaximumloadontheouterrollingelements

–Increaseofpermissiblemoments

Thepreloadinfluencesthedisplacementresistanceandratinglife.

Referencevalueforthepreload:2to3%ofC0.TheoptimumpreloadforconcreteloaddatascanbedeterminedusingEGIScalculationprogrammes.

Anoptimumpreloadreducesthepossibilityofuncontrolledmovementintheflatcageassembly(cageroaming).

Inordertoguaranteethattherigidityofourlinearguidancesystemsisfullyoptimised,caremustbetakentoensurethattheconnectingstructureissufficientlyrigidandprecise.

Inthecaseofimpreciseconnectingstructuresoroneswhichcanbeeasilydeformed,angleerrorsmayoccurbetweentheracewayswhichcreateanincreasedloadattheendsoftherollingelements.

Thiswouldnotresultinincreasedrigiditybutrathertheendloadwouldreducetheoperatinglife.

1.5 PRELOAD

1.5.1 SETTING THE PRELOAD

Thepreloadcanbemeasuredandsetusingdifferentmethods:

–usingpressurescrewswithasettingtorqueaccordingtothetableonpage35

–bymeansofFRVcarriagedisplacementresistance (seebelow)

–bymeasuringthedeformationoftheconnectingstructure.

FRV N Carriagedisplacementresistance


Requirements:

–Preload2,5%C0

–Lubricatedguidancesystemwithoutoperatingload–Movementatapprox.0,05m/s

FRV = C0w

40'000

PRELOAD 34

1.5.1.1 PRESSURE SCREWS

Inthecaseofsmallloads(S0>5)theguidancesystemcanbepreloadedbymeansofpressurescrews.Asmallereffectivespancanbeobtainedbyinsertingthepressurescrews(studscrewsaccordingtoISO4026,DIN913)betweentheattachmentscrewsandattheendoftheguideway(table18,figure19).

1)Torqueforapreloadof2,5%C0

Figure19.Positionofthepressurescrews

1.5.1.2 GUIDEWAYS WITH ADJUSTING GIb

TheuseofMLguidewayswithanadjustinggibisrecom-mendedwhereahighdegreeofrigidityisrequiredorwithlargerloads(S0<5).Thisensuresthatthepreload isdistributedevenlyovertheentireguidewaylength.

Guideways Flat cage assemblyPressure screw Setting torque

Dimension Distance / mm ME1) / Nm

M/V3015 E-HW10 M4 40 0.34

M/V4020 E-HW15 M6 80 1.2

M/V5025 E-HW16 M6 80 1.8

M/V4525 E-HRW50 M6 80 1

M/V6035 E-HW20 M8 100 2.9

M/V6535 E-HRW70 M8 100 3.5

M/V7040 E-HW25 M10 100 5.7

M/V8050 E-HW30 M12 100 7.7

TABLE18.PRESSURESCREWS/SETTINGTORQUE

PRELOAD 35

LUbRICATION

1.6.1 LUbRICANTS

Greaseoroilcanbeusedaslubricants.Thechoiceoflubricationprocedureismadeonthebasisoftechnicalandeconomicconsiderations:

Advantagesoflubricationwithgrease:

–longrelubricationintervals–reducedstructuralexpenditurewhenrelubrication isnotrequired

–thickenerinthegreasecreatesemergency operationfeatures

–supporttotheseal

Advantagesoflubricationwithoil:

–excellentlubricationapplication–dirtisflushedout–heatisdissipated

Flatcageguidancesystemsonlyrequireminimallubrica-tion.Theyaresuppliedwithapreservative.Thepreserv-ativeiscompatiblewithgreaseandoils.

Flatcageguidancesystemsaregenerallyoperatedinareasofmixedfriction.Forthisreason,dopedlubricantswithhigh-pressureadditivesshouldbeused(codeletterPaccordingtoDIN51502).

Coolinglubricantsmustnotbeusedastheythinoutthelubricantsandcancausecorrosion.Lubricantswithsolidadditivesmustnotbeused.

1.6.2 LUbRICATING WITH GREASE

Generalrecommendation:Lithium-soap,EP-dopedgreasewithmineraloilbase.SpecificationaccordingtoDIN51825:KP2N-20Baseoilviscosity:ISO-VG150toISP-VG220.

S0<8essentialwithlargeloads EP-dopedgreaseswithbaseoilviscosity ofISO-VG220shouldbeused.

1.6.2.1 PRIMARY OPERATION AND GREASE QUANTITY

Theguidancesystemmustbeprotectedagainstsoilingbeforeandduringassembly.

Withoutrelubricationequipment:Forthefirstlubricationapplication,spreadthegreasequantityaccordingtothetableoverbothsidesinthecagepocketsandthinlylubricatetheguidewayraceways.

Withrelubricationequipment:Firstfillthefeedlinewithgreaseandthinlylubricatetheraceways.Thenassembletheguidancesystemandfeedinthegreaseaccordingtothetable.Movetheguidesys-temseveraltimesduringthisprocedureovertheentirestroketoensurethatthegreaseisevenlydistributed.

TABLE20.GREASEQUANTITIESFORPRIMARYLUBRICATION(GUIDELINES)

Flat cage/SeriesGrease quantity for primary lubricationg/100mmcagelength1)

E-HW 10 0.6

E-HW 152)/E-FFW2025/E-FF2025ZW 0.6

E-HW 202)/E-FFW2535/E-FF2535ZW 1

E-HW 252)/E-FFW3045/E-FF3045ZW 1.3

E-HW 302)/E-FFW3555/E-FF3555ZW 2.1

E-HRW 50 1.5

E-HRW 70 3.5

E-HRW 100 6.6

E-H 102)/E-FF2010 0.3

E-H 152)/E-FF2515 0.5

E-H 202)/E-FF3020 0.7

E-H 252)/E-FF3525 1.1

1)Incaseofhighspeedsonlyabout25%ofthequantity

2)Withflatcageassemblieswithdampingabout80%ofthequantity

1.6 LUbRICATION

Machineperformanceisinfluencedconsiderablybytheinstalledflatcageguidancesystems.Lubricationplaysanimportantroleinthiscontext.

Thelubricantminimisesfrictionandwearintherollingcontactandatthebearingpointsbetweenthecageandtheroll-ingelements.Lubricantsalsoprotectagainstcorrosionandofferasupporttotheseal.

36

LUbRICATION

1.6.2.2 RELUbRICATION

Relubricationshouldbecarriedoutatleastonceayearwithapproximately50%ofthegreasequantityusedfortheprimarylubrication.Morefrequentrelubricationwithpartialquantitiesisrecommended.Theoptimumtimeandquantitiescanonlybedeterminedunderoperatingconditionsandwithanadequateobservationperiod.

1.6.3 LUbRICATING WITH OIL

Generalrecommendation:CLPlubricatingoilsaccordingtoDIN51517and HLPaccordingtoDIN51524 Operatingtemperaturesfrom0°Cto+70°C:ViscositybetweenISO-VG32andISO-VG68

Lowtemperaturerange:ViscosityISO-VG10toISO-VG22

CGLPracewayoilscanbeuseduptoISO-VG220

Oilisfedinbyoilimpulseordropfeed.Pneumaticoillubricationisrecommendedforworkingconditionswithasignificantriskofsoiling.Theslightexcesspressureoccurringintheguidancesystemenhancestheeffective-nessoftheexistingseals.

Itisimportanttoobservethelayout(figure21)whenfeedinginthelubricatingoilsothatthelubricantcanreachalltherollingelementrows.

Iftheoilmanufacturerhasnotprovidedanydetailsorexperiences,thebehaviourofthelubricatingoilmustbeverifiedunderoperatingconditionsincomparisonwiththematerialsusedintheguidancesystem. Mineraloilscangenerallybemixedtogether.

However,syntheticoilsmustbeverifiedinrelationtomiscibilityandcompatibility. Incaseofdoubt,contactthelubricantsupplier.

Primary operationOiltheguidancesystemandprotectitagainstsoilingduringassembly.

Figure21.Layouts

37

FRICTION

1.7 FRICTION

Asisthecaseofallrollerbearings,flatcageguidancesystemshavevirtuallylowfrictionduringthestart-uppro-cessandinmotion.Thismeansthatno“stick-slipeffect”isproducedcomparedwithslidingfriction.

Friction(displacementresistanceFR)ismadeupofthefollowingcomponentswithdifferentdependencies:

Friction component Dependency

RollingfrictionFR1 Load/lubricationconditionLubricantfriction FR0 Cagedimensions Strokespeed LubricantWiperfriction FRA Configuration,preload

Load-dependentrollingfrictionFR1

FR1 N Load-dependentfrictioncomponent

F N Flatcageload

µ - Frictioncoefficient

Withlubrication,thefrictioncoefficientamountsto0.00035forflatcageassemblies0.00050forangledflatcageassemblies

LubricantfrictionFR0

FR0 N Lubricantfrictioncomponent indisplacementfriction

f0 - Typefactor

f0=85forflatcageassemblies

f0=120forangledflatcage assemblies

ν mm2s-1 Lubricantviscosityatoperatingtemperature

Viscosityofbaseoilwithgreaselubrication

v m/min Speed

B1 mm Cagewidth

LK mm Bearingcagelength

Primarylubricationorrelubricationproducetemporarilyraisedlubricationfriction.

WiperfrictionFRA

Thewiperfrictionarisefromthelengthofthewiperlipandthelippreload.Thiscanbeinfluencedconsiderablybythewiperassembly.

Referencevalueperwiper:

ProfileshapeM/V FRA=0.20·B

ProfileshapeJ/S FRA=0.15·B

FRA N Frictionperwiper

B mm Guidewaywidth

FR = FR1 + FR0 + FRA

FR1=µ·F

FR0=f0·(ν·v)2/3·B1· Lk 1/3

·10-6

38

PROTECTION AGAINST SOILING– OPERATING LIMITS

1.8 PROTECTION AGAINST SOILING

Inordertoensurethatflatcageguidancesystemsoperatesafelyitisextremelyimportanttoprotectthemagainstsoiling. Inmanycases,wiperswillsufficetokeeptherace-waysclean.Theymustbepositionedontheracewaysthroughouttheentiremovement.

CompletesolutionsforMandVguidewayswithstandardwipersandintegratedlongitudinalseals (suffix..ZZ,..PP)orsealsintheconnectingstructuremaybeusedformoredemandingcases.

1.9 OPERATING LIMITS

Operating temperatures

Linearguidancesystemswithmetallicflatcagesare suitableforcontinuoustemperaturesofupto+150°c. Suitablelubricantsmustbeusedinthiscase. Theguidewaysmustbeheat-stabilisedathigheroperat-ingtemperatures(furtherinformationcanbeobtainedfromEGIS).

Linearguidancesystemswithflatcagesmadefrom plasticaresuitablefortemperaturesofupto+120°C.

Anoperatingtemperatureof+100°Cmustnotbe exceededwhenusingwipers.

Acceleration

Ifhighaccelerationsarerecordedinalinearguidancesystems,EGISlightmetalflatcagesareparticularlyrecommendedduetotheirreducedweight.Theycanbeusedforaccelerationsupto250m/s2.

39

INSTALLATION GUIDELINES

1.10 INSTALLATION GUIDELINES

1.10.1 PRECISION OF THE CONNECTING STRUCTURE

Theprecisionofthelocatingsurfaceshasadecisiveinfluenceontheaccuracyandsmoothrunningofalinearguidancesystem.

Perpendicularityandparallelism

Therightanglebetweenthelocatingsurfacesmustbemaintainedprecisely(permissibleerror±0,3mrad)

Parallelismerrorsonthelocatingsurfacesmustnotbesignificantlygreaterthanthecorrespondingtolerances oftheguideways.

Heightvariation

Inordertoensurethattheloadisdistributedasequallyaspossibleoverthelengthoftherollingelement,theheightvariationΔhshouldnotbeexceeded(figures22and23).

Permissibleheightvariationforneedleroller flatcageassembliesΔh<0,1·bPermissibleheightvariationforcylinderroller flatcageassembliesΔh<0,3·b

Δh µm Permissibleheightvariation

b mm Distancebetweenguidance systemcentres

Surface

Noparticulardemandsareplacedonthesurfacerough-nessofthelocatingsurfacesfromanoperationalpointofview.Inordertomaintainahighlevelofformprecisionandasuitablemeasurementbasis,itisneverthelessrecommendedthatthesurfacesshouldbeprecisionmachinedandtheholescarefullydeburred.

0.003/10

Figure22.Heightvariationwithaclosedlayout

Figure23.Equalisationoftheheightvariationwithanopenlayoutwithaninsertplate

40

1.1

3

1.1 1.2 1.2 1.3 1.3

1.4 1.4 1.5 1.5 1.6 1.6

3

Pair

Pair


1.10.2 ASSEMbLY INSTRUCTIONS

1.10.2.1 PRIOR TO INSTALLATION

Guidewaysarepreservedanddeliveredpackedinanticorrosionpaper.Partsarematchedbydimensions,packedinsetsandnumberedaccordingly.

Numbering:1 . 2

Unpackguidewaysshortlybeforeassemblyandremovethecorrosionprotectionwhereapplicable.Lightoilingprotectstheguidewaysagainstcorrosionduringassem-bly.Positionpartswithidenticalsetnumber.

Particularattentionshouldbepaidtothefollowingpoints:

–Guidewayswiththesamesetnumbershouldbein-sertedinthesameguidancesystemduringassembly.

–Attentionshouldbepaidtothejointnumberatthejoints.–TheMandVguidewaysmayhavedifferentsetnumbers intheclosedlayout(figure24).

Figure24.Numberingofsingleandmulti-partguideways

setnumber Jointnumber

41


1.10.2.2 CLOSED LAYOUT

Guidewayswhicharepackedinpairsmustalwaysbeinstalledinthesameguidancesystem.

Theguidewaylocatingfacesareunlabelledandcom-prisesignificantchamfer.

Assembletheguidewaypairwhichdoesnotrequireadjustment(1)(figure25).Clamptheguidewaysagainsttherearlocatingfaceandcheckforparallel-ismbeforetighteningthefixingscrews(figure26).

Assemblethestationaryopposingguideway(2)

Attachtheadjustingguideway(3),onlytighteningscrewsslightlysothattheguidewaycanstillmove.

Insertguidancesystemlengthways,insertcageassem-bliesbetweentheguidewaysandpositionsothattheydonotlieagainsttheendpiecesinthefinalpositions.

Preloadadjustingguideway(3)withpressurescrews(4)(figure27)(withgibforMLguideways) (figures29to31).

Initiallypreloadaroundtwicetherequiredvalueinordertoanticipatesettling.Releaseandthensetthepreloadtotherequiredvalue.Tightenfixingscrews.Screwonwipersorendpieces.

Whenpreloadingwithpressurescrews,adjustthelat-terintwostepstotherequiredtighteningtorqueandtightenwithacounternutorscrewlockingdevice.

Onlytightenpressurescrewswhicharesupported bytheflatcageassembly(seefigure28).

Figure27.Preload.

Figure28.Preloadadjustment.

Figure26.Parallelismverification

Figure25.Assembly.

42


IfthepreloadforceisadjustedoverML-guidewayswithanadjustinggib,thefollowingprocedureshouldbefollowed:pushtheadjustinggibundertheMLguidewayandadjusttheguidancesystemfreefromclearance(figure29).Shortentheunhardenedgibontheadjustmentsideoftheguidewaysothatitisapproximately3mmshortofthefrontsideoftheguideway(figure29).Shortentheoppo-sitesideofthegibflushwiththeendoftheguideway.

Preloadthegibbyinsertingasoftbolt(figure30). A1mmdisplacementofthegibproducesaheight adjustmentof15µm.

Aftersetting,attachtheadjustinggibtothefrontsideoftheguidewaywiththehexagonalsocketscrew(figure31).

Seechapterentitled“Settingthepreload”toverifythepreload

Figure29.Insertingandshorteningtheadjustinggib

Figure30.Settingthepreload

Figure31.Attachingtheadjustinggib

1.10.2.3 OPEN LAYOUT

Aftertheprecisionofthelocatingfaceshasbeenchecked,particularlytheheightvariation(seechapterontheprecisionoftheconnectingparts),theguidewayscanbeassembledintherequiredsequence.

Guidewayswhicharelabelledinsets(4SXmatching)mustbeassembledaccordingly.

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