Pocket Decomposition using DN and HARI Number. A Novel Approach

Table of Contents

1 Introduction

1.1 Background and Motivation

1.2 Organization of Thesis

2 Literature Review

2.1 Introduction

2.2 Basic Terminologies Associated with Pocket Machining

2.3 Tool Path Requirements for High Speed Pocket Machining

2.4 Organization of the Literature Review

2.5 Noteworthy Literature Reviews

2.6 Various Types of Pockets and Pocket Machining

2.7 Conventional Tool Path Strategies

2.7.1 Directional Parallel

2.7.2 Contour Parallel (Boundary Parallel or Offset) Tool Path

2.7.3 Space Filling Curves

2.8 Corner Machining Tactics

2.9 Advance Tool Path Strategies for HSM

2.9.1 Mapping Based Approaches for Tool Path Generation

2.9.2 Medial Axis Transform Based Method for Tool Path Generation

2.9.3 Clothoidal Spiral Tool Paths

2.9.4 Spiral Tool Paths Based on the Solution of PDE

2.9.5 Trochoidal Tool Paths

2.9.6 Interpolating Tool Paths Based on Bezier, B-spline and NURBS

2.9.7 Miscellaneous Tool Path Planning Strategies

2.10 Current Status of Development in Tool Path Strategies

2.11 Summary Table

2.12 Observations

2.13 Objective of Present Research

3 Spiral Tool Path Based on PDE and NURBS

3.1 Introduction

3.2 Methodology

3.2.1 The Algorithm for Generating Spiral Tool Path for Star-Shaped Polygon Using PDE

3.3 Extending the Method for Non-star-shaped Polygon and Free-form Curves

3.4 Results and Discussion

3.4.1 Effect of Mesh Size on Tool Path.

3.4.2 Effect of Permissible Error and Number of Degree Steps

3.5 Conclusions

4 Study of Elliptical-pocket Machining

4.1 Introduction

4.2 Experimental Details

4.2.1 Tool Path Strategy and Pocket Geometry

4.2.2 Tooling Details and Machining Conditions

4.3 Experimental Plan Procedure

4.4 Results and Discussion

4.4.1 Tool Path Length

4.4.2 Cutting Time

4.4.3 Percentage Utilization of a Tool (PUT)

4.4.4 Average Surface Roughness (Ra)

4.5 Conclusions

5 Quantitative Comparison of Pocket Geometries and Pocket Decomposition

5.1 Introduction

5.2 Dimensionless Number (DN) for Comparing Pocket Geometries

5.2.1 Analogy of Reynolds Number

5.2.2 Percentage Utilization of a Tool (PUT) as a Measure of Effectiveness of Spiral Tool Path

5.2.3 The Concept of Dimensionless Number (DN)

5.2.4 Various Ratios and Their Effects

5.2.5 Dimensionless Number, DN

5.2.6 Modified DN for Spiral Tool Path (DNspiral)

5.3 Results and Discussion

5.4 Pocket Decomposition

5.4.1 Decomposition of a Polygon Geometry

5.5 Free-form Pocket Decomposition

5.6 Decomposition of a pocket with an island

5.7 Conclusions

6 Study of speed, feed and step-over in pocket milling

6.1 Introduction

6.2 Experimental Investigation

6.2.1 Selection of Process Variables, Responses, Workpiece/Tool Material and Tool Path Strategy

6.3 Experimental Setup

6.3.1 Fixture Design

6.3.2 Designing the Experiments

6.3.3 Selection of Sampling Frequency

6.4 Results and Discussion

6.4.1 Cutting Time

6.4.2 Surface Roughness

6.4.3 A Method of Analysing Cutting Forces

6.5 A Crucial Test Before linear Cutting Forces Experiments

6.6 Conclusions

7 Overall Results and Discussion

7.1 Overall Results and Discussion

8 Conclusions

8.1 Conclusions

8.2 Scopes of Future Research

9 References

Objectives and Research Focus

The main objective of this work is to improve high-speed CNC pocket machining efficiency by developing a spiral tool path based on Partial Differential Equations (PDE) and NURBS, which eliminates limitations like stop-and-go motion and nonuniform step-overs found in conventional strategies. The research aims to establish a quantitative method for comparing pocket geometries and implementing an efficient decomposition algorithm to optimize machining performance for non-standard, bottle-necked, or complex pockets.

• Development of a spiral tool path generation algorithm using second-order elliptic PDEs and NURBS.
• Experimental analysis of the impact of aspect ratio, feed rate, and tool path strategy on machining performance.
• Introduction of a novel Dimensionless Number (DN) for the quantitative comparison of different pocket geometries.
• Creation of a decomposition algorithm to divide complex pockets into simpler sub-geometries to improve tool path efficiency.
• Validation of the developed tool path and cutting force analysis for high-speed pocket milling on AISI 304 and AISI P20 materials.

Excerpt from the Book

Summary of Chapters

1 Introduction: Provides the context of 2.5D CNC pocket machining, highlights the limitations of conventional tool path strategies, and outlines the research objectives.

2 Literature Review: Conducts an extensive review of pocket machining terminology, tool path requirements, conventional strategies, and advanced methods for high-speed machining.

3 Spiral Tool Path Based on PDE and NURBS: Describes the development of a spiral tool path generation algorithm based on second-order elliptic PDEs, including its application to different pocket geometries.

4 Study of Elliptical-pocket Machining: Presents an experimental investigation of various parameters and tool path strategies on AISI 304 stainless steel using elliptical pockets.

5 Quantitative Comparison of Pocket Geometries and Pocket Decomposition: Proposes a new dimensionless number (DN) for geometry comparison and an algorithm for decomposing complex pockets into more efficient sub-pockets.

6 Study of speed, feed and step-over in pocket milling: Reports experimental findings on the effects of machining parameters on cutting forces, surface roughness, and time during spiral tool path machining on AISI P20.

7 Overall Results and Discussion: Synthesizes the primary findings and results from the experimental and analytical studies presented in the previous chapters.

8 Conclusions: Summarizes the key contributions of the research and identifies potential areas for future exploration.

Keywords

CNC Pocket Machining, Spiral Tool Path, Partial Differential Equation (PDE), NURBS, High Speed Machining (HSM), Dimensionless Number (DN), Percentage Utilization of a Tool (PUT), Pocket Decomposition, AISI 304, AISI P20, Cutting Force Analysis, Surface Roughness, Design of Experiments (DOE), Aspect Ratio, Material Removal Rate

Frequently Asked Questions

What is the primary focus of this thesis?

The thesis focuses on improving the efficiency of 2.5D CNC pocket machining through the development of a novel spiral tool path strategy based on Partial Differential Equations (PDE) and NURBS, specifically targeting high-speed machining applications.

Which conventional tool path strategies are identified as limiting?

Directional parallel and contour parallel tool paths are identified as limiting due to issues like stop-and-go motion, sharp velocity discontinuities, and frequent tool retractions, which adversely affect machining time and surface finish.

How does the proposed spiral tool path overcome existing issues?

The proposed spiral tool path, derived from solving elliptic PDEs, avoids sharp corners and constant direction changes, allowing for smoother tool movement, consistent chip loads, and reduced tool wear compared to conventional methods.

What is the role of the Dimensionless Number (DN) mentioned in the study?

The Dimensionless Number (DN) is a novel quantitative metric developed to compare different pocket geometries objectively. It helps predict the effectiveness of a spiral tool path for a specific pocket shape prior to the actual tool path generation.

What methodology is used to validate the proposed tool path and findings?

The research employs both mathematical modeling (PDE and NURBS) and extensive experimental validation, including Design of Experiments (DOE) using AISI 304 and AISI P20 stainless steel on high-speed machining centers.

What is the purpose of pocket decomposition?

Pocket decomposition is used to break down complex, non-star-shaped, or bottle-necked geometries into simpler, star-shaped sub-geometries to prevent redundant tool path length and improve the overall efficiency of the spiral tool path.

What significance do the HARI numbers have in this research?

HARI numbers (Helps in Appropriate Rive-lines Identification) are used as a criterion during the pocket decomposition algorithm to determine the optimal split-lines for creating efficient sub-pockets.

Why was AISI P20 steel selected for the cutting force investigation?

AISI P20 was chosen due to its widespread industrial use in manufacturing plastic molds and large dies, and its specific machinability characteristics that require rigorous force analysis in high-speed milling environments.