Geometric Modeling and Analysis of Single Point Cutting Tools With Generic Profile

2011 ◽  
Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Sanjay G. Dhande
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Single Point ◽  
Cutting Tools ◽  
Free Form ◽  
Generic Model ◽  
Modeling And Analysis ◽  
Grinding Parameters ◽  
Two Generations ◽  
Free Form Surfaces

The presented work models the geometry of Single Point Cutting Tools (SPCTs) with generic profile. Presently few standard shapes of SPCTs defined in terms of projective geometry are being employed while there is a need to design free-form tools to efficiently machine free-form surfaces with few passes and chosen range of cutting angles. To be able to produce SPCT face and flanks with generic shapes through grinding, a comprehensive geometric model of the tool in terms of the varying grinding angles and the ground depths is required which helps design the tool with arbitrarily chosen tool angles. The surface modeling begins with the creation of a tool blank model followed by transformation of unbounded planes to get the cutting tool surfaces. The intersection of these surfaces with the blank gives the complete model of the tool. Having created the geometric model in two generations of generalization, the paper presents the methodology to obtain the conventional tool angles from the generic model. An illustration of the model has been provided showing variation of tool angles along the cutting edge with changing grinding parameters. When the geometric model is not to be related to the grinding parameters, the SPCT can be modeled as a composite NURBS surface which has been presented towards the end of the work.

A Solid Modeler Approach for Extracting Cutter Workpiece Engagements in Milling

2008 ◽  
Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi
Keyword(s):  
Geometric Modeling ◽  
Cutting Tools ◽  
Free Form ◽  
Tool Geometry ◽  
Depth Of Cut ◽  
Modeling Methodology ◽  
Engagement Angle ◽  
Solid Modeler ◽  
Free Form Surfaces ◽  
Boundary Curves

This paper presents a Solid modeling methodology for finding Cutter Workpiece Engagements (CWEs) generated during 3+2 -axis machining (spindle can tilt) of free – form surfaces using a range of different types of cutting tools and tool paths. Swept volumes of the cutters are generated utilizing the envelope theory. For the CWE extractions the removal volumes of the cutter constituent surfaces are used. For this purpose the cutter surfaces are decomposed with respect to the tool feed direction and then they intersected with their removal volumes for obtaining the boundary curves of the closed CWE area. The CWE boundary curves are mapped from Euclidean space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. The reported method has been implemented using a commercial geometric modeler (ACIS) which is selected to be the kernel around which the geometric simulator is built. The described geometric methodology is being developed as part of a Virtual Milling methodology that combines the geometric modeling aspects of milling material removal with the modeling of the process.

scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

Multiple-Points Constraints Based Deformation for Free-Form Surfaces

1999 ◽  
Author(s):  
J. M. Zheng ◽  
K. W. Chan ◽  
I. Gibson
Keyword(s):  
Surface Deformation ◽  
Single Point ◽  
Displacement Function ◽  
Surface Shape ◽  
Free Form ◽  
Surface Model ◽  
Deformation Method ◽  
Multiple Points ◽  
Free Form Surface ◽  
Free Form Surfaces

Abstract There is an increasing demand in the conceptual design for more intuitive methods for creating and modifying free-form curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user’s specified constraints and shapes. This paper presents a new surface representation model for free-form surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called parent surface. Based on the surface model, the authors develop two deformation methods which are named SingleDef (Single-point constraint based deformation method), and MultiDef (Multiple-points constraints based deformation method). The techniques for free-form surface deformation allow conceptual designer to modify a parent surface by directly applying point constraints to the parent surface. The deformation methods are implemented and taken in an experimental CAD system. The results show that the designer can easily and intuitively control the surface shape.

Multiresolution Representation of a Geometric Model for Free-Form Surfaces Turning Based on Mesh Simplification

2013 ◽  
Vol 823 ◽  
pp. 265-269
Author(s):  
Qing Zou ◽  
Jian Feng Lu ◽  
Yu Jiang Gao ◽  
Tao Wang ◽  
Jian Ning Yao ◽  
...  
Keyword(s):  
Tool Path ◽  
Control Method ◽  
Geometric Model ◽  
Mesh Simplification ◽  
Diamond Turning ◽  
Machining Process ◽  
Free Form ◽  
Multiresolution Representation ◽  
Resolution Model ◽  
Free Form Surfaces

In this paper, a new multi-resolution representation (MRR) of a series of intermediate shape models for FTS diamond turning based on mesh simplification is proposed. In this MRR, geometric relations between each resolution model can be controlled so as to avoid overcut and to level the cutting loads. The new control method for MRR is based on an improved Edge Collapse Algorithm with consideration of the curvature factor. In addition, the calculation method of machining allowance and tool path generation method are proposed to support the machining process. The effectiveness of the MRR has been verified through simulation.

Stability Analysis of the MRT-Based Compliant Polishing Tool System

2012 ◽  
Vol 201-202 ◽  
pp. 473-476
Author(s):  
Chong Yang Yuan ◽  
Di Zheng ◽  
Jian Ming Zhan ◽  
Li Yong Hu
Keyword(s):  
Geometric Modeling ◽  
Mixed Model ◽  
Simulation Software ◽  
Free Form ◽  
Cnc Milling ◽  
Element Analysis ◽  
Compliant Polishing ◽  
The Stability ◽  
Free Form Surfaces ◽  
Polishing Tool

In order to meet the needs for the precise polishing of free-form surfaces, a new compliant polishing tool system was designed based on a magnetorheological torque servo (MRT), and integrated into a CNC milling machine. Through analysis, it was pointed out that the key factor affecting the polishing quality of this system is the stability of the system. By means of the 3D geometric modeling software ProE, the finite element analysis software ANSYS, and the dynamic simulation software ADAMS, the rigid-flexible mixed model of the system was established and the stability of the polishing pressure and tool position was numerically analyzed.

scholarly journals Improving the accuracy of free-form surface machining on CNC milling machines

Mechanik ◽  
2018 ◽  
Vol 91 (12) ◽  
pp. 1100-1103
Author(s):  
Andrzej Werner
Keyword(s):  
Geometric Model ◽  
Free Form ◽  
Cnc Milling ◽  
Surface Machining ◽  
Machining Errors ◽  
Milling Machines ◽  
Coordinate Measurements ◽  
Free Form Surface ◽  
Free Form Surfaces

This article presents a method of increasing the accuracy of the production of free-form surfaces. This method is based on the execution of coordinate measurements of the pre-treated object and reconstruction of its nominal geometric model in order to compensate existing machining errors.

scholarly journals A generic mathematical model of single point cutting tools in terms of grinding parameters

2011 ◽  
Vol 35 (10) ◽  
pp. 5143-5164 ◽  
Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Sanjay G. Dhande
Keyword(s):  
Mathematical Model ◽  
Single Point ◽  
Cutting Tools ◽  
Grinding Parameters

Mathematical Modeling of Ball-End Cutter

2013 ◽  
Vol 284-287 ◽  
pp. 806-809 ◽  
Author(s):  
Jung Fa Hsieh ◽  
Fu Shou Wang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Coordinate Transformation ◽  
Lower Cost ◽  
Geometric Model ◽  
Cutting Performance ◽  
Free Form ◽  
Flank Face ◽  
Free Form Surfaces ◽  
The Mathematical Model

The ball-end cutter plays an important role in machining free-form surfaces due to its adaptability to a surface. It is widely used in aerospace, automobile, and die/mode industries. Thus, the demand for higher cutting performance and lower cost of the ball-end cutter has been increasingly focused. In this paper, based on normal helix cutting edge geometric model, the cone wheel, which was used to grind the rake and flank face of ball-end cutter, was designed. Then, we use homogenous coordinate transformation to derive for the ball-end cutter and establish the mathematical model for grinding this type cutter in terms of grinding parameters. Finally, the cutting angles of ball-end cutter were discussed.

Review of several precision finishing processes for optics manufacturing

2018 ◽  
Vol 1 (2) ◽  
pp. 170-188 ◽  
Author(s):  
Gourhari Ghosh ◽  
Ajay Sidpara ◽  
P. P. Bandyopadhyay
Keyword(s):  
Surface Finish ◽  
Single Point ◽  
Diamond Turning ◽  
Free Form ◽  
Shape Accuracy ◽  
Optical Components ◽  
Finishing Processes ◽  
Optics Fabrication ◽  
Free Form Surfaces ◽  
Precision Finishing

The ultrasmooth optical components with atomic-order surface roughness and nanometre-level shape accuracy are in immense demand with the rapid advancement of modern optical technology. In recent years, aspherical and free-form surfaces are gaining more interest for its favorable properties. Moreover, the new optical materials with immensely enhanced mechanical properties are being developed to meet the stringent requirements of modern optics. Fabrication of complex-shaped ultrasmooth optical components becomes a significant challenge as conventional finishing techniques are unable to machine aspherical or free-form surfaces precisely. This situation demands some highly deterministic finishing processes. Mostly, the optical components are fabricated by shaping or pre-finishing methods followed by final finishing processes. In the shaping or pre-finishing methods, the rigid abrasive tools are used to remove the material at an enhanced rate and near net shape of the elements can be attained. Surface finish and shape accuracy can also be improved to some extent. Owing to the presence of residual finishing marks generated by shaping methods, the application of the components is limited to the infrared (IR) optics. Final finishing processes include more deterministic and flexible polishing techniques that can achieve desired surface finish, figure accuracy and surface integrity to make it suitable for shorter wavelength applications. In recent years, single point diamond turning, precision grinding, plasma chemical vaporization machining and magnetorheological fluid-based finishing are widely used for fabricating ultrasmooth optics. In this article, principle, mechanism of material removal and applicability of the aforementioned precision finishing processes to different materials are discussed.

Tool Contact Maps by Rectangular Grid Decomposition

2011 ◽  
Author(s):  
Eyyup Aras
Keyword(s):  
Geometric Modeling ◽  
Free Form ◽  
Tool Geometry ◽  
Depth Of Cut ◽  
Force Model ◽  
Rectangular Grid ◽  
Ongoing Research ◽  
Circle Plane ◽  
Milling Operations ◽  
Free Form Surfaces

This paper is intended to contribute to ongoing research [1–3] in geometric modeling of the virtual machining. In geometric modeling the tool paths are verified by performing the machining simulations and also the cutter workpiece engagements (CWEs) are extracted. CWE geometry is a key input to force calculations and feed rate scheduling in milling operations. Finding these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. This paper presents a discrete model based methodology for extracting CWEs generated during a multi axis machining of free form surfaces using a range of different types of milling tools. In this method the in-process workpiece is represented by a set of z-axis aligned rectangular grids. Each grid is made up of four planes, with their normals aligned with respect to the x and y-axis of the Cartesian coordinate system. In developing the methodology the parametric representations of the automatically programmed tool (APT)-type milling cutters are used. The milling tool surfaces are decomposed into circles. During the material removal process only some portions of those circles which are called the engagement arcs may contact the in-process workpiece. To find the geometric limits of those arcs the concept of the feasible contact surface is utilized. The CWE extraction simulation is performed through intersecting those arcs with the planes of each rectangular grid. Thus the intersection calculations reduce to circle/plane intersections which can be performed analytically for the geometry found on milling cutters. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. Then using a sort algorithm the neighboring engagements in the same arc level are combined.

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