Axial Load Distribution in a Jet Engine Spline

Coupling

Justin McGrath

Master of Engineering Project

Rensselaer Polytechnic Institute

Hartford, CT

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

Spline Coupling Schematic

Spline Couplings used in several Pratt & Whitney Engines:

•F-119

•F-135

•PW4000

•PW2000

•PW6000

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

Theoretical Methodology

Derived equation of axial load distribution using Tatur’s method:

cRNe

e

eee

e

exp x

L

LLx

L

L 1

11

1)(

2

2

2

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

Finite Element Methodology

Create 3D model of the coupling system:

Import Geometry into ANSYS & apply loads:

Finite Element Methodology

Load data is extracted from the finite element model and compared to the theoretical equation:

Results

Both methods show the load peaking at either end of the contact length

The theoretical solution predicts a higher maximum load

Axial Load Distribution in Spline Coupling

0

20000

40000

60000

80000

100000

120000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Spline Tooth Contact Length (in.)

Co

nta

ct

Lo

ad

(p

si)

Analytical Sol.

Finite Element Sol. Left

Finite Element Sol. Right

Discussion The theoretical solution predicts higher loads because:

Tatur’s 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

Discussion

Both methods converge when looking at a normalized plot

Normalized Axial Load Distribution

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Spline Tooth Contact Length (in.)

p(x

)/p

(avg

)

Analytical Sol.

Finite Element Sol. Left

Finite Element Sol. Right

This confirms that the boundary conditions used in the FE model agree with the theoretical boundary conditions

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

Back Up Slides

Parameter Value Unit

α 10.67 (lb/in-rad)1/2

A 13.67 -

B 336.3 -

p(x)max 97.66 ksi

pavg 57.61 ksi

PR 1.70 -

Parameter Left Tooth Right Tooth Unit

p(x)max 71.13 68.51 ksi

pavg 47.06 45.34 ksi

PR 1.51 1.51 -

d(x)max 0.00015 0.00015 in

davg 0.0014 0.00014 in

DR 1.1 1.1 -

Analytical Calculations Finite Element Calculations

Back Up Slides

Table 1 – Material Properties of 3D Spline Coupling Model

Specification Symbol Sleeve Shaft Unit

Material - IN-100 INCO718 -

Density p 0.284 0.297 lb/in3

Weight w 0.118 0.173 lb

Modulus of Elasticity E 30.1 31.0 Gpa

Shear Modulus G 11.94 11.10 Gpa

Polar Moment of Inertia J 0.085 0.037 in4

Back Up Slides

Table 2 – Geometric Properties of 3D Spline Coupling Model

Specification Symbol Value Unit

Applied Torque τ 350 in-lb

Contact Length L 0.30 in

Pitch Radius R 0.70 in

Number of Teeth N 56 #

Tooth Height c 0.032 in

Root Fillet Radius r 0.010 in

Pressure Angle θ 30 deg

Torsional Stiffness Cθ 3332488 lb/in-rad