2007:251 CIV

M A S T E R ' S T H E S I S

Improved Aero Blade Design forMulti-Disciplinary Integration

Anders Olofsson

Luleå University of Technology

MSc Programmes in Engineering Mechanical Engineering

Department of Applied Physics and Mechanical EngineeringDivision of Computer Aided Design

2007:251 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--07/251--SE

Preface This report concludes the final step in reaching a Master of Science degree in Mechanical Engineering at Luleå University of Technology. The work was conducted at the department of Methods & Systems at Volvo Aero in Trollhättan, between April and September of 2007. First and foremost, I would like to thank my project supervisor Petter Andersson, project initiator Ola Isaksson, Patrik Boart, Peter Thor and Markus Andersson for introducing me into the captivating field of Knowledge Enabled Engineering and for your fellowship both in and outside working hours. A special recognition is honored to Patrik Boart and Peter Thor for their computer programming expertise, contributing to the result in this thesis. I would also like to thank my supervisors Stefan Sandberg and Mats Näsström at Luleå University of Technology for taking the time and giving me useful hints and project guidance throughout busy periods of their schedules. Furthermore I would like to acknowledge all the people at various departments at Volvo Aero for welcoming me with my questions and assisting me in between their concurrent projects. People like Fredrik Sandblom, Andreas Dahmm, Lars Ljungkrona, Jörgen Burman, Marcus Persson and Thomas Andersson among others have all provided valuable information for this thesis. Trollhättan, 2007-11-13 ___________________ Anders Olofsson

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Abstract Robust design and reduced lead-time are key issues in the general field of product development today. The meaning of KEE (Knowledge Enabled Engineering) can be generalized as a process to customize computer aided engineering systems to reduce the lead time for routine engineering work as well as securing the design “know-how” for specific components. As a part of the KEE development at Volvo Aero, methods and rules are defined and implemented in applications to secure repeatability and aid product developers in their routines. The aim of this thesis is to study and improve a knowledge based application programmed in Knowledge Fusion that describes an aero based definition in CAD, and to secure its downstream functionality. The problem statement is identified through surveys and an application study. Due to high complexity and surface inconsistencies, problems can arise in downstream work. Section curve definition is a problem since the methods used, are creating curves segmented by all points used as input. This leads to a complex and over-defined section curve with irregular curvature distribution. When the section curves are used to create the blade surface, the complexity and curvature peaks are inherited. From case studies and a CAD functionality study, a new approximation method is found for section curve definition, making it possible to reduce the number of segments. Since the spline complexity and curvature interference are found to be closely related, the new approximation method reduces both. New blade surface routines have been programmed where blade section curves are constructed with this approximation functionality. Reduced number of spline segments contributes to a smoother end surface with less curvature inconsistencies, more useful for further downstream work. Although the new application for modeling aero blade profiles requires further evaluation and data handling improvements, the first generated blade profiles demonstrates that an improved surface quality with lowered complexity and low deviation from aero point definition is possible. The availability of the spline approximation functionality also opens new possibilities for future project implementations and model improvements. Keywords: Knowledge Based Engineering, Knowledge Fusion, Geometric Modeling, Blade Design, Vane Design

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TABLE OF CONTENTS

1 INTRODUCTION ......................................................................................8

1.1 VOLVO AERO.......................................................................................8

1.2 THE JET ENGINE...................................................................................8

1.3 BLADES AND VANES..............................................................................9

2 THESIS BACKGROUND........................................................................10

2.1 THE BLADE GEOMETRY APPLICATION....................................................10

2.2 KNOWLEDGE BASED ENGINEERING......................................................11

2.3 GEOMETRIC MODELING.......................................................................11

2.3.1 Order of complexity ..................................................................11 2.3.2 Splines......................................................................................12 2.3.3 NURBS.....................................................................................12 2.3.4 Polynomial interpolation ...........................................................13 2.3.5 Interpolation or approximation ..................................................13 2.3.6 Continuity .................................................................................13

2.4 THESIS DESCRIPTION..........................................................................14

2.5 THESIS APPROACH .............................................................................14

3 METHODOLOGY ...................................................................................15

3.1 INTRODUCTION TO FUNCTIONAL PROGRAMMING ....................................15

3.2 COLLECTING KNOWLEDGE...................................................................15

3.3 CASE STUDIES ...................................................................................15

3.4 OBSERVED PROBLEMS WITH THE BLADE GEOMETRY ..............................16

3.5 WHERE IN THE DESIGN PROCESS DO PROBLEMS OCCUR? ......................17

3.5.1 Modeling blend surfaces...........................................................17 3.5.2 Aero simulations on the generated surface ..............................17 3.5.3 CAM simulations.......................................................................18

3.6 NX AND KF FUNCTIONALITY STUDY......................................................18

3.7 HOW TO IMPROVE THE SECTION CURVES ..............................................20

3.8 IMPLEMENTATION OF APPROXIMATION FEATURE ....................................20

3.9 CLOSING THE SECTION SPLINES...........................................................20

3.10 COMPARING THE RESULTING SURFACES...............................................21

4 RESULTS AND DISCUSSION...............................................................22

4.1 RECAPITULATION ...............................................................................22

4.2 IDENTIFIED PROBLEMS WITH THE EXISTING APPLICATION ........................22

4.3 DOWNSTREAM BENEFITS OF REDUCED COMPLEXITY ..............................23

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4.4 ROBUST DESIGN IN A MASTER MODELING CONCEPT ...............................23

4.5 IMPROVED SECTION CURVE GENERATION..............................................23

4.6 APPLICATION FOR ITERATION...............................................................24

4.7 RADIUS OF BLENDS ............................................................................25

4.8 VALIDATION OF GEOMETRY .................................................................25

4.9 FUTURE WORK ...................................................................................26

4.10 ADDITIONAL IMPLEMENTATIONS ...........................................................27

5 CONCLUSION........................................................................................28

6 LIST OF REFERENCES.........................................................................29

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APPENDIX A - PROJECT DEFINITION........................................................30

APPENDIX B – COLLECTING KNOWLEDGE .............................................32

B.1 POINT DATA SET .....................................................................................32

B.2 REFERENCE GEOMETRY ..........................................................................33

B.2.1 Blade generated from Volblade data .............................................33 B.2.2 Vane generated from Volvane data...............................................33

B.3 ISOLATING THE APPLICATION PROGRAM CODE ...........................................34

APPENDIX C – CASE STUDIES...................................................................35

C.1 POINT REDUCTION OR SELECTION ............................................................35

C.2 COMPLEMENTARY 2D SECTION INSERTION................................................37

C.3 FOUR SEPARATE IGES-CURVES PER SECTION ..........................................38

C.4 FOUR SEPARATE SPLINES PER SECTION....................................................40

APPENDIX D – NX AND KF FUNCTIONALITY............................................42

D.1 SPLINE THROUGH POINTS AND SPLINE BY POLES .......................................42

D.2 FITTED SPLINE........................................................................................43

D.3 SWEEP OPERATIONS...............................................................................43

APPENDIX E – ADDITIONAL TESTING.......................................................44

E.1 GEOMETRY IDEALIZATION ........................................................................44

E.2 NUMBER OF EVENLY DISTRIBUTED POINTS PER SECTION.............................45

E.3 POINTS DISTRIBUTED BY CHORDAL TOLERANCE .........................................45

E.4 DEGREE AND NUMBER OF SECTIONS.........................................................45

E.5 2D VS. 3D SECTION CURVES....................................................................46

APPENDIX F – RESULTS FROM ADDITIONAL TESTING..........................47

F.1 NUMBER OF EVENLY SPACED POINTS ON IDEALIZED GEOMETRY...................47

F.2 POINTS BY CHORDAL TOLERANCE ON IDEALIZED GEOMETRY........................48

F.3 DEGREE AND NUMBER OF SEGMENTS........................................................48

F.4 2D VS. 3D SECTION CURVES....................................................................50

APPENDIX G – COMPARING THE RESULTING SURFACES ....................51

G.1 BLADE GENERATED FROM VOLBLADE DATA...............................................51

G.2 BLADE GENERATED FROM VOLVANE DATA ................................................52

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INDEX OF FIGURES Figure 1 Jet engine components .............................................................................................. 8 Figure 2 Blades after assembly ................................................................................................ 9 Figure 3 Design iterations with the blade geometry application............................................. 10 Figure 4 Potential KBE contributions to a design process ..................................................... 11 Figure 5 Complexity propagation for basic geometrical entities............................................. 12 Figure 6 Oscillating section spline curve created from data with strong 3D variation............ 16 Figure 7 Self-intersecting blend surface................................................................................. 17 Figure 8 Combs analysis in NX4 ............................................................................................ 19 Figure 9 Reduced complexity with approximated section curves using 40 segments ........... 24 Figure 10 Blend surface without self-intersection................................................................... 25 Figure 11 Forced tangency at the trailing edge of a section .................................................. 26 Figure 12 Point data set example........................................................................................... 32 Figure 13 Volblade based surface with 2790 surface patches............................................... 33 Figure 14 Volvane based surface with 3270 surface patches................................................ 34 Figure 15 The application interface and a generated vane.................................................... 35 Figure 16 Intersecting the blade surface ................................................................................ 37 Figure 17 Four separate IGES curves used to create four separate surfaces....................... 38 Figure 18 Four separately swept surfaces stitched together ................................................. 39 Figure 19 Topographic view of a section curve created in four parts..................................... 40 Figure 20 “Spline by poles” and “spline through points”......................................................... 42 Figure 21 Idealized section geometry in two dimensions....................................................... 44 Figure 22 Fitted spline on 207 evenly spaced points ............................................................. 47 Figure 23 Fitted spline on 207 points positioned by chordal tolerance .................................. 48 Figure 24 3rd degree 20 segments and 3rd degree 60 segments ......................................... 49 Figure 25 5th degree 20 segments and 5th degree 60 segments ......................................... 50 Figure 26 Improved blade surface with 828 surface patches................................................. 51 Figure 27 Curvature distribution displayed with highly scaled combs.................................... 51 Figure 28 Improved vane surface with 480 surface patches.................................................. 52 Figure 29 Curvature distribution displayed with highly scaled combs.................................... 52

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NOMENCLATURE KBE Knowledge Based Engineering KEE Knowledge Enabled Engineering CFD Computational Fluid Dynamics CAD Computer Aided Design CAM Computer Aided Manufacturing KF Knowledge Fusion (Copyright to UGS) MOKA Methodology and software tools Oriented to Knowledge based engineering Applications TE Trailing Edge LE Leading Edge NURBS Non Uniform Rational B-Spline (or Beziér Spline) API Application Programming Interface

1 INTRODUCTION

1.1 Volvo Aero Volvo Aero is part of the Volvo group. As a partner in a global market, Volvo Aero develops and produces components for aircraft and rocket engines. In the commercial jet engine collaborations, Volvo Aero is responsible for the development of components such as the intermediate case (IMC) and turbine exhaust case (TEC). Both of these components contains an array of vanes designed to re-link the airflow and distribute structural loads.

1.2 The jet engine The most common types of jet engines found on commercial aircrafts are high by-pass turbo-fan jet engines. The fundamental components are the fan, compressor, combustion chamber and gas turbine.

Figure 1 Jet engine components Air is propelled into the compressor by the fan. The compressor increases the pressure before the air is oxidized in the combustion chamber. Fuel is here

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added to a mixture rate corresponding to the thrust. High velocity exhaust gas drives the generator before exiting through the turbine exhaust case. A shaft transmits the energy from the generator to both the compressor and fan to complete the power cycle. Most of the air propelled by the fan is led outside the engine in the by-pass hannel. This is mainly done to enhance fuel economy for subsonic aircrafts.

1.3 Blades and vanes

ting vanes are vital components in the jet engine. s will vary from large bulgy outlet guide vanes up to 0,5 m in

cOther benefits are cooling capabilities as well as noise reduction.

Rotating blades and non rotaThe geometrieheight to small high-pressure, high velocity compressor rotors with sharp edges. Due to their different purposes, the design criterions will differ from component to component. Sometimes guide vanes are made hollow to reduce weight and/or to allow wires or pipes to run through its interior. Blades and vanes are manufactured by casting or traditional machining while others needs to be manufactured by electrostatic discharge machining to achieve the specified tolerances.

Figure 2 Blades after assembly

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2 THESIS BACKGROUND This chapter gives a brief introduction to the background theory, as well as the thesis description and approach. Further descriptions are referred to the appendix section.

2.1 The blade geometry application An application previously developed at Volvo Aero, is currently in use for semi-automatic blade geometry generation in CAD. The intentions for the application are to reduce lead-time in the design process and secure repeatability for the intended design. The blade profile originates from CFD simulations where flow-path coordinates are defined. Two different methods are used for this purpose depending on the type of geometry (blade or vane). A uniform point data set is however utilized where the flow-path coordinates are presented equally, regardless of the aero definition method. The work order for the application is to draw spline curves through the imported section points. A following sweep operation uses the created spline curves to generate a hollow blade surface referred to as a “sheet body”. Further optional steps are to create a solid body, a mid-shell surface or to split the solid body at the leading and trailing edges.

Figure 3 Design iterations with the blade geometry application

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2.2 Knowledge Based Engineering There are a number of definitions of KBE (Knowledge Based Engineering). In this thesis, KBE is defined as “the use of advanced software techniques to capture and reuse product and process knowledge in an integrated way”, where knowledge is referred to as information in context [1]. In the engineering design process, the main intentions are to [1]:

• Secure engineering knowledge by storage and reusability. • Reduce lead-time and cost of the design process.

One way to accomplish this is to integrate knowledge into an application that automatically can take care of routine operations that are time consuming for the engineer. In the end, lead-time for routine work is reduced and more time can be spent on creative design tasks.

Figure 4 Potential KBE contributions to a design process

2.3 Geometric modeling Since the challenges surrounding this thesis are associated with geometric modeling, this section introduces some background theory to the subject.

2.3.1 Order of complexity Considering that simple entities such as curves are the basis for most geometry, it is important to ensure their individual quality. It is also important to minimize the complexity of each curve since all information will be inherited into the resulting model and further on into the downstream iterations. Experienced modelers are familiar with the benefits of simplicity in early design steps. It is always preferred to define geometries from simpler entities

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such as lines and arcs prior to using the more complex spline curves. Low complexity geometries will have less size and handling problems as well as avoiding mathematical errors that can arise during modifications. All in all, simple geometries will give less manufacturing problems and the final product will be more accurate to the intended design if the complexity is low.

1. A point is the simplest entity, defined by one coordinate in (X, Y, Z). 2. A line is defined by the shortest distance between two points with

coordinates in (X, Y, Z). 3. The information needed for an arc is center point in (X, Y, Z), radius, start

and end point in 2D. 4. A spline contains information for start and end points, plus multiple number

of weighted poles in (X,Y,Z), curve degree and number of segments.

Figure 5 Complexity propagation for basic geometrical entities

2.3.2 Splines A spline is a function defined by piecewise polynomials put together as one curve, sometimes referred to as piecewise polynomial parametric curves. Splines are popular curves in CAD because of their relative simplicity and their ability to form complex shapes through curve fitting and interactive design. When interpolating smaller data sets, a spline interpolation is usually preferred over polynomial interpolation (2.3.4) since it gives similar results when using only a low degree spline [2].

2.3.3 NURBS Non-Uniform Rational B-Splines (or Beziér-Splines) are defined by their mathematical order, weighted control points and knot vectors. Like regular splines, NURBS are a combination of multiple curves put together as one. The difference is that the multiple curves are B-splines with weighted control

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points, giving unique modification capabilities. Adjusting one of the weighted control points will only influence the spline locally. Simple entities such as conics and circles can easily be constructed with NURBS [2].

2.3.4 Polynomial interpolation Polynomial interpolation is a typical method used to interpolate a data set of coordinates with a polynomial function. The aim is to find a polynomial that will match the given points as closely as possible. The number of points needed to define a single polynomial of degree n is n+1. However, fitting one single polynomial to a large number of successive points will most likely result in oscillation between data points, especially for high-degree polynomials. As the number of points and polynomial degree increases it becomes more difficult to match the function to the defined points. By using piecewise polynomials or splines, this problem can be avoided since the points can be distributed on low degree polynomial spline segments [3].

2.3.5 Interpolation or approximation When speaking about free-form modeling in the sense of constructing NURBS curves to reach more complex shapes following data sets, we need to study fitting. Fitting can be used to match a curve to a larger set of arbitrary points, either by interpolation or approximation. When interpolating a NURBS curve, the curve is supposed to pass through the assigned points exactly, while the approximation method allows the curve to take shortcuts through the given points, resulting in a smoother curvature. Deviating data will also have less influence on the overall curve when the approximation method is used [2].

2.3.6 Continuity Both curves and surfaces can be further specified by continuity classifications to describe the curvature propagation. Specified at an arbitrary point along a spline, the three main states of continuity are C1, C2 and C3. The C1 continuity condition states that the spline connects at the point. C2 continuity states that the two splines connecting to the point with C1 continuity also shares the same tangency direction at the given point. C3 continuity adds that the two connecting curves also have the same curvature at the given point.

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2.4 Thesis description The main purpose of this thesis is to collect knowledge about the methods used in the design process for blades at Volvo Aero today. Based on this knowledge, the aim is to implement an improved application for aero blade definition in CAD that can be integrated in a multidisciplinary environment. See APPENDIX A for the complete thesis work description.

2.5 Thesis approach As mentioned earlier, this thesis is about improving an existing blade application. The first task will be to understand what the problem is with the existing blade generation methods. The current design process will be examined through interviews along with a study of the existing application. From these findings, case studies and a CAD functionality study will be conducted to investigate if there are better blade generation methods more suitable for downstream activities and if an enhanced implementation is possible.

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3 METHODOLOGY This chapter explains the methods used to understand and address the thesis description. Throughout this chapter, a more detailed description of the assignment is presented. More details are referred to in the appendix section.

3.1 Introduction to functional programming To understand the fundamentals of the existing application, a pre-study was made on the CAD software, NX4. Free form modeling was interactively studied through the built-in tutorials. A self-tutored programming course was taken in KF (Knowledge Fusion) which is the built-in KBE programming language in NX4. KF is a functional programming language where the use of expressions allows rule-based programs to be built in the CAD environment. Knowledge, such as design rules are hereby captured and implemented in automated applications. [4]

3.2 Collecting knowledge The source-code and the modeling steps for the existing blade application were analyzed along with the point data set described in APPENDIX B. Individual interviews were conducted with specialists in aero/thermo, CAD and CAM definition to find and understand the problems concerning this thesis. The interviews where mainly conducted with one person at a time to secure the individual opinion. Known issues, ideas and opinions were collected and evaluated.

3.3 Case studies

Four case studies were conducted where general modeling procedures were tried and evaluated. Both interactive modeling and KF programming was used for the different cases where applicable. See APPENDIX C for more details on the specific case studies. Keeping the modeling steps to a minimum will provide a robust application. By only creating one closed spline for each section, there will only be one single surface. No stitch operation is needed where tolerance uncertainty is

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introduced. Any form of trimming or mapping of the surface can be done as a secondary procedure on the existing surface.

3.4 Observed problems with the blade geometry From interviews and studies of the application, potential issues with the existing methods for generating the blade surface was understood and noted. An oscillating interference is experienced on the surface that originates from the complexity of the section spline curves. The complexity is referred to as the number of segments in the NURBS curve. The oscillations are usually most common on vanes at sections where the curves have strong variations in height.

Figure 6 Oscillating section spline curve created from data with strong 3D variation When using a large number of segments to describe each section curve, the complexity is inherited into the swept surface creating a high number of surface patches. Further modeling steps such as creating a solid body will continue to build on the complexity. In the same way as spline segments, the number of surface patches governs the mathematical description of the surface, noted as complexity. Generally speaking, a highly complex surface will cause handling problems in down-stream activities. The complexity of one blade may not be experienced as problematical, but when inserted into an array of blades in assembly configurations, the graphical representation will increase the requirements on computer power.

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3.5 Where in the design process do problems occur? From further interviews, the implications of working with blades with inconsistent surface curvature and high surface complexity were documented.

3.5.1 Modeling blend surfaces One issue experienced with the existing application is when the blade geometry is connected to surrounding parts with blend surfaces. The problem at hand is that the radius of the blend surface can only reach a certain radius before it self-intersects. Time consuming modifications might have to be done before the desired radius can be accomplished. This problem is most common at the trailing edge and is believed to be a result of the surface complexity.

Figure 7 Self-intersecting blend surface

3.5.2 Aero simulations on the generated surface From an aero/thermo perspective, the generated surface should have minimal deviation from the defined point data set. This desire is motivated by the flow simulations performed close to the surface where a nodal distance of down to 10-6 mm is required. The accepted deviation depends on the individual blade geometry and its purpose, making it difficult to specify a maximum tolerance. A maximum deviation of 0,05 to 0,01 mm is often accepted but the deviation should preferably be under 0,01 mm at all times in order to justify the intended aerodynamic design. Surface inconsistencies can result in problems for flow simulations where airflows are analyzed at high Mach values, the results can become doubtful and difficult to evaluate since the pressure is likely to be influenced by the surface inconsistencies.

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3.5.3 CAM simulations In the end, complex geometries with high number of surface patches will give handling errors in CAM simulations where additional tools and rigs are modeled. Too high surface complexities can in a worst case scenario cause linear tool-paths forcing the surface to be remodeled. Depending on the manufacturing method, the possible tolerance will vary. In the case of traditional machining, a tolerance of down to 0,01 mm is possible. However, when additional post processing operations are performed to reach a desired surface finish, the intended tolerance may be lost to an unknown extent. When faced with an oscillating surface, the tool-paths may have to be reconstructed, creating an additional deviation from the intended design and increased lead-time. All information in the generated geometry, including oscillations, will be present in the manufactured product, if the manufacturing is done without tool-path modifications or post processing methods.

3.6 NX and KF functionality study The existing spline features in NX4 are spline through points, spline by poles and fitted spline. All spline curve alternatives in NX4 will produce NURBS curves with weighted control vertices. Spline by poles assigns the weighted control vertices on the points selected, while the fitted spline approximates where the control vertices should be positioned for the curve to match the assigned points with as little deviation as possible. Spline through points however, interpolates the curve to pass exactly onto the assigned points, positioning its control vertices where needed. See APPENDIX D for more details. Depending on the specific points as well as the number and order of points selected, the resulting spline will take a unique shape. This was studied more closely to find a pattern in spline behavior compared to point distribution and selection. The section spline curves were analyzed with the curve analysis option “Combs” in NX4, showing the curvature distribution of the selected spline. Displaying the Combs makes it easy to detect possible discontinuities in the curvature, unwanted inflection points or sudden changes to the curvature. The inflection points are where the second derivative of the cubic function changes polarity. See APPENDIX E and F for detailed description of the tests preformed.

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Figure 8 Combs analysis in NX4

The Knowledge Fusion module is based on the functionality in NX where features are translated into an object based relationship. However, not all functionalities are available in KF due to what the manufacturer (UGS) has included in the software. Among the spline features, only spline by poles and spline through points are available in KF for NX4, not fitted spline. To access additional features with KF such as fitted spline, the API (Application Programming Interface) provided by UGS must be utilized. The API is a library with exported functions that can be called into a C-function and translated to work in KF.

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3.7 How to improve the section curves Approximating the spline curve with the fitted spline feature is a good method to create section curves from points positioned in a successive order. This can be recommended since the curve can be governed by the number of segments that directly corresponds to the complexity. The mathematical description of the model, referred to as complexity is always inherited into the surrounding model and into the down-stream design chain. A high number of segments will increase the model complexity as well as the possibility for surface oscillations. A low number of segments imply the opposite.

3.8 Implementation of approximation feature The fit spline functionality has been implemented into KF through the UGS supported API library. Two programs have been developed to work for blades and vanes independently of their definition basis. Both programs build the blade geometry from section curves consisting of fitted spline approximations. The difference between the two programs corresponds to the positioning of the points and the sharpness in curvature between blades and vanes, which are essential parameters for the fitted spline end-result. For a vane section, one fitted spline approximation is created through all successive points corresponding to the pressure side, leading edge, suction side, and trailing edge. For a blade section, four fitted spline approximations are created for the trailing edge, leading edge, pressure side and suction side respectively.

3.9 Closing the section splines One of the disadvantages with the fitted spline function is that the generated spline cannot be closed to form one unified section. This is resolved by the use of another function available in KF called “ug_spline_askpoles”. Since both the functions “fitted spline” and “spline by poles” in the end builds the same type of NURBS curve with weighted control vertices, a closed “spline by poles” curve can be created in KF where the points are specified by the poles computed by the “fitted spline” approximation.

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3.10 Comparing the resulting surfaces To compare the implementations, new geometries were generated with the developed program codes using the same point data set as in Appendix B.2. The compared parameters were the number of surface patches, the point deviation and the combs curvature distribution. Detailed results of the comparison are presented in APPENDIX G.

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4 RESULTS AND DISCUSSION This chapter reconnects to the previous chapters and continues to describe the thesis results.

4.1 Recapitulation The aim of this thesis has been to study and improve a knowledge based application that describes an aero based definition in CAD and to secure its downstream functionality. To identify the problems associated with the current application, interviews have been conducted with engineers involved with aero definition, CAD and manufacturing simulation. Case studies have been performed to evaluate different modeling steps for a master modeling concept. A functionality study in NX4 has been conducted to identify and evaluate the available methods for spline generation and to investigate if there are better blade generation methods more suitable for downstream activities.

4.2 Identified problems with the existing application The existing semi-automatic application for blade generation is at times creating a self-oscillating surface pattern. The oscillating inconsistency originates from the section spline curves created by “spline by poles” or “spline through points” with a high number of segments. The “high number of segment” -splines are linked to all defining data points causing the spline to wiggle its way through each section. A section curve created through successive points with strong geometric variation will cause strong oscillation, while a curve created through points along a straight line will cause no oscillation.

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4.3 Downstream benefits of reduced complexity Reducing the complexity of the blade geometry will give less handling problems for all further activities. Since the surface complexity is governed by the number of segments in the section curves, the reduced complexity will also reduce potential oscillations in the curvature distribution on the section curves, resulting in a better quality surface. The most significant benefit of low complexity geometry is that the manufacturing will be more realizable to the intended design, meaning that the desired tolerance will be easier to establish.

4.4 Robust design in a master modeling concept From the performed case studies, the existing blade application method is found suitable as a robust design methodology. The modeling method builds one closed spline curve for each section. The section curves are later swept in one operation to create a single blade surface. These steps are considered more robust than creating partially swept surfaces that are stitched together as one, since tolerances are added in the stitching operation. Downstream tasks that require a mapped or divided surface can later from the master model geometry create the required intersections when and where needed.

4.5 Improved section curve generation A new method to generate blade and vane section curves has been programmed in KF. The method uses the fit spline approximation feature in NX4. The benefits of using the approximation feature to create the section spline curves are that the deviation to the initial point data is comparatively small when reducing the number of segments, and oscillating interference on the surface can be minimized.

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Figure 9 Reduced complexity with approximated section curves using 40 segments When generating a vane with the new method using only 40 segments per section spline, the number of surface patches was reduced by 85% compared to the existing application (using the same input data, see Appendix B2.2). The point to surface deviation was between 0,01 and 0,05 mm and the visual combs curvature distribution was smooth.

4.6 Application for iteration To create an activity description for the application and to find a prime number of segments, the improved application should be implemented as an iteration tool. Section curves can be defined by curve degree and number of segments as design parameters. A built in deviation checker can automatically give the points that are outside an accepted tolerance measured to the generated surface, so that the ultimate surface can be obtained with a limited complexity, regarding number of spline segments and spline degree. The use of “through curve mesh” as a sweep feature should still be available. Notable is however that the usage of guide lines brings additional sources of information into the modeling, and if they are of low quality, might corrupt the surface in height to an uncertain extent. The sweep feature “through curves” in KF should be specified with the section spline curves as alignment parameter which will control the surface patches according to the section spline knot points. This will keep the overall complexity limited.

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4.7 Radius of blends As a first evaluation, the new script was tested on a problem area in a concurrent business project. The problem is a recurring issue where the blade connects to the hub through a blend. The problem experienced is that the radius of the blend cannot be increased as much as wanted before the surface self-intersects. An existing blade with a known maximum radius of 6 mm was substituted with the new scripted blade, resulting in that the radius could be increased to 27 mm before self-intersecting. This does not necessarily mean that the new blade is more easily modified because the complexity is lowered, it can simply be that the shape between sections is different, but it gives a hint on improved surface representation and that this need to be studied further.

Figure 10 Blend surface without self-intersection

4.8 Validation of geometry It is difficult to validate the resulting surface quality from a CAD modeling perspective. It is also difficult to say what the ideal number of segments and acceptable deviation is for all blades and vanes. Depending on type of blade or vane, specific surface geometry, section curvature variation, manufacturing method etc, the accepted point to surface deviation will vary. The number of segments used for the evaluations in this thesis was reduced to 40 segments per section but could probably be reduced further. This should be evaluated more closely for each specific down-stream activity.

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4.9 Future work When closing the section splines as described in section 3.9 there will be a local disruption in the curvature distribution. These disturbed curvature elongations needs to be evaluated to what extent they are corrupting the model. When the approximated poles from more than one approximation are added in a spline by poles feature, a tangency constraint can be forced on the slope of the adjacent curves, creating a better transition for the approximated curves. This is considered possible through KF implementation.

Figure 11 Forced tangency at the trailing edge of a section The two programs created in this thesis should be combined into the previous application, where a user interface governs the generation of specific blades. The main parameters should be the degree and number of segments for the approximation of section curves. If the new approximation method is found to be inadequate in terms of deviation to the aero defined data, more research could be spent on finding a better customized approximation algorithm for 3D blade section curves. This algorithm could be programmed in C and implemented through the API library as the fitted spline function. The programmed code should be reorganized for enhanced understanding with written comments for each step. A user-documentation should also be written to explain the meaning of each parameter in the user interface. More improvements of the KF code can be done were lists of points are written to a specified “dump-file” on the user’s hard-drive. This would improve the data handling lead-time, speeding up the blade generation process.

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4.10 Additional implementations The new KF functionality of fitted spline will be possible to implement in any application where a spline curve needs to be modeled close to a large data set of points in successive order. By doing so, the reduced model complexity will begin to show results when parts are inherited in large arrays inside assembly structures. A nearby implementation might be the modeling of the inner and outer aero flow path curves. These curves are usually inherited into the next stage of the product definition process making up the hub and shroud surfaces and would quickly make the model less complex and easier to handle.

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5 CONCLUSION The functionality made available in Knowledge Fusion for spline approximation, where the curve degree and number of sections are the ruling parameters, is a better method to create blade section curves than the previous methods. By limiting the number of segments, the complexity is lowered and oscillations avoided. The reduction of segments is limited by the point to surface deviation, which must be within tolerance. The new blade generation methods produce an improved surface quality with less surface patches and low deviation from aero defined data. From the blade based data used as input in the reference geometry (Appendix B.2.1) , the number of surface patches was reduced from 2790 patches to 828 patches (70% reduction). From the vane based data (Appendix B.2.2), the number of surface patches was reduced from 3270 patches to 480 patches (85% reduction). Since the modeling procedure is kept to creating one closed blade surface with minimal amount of steps, the robust design intention is withheld. The implications of a simplified blade description will aid further downstream iterations and reduce the inherited data size that can cause potential handling problems. If the complexity can be minimized in the modeling step, the desired tolerance will be more likely to sustain in the manufacturing process. If the section curve deviation to the point data set must be forced below 0,01mm resulting in a high number of segments and possible surface oscillations, the final manufacturing simulation might have to be adjusted, causing a even higher deviation on the final product.

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6 LIST OF REFERENCES [1] Melody Stokes. Managing Engineering Knowledge – MOKA: Methodology

for Knowledge Based Engineering. ASME Press, 2001. ISBN 0-7918-0165-9.

[2] Les Piegl, Wayne Tiller. The NURBS book 2nd edition. Springer-verlag

Berlin Heidelberg New York, 2007. ISBN 3-540-61545-8. [3] Michael E. Mortenson. (1997), Geometric modeling 2nd edition. John Wiley

& Sons, Inc. New York, USA. [4] Peter Thor. Knowledge driven preprocessing for weld simulation. Master’s

thesis, Luleå University of Technology, Sweden, April 2006.

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APPENDIX A - PROJECT DEFINITION Thesis Work – Definition 20p Aerospace Advanced Engineering, knowledge based approach for aero blade definition in CAD. Background: Volvo Aero Corporation is a partner in different jet engine programs on a global market. In this partnership is Volvo Aero responsible for the development and manufacturing of sub components such as the rear or mid frame. These components are rich on interfaces to surrounding parts and are main contributor to the overall stress image for the whole engine as well as the aerodynamic performance. The requirements on multidisciplinary design and global collaboration in a concurrent engineering process are a challenge for the product development engineers and support functions. It is not surprising that engineering efficiency is in focus and that product development lead-time and robustness are key issues. KEE (Knowledge Enabled Engineering) is a way to adapt CAD, CAM and CAE systems to reduce lead-times for engineering work. It has been of special interest to support the conceptual design phase whereas 80% of product cost is set. This thesis is a part of the engineering development within KEE at Volvo Aero. The aim is to implement a (semi) automatic method that supports CAD definition based on knowledge captured in the engineering process. A part of this process will be to define and implement rules to describe an aero blade definition in CAD and secure the usability in downstream work. This will give you as a student a fundamental knowledge of Knowledge Based Engineering and how this can be used to reduce lead-time and improve product and process quality. Deliverables:

• A survey for best practice and methods for aero definitions in CAD used at Volvo Aero today.

• An enhanced blade application module that supports a Master Model concept in a multidisciplinary CAD environment that enables a seamless update of context models for Aero/Thermo and mechanical analysis as well as secure downstream (Manufacturing process source definition) usability.

• Documentation of the application in English. • Thesis Report (in English)

The thesis work will begin with documentary research, project planning and training in Knowledge Fusion and other tools necessary for the work. Recommended academic bearing:

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M.sc. Mechanical Engineering and experience/interest in computer programming. For further information, contact: Petter Andersson. Tfn: 0520-943 77 or e-mail: petter.andersson@volvo.com Dep: 9610, Methods&Systems Volvo Aero Corporation, Trollhättan.

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APPENDIX B – COLLECTING KNOWLEDGE

B.1 Point data set The KBE application is built to handle a data set of points (VOLS_10025725) that describes a number of stacked section curves optimized by flow-path simulations. Blades are initially defined from a Matlab design optimization platform that uses a C-program named Volblade to generate flow-path curves. Vanes are generated from a different program named Volvane that uses an Excel- spreadsheet to find section flow-path coordinates from a camber line (blade section mid-line) thickness distribution.

Figure 12 Point data set example

The point data set input-file for the KBE application is formatted so that both blades and vanes can be implemented into the application with the same criterions regardless if Volvane or Volblade has been used in the aero definition. When creating the point data set from Volvane (vanes), the flow-path coordinates are exported directly from the Excel spreadsheet. When creating the point data set from Volblade (blades), an arbitrary number of points have manually been inserted onto the optimized flow-path curves before being exported. The number of sections produced will vary between 11 to 21 sections all depending on the geometry complexity and how much the design needs to be governed. The number of points on each section is usually around 111-121 points.

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B.2 Reference geometry As reference, one vane surface and one blade surface was generated using the existing application. This was the done to clarify and evaluate what the application was producing, and to decide what the thesis was going to investigate more closely. The surface generations were performed using the default settings “spline by poles” option for creating section curves and “through curves” option for creating the swept surface.

B.2.1 Blade generated from Volblade data The reference blade generated by Volblade consisted of 21 sections with 121 points on each section. The generated section curves modeled with “spline by poles” resulted in 3rd degree splines with 121 weighted poles corresponding to the number of points specified. Each spline also consisted of 121 segments with 121 knot points. The generated surface had 155 patches in u-direction and 18 patches in v-direction, giving 2790 surface patches in total.

Figure 13 Volblade based surface with 2790 surface patches

B.2.2 Vane generated from Volvane data The reference geometry generated by Volvane consisted of 13 sections with 111 points on each section. The generated section curves resulted in 3rd degree splines with 111 weighted poles corresponding to the number of points specified. Each spline also consisted of 111 segments with 111 knot points. The generated surface had 327 patches in u-direction and 10 patches in v-direction. This all put together, gave the surface 3270 surface patches.

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Figure 14 Volvane based surface with 3270 surface patches

B.3 Isolating the application program code As a part of understanding the existing application, the KF program code was reduced to work without the user interface. The main functions of reading in the data point set and listing the points for the different executing children was kept and evaluated. Also the executing children for the primary functions such as generating section curves and sweeping the blade surface was kept for evaluation and modification. The first successful script generation was isolating all of the section points to visualize the aero data point set. This made it possible to interactively test the different spline features in NX and analyze the point set dependency when drawing splines.

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APPENDIX C – CASE STUDIES

C.1 Point reduction or selection The first case study was conducted with a Volvane input file representing a larger vane with relative smooth contour at the leading and trailing edges.

Figure 15 The application interface and a generated vane

The original application builds one spline curve for each section that is either defined by the KF-feature “ug_spline_cntl” or “ug_spline_thru”, corresponding to the NX-features “spline by poles” or “spline through points”. The surface is created with “ug_swept” or “ug_thru_curve” corresponding to the “through curves” and “through curve mesh” interactive sweep operations. The application creates the solid aero body by revolving the shroud and hub aero curves through the sheet body and trimming the unwanted sections. The point data set for these types of vanes delivers points positioned by curvature, meaning that the leading and trailing edges contains more defining points than the suction and pressure sides. As an experiment on how the number of points influenced the resulting spline curve, the original semi-automatic blade profile script was modified and the listed points where selected by jumping over every other point. Since the point

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distribution is continuous through out each section (no sharp transitions from closely positioned points to widely positioned points), the list of points used to construct the section splines was modified to only put out every other points as a first evaluation. As a second evaluation, every three points were put out. The point selection evaluations were meant to show the relationship between the resulting curve smoothness and the number of points used by the spline curve definitions. C1 Conclusion This would result in a simple geometry with one curve per section as well as lowered complexity. The deviation would however not be controlled in between each point that is excluded from the curve construction. More points are needed where the curvature is strong. Too many points will result in a large number of curve segments which contributes to a large number of patches in the final model.

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C.2 Complementary 2D section insertion The second case study has been focused on the existing application where the surface is produced. The generated surface was intersected with datum planes to isolate new 2D section curves at optional spans where new points were added once again. Since the first generated surface is sometimes considered undesired with oscillations, new 2D sections with new points are able to produce better section curves resulting in better surface quality. The number and position of the new points was positioned by the curvature, all intended for the definition of the new section curves.

Figure 16 Intersecting the blade surface

C2 Conclusion Starting out from a 2D standpoint will give better chance of achieving high quality section splines and minimizing the unwanted oscillations and curvature inflections. Regenerating new section curves from previously created geometry will cause a new possible source of surface deviations in the sweep operation. The issue of using too many points when defining the section curves is unsolved and has to be addressed when creating new points along the intersected curves. Due to the number of modeling steps, new problems can arise which makes the model less robust than a simpler model, problems such as misalignments and mismatches between points and lines as well as points and surfaces.

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C.3 Four separate IGES-curves per section The third case study was conducted using a blade definition in IGES format originating from Volblade generated flow-path curves. The section curves was imported into NX and modeled interactively. The IGES file contains four curves on each section. The end curves at TE and LE is a 2nd degree rational B-spline, originally defined by 7-8 poles constrained by C1 continuity in between its 5-8 segments. The suction and pressure sides are a 4th degree polynomial defined by 15 poles and C2 continuity in between its 11 segments.

Figure 17 Four separate IGES curves used to create four separate surfaces

The slope was first modified between the edge curves and the suction and pressure side curves with a tangency condition. After fixing the section curves, four guideline splines were created at the four connecting points in V-direction (along the blades height) to connect the given sections. These spline curves where used as primary string curves in the “through curve mesh” feature to create four separate surfaces. First the suction and pressure side surfaces were created, followed by the trailing and leading surfaces.

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Figure 18 Four separately swept surfaces stitched together C3 Conclusion The design will be completely unaltered from the original aero/thermo curve definition since no reconstruction will be needed. The versatility would however be lost where the application could be utilized for both Volblade and Volvane defined geometries since Volvane only produces points. More research would have to be made to find whether Volvane could be redesigned to produce IGES-curves. This method would however result in a “stitch operation” where a tolerance is used causing a possible uncertainty in deviation.

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C.4 Four separate splines per section The final planned case study was preformed with the previously used Volvane input file. Four curves on each section were created from the data point set. The section curves were created interactively in NX with the spline feature “spline through points” and the curve degree was kept to three. All points were selected when chaining the spline function, disregarding the possible waviness issue. The leading edge (LE) area on each section was isolated by the leading edge point given by the point data set and 8 points on each side of it. The trailing edge area on each section was isolated by the given trailing edge point and 6 points on each side. It was important to ensure that the curvatures and slopes were matched for the connecting section curves before moving on with creating the surfaces.

Suction sideTE

Pressure side

LE

Figure 19 Topographic view of a section curve created in four parts After creating the section curves, four guideline splines in V-direction (along the height) were created, connecting the given sections. These spline curves were used for primary string curves in the “through curve mesh” feature when creating the four surfaces. First the suction side and pressure side surfaces were created, where after the trailing and leading surfaces were created. Here it was important to ensure that the continuity was set from the appropriate adjacent surface in the right sequential order. The G0, G1 and intersection tolerance was kept as low as possible.

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C4 Conclusion This method can release some of the oscillating effects that are most common where the suction and pressure side connects to the trailing edges, since the section consists of 4 separately defined curves that don’t have to adjust as much around strong curvature changes. The four individual section curves will probably be easier to control with more precision towards the given points than one single closed curve. The generated model will become large with more modeling steps. This will also mean that the application will be a bit slower. On the other hand, the generated model could become smaller in size if the number of segments and patches can be minimized and would hence be much quicker than previously. The issue of using too many points when defining the section curves is still imminent and has to be addressed. Due to the number of modeling steps, new problems can arise which makes the model less robust than a simpler model, problems such as misalignments and mismatches between points and lines as well as points and surfaces. The sew operation can be problematic to complete if the previous steps are not completed with low enough tolerances. This can result in time being spent on going back to find the initial area where the tolerances needs to be lowered. Eventually the tolerances may be controlled too low for the model to be of any further use when new geometries are added such as blends. Seams from the sewing operation will remain on the solid body and can cause new problems where additional geometry needs to be added.

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APPENDIX D – NX AND KF FUNCTIONALITY

D.1 Spline through points and spline by poles The “spline through points” functionality builds the spline curve through all assigned points exactly. The curve is in the end still a NURBS curve with weighted control vertices. The “through points” spline showed in Figure 20, specified by the five coordinates {0.0 1.2, 2.-3, 4.1 6.0}, draws a spline divided into 4 segments with 3 knot points and 7 weighted control vertices. In KF, this functionality is called “ug_spline_thru”. The “spline by poles” alternative builds the spline curve approximately with the selected points as the weighted control vertices. The “by poles” spline showed in Figure 20, specified by the same five coordinates {(0.0), (1.2), (2.-3), (4.1), (6.0)} draws a spline divided into two segments with one knot point and the 5 weighted control vertices as specified. In KF this functionality is called “ug_spline_cntl”. If the same points are selected for a “spline by poles” as a “spline through points”, the first spline by poles curve will have its weighted control points where the points are selected and the second spline through points curve will pass through the same points exactly. This implies that it requires a large number of points to create a spline by poles curve with low deviation to the selected points, especially with an uneven point distribution.

Figure 20 “Spline by poles” and “spline through points”

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D.2 Fitted spline The fitted spline feature approximates the curve to the chosen points with the following editable parameters. The approximation can be controlled by a given tolerance, allowing the spline to deviate from the points accordingly. The approximation can also be controlled by the number of segments in the spline, meaning that the complexity and quality of the NURBS curve becomes an indirect result. The resulting curve created by the fitted spline feature builds the same type of NURBS curve as “spline by poles”, the only difference being in the way it is created and specified. The fitted spline curve can not be closed and the feature is not available in KF by default.

D.3 Sweep operations The most useful features for sweeping a surface for the geometries in question are “through curves” and “through curve mesh”. Both alternatives work similarly, only that “through curve mesh” needs guidelines to control the sweep operation. Both of the features are available in KF for implementation.

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APPENDIX E – ADDITIONAL TESTING The fitted spline approximation functionality is here evaluated by the difference in point distribution and number of points.

E.1 Geometry idealization An idealized NURBS curve was created in a 2D plane to resemble a blade cross-section. A closed 4th degree curve was drawn with “spline by poles” using only 8 weighted control vertices giving 8 segments. The control points were positioned until the combs curvature was ideally distributed and a typical blade section was depicted. Points were then inserted onto the spline.

Figure 21 Idealized section geometry in two dimensions

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E.2 Number of evenly distributed points per section To evaluate the spline outcome by the number of points used, a number of different cases were tried on ideal section geometry. A spline was created according to E1. Points were then inserted evenly spaced by the number of 2000 points, 1000 points, 500 points, 207 points and 100 points. A 4th degree fitted spline with 40 segments was then drawn against these points to find patterns on the curve outcome depending on the number of points.

E.3 Points distributed by chordal tolerance On the same ideal geometry created in E.1, points were inserted by chordal tolerance, meaning that more points were positioned where the curvature was stronger. The specified chordal tolerance is a value corresponding to the maximum distance between the parent spline and a straight line between two adjacent points. The chordal tolerance of 0,001, 0,002 and 0,01 was used for this evaluation giving 620, 440 and 207 points respectively. A 4th degree fitted spline with 40 segments was then created through all points as in E.2.

E.4 Degree and number of sections The significance of the degree and number of segments used with the fitted spline option was tested to evaluate the smoothness of the curve compared to the fitting error from the approximated points. This evaluation was conducted with 207 points inserted on the ideal 2D curvature (E.1) with respect to the curvature (chordal tolerance 0,01).

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E.5 2D vs. 3D section curves An evaluation was made between section curves drawn in 3D space and section curves drawn on a 2D surface. The test was made with the point data set providing section points in 3D space. To evaluate the same type of data in 2D space, one of the sections was projected onto a vertical plane. A fitted spline was then drawn as in E.2 and evaluated with combs analysis.

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APPENDIX F – RESULTS FROM ADDITIONAL TESTING

F.1 Number of evenly spaced points on idealized geometry Increasing the number of evenly distributed points does not lower the maximum fitting error noticeably. The interesting data to analyze is the average fitting error where there is minimal change between 100 points and 2000 points. When all input points are spaced with exactly the same distance, and especially when the number of points increases, the spline tends to become over-defined and oscillations are more frequent.

4th degree fitted spline with 40 segments Number of evenly spaced points

Max. fitting error (mm) Av. fitting error (mm)

2000 0,05864 0,01219 1000 0,06197 0,01142 500 0,05419 0,01018 207 0,04198 0,00758 100 0,07530 0,01149

Figure 22 Fitted spline on 207 evenly spaced points

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F.2 Points by chordal tolerance on idealized geometry When creating a fitted spline on 207 points distributed depending on curvature, the resulting deviation is low and the spline curvature propagates evenly without oscillations. When increasing the number of points to 620, neither the average fitting error nor curvature distribution changes noticeably. 4th degree fitted spline with 40 segments Number of points spaced by curvature

Max. fitting error (mm) Av. fitting error (mm)

620 0,01737 0,00316 440 0,01204 0,00280 207 0,01100 0,00273

Figure 23 Fitted spline on 207 points positioned by chordal tolerance

F.3 Degree and number of segments Both the degree and number of segments are important parameters when approximating a curve with a fitted spline. A low order approximation can produce a more edgy curve than a curve of a higher degree.

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The number of segments is a very important parameter used to control the curve complexity and fitting error. A high number of segments will give less point deviation but the probability of oscillation is also greater. 3rd order fitted spline Number of segments Max. fitting error (mm) Av. fitting error (mm) 20 0,08274 0,02307 25 0,03984 0,00984 30 0,02781 0,00504 35 0,02345 0,00319 40 0,01894 0,00319 50 0,00655 0,00162 60 0,0035 0,00083

Figure 24 3rd degree 20 segments and 3rd degree 60 segments

4th order fitted spline Number of segments Max. fitting error (mm) Av. fitting error (mm) 20 0,05447 0,01665 25 0,02551 0,00497 30 0,01847 0,00508 35 0,00792 0,00211 40 0,00605 0,00246 50 0,00416 0,00145 60 0,00392 0,00136

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5th order fitted spline Number of segments Max. fitting error (mm) Av. fitting error (mm) 20 0,04422 0,01522 25 0,01551 0,00412 30 0,01731 0,00380 35 0,00721 0,00225 40 0,01269 0,00344 50 0,00489 0,00152 60 0,00393 0,00114

Figure 25 5th degree 20 segments and 5th degree 60 segments

F.4 2D vs. 3D section curves The test performed by projecting the point data set onto a vertical plane and drawing fitted spline curves on points positioned on a 2D representation gave improved results in curve quality. Since all curvature variations in v-direction are eliminated the spline can be approximated with a higher number of segments without increasing the chance for curvature interference. Due to the fact that the surface swept from 2D sections deviated from the 3D positioned point data, this case was not studied further.

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APPENDIX G – COMPARING THE RESULTING SURFACES

G.1 Blade generated from Volblade data When generating the same blade as in B.2.1 with the new programmed code for Volblade type of blades, using 40 segments per section curve, the complexity was reduced and the overall curvature was simplified. The overall deviation was between 0,01 to 0,05 mm. The total number of patches was 46 in u-direction and 18 in v-direction, giving 828 surface patches on the entire surface.

Figure 26 Improved blade surface with 828 surface patches

The combs curvature, visualized on the sections was without any larger inflections. Some oscillations were present but could only be detected when the scale factor for the combs analysis was increased to around 4000.

Figure 27 Curvature distribution displayed with highly scaled combs

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G.2 Blade generated from Volvane data When generating the same blade as in B.2.2 with the new script for Volvane type of vanes, using 40 segments, the complexity was once again reduced and the overall curvature was smoothened. The overall deviation was between 0,01 to 0,05 mm. The total number of patches was 48 in u-direction and 10 in v-direction, giving 480 surface patches on the entire surface.

Figure 28 Improved vane surface with 480 surface patches

The combs curvature, visualized on the sections was also here smoothened without unwanted inflections. Some disturbances can be seen in curvature at the start and stop coordinates for the fitted spline, but they did not become visible until the scale factor for the combs analysis was increased to 4000.

Figure 29 Curvature distribution displayed with highly scaled combs