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Strength assessment of a pinion-hollow shaft connectionDimensionnement d'une connexion compacte entre pignon et arbre moteur
S.Kœchlin
G.Kulcsar
Journées Transmissions Mécaniques – 10-11th July 2016
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Emerson Confidential
� Problem description
� Loads applied to the connection
� Failure modes
� Preliminary calculations
– Contact Pressure Calculation (DIN6892, 2012)
– Pinion Shaft Strength
� Finite Elements model
– Torque transmission through interference fit
– Fretting fatigue?
– Hollow shaft strength
� Towards a simplified model
� Testing device
� Conclusion
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Emerson Confidential
Problem description (2/4)Problem description (2/4)
� Material
– Hollow shaft : 42CrMo4+QT
– Pinion : 20MnCrS5
– Key : 42CrMo4+QT Rm min =1800 MPa
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Problem description (3/4)Problem description (3/4)
� IEC efficency requirementsneeds redimensioning electricmotors
� => starting torque larger on last motor generation
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Problem description (4/4)Problem description (4/4)
� Calculation standards for keywayconnections most likely not applicable
� Detailed modeling of keyway connections isstill a research topic
� Very few field failures up to now : good news, but…
� Diversity of gearbox application, thus of loadhistory on the connection
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Loads applied to the connectionLoads applied to the connection
Meshing
force
Screw compression
Starting torque � -189 Nm
Axial tightening force Fa -10400 N
Pinion pitch diameter �� 47.888 mm
Tooth width � 29.5 mm
Pressure angle � -20 °
Helix angle � -20 °
Pinion shaft diameter d 32 mm
Starting torque =3.3*Nominal torque
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From a literature review :
– Keyway plastic deformation
– Shaft breaking in case of rotative bending and repeated torsion combined with QA<0.7
– Hub breaking for repeated torsion with QA>0.7
Failure modesFailure modes
D
d QA=d / D
Source : Forbrig
Source : Bruzek
Source : Forbrig
Excessive contact pressure
– Fretting fatigue
Hub yielding
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Preliminary calculations (1/2)Preliminary calculations (1/2)
� Contact Pressure Calculation (DIN6892, 2012)
� => Contact pressure is safe !
0123456789
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Shaft Key /Shaft
Key /Hub
Hub
Contact pressure safety ratio
Unidirectionaltorque
Alternating torque1E6
Alternating torque1E10
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Preliminary calculations (2/2) Preliminary calculations (2/2)
� Pinion shaft strength (calculation based on nominal stress)
– Loads are supported by both hollow and pinion shafts, in a proportion given by their quadratic moment Ix .
• maximum of the bending and torsion stresses do not occur at the same point along the shaft
– σW,b,N=510MPa, τW,t,N=305MPa, Kf≤3.2 => ☺☺☺☺…
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FE Model descriptionFE Model description
loads at pinion
center, connected
to green surface
with RBE3-type
flexible link
cylindrical surface of
pitch diameter (green)
fixed support
(blue)
� Geometry is fixed in the global coordinate system, and meshing load rotates around the Z axis
� Load moment and force are applied at the center of the pinion
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Torque transmission throughinterference fitTorque transmission throughinterference fit
Analytical model :
225MPa
FE-Model (matching nodes at interface)
194MPa
Keyway slot causes a contact pressure drop
Except in case of maximal interference, interferencefit cannot transmit the whole starting torque.
µ=0.1 ∆D=0.028mm (maximal interference)
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Fretting fatigue? (1/2)Fretting fatigue? (1/2)� Depends on :
– pinion / hollow shaft relative motion
– local contact pressure
� axial tightning force applied by the screw is not sufficient for preventing the pinion from moving partly off the hollow shaft
Axial displacementAxial stress
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Fretting fatigue? (2/2) Fretting fatigue? (2/2)
Axial stress < 30MPa
1 revolution
=> Low stress level makes fretting fatigue unlikely
����
☺☺☺☺
Axial rel. displacement < 15µm
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Contact pressure on key Contact pressure on key
� Key is in contact at 4 locations (~4 lines)
� Contact is very localized : coarse contact pressure evaluation !
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Hollow shaft strengthHollow shaft strength
� Pressure distribution in cylindrical fit
� Stabilization
� Stress variation in keyway
� FKM strength assessment
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Pressure distribution pinion/h.shaftPressure distribution pinion/h.shaft
Step 1 : interference fit + screw compression
Step 2 : meshing load
Uneven pressure dis-
tribution due to keyway
Unloading of 2 areas on both
sides of keyway, and of a large
part of the front face
…
=> Simple analytical calculation of interference fit is unrealistic
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StabilizationStabilization
Friction => Steady
state is reached only
after several
revolutionsalso in case of loose interference !
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Hollow shaft : FKM strength assessment (1/2)Hollow shaft : FKM strength assessment (1/2)
no interference 15μm 28μm
Nb starting
cycles >1E6
(endurance limit)
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Hollow shaft: FKM strength assessment (2/2)Hollow shaft: FKM strength assessment (2/2)
2.5% interferenceprobability
S1 duty cycle => max 6 starts/h (IEC 60034-1)
10years=> 525 600 starts
=> +14% load (KBK=1.14)
∆� ∆���
� ∙ ���∙���
∆� 2.5%
3.1��
Assuming a uniform
distribution :
16 µm11 µm
1 µm
n5H6
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Torque inversionTorque inversion
� Similar FKM assessment possible : but stress surgesdue to shock at reversal would not be considered.
� Suggestion : extrapolate results from repeatedloading with specific factor from DIN6892
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Towards a simplified model (1/2)Towards a simplified model (1/2)
� optimize the FE-model : matching meshes in contact areas
� interference level : choose 2.5% probability?
� calculate only one angular position
– find the worst one
– progressive stabilization due to friction : try a 2-step simulation :
• 1 : full load without friction => approximate stabilized stessstate
• 2 : meshing load release with friction
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� worst angular position :
– not the max bending one!
– different for front and rear keyway end
– depends on interference
� 2-step simulation
Towards a simplified model (2/2)Towards a simplified model (2/2)
⇒ fair
approximation
comp. time
divided by 4
α
x
y
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Testing deviceTesting device
pitch
radius
coupling
motors axis
swivel axis
� gearbox mount raises the problem of overloading thepinion teeth : is it a problem?
� simulates meshing load (torque and radial force together)
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� Main points
– Connexion can withstand a limited number of starts
– Must be compared to gear capacity
– Complex system, model over-simplification is risky
– Reference configuration is suggested
� Further work
– Experimental testing is needed, must be carefully designed
– Improve the FE model : optimize the mesh regardingcontact
ConclusionConclusion26
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LiteratureLiterature
� BRUZEK, Bohumil. 2014. Neue Grenzlastbelastungen fürtorsionsbeanspruchte Passfederverbindungen, VDI-Berichte Nr.2238. 2014.
� DIN6892. 2012. Mitnehmerverbindung ohne Anzug-Passfedern -Berechnung und Gestaltung. 2012.
� DIN7190. 2001. Pressverbände, Berechnungsgrundlagen und Gestaltungsregeln. 2001.
� FKM. 2012. FKM-Richlinie, Rechnerischer Festigkeitsnachweis fürMaschinenbauteile. 2012.
� FORBRIG, Frank. 2007. Untersuchungen zur Gestaltfestigkeit von Passfederverbindungen, Dissertation TÜ Chemnitz. s.l. : Shaker Verlag, 2007.
� LEIDICH, Ehrard. 2003. Beanspruchungen in torsionsbelasteten Naben von Passfederverbindungen. Antriebstechnik. 2003, 42.
� LEIDICH, Ehrard. 1988. Mikroschlupf und Dauerfestigkeit beiPressverbänden. Antriebstechnik. 1988, 27.
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