PD 211 Principles of Metal Cutting Dr T Mwinuka
PD 211 Principles of Metal Cutting2hours Lecture + 1hour Tutorials Objectives • To impart to the science and theories underlying the metal cutting processes Rationale: Engineers need this knowledge to plan, supervise and optimize the process of machining of engineering components. Course Contents: Introduction to metal cutting: Action of metal cutting, workpiece-tool relationship. Tool geometry: single and multi point tools, abrasives. Theories of chip formation: Shear plane and shear zone theories, merchant theory of chip formation, current theory of chip formation. Assessment of chip formation: chip compression ratios, force and velocity relationships, types of chips. Cutting forces and cutting power, cutting tool materials. Tool wear and tool life Machineability of materials Economics of metal cutting: Taylor’s equation, economical tool life equation, economical tool life Metal cutting heat: generation and distribution of metal cutting heat
Recommended Text Books • Masuha, J R (1992): Basic Principles of Metal Cutting, Dar es Salaam University Press (DUP) • Ghosh, A and Mallik, A K (1986) Manufacturing Science, Ellis Horwood Limited Publishers. • G. Boothroyd, W A Knight (1988) Fundamentals of Machining and Machine Tools; 2nd Edition, Marcel Dekker, Inc Assessment Continuous Assessment 2 tests 40% University Exam 60%
1.0 Introduction to Metal Cutting 1.1 Action of Metal Cutting What happens in Metal Cutting? Many people compares the metal cutting action to what happens when an axe or knife splits wood. This is not a good comparison. In cutting wood the axe knife splits the wood fibres. In metal cutting the metal is compressed and then plastically deformed as follows: • The tool compresses the metal ahead of the tool when the workpiece moves on the face of the cutting tool • The compressed metal is then sheared whereby it slips. This process is known as plastic deformation. • As the cutting edge moves forward, the metal is strained at the cutting edge by what is known as concentration of stress. • The concentration of stress at the cutting edge causes a chip shear (break by force from the workpice)
Factors determining the action of metal cutting • The workpiece-its geometry and kind of material e.g. steel, aluminium, cast iron • The tool- its geometry and kind of material e.g. tool steel, HSS, carbides • The cutting conditions: speed, feed, engagement 1.2 The Workpiece As far as metal cutting is concerned, the geometry of the workpiece is defined by three surfaces: • Work Surface to be removed (raw surface)- geometry before cutting • Machined surface: surface produced by metal cutting process (geometry after cutting) • Transient surface: surface formed on the workpiece and removed during the following cut(geometry in transition) The properties of the workpiece material which determines its behaviour during cutting are called cutting constants. They will be discussed latter.
1.3 The Tool There are 7 elements which characterize the tool, but not all of them must be present in each type of tool. However each tool must have most of the elements: • The body that holds the cutting part/blades/inserts • The shank by which the tool is held • The tool bore by which the tool can be located and fixed by a spindle or arbour or mandrel • The cutting part, the chip producing elements (eg cutting edges, face and flank of a turning tool) • The wedge which is a portion of cutting part between face and flank • The base for orienting the tool for its manufacture and sharpening • The Tool Axis, an imaginary straight line with defined geometric relationship to the locating surfaces used to manufacture and sharpening of the tool Elements of a Tool
1.4 Cutting Conditions Cutting conditions are described as kinematic conditions geometric conditions other conditions 1.4.1 Kinematic Conditions • Motions There are basically three, two major motions which result into a third one • Primary Motion: causes a relative motion between tool and workpiece • Feed Motion: Causes continuous or repeated cutting • Resulting cutting motion: resultant of primary and feed motions • Other motions: approach motion, positioning motion and adjustment motion
2. Directions of Motions • Direction of Primary Motion: direction of instantaneous primary motion of a selected point on the cutting edge. • Direction of Feed Motion: direction of instantaneous feed motion of a selected point on the cutting edge • Resultant Cutting Direction: direction of instantaneous resultant cutting motion of a selected point on the cutting edge 3. Speeds • Cutting speed, v [m/min] the instantaneous velocity of the primary motion of a selected point on the cutting edge • Feed Speed, vf [mm/min] • Resultant Cutting Speed, ve [m/min]: the instantaneous velocity of the resultant cutting motion of a selected point on the cutting edge
1.4.2 Geometric Conditions Are of 2 types Those which are related to setting of the machine. These are called terms related to setting or simply machine variables Those which are related to the geometry of the material that is going to be cut. These are called terms which determine the cut. • Machine variables (i) Feed, f [mm]: displacement of the tool relative to the workpiece in the direction of feed motion (ii) Engagement a [mm]: depth of cut i.e. the length of the metal to be cut per unit revolution/stroke (iii) Cutting Speed, v [m/min]: the instantaneous velocity of the primary motion of a selected point on the cutting edge
1.4.3 Other Conditions A complete description of the metal cutting action requires the introduction of other quantities which • give the exact location of the metal cutting action- angle • give the rate of metal cutting action–rate of metal removed Angles • Feed Motion Angle Ψ: The angle between the directions of the simultaneous feed motion and primary motion • Resultant cutting speed angle η : The angle between the directions of the simultaneous primary motion and the resultant cutting motion.
Rate of Metal Removal Definition: The volume of material removed per unit time at a particular instant. In turning the metal removal rate is the product of mean speed and the cross sectional area of the cut A, thus Q=A.vmean =a.f.vmean =b.h.vmean For turning Where dw=work surface diameter and dm=machined surface diameter
2 A Cut Is a layer of workpiece material that is going to be removed by a single action of a cutting tool. In turning it is the workpiece material that is going to be removed by the cutting tool when the workpiece rotates once under feed 2.1 Width of Cut, b[mm] Is the distance between two extreme points of the active cutting edge perpendicular to the primary motion
2.2 Thickness of Cut, h [mm] Is the thickness of undeformed chip. It is defined as the product of feed and the sine of the cutting edge angle: Another quantity which is derived from the width and thickness of cut is the Area of cut, A [mm2]: cross sectional area of cut
3 Tool Geometry 3.0 Introduction • The tool must have an appropriate shape to be able to cut. • This shape is the tool geometry • The tool geometry is provided by grinding the tool • The tool geometry of each type of tool differs from another type, but the general geometry is common to all tools 3.1 General geometry of a Tool The general geometry of a metal cutting tool is given by the following terms: • Tool Elements • Tool Surfaces • Cutting Edges • Tool Angles 3.1.1 Tool Elements These are 7 elements described in section 1.3
Face Minor Flank Major Flank Minor Cutting Edge The Corner Major cutting edge 3.1.2 Tool Surfaces Faces of the cutting tool (Turning Tool) The tool has two major surfaces • The FACE (Aγ): is the surface of the tool over which the chip flows • The FLANK (Aα): is the surface of the tool over which the machined surface flow 3.1.3 Cutting Edges
3.2 Reference Systems Reference planes are required for defining tool angles. There are two major reference systems in which the angle of a cutting tool are defined. • Tool in hand reference system: Angles are defined with tool held in hand or put on table or flat surface. The system is used for the manufacture and measurement of tool angles. Planes in this system are called Tool-In-Hand Planes and angles measured in these planes all except one start with the word Tool • The tool in use reference system: Angles are defined when the tool is in application, i.e. when cutting. The system is used for describing the actual metal cutting process Planes in this system are called Tool-In-Use Planes and angles measured in this system all except one start with the word effective or working and are denoted by ve.
3.2.1 Planes in the Tool-in-Hand Reference System • Tool Reference Plane Pr: Plane perpendicular or parallel to the plane or axis of the tool convenient for locating or orienting the tool for manufacture or sharpening. • Assumed Working Plane Pf: Plane perpendicular to Pr and so chosen as to be either parallel or perpendicular to a plane or axis of the tool convenient for locating or orienting the tool for its manufacture, sharpening or measurement. • Tool Back Plane Pp: Plane perpendicular to Pr and Pf • Tool Cutting Edge Plane Ps: Plane tangential to the cutting edge and perpendicular to Pr • Cutting Edge Normal Plane Pn: Plane perpendicular to the cutting edge • Tool Orthogonal Plane Po: Perpendicular to both Pr and Ps
3.2.2 Planes in the Tool-in-Use Reference System The important factor here is the relative resultant cutting speed ve, which is the vectorial product of the cutting velocity v and feed velocity f. The planes are: • Working Reference Plane Pre: Plane perpendicular or parallel to the plane or axis of the tool convenient for locating or orienting the too • Working Plane Pfe: Plane perpendicular to Pre and so chosen as to be either parallel or perpendicular to a plane or axis of the tool 3. Working Back Plane Ppe: Plane perpendicular to Pre and Pfe 4. Working Cutting Edge Plane Pse: Plane tangential to the cutting edge and perpendicular to Pre 5. Cutting edge normal plane Pne: plane perpendicular to the cutting edge; 6. Working orthogonal Plane Poe: Perpendicular to both Pr and Ps
Pp Χ Х’ Pf ε 3.3 Angles of the Cutting Tool The tool angles are defined in the planes described above (except the cutting edge plane), each plane containing a complete set of tool angles. The tool reference plane gives the main view of the tool geometry while the other four planes give the cross sectional views. 3.3.1 Tool Angles in the Tool Reference Plane Pr • The main view gives 3 angles • χ: The cutting edge angle • ε: Included angle • Х’: Minor cutting edge angle • Χ+ ε+ Х’ = 180o
γ β α 3.3.2 Tool Angles in the Tool Working Plane Pf Tool angles in the four remaining planes give a cross sectional view. Basically there are three angles that can be obtained with different magnitudes depending on the type of plane in which they are taken. The name, size and the shape of tool angles in the four cross section views depend on: • The reference system in which they are measured • The plane in which they are measured α : Clearance angle β : wedge angle γ : Rake angle
Accordingly we have • Side rake angle γf • Back rake angle γp • Orthogonal rake angle γo • Normal rake angle γn • Orthogonal clearance angle αo • Side clearance angle αf • Back clearance angle αp • Normal clearance angle αn • Orthogonal wedge angle βo • Side wedge angle βf • Back wedge angle βp • Normal wedge angle βn 3.3.3 The Cutting Edge Inclination Angle λ Another important angle of the tool is obtained by view S. It shows that the cutting edge is inclined towards the end (corner). This is called the cutting edge inclination angle λ. Its main function is to prevent cutting vibrations
S Pn Po Pr + -
4.0 Theories of Chip Formation 4.1 Introduction The purpose of Chip Studies is to establish optimum conditions for metal cutting (machining) through • Optimization of Cutting Parameters • Improvement of machinability of materials • Improvement of cutting tools • Optimization of machine tool design and • Optimization of tool design 4.2 Historical Development • Chip Formation research started in early 19th century • Seriously between 1851 and 1900 • discovery of steam engine (1769) and industrial revolution made the research more lively • Was devoted to manufacturing of machine tools but latter research also involved tool materials and machining costs • Today is a big part of industry research
4.2 Definition Chip formation is the removal a thin layer of metal called chip or swarf, from a lager body by a wedge shaped tool. It involves plastic deformation of the workpiece material through the tool, under the effect of cutting forces. 4.3 Theories of Chip Formation 4.3.1 Introduction Early attempts compared metal cutting to cutting of wood. However the modern view involves plastic deformation of the workpiece material during chip formation 4.3.2 Methods of Study The process of chip formation cannot be observed by naked eye nor by ordinary photography. The following methods have been developed to study the nature of chip formation 1. Optical observations: can provide good information about the chip formation process. 2. By suddenly stopping (freezing) the chip formation action: Most of the important details of chip formation can be retained. 3. High speed cine-photography at low magnification, was used to reveal the changing external shape of a chip. Now replaced by high speed digital video camera.
4.3.3 Assumptions • Orthogonal cutting: Tool edge is straight, normal to the direction of cutting; also normal to the direction of feed motion 2. Continuous chip 3. Small ratio of chip thickness hc to chip width bc i.e. (hc:bc) 4. No built up edge
4.3.4 Theories • Shear Plane Theory • First theory to be developed by Russian scientist (1870) and then stated again by French scientist, Tresca in 1873. Other researchers who followed this theory are Svorkin, Piispanen, Schwerd and most recent Ernst and Merchant (1941) • It states “During chip formation the material ahead of the cutting edge is considered to be without stress. As the material advances towards the cutting edge with the relative speed v, stress suddenly builds up in the shear plane and the material is deformed along the shear plane into chip” Fig. The Shear Plane Theory Model
However, there are some contradictions facing this theory: 1. The moving particle attain infinite acceleration when crossing the shear plane. This is against nature. It always takes time for a particle to accelerate 2. A big stress gradient exists on the shear plane. This is unnatural 3. large sudden strain is obtained at the shear plane. This is also unnatural Another theory had to be developed which clears these contradictions
(2) The Shear Zone Theory The theory was founded by Russian scientist, A. A. Bricks and updated by two Japanese Okushima and Hitomi in 1960 The shear zone explains many processes associated with metal cutting. Because of this the modern theory of chip formation is based on the shear zone theory The theory states: “During chip formation the material ahead of the cutting edge is considered to be without stress. As the material enters a zone, called a shear zone, it moves with a relative speed v, stress slowly builds up and the material is deformed into a chip
(3) Modern Theory of Chip Formation Introduction: In general Chip Formation is regarded as a process in which the workpiece material is plastically deformed by the tool, whereby the workpiece material is sheared after which it slips along favourable slip lines. The material loses its strength and becomes chip, whereby it slides over the tool face. Modern Theory “Material ahead of the cutting edge is compressed and as a result stresses build up gradually as the material approaches the cutting edge of the tool until the material is sheared when the yield stress is reached. The material then slips along favourable directions of shear and finally slides along the face of the tool chip”
4.3.5 Energy Use in Chip Formation: • Plastic deformation zone (in shear zone). About 74% of the chip formation energy is dispersed here • Secondary plastic flow (in chip), about 24% of energy • Sub-surface plastic flow (on machined surface), about 2% of energy
4.4 Theory of Ernst and Merchant • This is based on the assumption that the chip is a rigid body held in equilibrium by the forces transmitted across the chip-tool interface and across the shear zone. • The whole of the resultant tool force is transmitted across the chip-tool interface • No force acts on tool edge or flank (Orthogonal Cutting)
Basis of Theory: Shear angle takes up such a value as to reduce the work done in cutting to a minimum. This means it was necessary to express in terms of the shear angle Φ then obtain the value of Φ for which Fc is minimum. Differentiating eq. 4.5 with respect toΦ and equating to zero to find the value of Φ for which the force is minimum gives:
4.5 Evaluation of Chip Formation Process The effectiveness of the chip formation process can be evaluated in many ways. Following are some of the most common methods: 1. Chip Compression Ratios 2. Shear angle relations 3. Velocity relations 4. Types of chips 5. Forms of Chips These quantities are also used to compare different chip formation processes. 4.5.1 Chip Compression Ratio The chip compression ratio denotes the change in size and form of the cut after it has undergone chip formation. Its numerical value gives the degree of deformation of the cut.
(i) Chip thickness compression ratio • Chip width compression ratio (iii) Chip length compression ratio (iv) Chip area compression ratio
4.5.2 Shear Angle Relations From the geometry of the figure follows:
chip 90o+(γ-Φ) vc vc vs tool vs Φ γ v workpiece Φ 90o- γ v Fig. Velocity relations in an orthogonal cutting 4.5.3 Velocity Relations 3 velocities are of interest: 1. The cutting velocity (normally known as the cutting speed), v 2. The chip velocity vc and 3. The shear velocity, vs
The above diagram shows first the velocities as they are during the chip formation process (left), and as they can be combined into a force triangle (right) The velocity triangle has two known angles and one unknown angle. This can be obtained from the equation: Xo = 180o-[(90o-γ)+φ] = 90o+(γ-φ) Applying the sine rule to the triangle, we get: or similarly
Chip TOOL (a) Continuous Chip W/p Cutting speed v 4.5.4 Types of Chips The formation of chips involves a shearing of workpiece material in a shear plane zone. A very large amount of strain takes place in this region in a very short time and not all metals and alloys can withstand this strain without fracture. As a result three types of chips are obtained in a chip formation process: • Continuous (shear) Chip • Discontinuous (tear) Chip and • Continuous Chip with built up edge
(b) Discontinuous (tear) chip Fig. Type of chips in a metal cutting • Continuous Chips • Are produced under the following cutting conditions: • Ductile material • High cutting speeds • Large rake angles • Small engagements • Minimum friction at tool-chip inter face
Discontinuous Chips Are produced under the following conditions: • Brittle materials • Small and negative rake angles • Small cutting speeds • Big engagements • Large friction at tool-chip interface Continuous Chips with built up edge (BUE) BUE are pseudo unstable cutting edge temporarily formed on the actual cutting edge during chip formation involving some materials. Its life varies from mili-seconds to several seconds. These chips are formed under the following cutting conditions • Ductile materials • Low cutting speed • Small rake angles • High feeds • Poor cooling • High molecular affinity between tool and workpiece materials
Total tool resitance Force workpiece Tool Fig 5.1 Real area of action of cutting forces 5.0 Metal Cutting Forces 5.1 Introduction 5.1.1 Nature of the Cutting Forces Cutting force is the total resistance given by a workpiece material against the process of chip formation effected by the penetrating tool. The cutting force is exerted along the entire length of the cutting edge.
Total tool resistance Force acting at a point on the cutting edge workpiece Tool Fig. 5.2: Assumed point of action of cutting forces 5.1.2 Point of Action of Cutting Force • 5.2 Major cutting Forces • The total resistance Fr (also known as resultant cutting force) lies in a plane perpendicular to the tool cutting edge. • Fr is usually resolved in directions convenient for its measurement, normally resolved in three convenient coordinates. • There are two systems in use today:
Chip Fc Tool Fr Ft Fig. 5.3a Resultant tool force resolved in a coordinate system containing v Motion of workpiece • The old (English) system, whereby Fr is resolved in two orthogonal components one of them containing the cutting velocity: one in the direction of cutting velocity: the cutting force, Fc The other normal to the direction of the cutting-the thrust force, Ft • Two cutting forces are obtained with this system • The cutting force Fc in the direction of cutting • The thrust force Ft in the direction normal to the direction of cutting 2. Modern system, whereby Fr is resolved in three direction: (i) in the direction of primary motion - main cutting force (ii) in the direction of feed motion – feed force (iii) in the direction perpendicular to the generated surface