Simulation method

Abstract

The invention relates to a simulation method for simulating processing of a workpiece by means of a tool which is guided by a robot, comprising the following steps (S1-S3): a) specifying a grid model of the workpiece (S1) composed of numerous geometric elements, b) specifying a robot path having numerous path points (S2), c) specifying an operating mode of the tool at the individual path points of the robot path (S3), wherein the following steps (S5-S11) are carried out for the individual path points of the robot path: d) determining a control volume and / or an effect range, the control volume being the volume within which the tool can theoretically possibly exert an effect on the workpiece at the particular path point of the robot path regardless of the operating mode of the tool (S5), while effect range is the volume within which, for the specified operating mode of the tool, the tool actually exerts an effect on the workpiece at the particular path point of the robot path, the effect range preferably excluding those geometric elements that lie within the control volume but, from the perspective of the tool, are concealed by other geometric elements (S6), e) determining those geometric elements of the grid model that lie within the control volume / effect range of the tool (S7), f) generating a simplified grid model composed of the geometric elements of the grid model that lie within the control volume / effect range of the tool, and g) simulating the processing of the workpiece by the tool on the basis of the simplified grid model (S11).

Description

[0001] DESCRIPTION

[0002] Simulation methods

[0003] area of

[0004] The invention relates to a simulation method for simulating the machining of a workpiece using a tool guided by a robot. For example, the coating of a motor vehicle body component using an applicator can be simulated.

[0005] Hi the

[0006] In modern paint shops for painting automotive body components, rotary atomizers are typically used as application devices, guided by a painting robot according to a painting program. The painting process can be simulated to optimize the painting program. In this well-known simulation, a mesh model of the automotive body component to be painted is defined. Furthermore, a robot path is defined, consisting of numerous waypoints that the application device is to traverse. At each waypoint, the position and orientation of the application device are specified. Additionally, the painting parameters (e.g., paint flow, guiding air flow, etc.) are defined at the respective waypoints. However, the known simulation methods have several disadvantages, which are briefly explained below.

[0007] Firstly, the given grid model of the vehicle body component to be painted may have too low a spatial resolution, so that the simulation result is not very meaningful.

[0008] Furthermore, the mesh model contains a wealth of information that is irrelevant to the desired simulation. For example, when simulating the interior paint finish of a vehicle body component, the design of the component's exterior is irrelevant. Including a large amount of irrelevant information unnecessarily increases computation time. Moreover, manually selecting or extracting a relevant geometry from the mesh model is difficult or even impossible if, for instance, the original assembly structure of the CAD file is no longer available.

[0009] Furthermore, in practice, the grid model often consists of slender triangles, which causes problems during simulation. In particular, slender triangles can lead to an unnecessarily high number of triangles and thus to computational time disadvantages.

[0010] Furthermore, the known simulation methods often require extensive preliminary tests to achieve acceptable paint quality before the start of production of a paint shop.

[0011] Furthermore, physics-based simulation methods require very long computing times and / or high-performance computers.

[0012] Finally, the known simulation methods for coating processes, which are directly based on the projection or extrapolation of real spray patterns, require considerable measurement effort before the actual simulation can take place. Furthermore, spray patterns are needed for the simulation-based investigation of parameter variations, and these must first be measured.

[0013] For general technical background information on the invention, reference should also be made to the following publications:

[0014] • INUI, Masatomo; UMEZU, Nobuyuki; SHINOZUKA, Yuuki: "A comparison of two methods for geometric milling simulation accelerated by GPU", International Symposium on Flexible Automation. American Society of Mechanical Engineers, Vol. 26, No. 3, pp. 95-102, 2013.

[0015] • INUI, Masatomo; KANEDA, Mitsuhiro; KAKIO, R: "Fast simulation of sculptured surface milling with 3-axis nc machine", Machining Impossible Shapes: I Fl P TC5 WG5. 3 International Conference on Sculptured Surface Machining (SSM98) November 9-11, 1998 ChryslerTechnology Center, Michigan, USA. Springer US, 1999. pp. 97-108.

[0016] • DE 101 44 932 Al.

[0017] • DE 10 2022 108 004 Al.

[0018] • RUPPERT, Jim: "A Delaunay refinement algorithm for quality 2-dimensional mesh generation.", Journal of algorithms, 1995, Vol. 18, No. 3, pp. 548-585. Description of the invention

[0019] The invention is therefore based on the objective of improving the known simulation methods accordingly.

[0020] This problem is solved by a simulation method according to the invention as claimed in claim 1.

[0021] The simulation method according to the invention is generally used to simulate the machining of a workpiece using a tool guided by a robot. In a preferred embodiment of the invention, the workpiece is a vehicle body component, while the tool is an applicator (e.g., a rotary atomizer) guided by a painting robot, as is known from the prior art. However, the invention is not limited to painting processes or coating processes in general with regard to the machining process to be simulated, but is also fundamentally suitable for simulating other machining processes. For example, the simulation of cleaning a vehicle body component using a cleaning brush can be mentioned.

[0022] The simulation method according to the invention, in accordance with the known simulation methods described at the outset, provides that a lattice model of the workpiece is specified, wherein the lattice model is composed of numerous geometric elements (e.g. triangles) and represents the geometry of the workpiece.

[0023] Furthermore, the simulation method according to the invention, in accordance with the known simulation methods described above, also provides for the definition of a robot path consisting of numerous path points, wherein the robot moves the tool along the robot path while processing the workpiece. In the simulation of a coating process, the individual path points can, for example, define the desired points of color contact on the surface of the workpiece to be coated. It should be noted that at each path point, preferably both the spatial position of the path point and the orientation of the tool (e.g., applicator) at that respective path point are defined.

[0024] Furthermore, the simulation method according to the invention also provides that an operating mode of the tool is specified at each individual path point. When simulating a painting process, virtual spray patterns or painting parameters can be specified at the individual path points, such as paint flow, airflow, or charging voltage of an electrostatic high-voltage charger, to name just a few examples. In practice, virtual spray patterns are preferably specified, i.e., idealized layer thickness profiles whose geometric shape is parameterizable, for example, by SB50 width and height scaling. The so-called SB50 width is the width of the layer applied to the component surface within which the layer thickness is at least 50% of the maximum layer thickness.In general, the term "operating mode" of the tool, as used within the scope of the invention, can also be defined by a machining profile that represents the interaction of the tool (e.g., milling head, cleaning brush, thick material applicator, rotary atomizer, etc.) with the workpiece or a workpiece surface under specific machining conditions (e.g., at a momentary machining point along a machining path, etc.). The shape / dimensions / extent of the machining profile (e.g., round, triangular, square, Gaussian, etc.) depend on the machining process and the corresponding machining conditions (e.g., feed rate, flow rate, rotational speed, etc.). Examples of virtual machining profiles include:

[0025] • Material removal of a milling head,

[0026] • Spray pattern of a thick material applicator,

[0027] • Spray pattern of a rotary atomizer,

[0028] • Effective area of ​​an airless applicator,

[0029] • Contact surface of a cleaning brush,

[0030] • Pressure profile of a cleaning brush.

[0031] A spray pattern is a coating profile that results on a workpiece under specific coating conditions (e.g., application method, application parameters, coating material). In simulation, virtual machining profiles corresponding to the tool path are preferably calculated and visualized (e.g., using false-color representation) to create a simulation result on the workpiece surface. Examples of simulation results include:

[0032] • Surface area processed / crossed by the tool,

[0033] • Distribution of cleaning intensity,

[0034] • Coating coverage,

[0035] • Layer thickness distribution,

[0036] • Wetness level of a paint layer. Virtual processing profiles represent realistically representable / possible processing profiles in the simulation, possibly in an idealized / standardized form. The simulation method is particularly useful for coating processes and workpieces to be coated, e.g., thick material application, seam sealing, adhesive application, painting with rotary atomizers, painting with print heads, exterior and interior car body painting, painting of small parts / add-on components, etc.

[0037] The simulation method according to the invention is characterized by the fact that the steps described below are carried out at the individual points along the robot path.

[0038] As mentioned above, not all geometric elements of the lattice model are required for the simulation. For example, the geometric elements of the lattice model of the outer skin of a vehicle body component are irrelevant for the simulation if the simulation is for the interior painting of the vehicle body component. Furthermore, those geometric elements of the lattice model that cannot be reached by the tool at the respective point in the robot's path are also irrelevant. The invention therefore provides for the determination of a control volume, which is the volume within which the tool (e.g., a rotary atomizer) could theoretically have an effect on the workpiece (e.g., a vehicle body component) at the respective point in the robot's path, regardless of the tool's operating mode.The control volume is therefore essentially the volume in the vicinity of the respective point on the robot's path that lies within the reach of the tool.

[0039] Furthermore, the invention preferably provides that the effective area of ​​the tool (e.g., rotary atomizer) is determined at each point along the robot path, depending on the tool's operating mode. The effective area is the volume within which the tool can actually exert an effect on the workpiece at that point, given the specified operating mode. Thus, determining the effective area considers not only the theoretically possible reach of the tool (e.g., rotary atomizer) but also the specific operating mode of the tool (e.g., rotary atomizer) at that point. Moreover, determining the effective area preferably also takes into account geometric elements (e.g.,...Triangles of the grid model are excluded if they lie within the control volume but are obscured by other geometric elements from the tool's perspective. This is relevant, for example, when simulating the interior paintwork of a vehicle body component, as the geometric elements of the grid model's outer skin are irrelevant for the simulation. The area of ​​effect is therefore a part of the larger control volume.

[0040] It should be noted that, according to the invention, the control volume is preferably determined first, followed by the effective area. However, it is also possible according to the invention to determine only the control volume or only the effective area.

[0041] In the next step, those geometric elements of the lattice model are determined that lie within the control volume and / or within the area of ​​effect of the tool.

[0042] The originally specified complex grid model is then simplified by considering only those geometric elements (e.g. triangles) that lie within the control volume or within the area of ​​effect.

[0043] The subsequent simulation of the machining of the workpiece by the tool is then based on the simplified lattice model.

[0044] It should be noted that the method according to the invention is preferably carried out for all points along the robot's path. However, within the scope of the invention, it is also possible, in principle, for the method to be applied only to individual path sections, each containing several points. Furthermore, it is also possible for the method to be applied only to individual points along the path.

[0045] As mentioned earlier regarding the prior art, a disadvantage of the lattice model is that it may have insufficient spatial resolution for simulation. Therefore, within the framework of the simulation method according to the invention, it is preferably also checked whether the individual geometric elements of the lattice model have sufficient spatial resolution for the subsequent simulation. If this is not the case, the geometric elements are preferably refined. For example, if the lattice model is composed of triangles as geometric elements, the triangles can be divided into two or more triangles to increase the spatial resolution of the lattice model to such an extent that a meaningful simulation is possible.

[0046] The testing of the spatial resolution of the geometric elements (e.g. triangles) and the refinement of these geometric elements is preferably repeated in an iteration loop until the refined geometric elements have a sufficient spatial resolution for the simulation.

[0047] When checking whether the geometric elements of the lattice model have sufficient spatial resolution for the simulation, the following steps are preferably carried out:

[0048] • Determining the largest edge length of the respective geometric element (e.g. triangle),

[0049] • Comparison of the determined largest edge length of the respective geometric element with a maximum permissible edge length, and

[0050] • Division of the respective geometric element into several smaller geometric elements if the determined largest edge length of the respective geometric element exceeds the maximum permissible edge length.

[0051] It has already been mentioned above that the individual geometric elements of the grid element are preferably triangles. Furthermore, it has already been mentioned above, with regard to the prior art, that slender triangles in the grid model can cause problems in the simulation. In particular, slender triangles can lead to an unnecessarily high number of triangles and thus to computation time disadvantages. Therefore, within the framework of the simulation method according to the invention, the slenderness ratio of the individual triangles is preferably determined as the ratio between the longest and shortest edge lengths of the triangles. Depending on the slenderness ratio of the respective triangle, it can then be divided into two triangles in the case of a non-slender triangle with a low slenderness ratio, or more than two (e.g., four) triangles in the case of a slender triangle with a high slenderness ratio.

[0052] It should be noted that the division of individual triangles into several smaller triangles can theoretically lead to the vertices of adjacent triangles no longer coinciding. For example, a vertex of a refined triangle might, after refinement, lie in the middle of an edge of an adjacent triangle, which may be impractical. Therefore, the simulation method according to the invention preferably provides that the respective triangle is divided into two triangles, regardless of its slenderness ratio, if the longest edge length of the triangle is less than a limit value, in particular less than twice the maximum permissible edge length. As mentioned above, the division of the triangle into smaller triangles depends on the slenderness ratio of the respective triangle.Preferably, in the simulation method according to the invention, a triangle is divided into two triangles if the slenderness ratio S of the respective triangle is S<4, while the respective triangle is divided into more than two (e.g. four) triangles if the slenderness ratio S of the respective triangle is S>4.

[0053] The division of a non-slender triangle into two refined triangles is preferably carried out in the following manner. First, the longest edge of the triangle is divided into two equal edge segments, thereby forming a new vertex between the two edge segments. The three vertices of the original, unrefined triangle then combine with the newly created vertex between the two edge segments to form two refined triangles.

[0054] The division of a slender triangle into four refined triangles is preferably carried out in the following manner. First, the longest edge of the unrefined triangle is subdivided into three edge segments: a first segment with half the length of the longest edge of the triangle, and two further shorter edge segments, each with a length equal to one-quarter of the length of the longest edge. This division of the longest edge of the triangle into three edge segments creates two new nodes. The second-longest edge of the triangle is then subdivided into two equal edge segments, thus forming a new node. This division of the longest and second-longest edges into multiple edge segments therefore creates three new nodes. These three new nodes, together with the three original nodes of the unrefined triangle, then form a total of four refined triangles.

[0055] As mentioned above, the simulation method according to the invention provides for the determination of the control volume and / or the effective area of ​​the tool. This determination of the control volume and / or effective area can optionally be carried out serially for the individual path points of the robot path or in parallel and simultaneously for several or all path points of the robot path.

[0056] The same principle applies, mutatis mutandis, to the refinement of the geometric elements of the grid model. This refinement can be performed serially for the individual points along the robot's path, or in parallel and simultaneously for several or all points along the robot's path.

[0057] The simulation method according to the invention preferably uses a grid model in which the individual geometric elements are triangles. However, it is also possible, in principle, for the grid model to initially consist of geometric elements other than triangles. In this case, the simulation method according to the invention preferably first provides for the grid model to be converted into a grid model consisting of triangles.

[0058] Furthermore, it should be noted that the determination of the relevant geometric elements lying within the control volume or within the tool's working area along the robot path can be performed with a greater distance between adjacent path points than the subsequent simulation of the workpiece machining by the tool. This is because a finer spatial resolution is desirable for the simulation in order to obtain a meaningful simulation result.

[0059] As mentioned above, the invention is not limited to a specific type of tool. For example, the tool could be an applicator (e.g., an atomizer, a pressure head, a sealant applicator, an airless applicator). Alternatively, the tool could also be a cleaning brush or a milling head, to name just two further examples.

[0060] In the simulation of a coating process, the invention is not limited to specific types of coating processes. For example, the coating process to be simulated could be a painting process, in which case the coating material would be a paint. However, it is also fundamentally possible within the scope of the invention to simulate the application of viscous materials (e.g., sealants, adhesives), to name just one further example.

[0061] Furthermore, the invention is not limited to automotive body components that are to be coated or cleaned, with regard to the workpiece. Rather, the invention can also be used to simulate the machining of other types of workpieces.

[0062] As mentioned above, the operating mode of the tool is predetermined, for example, by specifying so-called processing profiles (e.g., spray patterns) for the respective tool (e.g., rotary atomizer). The processing profiles do not need to be known for every possible parameter setting (e.g., tool feed, guide air, coating material flow rate, rotational speed, pressure, opening angle, painting distance, speed, etc.) for each operating point. Within the scope of the invention, it is also possible to transform the processing profiles stored for specific operating points into the processing profile of the current operating point. Transformation rules (e.g., characteristic curves, characteristic maps, assignment functions, causal relationships, selection matrices) can be used for this purpose, which convey the relationship between geometric properties (e.g., width, height, area, shape profile, gradient, etc.).The transformation rule is based on the virtual machining profiles used in the simulation and the parameter settings (e.g., tool feed, steering air, coating material flow rate, rotational speed, pressure, opening angle, painting distance, velocity, etc.) for the corresponding real-world manufacturing or cleaning process, depending on the tool (e.g., applicator). A transformation rule can be based, for example, on calibration tests, existing test data, or derivations from a database using artificial intelligence. A transformation rule can consist of one or more mathematical functions, e.g., 2D, 3D, planar surfaces, curved surfaces, straight lines, etc.The transfer of virtual machining profiles into parameter settings using transformation rules can be performed "forward" (virtual machining profiles --> parameter settings for the real tool) or "backward" (parameter settings of the real tool --> virtual machining profiles). Several individual variables (e.g., parameter settings of a tool, such as airflow settings of an atomizer) can first be appropriately grouped / normalized / formulated in a mathematical function before being subjected to an assignment rule.

[0063] Other advantageous embodiments of the invention are characterized in the dependent claims or are explained in more detail below together with the description of the preferred embodiment of the invention with reference to the figures.

[0064] Brief description of the drawings

[0065] Figure 1 shows a general flowchart to illustrate the principle of the simulation method according to the invention.

[0066] Figure 2 shows a flowchart illustrating the subdivision of the triangles in the grid model into smaller triangles. Figure 3A illustrates the subdivision of a slender triangle in the grid model into four smaller triangles.

[0067] Figure 3B shows the division of a non-slender triangle into two smaller triangles.

[0068] Figure 4 shows a specific flowchart to illustrate the preferred implementation of the invention.

[0069] Detailed description of the drawings

[0070] The following section describes the general flowchart according to Figure 1, which is intended to illustrate the principle according to the invention.

[0071] In a first step S1, a grid model of the workpiece to be processed (e.g., a motor vehicle body component) is specified, whereby the grid model consists of numerous triangles.

[0072] In a further step S2, a robot path is defined, consisting of numerous path points for a painting robot. At each path point, the spatial position of a paint application point and the spatial orientation of an applicator (e.g., rotary atomizer) are specified, which the painting robot is to guide along the robot path.

[0073] In a further step, S3, the operating mode of the applicator is then specified for the individual path points by defining, for example, painting parameters. Virtual spray patterns can be specified here, which, depending on the painting parameters, represent a layer thickness distribution on the component surface.

[0074] In the next step S4, the calculation for the first path point n=l is initialized.

[0075] In the next step, S6, a control volume is determined for each nth point along the path. This represents the theoretically possible effective area of ​​the applicator, independent of its actual operating mode. This calculation does not yet take into account that certain triangles of the grid model are completely inaccessible to an applicator at a given point along the path because they are obscured by other triangles. Therefore, the control volume also includes triangles of the grid model that are actually obscured in practice and thus irrelevant for the calculation.

[0076] In the next step S6, those triangles of the grid model are then determined that lie at the nth orbit point within the control volume.

[0077] In the next step, S7, the area of ​​influence of the applicator at the nth path point is determined, depending on the specific operating mode of the applicator. This also excludes those triangles of the grid model that, although lying within the control volume, are covered by other triangles of the grid model from the applicator's perspective.

[0078] In the next step S8, those triangles of the grid model are then determined that lie within the previously determined area of ​​influence at the nth orbit point.

[0079] Optionally, in step S9, the triangles can then be refined, as will be described in detail later.

[0080] In the next step S10, the determined triangles are then stored in a simplified grid model.

[0081] In the next step, Sil, it is checked whether the last point of the robot's path has been reached. If this is not the case, in step S12, the system moves to the next point n=n+l and repeats steps S5-S11 until the last point of the robot's path is reached.

[0082] In the next step S13, a simulation of the painting operation is then carried out based on the simplified grid model.

[0083] The following describes the flowchart according to Figure 2, which explains the refinement of the triangles of the grid model in step S8 in Figure 1.

[0084] In a first step S1, the smallest edge length LI is determined for the respective triangle.

[0085] In the second step, S2, the largest edge length L2 is determined for each triangle. In the next step, S3, it is then checked whether the largest edge length L2 of the respective triangle is greater than a maximum permissible edge length L. M AX - If this is not the case, no simplification takes place because the spatial resolution of the respective triangle is already sufficiently fine.

[0086] Otherwise, in a next step S4, it is checked whether the largest edge length L2 of the respective triangle is less than twice the maximum permissible edge length L. M AX- If this is not the case, then in the next step S5 the slenderness ratio S of the respective triangle is determined as the ratio between the largest edge length L2 of the respective triangle and the smallest edge length LI of the respective triangle.

[0087] In the next step S6, it is then checked whether the slenderness ratio S of the respective triangle is less than four, in order to distinguish a slender triangle from a non-slender triangle.

[0088] For a non-slender triangle with a slenderness ratio of S<4, the respective triangle is then divided into two triangles in a step S7, as shown in Figure 3B.

[0089] In contrast, in a slender triangle with a slenderness ratio S>4, the respective triangle is divided into four triangles in a step S8, as shown in Figure 3A.

[0090] Regardless of the slenderness ratio S, a division into two triangles also occurs if the largest edge length L2 is less than twice the maximum permissible edge length L. M AX, as shown in Fig. 3B.

[0091] The following section, using Figure 3A as an example, explains how a slender triangle is divided into four refined triangles. First, the longest edge of the triangle, with side length L2, is divided into three segments: two equal segments with side lengths L2 / 4 and one segment with side length L2 / 2. This division of the longest edge creates two new nodes. The second-longest edge of the triangle, with side length Lmit, is then divided into exactly two equal segments, each with side length Lmit / 2, creating another new node. The three original nodes of the unrefined triangle, together with the three newly created nodes, form a total of four refined triangles. The following section, using Figure 3B as an example, explains how a non-slender triangle is divided into two refined triangles.First, the longest edge of the triangle with side length L2 is divided into two equal edge segments with length L2 / 2, thus forming a new node. The three original nodes of the unrefined triangle then combine with the newly created fourth node to form two refined triangles.

[0092] The following section describes the specific flowchart shown in Figure 4, which illustrates the simulation method according to the invention.

[0093] In the first step S1, a lattice model of the workpiece to be machined (e.g., a vehicle body component) is defined, whereby the lattice model consists of numerous triangles. It should be noted that the lattice model can initially consist of geometric elements other than triangles. In this case, the lattice model is first converted into a suitable lattice model consisting of numerous triangles.

[0094] In the next step, S2, a robot path is defined, consisting of numerous path points for the painting robot. At each path point, the spatial position of the desired paint application point and the spatial orientation of the applicator (e.g., rotary atomizer) are specified. Furthermore, the desired operating mode of the applicator at each path point is also defined, for example, by specifying painting parameters such as paint flow, guiding air flow, or charging voltage for an electrostatic paint charge.

[0095] In the next step S3, virtual spray patterns of the applicator (e.g. rotary atomizer) are then specified for the individual path points of the robot path.

[0096] In the next step S4, the simplification of the grid model is then initialized for the first orbit point n=l.

[0097] In the next step, S5, a coordinate transformation is performed using a shader. Such shaders are known from the prior art and therefore do not need to be described in detail. An imaginary camera looks towards the applicator axis at the lattice model of the workpiece. The view frustum corresponds to the control volume for the respective path point, representing the theoretically possible effective area of ​​the applicator (e.g., rotary atomizer) in conjunction with the specified spray pattern at that point.

[0098] In the next step, S6, a depth map ("z-buffer") for the viewing volume is calculated using shaders. This depth map represents the distance of the visible surface from the viewpoint.

[0099] In the next step, S7, the triangles contained in the view volume are compared to the depth map, and the relevant triangles are extracted using a shader. This identifies the triangles whose spacing corresponds to the values ​​stored in the depth map, taking a depth tolerance into account. These are the triangles within the applicator's effective range for the respective path point, in conjunction with the predefined virtual spray pattern.

[0100] In the next step, S8, it is checked whether the spatial resolution of the identified relevant triangles within the area of ​​effect is sufficiently fine. If this is not the case, the relevant triangles are refined, as described below with reference to Figure 2.

[0101] The relevant and, if necessary, refined triangles identified in this way are then stored in a simplified grid model in step S9.

[0102] In the next step, S10, it is checked whether the last path point has been reached. If this is the case, a simulation of the painting process can be carried out in the next step, Sil, based on the simplified mesh model.

[0103] Otherwise, in step S12, the robot moves to the next path point n=n+l and the loop from steps S5-S10 is repeated until the last path point of the robot path is reached.

[0104] The following describes the flowchart according to Figure 2, which explains the refinement of the triangles of the grid model in step S8 in Figure 1.

[0105] In the first step S1, the smallest side length LI is determined for each triangle. In the second step S2, the largest side length L2 is then determined for each triangle.

[0106] In the next step S3, it is then checked whether the largest edge length L2 of the respective triangle is greater than a maximum permissible edge length L. M AX - If this is not the case, no simplification takes place because the spatial resolution of the respective triangle is already sufficiently fine.

[0107] Otherwise, in a next step S4, it is checked whether the largest edge length L2 of the respective triangle is less than twice the maximum permissible edge length L. M AX- If this is not the case, then in the next step S5 the slenderness ratio S of the respective triangle is determined as the ratio between the largest edge length L2 of the respective triangle and the smallest edge length LI of the respective triangle.

[0108] In the next step S6, it is then checked whether the slenderness ratio S of the respective triangle is less than four, in order to distinguish a slender triangle from a non-slender triangle.

[0109] For a non-slender triangle with a slenderness ratio of S<4, the respective triangle is then divided into two triangles in a step S7, as shown in Figure 3B.

[0110] In contrast, in a slender triangle with a slenderness ratio S>4, the respective triangle is divided into four triangles in a step S8, as shown in Figure 3A.

[0111] Regardless of the slenderness ratio S, a division into two triangles also occurs if the largest edge length L2 is less than twice the maximum permissible edge length L. M AX, as shown in Fig. 3B.

[0112] The invention is not limited to the preferred embodiment described above. Rather, the invention also claims protection for the subject matter and features of the dependent claims independently of the respective referenced claims and, in particular, also without the features of the main claim. The invention thus comprises various aspects of the invention that enjoy independent protection.

[0113] Advantages of

[0114] The invention is associated with various advantages, which are briefly explained below.

[0115] • The digital original geometry is prepared / converted, the relevant triangles are extracted, and, if necessary, these triangles are refined. The manufacturing or cleaning process is then simulated in an integrated, compact calculation process. Any workpiece geometry can be loaded into the simulation program and processed efficiently.

[0116] No manual or other preparation (e.g. with third-party programs) of the workpiece geometry or geometry file is necessary.

[0117] For the simulation, only parts / areas of the workpiece geometry relevant to the simulation are automatically considered; that is, only relevant nodes / triangles of the digital workpiece geometry are taken into account in the simulation process.

[0118] The invention enables a practical, adaptive refinement method for the simulation of manufacturing or cleaning processes, taking into account the slenderness of the triangles.

[0119] Relevant triangles are automatically refined if necessary.

[0120] In the case of triangular meshes with a high proportion of narrow triangles, the refinement algorithm delivers a smaller number of refined triangles than a common tessellation shader.

[0121] To achieve the shortest possible computing times, software and / or hardware modules for graphics / rendering processes, so-called shaders, can be used.

[0122] The simulation enables offline optimization of manufacturing or cleaning processes even in early phases of process planning.

[0123] The invention enables optimal initial parameterization for real trials or test runs, e.g. for the first coating of a car body; thereby potentially a higher quality level in the first real test.

[0124] The invention enables short optimization times and integration into industrial manufacturing processes, e.g., paint shops for car bodies.

[0125] The invention enables cost savings for faster production ramp-up, e.g. in the case of coating processes of a new body model, application of a new paint / thickness material, commissioning of a new zone, a new line or a paint shop.

[0126] The invention enables a reduction in the number of test pieces required.

[0127] The invention enables transparency and an objective assessment of the results.

Claims

REQUIREMENTS 1. Simulation method for simulating the machining of a workpiece using a tool guided by a robot, in particular for simulating the coating of the workpiece with a coating agent using an applicator guided by a coating robot, comprising the following steps (S1-S3): a) specification of a lattice model of the workpiece (S1), wherein the lattice model is composed of numerous geometric elements and represents the geometry of the workpiece, the geometric elements of the lattice model preferably being triangles, b) specification of a robot path with numerous path points (S2), wherein the robot is to move the tool along the robot path during the machining of the workpiece, c) specification of an operating mode of the tool at the individual path points of the robot path (S3), characterized in thatthat the following steps (S5-S11) are carried out for the individual path points of the robot path: d) determination dl) of a control volume, wherein the control volume is the volume within which the tool at the respective path point of the robot path could theoretically possibly have an effect on the workpiece regardless of the operating mode of the tool (S5), and / or d2) of an effective area of ​​the tool depending on the operating mode of the tool at the respective path point of the robot path, wherein the effective area is the volume within which the tool at the respective path point of the robot path actually has an effect on the workpiece under the given operating mode of the tool, wherein the effective area preferably excludes such geometric elements which, although they lie within the control volume, are obscured from the perspective of the tool by other geometric elements (S6),e) Determining those geometric elements of the lattice model that lie within the control volume and / or within the area of ​​effect of the tool (S7), f) Generating a simplified lattice model from the geometric elements of the lattice model that lie within the control volume and / or within the area of ​​effect of the, tool, and g) simulation of the machining of the workpiece by the tool based on the simplified lattice model (Sil).

2. Simulation method according to claim 1, characterized in that a) steps d) and e) of claim 1 are performed for all path points of the robot path, or b) steps d) and e) of claim 1 are performed only for a part of the path points of the robot path, wherein these path points form a path section of the robot path.

3. Simulation method according to one of the preceding claims, characterized in that the following steps are carried out for the individual path points of the robot path: a) checking whether the geometric elements of the grid model have a sufficient spatial resolution for the simulation (S3), and b) refining the geometric elements (S7, S8) if the geometric elements of the grid model do not have a sufficient spatial resolution for the simulation.

4. Simulation method according to claim 3, characterized in that the testing of the spatial resolution of the geometric elements and the refinement of the geometric elements are repeated in an iteration loop until the refined geometric elements have a sufficient spatial resolution for the simulation.

5. Simulation method according to one of claims 3 to 4, characterized by the following steps in checking whether the geometric elements of the grid model have a sufficient spatial resolution for the simulation: a) Determination of the largest edge length (L2) of the respective geometric element (Sl), b) Comparison (S3) of the determined largest edge length (L2) of the respective geometric element with a maximum permissible edge length (L M AX), and c) refinement (S7, S8) of the respective geometric element into several smaller geometric elements if the determined largest edge length (L2) of the respective geometric element does not exceed the maximum permissible edge length (L M AX).

6. Simulation method according to one of claims 3 to 5, characterized in that a) the individual geometric elements of the grid model are triangles, b) a slenderness ratio (S) of the individual triangles is determined as a ratio between the largest edge length (L2) of the triangle to the smallest edge length (LI) of the triangle (S5), and c) that the triangles are divided during the refinement depending on the slenderness (S) of the respective triangle into cl) two triangles (S7) in the case of a non-slender triangle with a low slenderness (S), or c2) more than two triangles (S8) in the case of a slender triangle with a high slenderness (S).

7. Simulation method according to claim 6, characterized in that the respective triangle is divided into two triangles regardless of its slenderness ratio (S) if the largest edge length (L2) of the triangle is smaller than a limit value, in particular smaller than twice the maximum permissible edge length (L M AX).

8. Simulation method according to claim 6 or 7, characterized in that a) a triangle is divided into two triangles if the slenderness ratio (S) of the respective triangle is less than four, and b) a triangle is divided into more than two triangles, in particular into four triangles, if the slenderness ratio (S) of the respective triangle is greater than or equal to four.

9. Simulation method according to claim 8, characterized in that the division into two triangles at a small slenderness ratio (S) is carried out as follows: a) division of the longest edge of the triangle into two edge segments of equal length with a new node between the two edge segments, and b) formation of the two refined triangles from three nodes of the original triangle and the new node.

10. Simulation method according to claim 8 or 9, characterized in that the division into more than two triangles with a large slenderness ratio (S) is carried out as follows: a) division of the longest edge of the triangle into three edge segments, namely two edge segments with each one quarter of the edge length (L2) of the longest edge and one edge segment with half the edge length (L2) of the longest edge, wherein the edge segments each form a new node in pairs, and b) division of the second longest edge of the triangle into two edge segments of equal length with a new node between the two edge segments, and c) Formation of four refined triangles from three nodes of the original triangle and the three new nodes.

11. Simulation method according to one of the preceding claims, characterized in that a) the determination of the geometric elements of the lattice model lying within the area of ​​effect of the tool is carried out serially for the individual path points of the robot path, or b) the determination of the geometric elements of the lattice model lying within the area of ​​effect of the tool is carried out in parallel and simultaneously for several or all path points of the robot path.

12. Simulation method according to one of the preceding claims, characterized in that a) the refinement of the geometric elements of the grid model is carried out serially for the individual path points of the robot path, or b) the refinement of the geometric elements of the grid model is carried out in parallel and simultaneously for several or all path points of the robot path.

13. Simulation method according to one of the preceding claims, characterized in that a) the lattice model of the workpiece initially consists of geometric elements other than triangles, and b) the lattice model is then transformed into a lattice model consisting of triangles.

14. Simulation method according to one of the preceding claims, characterized in that the determination of the relevant geometric elements lying within the control volume and / or the area of ​​effect of the tool along the robot path is carried out with a greater distance between the adjacent path points than the subsequent simulation of the machining of the workpiece by the tool.

15. Simulation method according to one of the preceding claims, characterized in that a) the tool is an applicator that applies a coating agent, in particular one of the following types of applicators: a) a sprayer for dispensing a paint, in particular a rotary sprayer, a2) a printhead for overspray-free application of a paint, a3) a thick material applicator for applying a thick material, in particular a sealant or an adhesive, a4) an airless applicator, or b) that the tool is a cleaning brush, or c) that the tool is a milling head.

16. Simulation method according to one of the preceding claims, characterized in that a) the workpiece is a motor vehicle body component to be coated and / or cleaned, and / or b) the specified robot path at each path point defines not only the spatial position of the respective path point, but also the spatial orientation of the tool at the respective path point.

17. Simulation method according to one of the preceding claims, characterized in that a) the tool is an applicator and the predetermined operating mode of the applicator comprises the following operating parameters of the applicator: a) coating medium flow rate, a) steering air flow rate, and / or a) charging voltage and / or charging current of an electrostatic coating medium charge, or b) that the tool is a cleaning brush and the predetermined operating mode of the cleaning brush defines the rotational speed of the cleaning brush and / or the linear movement speed of the cleaning brush along the robot path, and / or c) that the predetermined operating mode defines a virtual spray pattern of the applicator.

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