Integration of Rule-based Process Selection with Virtual Machining for Distributed Manufacturing Planning
3.4 Virtual Machining of Milling Operations
combinations of part and tool materials. A small database has been implemented in XML format, but the system can also be connected to other databases.
Figure 3.12. Three models for virtual machining 3.4.1 Geometric Model
The geometric model provides a geometric representation of the tool, the workpiece and the feature. All these components are represented as geometric objects in 3D Euclidean space using a simplified boundary representation of solid objects to represent coordinate points, lines and surfaces in 3-dimensional space.
The workpiece (or stock) is represented using a polyhedron with planar faces.
The stock model can be imported from a CAD model, or it is generated from a parameterised box. The current implementation covers stocks with planar faces, and curved surfaces are not considered due to the extensive geometric computations involved in representing these surfaces. The topological information of the points in the model maintains the closed solid volume [3.13] for the stock. The point set and topological relations between individual points completely describe the stock shape and they constitute its geometric model. The solid representation is based on polygon-based boundary model data structures [3.14] that is implemented using the coordinate point data array and the topology through an index array, the utilities available in Java 3D [3.15].
Feature models are based on feature parameters. The feature may have a fixed number of parameters (dimensions, position), or a variable number of parameters (like number of curves in its profile). Features are represented in parametric form, which is based on research results in feature modelling and feature recognition, and from this parametric form a geometric model is computed. The set of features machinable by end-milling processes may be represented with the following types:
slots, grooves, pockets, profiles.
Current implementation of virtual machining module includes slots and pockets.
For each feature type a set of parameters that completely describe the feature has been defined. The reader is directed to [3.16][3.17] for complete specifications. As an illustration, Figure 3.13 shows the definition of an open blind pocket. The open blind pocket has these parameters: 1) a profile (usually floor profile), 2) a normal n, 3) local reference point P0, 4) corner radius r, and 5) bottom distance bd. Figure 3.13(a) shows the open blind pocket, with its normal in the positive z-direction n=(0,0,1), and profile A-B-C-D-E. The pocket’s geometric model is computed from its parametric definition and stock’s solid model by extending pocket faces and lines to intersect with the stock faces. Application of the algorithm described in [3.17]
that generates the pocket’s delta volume from stock is shown in Figure 3.13(b).
Stock
Pocket Normal
Feature Accessibility Direction - 1
Feature Accessibility Direction - 2 Bottom Distance B A
C A, B, C, D, E - Floor profile
D
E
Corner Radius
(a) (b)
Figure 3.13. Open blind pocket: (a) pocket parameters, (b) geometry model
The tool geometric model is created to represent a tool as a hollow cylinder that moves in 3D space and interacts with the stock to perform machining. The tool geometry is aligned with the feature geometry such that the tool swept volume generates the feature faces. This model is shown in Figure 3.14. The cutting-edge surface is represented by a hollow cylinder that generates a rectangular surface after it is projected on the part’s face along the feed vector. The combination of this projection surface with the feed vector direction, which intersects with the delta volume during transformation, generates the swept volume.
(a) (b)
Figure 3.14. End-milling process: (a) tool sweep, (b) tool-path parameters 3.4.2 Kinematic Model
The kinematic model is a schematic representation of the interaction between the tool and workpiece, as mentioned in the previous section. It encapsulates the changing geometry of the workpiece due to the relative motion between the tool and stock. The kinematic model is developed in three steps: feature and stock face classification and segmentation, tool-path generation, and tool-path classification.
In order to perform cutting, the tool needs to be properly positioned with respect to the stock, and its initial location should be computed. The tool location calculation, which is based on the feature and stock parameters, links the tool and stock geometry models to generate the feature model. The line segment formed by these limiting points (start and end points) is called the tool path and forms the tool movement profile during machining. Figure 3.14(b) shows an example of a slot that is specified by a point on its central plane (P), normal vector (N&
), sweep vector (S&
) and the bottom distance from point P (bd), and corresponding tool-path parameters.
During motion along this tool path, the tool modifies some of the workpiece surfaces and generates an intermediate geometry. Therefore, it is necessary to classify stock faces as static and dynamic and identify the way feature faces are generated. Face classification is illustrated in Figure 3.15. It is clear that the stock top face is a dynamic face, which can be segmented into three parts: two sides that are not modified, and the slot top face, which is removed by machining. Also, all slot faces are generated during the milling process. Similar analysis is performed for pocket milling with the difference being that each tool path needs to be considered separately.
Figure 3.15. Face classification for slot milling
For machining a pocket, a list of tool-path segments needs to be computed both within the workpiece and while engaging the workpiece to extrapolate the motion of the tool. For pockets, end milling requires generation of tool-path segments. We have applied the well-known zig-zag method using offset procedures from [3.18] for generation of tool paths from the pocket geometry.
The animation of the workpiece along the tool path depends on the type of tool- path motion. Several cases need to be considered. For example, if the tool path segment starts outside the stock and ends outside the stock, the tool-path movement would result in the generation of a rectangular open slot. However, for milling of an open pocket, the first tool path should start outside and end inside. For two of these cases, changes of intermediate geometry happen in different ways, because for a pocket the tool must not leave the workpiece. In general, any tool-path segment may be classified based on whether the tool’s initial and final locations are inside or
outside of the stock. This leads to four cases, as illustrated in Figure 3.16:
startoutside_endinside (“AB”), startoutside_endoutside (“EF”), startinside_endinside (“BC”) and startinside_endoutside (“CD”). These four tool-path-segment cases may further be classified based on the orientation of the workpiece entry or exit face and the tool’s orientation. Illustration of this classification is shown in Figure 3.16(b).
The trapezoid represents the stock for machining, the full arrow represents the sweep vector, and the hollow arrow represents the tool axis. The angle between the tool axis and the entry and exit face normal defines engagement and disengagement topology. When the tool axis is parallel to a stock face (front face in the figure), tool engagement/disengagement happens along a line of contact; when the axis is not parallel (the case of the back face), tool engagement/disengagement happens at a single point that needs to be calculated. These cases are classified as parallel start/end, bottom start/end, and top start/end. Each of these cases requires different calculation of the engagement/disengagement topology, with a detailed explanation given in [3.16][3.19].
B
C E
F
A
D
Stock Slot
Front Face : Parallel_Start Back Face : Bottom_Start
(a) (b)
Figure 3.16. Tool-path classifications: (a) in-out classes, (b) orientation classes 3.4.3 Animation Model
Animation of a single tool path consists of four major steps: (1) displaying the tool motion according to the cutting parameters (feed and speed), (2) displaying the feature generation when the tool is engaging with the workpiece, (3) displaying the moving feature surfaces as the tool progresses, and (4) displaying the opening of the feature when machining is being completed. In Step (1), the tool geometry, cylinder, is translated along the tool-path’s trajectory giving a notion of its interaction with the workpiece geometry. This movement needs to be synchronised with the modifying workpiece geometry at that time instant. The workpiece geometry modifications are carried out by combination of the three steps (2), (3) and (4).
In order to animate workpiece modification, time instants when the topology of the workpiece geometry changes need to be computed. We explored the tool-path time interval and decided to linearly interpolate the geometry between the two instants of changing topology. As a result, Figure 3.17 shows the relation between
tool motion and corresponding time instants. Various subintervals “a”, “b”, “c” …
“i”, computed from the tool’s initial location for the top start approach, represent the fraction of the total machining time from the beginning of the process. The fractions are “a”: the time until the tool touches the workpiece; “b”: the time needed to create a half-circle on the top face; “c”: the time until the tool’s bottom cutting edge touches the entry face; “d”: the time needed to create a half-circle at the bottom of the feature; “i”: the time after all faces are created and the tool is completely engaged; “e”: the time interval for opening the top back face; “f”: the time before the feature bottom is open; “g”: the time interval for opening the bottom back face; and
“h”: the time interval for moving away from the workpiece. For each of the identified time instants, the corresponding geometry of the workpiece is computed and triangulation is performed using Java 3D utilities. Interpolation of geometry changes between these time instants (or for each time interval “a” to “h”) is performed using linear morphing of the shape in Java 3D. The morphing geometry models are included into a virtual world scene graph to perform animation.
Figure 3.17. Total machining time and workpiece geometry modifying time instants The illustration of geometry and topology changes is shown in Figure 3.18, which illustrates shrinking of the back face starting at time interval “e” (in Figure 3.17). Figure 3.18 shows the following cases: (a) the back face before interval “e”;
(b) the back face change during interval “e”; (c) and (d) two instants during interval
“f”; (e) and (f) the back face changes in interval “g”; and (g) the back face in interval
“h”, when the tool has finished cutting and it is not touching the workpiece.
(a) (b) (c) (d) (e) (f) (g) Figure 3.18. Shrinking slot back face at various stages
3.4.4 Virtual Machining Scene Graph
The animation model of stock, tool and feature (workpiece) are schematically represented in a tree-like diagram in the virtual world that is called a scene graph (SG) [3.15]. This section provides a description of the scene graph for virtual machining and its component subgraphs for the stock, tool and workpiece, which together generate the animation model of machining in the virtual world. The EndMilling class implements the top level SG, which includes other sub-SG for visualising the machining components in 3D space. The other sub-SG includes tool SG, stock SG, and workpiece SG, as explained in the following sections.
(1) End-milling Scene Graph
A high-level structure of the end-milling scene graph is shown in Figure 3.19. This SG is appended to the virtual universe for machining, which provides the view platform and lighting for the scene. The end-milling process provides nodes required for virtual machining of a feature. The ObjRoot branch group (BG) acts as the parent node with AnimRoot BG and Light BG as its child nodes. The Light BG has lights as leaf nodes, and it lightens the scene using a set of ambient lights, directional lights, point lights, and spotlights. These lights are positioned in space to impart effective brightness and shine in combination with material and appearance of shape 3D object.
Light BG
BG BG
Locale Object
BG BG BG: Branch Group
Stock BG Tool BG Axis BG
AnimRoot BG BG
BG ObjRoot BG Virtual Universe
supplied by Anim Applet
TG Mouse Behavior TG Set of Branch
Groups supplied by End Milling
Figure 3.19. End-milling scene graph
The AnimRoot BG is the main BG that handles the process animation. The Axis BG, a child node of AnimRoot BG, sets up a coordinate system in the universe for visually displaying spatial orientation and location to the user. The AnimRoot BG contains nodes of tool and workpiece. The stock BG represents the stock geometry, which is replaced with the workpiece BG during the animation phase. The tool BG, which holds a cylindrical primitive shape representing the cutting tool, provides the tool transformation model for displaying feed motion. The AnimRoot BG also holds
a utility transform group, named MouseBehavior TG. This group facilitates user interaction with virtual animation through a mouse device.
(2) Tool Scene Graph
The tool BG (see Figure 3.20(a)) represents the tool that is modelled using a solid shape located in space as defined by the tool path and the machining feature. The position and orientation of this cylinder are changed as required by the stock and feature. This change is achieved using a sequence of transformations (rotate by 90 degrees TG) applied on the cylinder’s default location, as shown in Figure 3.20(a).
Transformation groups are added for rotation and translation of the cylinder, which represent the cutting speed and feed motions. These two motions are defined by using a Rotational Interpolator (RI) and a Position Path Interpolator (PPI). The RI simulates the tool’s rotation, and its angular speed is computed from the cutting speed. The PPI provides translation movement based on tool-path computation. The tool path supplies the starting and ending point locations and, using these points, the PPI computes the position on the path and corresponding position indices along which the tool traverses.
(a) (b)
Figure 3.20. Component scene graphs: (a) tool, (b) workpiece (3) Stock Scene Graph
The stock shape geometry model is represented in a 3D scene with the data structure stored in an Indexed Geometry Array [IGA]. This complete geometry along with its appearance is set to a Shape3D, which is part of the process SG. The stock scene graph is replaced by the workpiece scene graph during virtual machining.
(4) Workpiece Scene Graph
The workpiece geometry BG handles the workpiece dynamic geometry to execute virtual machining. This BG contains pre-machining and post-machining workpiece geometry. The transition between the two geometries is carried out using the
animated feature generation, which morphs the pre-machining geometry to the post- machining geometry. The workpiece SG shown in Figure 3.20(b) provides an outline of this functionality. As the user starts the animation for virtual machining, the BG of the stock geometry is replaced with the BG pre-machining feature static workpiece geometry and, at the same moment, the morphing in dynamic behaviour is also initiated. An alpha object, which decides the timeframe for the animation is started at this instant. The same alpha object is used in the tool BG and, therefore, coordinates the translation motion of the tool with the changes in workpiece shown using intermediate geometry. This coordinating action is performed inside the dynamic behaviour node by smoothly transforming an intermediate geometry into the next geometry, assigned to that time instant. When the workpiece is completely transformed into its final geometry, a static workpiece geometry BG is replaced with the previous BG, having dynamic behaviour.