1. WARNING -- This document contains technical data the export of which is or may be restricted by the Arms Export Control Act and the International Traffic in Arms Regulations (ITAR), 22 C.F.R. parts 120 – 130. Diversion contrary to U.S. law is prohibited. The export, reexport, transfer or re-transfer of this technical data to any other company, entity, person, or destination, or for any use or purpose other than that for which the technical data was originally provided by P&W, is prohibited without prior written approval from P&W and authorization under applicable export control laws. ITAR/USML Category(subcategory): VIII(i). This document is marked to the highest level of export control and may contain technical data that is controlled at a lower level. Consult your local Business Area Export Representative to determine if it is possible to revise or redact the document to change the level of export control. P&W Proprietary contained in this presentation Evaluating and Accounting for Stiffness Differences between 2D Axisymmetric and 3D Cyclic Symmetric Models at Slotted Interfaces Kurt Leach 3/21/2012

2. Problem: The 2D Stiffness using Plane Stress Elements is Different than the True Stiffness at Slotted Interfaces 2 This page contains no technical data. 2D Model uses plane stress with thickness elements to model the tab Thickness applied = (Number of Tabs) X (Thickness of One Tab) Does not differentiate between thick low count tabs, or thin high count tabs –i.e. 2 tabs 10” thick is accounted for the same way as 100 tabs 0.2” thick Interface load differences can be as high as 15-20% in some cases

3. Two Main Objectives: Evaluate 2D vs. 3D Stiffness Differences, and Account for the Stiffness in 2D Use 2D and 3D models to evaluate stiffness differences Evaluate the effect of: Number of Tabs % Material Removed by the Tab Come up with a way to accurately account for the stiffness in the 2D model 3 This page contains no technical data.

4. Model Parameters are Typical of a High Turbine Rotor 4 1.250”1.500” Tab Height 0.400” Θ 12.000” Θ 20.000” Θ 12.000” Θ 21.000” 1.500” 2.500” Tab Length

5. Model Parameters are Typical of a High Turbine Rotor 5 Common contact stiffnesses (KN = 1e10) were used between 2D and 3D models (2D uses CONTAC12s, 3D uses CONTA174s)

6. Four main variables are captured: % Material Removed, Tab Length, Tab Height, Number of Tabs 6 Tab Width

7. % Material Removed does not drive 2D vs. 3D difference, but number of tabs does % Material Removed is not a large driver The number of tabs has the greatest effect here As number of tabs decreases: Tabs get wider 3D Interface Load decreases As tabs get wider, plane stress for the tab is no longer applicable 7 For this portion of the study, Plane Stress with Thickness elements were used in 2D to model the tab. Tab Height was held constant at 0.400” and Tab Length was held constant at 1.000”

8. There are a number of ways to alter the 2D model to achieve the true stiffness of the tab 8 Ideas to alter the 2D model to more accurately account for stiffness: Use Plane Strain Elements for Tab Use Axisymmetric Element with Zero Out-of-plane Modulus for Tab Modify Axial Modulus of Tab to reduce bending stiffness Maybe use simple shell model to evaluate what the 3D stiffness should be Modify Full Hoop Region Adjacent to tab to reduce bending stiffness of full hoop region Open to more suggestions!!!

9. Plane Strain Elements at Tab Provide More Accuracy at Low Tab Counts, but Still Not within 10% in some cases 9 Using Plane Strain Elements at the does not accurately capture the stiffness of very low tab counts (4 tabs), and can be too soft for high tab counts. Plane Strain Elements were used at Tab for this Study

10. Axisymmetric Elements with Zero Hoop Modulus at Tab are No Better than the Plane Stress with Thickness Elements 10 These results are very similar to the plane stress with thickness results, and do not provide any better capability than the Plane Stress with Thickness Elements Axisymmetric Elements with Zero Hoop Modulus were used at Tab for these results

11. Reducing the Axial Modulus of the Tabbed Region Does Not Significantly Effect the Stiffness of the Flange 11 Reducing the axial modulus does not significantly reduce the bending stiffness of the flange. Something else other than the tab is driving stiffness difference. Plane Stress with Thickness Elements were used at the tab, with reduced axial modulus to reduce the bending stiffness

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