A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces

2013 ◽  
Vol 70 (5-8) ◽  
pp. 1355-1368 ◽  
Author(s):  
Zezhong C. Chen ◽  
Maqsood A. Khan
Keyword(s):  
Arc Length ◽  
Sculptured Surfaces ◽  
New Approach ◽  
Tool Paths

A New Approach to G1 Biarc Approximations for Making Smooth, Accurate, and Non-Gouged Profile Features Using CNC Contouring

2006 ◽  
Author(s):  
Zezhong C. Chen ◽  
Xujing Yang
Keyword(s):  
Manufacturing Industry ◽  
Cutting Tool ◽  
Minimum Size ◽  
Free Form ◽  
New Approach ◽  
B Spline ◽  
Tool Paths ◽  
The Past ◽  
Approximation Errors ◽  
The Individual

Extensive research on G1 biarcs fitting to free-form curves (i.e., Bezier, B-spline, and NURBS curves) has been conducted in the past decades for various purposes, including CNC contouring to make smooth, accurate profile features such as pockets, islands, and sides. However, all the proposed approaches only focused on the approximation errors and the biarc number, not on the radius of the individual fitting arc; so it could be smaller than the cutting tool, which would cause gouging during machining. This work, based on the tool radius pre-determined by the minimum size of the concavities of the design profile, proposes a new approach to approximating the profile with a G1 biarc curve in order to make smooth, accurate, and non-gouged profile features using CNC contouring. The significant new contribution of this work is a new mechanism that ensures all the concave arcs of the fitting curve are larger than the pre-determined tool and the fitting errors meet the specified tolerance. This approach can promote the use of G1 biarc tool paths in the manufacturing industry to make high precision profile features.

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.

ROUGH MACHINING FOR MULTI-SCULPTURED SURFACES

1999 ◽  
Vol 23 (2) ◽  
pp. 275-286
Author(s):  
A. Vafaeesefat ◽  
H.A. EIMaraghy
Keyword(s):  
Cutting Planes ◽  
Tool Path ◽  
Tool Path Generation ◽  
Parallel Projection ◽  
Geometric Description ◽  
Sculptured Surfaces ◽  
Rough Machining ◽  
Tool Paths ◽  
Rough Milling ◽  
Bounding Surfaces

This paper present a method to generate 3-axis NC programs for rough milling processes. A raster digitizing of the solid volume delimitated by sculptured surfaces to be machined is first created. This is accomplished by using the so-called Z-buffer created from a parallel projection of all surfaces. Conventional rendering software can be used to generate the Z-buffer. This volume is transformed into a 3-D mesh composed of “empty”, “full”, and “mixed” blocks. Machining is preformed from top to bottom in a sequence of horizontal cutting planes. At each level of planar machining, spiral routines are used to generate the tool path. The proposed method is valid for generating tool paths for general cavities bounded by arbitrary surfaces. One of the notable advantages of the proposed method is that the tool path generation is independent from the geometric description of bounding surfaces. An example is used to illustrate the approach and its advantages.

A Generic, Geometric Approach to Accurate Machining-Error Predictions for 3-Axis CNC Milling of Sculptured Surface Parts: Part II — Applications and Analysis

2006 ◽  
Author(s):  
Zezhong C. Chen ◽  
Wei Cai
Keyword(s):  
Tool Path ◽  
Geometric Approach ◽  
Sculptured Surface ◽  
Cnc Milling ◽  
Sculptured Surfaces ◽  
Machining Error ◽  
Tool Paths ◽  
Machining Errors ◽  
Tool Surface ◽  
Cam Software

As sculptured surfaces are widely used in mechanical design, machining sculptured surface parts accurately is highly demanded in industry; however, it is quite challenging to meet their demand. Due to the geometric complexity of these surfaces, the tool-surface geometric mismatch always causes machining errors when the tool cuts along the tool paths. To prevent surface gouging, where the machining error is greater than the part tolerance, state-of-the-art CAM software usually determines cutter contact (CC) points on the tool paths first, and then simulates the machining to check the errors caused by this tool-surface mismatch. If surface gouging occurs, the CC points are adjusted using the CAM software. But this established method is quite time consuming and sometimes ineffective. To overcome these problems, a new system, based on the accurate predictions of machining errors, is proposed in this research paper for the optimization of CC points on the tool paths. First, two established CC point generation methods, the chordal deviation method and the circular arc approximation method, are introduced; and their limitations are addressed. Second, a sensitivity study of the machining errors with respect to the cutting tools is conducted. Then a system implementing the generic, geometric approach to accurate machining-error predictions is proposed to optimize CC points on the tool paths. Finally, this CC point optimization system is applied to two practical parts to demonstrate its advantages over the two established methods. This proposed work provides a profound understanding of the machining errors caused by the tool-surface mismatch and contributes to tool path planning for 3-axis CNC milling of sculptured surface parts.

Curvature catering-a new approach in manufacture of sculptured surfaces (part 1. theorem)

1993 ◽  
Vol 38 (1-2) ◽  
pp. 159-175 ◽  
Author(s):  
X.C. Wang ◽  
S.K. Ghosh ◽  
Y.B. Li ◽  
X.T. Wu
Keyword(s):  
Sculptured Surfaces ◽  
New Approach

A New Approach to Generating Accurate NURBS Cutter Location Paths With Approximate Arc Length Parameter

2010 ◽  
Author(s):  
Maqsood A. Khan ◽  
Zezhong C. Chen
Keyword(s):  
Tool Path ◽  
Arc Length ◽  
Good Tool ◽  
New Approach ◽  
Interpolation Methods ◽  
Reference Path ◽  
Sampling Points ◽  
Nurbs Interpolation ◽  
New Type ◽  
Arc Lengths

For accurate tool trajectories with respect to predetermined NURBS cutter location paths (refer to reference paths) and good tool kinematics in NC machining, many NURBS interpolation algorithms are trying to compute appropriate cutter locations on the paths during machining. Due to the high non-linearity between each interpolating chord (connecting two adjacent cutter locations) and its corresponding path segment, the existing methods can only interpolate the reference path with approximation, resulting in actual cutter trajectory with error beyond the tolerance and large feed rate fluctuations. To address problems of the current interpolation methods in this work, a new type of tool path, NURBS cutter location path with the arc length parameter, is proposed and a new approach to generating accurate paths of this type is provided through re-parameterization of the reference paths with the arc length parameter. The main features of this approach include (1) sampling points and calculating their arc lengths by decomposing an input reference path into Bezier curve segments according to criteria, and (2) fitting a NURBS tool path with the arc length parameter to the sample points until the parameterization error is less than the tolerance. This approach is applied to a benchmark for a NURBS path with the arc length parameter, and this path is then compared with the results generated using three existing interpolation methods, in order to demonstrate the advantage of this new approach.

Piecewise B-Spline Tool Paths With the Arc-Length Parameter and Their Application on High Feed, Accurate CNC Milling of Free-Form Profiles

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Zezhong C. Chen ◽  
Maqsood A. Khan
Keyword(s):  
Tool Path ◽  
Free Form ◽  
Arc Length ◽  
Cnc Milling ◽  
B Spline ◽  
Tool Paths ◽  
High Feed ◽  
Genuine Solution ◽  
Cnc Controller ◽  
Very High

To conduct B-spline curve machining, first, B-spline tool paths with feed rates are planned; and second, the B-spline interpolator generates tool trajectories in real-time based on the paths fed into the computer numerically controlled (CNC) controller. Currently, the paths are often planned geometrically with a nonarc-length parameter. Literally, the interpolator can process B-spline paths with the arc-length parameter well, while it sometimes is challenged to work with the nonarc-length parameterized B-spline paths. As a consequence, it is difficult to ensure high accuracy of the tool trajectories in B-spline machining in terms of their corresponding paths; especially, if the feed is very high, smooth tool kinematics cannot be well maintained. To root out these problems, a new type of tool path—piecewise B-spline tool paths with the arc-length parameter—is first proposed in this work. Given a B-spline path with a nonarc-length parameter, it is accurately converted into a B-spline path with an arc-length parameter before sending it into the CNC controller. Furthermore, if the prescribed feed rate is very high and the arc-length parameterized B-spline path is disqualified, it is split into pieces represented with distinct arc-length parameterized B-spline paths in different feed rates. The main advantage of these piecewise paths is that they can eliminate the problems encountered by the existing B-spline interpolator with input of nonarc-length parameterized B-spline paths. Therefore, the piecewise arc-length parameterized B-spline paths are a genuine solution to high feed-and-accuracy B-spline machining.

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