Princilples of modern grinding technology

Coverage includes abrasives and superabrasives, wheel design, dressing tech-nology, machine accuracy and productivity, machine design, high-speed grindingtechnology, cost optimization, u

Principles of Modern Grinding Technology

Tai ngay!!! Ban co the xoa dong chu nay!!!

Principles of Modern Grinding Technology

Second Edition

W Brian Rowe

AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO William Andrew is an imprint of Elsevier

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14 15 16 17 18 10 9 8 7 6 5 4 3 2 1

I dedicate this book to my wife Margaret Ruth for her love and support throughout my work, the mother of my children Ivor and Ella and my constant companion.

Principles of Modern Grinding Technology explains in simple terms the principlesthat led to rapid improvements in modern grinding technology over recent decades.Removal rates and quality standards have increased a hundred-fold Very fine toler-ances are routine due to improved understanding of the process and the factors thatneed to be controlled

Superb grinding machines now produce optical-quality finishes due to ments in process control and machine design It is the same for extremely highremoval rates This book shows how best quality can be improved and costs can bebrought down at the same time as output is increased

develop-The book is aimed at practitioners, engineers, researchers, students and teachers.The approach is direct, concise and authoritative This edition introduces additionalmaterials including data, photographs, updated references and design examples.There are additions in most chapters including abrasives, dressing, cooling, high-speed grinding, centreless grinding, materials, wear, temperatures and heat transfer.There are numerous worked examples Progressing through each major element of

a grinding system and then on to machine developments, the reader becomes aware

of all aspects of operation and design Trends are described demonstrating key tures Coverage includes abrasives and superabrasives, wheel design, dressing tech-nology, machine accuracy and productivity, machine design, high-speed grindingtechnology, cost optimization, ultra-precision grinding, process control, vibrationcontrol, coolants and fluid delivery, thermal damage and grinding temperatures.Advances in the field are supported with references to leading research.Analysis is presented in later chapters and appendices with new contributions tomachine design, intelligent control, centreless grinding, fluid delivery, cost analysisand thermal analysis for prediction and control of grinding temperatures are pro-vided By selecting the right conditions, extremely high removal rates can beachieved accompanied by low temperatures Techniques for measurement of grind-ing temperatures are also included

fea-This edition includes recent process developments and additional designexamples

G Trends in high precision and high-speed grinding are explored

G Principles underlying improvements in machines and processes are explained

G Numerical worked examples give scale to essential process parameters

G Recent research findings and original contributions to knowledge are included

G A number of ultra-precision grinding machine developments are included

I wish to record sincere gratitude for the help and friendship provided by researchstudents, research fellows, colleagues and visiting scholars with whom I had theprivilege to work and whose valuable contributions made this volume possible Anumber of these have achieved well-deserved distinction in academic and industrialspheres The list, roughly in date order, includes D.L Richards, J.I Willmore, M.J.Edwards, P.A Mason, J.P O’Donoghue, K.J Stout, S Spraggett, D Koshal, W.F.Bell, F.S Chong, R Gill, N Barlow, R.N Harrison, S.P Johnson, T.W Elliott, S.Yoshimoto, D Ives, C Goodall, G.K Chang, J.A Pettit, S Kelly, D.R Allanson,D.A Thomas, K Cheng, M Jackson, M.N Morgan, H.S Qi, X Chen, S Black,

N Shepherd, Y Chen, Y Li, C Statham, C.T Schaeffer, X.Z Lin, D.McCormack, S Ebbrell, R Cai, V Gviniashvili, T Jin, A.D Batako, D Cabrera,A.R Jackson, V Baines-Jones and Zhang Lei I would especially like to mentionPaul Wright who, through his invaluable contributions, helped me and manyresearchers succeed in their projects Eventually he became manager of the labora-tories within the School of Engineering at Liverpool John Moores University

W Brian Rowe

About the Author

W Brian Rowe is a research and consulting engineer, Emeritus Professor and vious Director of Advanced Manufacturing Technology and Tribology ResearchLaboratory (AMTTREL) at Liverpool John Moores University in the UnitedKingdom A multiple recipient of prizes from The Institution of MechanicalEngineers (IMECHE), Dr Rowe has four decades of experience in academic andindustrial positions concerned with machine tools, grinding processes and tribol-ogy His accomplishments include over 250 published papers, several books,international visiting professorships and international consulting in industry

CBN Cubic boron nitride

CIRP International Academy of Production Engineering ResearchCNC Computer numerical control

CVD Chemical vapour deposited

ED Electrical discharge

EDD Electrical discharge dressing

ELID Electrolytic in-process dressing

FEPA Federation of European Producers of Abrasives

FWM Fluid wheel model of fluid convection

HEDG High-efficiency deep grinding

HEG High-efficiency grinding

HSS High speed steel

ISO International Standards Organization

JIS Japanese Industrial Standards

LFM Laminar flow model of fluid convection

MQL Minimum quantity lubrication

MRR Material removal rate

PCD Poly-crystalline diamond

PLCs Programmable logic controls

PVD Physical vapour deposition

RMS Root mean square

SD Single-point diamond

SEM Scanning electron microscope

SG Seeded gel (alumina composite abrasive) trade name

SI ISO international system (e.g units)

SiC Silicon carbide

UFM Useful flow model

VHN Vickers Hardness Number

Notation for Grinding Parameters

Note: Symbols within a special context are explained in the relevant text

a Depth of cut or hydrostatic bearing land width

ad Dressing depth of cut

ae Effective (real) depth of cut in grinding

ap Programmed (set) depth of cut in grinding

b, br,bw Width of grinding wheel contact with work

bcu Width of uncut chip

bd Dressing tool contact width

c, cp Specific heat capacity

cd,cv,ca Discharge, velocity and area coefficients in nozzle flow

dc Control wheel diameter in centreless grinding

de Effective grinding wheel diameter

dg Mean abrasive grain diameter

ds Actual grinding wheel diameter

ec,u Specific grinding energy (energy per unit volume removed)

ech Specific energy carried in chips

erf( ) Error function given in math tables

f Frequency in cycles per second (Hz)

f Interface friction factor5 τ/k

h Thin film or chip thickness

h, hf Convection factor and work-fluid convection factor

hcu Uncut chip thickness

heq Equivalent chip thickness

hg Convection factor into a grain

hw Work height in centreless grinding

hwg Convection factor into the workpiece at a grain contact

kw,kg Thermal conductivity of work material and abrasive grain

lf Contact length due to force and deflection of grinding wheel and workpiece

lg Geometric contact length due to depth of cut

n Number of grinding passes

nd Number of dressing passes

ns Grinding wheel rotational speed

pp Fluid pumping pressure

q Flux value5 heat per unit area in unit time

qd Dressing roll speed ratio5 vd/vs

qflash Flux into the workpiece at a flash contact

rcu Uncut chip width/chip thickness ratio5 bcu/hcu

ro Average effective grain contact radius

s Laplace operator in vibration theory

tp Point/flash contact time of grain and workpiece

ts Grain contact time within contact length

tt Total cycle time including grinding and dressing

ui Input to a control system

uo Output from a control system

v Mean velocity in pipe flow

vfd Dressing feed rate

A Geometric stability parameter in centreless grinding

A Wear flat area on grinding wheel as fraction or percentage

Ac Apparent area of grinding contact zone5 lcGb

Acu Cross-section area of uncut chip

Al2O3 Aluminium oxide, alumina

C Number of active abrasive grains per unit area5 cutting edge density

C C-factors giving temperature for particular grinding conditions

Ct Total cost per part

D Diameter as in journal diameter

E Young modulus of elasticity

Fa,F0a Axial force and specific value per unit width

Fn,F0n Normal force and specific value per unit width

Ft,F0t Tangential force and specific value per unit width

H Feedback function in a control system

Ha Depth of cut function in vibrations

Hf Fluid drag power

Hs Wheel wear function in vibrations

K Grinding stiffness factor5 ae/ap

Ks Grinding stiffness5 Fn/ae

K1 Work-plate factor in centreless grinding

K2 Control wheel factor in centreless grinding

L, B Grain spacing in grinding direction and in lateral direction

L Length as in bearing length or work length

L Peclet number related to thermal diffusivity

Nd Number of parts per dress

P, P0 Grinding power and power per unit width

Ps,Pp Supply pressure and pumped pressure

Q Dynamic magnifier of machine deflection

Q, Qw Removal rate, workpiece removal rate

Q0 Q0w Removal rate per unit width

Qf Nozzle fluid flow-rate

Qu Useful fluid flow-rate

Ra,Rt,Rz ISO surface roughness parameters

RL Contact length ratio5 lc/lg

Rr Roughness factor5 lfr/lfs

Rw Fraction of heat going into workpiece

Rws Work-wheel interface fraction of heat into workpiece

Scu Surface area of the uncut chip

SG Seeded gel (alumina composite abrasive) trade name

T, ΔT Temperature or temperature rise

Ud Dressing overlap ratio

β Tangent contact angle in centreless grinding

β Bearing pressure ratio5 design value of recess pressure/supply pressure

γ Work-plate angle in centreless grinding

γ Friction angle5 (cos-1

f )/2

γd Dressing sharpness ratio5 ad/bd

ϕ Grinding contact angle5 lc/deradians

Φ Through-feed angle in centreless grinding

ρ Density5 mass per unit volume

xxxv Notation for Grinding Parameters

σ Direct stress

τ Time constant of an exponential decay or growth

λ Static grinding system stiffness

λ(jω) Dynamic grinding system stiffness

ω Frequency (radians per second)

ωnωo Natural frequency, resonant frequency (radians per second)

Ω Work angular speed (radians per second)

Commonly Used Suffixes and Affixes Which Modify a General Symbol Depending on the Context in Which It Is Used

o Datum or zero or natural or output

p Pressure or pumping or programmed or ploughing

Basic Units and Conversion Factors

inch

1 bar5 14.5 pounds per square inch

1 atm14.7 pounds per square inchTemperature 1 celsius degree rise5 1.8 fahrenheit degrees riseGravitational acceleration in free

fall

9.807 m/s25 32.175 ft/s2Dynamic viscosity 1 N s/m25 0.000145 lbf s/in.25 0.000145 reyns

Cost, Quality and Speed of Production 3

Machining Hard Materials and Ceramics 3

Accuracy 4

Surface Quality and Surface Texture 4

Speed of Production 4

The Value-Added Chain 5

Reducing the Number of Operations 5

Flexible Grinding Operations and Peel Grinding 5

1.2 Basic Grinding Processes 6

Basic Surface and Cylindrical Grinding Processes 6 Internal and External Variants 7

The Range of Grinding Processes and Bibliography 7

1.3 Specification of the Grinding System Elements 8

Basic Elements 8

System Elements 8

Element Characteristics 8

The Tribological System 9

The Grinding Machine 10

The Grinding Fluid 10

Basic Material Removal (Chapter 2) 11

Grinding Wheels and Dressing (Chapters 3 and 4) 11 Grinding Wheel Behaviour (Chapter 5) 12

High-Speed Grinding (Chapter 6) 12

Thermal Damage (Chapter 7) 12

Fluid Delivery (Chapter 8) 12

Grinding Costs (Chapter 9) 12

Grinding Machine Developments (Chapter 10) 13 Grinding Process Control (Chapter 11) 13

Principles of Modern Grinding Technology.

© 2014 Elsevier Inc All rights reserved.

Vibrations in Grinding (Chapter 12) 13

Centreless Grinding (Chapter 13) 13

Mechanics of Grinding Behaviour (Chapters 14 17) 13

Energy Partition and Temperatures in Grinding (Chapter 18) 13

Grinding developed as a metal manufacturing process in the nineteenth century(Woodbury, 1959) Grinding played an important part in the development of toolsand in the production of steam engines, internal combustion engines, bearings,transmissions and ultimately jet engines, astronomical instruments and microelec-tronic devices

What Is Grinding?

Grinding is a term used in modern manufacturing practice to describe machiningwith high-speed abrasive wheels, pads and belts Grinding wheels come in a widevariety of shapes, sizes and types of abrasive Important types of wheels and abra-sives are described in the following chapters Grinding is an abrasive machiningprocess Abrasive machining technology also embraces polishing, lapping, honingand related superfinishing processes Some areas of grinding technology overlapwith this extended range of processes A distinction between grinding and otherprocesses may be purely kinematic, in some cases involving for example very lowabrasive speeds as in lapping In other cases, the extension of the grinding processinto superfinishing is found in the application of chemical or electrochemical prin-ciples to assist the abrasive process The techniques and principles described in thisbook are concerned mainly with the mechanical abrasion process and also extendinto other aspects of superfinishing

manufacturers of aero-engines and missile guidance systems, that grinding was thekey to achieving the necessary quality This provided the motivation for rapiddevelopment in the latter part of the twentieth century More recent still, grindinghas become a strategic process for production of optical quality surfaces for com-munications and for electronic devices Modern technology has also seen a trendtowards hard ceramic materials that bring new challenges for economicmanufacture.

Cost, Quality and Speed of Production

Industrial competitiveness is a balance between the competing requirements ofcost, quality and speed of production In recent decades, grinding has been trans-formed both for producing very high-quality parts and for fast economic production(Inasaki et al., 1993) This trend is illustrated inFigure 1.1where grinding and cut-ting tools are seen as increasingly competitive both for machining accuracy and forproduction rate Due to modern developments, grinding has a large role in efficientmanufacturing industry both in terms of volume and in terms of value For exam-ple, in a process known as planar grinding, many flat parts can be ground simulta-neously on one worktable This allows extremely high removal rates to be achievedand also high accuracy

Machining Hard Materials and Ceramics

Abrasive processes are the natural choice for machining very hard materials It is ageneral rule with few exceptions that the tool used for machining should be harderthan the material being machined Suitable abrasives to grind hardened steels andaerospace alloys include aluminium oxide, silicon carbide, sintered alumina andcubic boron nitride

Diamond abrasive is used to grind hard ceramics and other highly abrasivematerials Hard ceramics are difficult to machine because they are not only veryhard and very abrasive but also extremely brittle Diamond grinding is well suited

to coping with the challenges presented by new engineering structural materials,such as silicon nitride, silicon carbide and zirconia Hard ceramics are employed in

Cutting tools Grinding

High removal rate

Figure 1.1 Trends in the application of grindingwheels and cutting tools

3 Introduction

electronics, cutting tools, telecommunications, optical systems, bone replacements,heat exchangers, bearings, flow valves and heat engines (Marinescu et al., 2000).Grinding is often the simplest and least expensive process for machining hardmaterials Alternative processes such as hard turning may be feasible but often it isgrinding that is least expensive and achieves the quality and speed of productionrequired together with process reliability (Klocke et al., 2005).

Accuracy

Grinding allows high accuracy to be achieved and close tolerances can be held for size,shape and surface texture Grinding is used to machine large parts, such as machinetool slideways where straightness is important and tolerances are usually specified inmicrons Grinding is also used to machine small parts including contact lenses, needles,electronic components, silicon wafers and rolling bearings where all aspects of accu-racy are important and tolerances extend from micron to submicron and can evenapproach the nano range Nanogrinding is where accuracies of less than 0.1µm arerequired Nanogrinding using the Electrolytic In-Process Dressing (ELID) processreplaces polishing and achieves vastly improved removal rates for such applications asmirror-finish grinding and production of micro tools used in nanotechnology

Surface Quality and Surface Texture

Quality is a term that includes all aspects required for parts to function correctly.Accuracy of dimensions, form and surface texture are obvious aspects of quality.Grinding carefully can ensure good quality where other processes may have diffi-culty meeting specifications Another aspect is surface quality The integrity of thematerial at the machined surface may not always be obvious but is vitally important

in many situations For example, the surface of a hardened part should not be ened or cracked It may also be important to avoid tensile residual stresses thatreduce strength and shorten service life All these aspects of quality require carefuldesign and control of the grinding process

soft-Roughness can be reduced down to mirror finishes and optical quality of ness The achievement of this quality depends on the roughness of the abrasive, thequality of the grinding machine and the removal rates employed

flat-Speed of Production

Speed of production depends on the material being machined and the accuracy andquality required Grinding can be used to combine high removal rate with accuracy,for example, flute-grinding of hardened twist drills from a solid bar is accom-plished in seconds Alternatively, grinding can be employed with moderate removalrates to produce high-accuracy parts in large volumes Examples are bearing ringsand rolling elements for bearings Nanogrinding can be considered as a highremoval rate process because it replaces much slower processes, such as lappingand polishing

The Value-Added Chain

Grinding usually comes towards the end of product manufacture when the value ofthe parts is already significant and when mistakes can be expensive The buildup ofcosts in product manufacture is illustrated schematically inFigure 1.2

As parts move from one operation to another, such as turning, hardening andtempering, and then grinding, the parts achieve greater value and the cost of hold-ing stocks is increased There are costs of moving parts and protecting them fromdamage The cost of scrapping parts is greatly increased The increase in cost andlead time with the number of operations is not linear but exponential

Reducing the Number of Operations

If the number of operations and the lead time can be reduced, it is found that theoverall cost of manufacture can be greatly reduced

Manufacturers want either to eliminate the grinding process altogether if therequired quality can be achieved through an earlier process or else to eliminate anearlier process if grinding can achieve the form and accuracy in one operation oreven on one machine Grinding tends to govern the accuracy of the parts producedand is often the key to the required quality For example, the grinding of the flutes

of hardened twist drills to full form in one operation is very efficient

Flexible Grinding Operations and Peel Grinding

Flexible grinding operation suggests that a family of components or possibly eral families can be produced flexibly on one automatically controlled machinetool For example, it is possible that cylindrical components having several dia-meters and shoulders could be produced with a single machine setup

sev-Many grinding machine companies are now using the term peel grinding Peelgrinding combines high-speed grinding techniques with computer numerical control

to allow the grinding wheel to be employed similarly to a hard-turning tool.Typically, a 5 mm wide grinding wheel follows a programmed path to produce aform or multiple diameters The peel grinding machine introduces increased flexi-bility in the range of parts or operations that can be performed on a single machine

Number of operations

processes

Finishing processes Grinding

Figure 1.2 The buildup of costs and value added inproduct manufacture

5 Introduction

1.2 Basic Grinding Processes

Basic Surface and Cylindrical Grinding Processes

Two main classes of grinding are flat surface grinding and cylindrical grinding.Photographs of typical machines appear in Chapters 10 and 11 These two classes

of machine provide the four basic processes illustrated in Figure 1.3 The figureshows peripheral grinding of flat surfaces and cylindrical surfaces Peripheralgrinding employs the periphery of the grinding wheel The figure also shows facegrinding of nonrotational flat surfaces and face grinding of rotational flat surfaces.Face grinding employs the face of the grinding wheel Face grinding of rotationalflat surfaces can be carried out on a cylindrical grinding machine and is termedcylindrical face grinding Basic cylindrical grinding processes include external,internal and centreless variants

Figure 1.3 Four basic grinding processes

(a) Peripheral surface grinding, (b) peripheralcylindrical grinding, (c) face surface grinding and(d) face cylindrical grinding

Internal and External Variants

Figure 1.4shows important variants of the basic grinding process The three ples include internal cylindrical grinding, external centreless grinding and externalangle grinding Internal grinding of bores is a cylindrical process where a smallgrinding wheel is mounted on a slender spindle known as a quill and the workpiece

exam-is held in a chuck or collet In the internal centreless process, the workpieces may

be held and rotated on a faceplate External centreless grinding is a cylindrical cess where the workpiece is supported at its external surface against a workrest andagainst a control wheel Angle approach grinding may be employed for either inter-nal or external cylindrical grinding and allows a face to be machined at the sametime as a diameter Angle grinding allows material removal to be spread across theface and periphery of the wheel thus prolonging wheel life between redress

pro-The Range of Grinding Processes and Bibliography

In practice, the complete range of grinding processes is very large including sided or double-sided face grinding of multiple components mounted on a planesurface The range also includes profile generating operations and profile copyingoperations Profiling processes include grinding of spiral flutes, screw threads, spurgears and helical gears using methods similar to gear cutting, shaping, planing, orhobbing with cutting tools There are other processes suitable for grinding camplates, rotary cams and ball joints

single-Examples of a variety of these processes are illustrated in previous books (Marinescu

et al., 2006, 2013) Other useful books for reference are Andrew et al (1985),

Grinding wheel

Workpiece (a)

Grinding wheel Control wheel

Workrest (b)

Grinding wheel

Workpiece (c)

Figure 1.4 (a) Internal cylindrical grinding,(b) external centreless grinding and (c) externalangle grinding

7 Introduction

CIRP (2004),King and Hahn (1986),Malkin and Guo (2008),Marinescu et al (2000),Shaw (1996)andTawakoli (1990) The Annals of International Academy of ProductionEngineering Research (CIRP) published over many years provide a rich source of data

on specific materials and grinding processes For example, keynote papers byWebsterand Tricard (2004)review developments in grinding wheels.Brinksmeier et al (2006)review developments in modelling and simulation of grinding

Basic Elements

Figure 1.5illustrates the basic elements of a grinding system that the engineer has

to coordinate Grinding is most productive when all the elements of the systemhave been selected to work well together Elements to be considered are the grind-ing machine, the grinding wheel, the workpiece, the grinding fluid, the atmosphereand the grinding swarf Another is the wheel dressing tool

System Elements

Systems consist of inputs, disturbances, productive outputs and nonproductive puts (Czichos, 1978) Elements of a grinding system are illustrated inFigure 1.6

out-Element Characteristics

A system specification includes the following details

G Workpiece material: Shape, hardness, stiffness, thermal and chemical properties

G Grinding machine: Type, control system, accuracy, stiffness, temperature stability andvibrations

Grinding machine Workpiece

Grinding wheel Grinding

swarf Fluid

The atmosphere – air

Dressing tool

Figure 1.5 Elements of a basic grinding system

G Kinematics: The geometry and motions governing the engagement between the grindingwheel and the workpiece Speeds and feeds of the workpiece and the wheel.

G Grinding wheel: Abrasive, grain size, bond, structure, hardness, speed, stiffness, thermaland chemical properties

G Dressing conditions: Type of tool, speeds and feeds, cooling, lubrication andmaintenance

G Grinding fluid: Flowrate, velocity, pressure, physical, chemical and thermal properties

G Atmospheric environment: Temperature, humidity and effect on environment

G Health and safety: Risks to the machine operators and the public

G Waste disposal

G Costs

The Tribological System

The elements in the grinding process form a complex tribological system This isnot a nicety; it is a harsh physical reality The workpiece material surface is heatedand brought into violent interaction with the abrasive material, the fluid and theatmosphere The resulting workpiece surface and wheel wear behaviour is stronglyrelated to the material constituents and the chemistry that occurs under these tribo-logical conditions of high temperatures and high speeds The behaviour is tribologi-cal which is a term used to describe the rapid mechanochemical interactions thatoccur under high-speed abrasive and rubbing contacts involving high flash tem-peratures Manufacturing engineers are therefore pushed to the boundaries of theirknowledge to take account of the various work material elements, abrasive ele-ments, grinding fluid elements and elements in the gaseous grinding environment.Specialist knowledge is acquired with increasing experience for different workmaterials and is required to optimize grinding performance Manufacturing

Nonproductive outputs

Swarf Waste fluids Heat Noise Mist Tool wear

Disturbances

Static deflections Vibrations Initial workpiece shape Tool shape errors Temperature fluctuations Machine errors

Grinding process

Productive outputs

Machined parts Production rate Shape and accuracy Surface texture Surface integrity

engineers will draw not only on their own experience but will call on the ence of other specialists in materials science, abrasives application and fluidapplication.

experi-The Grinding Machine

The importance of the grinding machine is clear The machine structure providesstatic and dynamic constraint on displacements between the tool and the workpiece

A well-designed machine limits vibrations and provides high-accuracy movements.The specification, design and manufacture of the grinding machine is therefore key

to grinding performance Chapter 10 on grinding machine developments outlineskey principles

The Grinding Fluid

Grinding fluid serves three main functions:

G Reduce wheel wear

G Cool the workpiece

G Flush away the swarf

As knowledge and awareness of environmental concerns increases, there is amove towards a closer specification of the grinding fluid and the quantities sup-plied This issue is addressed in Chapter 8

The Atmosphere

The atmosphere is important for effective grinding Most metals when they aremachined experience increased chemical reactivity, due to two effects:

G Newly created surfaces are more highly reactive than an already oxidized surface

G High temperatures and rubbing at the interfaces increase speed of reaction

Oxides or other compounds are formed very rapidly on the underside of thechips and on the new surfaces of the workpiece Oxides of low shear strengthreduce friction whereas hard oxides increase wheel wear It is important to empha-size that physical, chemical and thermal aspects all play an important role

The Emphasis

The book is aimed at the industrialist, user, teacher, or researcher concerned withdevelopments in grinding technology This second edition includes additional refer-ences and research material

The book explores modern trends in grinding through consideration of theunderlying principles that make these machine and process developments possible.The emphasis is on why things happen Readers will be able to see how to over-come problems and find their own solutions The book identifies aims and objec-tives whether these are better quality, increased production rate, lower costs, orincreased flexibility of manufacture.

Conventional and New Processes

Conventional and new processes are described New processes include use of abrasives, high-efficiency deep grinding (HEDG) and peel grinding, speed-strokegrinding, ELID grinding, ultrasonic grinding, and nanogrinding Recent develop-ments often involve advanced technologies to control workpiece motions and theassociated kinematics of the tool path This is true not only for the main grindingoperations but also for the extensions of grinding into the areas of lapping, superfin-ishing and polishing New abrasives structures include the new ranges of microcrys-talline abrasives and high-aspect ratio abrasives Superabrasives include cubicboron nitride and diamond in resin, vitrified and metal-bonded forms for either con-ventional grinding or for ELID grinding A substantial chapter (Chapter 10)describes developments in ultraprecision grinding

super-Worked Examples

Numerous worked examples provide scale and magnitude in typical grindingapplications

Book Outline

Basic Material Removal (Chapter 2)

Basic grinding parameters are introduced together with practical grinding results,principles of material removal and practical measures for improvement of perfor-mance Results are presented showing that material removal rate can be optimized

by selection of suitable grinding conditions

Grinding Wheels and Dressing (Chapters 3 and 4)

Types of grinding wheels are introduced and grinding wheel developments Trendstowards new abrasives are described including design of wheels for higher speedsand wheels for high accuracy The latest developments in grinding wheels anddressing are essential for the development of ultraprecision grinding systems It isshown how modern developments in abrasives and machines have enabled enor-mous increases in productivity and also, achievement of submicron tolerances.Chapter 4 introduces the technology of dressing for preparation and use of grindingwheels Results are presented showing how different dressing conditions affect

11 Introduction

grinding performance Techniques are described to cope with modern grindingwheels for both high production rates and for extremely high accuracies going intothe nano range.

Grinding Wheel Behaviour (Chapter 5)

Wheel contact and wear effects introduce factors that strongly affect grindingwheel behaviour These factors include the number and sharpness of the abrasivegrains in contact with the workpiece and the wheel workpiece contact conformity.These factors either make a wheel glaze or make a wheel experience self-sharpening behaviour Another factor is elasticity that can change the contact con-formity and damp out vibrations This chapter is essential reading for understandingthe performance of grinding wheels in production operations and explains differentwear rates in different operations Contact behaviour is analysed in greater depthlater in Chapters 12 and 15

High-Speed Grinding (Chapter 6)

Very high wheel speeds are employed in the pursuit of higher production rate andreduced costs However, the introduction of high wheel speeds and high removalrate grinding has a number of implications for the user The different domains ofcreep grinding, speed-stroke grinding, HEDG and peel grinding are distinguished.This chapter also introduces the challenges to maintain workpiece integrity.Thermal Damage (Chapter 7)

Thermal damage is often the limiting factor for removal rate in high-speed ing Types and causes of thermal damage are explained and how to avoidproblems

grind-Fluid Delivery (Chapter 8)

Grinding fluids and fluid delivery requirements are introduced Effective fluiddelivery is of key importance in avoiding thermal damage and also in the economicachievement of acceptable quality levels Fluid delivery has become a more criticalelement in grinding system design A new treatment of this subject points the way

to economic delivery solutions New material is presented on convection coolingusing water-based and oil-grinding fluids

Grinding Costs (Chapter 9)

A systematic approach is provided for analysis of costs The approach allows theevaluation of potential avenues for reducing costs depending on the particularrequirements of an application Experimental results are given showing potentialbenefits of more expensive abrasives It is also shown that the number of parts perdress can be critical for selection of economic grinding conditions

Grinding Machine Developments (Chapter 10)

Design principles are defined for the achievement of high accuracy and highremoval rates Very few grinding machines follow all these principles but it isshown that application of these design principles can lead to remarkable improve-ments in performance A number of recent developments in grinding machinedesigns are described This chapter also introduces recent ultraprecision develop-ments for submicron and nanogrinding

Grinding Process Control (Chapter 11)

Chapter 11 introduces the control of grinding processes to achieve high accuracyand high removal rates Modern principles of process control are introduced includ-ing automatic process compensation and optimization

Vibrations in Grinding (Chapter 12)

Vibration behaviour is described in Chapter 12 including methods of avoidingvibration problems Impulsive vibrations, forced vibrations and self-excited vibra-tions are analysed and stability charts are presented

Centreless Grinding (Chapter 13)

Centreless grinding has rather special characteristics due to the unique method ofworkpiece location Avoiding vibration problems and achieving roundness for cen-treless grinding is explored Results are presented showing suitable setup conditionsfor achievement of rapid rounding

Mechanics of Grinding Behaviour (Chapters 14 17)

Factors governing grinding behaviour are explored in greater depth Chapter 14deals with the material removal by individual grains and relates grain removal togrinding behaviour Results are presented showing how small differences in wheelstructure can affect surface roughness and wheel life achievable A major differ-ence between grinding and milling lies in the random spread of grinding grits.Ideally, the distribution should be uniformly random Sometimes, grains clumptogether giving rise to nonuniform randomness This changes the way a wheelbehaves Expressions are given for chip size and relationships with surface rough-ness and forces Chapter 15 analyses abrasive contact for rigid and elastic wheels.Elastic wheels behave differently from rigid wheels Chapters 16 and 17 explorethe energy required in grinding and how to minimize energy Chapter 17 describesmaterial behaviour in the process of removal and effects on wheel wear

Energy Partition and Temperatures in Grinding (Chapter 18)

The important subject of temperature rise is presented for improved accuracy ofprediction and monitoring grinding processes Based on many years of research, it

13 Introduction

is possible to reveal how temperatures vary dramatically in different grindingregimes For traditional grinding processes energy mostly goes straight into theworkpiece often causing thermal damage In modern creep-feed grinding and also

in high-efficiency grinding, only a very small proportion of the energy enters theworkpiece and quality can be maintained at extremely high removal rates Newcase studies have been added to demonstrate effects of grinding conditions usingworked examples comparing shallow-cut grinding and deep-cut grinding includingHEDG New derivations have been added to the appendices for further explanation

of heat conduction principles

References

Andrew, C., Howes, T.D., Pearce, T.R.A., 1985 Creep Feed Grinding Holt Rinehart andWinston, London, UK

Brinksmeier, E., Aurich, J., Govekar, E., Heinzel, C., Hoffmeister, H., Klocke, F., et al.,

2006 Advances in modeling and simulation of grinding processes Ann CIRP 55 (2),

667 696

CIRP (International Academy of Production Engineering Research), 2004 Dictionary of

grind-Malkin, S., Guo, C., 2008 Grinding Technology Industrial Press, New York, NY

Marinescu, I.D., Toenshoff, H.K., Inasaki, I., 2000 Handbook of Ceramic Grinding andPolishing Noyes Publications/William Andrew Publishing, Norwich, NY

Marinescu, I.D., Hitchiner, M., Uhlmann, E., Rowe, W.B., Inasaki, I., 2006 Handbook ofMachining with Grinding Wheels CRC Press (Taylor and Francis), Boca Raton, FL.Marinescu, I.D., Rowe, W.B., Dimitrov, B., Ohmori, H., 2013 Tribology of AbrasiveMachining Processes, second ed Elsevier, USA and Europe

Shaw, M.C., 1996 Principles of Abrasive Processing Clarendon Press, Oxford

Tawakoli, T., 1990 High Efficiency Deep Grinding VDI-Verlag GmbH, Du¨sseldorf,Germany; English language edition 1993, Mechanical Engineering Publications,London, UK

Webster, J., Tricard, M., 2004 Innovations in abrasive products for precision grinding Ann.CIRP 53 (2), 597

Woodbury, R.S., 1959 History of the Grinding Machine Technology Press, Cambridge,MA

2 Basic Material Removal

2.1 The Material Removal Process 15

2.2 Depth of Material Removed 17

Set Depth of Cut and Real Depth of Cut 17

Deflection and the Stiffness Factor K 20

Size Error 20

Barrelling 21

2.3 Equivalent Chip Thickness 21

2.4 Removal Rate, Contact Width and Contact Area 22

Removal Rate and Specific Removal Rate 22

Grinding Contact Width 23

Grinding Contact Area 24

2.5 Specific Energy and Grindability 24

2.6 Forces and Power 26

Grinding Power 26

Grinding Force Ratio 27

Typical Forces 28

Wet Grinding 29

Effect of Abrasive Type 30

2.7 Maximizing Removal Rate 30

Process Limits 30

Limit Charts 31

References 33

A grinding wheel cuts through the workpiece material as the workpiece passesunderneath Normal and tangential forces are generated between the grinding wheeland the workpiece as inFigure 2.1 The forces cause abrasive grains of the grindingwheel to penetrate the workpiece

A grain that cuts deeply into the workpiece carves out a chip whereas a grainthat rubs the workpiece very lightly may fail to penetrate the surface A grain thatrubs without penetration causes mild wear of the surface that may be hardly detect-able There is a third situation where the grain penetrates and ploughs the surfacecausing ridges without necessarily removing material as in Figure 2.2 (Hahn,

1966) Rubbing, cutting and ploughing are three stages of metal removal Somegrains rub without ploughing Some grains plough without cutting and some grains

Principles of Modern Grinding Technology.

© 2014 Elsevier Inc All rights reserved.

experience all three stages The transition from rubbing to ploughing and then fromploughing to cutting depends on increasing depth of grain penetration into thesurface.

These three regimes of material removal apply to all materials However, theextent of each stage depends strongly on the physical characteristics of the workmaterial, its deformation characteristics and its reactivity with the abrasive and theenvironment For example, most materials subjected to abrasive action exhibit apredominantly elastic regime followed by a plastic regime However, extremelybrittle materials such as the advanced ceramics exhibit very little plasticity anddemonstrate complex modes of fracture behaviour depending on the number, shapeand size of structural defects Surprisingly, the concept of a transition from rubbing,

to ploughing and to cutting applies for brittle materials even where crack tion is dominant

propaga-Many aspects of grinding behaviour depend on the extent of rubbing, ploughingand cutting involved Abrasive grains that are mainly rubbing, wear differentlyfrom grains involved in heavy chip removal As a consequence, grinding forces,grinding energy, surface texture and wheel life are all affected so that grinding

Rubbing

Chip removal Ridge

behaviour can only be explained in terms of the nature of the grain contact andeffects on grain wear The following is an introduction to these effects.

Figure 2.1 illustrates the down-cut grinding direction of wheel rotation

In down-cut grinding, abrasive grains penetrate to a maximum depth immediatelyafter contacting the workpiece and penetration reduces to zero as the grains movethrough the contact Up-cut grinding is where the wheel rotates in the oppositedirection so that grain penetration steadily increases as the grains pass through thecontact Up-cut and down-cut grinding modes exhibit small differences in grindingenergy, grinding forces, surface finish, tendency to burn and wheel wear(Tawakoli, 1993) Partly, these differences are due to differences in grain impactand the extent of rubbing, ploughing and cutting

In down-cut grinding, chip removal occurs at the beginning of contact by anindividual grain In conventional down-cut grinding, forces tend to be lower, andthere are advantages for surface roughness and reduced wheel wear In up-cutgrinding, an individual grain coming into contact rubs against the workpiece ini-tially and chip removal is achieved later in the passage through the contact

Up-cut grinding tends to be less aggressive towards the abrasive grains Rubbingcontinues for a greater extent than in down-cut grinding The grains have a greatertendency to become blunt in up-cut grinding leading to higher grinding forces andhigher wheel wear In down-cut grinding, there is a greater initial impact betweenthe grain and the workpiece and a greater tendency for grain micro-fracture Thishelps to maintain wheel sharpness and reduces the overall rate of wheel wear.Cooling is more efficient in up-cut grinding since fluid is carried into the contact

on the finished portion of the workpiece

Depth of grain penetration plays an important role in grinding as argued pendently byGuest (1915)andAlden (1914)100 years ago In practice, it is quitedifficult to determine the depth of grain penetration with any degree of accuracy.However, that is less important than being able to predict effects of changingspeed, feed and depth of cut

inde-Figure 2.3 shows wheel speed vs, work speed vw and depth of cut ae for fourbasic grinding operations Work speed is often termed feed rate (vf) and given interms of components tangential to the wheel, normal to the wheel and parallel to thewheel axis These components may then be labelled vft, vfnand vfarespectively Thedepth of cut is sometimes known as the feed increment or sometimes as the infeed

Set Depth of Cut and Real Depth of Cut

The most basic grinding parameter is real depth of cut ae The machine operatorsets or programmes a depth of cut ap As every operator knows, in a single pass ofthe grinding wheel across the workpiece, the real depth of material removed ismuch less than the programmed depth of cut This is illustrated inFigure 2.4

In horizontal surface grinding, the set depth of cut apis the down-feed

17 Basic Material Removal

In plunge cylindrical grinding between centres, the set depth of cut is the infeedper revolution of the workpiece The time required for one revolution of a work-piece of diameter dw is π
dw=vw That gives a depth of cut ap5 π
dw
vf=vw,where vfis the infeed rate and vwis the work speed After a number of revolutions,the real depth of cut approaches the value of the set depth of cut as analysed below.

In plunge centreless grinding, the set depth of cut is the infeed per revolution of the workpiece The depth of cut in centreless grinding is

Traverse cylindrical grinding

Abrasive belt machining

Wheel deflected upwards

Set position of wheel

x deflection

Figure 2.4 Effect of grinding forces on wheel deflection and real depth of cut

such as workpiece hardness, grinding wheel sharpness, machine tool stiffness,grinding wheel stiffness, contact width, work speed and wheel speed These can allaffect grinding forces substantially and hence the resulting deflection x of a system.Wheel wear as reduces the real depth of cut and thermal expansions xexp of theworkpiece and machine elements usually increase real depth of cut as inEq (2.1).

ae5 ap2 x 2 as1 xexp real depth of cut ð2:1Þ

Example 2.1 The programmed depth of cut in horizontal surface grinding isset by the machine operator first detecting contact between the wheel and theworkpiece The machine operator then sets a down-feed of 25µm (or0.00098 in.) At the beginning of the pass, the grinding wheel surface deflectsupwards by 15µm (or 0.00059 in.), the wheel has not had time to wear and theworkpiece has not had time to expand At the end of a pass in horizontal sur-face grinding, the grinding wheel has reduced in radius by 4µm (or0.00016 in.), the grinding wheel surface is deflected upwards by 13µm (or0.00051 in.) and the workpiece has expanded by 1µm (0.00004 in.) What isthe difference in real depth of cut along the workpiece length?

Start ae5 25 2 15 2 0 1 0 5 10 μm (or 0.000394 in.)

End ae5 25 2 13 2 4 1 1 5 9 μm (or 0.000354 in.)

The difference in real depth of cut along the length is 102 9 5 1 μm (or0.00004 in.)

InFigure 2.5, the first example is for a single infeed apfollowed by a number ofpasses without further feed With successive passes, the total material removedapproaches the set value The second example is for additional feed increments apapplied after each pass In this case, deflections build up until the real depth of cutapproaches the magnitude of the feed increment

Depth removed Infeed position

1 2 3 4 5 6 7 8 9 10 11 12 2

4 6 8 10

Deflection and the Stiffness Factor K

Ignoring wheel wear and thermal expansion, set depth of cut equals real depth ofcut plus deflection That is ap5 ae1 x The proportion of the set depth removeddepends on machine stiffness and grinding stiffness The proportion is termed thestiffness factor K where K 5 ae=ap Deflection x depends on overall machine stiff-nessλ since x 5 Fn=λ Normal grinding force Fndepends on how hard it is to grindthe workpiece material and is given by Fn5 KsUaewhere Ks is termed the grindingstiffness It follows that x=ae5 Ks=λ The stiffness factor is therefore given by

K 5 1=ð1 1 Ks=λÞ This means that when Ks=λ 5 1 the stiffness factor K 5 0.5, and

it will be found that real depth of cut is only half the programmed depth of cut Inpractice, it is found that grinding stiffness Ksincreases proportionally with grindingwidth Doubling Ks=λ to a value of 2, reduces the stiffness factor to K 5 0.333

In finish grinding, a value K 5 0.4 represents a reasonably stiff machine andmoderate grinding forces A value K 5 0.1 represents a compliant machine andhigh grinding forces In high-efficiency deep grinding (HEDG) using high wheelspeeds and taking very deep cuts, the value of K is usually much higher

Size Error

Figure 2.5 illustrates a size error between set depth removed and actual depthremoved during spark-out It can be seen that the size error is given by

where n is the number of traverse passes after the last feed increment Increasingthe number of spark-out passes reduces the size error Taking 12 spark-out passeswith K 5 0.25, reduces the error down to 3.2% of ap The size error can be reduced

by increasing machine stiffness, reducing grinding stiffness or increasing the ber of passes

num-Example 2.2 The wheel is given a down-feed of 25µm (or 0.00098 in.) in zontal surface grinding The stiffness factor is K 5 0.3 After 10 spark-outpasses without further down-feed, what is the size error due to systemdeflection?

hori-Set depth of material removed: 25μm (or 0.00098 in.)

Material removed after 1 pass: 253 0.3 5 7.5 μm (or 0.0003 in.)

Size error after 1 pass: 252 7.5 5 17.5 μm (or 0.00069 in.)

Size error: e 5 25 3 (1 2 0.3)105 0.71 μm (or 0.000028 in.)

Example 2.3 In horizontal surface grinding, the wheel is given a down-feed of

25µm (or 0.00098 in.) before each pass The stiffness factor K is 0.3 After alarge number of down-feeding passes, what will be the size error due todeflections?

After a large number of passes, the real depth of cut is equal to the down-feed per pass:

ae5 25 μm (or 0.00098 in.)

Since aeis K
ap: set depth of cut ap5 25/0.3 5 83 μm (or 0.00327 in.)

The size error is therefore 832 25 5 58 μm (or 0.00317 in.)

In plunge cylindrical grinding between centres we can perform the same errorcalculation but n is now the number of complete workpiece revolutions In centre-less grinding, the diameter is adjusted approximately twice per revolution In thiscase, n is the number of half revolutions

Barrelling

In traverse cylindrical grinding, the depth of cut is further affected by workpiecebending In this case, the total deflection is larger when grinding at the mid-pointalong the workpiece length As a consequence, the depth of cut is larger at the ends

of the workpiece than in the middle The workpiece becomes barrel shaped as trated inFigure 2.6

illus-Barrelling can be reduced by taking a large number of passes for spark-out asdescribed earlier Unfortunately, this is time consuming To reduce the time taken,

a work-steady can be employed to support a long workpiece at the mid-point

The depth of material removed ae is very much larger than the thickness of thelayer emerging from the grinding zone at wheel speed The material is speeded upfrom work speed to wheel speed and if the material emerged as a solid extrudedsheet would have a thickness reduced to the equivalent chip thickness heq

heq5 ae:vw

vs

Example 2.4 The real depth of cut after a number of revolutions of the piece in a plunge cylindrical grinding operation is 10µm (or 0.00039 in.) The

work-Deflection Barrelling

Fn

Figure 2.6 Workpiece deflection in traverse grinding leading to barrelling after grinding

21 Basic Material Removal

grinding wheel speed is 60 m/s ( 12,000 ft/min) and the work speed is 0.3 m/s(or 0.98 ft/min) What is the equivalent chip thickness?

Working in consistent units of millimetres: heq5 0.010 3 300/60,000 5 0.00005 mm or0.05μm (or 0.000002 in.)

Equivalent chip thickness is often used as a proxy for actual chip thickness sincechip thickness cannot be easily defined or measured (Snoeys et al., 1974).Equivalent chip thickness has been found to be valuable particularly for correlatingeasily measured grinding parameters with removal rate parameters for a particulargrinding wheel type It can be seen that increasing depth of cut and work speedtends to increase the equivalent chip thickness whereas increasing wheel speedreduces it Increasing equivalent chip thickness implies increasing the stress on theabrasive grains whereas reducing equivalent chip thickness reduces the stress onthe abrasive grains This gives an immediate explanation for the trend to increasewheel speeds

Of course, the material does not emerge as a solid sheet It is cut into many ler chips Thickness of the chips must greatly exceed the equivalent chip thickness

smal-to account for the discrete nature of material emerging Facsmal-tors which affect thechip thickness include the distribution of cutting edges on the wheel surface and theeffect of chip thickness on grinding behaviour is considered further in Chapter 14

Removal Rate and Specific Removal Rate

The rate at which material is removed is the product of work feed rate in the tion of material removal and contact area in the direction of material removal.These quantities are illustrated inFigure 2.7

direc-Removal rate has great relevance for machine forces, deflections and power sumption Increasing grinding contact width leads to increase grinding forces andgrinding power in direct proportion to the contact width

con-Specific removal rate Q0 is removal rate per unit width of grinding contact andallows data to be presented in a more general way This form will be widely quoted

in the following chapters

Figure 2.7(a) and (b)show examples of peripheral grinding Removal rate Q andspecific removal rate Q0are given by:

Figure 2.7(c) shows plunge face grinding In plunge face grinding, the feeddirection is perpendicular to the face of the grinding wheel The removal rate istherefore given by Q 5 bw
lc
vwand specific removal rate is Q05 lc
vw

Specific removal rate has particular relevance for stresses on the abrasive grains,rate of abrasive wear and all aspects of abrasive behaviour including workpiececontact temperatures and thermal damage It is also a measure of the effectiveness

of the abrasive grains in removing material Specific removal rate reduces the ber of variables and allows direct comparison of removal efficiency across a widerange of operations

num-A moderate removal rate of Q 5 50 mm3/s over a 25 mm wide cut is quoted as

Q05 2 mm3/s per mm width or 2 mm2/s equivalent to 0.186 in.2/min in Britishunits In HEDG, a possible removal rate as high as Q 5 1200 mm3/s over a grindingwidth of 2 mm translates to Q05 600 mm2/s (or 55.8 in.2/min) Such high specificremoval rates create high stresses on the grinding wheel grains and require appro-priate grinding wheel design to avoid rapid wear The HEDG operation in thisexample removes material 300 times faster

Grinding Contact Width

Grinding contact width bw shown inFigure 2.7 is the width of the abrasive wheelactively involved in removing material Material removal rate in grinding is usually

quoted in terms of removal rate per unit width of grinding contact because energy,forces, grinding power and deflections due to the grinding force are all directly pro-portional to contact width A machine designed for a large grinding contact widthmust be able to withstand the larger forces involved and have sufficient power.Machine deflections must be small enough to allow the required accuracy to beachieved.

Example 2.5 The width of grinding contact in a horizontal surface grindingmachine as shown inFigure 2.7(a)is 15 mm (or 0.59 in.), the real depth of cut

is 10µm (or 0.000394 in.) and the work speed is 300 mm/s (or 709 in./min).What is the removal rate and what is the specific removal rate? The contactlength is 2 mm (or 0.0787 in.) What is the nominal grinding wheel contactareaAc?

Q 5 15 3 0.010 3 300 5 45 mm3/s (or 0.165 in.3/min)

Q05 0.010 3 300 5 3 mm3

/mm s or 3 mm2/s (or 0.28 in.2/min)

Ac5 15 3 2 5 30 mm2(or 0.0465 in.2)

Grinding Contact Area

Another way to increase removal rate without increasing the stress on the grindingwheel grains is to increase the active surface area of the grinding wheel in grindingcontact The contact area between the wheel and the workpiece is Ac5 bw:lc.Contact area and removal rate are increased by increasing the contact width bw.However, in a surface grinding operation, the contact area is not always so sim-ply defined Large vertical axis surface grinding machines, for example, are used togrind a number of workpieces simultaneously This allows very high removal rates.Figure 2.7(b)illustrates a vertical axis slab grinding operation In such applications,careful consideration is required to identify the active part of the grinding wheelthat removes material An important point is to realize that material removal at thecommencement of grinding before wheel wear takes place is concentrated on theperiphery of the wheel at the corner where the wheel grains first meet the work-piece This means the initial active grinding contact area is Ac5 aeUlc However,the extremely long contact length of the abrasive grains actively removing materialleads to rapid grain wear This causes the depth of cut at the periphery of the wheel

to reduce and brings other grains across the face of the wheel into active materialremoval As the wheel wears, the active contact area tends towards the value

Ac brUlc

Grinding energy provides a valuable measure of the ability of a grinding wheel toremove material Grinding energy depends on grinding wheel sharpness and

grindability of the workpiece material Some work materials are much more cult to grind than others.

diffi-Grindability is a commonly used term to describe the ease of grinding a workmaterial employing a particular combination of abrasive and grinding conditions.Unfortunately, there is no scientific definition of grindability Loosely speaking,work materials that give rise to a low specific grinding energy may be considered

to be more easily ground than materials that give rise to a high specific energy.However, there are also other aspects of importance in assessing grinding condi-tions and grindability such as rate of wheel wear and G ratio discussed further inChapter 5

The grinding energy required to remove a volume of material is given by thegrinding power P divided by the removal rate Q This quantity is generally known

in manufacturing technology as the specific cutting energy ec Since we are ering the grinding process, it will also be known as the specific grinding energy orsimply as specific energy

consid-ec5 P

Example 2.6 The maximum grinding power in steady grinding after ing the no-load power and the power required to accelerate the grinding fluidhas a mean value of 2 kW (or 2.68 hp) The removal rate is 50 mm3/s (or0.183 in.3/min) What is the specific grinding energy?

subtract-ec5 2000/50 5 40 J/mm3

(or 14.7 hp min/in.3)Specific energy is typically between 15 and 700 J/mm3 (equivalent to5.5256 hp min/in.3) The value of specific energy depends particularly on work-piece hardness and wheel sharpness The high value is typical of a difficult-to-grind material and the low value of an easy-to-grind material In HEDG, specificenergy values lower than 10 J/mm3(or 3.7 hp min/in.3) may be found

Internationally, specific energy is always quoted in joules per cubic millimetre(J/mm3) It is a straight-forward conversion from SI units to evaluate horsepowerrequired for removal rate quoted in cubic inches per minute (in.3/min) using thefactor 1 J/mm3is equivalent to 0.3663 hp min/in.3

Specific energy values reduce with increasing removal rate as found by manyresearchers (Figure 2.8) The example shown is for HEDG of crankshafts (Comley

et al., 2004) Using electroplated cubic boron nitride (CBN) grinding wheels,extremely high specific removal rates were achieved up to 2000 mm2/s (or

186 in.2/min) It can be seen that specific energy values decreased down towards

10 J/mm3(or 3.66 hp min/in.3) at these removal rates

Grinding energy can be identified by monitoring wheel spindle power during agrinding cycle as follows

25 Basic Material Removal

2.6 Forces and Power

Grinding Power

An example is shown schematically inFigure 2.9 forplunge cylindrical grinding.Initially with the grinding wheel running, a no-load power PNLis dissipated inthe spindle bearings and by motor windage With the grinding fluid switched onand the grinding wheel close to the workpiece, additional power Pfis dissipated bygrinding fluid drag on the grinding wheel After contact is made between the grind-ing wheel and the workpiece the depth of cut builds up and hence the spindlepower The grinding power P can be identified by subtracting no-load power andfluid drag power from the maximum power It is best to identify P after a steadylevel of maximum power has been achieved

Grinding power can also be identified by measuring grinding forces Grindingforce resolved into three components, tangential force Ft, normal force Fnand axialforce Fa, is illustrated in Figure 2.10 for two grinding situations In shallow cut

0 10 20 30 40 50

0 200 400 600 800 1000

3 )

Specific removal rate Q' (mm2 /s)

Figure 2.8 Specific energy in HEDG of camshaft webs using electroplated CBN wheels.Source: Data based onComley et al (2004)

cylindrical grinding, Figure 2.10(a), the tangential force Ftis the vertical force Fv

and the normal force Fn is the horizontal force Fhmeasured perpendicular to thecontact point Total grinding power is given by:

P 5 FtUðvs6 vftÞ 1 FnUvfn1 FaUvfa Ftvs ð2:7ÞThe plus sign applies for up-cut grinding where the workpiece motion opposesthe grinding wheel motion and the minus sign applies for down-cut grinding wherethe workpiece motion assists the grinding wheel motion In practice, taking account

of the workpiece speed has a small effect since vsis typically 60200 times largerthan vft The normal and axial feed speeds vfn and vfa are much smaller again thanthe wheel speed vs, so that grinding power is given quite closely by P 5 FtUvs.Care must be taken using a dynamometer to ensure that grinding forces are cor-rectly identified For example, in deep cut surface grinding Figure 2.10(b), Ft isinclined at an angleθ so that Ft5 Fhcosθ 2 Fvsinθ In this case ignoring the verti-cal force leads to a large error

Grinding Force Ratio

Grinding force ratio is a parameter that gives indirect information about the ciency of grinding Force ratio is defined as:

When grinding with sharp wheels grinding force ratio is high since normal force islow compared to tangential force Conversely, when grinding with blunt wheelsgrinding force ratio is low The reader will notice that grinding force ratio is similar

to friction coefficient and the same symbol is employed This is because of ities in the mechanics of friction and grinding Whereas an efficient grinding wheelremoves material from the workpiece an efficient slider or bearing is expected tominimize wear of the sliding surfaces