Rule-Based software tool to specify the manufacturing process parameters for a contoured EB-PVD coating

Rule-Based software tool to specify the manufacturing process parameters for a contoured EB-PVD coating W.C.S. Weir a, R.D. Sisson, Jr. a, S. Bose b a Worcester Polytechnic Institute Manufacturing Engineering Program Worcester, MA 01609 USA b Pratt and Whitney Turbine Module Center North Haven, CT 06473 USA ABSTRACT A rule-based design software tool has been developed to specify the manufacturing process parameters to fabricate a contoured electron beam physical vapor deposited (EB-PVD) partially stabilized zirconia (PSZ) thermal barrier coating (TBC) on a curved surface. The expert data for this tool was developed from model predictions based on an experimentally verified, theoretical model of coating deposition rates as a function of position in the PVD vapor cloud (Knudsen cosine law). The predictive model was used for a wide variety of process parameters, including shadowing and non-uniform angular rotational velocity, to develop a database of contoured coating profiles (forward chaining). A coating profile matching routine was developed to identify the process parameters that yield a coating profile that matches the designers coating profile. The focus of this presentation will be on the software tool with emphasis on the expert database development and the coating thickness profile matching for a curved surface. Keywords: EB-PVD, rule-based design, TBC, PSZ 1. INTRODUCTION: New process development in Electron Beam Physical Vapor Deposition (EB-PVD) at Pratt and Whitney is currently based on experience and multiple process trials. A system capable of specifying the process parameters required to yield a required partially stabilized zirconia (PSZ) thermal barrier coating (TBC) thickness on complex curved surfaces could reduce the time and expense of new process development and expand the utility of the EB-PVD coating process. A model capable of predicting TBC thickness as a function of position in the one of Pratt and Whitney s coating chambers has been developed and experimentally verified for a flat plate and a cylinder. The model is based on the application of the Knudsen s cosine law of emissions. [1] This model has been run repeatedly to populate a database with TBC thickness data from 24 points on a cylinder for a wide range of EB-PVD process parameters. A program has been created which will search the database of virtually coated cylinders created by the TBC thickness prediction model, and given the TBC thickness at one or more points on the cylinder, the database can be queried in order to find the EB-PVD process parameters required to apply the requested coating thickness. 2. RULE-BASED EXPERT SYSTEM The goal of this paper is to present the methods and development of a rule-based expert system created for predicting the EB-PVD process control parameters required to generate any reasonable TBC profile on a cylinder. The parameters being controlled include, amount of coating material or ingot evaporated, height above the ingots and depth of insertion into the coating chamber. 330 Intelligent Systems in Design and Manufacturing III, Bhaskaran Gopalakrishnan, Angappa Gunasekaran, Editors, Proceedings of SPIE Vol. 4192 (2000) 2000 SPIE 0277-786X/00/$15.00

A rule-based expert system that can function as an expert in a narrow knowledge domain is typically made up of three parts. First, there is a knowledge base, which is collected through interviews, recorded case knowledge, experimental results, and other interactions with experts in the desired field. [4] Second, there is an inference engine which sorts through the knowledge base to retrieve the requested knowledge. [4] Third there is a user interface, which accepts inputs and returns the requested knowledge in a cogent format. [4] 2.1. Knowledge Base Pratt and Whitney s ability to predict TBC thickness is based on process control data, and the accumulated experience of process experts. New process development depends almost entirely on conducting trial runs and the ability to extrapolate using current process data. Forward Chaining Mass of Ingot Evaporated Position in the Chamber TBC Thickness Prediction Model Knowledge Base of EB-PVD Coating Profiles Angular Velocity Density of Ingot and TBC Knowledge Base Interface Backward Chaining Figure 1. Basic Structure of the EB-PVD Rule-Based Expert System [5] Since the available knowledge of the EB-PVD process is limited to current practice and standard operating conditions, the development of an expanded knowledge base will have to rely on an experimentally validated TBC thickness prediction model. 2.2. Forward Chaining Inference engines typically fall into two categories, forward chaining and backward chaining. [6] A forward chaining system uses given input values to query the knowledge base using a predetermined set of questions in a systematic fashion. [7] Proc. SPIE Vol. 4192 331

The forward chaining half of the system developed for the EB-PVD process relies on the TBC thickness prediction model. Since the amount of knowledge is limited, the TBC thickness prediction model has been run repeatedly for a series of cylinders located at different heights and different positions using different weights of ingot material. These iterative calculations represented in Figure 1 by the arrow in the center of the figure, represent the coating profile prediction routine. This routine was run repeatedly to develop the expert knowledge database that is represented by the pink square in Figure 1. Unlike a forward chaining system, a backward chaining expert system begins at the desired goal and attempts to prove the related assumptions. [7] 2.3. Backward Chaining A backward chaining expert system arbitrarily chooses a statement from a large list of possible solutions, and then applies the system rules to the values input by the user in order to test the arbitrarily selected result. If the application of the system rule to the user inputs does not yield the chosen result, the system simply chooses another result and continues to apply the user inputs to the rules until the a satisfactory match is found. [7] The backward chaining half of the system developed for the EB-PVD process systematically chooses an arbitrary coating profile from the knowledge database and compares the TBC thickness values input by the user or coating engineer in order to find a match within the tolerance specified by the coating engineer. When several acceptable TBC thickness profiles are found for the user input TBC thickness and tolerance values, the system returns both the TBC thickness values and the process parameters required to apply these coatings in a Pratt and Whitney EB-PVD coating chamber. Backward chaining is particularly useful when there are a reasonable number of possible conclusions, or when the number of possible conclusions can be narrowed using the users inputs. [7] In the EB-PVD system the number of possible conclusions can be immediately narrowed using the user inputs. 3. DEVELOPMENT OF THE EB-PVD KNOWLEDGE BASE Since the amount of available knowledge regarding new EB-PVD process parameters was limited to current practice the EB-PVD knowledge base for the software system relies heavily on an experimentally verified TBC thickness prediction model which is capable of predicting TBC thickness as a function of position in the EB-PVD coating chamber. 3.1. TBC Thickness Model The TBC thickness model is an application of Knudsen s cosine law of emissions [1] to a cylinder. d M e cosφ cosθ ρπ r = 2 (1) Equation 1 states that the coating thickness deposited at a point (r, φ,ϕ ) on a receiving surface, from an ideal point source is equal to a function of the mass evaporated (M e ), the coated material density ( ρ ) and the radial distance from the point source (r). Γ M e dae dt (2) = tae In order to account for the contribution of a surface rather than a point vapor source, Equation 1 must be integrated over the entire surface of the circular vapor source. Since every point on the emitting surface or ingot surface area can be defined by it s own radial distance (s) and angle (α ) from the ingot center. The double 332 Proc. SPIE Vol. 4192

integral over time (t) and emitting area (da e ) in Equation 2 [1] can be rewritten as a triple integral over time (t), radial distance (s) and angle (α ) and combining it with Equation 1 results in Equation 3. d = tsα Γs cosφ cosϕ dαds dt 2 ρπ r (3) Using simple geometry the terms cos φ, cos ϕ, and r 2 must be written in terms of radial distance from ingot center (s) and angle(α ) in order to solve the integration. The cosine of the angles ϕ can be found by calculating the gradient of the surface of the surface receiving coating at any point (x,y,z) cylinder, and dotting it with the radial vector between any (x,y,z) cylinder and any (x,y,z) ingot surface. From geometry the cosine of the angle ϕ is simply equal to z cylinder divided by the radial distance r. Making the necessary substitutions and solving the double integral using a Rhomberg integration technique yields Equation 4. d = M e 2 2 [Rhomberg Integration Result] (4) π 1 s ρ The mass of PSZ evaporated (M e ) is recorded for each run in terms of inches of ingot burned. The density of the TBC ( ρ ), was experimentally determined to be approximately 60% of the theoretical density of ZrO 2.[3] Therefore, Equation 4 can be used to estimate the coating thickness applied to any given point (x,y,z) on the surface of a cylinder locate at any given position in the coating chamber. Assuming that the affect of two ingots is cumulative, Equation 4 can be applied twice and the result can be summed to yield the total applied coating thickness to any point (x,y,z) on the surface of a cylinder. 3.2. Experimental Procedure: The model was verified with seventeen different experiments. Three cylinders and fourteen flat plates were coated. Each experiment was static, and the parts being coated were held stationary at a specified distance from the vapor sources. The three twelve inch long cylinders were cut and mounted in six places per cylinder. From these mounted cross sections photomicrographs of the TBC were taken and the TBC thickness was measured at approximately every eleven degrees around the entire circumference of each section yielding 192 measurements per cylinder. The flat plate experimental fixture had 210 different positions in which the small flat experimental pieces could be mounted. Each of the 1010 samples collected were measured with a micrometer and weighted before and after EB-PVD coating. Several of the small flat experimental pieces from each experiment were cut and mounted and photomicrographs were taken in order to measure the TBC thickness and verify the weight gain and measured thickness data being collected. 3.3. Experimental Results: The results of the experimental work confirmed that Knudsen s cosine law could be calibrated to accurately predict TBC thickness applied to flat plates and cylinders coated using EB-PVD. Figure 2 shows a plot of coating thickness versus polar position for one cross section of the first cylinder that was coated. One of the data series shows the actual experimental results and the other shows the calibrated model prediction. Figure 3 is a scatter plot comparison of the experimental data versus the experimental data from the same cross section. Proc. SPIE Vol. 4192 333

Thickness vs. Polar Position Experiment #90 (9th cross section) Thickness (mils) 16 14 12 10 8 6 4 Actual Adjusted Model 2 0 0 22.5 45 67.5 90 113 135 158 180 203 225 248 270 293 315 338 360 Angle on cross section (degrees) Figure 2. TBC thickness as a function of polar position on a circular cross section Measured Thickness vs. Predicted Thickness Experiment #90 (9th cross section) y = 1.0436x - 0.2894 R 2 = 0.9794 16.0 Adjusted Predicted Thickness (mils) 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Actual Thickness (mils) Figure 3. Scatter plot of experimental TBC thickness versus predicted thickness from the first cylinder experiment 334 Proc. SPIE Vol. 4192

y = 1.1046x - 0.8644 Measured Thickness vs. Predicted Thickness R 2 = 0.9365 Experiment #4 Measured Thickness (mils) 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 Predicted Thickness (mils) Figure 4. Thickness measured with a micrometer versus predicted thickness from the 4 th flat plate experiment. Figure 4 shows a scatter plot of the flat plate data versus the predicted data from the fourth flat plate experiment. This plot is characteristic of the other eleven flat plate experiments, which indicate that the cosine law of emissions can be applied successfully to evaporation from EB-PVD sources. 3.4. The Knowledge Base: Once the predictive model was experimentally verified a routine was written in Microsoft Visual Basic to loop the TBC thickness model for a cylinder through a range of all possible cylinder locations in the coating chamber and weight of vapor source material evaporated. The output from the routine was stored in a Microsoft Access database and became the knowledge base for the remainder of the system. The output consisted of TBC thickness values for 8 points for three cross sections on a twelve-inch long cylinder. The eight points per cross section were evenly located at every 45 degrees around the circumference of the cylinder. One cross section was located at each end of the cylinder and one was located in the middle, 6 inches from the end. The TBC thickness values were stored in 24 different fields, one for each of the 24 points. The position of the cylinder and the amount of source material consumed were stored along with each of the predicted TBC thickness profiles. This enabled the database to return the EB-PVD process parameters required to create the TBC coating profile to which is was associated for any of the virtually coated cylinders stored in the dat abase. 4. DEVELOPMENT OF THE KNOWLEDGE BASE INTERFACE: The goal of this project was to create a rule-based software system capable of predicting EB-PVD process parameters needed to create any reasonable EB-PVD coating profile on a curved surface. A database interface utility was written in Visual Basic to complete the system, and allow the coating designers to quickly retrieve the knowledge stored in the database. The graphical user interface of the database interface utility for the cylinder database is shown in Figure 5. [2] The display features 24 input boxes, one for each of the 24 points labeled on the cylinder shown on the right hand Proc. SPIE Vol. 4192 335

side of the display. The user can input a required coating thickness for one or all of the points labeled on the cylinder. After inputting the required coating thickness values in the boxes on the left, the user is required to select a critical point from the pull down menu in the middle of the screen. The critical point is the point of principal interest to the user. Often the coating engineers are asked to produce a coating thickness at a specific point or region within a tight tolerance, while maintaining TBC thickness in other regions within a larger tolerance. This critical point feature was incorporated to address that specific need. Before the search can be initiated the user must input a general tolerance that will be applied to all the search values input by the user. The only exception to the general tolerance is the critical point that will be searched on one half of the general tolerance. Once the Match Coating button is pushed the interface utility compares the critical point to the Access database of virtually coated cylinders, and during the initial search on the critical point applies a tolerance equal to one half of the general tolerance. Once the software finds all the virtually coated cylinders that have a critical point value within one half of the general tolerance, the utility searches them to find the profiles that match the user specified coating thickness values with the general tolerance value. When all the virtually coated cylinders that meet the criteria are located, the TBC thickness values and the process parameters are displayed in the box along the bottom of the screen. The user can then adjust the tolerance and repeat the search in order to expand or limit the number of choices returned. In addition the user can compare the returned values with the input values on the same screen and select the process parameters that best fit the users requirements. Figure 5. The database interface utility graphical user interface [2] 336 Proc. SPIE Vol. 4192

5. CONCLUSIONS: The predictive model is capable of predicting EB-PVD TBC thickness on a variety of flat plates and cylinders to within one mil of TBC thickness. The software system and user interface allow effective access to the expert knowledge base created by the TBC thickness prediction model. Future versions of the prediction model and software system will be designed for gas turbine blades and vanes using several hundred points instead of the twenty four used in the cylinder software. In addition, a Chi-square profile sorting feature may be incorporated into the final version of the user interface. 6. ACKNOWLEDGEMENTS: The authors are grateful to Mr. Mark Zelesky, Pratt and Whitney, for his technical advice and enthusiastic support of this work, and to Mr. Steve Burns, Pratt and Whitney, for providing manufacturing support. 7. REFERENCES: 1. Glang R. Vacuum Evaporation. In: Maissel LI, Glang R, editors. Handbook of Thin Film Technology. New York: McGraw-Hill; 1970. p 1-3 to 1-123. 2. Goodwin S, Jasinski M, Munyon M, Niccoli E, Quitadamo M. Pratt and Whitney EB-PVD TBCs[MQP]. Worcester (MA): WPI; 2000. 3. Stevens R. Zirconia and Zirconia Ceramics. New Jersey: Magnesium Elektron Inc.; 1986. 56 p. 4. Ginsberg A. Automatic Refinement of Expert System Knowledge Bases. London: Pitman; 1988. 176p. 5. Careau AJ, Gautschi SB, Kelley RD, Serefli SA, Wright S. Pratt and Whitney EB-PVD TBCs[MQP]. Worcester (MA): WPI; 1999. 179p. 6. Ignizio JP, An introduction to expert systems: the development and implementation of rule -based expert systems. New York: McGraw-Hill; 1991. 402p. 7. Badiru AB. Expert Systems Applications in Engineering and Manufacturing. New Jersey: Prentice-Hall; 1992. 436p. Proc. SPIE Vol. 4192 337