INTRODUCTION

Numerically controlled (NC)machine tools were developed to fulfill the contourmachining requirements of complex aircraft parts and forming dies. The first NC machine tool was developed by Parsons Company and MIT in 1952 [63]. The first-generation NC units used digital electronic circuits and did not contain any actual central processing unit; therefore, they were called NC or hardwired NC machine tools. In the 1970s, computer numerically controlled (CNC) machine tools were developed with minicomputers used as control units. With the advances in electronics and computer technology, current CNC systems use several high-performance microprocessors and programmable logical controllers that work in a parallel and coordinated fashion. Current CNC systems allow simultaneous servoposition and velocity control of all the axis monitoring of controller and machine tool performance, online part programming with graphical assistance, in-process cutting processmonitoring, and in-process part gauging for completely unmanned machining operations. Manufacturers offer most of these features as options.

COMPUTER NUMERICALLY CONTROLLED UNIT

A typical CNC machine tool has three fundamental units: the mechanical machine tool unit, power units (motors and power amplifiers), and the CNC unit. Here, a brief introduction of a CNC system from the user's point of view is presented.

Organization of a CNC Unit

A CNC unit of a machine tool consists of one or more central processing units (CPUs), input/output devices, operator interface devices, and programmable logical controllers.

INTRODUCTION

The first step in automating machining systems was the introduction of computer numerically controlled (CNC) machine tools. The primary function of CNC is to automatically execute a sequence of multiaxis motions according to a part geometry. However, safe, optimal, and accurate machining processes are generally planned by manufacturing engineers based on their experience and understanding of the process. It is difficult to predict vibration, tool wear and breakage, thermal deformation of the machine tools, and similar process-based events by using off-line theoretical models. In addition to engineering the process plans before actual machining, the machine tools are instrumented with vibration, temperature, displacement, force, vision, and laser sensors to improve the productivity and reliability of the cutting operations on-line. The sensors must have reliable frequency bandwidth, have a good signal-to-noise ratio, and provide signals with reliable correlation to the state of the process. They must also be practical for installation on machine tools. The measured sensor signals are processed by real-time monitoring and control algorithms, and the corrective actions are taken by the CNC accordingly. The corrective actions may be manipulation of spindle speed, feed, tool offsets, compensation of machine tool positions, feed stop, and tool change depending on the process monitoring and control application. Such a sensor-assisted cutting is called intelligent machining in the literature [16, 17]. The architecture of CNC must be organized in such a way that it allows real-time manipulation of the machine tool's operating conditions.

Metal cutting is one of the most widely used manufacturing processes to produce the final shape of products, and its technology continues to advance in parallel with developments in materials, computers, sensors, and actuators. A blank is converted into a final product by cutting extra material away by turning, drilling, milling, broaching, boring, and grinding operations conducted on computer numerically controlled (CNC) machine tools. The second edition of this book helps students and engineers understand the scientific principles of metal cutting technology and the practical application of engineering principles to solving problems encountered in manufacturing shops. The book reflects the author's industrial and research experience, and his manufacturing engineering philosophy as well.

Engineers can learn best by being shown how to apply the fundamentals of physics to actual machines and processes that they can feel and visualize. Mathematics, physics, computers, algorithms, and instrumentation then become useful integration tools in analyzing or designing machine tools and machining processes.

Metal cutting operations take place between a cutting tool and workpiece material mounted on a machine tool. The motion of the machine tool is controlled by its CNC unit, and the numerically controlled (NC) commands to CNC are generated on computer-aided design/computer-aided manufacturing (CAD/CAM) systems. The productivity and accuracy of themetal removal operation depend on the preparation of NC programs, planning of machining process parameters and cutting conditions, cutter geometry, work and tool materials, machine tool rigidity, and performance of the CNC unit.

INTRODUCTION

Machine tools are called machine making machines. Various machining and forming operations are executed by a variety of machine tools to produce mechanical parts. To maintain specified tolerances, the machine tools must have greater accuracy than the tolerances of the manufactured parts. The precision of a machine tool is affected by the positioning accuracy of the cutting tool with respect to the workpiece and the relative structural deformations between them. The engineering analysis and modeling of relative static and dynamic deformations between the cutting tool and workpiece are covered in this chapter.

MACHINE TOOL STRUCTURES

A machine tool system has three main groups of parts: mechanical structures, drives, and controls. The components can be observed from the horizontal computer numerically controlled (CNC) machining center shown in Figure 3.1.

Mechanical Structure

The structure consists of stationary and moving bodies. The stationary bodies include beds, columns, bridges, and gear box housings. They usually carry moving bodies, such as tables, slides, spindles, gears, bearings, and carriages. The structural design of machine tool parts requires high rigidity, thermal stability, and damping. In general, the dimensions of machine tools are overestimated to minimize static and dynamic deformations during machining. The general design of machine tool structures will not be covered in this text. Instead, it is assumed that the relative static and dynamic compliance between the tool and the workpiece is measured experimentally or predicted with analytical methods.

INTRODUCTION

A diagram of a typical three-axis computer numerically controlled (CNC) machining center is shown in Figure 6.1. The CNC machining center consists of mechanical, power electronic, and CNC units. The mechanical unit consists of beds, columns, spindle assembly, and feed drive mechanisms. Spindle and feed drive motors and their servoamplifiers, high-voltage power supply unit, and limit switches are part of the power electronics group. The CNC consists of a computer unit and position and velocity sensors for each drive mechanism. The operator enters the numerically controlled (NC) program to the CNC unit. The CNC computer processes the data and generates discrete numerical position commands for each feed drive and velocity command for the spindle drive. The numerical commands are converted into signal voltage (±5V or ±10 V) and sent to servoamplifiers of analog drives, or sent numerically to digital drives that process and amplify them to the high-voltage levels required by the motors. As the drives move, sensors measure their velocity and position. The CNC periodically executes digital control laws at fixed sampling intervals that maintain the feed speed and tool path at programmed rates by using sensor feedback measurements.

The fundamental principles of designing CNC systems are covered in this chapter. First, the sizing and selection of drive motors are presented, followed by physical structure and modeling of a servodrive control system. The mathematical modeling and analysis of drive systems are covered both in the time and frequency domain.

The areas of machine tools, metal cutting, computer numerically controlled (CNC), computer-aided manufacturing (CAM), and sensor-assisted machining are quite wide, and each requires the academic and engineering experience to appreciate a manufacturing operation that uses all of them in an integrated fashion.

Although it is impossible to be an expert in all these subjects, a manufacturing engineer must be familiar with the engineering fundamentals for the precision and economical manufacturing of a part. This book emphasizes only the fundamentals of metal cutting mechanics, machine tool vibrations, feed drive design and control, CNC design principles, sensor-assisted machining, and the technology of programming CNC machines. The book is based on more than 120 journal articles and more than 60 research theses that reflect the engineering, research, and teaching experience of the author.

The book is organized as follows.

Chapter Two covers the fundamentals of metal cutting mechanics. The mechanics of two-dimensional orthogonal cutting is introduced first. The laws of fundamental chip formation and friction between the rake and flank faces of a tool during cutting are explained. The relationships among the workpiece material properties, tool geometry, and cutting conditions are presented. Identification of the shear angle, the average friction coefficient between the tool's rake face and moving chip, and the yield shear stress during machining is explained. The oblique geometry of practical cutting tools used in machining is introduced.

INTRODUCTION

Machine tools experience both forced and self-excited vibrations during machining operations. The cutting forces can be periodic, as in the case of milling. The nonsymmetric teeth in drilling, unbalance, or shaft runout in turning and boring can also produce periodically varying cutting forces. In all cases, the cutting forces can be periodic at tooth- or spindle-passing frequencies, which may have strong harmonics up to four to five times the tooth- or spindlepassing frequencies. If any of the harmonics coincide with one of the natural frequencies of the machine and/or workpiece structure, the system exhibits forced vibrations. The forced vibrations can simply be solved by applying the predicted cutting or disturbance forces on the transfer function of the structure by the use of the solution of ordinary differential equations in the time domain. However, self-excited, chatter vibrations are the most detrimental for the safety and quality of the machining operations, which are covered in this chapter.

Machine tool chatter vibrations result from a self-excitation mechanism in the generation of chip thickness duringmachining operations. One of the structural modes of the machine tool–workpiece system is initially excited by cutting forces. A wavy surface finish left during the previous revolution in turning, or by a previous tooth in milling, is removed during the succeeding revolution or tooth period, which also leaves a wavy surface owing to structural vibrations [112].

Geometry is one branch of mathematics that has an obvious relevance to the ‘real world’. Earlier, we studied some results in Euclidean geometry and we described the group of Euclidean transformations, the isometries. We saw that the Euclidean transformations preserve distances and angles, and have a definite physical significance.

In this chapter we study projective geometry, a very different type of geometry, that has important but less obvious applications. It was discovered through artists' attempts over many centuries to paint realistic-looking pictures of scenes composed of objects situated at differing distances from the eye. How can three-dimensional scenes be represented on a two-dimensional canvas? Projective geometry explains how an eye perceives ‘the real world’, and so explains how artists can achieve realism in their work.

In Section 3.1, we look at the development of perspective in Art and explain the concept of a perspectivity. We describe Desargues' Theorem, which concerns a curious property of two triangles whose vertices are in perspective from a single point, and so explain that perspective can play a key role in the statement and the proof of theorems in mathematics.

In Section 3.2, we define the term projective point (or Point) and call the set of all such Points the projective plane, which we denote by ℝℙ2. We also define a projective line (or Line). To enable us to tackle problems in projective geometry algebraically, we introduce homogeneous coordinates to specify the Points in ℝℙ2.

In Chapter 1 we studied conics in Euclidean geometry. In the rest of the book we prove a whole range of results about figures such as lines and conics, in geometries other than Euclidean geometry. In the process of doing this, we meet two particular features of our approach to geometry which may be new to you.

The first feature is the use of transformations in geometry to simplify problems and bring out their essential character. You may have met some of these transformations previously in courses on Group Theory or on Linear Algebra.

The second feature arises from the fact that the transformations we introduce form groups. Generally, we restrict our attention to geometry in the plane, ℝ2, but even in this familiar setting there may be more than one group of transformations at our disposal. This leads to the exciting new idea that there are many different geometries!

Each geometry consists of a space, some properties possessed by figures in that space, and a group of transformations of the space that preserve these properties. For example, Euclidean plane geometry uses the space ℝ2, and is concerned with those properties of figures that depend on the notion of distance. The group associated with Euclidean geometry is the group of isometries of the plane.

This idea, that geometry can be thought of in terms of a space and a group acting on it, is called the Kleinian view of geometry, after the 19th-century German mathematician Felix Klein who proposed it first.