Min. Life for a Titanium Turbine Blade

1
Min. Life for a Titanium Turbine Blade

• Workshop 9
• Robust Design DesignXplorer

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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.

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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.

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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 blades 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 gt Solve Automatic
  Design Points.
• Note with 2 input parameters the DOE method will
  evaluate 9 solutions to build a response surface.

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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.

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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.

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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.

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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
• Well 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
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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. Well
  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.

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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.

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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. Well 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.

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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.

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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.

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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