Solid Modeling of In-Process Workpiece Geometry for Hole Milling

2012 ◽  
Author(s):  
Jue Wang ◽  
Derek Yip-Hoi
Keyword(s):  
Cutting Forces ◽  
Tool Path ◽  
Solid Modeling ◽  
Solid Model ◽  
Virtual Machining ◽  
Solid Models ◽  
Milling Operation ◽  
Swept Volumes ◽  
Swept Volume ◽  
Physics Based Simulation

Capturing the in-process workpiece geometry generated during machining is an important part of tool path verification and increasingly the physics-based simulation of cutting forces used in Virtual Machining. Swept volume generation is a key supporting methodology that is necessary for generating these in-process states. Hole milling is representative of one class of milling operation where the swept volume is continuously intersecting. Due to this it is impossible to decompose the tool path into non-intersecting regions which is typically the approach used in solid model based swept volume generation. In this paper an approach to generating NURBS based solid models for self-intersecting swept volumes generated during hole milling is presented. NURB surfaces are generated that compactly represent the surfaces of the swept volume. This utilizes the geometry of the helical curve as opposed to a linearly interpolated tool path that is used for more generic approaches to generating swept volumes. Examples applying the approach to various types of cutter geometries used in milling are presented.

An Efficient, Accurate Approach to Representing Cutter-Swept Envelopes and Its Applications to Three-Axis Virtual Milling of Sculptured Surfaces

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Zezhong C. Chen ◽  
Wei Cai
Keyword(s):  
Tool Path ◽  
Basic Mechanism ◽  
Cnc Milling ◽  
Sculptured Surfaces ◽  
Machining Error ◽  
Tool Paths ◽  
Virtual Machining ◽  
Machining Errors ◽  
Computer Numerically Controlled ◽  
Swept Volume

To address a major technical challenge in simulating geometric models of machined sculptured surfaces in three-axis virtual machining, this paper presents an efficient, accurate approach to representing the 3D envelopes of a cutter sweeping sequentially through cutter locations; these envelopes embody the furrow patches of the machined surfaces. In our research, the basic mechanism of removing stock material in three-axis computer numerically controlled (CNC) milling of sculptured surfaces is investigated, and, consequently, an effective model is proposed to represent the 3D envelopes (or furrow patches). Our main contribution is that a new directrix (or swept profile) of the furrow patches (mathematically, ruled surfaces) is identified as a simple 2D envelope of cutting circles and is formulated with a closed-form equation. Therefore, the 3D cutter-swept envelopes can be represented more accurately and quickly than the existing swept-volume methods. With this innovative approach, a method of accurate prediction of the machining errors along tool paths in three-axis finish machining is provided, which is then applied to the optimization of tool-path discretization in two examples. Their results demonstrate the advantages of our approach and verify that the current machining-error-prediction methods can cause gouging in three-axis sculptured surface milling.

Surface Reconstruction From Triple Dexel Model for Virtual Sculpting

2007 ◽  
Author(s):  
Weihan Zhang ◽  
Ming C. Leu
Keyword(s):  
Differential Equation ◽  
Surface Reconstruction ◽  
Boundary Surface ◽  
Solid Modeling ◽  
Haptic Interface ◽  
Solid Model ◽  
Virtual Sculpting ◽  
Novel Method ◽  
Swept Volume ◽  
Differential Equation Method

This paper presents a novel method for surface reconstruction from triple dexel data for virtual sculpting. A triple dexel based virtual sculpting system is developed to provide the capability of interactive solid modeling with haptic interface. A solid model is converted to triple dexel data, which depicts the intersections of the solid with rays cast in three orthogonal directions, and modified during the virtual sculpting process. The boundary of the tool swept volume is computed based on the Sweep Differential Equation method. Contour generation and combination algorithms convert the triple dexel data to three sets of orthogonal slices of contours. A tiling algorithm then generates the solid’s boundary surface in triangular facets from these contours. Examples are given to demonstrate the ability of the developed method and software to realistically simulate the physical sculpting process and to allow viewing the sculpted models in any directions.

Topological and Geometric Consistency in Boundary Representations of Solid Models of Mechanical Components

1993 ◽  
Vol 115 (4) ◽  
pp. 762-769 ◽  
Author(s):  
A. G. Jablokow ◽  
J. J. Uicker ◽  
D. A. Turcic
Keyword(s):  
Data Exchange ◽  
Solid Modeling ◽  
Boundary Representation ◽  
Solid Model ◽  
Design Data ◽  
Solid Models ◽  
Geometric Consistency ◽  
Boundary Representations ◽  
Mechanical Components ◽  
Manufacturing Applications

This paper describes a method of verifying the consistency (i.e., agreement) between the topology and geometry of boundary representation (B-rep) solid models of mechanical components. This verification is well-suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow, 1989). This technique and algorithm is important in the design of mechanical components for design documentation, integration with analysis and manufacturing applications, and design data exchange between solid modeling systems. Information regarding boundary representations has typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of a solid model of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.

Error Estimation of Machined Surfaces in Multi-Axis Machining with Machine Tool Errors Including Tool Self-Intersecting Motion Based on High-Accuracy Tool Swept Volumes

2018 ◽  
Vol 12 (5) ◽  
pp. 680-687 ◽  
Author(s):  
Wataru Arai ◽  
◽  
Fumiki Tanaka ◽  
Masahiko Onosato
Keyword(s):  
Machine Tool ◽  
Evaluation Method ◽  
Tool Path ◽  
Approximation Accuracy ◽  
Method Error ◽  
Machining Errors ◽  
Generating Method ◽  
Swept Volumes ◽  
Swept Volume ◽  
Machined Surfaces

A novel method is proposed for estimating the machining errors on machined surfaces caused by errors of multi-axis machine tools, such as geometric errors, based on a new generating method of tool swept volumes. In the proposed tool swept volume generation method, the boundary surfaces of the tool swept volumes are derived as triangular mesh models satisfying the required approximation accuracy based on the tangency condition. Using the proposed method, tool swept volumes can be derived for various tool paths including the tool self-intersecting motion. A tool path evaluation method based on the error vectors with respect to the start position of a specific tool path is also proposed. In the proposed evaluation method, error vectors on machined surfaces are derived by comparing the points on the nominal tool swept volumes (excluding the machine tool errors) with the triangles on the error tool swept volumes (including the machine tool errors).

State-of-the-Art in Geometric Modeling for Virtual Machining

2012 ◽  
Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi
Keyword(s):  
Computer Technology ◽  
Process Modeling ◽  
Geometric Modeling ◽  
Tool Path ◽  
State Of The Art ◽  
Machining Process ◽  
Work Piece ◽  
Virtual Machining ◽  
Swept Volumes ◽  
Process Work

Advances in computer technology have made possible the integration of complex geometric and process modeling capabilities for use in engineering design and process planning. This is evident in the area of machining where it is now possible to integrate the physics of the machining process with changes that are taking place to the geometry of a work piece during the execution of complex operations. This capability is referred to as Virtual Machining (VM). Geometric modeling capabilities include the ability to generate complex swept volumes created during execution of tool path moves, to subtract these from a dynamically changing in-process work piece model, and to extract the instantaneous cutter/workpiece engagement as the tool moves in the feed direction. Process modeling includes the use of this engagement geometry to calculate cutting forces, deflection of structures, vibrations and to use these in process optimization. This paper reviews advances in the first part of this tandem, the geometric modeling methods and techniques that make Virtual Machining possible. It further highlights important directions that can be taken to further advances in this field.

Extraction of Cutter-Workpiece Engagement for Multi-Axis Milling

2013 ◽  
Vol 770 ◽  
pp. 357-360
Author(s):  
Yun Yang ◽  
Min Wan ◽  
Wei Hong Zhang ◽  
Ying Chao Ma
Keyword(s):  
Contact Zone ◽  
Cutting Forces ◽  
Solid Modeling ◽  
Depth Of Cut ◽  
Chatter Stability ◽  
Machining Error ◽  
Contact Surfaces ◽  
Swept Volume ◽  
Feasible Contact Surfaces

Cutter-workpiece engagement (CWE) is the contact zone where the cutting flutes enter and exit the workpiece as a function of axial depth of cut. Determination of CWE is the basis for predictions of cutting forces, machining error and chatter stability in multi-axis milling. In this paper, a solid modeling approach is developed to extract CWE for multi-axis milling by means of removal volume, which is obtained by subtracting analytic tool swept volume from in-process workpiece. Meanwhile, the feasible contact surfaces are used to trim the removal volume in order to determine CWE surfaces. Simulations are also performed to confirm the validity of the proposed method.

Topological and Geometric Consistency in Boundary Representations of Solid Models

1990 ◽  
Author(s):  
Andrei G. Jablokow ◽  
John J. Uicker ◽  
David A. Turcic
Keyword(s):  
Solid Modeling ◽  
Boundary Representation ◽  
Solid Model ◽  
Geometric Complexity ◽  
And Topology ◽  
Solid Models ◽  
Geometric Consistency ◽  
Boundary Representations ◽  
Bonnet Theorem

Abstract This paper describes a method of verifying the consistency between the topology and geometry of boundary representation (B-rep) of solid models. This verification is well suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow 1989). Information regarding boundary representations is typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.

Verification of Boundary Representations of Solid Models

1994 ◽  
Vol 116 (2) ◽  
pp. 666-668
Author(s):  
A. G. Jablokow ◽  
J. J. Uicker ◽  
D. A. Turcic
Keyword(s):  
Design Automation ◽  
Solid Modeling ◽  
Solid Model ◽  
Object Model ◽  
Application Program ◽  
Solid Models ◽  
Verification Algorithms ◽  
Boundary Representations ◽  
Object Models

Verification of polyhedral boundary representations (B-reps) of solid models through the use of an algorithm is addressed here. The validity conditions for B-rep models are presented in a format which leads directly to a set of verification algorithms. The validity verification algorithms are intended for design automation through execution after each solid modeling operation, after localized geometry modification, on imported object model databases, prior to storage of object models, or prior to execution of an application program on the solid model.

Generating Swept Volumes With Instantaneous Screw Axes

1994 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Moving Object ◽  
Ruled Surfaces ◽  
Screw Axis ◽  
Spherical Surfaces ◽  
Swept Volumes ◽  
Instantaneous Screw Axis ◽  
Swept Volume ◽  
Instantaneous Screw ◽  
Plane Polygon ◽  
Boundary Surfaces

Abstract The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

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