Journées Transmissions Mécaniques 10-11th July 2016 Strength assessment of a pinion-hollow shaft connection Dimensionnement d'une connexion compacte entre pignon et arbre moteur S.Kœchlin G.Kulcsar 1
2 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
3 Problem description (1/4) Universal Compact
4 Problem description (2/4) Material Hollow shaft : 42CrMo4+QT Pinion : 20MnCrS5 Key : 42CrMo4+QT Rm min =1800 MPa
5 Problem description (3/4) IEC efficency requirements needs redimensioning electric motors => starting torque larger on last motor generation
6 Problem description (4/4) Calculation standards for keyway connections most likely not applicable Detailed modeling of keyway connections is still a research topic Very few field failures up to now : good news, but Diversity of gearbox application, thus of load history on the connection
7 Loads applied to the connection Meshing force Screw compression Starting torque =3.3*Nominal torque Starting torque -189 Nm Axial tightening force F a -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
Failure modes From a literature review : Keyway plastic deformation Shaft breaking in case of rotative bending and repeated torsion combined with Q A <0.7 Hub breaking for repeated torsion with Q A >0.7 D d Source : Bruzek Q A =d / D 8 Source : Forbrig Excessive contact pressure Fretting fatigue Hub yielding Source : Forbrig
9 Preliminary calculations (1/2) Contact Pressure Calculation (DIN6892, 2012) 10 9 8 7 6 5 4 3 2 1 0 Contact pressure safety ratio Shaft Key / Shaft Key / Hub Hub Unidirectional torque Alternating torque 1E6 Alternating torque 1E10 => Contact pressure is safe!
10 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 I x. maximum of the bending and torsion stresses do not occur at the same point along the shaft σ W,b,N =510MPa, τ W,t,N =305MPa, Kf 3.2 =>
11 FE Model description loads at pinion center, connected to green surface with RBE3-type flexible link fixed support (blue) cylindrical surface of pitch diameter (green) 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
Torque transmission through interference fit µ=0.1 D=0.028mm (maximal interference) Analytical model : FE-Model (matching nodes at interface) 225MPa 194MPa Keyway slot causes a contact pressure drop Except in case of maximal interference, interference fit cannot transmit the whole starting torque. 12
13 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 displacement Axial stress
14 Fretting fatigue? (2/2) 1 revolution Axial rel. displacement < 15µm Axial stress < 30MPa => Low stress level makes fretting fatigue unlikely
15 Contact pressure on key Key is in contact at 4 locations (~4 lines) Contact is very localized : coarse contact pressure evaluation!
16 Hollow shaft strength Pressure distribution in cylindrical fit Stabilization Stress variation in keyway FKM strength assessment
17 Pressure distribution pinion/h.shaft => Simple analytical calculation of interference fit is unrealistic Step 1 : interference fit + screw compression Uneven pressure distribution due to keyway Step 2 : meshing load Unloading of 2 areas on both sides of keyway, and of a large part of the front face
18 Stabilization Friction => Steady state is reached only after several revolutions also in case of loose interference!
19 Stress variation in keyway for each point Stress amplitude
20 Hollow shaft : FKM strength assessment (1/2 Nb starting cycles >1E6 (endurance limit) no interference 15μm 28μm
21 Hollow shaft: FKM strength assessment (2/2) Assuming a uniform distribution : 2.5% 3.1 H6 16 µm 1 µm n5 11 µm 2.5% interference probability S1 duty cycle => max 6 starts/h (IEC 60034-1) 10years=> 525 600 starts => +14% load (K BK =1.14)
22 Torque inversion Similar FKM assessment possible : but stress surges due to shock at reversal would not be considered. Suggestion : extrapolate results from repeated loading with specific factor from DIN6892
23 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 stess state 2 : meshing load release with friction
24 Towards a simplified model (2/2) worst angular position : not the max bending one! different for front and rear keyway end depends on interference 2-step simulation α y x fair approximation comp. time divided by 4
25 Testing device gearbox mount raises the problem of overloading the pinion teeth : is it a problem? simulates meshing load (torque and radial force together) swivel axis pitch radius coupling motors axis
26 Conclusion 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 regarding contact
27 Literature BRUZEK, Bohumil. 2014. Neue Grenzlastbelastungen für torsionsbeanspruchte 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 für Maschinenbauteile. 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 bei Pressverbänden. Antriebstechnik. 1988, 27.