Strength assessment of a pinion-hollow shaft connection · Strength assessment of a pinion-hollow...

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

1

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

2


Problem description (1/4)Problem description (1/4)

Universal Compact

3



� Material

– Hollow shaft : 42CrMo4+QT

– Pinion : 20MnCrS5

– Key : 42CrMo4+QT Rm min =1800 MPa

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� IEC efficency requirementsneeds redimensioning electricmotors

� => starting torque larger on last motor generation

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� 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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Stress variation in keywayStress variation in keyway

Stress

amplitude

for each point

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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


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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