Min. Life for a Titanium Turbine Blade

1. Workshop 9 Robust Design – DesignXplorer Min. Life for a Titanium Turbine Blade

2. Robust Design Z • Goals: Based on stress and fatigue analysis we wish to optimize the minimum life for the titanium turbine blade shown here. • Problem setup: The optimal X and Y location for the blade will first be determined by holding the fillet radius constant and running a DX DOE optimization for minimum fatigue life. After determining this optimal location we will account for manufacturing uncertainty in a Six Sigma Analysis. Finally we will use Robust Design to determine the optimum fillet radius given the uncertainty. • The airfoil root is a fillet radius which represents a design variable. • The analysis and fatigue preparation is detailed on the next several slides. The workshop uses the Simulation database as a starting point for our robust design. X Y

3. Robust Design • An initial set of parametric values has been chosen: • Xtilt = 1.5 • Ytilt = 1.0 • Radius = 0.25 • A preliminary analysis has been completed using the Simulation Fatigue tool to determine fatigue life. Each cycle represents one startup sequence for the unit from 0 to 7000 rpm. • Note: throughout this workshop the effect of mesh density, number of statistical samples, etc. has been largely ignored in the interest of time. The results obtained in repeating this workshop may not exactly match those show in the accompanying figures. In actual practice, as with any analysis, proper care should be given when addressing each of these.

4. Robust Design • The preliminary analysis predicts a minimum fatigue life to be 1591 cycles for this configuration (note, the result has been scoped only to the blade surfaces shown here). • Minimum fatigue life has been made parametric in order to proceed with the study.

5. Robust Design • An initial DOE study will be performed on the blade to determine the initial configuration for the X and Y blade tilt. • From the project page choose “New DesignXplorer study”. • When prompted, Save the database file to proceed. • Initially we wish to optimize the blade’s angular location (x and y tilt). For this study uncheck the fillet radius to remove it from the process. • The 2 input parameters will be treated as design parameters and we will allow a +/- 10% variation in their values (default). • From the top menu choose “Run” > “Solve Automatic Design Points”. • Note: with 2 input parameters the DOE method will evaluate 9 solutions to build a response surface.

6. Robust Design • When the solutions are complete the response surface can be viewed by highlighting the “Responses” view. • As the response surface indicates there appears to be an optimal location for the minimum fatigue life. That is, a particular combination of x and y tilt that will result in a maximum fatigue life. • We could, of course query the response surface to find this location but the Goals Driven Optimization (GDO) feature is ideal for this task.

7. Robust Design • To use the GDO feature we must first generate a sample set from the response surface. • Switch to the “Goals Driven Optimization” view. • For this workshops we will generate a set based on 1000 samples. • Choose 1000 and “Generate”.

8. Robust Design • From the sample set we can now generate candidate designs based on goals of our choosing. Select “Maximum Possible” as a desired value for Life Minimum. • Generate the candidate designs.

9. Robust Design • Recall our initial analysis predicted a minimum fatigue life of approximately 1600 cycles. The candidates from this DOE study indicate we can improve the fatigue life. The optimum configuration chosen is: • Xtilt = 1.58 • Ytilt = 0.9 • We’ll use this information to proceed with the Six Sigma Analysis. • Return to Simulation and insert the geometry parameters. • From the geometry menu choose to “Update: Use Simulation Parameter Values”. • When updated, “Solve” this configuration.

10. Robust Design • Design For Six Sigma: We have determined that the minimum fatigue life in the model is approximately 38,000 cycles. However several of our input parameters represent uncertainty variables thus there will be some variation in this minimum life. The response variation will be represented by some distribution (see right). • For example the data shown here is based on a Gaussian distribution of the X and Y tilt with the fillet radius held constant. As can be seen, the probability that the blade will fail is represented by a function related to the input variation. • Previously our deterministic study predicted a single value for minimum life. With the uncertainty included we can see that figure can be as low as 722 cycles. Minimum Life

11. Robust Design • With the new analysis complete return to the Project page and choose to start a “New DesignXplorer study”. • When prompted “Save” the existing study. • For this study we wish to account for manufacturing uncertainty in our optimal tilt values. Switch the parameters ds_xtilt and ds_ytilt to be “Uncertainty Variables”. We’ll leave the distribution type as Gaussian and use the default ranges. • For this study we also include the fillet radius “ds_rootrad” as a design variable with a +/- 20% range.

12. Robust Design • From the top menu choose “Run” then “Solve Automatic Design Points”. With 3 input parameters DX will perform 15 solutions. • In order to complete a robust design study we must first generate a six sigma analysis (SSA) sample set and flag the uncertainty in the response as parametric. • Highlight the Six Sigma Analysis view. • Activate 1000 and generate the sample set.

13. Robust Design • With the sample set generated select the “Life Minimum” response from the drop down list. • Based on maintenance schedules, warranty, etc. it has been determined that a fatigue life of 4500 cycles is acceptable. As the probability table shows, this represents approximately a –3 sigma level. We’ll base our robust design around this level. This level represents a design point where 99.9 % of our samples perform acceptably. • Enter 0.001 in the field and choose “Insert New Probability Value”. • With the new entry in the table toggle the ‘P’ to make the minimum life for this probability parametric.

14. Robust Design • With six sigma parameters flagged notice the “Robust Design” view is now available. • Robust Design contains a Goals and Candidates section much like the main GDO view used previously. • To perform a Robust Design we must again generate a sample set based on the DFSS responses calculated earlier. • Activate 100 for the sample size and “Generate”. • Note: as shown, to generate 100 samples DX must perform 100,000 evaluations of the DFSS response surface.

15. Robust Design • The goals and candidates used in robust design are obtained by evaluating a number of screening samples from the SSA. • Set the desired value for life to “Maximum Possible” • Candidate designs can be generated based on the stated goals.

16. Robust Design • Conclusion: Recall that our initial configuration resulted in a predicted minimum fatigue life of around 1600 cycles. In addition we had no “feel” for the predictability of this number. After completing the Robust Design we have improved the performance (minimum life) but can now attach a level of confidence to that prediction. Initial Results Final Results