Chapter Three

FLOW THROUGH CONICAL CONVERGING DIES

Nomenclature

3.1. Introduction

3.1.1 The Subject

3.1.2 Friction

3.1.3 Other Independent Process Parameters

3.1.4 The Dependent Variable

3.2. The Experimental Approach

3.2.1 The Equipment

3.2.2 Recording of the Readings

3.2.3 Plotting the Data

3.3. The Analytical Approach

3.3.1 Exact Solutions vs. Limit Analysis

3.3.2 Detailed Flow Pattern Studies

3.3.3 The Changing Flow Patterns

3.3.4 Conjugating Surfaces of Velocity Discontinuities

3.3.5 The Spherical Velocity Field and the Distorted Grid Pattern

3.3.6 The Powers

3.3.7 Total Power and Force

3.3.8 The Optimal Die Design

3.3.9 Inertia Forces

3.3.10 Maximum Possible Reduction

3.4. Comparison Between Analytical And Experimental Data

3.5. Sound Flow Vs. Other Patterns Of Flow

3.5.1 Possible Patterns

3.5.2 The Concept of Minimum Energy

3.5.3 Dead-Zone Formation

3.5.4 Shaving

3.5.5 Central Burst

3.5.6 Summary

3.6 Measurement Of Friction

3.6.1 The Phenomenon

3.6.2 Optimal Die Angle

3.7 Hydrodynamic Lubrication

3.7.1 Foreword

3.7.2 Implementation of Hydrodynamic Lubrication

3.7.3 The Principles of Hydrodynamic Lubrication

3.8 From Conventional Bull Block To Wet-Drawing With Slip

3.8.1 The Bull Block

3.8.2 The Multi-Die Wire-Drawing Machine

3.8.3 The Multi-Die Wire-Drawing Machine with a Dancer

3.8.4 Drawing With Slip

3.8.5 Recapitulation of the Evolution of Wire-Making Machines

3.8.6 The Dependence of Pull on Slip and Other Processing Parameters

3.8.7 A Study of Fine-Wire Process Limitations

3.8.8 The Characteristics of the Effect of Individual Factors

3.8.9 The Multi-Die Fine Wire Machine with Parallel Cylinders

3.9 Limit Analysis

3.9.1 Foreword

3.9.2 The Triangular Field

3.9.3 The Trapezoidal Velocity Field

3.9.4 Lower-Bound Solution

3.9.5 Limit Analysis

3.9.6 Adiabatic vs. Isothermal Flow

3.10 References