System and method for weld path generation

Abstract

A system and method for weld path generation. In some embodiments, the method includes adding a volume of material, by welding, to a deficient part, the deficient part differing from a nominal part by distortion, and by absent material. The adding of the material may include generating a model of the absent material and adapting the model of the absent material based on the distortion. The volume of material may have a curvature based on a curvature of the absent material.

Description

SYSTEM AND METHOD FOR WELD PATH GENERATIONFIELD

[0001] One or more aspects of embodiments according to the present disclosure relate to welding, and more particularly to a system and method for weld path generation.BACKGROUND

[0002] The addition of metal, by welding, to a part being fabricated or repaired may involve the generation of three-dimensional curved tool paths to be followed by a welding system.

[0003] It is with respect to this general technical environment that aspects of the present disclosure are related.SUMMARY

[0004] According to an embodiment of the present disclosure, there is provided a method, including: adding a volume of material, by welding, to a deficient part, the deficient part differing from a nominal part by distortion, and by absent material, the adding of the material including: generating a model of the absent material; and adapting the model of the absent material based on the distortion, the volume of material having a curvature based on a curvature of the absent material.

[0005] In some embodiments, the absent material includes: material lost due to wear during service of the deficient part; and material lost due to a cut-back operation after removal of the deficient part from service.

[0006] In some embodiments, the generating of the model of the absent material includes removing, from a master model, material corresponding to the absent material, to form a cutback model.

[0007] In some embodiments, the generating of the model of the absent material further includes fitting, to a difference volume, a plurality of nominal offset vectors, the difference volume being a volume of the master model absent from the cutback model.

[0008] In some embodiments, the method further includes fitting a first nominal tool path to the difference volume, wherein each of the nominal offset vectors corresponds to a respective point of the first nominal tool path.

[0009] In some embodiments, the first nominal tool path follows a cutback surface of the deficient part.

[0010] In some embodiments, a first offset vector of the nominal offset vectors further corresponds to a respective point of a second nominal tool path, the separation between the point of the second nominal tool path and the point of the first nominal tool path being proportional to the first offset vector.

[0011] In some embodiments: the first offset vector is perpendicular to a separation between the point, of the first nominal tool path, corresponding to the first offset vector, and an adjacent point of the of the first nominal tool path; and the first offset vector is substantially parallel to a first wall of the difference volume.

[0012] In some embodiments, the point of the second nominal tool path is mid-way between the first wall and a second wall of the difference volume.

[0013] In some embodiments, the adapting of the model of the absent material based on the distortion includes rotating or translating the first nominal tool path and the second nominal tool path, to fit a measured cutback surface of the deficient part, to form a first adjusted tool path and a second adjusted tool path.

[0014] In some embodiments, the method further includes measuring the cutback surface of the deficient part using a structured light system.

[0015] According to an embodiment of the present disclosure, there is provided a system, including: a system for welding; and a processing circuit, the processing circuit being operatively coupled to a memory, the memory storing instructions that, when executed by the processing circuit, cause the processing circuit to perform a method, the method including: adding a volume of material, by welding, to a deficient part, the deficient part differing from a nominal part by distortion, and by absent material, the adding of the material including: generating a model of the absent material; and adapting the model of the absent material based on the distortion, the volume of material having a curvature based on a curvature of the absent material.

[0016] In some embodiments, the absent material includes: material lost due to wear during service of the deficient part; and material lost due to a cut-back operation after removal of the part from service.

[0017] In some embodiments, the generating of the model of the absent material includes removing, from a master model, material corresponding to the absent material, to form a cutback model.

[0018] In some embodiments, the generating of the model of the absent material further includes fitting, to a difference volume, a first plurality of nominal offset vectors, the difference volume being a volume of the master model absent from the cutback model.

[0019] In some embodiments, the method further includes fitting a first nominal tool path to the difference volume, wherein each of the nominal offset vectors corresponds to a respective point of the first nominal tool path.

[0020] In some embodiments, the first nominal tool path follows a cutback surface of the deficient part.

[0021] In some embodiments, a first offset vector of the nominal offset vectors further corresponds to a respective point of a second nominal tool path, the separation between the point of the second nominal tool path and the point of the first nominal tool path being proportional to the first offset vector.

[0022] In some embodiments: the first offset vector is perpendicular to a separation between the point, of the first nominal tool path, corresponding to the first offset vector, and an adjacent point of the of the first nominal tool path; and the first offset vector is substantially parallel to a first wall of the difference volume.

[0023] In some embodiments, the point of the second nominal tool path is mid-way between the first wall and a second wall of the difference volume.BRIEF DESCRIPTION OF THE DRAWINGS

[0024] These and other features and advantages of the present disclosure will be appreciated and understood with reference to the specification, claims, and appended drawings wherein:

[0025] FIG. 1 is a perspective view of a portion of a turbine wheel, according to an embodiment of the present disclosure;

[0026] FIG. 2 is a perspective view of a portion of a turbine wheel, according to an embodiment of the present disclosure;

[0027] FIG. 3 is a block diagram of a system for welding, according to an embodiment of the present disclosure;

[0028] FIG. 4 is a schematic drawing of tool paths and offset vectors, according to an embodiment of the present disclosure;

[0029] FIG. 5 shows a plurality of search boxes on an edge of a turbine blade, according to an embodiment of the present disclosure;DETAILED DESCRIPTION

[0030] The detailed description set forth below in connection with the appended drawings is intended as a description of exemplary embodiments of a system and method for weld path generation provided in accordance with the present disclosure and is not intended to represent the only forms in which the present disclosure may be constructed or utilized. The description sets forth the features of the present disclosure in connection with the illustrated embodiments. It is to be understood, however, that the same or equivalent functions and structures may be accomplished by different embodiments that are also intended to be encompassed within the scope of the disclosure. As denoted elsewhere herein, like element numbers are intended to indicate like elements or features.

[0031] In various applications, material (e.g., metal) may be added to a part using a machine (such as a computer numerically controlled (CNC) welder) with a tool head (e.g., a weld head) that follows a tool path to deposit material on the part. For example, the blades of a gas turbine wheel may become worn during service, degrading the performance of the turbine wheel. The performance of such a turbine wheel may be partially or fully restored by adding metal, by welding, to the worn blades, and then trimming the added metal to restore each blade to have substantially the shape it had when new. Worn parts other than turbine wheels may be restored in a similar fashion.As used herein, the term “turbine wheel” includes components such as impellers, fan blades, and blisks.

[0032] To perform such a restoration, the part may initially be cut back (e.g., using a suitable cutting or grinding operation) to expose a clean surface (which may be referred to as the cutback surface), the surface of the cut having an orientation (e.g., being perpendicular to the walls of the turbine blade) and width suitable for the deposition of the first layer (or “base layer”) of the weld. This operation may be referred to as an initial cut back operation; the trimming of the added metal (after the welding operation) may be referred to as a final cut back operation. Each of the initial cut back operation and the final cut back operation may be performed using a fixture (e.g., a fixture attached to a precision surface or attachment point of the part (e.g., of the turbine wheel)) that makes it possible to perform the cutting or grinding operations with high precision and repeatability.

[0033] The creation of a series of tool paths for adding metal, in the correct shape, to a part (e.g., a worn turbine blade) may be challenging. Gas turbine and aerospace components, for example, or various other metal parts, may be manufactured to exacting tolerances through a variety of processes, such as, but not limited to casting and forging, based, e.g., on a computer aided design (CAD) model. Some complex gas turbine components may, after a period of service, deviate from the CAD model due to the stress the component is exposed to during the manufacturing process or during operation in the turbine. Such a component, which may be referred to herein as a “distorted servicerun part”, may differ from an original part (a part that matches the CAD model) by distortion, and by lost material (the material lost due to wear during service of the servicerun part and material lost after removal of the part from service due to the initial cut back operation).

[0034] FIG. 1 shows a portion of a turbine wheel with blades in several different stages of wear and repair, for purposes of illustration. For example, a first blade 202 has lost material at its tip edge 204 (as a result of wear and of an initial cut back operation), exposing a cutback surface 206 along the tip edge. As a next step of the repair of this first blade 202, one or more layers of metal may be added, by welding. A second blade 210 has lost material at its trailing edge 212 (as a result of wear and of an initial cut backoperation), exposing a cutback surface 213 along the trailing edge. A third blade 220 had lost material at its trailing edge (as a result of wear and of an initial cut back operation), exposing a cutback surface along the trailing edge, and several layers of metal 224 have been added to the trailing edge of the third blade 220, the first layer having been deposited on the cutback surface of the trailing edge of the third blade 220, and each subsequent layer having been deposited on the previously deposited layer. A fourth blade 230 shows a repaired trailing edge, at which material had been lost due to wear and due to an initial cut back operation at the trailing edge; metal has been added using a welding operation according to embodiments described herein, and the correct shape and surface finish of the trailing edge of the fourth blade 230 has been restored using a final cut back operation.

[0035] The material deposited by the welding operation (e.g., the welding operation performed on the third blade 220) may be curved, e.g., non-planar. This may enable the final cut back operation to restore the original (correct) curved shape of the blade.

[0036] FIG. 2 is an enlarged view of the trailing edge of the second blade 210. The cutback surface 212 extends between (and is substantially perpendicular to) two faces (or “principal surfaces”, or “walls”) of the turbine blade which may be the surfaces of the pressure side and the suction side of the blade, respectively. In FIG. 2 a first principal surface 214 is visible and the second principal surface 216 is not visible because it is the back surface of the second blade 210, in the view of FIG. 2. The cutback surface 212 is a narrow, elongated surface that is substantially straight (and flat) over most of its length (except for a curved portion 218). The direction parallel to the straight portion of the cutback surface 212 may be referred to as the longitudinal direction, the direction perpendicular to the cutback surface 212 may be referred to as the vertical direction, and the direction perpendicular to both the longitudinal direction and the vertical direction may be referred to as the “transverse” direction.

[0037] As mentioned above, as part of the process of restoring a distorted service- worn part (such as a turbine blade), multiple layers of metal may be added to the cutback surface by a welding process. The distorted service-worn part may also be referred to as a substrate for the welding process.

[0038] FIG. 3 is a block diagram of a system for welding. In some embodiments a welding system includes a heating head (e.g., a laser head 120 (as illustrated), or an arc source (such as a tungsten electrode of a tungsten inert gas (TIG) system)) and a filler wire feed unit 310 for supplying a filler wire 140 to the weld pool. In some embodiments the filler material is powder instead of wire. The system further may include a plurality of position actuators 315 (labeled "PA") for controlling the position of the substrate 110, the laser head 120, and the distal end of the filler wire 140. The welding system may also include a control circuit 325, including (i) a position actuator drive circuit 330, for interfacing to the position actuators 315, and (ii) a wire feed drive circuit 335, for controlling the feed speed of the filler wire 140, and (iii) a processing circuit 345 (described in further detail below) for performing high-level control functions such as calculating tool paths and commanding the position actuators 315. The system may also include other elements (not shown) such as a laser power supply and controller, and a user interface device. As used herein, “welding” includes any process used to add molten metal to a metal part, such as TIG welding, laser welding, or gas metal arc welding (GMAW) (which may be referred to as metal inert gas (MIG) welding), or Directed Energy Deposition (DED).

[0039] Two position actuators 315 are shown in FIG. 3 controlling the position of the substrate 110, but more or fewer may be used. For example, three position actuators 315 may be used, to control position along three orthogonal directions (e.g., "translational degrees of freedom", that may be referred to as X, Y, and Z) or six position actuators 315 may be used to control three rotational degrees of freedom in addition to the three translational degrees of freedom, or more than six position actuators 315 may be used, providing a redundant capability to control one or more degrees of freedom. Similarly, the position of the laser head 120 may be controlled by two position actuators 315, or by more or fewer position actuators 315. As used herein, the "laser head" is one or more optical elements that determine the position of a focal volume within which the laser light is capable of producing significant heating. The moving of optical elements so that the focal volume moves (relative to the substrate 110 or the filler wire 140) is referred to herein for brevity as "moving the laser head", although in some embodiments the moving of the focal volume may be accomplished by moving one or more mirrors orlenses within the laser. Two position actuators 315, or more or fewer position actuators 315, may be mechanically connected to the filler wire feed unit 310 and used to control the position of the distal end of the filler wire 140. In some embodiments the position of the entire filler wire feed unit 310 is controlled by position actuators 315 connected to it. In other embodiments the position actuators 315 are connected instead to a smaller, movable element, such as a sleeve 320 through which the filler wire 140 passes, and which may be used to control the position of the distal end of the filler wire 140 without moving the entire filler wire feed unit 310.

[0040] It will be understood that motion of the system as a whole generally will have little or no effect on the welding operation, and that it is the relative positions and velocities of elements of the system, such as the substrate 110, the weld pool, the distal end of the filler wire 140, and the laser head 120 that affect the weld. As such, "moving" a first element relative to a second element may be accomplished either by changing the position of the first element (e.g., with position or speed actuators connected to the first element) or by changing the position of the second element, or by changing the position of one of the first element and the second element by a first amount, and changing the position of the other of the first element and the second element by a second amount, different from the first amount. Accordingly, in some embodiments one or more elements of the substrate 110, the laser head 120 and the filler wire 140 have no position actuators 315 and relative motion is accomplished by moving other elements. For example, instead of moving the filler wire 140 and laser head along the tool path, the substrate 110 may be moved horizontally (e.g., at constant speed) to produce the horizontal component of the relative motion along the tool path and the filler wire 140 (or the filler wire 140 and the laser head 120) may be moved vertically to produce the vertical component of the relative motion along the tool path. In other embodiments the substrate 110 is stationary and the filler wire 140 and the laser head 120 move across the substrate 110, according to the tool path, or the wire 140 and the laser head 120 are stationary and the substrate 110 moves horizontally and vertically so that the relative position of the substrate 110 and the filler wire 140 follows the tool path. In some embodiments the feed speed of the filler wire feed unit 310 may be controlled (through the wire feed drive circuit 335) as an additional method for moving the distal end of the filler wire 140 relativeto the substrate 110, in a direction that is parallel to the filler wire 140 at the distal end of the filler wire 140. In some embodiments the filler wire 140 or the laser head 120 may be caused to move laterally (e.g., in a horizontal direction perpendicular to the direction of the weld), to follow the tool path.

[0041] In some embodiments, an array of offset vectors is used to determine the tool path for each weld pass. As used herein, the “tool path” is the path that the weld pool follows as the weld progresses. The tool path is defined relative to the substrate (i.e. , the distorted service-run part, or the distorted service-run part with one or more weld beads deposited on it). As such, the tool path may be determined by the motion of the substrate during the weld, or by the motion of the heating head and the distal end of the filler wire, or both.

[0042] The offset vectors may be generated by comparing a model of the original part (e.g., the CAD model mentioned above, which may be referred to as the “master” model) and a “cutback model”, which may be a model in which a portion of the material (corresponding to material lost due to wear during service of the service-run part and to material lost due to the initial cut back operation) has been removed. As such, the cutback master may be a model of the shape that would be expected if an un-warped part were to be processed using the initial cut back operation; the cutback master model may differ from the master model only by the removal of material (and not by any warping). A difference volume (which is the difference between the master model and the cutback master model (e.g., which consists of a volume of material that is in the master and absent from the cutback model)) may then be used to generate offset vectors (or “nominal offset vectors”) that may subsequently be used to generate tool paths for adding material to the distorted service-run part.

[0043] The offset vectors may include a set of offset vectors for each tool path to be generated (each tool path corresponding to one weld pass). For the first pass (which forms the “base layer” of the material being added), a set of uniformly spaced points may be selected along the cutback surface, and the first tool path may follow this set of uniformly spaced points, possibly offset by a set offset (which may be referred to as the “working surface offset”) between the tool path and the cutback surface. The set offset may be, for example, the nominal height of the distal end of the filler wire above thesurface of the substrate. The first tool path may thus be defined by a set of (uniformly spaced) tool path points.

[0044] For the second weld pass, an offset vector may be calculated for each of the tool path points of the first weld pass, by finding the direction that is (i) perpendicular to the separation between the point and the next point (of the tool path points of the first weld pass) and (ii) substantially parallel to a wall of the difference volume (e.g., having a direction parallel to a line that passes through a first point and a second point, the first point being the current point of the first tool path, and the second point being mid-way between the two walls of the difference volume). A preliminary set of tool path points for the second tool path may then be generated by finding a point, for each of the first set of tool path points, separated from the corresponding point of the first set of tool path points by a vector having a length equal to a weld layer thickness and a direction parallel to the offset vector for the corresponding point of the first set of tool path points. This process may be performed in an analogous manner for subsequent tool paths.

[0045] In some circumstances one end of the second tool path may extend too far (e.g., outside of the difference volume, or too near to the boundary of the difference volume) or not far enough (e.g., the end may be inside, and too far from the boundary of, the difference volume). In such a case, points may be added (e.g., uniformly spaced points) parallel to the walls of the difference volume, or points may be deleted, so that the tool path ends within, and sufficiently close to, the boundary of the difference volume. FIG. 4 shows a cutback surface 400, tool paths 405, offset vectors 410, and points 415 added to tool paths to bring the ends of the tool paths sufficiently close to the boundary of the difference volume.

[0046] Once all of the tool paths have been generated (i.e. , a set of tool paths that when followed by the welder, will fill the difference volume), they (or the corresponding sets of offset vectors) may form a model of the lost material which may be translated and rotated to fit on the cutback surface of the distorted service-run part. This may be accomplished by (i) creating a numerical model of the cutback surface and of the walls near the cutback surface and (ii) scaling, rotating, and translating the set of tool paths such that (1 ) the first tool path is parallel to, and separated by the working surface offset, from the cutback surface, and (2) each of the offset vectors of the first tool path is parallel,or substantially parallel, to the walls at the tool path point corresponding to the offset vector. The scaling may be used, for example, if leading or trailing edge wear has caused a turbine blade to be slightly reduced in size, so that the length of the cutback surface is less on the part being repaired than in the cutback model. In such a case, the scaling may cause the length of the first tool path to be substantially the same as the length of the cutback surface of the part being repaired. The scaling may introduce a small error in curvature, which may be acceptable, or which may be corrected in post-weld processing (e.g., post-weld grinding or other machining).

[0047] The numerical model of the cutback surface may be created based on a suitable point cloud representing points on the surface of the distorted service-run part. Such a point cloud may be obtained, for example, using an imaging system (or “scanner”) such as a structured light system or a laser line scanner, by amalgamating the line scan data to create point clouds. Poisson surface reconstruction may be used to form surfaces (e.g., defined by triangles) corresponding to the point cloud, a smooth surface (e.g., a planar surface, or a parametrized non-planar smooth surface) may be fit to the cutback surface, two lines (e.g., straight lines, or parameterized curved lines) may be fit to the edges at which the cutback surface intersects the walls, and two smooth surfaces may be fit to the two walls. One or more calibration steps may be performed to coordinate point cloud data with the coordinate system of the welding system (e.g., of the robot welding system) such that the two agree on the position of objects. The scanner (e.g., the structured light system or the laser line scanner) may be secured to the welding system and calibrated to obtain a transformation between the coordinates of the scanner and the coordinates in which the tool path is defined (which may be referred to as the tool path coordinate system, and which may be a coordinate system employed by the actuators (e.g., robot actuators) moving the substrate and the weld head). The weld head may include a camera (the position of which, in the tool path coordinate system, is known (by prior calibration or alignment)) and the calibration of the scanner with respect the camera (and the tool path coordinate system) may be performed, for example, by obtaining images of a simple shape (e.g., a sphere or a cube) with both the scanner and the camera, and finding the coordinate transformation that maps the shape, in the coordinate system of the scanner, into the tool path coordinate system. The pose ofobjects which are being scanned may be changed and the multi-pose scans may be recombined into one complete object. The calibration steps used for such multi-pose scans may also make it possible to extend the generated toolpaths to five axes.

[0048] To aid in identifying the relevant features (the cutback surface, and the edges at which the cutback surface intersects the walls) in the point cloud, a user interface may be provided allowing a user to identify, within the point cloud, portions of the cutback surface to be used for fitting the cutback surface and the walls. For example, referring to FIG. 5, the user may be able to place a plurality of cubical volumes (which may be referred to as “search boxes”) 505 in the point cloud, each cubical volume having a side length greater than the width of the cutback surface and containing a portion of the cutback surface, thereby identifying the cutback surface to which the tool paths are to be adapted.

[0049] In some embodiments, the method described above or a similar method may be employed on a new part instead of on a service-worn part. In such an embodiment, the new part may, for example, be a cast part fabricated using a casting process not suitable for forming certain features to be included in the finished part (e.g., features too fine to be produced by casting, or features that are to be composed of a different material). A portion of the part may then be cast, and the additional features may be added by welding as described herein, e.g., using a material different from the material used for the casting. As in the case of the service-worn part, the cast part may initially be cut back (e.g., using a suitable cutting or grinding operation) to expose a clean, smooth surface (which may be referred to as the cutback surface), and the first layer of new material may then be deposited on the cutback surface. As used herein, a “deficient part” means a part to which metal is to be added using the methods described herein, such as a service-worn part, or a cast part lacking certain features. As used herein, “absent material” means material that was lost as a result of wear, or material that is present in the final part but not in the casting. As used herein a “nominal part” is a part having the shape the part was designed to have, e.g., an un-warped part that is not service-worn, or a part that has all of the features of a final part (e.g., including features that were added after casting, if certain features were missing from the casting).

[0050] As used herein, “a portion of” something means “at least some of’ the thing, and as such may mean less than all of, or all of, the thing. As such, “a portion of” a thing includes the entire thing as a special case, i.e., the entire thing is an example of a portion of the thing. As used herein, when a second quantity is “within Y” of a first quantity X, it means that the second quantity is at least X-Y and the second quantity is at most X+Y. As used herein, when a second number is “within Y%” of a first number, it means that the second number is at least (1 -Y / 100) times the first number and the second number is at most (1 +Y / 100) times the first number. As used herein, the word “or” is inclusive, so that, for example, “A or B” means any one of (i) A, (ii) B, and (iii) A and B.

[0051] Each of the terms “processing circuit” and “means for processing” is used herein to mean any combination of hardware, firmware, and software, employed to process data or digital signals. Processing circuit hardware may include, for example, application specific integrated circuits (ASICs), general purpose or special purpose central processing units (CPUs), digital signal processors (DSPs), graphics processing units (GPUs), and programmable logic devices such as field programmable gate arrays (FPGAs). In a processing circuit, as used herein, each function is performed either by hardware configured, i.e., hard-wired, to perform that function, or by more general- purpose hardware, such as a CPU, configured to execute instructions stored in a non- transitory storage medium. A processing circuit may be fabricated on a single printed circuit board (PCB) or distributed over several interconnected PCBs. A processing circuit may contain other processing circuits; for example, a processing circuit may include two processing circuits, an FPGA and a CPU, interconnected on a PCB.

[0052] As used herein, when a method (e.g., an adjustment) or a first quantity (e.g., a first variable) is referred to as being “based on” a second quantity (e.g., a second variable) it means that the second quantity is an input to the method or influences the first quantity, e.g., the second quantity may be an input (e.g., the only input, or one of several inputs) to a function that calculates the first quantity, or the first quantity may be equal to the second quantity, or the first quantity may be the same as (e.g., stored at the same location or locations in memory as) the second quantity.

[0053] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the inventive concept. As usedherein, the terms “substantially,” “about,” and similar terms are used as terms of approximation and not as terms of degree, and are intended to account for the inherent deviations in measured or calculated values that would be recognized by those of ordinary skill in the art.

[0054] Although exemplary embodiments of a system and method for weld path generation have been specifically described and illustrated herein, many modifications and variations will be apparent to those skilled in the art. Accordingly, it is to be understood that a system and method for weld path generation constructed according to principles of this disclosure may be embodied other than as specifically described herein. The invention is also defined in the following claims, and equivalents thereof.

Claims

WHAT IS CLAIMED IS:1 . A method, comprising: adding a volume of material, by welding, to a deficient part, the deficient part differing from a nominal part by distortion, and by absent material, the adding of the material comprising: generating a model of the absent material; and adapting the model of the absent material based on the distortion, the volume of material having a curvature based on a curvature of the absent material.

2. The method of claim 1 , wherein the absent material comprises: material lost due to wear during service of the deficient part; and material lost due to a cut-back operation after removal of the deficient part from service.

3. The method of claim 1 or claim 2, wherein the generating of the model of the absent material comprises removing, from a master model, material corresponding to the absent material, to form a cutback model.

4. The method of claim 3, wherein the generating of the model of the absent material further comprises fitting, to a difference volume, a plurality of nominal offset vectors, the difference volume being a volume of the master model absent from the cutback model.

5. The method of claim 4, further comprising fitting a first nominal tool path to the difference volume, wherein each of the nominal offset vectors corresponds to a respective point of the first nominal tool path.

6. The method of claim 5, wherein the first nominal tool path follows a cutback surface of the deficient part.

7. The method of claim 5 or claim 6, wherein a first offset vector of the nominal offset vectors further corresponds to a respective point of a second nominal tool path, the separation between the point of the second nominal tool path and the point of the first nominal tool path being proportional to the first offset vector.

8. The method of claim 7, wherein: the first offset vector is perpendicular to a separation between the point, of the first nominal tool path, corresponding to the first offset vector, and an adjacent point of the of the first nominal tool path; and the first offset vector is substantially parallel to a first wall of the difference volume.

9. The method of claim 8, wherein the point of the second nominal tool path is mid-way between the first wall and a second wall of the difference volume.

10. The method of claim 8 or claim 9, wherein the adapting of the model of the absent material based on the distortion comprises rotating or translating the first nominal tool path and the second nominal tool path, to fit a measured cutback surface of the deficient part, to form a first adjusted tool path and a second adjusted tool path.11 . The method of any one of claims 8 to 10, further comprising measuring the cutback surface of the deficient part using a structured light system.

12. A system, comprising: a system for welding; and a processing circuit,the processing circuit being operatively coupled to a memory, the memory storing instructions that, when executed by the processing circuit, cause the processing circuit to perform a method, the method comprising: adding a volume of material, by welding, to a deficient part, the deficient part differing from a nominal part by distortion, and by absent material, the adding of the material comprising: generating a model of the absent material; and adapting the model of the absent material based on the distortion, the volume of material having a curvature based on a curvature of the absent material.

13. The system of claim 12, wherein the absent material comprises: material lost due to wear during service of the deficient part; and material lost due to a cut-back operation after removal of the part from service.

14. The system of claim 12 or claim 13, wherein the generating of the model of the absent material comprises removing, from a master model, material corresponding to the absent material, to form a cutback model.

15. The system of claim 14, wherein the generating of the model of the absent material further comprises fitting, to a difference volume, a first plurality of nominal offset vectors, the difference volume being a volume of the master model absent from the cutback model.

16. The system of claim 15, wherein the method further comprises fitting a first nominal tool path to the difference volume, wherein each of the nominal offset vectors corresponds to a respective point of the first nominal tool path.

17. The system of claim 16, wherein the first nominal tool path follows a cutback surface of the deficient part.

18. The system of claim 16 or claim 17, wherein a first offset vector of the nominal offset vectors further corresponds to a respective point of a second nominal tool path, the separation between the point of the second nominal tool path and the point of the first nominal tool path being proportional to the first offset vector.

19. The system of claim 18, wherein: the first offset vector is perpendicular to a separation between the point, of the first nominal tool path, corresponding to the first offset vector, and an adjacent point of the of the first nominal tool path; and the first offset vector is substantially parallel to a first wall of the difference volume.

20. The system of claim 19, wherein the point of the second nominal tool path is mid-way between the first wall and a second wall of the difference volume.

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