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

What are we trying to accomplish?

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

Project Overview  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 Cold part dimensions DAS Info. (Hot part surface Temp. and Dimensions) TIG Dimensional Specifications Dimensional Error PPCS Cooling Process Information

 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 Research Objectives

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

Finite Element Analysis Part Geometry Cooling Process Simulation Forging Process Simulation

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

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

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

DOE Extract Responses Criteria for Design Of Experiments Process VariablesSimulation Time Accuracy Required Conduct Simulations at DOE points Design Scheme

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

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

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

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

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

Research Approach Monte Carlo Simulations Input variables(X) x1x1 x2x2 xnxn  Responses (Y) y1y1 y2y2 ymym  Uncertainty Quantification Analysis Trade-Off Studies Uncertainties Analysis

 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

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

Forging ProcessCooling process Forging load  Conduct Design of Experiments  Initial temperature ° C  Stoke length mm  Friction  Heat transfer coefficient KW/m 2 K  Obtain responses  Load  Percentage change in hub dimensions A B C Material used: AISI 4140 Design process

Percentage Change in Dimensions Heat Transfer Coefficient (kW/m 2 K) Dimensional Variation With Cooling Rate Percentage change in dimensions Initial dimension – Final Dimension Initial dimension 100 * Outer Diameter Hub Diameter Hub Thickness

Dimensional Variation with Initial Temperature Percentage Change in Dimensions Heat Transfer Coefficient (kW/m 2 K)  Initial temperature effects part dimensions  No significant dimensional variations due to change in cooling rate

Dimensional Variation With Variation in Stroke Length Stroke lengths variation ±1mm Percentage Change in Dimensions Heat Transfer Coefficient (kW/m 2 K)  Significant variation in hub thickness due to change in stroke length  Stroke length has no effect on other part dimensions

Correlation effect on Dimensional Variation Percentage Change in Dimensions Heat Transfer Coefficient (kW/m 2 K)  Coupling effect is observed  Effect of Stroke length is greater than part temperature

 Stroke length has significant effect on load  Load decreases with increase in temperature and decrease in friction Load (10 6 N) Design variables Sensitivities on Load

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

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

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

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

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

Quality Control Parameters Hub Front Axle Parallel between planes 1 I.D to O.D run out Perpendicularity between planes  14 dimensions checked for quality control

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

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

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

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

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

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

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

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

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

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

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

Any questions ???

Thank you

Kinetic Models Kinetic Models (DEFORM) where ξ p = Volume fraction f T (T) = Temperature dependent transformation = Constants T = Temperature in Kelvin t = Time n = Integer from 1- 4 ξ = volume fraction = constants T = Temperature in Kelvin Diffusion phase transformationDiffusionless phase transformation

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

FE-C Diagram

Temperature distributionEffective stress Heat transfer coefficient 0.05 KW/m 2 K Point locations Output Parameters Time (sec) Temperature ( o C) Time (sec) Effective Stress ( MPa )

Section A Section B Section C Initial Area of the component = mm 2 (KW/m 2 K) Distortion Variation With Cooling Rate Representation of distortion as area  No significant change in distortion for air cooling

Section A Section B Section C Initial Area of the component = mm 2 At stroke Length +1 mm (KW/m 2 K) Distortion Variation With Cooling Rate

Section A Section B Section C Initial Area of the component = mm 2 Distortion Variation With Cooling Rate At stroke Length -1 mm (KW/m 2 K)

Phase Transformation model Axisymmetric disk

AT1= AT2= AT3=200 AT4=6 AT5= AT6=200 AT7=6 n= 1 AT1= 8E-8 AT2=300 AT3=300 AT4=6 AT5=300 AT6=900 AT7=6 n= 2.5 Ferrite Pearlite Martensite = = Constants for the equation AT1=.305e-4 AT2=150 AT3=200 AT4=6 AT5=550 AT6=200 AT7=6 n= 4 Bainite

Time Vs Temperature

Volume Fraction of Ferrite

Volume Fraction of Pearlite

Volume Fraction Of Bainite

Approach DEFORM HTABAQUS/DANTE Finite Element Package  Easy to model  Less convergence problems  NO Phase Transformation Models  Material data needed  Easy to model  Some convergence problems  Contains Phase Transformation and Material property data

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

Enhanced Design Uncertainties Initial billet temperature Ambient temperatures Material properties Scaling Press accuracy Operators repeatability Control system time lag Defects in bulk formed materials + Lubrication system Cooling rates Forging / Cooling Process Design Material waste Final product dimensions Product quality and reliability Process design Design Variables Material properties Press specifications Initial billet temperature Friction Die temperature Ambient temperature Heat transfer coefficient Finite Element Analysis Part Geometry Cooling Process Simulation Forging Process Simulation Surrogate Models DOE Extract Responses

Enhanced Design Uncertainties Initial billet temperature Ambient temperatures Material properties Scaling Press accuracy Operators repeatability Control system time lag Defects in bulk formed materials + Lubrication system Cooling rates Forging / Cooling Process Design Material waste Final product dimensions Product quality and reliability Process design Design Variables Material properties Press specifications Initial billet temperature Friction Die temperature Ambient temperature Heat transfer coefficient

 Identify critical process parameters  Computationally evaluate variations in the parameters  Develop surrogate models for forging and cooling processes  Conduct Monte Carlo simulations  Predict the probability of part failure  Determine effect on production cost  Generate acceptable hot part dimensions before cooling Approach