1. Axial Load Distribution in a Jet Engine Spline Coupling Justin McGrath Master of Engineering Project Rensselaer Polytechnic Institute Hartford, CT

2. Spline Coupling Background Elongated gear teeth Used in high torque applications Used in jet engines to transfer torque from disks to shafts The pressure faces of the teeth distribute the load

3. Spline Coupling Schematic Spline Couplings used in several Pratt & Whitney Engines: F-119 F-135 PW4000 PW2000 PW6000

4. Challenges in Spline Design Even distribution of the torque load on the pressure face of the spline teeth Uneven loading causes premature wear and reduces the life of the coupling system Designers must understand the load behavior of the coupling system to make changes that will even the load This project looks into analyzing axial load distribution in a representative spline coupling

5. Theoretical Methodology Derived equation of axial load distribution using Taturs method: p(x) – axial load at the root fillet radius L – Contact length of the coupling system c – effective tooth height R – pitch radius N – Number of teeth T – tau, the applied torque α – constant of integration

6. Finite Element Methodology Create 3D model of the coupling system: Import Geometry into ANSYS & apply loads:

7. Finite Element Methodology Load data is extracted from the finite element model and compared to the theoretical equation:

8. Results Both methods show the load peaking at either end of the contact length The theoretical solution predicts a higher maximum load

9. Discussion The theoretical solution predicts higher loads because: Taturs Method assumes 100 % transfer of load with no deflection FE model shows only about 75% of the load is transferred The other 25% is used in bending the teeth, and torsionally deflecting the coupling system

10. Discussion Both methods converge when looking at a normalized plot This confirms that the boundary conditions used in the FE model agree with the theoretical boundary conditions

11. Conclusion The theoretical equation is the more conservative method in analyzing axial load distribution in a spline coupling system as it predicts higher maximum & average loads The theoretical equation is also a much faster method The Finite Element solution more accurately predicts the load that will be seen during engine operation, but it is a time consuming apporach The Finite Element model shows that all else being equal there is more capability in the coupling system when compared to the theorecitcal approach

12. Back Up Slides ParameterValueUnit α10.67(lb/in-rad) 1/2 A13.67- B336.3- p(x) max 97.66ksi p avg 57.61ksi PR1.70- ParameterLeft ToothRight ToothUnit p(x) max 71.1368.51ksi p avg 47.0645.34ksi PR1.51 - d(x) max 0.00015 in d avg 0.00140.00014in DR1.1 - Analytical CalculationsFinite Element Calculations

13. Back Up Slides Table 1 – Material Properties of 3D Spline Coupling Model SpecificationSymbolSleeveShaftUnit Material-IN-100INCO718- Densityp0.2840.297lb/in 3 Weightw0.1180.173lb Modulus of ElasticityE30.131.0Gpa Shear ModulusG11.9411.10Gpa Polar Moment of InertiaJ0.0850.037in 4

14. Back Up Slides Table 2 – Geometric Properties of 3D Spline Coupling Model SpecificationSymbolValueUnit Applied Torqueτ350in-lb Contact LengthL0.30in Pitch RadiusR0.70in Number of TeethN56# Tooth Heightc0.032in Root Fillet Radiusr0.010in Pressure Angleθ30deg Torsional StiffnessCθCθ 3332488lb/in-rad