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.

An Effective Approach to Approximating 2-D Free-Form Curve Offsets for B-Spline NC Tool Paths With Offset Error Globally Bounded

2010 ◽  
Author(s):  
Maqsood A. Khan ◽  
Zezhong C. Chen
Keyword(s):  
Computer Aided Design ◽  
Tool Path ◽  
Error Function ◽  
Industrial Applications ◽  
Cnc Machining ◽  
Free Form ◽  
Control Points ◽  
Base Function ◽  
B Spline ◽  
Tool Paths

The topic of representing the offset of a 2-D B-spline curve in the same form has been under research for a long time, and it has many industrial applications, especially, in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and higher geometric accuracy. However, the existing methods often generate the offsets of 2-D free-form curves in the form of B-spline curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by adding more offset points at the appropriate locations. The proposed new approach is more efficient, and the resulting offsets in B-spline are more accurate with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, and has potential for other applications in industry.

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.

Adaptive Tool Path Planning Strategy for 5-Axis CNC Machining of Free Form Surfaces

2019 ◽  
Author(s):  
Hrishikesh Mane ◽  
S. S. Pande
Keyword(s):  
Tool Path ◽  
Cnc Machining ◽  
Memory Storage ◽  
Free Form ◽  
Cnc Machine ◽  
Planning Strategy ◽  
Part Quality ◽  
Tool Paths ◽  
Path Topology ◽  
Free Form Surfaces

Abstract This paper presents a curvature based adaptive iso-parametric strategy for the efficient machining of free form surfaces on 5-axis CNC machine using the flat end mill tool. One iso-parametric boundary of the surface is selected as the initial tool path. Set of cutter contact (CC) points are chosen adaptively on the initial tool path considering desired profile tolerance. Adjacent iso-parametric tool paths are computed adaptively based on the scallop height constraint unlike the traditional iso-parametric approach. The path topology is post-processed to generate the part program for 5-axis CNC machine in ISO format. The system was rigorously tested for various case studies by comparing the results with the traditional 5-axis iso-parametric tool path strategy, iso-scallop strategy and iso-planar strategy of a commercial software. Our system was found to generate efficient tool paths in terms of part quality, productivity and memory storage compared to the conventional strategies.

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.

Spiral Tool Path Planning Using Eccentric Parameters

2014 ◽  
Author(s):  
Baosu Guo ◽  
Qingjin Peng ◽  
Xiaosheng Cheng ◽  
Ning Dai
Keyword(s):  
High Speed ◽  
Tool Path ◽  
Free Form ◽  
Tool Path Planning ◽  
Inverse Mapping ◽  
Machined Surface ◽  
Tool Paths ◽  
Spiral Tool Path ◽  
Free Form Surfaces ◽  
The Relationship

Free-form surfaces can be machined continuously with minimum tool retractions and at the high speed by following a spiral tool path. This paper presents an improved planning method of the spiral tool path using eccentric parameters for machining free-form surfaces. The relationship between a 3D machined surface and the 2D circular region is established through the conformal mapping. In order to generate an even path, eccentric parameters are used in 2D parametric circular regions to optimize the path interval. The proposed method produces planar spiral segments as a diagonal curve between every two adjacent parametric tool paths. A 2D spiral tool path is gained by linking spiral segments in sequence. Inverse mapping of the 2D spiral tool path onto the machined surface generates the 3D spiral tool path. The main processes of the proposed method include reducing dimensions of free-form surfaces, calculating the eccentric parametric tool path, and generating the planar diagonal spiral tool path. Some applications are used to verify the proposed methods. The proposed method allows the start point to be arbitrary and generates more even tool paths than the existing methods by introducing the mapping distortion.

Constant Scallop-height Machining of Free-form Surfaces

1994 ◽  
Vol 116 (2) ◽  
pp. 253-259 ◽  
Author(s):  
K. Suresh ◽  
D. C. H. Yang
Keyword(s):  
Tool Path ◽  
End Milling ◽  
Free Form ◽  
Machining Time ◽  
Scallop Height ◽  
Location Data ◽  
Tool Paths ◽  
Novel Approach ◽  
Constant Scallop Height ◽  
Free Form Surfaces

A novel approach for the NC tool-path generation of free-form surfaces is presented. Traditionally, the distance between adjacent tool-paths in either the Euclidean space or in the parametric space is kept constant. Instead, in this work, the scallop-height is kept constant. This leads to a significant reduction in the size of the CL (cutter location) data accompanied by a reduction in the machining time. This work focuses on the zig-zag (meander) finishing using a ball-end milling cutter.

Generation of Optimal Tool-Paths for Five-Axis Finish Milling of Free-Form Surfaces

2012 ◽  
Vol 500 ◽  
pp. 440-446
Author(s):  
Lin Geng ◽  
Yun Feng Zhang
Keyword(s):  
Genetic Algorithm ◽  
Tool Path ◽  
Free Form ◽  
Machining Efficiency ◽  
Interference Avoidance ◽  
Tool Paths ◽  
Modified Genetic Algorithm ◽  
Novel Method ◽  
Five Axis ◽  
Free Form Surfaces

In this paper, a novel method is proposed to generate optimal 5-axis finish tool-paths regarding joint movements and machining efficiency. A modified genetic algorithm is used to search for the optimal posture sequence along a tool-path while interference avoidance and surface finish quality act as constraints. Case studies are then provided to prove the effectiveness of the algorithm.

Boundary-conformed machining of turbine blades

2005 ◽  
Vol 219 (3) ◽  
pp. 255-263 ◽  
Author(s):  
S Ding ◽  
D C H Yang ◽  
Z Han
Keyword(s):  
Computer Aided Design ◽  
Tool Path ◽  
Flow Line ◽  
Turbine Blades ◽  
Free Form ◽  
Implementation Processes ◽  
Tool Marks ◽  
Tool Paths ◽  
Continuous Boundary ◽  
Free Form Surfaces

Boundary-conformed machining is a new method to mill free-form surfaces with tool paths that reflect the natural shapes of the surfaces. It is suitable for the machining of turbine blades taking into account the direction of tool marks left on the vanes. To facilitate this type of machining, this paper introduces an application of the ‘boundary-conformed algorithm’ to generate continuous boundary-conformed flow line tool paths for the milling of blade surfaces. With this approach, the initial segment of the flow line tool paths is along the top edges of the blade while the final segment follows the intersection curves between the blade and the hub surface. The intermediate segments cover the surface by changing smoothly from the initial tool path to the final tool path. The two opposite sides of the blade, which are two trimmed surfaces, are machined together continuously from top to bottom with these continuous boundary-conformed tool paths. This method has been successfully integrated into an industrial computer-aided design and manufacture system (Pro/Engineer) by using Pro/Toolkit. A detailed algorithm and implementation processes have been introduced.

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