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Citation: Härtel, M.; Duc, L.L.; Grund,
T.; Suchý, L.; Lampke, T.; Hasse, A.
Experimental and FE Investigation on
the Influence of Impact Load on the
Moment Transmission of Smooth
Shaft–Hub Connections. Appl. Sci.
2024,14, 8916. https://doi.org/
10.3390/app14198916
Academic Editors: Krzysztof Grzelak,
Robert Kosturek and Tomasz ´
Sl˛ezak
Received: 11 September 2024
Revised: 24 September 2024
Accepted: 26 September 2024
Published: 3 October 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Experimental and FE Investigation on the Influence of
Impact Load on the Moment Transmission of Smooth
Shaft–Hub Connections
Markus Härtel 1, * , Loc Le Duc 2, * , Thomas Grund 1, Lukáš Suchý2, Thomas Lampke 1and
Alexander Hasse 2
1Materials and Surface Engineering Group, Institute of Materials Science and Engineering,
Chemnitz University of Technology, Erfenschlager Str. 73, 09125 Chemnitz, Germany;
thomas.grund@mb.tu-chemnitz.de (T.G.); thomas.lampke@mb.tu-chemnitz.de (T.L.)
2Professorship Machine Elements and Product Development, Chemnitz University of Technology,
09107 Chemnitz, Germany; lukas.suchy@mb.tu-chemnitz.de (L.S.);
alexander.hasse@mb.tu-chemnitz.de (A.H.)
*Correspondence: markus.haertel@mb.tu-chemnitz.de (M.H.); loc.le-duc@mb.tu-chemnitz.de (L.L.D.)
Featured Application: Safety calculation for shaft–hub connections.
Abstract: A well-known phenomenon in machinery systems is the easing of a blocked connection
of mechanical parts after an impact hit close to the connection. Such impact hits may also arise
in shaft–hub connections such as gears, crankshafts, or other parts. The objective of this study is
to investigate the influence of local impact loads on the transmittable torque of smooth shaft–hub
connections. In a specially designed test rig, it was demonstrated that the transmittable torque of
the shaft–hub connection is reduced as a consequence of the impact, resulting in a reduction in
the frictional force and slippage of the hub. Increasing the impact load leads to an increase in the
reduction in the frictional force as well as the slippage and reduces the transmittable torque. By
carrying out a modal analysis of the relevant parts and FE simulations of the impact, two possible
reasons have been identified: (i) the impact load excites a vibration mode in the connection which
reduces the frictional force and the transmittable torque; and (ii) the impact causes local deformation
of the shaft, which results in local slip.
Keywords: impact investigations; shaft–hub connection; FE simulation; modal analysis; failure
1. Introduction
Many complex products are manufactured through complex joining techniques, which
often exhibit functional characteristics within the assembled structure. In the field of
mechanical engineering, joining by forming is a conventional method [
1
,
2
] that is frequently
employed in conjunction with other techniques such as welding or brazing [
3
]. Press-fit
connections are particularly prevalent in shaft–hub connections [
4
–
8
]. With the help of
hydroforming [
9
] or shrinkage connections [
10
] with warmer hubs and colder connections,
a frictional connection is adjusted between the two components. In typical applications,
more often, several hubs are adjusted on a single shaft. This is exemplified in gear boxes and
crank or rotor shafts [
1
,
4
,
11
]. Typically, the safety calculation for the transmittable torque of
shaft–hub connections is conducted in accordance with the specifications outlined in DIN
7190 [
12
]. Furthermore, it is well-documented that materials exhibit disparate behaviors
when subjected to varying strain rates: some display increased strength [
13
], some become
brittle [
14
], and some even generate acoustic emissions during the loading process [
15
].
Complex assemblies may also result in the generation of complex and superimposed loads.
For instance, vibrations emanating from one component can have a significant effect on the
bearing [
16
–
18
]. This may lead to failure [
17
] in contact zones, but it may also overcome a
Appl. Sci. 2024,14, 8916. https://doi.org/10.3390/app14198916 https://www.mdpi.com/journal/applsci
Appl. Sci. 2024,14, 8916 2 of 12
disadvantage of press-fit connections: their non-destructive disassembly (in terms of not
cutting both joining partners) [
19
]. In addition to low-frequency vibration-wave-assisted
disassembly [
19
], it is also common practice to loosen up blocked mechanical parts caused
by fretting [
20
–
22
] with an impact hit close to the connection. Similar effects are also
described in so-called Impact Drive Mechanisms (IDMs), which deal with the frictional
force and stick–slip in mechanical systems during the interactions of the surfaces and
the near regions of two materials [
23
,
24
], mostly in piezoelectric materials. Furthermore,
somehow, similar effects were investigated in the classical tribological research area. In
several papers, other groups investigated the influence of tangential vibration at low [
25
],
high [
26
,
27
], and very high frequencies [
28
]. At all frequency levels, specific values were
found where the friction between both tribological partners was intensively reduced due
to this transverse vibration. In [
26
,
27
], computational models were developed that were
able to reproduce the effects numerically. In [
29
], it was also found that even very low
frequencies may influence failures under cycling load in what the authors called a
creep–slip
phenomenon. In a review work by Plooij et al. [
30
], three different locking mechanisms
(to avoid such reduction in the frictional forces) were introduced: mechanical locking,
friction-based locking, and singularity locking. The prevention of failure in the relative
bolt connections is the focus of the work of [
31
]. The detailed experimental and numerical
work comprises giving recommendations on the design features of threaded connections
with collet nuts to prevent unintentional self-unscrewing [
31
]. In a more recent work, the
same group proposed the concept of shell dampers with a shock absorber. They used the
same mechanism backwards while filler material in the damper transformed longitudinal
displacements of a piston into radial deformations of the shell so that no vibrational load
may reduce friction in the connection, and to prevent unintentional self-unscrewing [32].
However, understanding the influence of single impact loads without permanent
vibration on the transmittable torque of shaft–hub connections is so far not investigated.
The mechanism described above may help to understand the result. In any case, it is
essential to investigate this phenomenon for predicting and mitigating potential failures in
mechanical systems.
The object of this study is to examine the influence of local impact loads on the trans-
mittable torque of smooth shaft–hub connections. To the best of the authors’ knowledge,
no such study has yet been carried out. In a specially designed test rig, it was demon-
strated that the transmittable static torque of the shaft–hub connection is reduced as a
consequence of the impact, resulting in a reduction in the frictional force and the slippage
of the hub: press fits with the same interference fit will start to rotate at a lower torque
than they would withstand in a static torsion test rig without an impact load. Additionally,
this study aims to identify the underlying mechanisms that contribute to the observed
changes in performance through modal analysis and finite element (FE) simulations; the
influence of the ball mass, impact velocity, preload, and distance between the ball and hub
is systematically studied. The findings are expected to provide valuable insights into the
design and maintenance of mechanical connections, enhancing the reliability and longevity
of machinery systems.
2. Models and Methods
In this study, the base material of the shaft is a low-alloyed construction steel, 1.0580,
according to [
33
]. The base material of the hub is a heat-treated medium alloy cold work
tool steel, 1.3505, according to [
34
]. A detailed microstructural material analysis as in [
35
]
is not performed in this paper but might be the content of future work. The hollow shaft
and hub were thermally joined. There is a smooth connection between the joining parts.
The interference fit of the shaft–hub connection is approximately 21 µm.
In order to investigate the possible phenomena during the impact load, a test rig was
developed, which is shown in Figure 1. The torque is applied in the shaft by a bolt, which
introduces a force on a lever of a defined length. The rotation forces the hub to press against
a part of the frame. This leads to a preload torque of the shaft–hub connection. In order to
Appl. Sci. 2024,14, 8916 3 of 12
determine the preloaded torque, the force is measured via a load cell (5
kN
, A. S. T. GmbH,
Dresden, Germany). By multiplying the measured force with the length of the lever, the
preloaded torque can be calculated. It is important to note that the preload torque must
not reach the static transmittable torque of the connection. A mass is then dropped from
a height at a defined position. The mass falls perpendicularly to the frame on the shaft
(not the hub) to minimize any further torque load on the shaft–hub connection that may
arise from the introduced impulse. Please note that the test rig also obtains a bearing frame
to stabilize the shaft–hub connection and avoid effects from the bending of the shaft. A
marker is placed on the shaft and hub to detect any slippage of the hub. The slippage of
the hub is indicated by the markers moving in relation to each other.
Appl.Sci.2024,14,xFORPEERREVIEW3of13
introducesaforceonaleverofadefinedlength.Therotationforcesthehubtopress
againstapartoftheframe.Thisleadstoapreloadtorqueoftheshaft–hubconnection.In
ordertodeterminethepreloadedtorque,theforceismeasuredviaaloadcell(5 kN,A.S.
T.GmbH,Dresden,Germany).Bymultiplyingthemeasuredforcewiththelengthofthe
lever,thepreloadedtorquecanbecalculated.Itisimportanttonotethatthepreload
torquemustnotreachthestatictransmiabletorqueoftheconnection.Amassisthen
droppedfromaheightatadefinedposition.Themassfallsperpendicularlytotheframe
ontheshaft(notthehub)tominimizeanyfurthertorqueloadontheshaft–hubconnection
thatmayarisefromtheintroducedimpulse.Pleasenotethatthetestrigalsoobtainsa
bearingframetostabilizetheshaft–hubconnectionandavoideffectsfromthebendingof
theshaft.Amarkerisplacedontheshaftandhubtodetectanyslippageofthehub.The
slippageofthehubisindicatedbythemarkersmovinginrelationtoeachother.
Figure1.Experimentalsetupfortheimpacttestingofthepreloadedhubs.Withthehelpofthebolt,
theleveristurned(thelengthoftheleverisknown).Theforce,generatedbypressingtheboltonto
theloadcell,exertsatorque𝑀
,becausethehubislocked.Aspecificmassisdroppedfroma
definedheightviaanotherhollowshaft.Thatresultsindifferentimpactenergiesdependingonthe
heightofdropping.
Theimpactofthemassinducesanoscillationwhichthenleadstothestimulationof
theconnectionataspecificfrequency.Asaresult,thefrictionalforceandthecontact
pressureintheconnectionisreducedlocally[23,26,27,31]andthetransmiabletorqueof
theshaft–hubconnectionistemporarilyreduced.Simulativeinvestigationswere
conductedalongsidetheexperimentalteststoverifythisassumption.Thesimulations
wereperformedwiththesoftwareAbaqus™2019(Co.Simulia,Vélizy-Villacoublay,
France)andthegeneralworkof[36]wastakenintoaccount.Linearhexahedralelements
oftypeC3D8Rwithreducedintegrationwereusedinallsimulations.
Modalanalyseswereconductedtodeterminethenaturalfrequenciesandmode
shapes.Ascontactsareunaccountable,theshaft–hubconnectionismodelledasa
monolithicstructureinthesimulationmodel.
Subsequently,theidentifiednaturalfrequencieswereemployedinafrequency
responseanalysis.Inordertosimulatecontactpressureaccurately,theshaftandthehub
aredefinedastwodistinctpartswithdifferentmaterialproperties.Dependingonthe
stimulatedeigenmodes,theradialstressbetweentheshaftandthehubcanbereduced.
Figure 1. Experimental setup for the impact testing of the preloaded hubs. With the help of the bolt,
the lever is turned (the length of the lever is known). The force, generated by pressing the bolt onto
the load cell, exerts a torque
Mt
, because the hub is locked. A specific mass is dropped from a defined
height via another hollow shaft. That results in different impact energies depending on the height
of dropping.
The impact of the mass induces an oscillation which then leads to the stimulation
of the connection at a specific frequency. As a result, the frictional force and the contact
pressure in the connection is reduced locally [
23
,
26
,
27
,
31
] and the transmittable torque of
the shaft–hub connection is temporarily reduced. Simulative investigations were conducted
alongside the experimental tests to verify this assumption. The simulations were performed
with the software Abaqus™ 2019 (Co. Simulia, Vélizy-Villacoublay, France) and the general
work of [
36
] was taken into account. Linear hexahedral elements of type C3D8R with
reduced integration were used in all simulations.
Modal analyses were conducted to determine the natural frequencies and mode shapes.
As contacts are unaccountable, the shaft–hub connection is modelled as a monolithic
structure in the simulation model.
Subsequently, the identified natural frequencies were employed in a frequency re-
sponse analysis. In order to simulate contact pressure accurately, the shaft and the hub
are defined as two distinct parts with different material properties. Depending on the
stimulated eigenmodes, the radial stress between the shaft and the hub can be reduced.
These radial stress reductions indicate the changing of the real contact pressure in a
shaft–hub connection.
Appl. Sci. 2024,14, 8916 4 of 12
In addition to the modal analysis, the experimental test setup is numerically evaluated.
The geometry and boundary conditions in the simulation are based on the test setup, which
is shown in Figure 2.
Appl.Sci.2024,14,xFORPEERREVIEW4of13
Theseradialstressreductionsindicatethechangingoftherealcontactpressureinashaft–
hubconnection.
Inadditiontothemodalanalysis,theexperimentaltestsetupisnumerically
evaluated.Thegeometryandboundaryconditionsinthesimulationarebasedonthetest
setup,whichisshowninFigure2.
Figure2.Modellingoftheshaft–hubconnectionintheFEsoftwareAbaqus™.Themeshforthe
simulationconsistsoflinearhexahedralelements(C3D8R).
Theimpactofthemassontheshaftcanproduceaslipzoneinthecontact,inaddition
tothevibrationmodes.Thisslipzonetemporarilyreducesthetransmiabletorque.To
testthisphenomenon,thegivengeometrydataandparameterswereusedtosimulatethe
testsequenceinAbaqus™.Thesimulationmodelconsistsofahollowshaftonwhicha
hubhasbeenmountedwithaninterferencefit.Theimpactisintroducedbyaball(point
contact)—seeFigure3.Thepreloadedtorqueontheshaft–hubconnectionisdefinedviaa
virtualspringwithaspringstiffnessof𝐷270,000 N mm
⁄.Theelementnodesofthe
twoareas,markedinred,areeachlinkedtothevirtualpointsRP1andRP2.Thisallows
theelementnodestobecontrolledviatheaforementionedvirtualpoints.Accordingto
DIN7190[8],thecoefficientoffrictioninthecontactcanbeassumedas𝜇0.2.The
component’smeshingisdevelopedaccordingtothematchingmeshstrategy,inwhichall
thecontactnodesbetweenthehubandtheshaftarecoincident.
Figure3.Simulationdetailsoftheimpactintroductionbytheballasapointcontact.Thepreloaded
torqueisdefinedasavirtualspring.Thereferencepointsforthedefinitionofboundaryconditions
aremarkedasvirtualpointsRP1andRP2.
Inthesimulationmodel,alltranslationaldegreesoffreedom𝑈andtherotational
degreesoffreedom𝑈
areconstrainedatRP2oftheshaft.Conversely,thetranslational
𝑈
,𝑈
androtationaldegreesoffreedom𝑈
,𝑈
arerestrictedattheotherendofthe
shaft—seeFigure4.Thevirtualspringiscompressedbyadefineddistance𝑈
inthe𝑈
direction,which,inturn,twiststheshaft.ThisleadstoareactionmomentinRP2.Theball
Figure 2. Modelling of the shaft–hub connection in the FE software Abaqus™. The mesh for the
simulation consists of linear hexahedral elements (C3D8R).
The impact of the mass on the shaft can produce a slip zone in the contact, in addition
to the vibration modes. This slip zone temporarily reduces the transmittable torque. To
test this phenomenon, the given geometry data and parameters were used to simulate the
test sequence in Abaqus™. The simulation model consists of a hollow shaft on which a
hub has been mounted with an interference fit. The impact is introduced by a ball (point
contact)—see Figure 3. The preloaded torque on the shaft–hub connection is defined via
a virtual spring with a spring stiffness of
D=
270, 000
N/mm
. The element nodes of the
two areas, marked in red, are each linked to the virtual points RP1 and RP2. This allows
the element nodes to be controlled via the aforementioned virtual points. According to
DIN 7190 [
8
], the coefficient of friction in the contact can be assumed as
µ=
0.2. The
component’s meshing is developed according to the matching mesh strategy, in which all
the contact nodes between the hub and the shaft are coincident.
Appl.Sci.2024,14,xFORPEERREVIEW4of13
Theseradialstressreductionsindicatethechangingoftherealcontactpressureinashaft–
hubconnection.
Inadditiontothemodalanalysis,theexperimentaltestsetupisnumerically
evaluated.Thegeometryandboundaryconditionsinthesimulationarebasedonthetest
setup,whichisshowninFigure2.
Figure2.Modellingoftheshaft–hubconnectionintheFEsoftwareAbaqus™.Themeshforthe
simulationconsistsoflinearhexahedralelements(C3D8R).
Theimpactofthemassontheshaftcanproduceaslipzoneinthecontact,inaddition
tothevibrationmodes.Thisslipzonetemporarilyreducesthetransmiabletorque.To
testthisphenomenon,thegivengeometrydataandparameterswereusedtosimulatethe
testsequenceinAbaqus™.Thesimulationmodelconsistsofahollowshaftonwhicha
hubhasbeenmountedwithaninterferencefit.Theimpactisintroducedbyaball(point
contact)—seeFigure3.Thepreloadedtorqueontheshaft–hubconnectionisdefinedviaa
virtualspringwithaspringstiffnessof𝐷270,000 N mm
⁄.Theelementnodesofthe
twoareas,markedinred,areeachlinkedtothevirtualpointsRP1andRP2.Thisallows
theelementnodestobecontrolledviatheaforementionedvirtualpoints.Accordingto
DIN7190[8],thecoefficientoffrictioninthecontactcanbeassumedas𝜇0.2.The
component’smeshingisdevelopedaccordingtothematchingmeshstrategy,inwhichall
thecontactnodesbetweenthehubandtheshaftarecoincident.
Figure3.Simulationdetailsoftheimpactintroductionbytheballasapointcontact.Thepreloaded
torqueisdefinedasavirtualspring.Thereferencepointsforthedefinitionofboundaryconditions
aremarkedasvirtualpointsRP1andRP2.
Inthesimulationmodel,alltranslationaldegreesoffreedom𝑈andtherotational
degreesoffreedom𝑈
areconstrainedatRP2oftheshaft.Conversely,thetranslational
𝑈
,𝑈
androtationaldegreesoffreedom𝑈
,𝑈
arerestrictedattheotherendofthe
shaft—seeFigure4.Thevirtualspringiscompressedbyadefineddistance𝑈
inthe𝑈
direction,which,inturn,twiststheshaft.ThisleadstoareactionmomentinRP2.Theball
Figure 3. Simulation details of the impact introduction by the ball as a point contact. The preloaded
torque is defined as a virtual spring. The reference points for the definition of boundary conditions
are marked as virtual points RP1 and RP2.
In the simulation model, all translational degrees of freedom
U
and the rotational
degrees of freedom
UR
are constrained at RP2 of the shaft. Conversely, the translational
UX
,
UY
and rotational degrees of freedom
URX
,
URY
are restricted at the other end of the
shaft—see Figure 4. The virtual spring is compressed by a defined distance
UF
in the
UX
direction, which, in turn, twists the shaft. This leads to a reaction moment in RP2. The ball
drops onto the shaft at a defined speed
v
. If the hub will slip as the result of the impact
of the ball, the compressed spring relaxes. Consequently, the reaction moment in RP2
decreases in a manner analogous to that observation in the experiment—see Figure 4.
Appl. Sci. 2024,14, 8916 5 of 12
Appl.Sci.2024,14,xFORPEERREVIEW5of13
dropsontotheshaftatadefinedspeed𝑣.Ifthehubwillslipastheresultoftheimpactof
theball,thecompressedspringrelaxes.Consequently,thereactionmomentinRP2
decreasesinamanneranalogoustothatobservationintheexperiment—seeFigure4.
Figure4.Simulationsetupforalldegreesoffreedomattherelevantpointsandallappliedvectors
forthesimulation.
3.ResultsandDiscussion
Thefirstexperimentalserieswerecarriedouttodeterminethetransmiabletorque
oftheconnectionwithouttheinfluenceofimpulse.Theinterferencefitofallanalyzed
shaft–hubconnectionsisapproximately21µm.Aboltisusedtosteadilyincreasethe
torqueuntilitsuddenlydropsasthehubslips,whichisshowninFigure5.Twodifferent
hubsweretested.Themaximumtransmiabletorqueforthefirsthub(orange)is170 Nm
and,forthesecondhub(blue),150 Nm.Afterthefirstslip,thehubshavebeenfurther
loaded.Thetransmiabletorqueafterthefirstslippagedropsforbothhubsto
approximately125 Nm.Attheendoftheexperiment,theleverreturnstotheinitial
positionandthetorquedropstozero.Itcanbeassumedthatthereductioninthefrictional
forceandaccompaniedslippagecausethedamagetothecontactsurfacebetweentheshaft
andthehub[20,22]suchasfreing,whichcanleadtoachangeinthecoefficientoffriction
andtheresultingtransmiabletorque.
Figure5.Experimentalresultsofthestatictorquetestofdifferenthubs(blueandorangelines).The
connectionsinitiallytransmit170Nmand150Nm,followedbyadropandacertainstabilizationof
thetransmittabletorqueduetothelocaldamageofthecontactsurfacebetweentheshaftandthehub.
Figure6displaystheresultsforthesecondexperimentalseries.Thepreloadtorque
variesbetween110 Nmand115 Nm,belowthepreviouslydeterminedlimit.Theimpact
0
50
100
150
200
0 200 400 600 800
TorqueM
stat
/Nm
Testduration/s
hub-01
hub-02
Figure 4. Simulation setup for all degrees of freedom at the relevant points and all applied vectors for
the simulation.
3. Results and Discussion
The first experimental series were carried out to determine the transmittable torque
of the connection without the influence of impulse. The interference fit of all analyzed
shaft–hub
connections is approximately 21
µ
m. A bolt is used to steadily increase the torque
until it suddenly drops as the hub slips, which is shown in Figure 5. Two different hubs
were tested. The maximum transmittable torque for the first hub (orange) is 170
Nm
and,
for the second hub (blue), 150
Nm
. After the first slip, the hubs have been further loaded.
The transmittable torque after the first slippage drops for both hubs to approximately
125
Nm
. At the end of the experiment, the lever returns to the initial position and the
torque drops to zero. It can be assumed that the reduction in the frictional force and
accompanied slippage cause the damage to the contact surface between the shaft and the
hub [
20
,
22
] such as fretting, which can lead to a change in the coefficient of friction and the
resulting transmittable torque.
Appl.Sci.2024,14,xFORPEERREVIEW5of13
dropsontotheshaftatadefinedspeed𝑣.Ifthehubwillslipastheresultoftheimpactof
theball,thecompressedspringrelaxes.Consequently,thereactionmomentinRP2
decreasesinamanneranalogoustothatobservationintheexperiment—seeFigure4.
Figure4.Simulationsetupforalldegreesoffreedomattherelevantpointsandallappliedvectors
forthesimulation.
3.ResultsandDiscussion
Thefirstexperimentalserieswerecarriedouttodeterminethetransmiabletorque
oftheconnectionwithouttheinfluenceofimpulse.Theinterferencefitofallanalyzed
shaft–hubconnectionsisapproximately21µm.Aboltisusedtosteadilyincreasethe
torqueuntilitsuddenlydropsasthehubslips,whichisshowninFigure5.Twodifferent
hubsweretested.Themaximumtransmiabletorqueforthefirsthub(orange)is170 Nm
and,forthesecondhub(blue),150 Nm.Afterthefirstslip,thehubshavebeenfurther
loaded.Thetransmiabletorqueafterthefirstslippagedropsforbothhubsto
approximately125 Nm.Attheendoftheexperiment,theleverreturnstotheinitial
positionandthetorquedropstozero.Itcanbeassumedthatthereductioninthefrictional
forceandaccompaniedslippagecausethedamagetothecontactsurfacebetweentheshaft
andthehub[20,22]suchasfreing,whichcanleadtoachangeinthecoefficientoffriction
andtheresultingtransmiabletorque.
Figure5.Experimentalresultsofthestatictorquetestofdifferenthubs(blueandorangelines).The
connectionsinitiallytransmit170Nmand150Nm,followedbyadropandacertainstabilizationof
thetransmittabletorqueduetothelocaldamageofthecontactsurfacebetweentheshaftandthehub.
Figure6displaystheresultsforthesecondexperimentalseries.Thepreloadtorque
variesbetween110 Nmand115 Nm,belowthepreviouslydeterminedlimit.Theimpact
0
50
100
150
200
0 200 400 600 800
TorqueM
stat
/Nm
Testduration/s
hub-01
hub-02
Figure 5. Experimental results of the static torque test of different hubs (blue and orange lines). The
connections initially transmit 170 Nm and 150 Nm, followed by a drop and a certain stabilization of
the transmittable torque due to the local damage of the contact surface between the shaft and the hub.
Figure 6displays the results for the second experimental series. The preload torque
varies between 110
Nm
and 115
Nm
, below the previously determined limit. The impact
energy from the falling mass is 9
J
. At the start of the experiment, the markers on the hub
and the shaft lie on top of each other. The impulse forces the hub to slip, which, in turn,
reduces the preloaded torque. This is reflected in the measured curve by the drop of the
torque. Upon completion of the experiment, a discrepancy between the marker positions
can be observed. In other studies, attempts are made to avoid this effect of unintentional
“self-unscrewing” [31,32].
Appl. Sci. 2024,14, 8916 6 of 12
Appl.Sci.2024,14,xFORPEERREVIEW6of13
energyfromthefallingmassis9 J.Atthestartoftheexperiment,themarkersonthehub
andtheshaftlieontopofeachother.Theimpulseforcesthehubtoslip,which,inturn,
reducesthepreloadedtorque.Thisisreflectedinthemeasuredcurvebythedropofthe
torque.Uponcompletionoftheexperiment,adiscrepancybetweenthemarkerpositions
canbeobserved.Inotherstudies,aemptsaremadetoavoidthiseffectofunintentional
“self-unscrewing”[31,32].
Figure6.Experimentalresultsontheimpactbehavioroftheshaft–hubconnection.Theimpacton
thepreloadedhubcauseslocalslippage,whichreducesthetransmiabletorque.Themarkeron
hubismovingawayfromthemarkeroftheshaft.Furtherimpactleadsagaintothesame
phenomena.Attheendoftheexperiment,thedistancebetweenthemarkeroftheshaftandthe
markerofthehubisclearlyvisible.
ThediagraminFigure7illustratesatestinwhichthehubwaspreloadedonceto
80 Nmandthesameimpulse(𝑚1.6 kg,𝑣990 mm s
⁄)wasinitiatedseveraltimeson
thesamepositionoftheshaft.Themeasuredcurveshowsthatthehighestreductionin
thetorque,about20 Nm,isobservedwiththeinitialimpulse.Furtherimpulseinitiation
leadstoalowerreductioninthetorqueduetothegradationalreductioninthefrictional
forceintheconnection[25–28].Asaturationoftheminimumtransmiabletorquecanbe
seenat35 Nm.
Figure7.Experimentalresultsoftheimpactbehavioroftheshaft–hubconnection.Thefirstimpact
onthepreloadedhubresultsinthehighestreductioninthetorque.Therelativetorquereduction
decreaseswiththenumberofimpulses.
0
10
20
30
40
50
60
70
80
90
0 400 800 1200 1600
Tor que M
stat
/Nm
Tes tduration/s
Figure 6. Experimental results on the impact behavior of the shaft–hub connection. The impact on
the preloaded hub causes local slippage, which reduces the transmittable torque. The marker on hub
is moving away from the marker of the shaft. Further impact leads again to the same phenomena. At
the end of the experiment, the distance between the marker of the shaft and the marker of the hub is
clearly visible.
The diagram in Figure 7illustrates a test in which the hub was preloaded once to
80
Nm
and the same impulse (
m=
1.6
kg
,
v=
990
mm/s
) was initiated several times on
the same position of the shaft. The measured curve shows that the highest reduction in the
torque, about 20
Nm
, is observed with the initial impulse. Further impulse initiation leads
to a lower reduction in the torque due to the gradational reduction in the frictional force in
the connection [
25
–
28
]. A saturation of the minimum transmittable torque can be seen at
35 Nm.
Appl.Sci.2024,14,xFORPEERREVIEW6of13
energyfromthefallingmassis9 J.Atthestartoftheexperiment,themarkersonthehub
andtheshaftlieontopofeachother.Theimpulseforcesthehubtoslip,which,inturn,
reducesthepreloadedtorque.Thisisreflectedinthemeasuredcurvebythedropofthe
torque.Uponcompletionoftheexperiment,adiscrepancybetweenthemarkerpositions
canbeobserved.Inotherstudies,aemptsaremadetoavoidthiseffectofunintentional
“self-unscrewing”[31,32].
Figure6.Experimentalresultsontheimpactbehavioroftheshaft–hubconnection.Theimpacton
thepreloadedhubcauseslocalslippage,whichreducesthetransmiabletorque.Themarkeron
hubismovingawayfromthemarkeroftheshaft.Furtherimpactleadsagaintothesame
phenomena.Attheendoftheexperiment,thedistancebetweenthemarkeroftheshaftandthe
markerofthehubisclearlyvisible.
ThediagraminFigure7illustratesatestinwhichthehubwaspreloadedonceto
80 Nmandthesameimpulse(𝑚1.6 kg,𝑣990 mm s
⁄)wasinitiatedseveraltimeson
thesamepositionoftheshaft.Themeasuredcurveshowsthatthehighestreductionin
thetorque,about20 Nm,isobservedwiththeinitialimpulse.Furtherimpulseinitiation
leadstoalowerreductioninthetorqueduetothegradationalreductioninthefrictional
forceintheconnection[25–28].Asaturationoftheminimumtransmiabletorquecanbe
seenat35 Nm.
Figure7.Experimentalresultsoftheimpactbehavioroftheshaft–hubconnection.Thefirstimpact
onthepreloadedhubresultsinthehighestreductioninthetorque.Therelativetorquereduction
decreaseswiththenumberofimpulses.
0
10
20
30
40
50
60
70
80
90
0 400 800 1200 1600
Tor que M
stat
/Nm
Tes tduration/s
Figure 7. Experimental results of the impact behavior of the shaft–hub connection. The first impact
on the preloaded hub results in the highest reduction in the torque. The relative torque reduction
decreases with the number of impulses.
The modal analysis yields natural frequencies and their corresponding mode shapes, as
illustrated in Figure 8. Two specific mode shapes have been identified with their respective
natural frequencies. The initial form indicates a torsional mode occurring at a frequency
of 5578 Hz, which can lead to an additional torque load experienced by the shaft–hub
connection. In Figure 9a, the resulting radial stress as a function of the peripheral angle is
shown. The accumulation with the preloaded torque on the connection may surpass the
maximum limit, leading to a hub slippage.
Appl. Sci. 2024,14, 8916 7 of 12
Appl.Sci.2024,14,xFORPEERREVIEW7of13
Themodalanalysisyieldsnaturalfrequenciesandtheircorrespondingmodeshapes,
asillustratedinFigure8.Twospecificmodeshapeshavebeenidentifiedwiththeir
respectivenaturalfrequencies.Theinitialformindicatesatorsionalmodeoccurringata
frequencyof5578Hz,whichcanleadtoanadditionaltorqueloadexperiencedbythe
shaft–hubconnection.InFigure9a,theresultingradialstressasafunctionofthe
peripheralangleisshown.Theaccumulationwiththepreloadedtorqueontheconnection
maysurpassthemaximumlimit,leadingtoahubslippage.
Thesecondmodeindicatesabendingshapeatanaturalfrequencyof8155Hz,
resultinginadecreaseinthelocalizedcontactpressureand,therefore,alower
transmiabletorque.Furthermore,localizedslipzonescanoccuratthehubedge.In
conjunctionwithapreload,theslipzonescanspreadthroughouttheentirewidthofthe
hub(seeFigure9b)andleadtoaslippageandmaycausethefreingphenomena.Please
notethatanadditionalpreloadingincreasesthemode-dependentnaturalfrequencies[17].
Thosenaturalfrequenciesareabovethosefromthestudiesof[25–27]butunderthose
from[28]anditcanbeproventhatfrictionalforcesandtheresultingcontactpressures
mayreduceatvaryingfrequencies.Asalsomentionedin[28],wecanachieveonlyarough
qualitativeagreementoftheexperimentalandnumericalworksofar.
Figure8.Resultsofthemodalanalysisexhibitatorsionalnaturalfrequencyof5578Hzanda
bendingnaturalfrequencyof8155Hz.
Figure9.Thedeterminednaturalfrequenciesareleadingtoaradialloadatthetorsionalnatural
frequency(a)whichmaysurpassthemaximumoftransmiabletorqueandmayleadtoaslippage.
Theresultingradialloadduetothebendshapenaturalfrequencyisshownin(b).
Figure10showstheresultsofasimulation,inwhichaballwithamass𝑚1.6 kg
fallswiththevelocity𝑣3000 mm s
⁄atanangularposition𝛼90°ontheshaft.The
upperplotshowsthecontactpressurebeforetheimpulseisinitiated.Theapplicationof
theimpactleadstoadeformationoftheshaftwhichresultsinachangeinthecontact
pressureforashortperiodoftime.Attheedgezone,thepressuredecreasesatanangleof
0° to90° and,attheangle90° to300°,thepressureincreases.Thereductioninthe
−20
−15
−10
−5
0
0 100 200 300
Radialstress/MPa
Peripheralangle/°
−40
−20
0
20
40
0 100 200 300
Radialstress/MPa
Peripheralangle/°
(a) (b)
Figure 8. Results of the modal analysis exhibit a torsional natural frequency of 5578 Hz and a bending
natural frequency of 8155 Hz.
Appl.Sci.2024,14,xFORPEERREVIEW7of13
Themodalanalysisyieldsnaturalfrequenciesandtheircorrespondingmodeshapes,
asillustratedinFigure8.Twospecificmodeshapeshavebeenidentifiedwiththeir
respectivenaturalfrequencies.Theinitialformindicatesatorsionalmodeoccurringata
frequencyof5578Hz,whichcanleadtoanadditionaltorqueloadexperiencedbythe
shaft–hubconnection.InFigure9a,theresultingradialstressasafunctionofthe
peripheralangleisshown.Theaccumulationwiththepreloadedtorqueontheconnection
maysurpassthemaximumlimit,leadingtoahubslippage.
Thesecondmodeindicatesabendingshapeatanaturalfrequencyof8155Hz,
resultinginadecreaseinthelocalizedcontactpressureand,therefore,alower
transmiabletorque.Furthermore,localizedslipzonescanoccuratthehubedge.In
conjunctionwithapreload,theslipzonescanspreadthroughouttheentirewidthofthe
hub(seeFigure9b)andleadtoaslippageandmaycausethefreingphenomena.Please
notethatanadditionalpreloadingincreasesthemode-dependentnaturalfrequencies[17].
Thosenaturalfrequenciesareabovethosefromthestudiesof[25–27]butunderthose
from[28]anditcanbeproventhatfrictionalforcesandtheresultingcontactpressures
mayreduceatvaryingfrequencies.Asalsomentionedin[28],wecanachieveonlyarough
qualitativeagreementoftheexperimentalandnumericalworksofar.
Figure8.Resultsofthemodalanalysisexhibitatorsionalnaturalfrequencyof5578Hzanda
bendingnaturalfrequencyof8155Hz.
Figure9.Thedeterminednaturalfrequenciesareleadingtoaradialloadatthetorsionalnatural
frequency(a)whichmaysurpassthemaximumoftransmiabletorqueandmayleadtoaslippage.
Theresultingradialloadduetothebendshapenaturalfrequencyisshownin(b).
Figure10showstheresultsofasimulation,inwhichaballwithamass𝑚1.6 kg
fallswiththevelocity𝑣3000 mm s
⁄atanangularposition𝛼90°ontheshaft.The
upperplotshowsthecontactpressurebeforetheimpulseisinitiated.Theapplicationof
theimpactleadstoadeformationoftheshaftwhichresultsinachangeinthecontact
pressureforashortperiodoftime.Attheedgezone,thepressuredecreasesatanangleof
0° to90° and,attheangle90° to300°,thepressureincreases.Thereductioninthe
−20
−15
−10
−5
0
0 100 200 300
Radialstress/MPa
Peripheralangle/°
−40
−20
0
20
40
0 100 200 300
Radialstress/MPa
Peripheralangle/°
(a) (b)
Figure 9. The determined natural frequencies are leading to a radial load at the torsional natural
frequency (a) which may surpass the maximum of transmittable torque and may lead to a slippage.
The resulting radial load due to the bend shape natural frequency is shown in (b).
The second mode indicates a bending shape at a natural frequency of 8155 Hz, resulting
in a decrease in the localized contact pressure and, therefore, a lower transmittable torque.
Furthermore, localized slip zones can occur at the hub edge. In conjunction with a preload,
the slip zones can spread throughout the entire width of the hub (see Figure 9b) and lead to a
slippage and may cause the fretting phenomena. Please note that an additional preloading
increases the mode-dependent natural frequencies [
17
]. Those natural frequencies are
above those from the studies of [
25
–
27
] but under those from [
28
] and it can be proven
that frictional forces and the resulting contact pressures may reduce at varying frequencies.
As also mentioned in [
28
], we can achieve only a rough qualitative agreement of the
experimental and numerical work so far.
Figure 10 shows the results of a simulation, in which a ball with a mass
m=
1.6
kg
falls with the velocity
v=
3000
mm/s
at an angular position
α=
90
◦
on the shaft. The
upper plot shows the contact pressure before the impulse is initiated. The application of the
impact leads to a deformation of the shaft which results in a change in the contact pressure
for a short period of time. At the edge zone, the pressure decreases at an angle of 0
◦
to 90
◦
and, at the angle 90
◦
to 300
◦
, the pressure increases. The reduction in the pressure results in
a slippage of the hub. While the hub is changing in thickness, the results from [
26
] can be
confirmed: the tangential stiffness (which is dependent on the thickness) is very important
for the friction force reduction.
Figure 11 displays the average contact pressure and the reaction moment at virtual
point RP2 in the simulation as a function of time. The torsional preload was measured with
a value of 145 Nm. As described above, the deformation of the shaft caused by the impulse
results in a change in the mean pressure. It also causes a vibration in the shaft, which can
be seen in the wave-shaped mean pressure curve. After the vibration has stopped, the
mean pressure returns to its initial state. This brief reduction in the frictional force due to
the vibration [
25
–
28
] is sufficient for the hub to slip, as evidenced by the reaction moment’s
progression. The torque drops from 146 Nm to 134 Nm.
Appl. Sci. 2024,14, 8916 8 of 12
Appl.Sci.2024,14,xFORPEERREVIEW8of13
pressureresultsinaslippageofthehub.Whilethehubischanginginthickness,theresults
from[26]canbeconfirmed:thetangentialstiffness(whichisdependentonthethickness)
isveryimportantforthefrictionforcereduction.
Figure10.Uppersubfigureisshowingthecontactpressureintheshaft–hubconnectionwithout
impulse.Thelowersubfigureisshowingtheimmediateinfluenceoftheimpactonthecontact
pressurewhichisdecreasingbetween0°and90°andincreasingbetween90°and300°.Thelocal
changeincontactpressuremayresultinaslippageoftheconnection.
Figure11displaystheaveragecontactpressureandthereactionmomentatvirtual
pointRP2inthesimulationasafunctionoftime.Thetorsionalpreloadwasmeasured
withavalueof145Nm.Asdescribedabove,thedeformationoftheshaftcausedbythe
impulseresultsinachangeinthemeanpressure.Italsocausesavibrationintheshaft,
whichcanbeseeninthewave-shapedmeanpressurecurve.Afterthevibrationhas
stopped,themeanpressurereturnstoitsinitialstate.Thisbriefreductioninthefrictional
forceduetothevibration[25–28]issufficientforthehubtoslip,asevidencedbythe
reactionmoment’sprogression.Thetorquedropsfrom146Nmto134Nm.
Figure11.Simulationresultoftheimpactbehavioroftheshaft–hubconnection.Theimpactleads
totemporarychangeinthemeanpressure(orange),whichmayresultinaslippageofthe
connection.Theslippageisindicatedbythereductioninthereactionmoment(blue).
0
20
40
60
80
100
120
140
160
400
410
420
430
440
450
460
470
480
0 0.002 0.004 0.006 0.008 0.01
Reactionmoment/Nm
Meanpressure/MPa
Timestep/-
Figure 10. Upper subfigure is showing the contact pressure in the shaft–hub connection without
impulse. The lower subfigure is showing the immediate influence of the impact on the contact
pressure which is decreasing between 0
◦
and 90
◦
and increasing between 90
◦
and 300
◦
. The local
change in contact pressure may result in a slippage of the connection.
Appl.Sci.2024,14,xFORPEERREVIEW8of13
pressureresultsinaslippageofthehub.Whilethehubischanginginthickness,theresults
from[26]canbeconfirmed:thetangentialstiffness(whichisdependentonthethickness)
isveryimportantforthefrictionforcereduction.
Figure10.Uppersubfigureisshowingthecontactpressureintheshaft–hubconnectionwithout
impulse.Thelowersubfigureisshowingtheimmediateinfluenceoftheimpactonthecontact
pressurewhichisdecreasingbetween0°and90°andincreasingbetween90°and300°.Thelocal
changeincontactpressuremayresultinaslippageoftheconnection.
Figure11displaystheaveragecontactpressureandthereactionmomentatvirtual
pointRP2inthesimulationasafunctionoftime.Thetorsionalpreloadwasmeasured
withavalueof145Nm.Asdescribedabove,thedeformationoftheshaftcausedbythe
impulseresultsinachangeinthemeanpressure.Italsocausesavibrationintheshaft,
whichcanbeseeninthewave-shapedmeanpressurecurve.Afterthevibrationhas
stopped,themeanpressurereturnstoitsinitialstate.Thisbriefreductioninthefrictional
forceduetothevibration[25–28]issufficientforthehubtoslip,asevidencedbythe
reactionmoment’sprogression.Thetorquedropsfrom146Nmto134Nm.
Figure11.Simulationresultoftheimpactbehavioroftheshaft–hubconnection.Theimpactleads
totemporarychangeinthemeanpressure(orange),whichmayresultinaslippageofthe
connection.Theslippageisindicatedbythereductioninthereactionmoment(blue).
0
20
40
60
80
100
120
140
160
400
410
420
430
440
450
460
470
480
0 0.002 0.004 0.006 0.008 0.01
Reactionmoment/Nm
Meanpressure/MPa
Timestep/-
Figure 11. Simulation result of the impact behavior of the shaft–hub connection. The impact leads to
temporary change in the mean pressure (orange), which may result in a slippage of the connection.
The slippage is indicated by the reduction in the reaction moment (blue).
Figure 12 is showing the simulation result in which the impact (
m=
1.6
kg
,
v=
3000
mm/s
,
Ekin =
1.9
J
) was initiated three times at the same position during the captured time.
Following the initiation of the first impulse, a significant reduction in the reaction moment
is noticeable. The reaction moment drops from 144
Nm
to 126
Nm
. On triggering the
second impulse, the reaction moment decreases only by 1
Nm
. No shift in the reaction
moment is apparent upon initiating the third impulse.
In Figure 13, the influence of the distance between the hub and the point of impact
(
h
) on the transmittable torque is shown. The results indicate that the biggest reduction
in the torque (20
Nm
) occurred at the smallest distance of
h=
10
mm
. As the distance (
h
)
was increased, the effect of the impulse was diminished, with a barely noticeable drop in
the reaction moment up to
h=
35
mm
. The results indicate that the closer the deformation
field is to the hub due to the impulse, the greater the change in contact pressure and
the associated drop in torque. In addition, the results may differ with different natural
frequencies of the shaft or a different impact energy which causes different transverse
vibrations and may arise in different locking mechanisms in the connection [30].
Appl. Sci. 2024,14, 8916 9 of 12
Appl.Sci.2024,14,xFORPEERREVIEW9of13
Figure12isshowingthesimulationresultinwhichtheimpact(𝑚1.6 kg,𝑣
3000 mm s
⁄,𝐸
1.9 J)wasinitiatedthreetimesatthesamepositionduringthe
capturedtime.Followingtheinitiationofthefirstimpulse,asignificantreductioninthe
reactionmomentisnoticeable.Thereactionmomentdropsfrom144 Nmto126 Nm.On
triggeringthesecondimpulse,thereactionmomentdecreasesonlyby1 Nm.Noshiftin
thereactionmomentisapparentuponinitiatingthethirdimpulse.
Figure12.FEresultsfromtimedependentprogressofkineticenergyandtransmiabletorquein
theshaft–hubconnectionafteroverallthreeimpacts.Theimpactiscausingadecreaseincontact
pressurewhichalsoresultsinadecreaseinthetransmiabletorque.
InFigure13,theinfluenceofthedistancebetweenthehubandthepointofimpact
(ℎ)onthetransmiabletorqueisshown.Theresultsindicatethatthebiggestreductionin
thetorque(20 Nm)occurredatthesmallestdistanceofℎ10 mm.Asthedistance(ℎ)
wasincreased,theeffectoftheimpulsewasdiminished,withabarelynoticeabledropin
thereactionmomentuptoℎ35 mm.Theresultsindicatethatthecloserthedeformation
fieldistothehubduetotheimpulse,thegreaterthechangeincontactpressureandthe
associateddropintorque.Inaddition,theresultsmaydifferwithdifferentnatural
frequenciesoftheshaftoradifferentimpactenergywhichcausesdifferenttransverse
vibrationsandmayariseindifferentlockingmechanismsintheconnection[30].
Figure13.Influenceofthedistancehbetweenimpactpointandshaft–hubconnection.Thesmallest
distanceh=10mmresultsinthebiggestslippageaccompaniedwiththebiggestdecreasein
transmiabletorquewhilethebiggestdistanceh=35mmresultsinthesmallestslippage/decrease
intransmiabletorque.
0
20
40
60
80
100
120
140
160
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0 0.01 0.02 0.03
Reactionmoment/Nm
Kineticenergy/J
Timestep/-
Figure 12. FE results from time dependent progress of kinetic energy and transmittable torque in the
shaft–hub connection after overall three impacts. The impact is causing a decrease in contact pressure
which also results in a decrease in the transmittable torque.
Appl.Sci.2024,14,xFORPEERREVIEW9of13
Figure12isshowingthesimulationresultinwhichtheimpact(𝑚1.6 kg,𝑣
3000 mm s
⁄,𝐸
1.9 J)wasinitiatedthreetimesatthesamepositionduringthe
capturedtime.Followingtheinitiationofthefirstimpulse,asignificantreductioninthe
reactionmomentisnoticeable.Thereactionmomentdropsfrom144 Nmto126 Nm.On
triggeringthesecondimpulse,thereactionmomentdecreasesonlyby1 Nm.Noshiftin
thereactionmomentisapparentuponinitiatingthethirdimpulse.
Figure12.FEresultsfromtimedependentprogressofkineticenergyandtransmiabletorquein
theshaft–hubconnectionafteroverallthreeimpacts.Theimpactiscausingadecreaseincontact
pressurewhichalsoresultsinadecreaseinthetransmiabletorque.
InFigure13,theinfluenceofthedistancebetweenthehubandthepointofimpact
(ℎ)onthetransmiabletorqueisshown.Theresultsindicatethatthebiggestreductionin
thetorque(20 Nm)occurredatthesmallestdistanceofℎ10 mm.Asthedistance(ℎ)
wasincreased,theeffectoftheimpulsewasdiminished,withabarelynoticeabledropin
thereactionmomentuptoℎ35 mm.Theresultsindicatethatthecloserthedeformation
fieldistothehubduetotheimpulse,thegreaterthechangeincontactpressureandthe
associateddropintorque.Inaddition,theresultsmaydifferwithdifferentnatural
frequenciesoftheshaftoradifferentimpactenergywhichcausesdifferenttransverse
vibrationsandmayariseindifferentlockingmechanismsintheconnection[30].
Figure13.Influenceofthedistancehbetweenimpactpointandshaft–hubconnection.Thesmallest
distanceh=10mmresultsinthebiggestslippageaccompaniedwiththebiggestdecreasein
transmiabletorquewhilethebiggestdistanceh=35mmresultsinthesmallestslippage/decrease
intransmiabletorque.
0
20
40
60
80
100
120
140
160
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0 0.01 0.02 0.03
Reactionmoment/Nm
Kineticenergy/J
Timestep/-
Figure 13. Influence of the distance h between impact point and shaft–hub connection. The smallest
distance h = 10 mm results in the biggest slippage accompanied with the biggest decrease in trans-
mittable torque while the biggest distance h = 35 mm results in the smallest slippage/decrease in
transmittable torque.
The result of the simulation with a cylinder instead of a sphere-shaped mass (
m=
1.6
kg
,
v=
3000
mm/s
) is shown in Figure 14. Instead of being point-shaped, the contact during
the impact is line-shaped. This results in a small decrease in the reaction moment of
approximately 1
Nm
. This underlines the influence of the contact between the impact
mass and the shaft. A change in the shape of the contact leads to a change in the energy
transfer and a different tangential vibration between the point mass and the shaft due to
the impulse. This results in a different deformation due to the reduction in the friction force
of the shaft and the slip zone between the shaft and the hub which may arise from several
influencing factors. Furthermore, a different vibration excitation of the shaft can occur.
Different studies on the influence of the impact velocity, the preload, the mass of
the ball, and the distance between the impact and the shaft–hub connection were carried
out. The results of all those factors are shown in Figure 15. The biggest decrease in the
transmittable torque is obtained at the highest impact energies (big mass and high velocity),
the closest distance to the hub, and with the highest preload. All of these changes can be
attributed to the effects of vibration excitation of the shaft [
17
] and the temporary reduction
in the contact pressures caused by the deformation and the reduction in the frictional
force [
19
,
26
–
28
], with the associated increase in slippage [
22
]. The highest energies lead
to the biggest decrease in the contact pressure in the connection and the decrease in the
transmittable torque. The highest preload puts so much tension on the connection that even
Appl. Sci. 2024,14, 8916 10 of 12
a slight reduction in the contact pressure can cause slippage. The influence of the distance
may be related to damping effects in the material. Further studies may follow on this.
Appl.Sci.2024,14,xFORPEERREVIEW10of13
Theresultofthesimulationwithacylinderinsteadofasphere-shapedmass(𝑚
1.6 kg,𝑣3000 mm s
⁄)isshowninFigure14.Insteadofbeingpoint-shaped,thecontact
duringtheimpactisline-shaped.Thisresultsinasmalldecreaseinthereactionmomentof
approximately1 Nm.Thisunderlinestheinfluenceofthecontactbetweentheimpactmass
andtheshaft.Achangeintheshapeofthecontactleadstoachangeintheenergytransfer
andadifferenttangentialvibrationbetweenthepointmassandtheshaftduetotheimpulse.
Thisresultsinadifferentdeformationduetothereductioninthefrictionforceoftheshaft
andtheslipzonebetweentheshaftandthehubwhichmayarisefromseveralinfluencing
factors.Furthermore,adifferentvibrationexcitationoftheshaftcanoccur.
Figure14.Influenceoftheshapeoftheimpactbodyonthedecreaseinthetransmiabletorque.The
impactcylinderwiththesamemassandvelocitycomparedtoaballresultsinamuchsmaller
decreaseinthetransmiabletorqueatthedistanceofh=10mm.
Differentstudiesontheinfluenceoftheimpactvelocity,thepreload,themassofthe
ball,andthedistancebetweentheimpactandtheshaft–hubconnectionwerecarriedout.
TheresultsofallthosefactorsareshowninFigure15.Thebiggestdecreaseinthe
transmiabletorqueisobtainedatthehighestimpactenergies(bigmassandhigh
velocity),theclosestdistancetothehub,andwiththehighestpreload.Allofthesechanges
canbeaributedtotheeffectsofvibrationexcitationoftheshaft[17]andthetemporary
reductioninthecontactpressurescausedbythedeformationandthereductioninthe
frictionalforce[19,26–28],withtheassociatedincreaseinslippage[22].Thehighest
energiesleadtothebiggestdecreaseinthecontactpressureintheconnectionandthe
decreaseinthetransmiabletorque.Thehighestpreloadputssomuchtensiononthe
connectionthatevenaslightreductioninthecontactpressurecancauseslippage.The
influenceofthedistancemayberelatedtodampingeffectsinthematerial.Furtherstudies
mayfollowonthis.
Figure 14. Influence of the shape of the impact body on the decrease in the transmittable torque.
The impact cylinder with the same mass and velocity compared to a ball results in a much smaller
decrease in the transmittable torque at the distance of h = 10 mm.
Appl.Sci.2024,14,xFORPEERREVIEW11of13
Figure15.Resultsoftheinfluenceoftheimpactvelocityandthepreloadtorque(a),themassofthe
impactball(b),thedistancehbetweenpointoftheimpactandtheshaft–hubconnection(c),andthe
typeofcontactbetweentheimpactmassandtheshaft(d).Increasingimpactenergies(higher
velocityandbiggermass)leadtoahigherdecreaseinthetransmiabletorque.Ahigherpreload
alsoresultsinahigherdecreaseinthetransmiabletorque.Higherdistancesbetweentheshaft–
hubconnectionandthepointofimpactleadtosmallerdecreasesinthetransmiabletorque.The
reducedtorquealsodependsonthecontacttypebetweentheimpulsemassandtheconnection.
4.Conclusions
Inthisstudy,weinvestigatedtheinfluenceoflocalimpactloadsonthetransmiable
torqueofashaft–hubconnection.Theexperimentscarriedoutshowthat,inapressfit,a
reductioninthefrictionalforceandaslippagecanoccuratalowertorquethanastatic
torquetestwithoutanyimpactload.Thisstudyalsoshowsthatincreasingtheimpact
resultsinanincreaseintheslippageandareductioninthetransmiabletorque.The
modalanalysesandFEsimulationsoftheimpactcarriedoutshowthefollowing:the
impactloadexcitesavibrationmodethatcausesalocaldeformationoftheshaft,resulting
inalocalslippage(andprobablyfreing)andreducesthetransmiabletorqueduetoa
localreductioninthecontactpressure.Wehavealsosystematicallystudiedtheinfluence
oftheshapeofthemass,theimpactvelocity,thepreload,andthedistancebetweenthe
impactmassandthehub,andcametothefollowingconclusions:
- Higherpreloadsresultinanincreaseinslippagecausedbytheimpact;
- Theincreaseinimpactvelocitiesorimpactmassreducethetransmittabletorque;
- Reducingthedistancesbetweenpointoftheimpactandthehubreducethe
transmittabletorque.
Aut horContributions:M.H.:conceptualization,methodology,projectadministration,andoriginal
draftpreparation.L.L.D.:experimentalworkandanalysis,modalanalysis,FEsimulation,
visualization,andoriginaldraftpreparation.T.G.:supervision;L.S.:supervision;T.L. :supervision,
andfundingacquisition,A.H.:conceptualization,methodology,supervision,andfunding
acquisition.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:Thisresearchreceivednoexternalfundingfromfoundingorganizations.Thisworkis
intendedasapre-workforfuturefundingacquisition.
InstitutionalReviewBoardStatement:Notapplicable.
InformedConsentStatement:Notapplicable.
Figure 15. Results of the influence of the impact velocity and the preload torque (a), the mass of the
impact ball (b), the distance h between point of the impact and the shaft–hub connection (c), and
the type of contact between the impact mass and the shaft (d). Increasing impact energies (higher
velocity and bigger mass) lead to a higher decrease in the transmittable torque. A higher preload
also results in a higher decrease in the transmittable torque. Higher distances between the shaft–hub
connection and the point of impact lead to smaller decreases in the transmittable torque. The reduced
torque also depends on the contact type between the impulse mass and the connection.
4. Conclusions
In this study, we investigated the influence of local impact loads on the transmittable
torque of a shaft–hub connection. The experiments carried out show that, in a press fit, a
reduction in the frictional force and a slippage can occur at a lower torque than a static
torque test without any impact load. This study also shows that increasing the impact
results in an increase in the slippage and a reduction in the transmittable torque. The modal
analyses and FE simulations of the impact carried out show the following: the impact
load excites a vibration mode that causes a local deformation of the shaft, resulting in a
local slippage (and probably fretting) and reduces the transmittable torque due to a local
reduction in the contact pressure. We have also systematically studied the influence of the
Appl. Sci. 2024,14, 8916 11 of 12
shape of the mass, the impact velocity, the preload, and the distance between the impact
mass and the hub, and came to the following conclusions:
- Higher preloads result in an increase in slippage caused by the impact;
- The increase in impact velocities or impact mass reduce the transmittable torque;
-
Reducing the distances between point of the impact and the hub reduce the transmit-
table torque.
Author Contributions: M.H.: conceptualization, methodology, project administration, and original
draft preparation. L.L.D.: experimental work and analysis, modal analysis, FE simulation, visual-
ization, and original draft preparation. T.G.: supervision; L.S.: supervision; T.L.: supervision, and
funding acquisition, A.H.: conceptualization, methodology, supervision, and funding acquisition. All
authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding from founding organizations. This work is
intended as a pre-work for future funding acquisition.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding authors.
Acknowledgments: The authors acknowledge the open-access-funding support of the library of
Chemnitz University of Technology.
Conflicts of Interest: The authors declare no conflicts of interest.
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