Uncertainty Quantification and Dimension Prediction in Forging and Cooling Processes

1. Uncertainty Quantification and Dimension Prediction in Forging and Cooling Processes Belur K. Badrinarayan Adviser: Dr. Ramana V. Grandhi

2. What are we trying to accomplish?

3. Introduction Closed-die forging Roll forging Trimming A B C D E Cooling process Inspection Inspection after cooling • Computer simulations (Database generation) Comparator/Estimator (TIG) Image Processing Billet is cut and induction heated

4. Project Overview Cooling Process Information Dimensional Error DAS Info. (Hot part surface Temp. and Dimensions) TIG Cold part dimensions Dimensional Specifications PPCS • Thermo-mechanically Induced Geometric variation estimator • Online software compatible with Predictive Process Control System and Data Acquisition System • Estimates the dimensional and geometrical relations between the hot and cooled states of forgings • Predicts dimensional error and suggests corrective measures

5. Research Objectives • Determine factors affecting final part dimensions • Quantify uncertainties in forging/cooling process • Predict hot part dimensions after forging • Incorporate into TIG • Reduce part rejection and production costs

6. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation DOE Extract Responses Surrogate Models Hot Part Dimension Prediction Uncertainties Analysis

7. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation

8. Research Approach Forging Process Simulation Finite Element Analysis Inputs Outputs Forging Process Simulation Part Geometry Cooling Process Simulation Billet Shape Computer Simulation of Forging Process Part Geometry Billet Temperature Under-fill Die Geometry Strain Distribution Friction Factor Loads Press Characteristics Strain-rates Material Properties

9. Research Approach Cooling Process Simulation Finite Element Package Outputs Inputs Finite Element Analysis DEFORM HT ABAQUS/DANTE Part Geometry Part Geometry Forging Process Simulation Computer Simulation of Cooling Process Part Geometry Cooling Process Simulation Nodal Coordinates Heat Transfer Coefficient • Easy to model • NO Phase Transformation and Material property data • Easy to model • Contains Phase Transformation and Material property data Stress Distribution Kinetic Models Hardness Distribution Environment Temperature Material Properties Volume Fraction of Phases Sensitivity Analysis

10. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation DOE Extract Responses Surrogate Models Hot Part Dimension Prediction Uncertainties Analysis

11. Research Approach Criteria for Design Of Experiments Process Variables Simulation Time Design Scheme Accuracy Required Extract Responses Conduct Simulations at DOE points DOE

12. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation DOE Extract Responses Surrogate Models Hot Part Dimension Prediction Uncertainties Analysis

13. Research Approach Surrogate Models Response Surface Models Spline fit data • Regression curves • Linear, quadratic,…etc • and denote design variables • is the number of independent variables • Interpolations, ensure that the curve fit passes exactly through each data point • Linear, quadratic,…etc Surrogate models (Response Surface Models/ Spline fit) Surrogate Models

14. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation DOE Extract Responses Surrogate Models Hot Part Dimension Prediction Uncertainties Analysis

15. Research Approach Measured part temperature after forging Acceptable cold part limits from industry Upper and lower limit of the hot part Hot Part Dimension Prediction

16. Research Approach Finite Element Analysis Forging Process Simulation Part Geometry Cooling Process Simulation DOE Extract Responses Surrogate Models Hot Part Dimension Prediction Uncertainties Analysis

17. Research Approach Uncertainty Quantification Analysis Input variables(X) Monte Carlo Simulations Responses (Y) x1 y1 x2 y2   xn ym Trade-Off Studies Uncertainties Analysis

18. Billet Shape Initial temperature Position Lubrication system Spray angle Spray time Spray speed Operational and equipment uncertainties Stroke length Environment temperature Heat Transfer Control system time lag Human repeatability Cooling Fan speed Conveyer speed Material properties Non-Homogeneity Scaling Hot Forging Process Uncertainties

19. Case Study-I Stroke Metal wheel Finite element model • Conduct forging and cooling simulations • Check effective stresses • Extract forging load after forging • Determine part dimensions after cooling • Conduct trade-off studies

20. Design process Forging load B C A Forging Process Cooling process • Conduct Design of Experiments • Initial temperature 1000 - 1300°C • Stoke length 19 - 21 mm • Friction 0.3 - 0.7 • Heat transfer coefficient 0.01 - 0.09 KW/m2 K • Obtain responses • Load • Percentage change in hub dimensions Material used: AISI 4140

21. Dimensional Variation With Cooling Rate Hub Diameter Hub Thickness Outer Diameter Percentage Change in Dimensions Heat Transfer Coefficient (kW/m2 K) Initial dimension – Final Dimension Percentage change in dimensions 100 * Initial dimension

22. Dimensional Variation with Initial Temperature Percentage Change in Dimensions Heat Transfer Coefficient (kW/m2 K) • Initial temperature effects part dimensions • No significant dimensional variations due to change in cooling rate

23. Dimensional Variation With Variation in Stroke Length • Significant variation in hub thickness due to change in stroke length • Stroke length has no effect on other part dimensions Stroke lengths variation ±1mm Percentage Change in Dimensions Heat Transfer Coefficient (kW/m2 K)

24. Correlation effect on Dimensional Variation • Coupling effect is observed • Effect of Stroke length is greater than part temperature Percentage Change in Dimensions Heat Transfer Coefficient (kW/m2 K)

25. Sensitivities on Load Load (106 N) Design variables • Stroke length has significant effect on load • Load decreases with increase in temperature and decrease in friction

26. Sensitivities on Dimensional change Percentage change (%) Design variables • Change in Stroke length has significant effect on dimensional change • Friction factor has no effect on dimensional change

27. Uncertainty Quantification • Generate Response Surface model • Conduct Monte Carlo simulations • Input variables have normal distribution • Plot Probability Density Function (PDF) • Undersize parts are rejected • Oversize parts are machined

28. Effects of Stroke Length Variation Probability Probability Probability Percentage change in dimensions Percentage change in dimensions Percentage change in dimensions Mean stroke length 19.6 mm Mean stroke length19.4 mm • Mean initial temperature: 1200o C standard deviation: 10 • Mean friction factor: 0.3 standard deviation: 0.02 • Mean stroke length: 19.4-19.8 mm standard deviation: 0.1 Mean stroke length 19.8 mm Negative value indicates increase in part thickness

29. Probability of Parts Out of Limits • Changing mean values affects the number of out-of-limit parts • Cost of acceptance and rejection influences the mean values • Costs are part dependent

30. Case II • Model Metaldyne hub front axle (part no. 4638) • Conduct sensitivity of cold part dimensions in the cooling process • Initial temperature • Dimensional variation during forging • Develop a mathematical model representing the cooling process • Determine acceptable hot part dimensions before cooling for TIG • Aids in better quality control

31. Quality Control Parameters 12 I.D to O.D run out 9 6 1 5 7 10 4 Hub Front Axle 3 14 2 11 Parallel between planes 13 Perpendicularity between planes • 14 dimensions checked for quality control

32. Part Modeling • Validate section assumption for further analysis Section II Section I (upper limit) Section II (lower limit) Section I Material used : AISI 5140 All dimensions in mm • Dimensions of both sections do not change significantly after cooling; section I is considered for further analysis

33. Cooling Process Validation Location - 1 Location - 2 Location -3 • Parameters checked at three critical locations • Temperature drop • Volume fraction • Principal stresses Maximum Principal Stress (Mpa)

34. Volume Fraction (Location-1) Volume Fraction Temperature (º C) Time (sec) Location -1 • Martensite formation is insignificant

35. Volume Fraction (Location-2) Volume Fraction Temperature (° C) Time (sec) Location -2

36. Volume Fraction (Location-3) Volume Fraction Temperature (° C) Time (sec) • Volume of the part increases at this location Location -3

37. Principal Stresses Max Principal Stress (Mpa) Time (sec) • Martensite formation is less • Principal stresses follow acceptable industrial trend

38. Development of Dimension Estimator • Conduct Design Of Experiments • Compute percentage change in final cold part dimensions as responses • Determine correlation effect of process variables to obtain number of parameters for the surrogate model • Spline fit DOE data to obtain surrogate model • Surrogate model predicts acceptable hot part dimensional limits • Validate predicted dimensions

39. Correlation effect on Final Dimension Percentage Change in Dimensions (D10) D10 Plotted Dimension Design Of Experiments • Initial part dimensions varied individually to determine correlation effects • No correlation effect • Final dimensions depend on the individual initial part dimensions and temperature

40. Final Dimensional Variation Temperature - 1000º C Percentage change in dimension Dimensions • Responses are different and independent for all part dimensions • Spline fit variations to predict the limits on hot part dimensions as a function of initial part temperature

41. Mathematical Model Validation All dimensions in mm Upper dimensional limit Lower dimensional limit • Compare predicted and computed dimensions (upper and lower limit) • Error is found to be within permissible limits

42. Summary • Quantified forging/cooling process uncertainties • Investigated trade-off studies to improve process design • Developed surrogate model to predict hot part dimensional limit for various input temperature • Incorporated hot part dimension predictor into TIG • Reduced part rejection rate during forging

43. Any questions ???

44. Thank you

48. Kinetic Models ξ = volume fraction = constants T = Temperature in Kelvin = Constants T = Temperature in Kelvin t = Time n = Integer from 1- 4 • Kinetic Models (DEFORM) Diffusion phase transformation Diffusionless phase transformation where ξp = Volume fraction fT(T) = Temperature dependent transformation

49. Kinetic Model Volume fractions of the phases are denoted by , with subscripts of A,F,P,B, and M referring to austenite, ferrite, pearlite, bainite, and martensite. Time is represented as t, temperature as T, Carbon wt. % by C. The mechanical properties of each phase are input from the DANTE material datafiles, and the mechanical response of the composite structure as it changes during heat treatment is calculated. Diffusive mobility functions are a function of temperature, while the martensite mobility is a function of carbon. mobility equations

50. FE-C Diagram