Jackson Mark. Machining with Abrasives

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600 800 1000 1200

Abrasive Number

Grinding Ratio

High quartz content

Low quartz content

ASP23

T15M15

M42

Fig. 2.37 Effect of the

abrasive number on the

grinding ratio for a high-

quartz content and a low

quartz-content bonding

system grinding tool steel

materials in the cylindrical

surface grinding mode. Tool

steel material is marked on

the trend lines, and is a

function of the carbide

content in their

microstructure expressed as

an abrasive number

0.5

1.5

2.5

3.5

0.015 0.02 0.025 0.03 0.035 0.04

Feed rate (mm/s)

Power (kW)

Bond A - Low Quartz Bond A - High Quartz

Bond B - Low Quartz

Bond B - High Quartz

Bond C - Low Quartz Bond C - Hi

h Quartz

Fig. 2.38 Grinding power as

function of feed rate for

vitriﬁed aluminum oxide

grinding wheels with

different types of abrasive and

bond. Grinding conditions:

wheel surface

speed ¼33 m s

1

; depth of

cut ¼0.25 mm; dress

conditions ¼diamond blade

traversed at 0.15 mm rev

1

a depth of cut of 0.03 mm

2 Heat Treatment and Performance of Vitriﬁed Grinding Wheels 125

level, surface roughness, and grinding ratio. At low grinding rates, it was possible to

differentiate between the grinding performance of each wheel.

The sol-gel wheel gave the best performance in terms of surface roughness and the

highest grinding ratio whilst the angular white alumina wheel provided the worst

results that resulted in rapid wheel wear. The use of monocrystalline abrasives at

moderate metal removal rates ground approximately 30 workpiece materials before it

started to breakdown . From these initial results, it can be shown that sol-gel abrasive

wheels operate well at high power levels and can grind more efﬁciently at higher

metal removal rates compared to angular white and monocrystalline abrasive grind-

ing wheels. At low metal removal rates, there appears to be no signiﬁcant difference

between the grinding wheels used in the experiments. These experiments also show

that bonding systems that are rich or depleted in quartz particles have a signiﬁcant

effect on the breakdown of the grinding wheel during grinding experiments – a

signiﬁcant factor in the subsequent change in grinding ratio.

2.5 Discussion

A mode l describing the dissolution of quartz has been used to predict the mass

fraction of quartz remaining after a period of heat treatment in vitriﬁed grinding

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.015 0.02 0.025 0.03 0.035 0.04

Feed rate (mm/s)

Surface roughness (um)

Bond A - Low Quartz Bond A - High Quartz

Bond B - Low Quartz Bond B - High Quartz

Bond C - Low Quartz Bond C - Hi

h Quartz

Fig. 2.39 Surface roughness

as function of feed rate for

vitriﬁed aluminum oxide

grinding wheels with

different types of abrasive and

bond. Grinding conditions:

wheel surface

speed ¼33 m s

1

; depth of

cut ¼0.25 mm; dress

conditions ¼diamond blade

traversed at 0.15 mm rev

1

a depth of cut of 0.03 mm

126 M.J. Jackson

wheel bonding systems. The model has been compared with experimentally

determined mass fractions of quartz in an industrial vitriﬁed bonding system.

However, the assumptions made when formulating the model may invalidate its

wider application. In diffusion controlled processes, the total ﬂux per unit time is

proportional to the total surface area available and the concentration gradient at the

interface between quartz particle and viscous melt. The model assumes that a linear

concentration gradient exists across the spherical shell of reaction products that

invalidates the real situation where quartz particles are anything but perfect spheres.

The model does obey the parabolic law for diffusion around a sphere that can

only apply when the sphere has a very low solubility in the solvent. However, this is

not the case for quartz in most silicate systems. Also, the bonding between quartz

particle and viscous glass melt is moving and not stationary. This implies that the

concentration gradient is transient and not constant. Th e experimental data used to

justify the accuracy of the dissolution model do not meet the conditions implicit in

the model. The reactions between the three basic components of the bonding

system, i.e. clay, feldspar, and quartz, cannot solely be described as diffusion-

controlled dissolution of quartz in a liquid phase of constant composition and

0.015 0.02 0.025 0.03 0.035 0.04

Feed rate (mm/s)

Grinding ratio

Bond A - Low Quartz Bond A - High Quartz

Bond B - Low Quartz Bond B - High Quartz

Bond C - Low Quartz Bond C - Hi

h Quartz

Fig. 2.40 Grinding ratio as function of feed rate for vitriﬁed aluminum oxide grinding wheels

with different types of abrasive and bond. Grinding conditions: wheel surface speed ¼33 m s

1

;

depth of cut ¼0.25 mm; dress conditions ¼diamond blade traversed at 0.15 mm rev

1

at a depth

of cut of 0.03 mm

2 Heat Treatment and Performance of Vitriﬁed Grinding Wheels 127

properties. It seems unlikely that the model can predict the mass fraction of quartz

in any silicate system with great accuracy. However, over short soaking periods at

the vitriﬁcation temperature, the results of the model compare well with experi-

mental data.

X-ray diffraction methods can be used to identify planes in vitriﬁed bonding

systems during and after heat treatment, which can be used to determine the correct

bond formulations for grinding wheels used in speciﬁc applications. The experi-

mental results show that bonds with high quartz contents lead to much lower

grinding ratios and surface roughness levels. This implies that x-ray methods can

be used to increase the econom ic productivity of using such tools.

2.6 Conclusions

The behaviour of abrasive cutting tools is dependent on the type of abrasive grain

used, its heat treatment schedule, and its bond content. The vitriﬁcation behaviour is

dependent on certain processing variables and the bonding systems used for preci-

sion grinding wheels . It is evident that rutile needles have a signiﬁcant effect on the

mechanical properties and the behaviour of conventional abrasive cutting tools.

If titanium-doped aluminum oxide is used as the cutting medium then heat treat-

ment cycles should be designed that preve nt the growth of the needles into the

bonding system. The development of strength during heat treatment depends upon

the nature of the compounds formed at the interfacial layer between abrasive grain

and bonding material. Further studies are required to understand the nature of this

bonding with new abrasive grains and glass ceramic bond formulations.

Vitriﬁed cBN grinding wheels tend to fracture at the bond bridge rather than at

the interface between cBN and its glass bonding bridge. This implies that the

relatively thin layer of boric oxide is stronger than the bondi ng bridge material.

However, the choice of bonding composition may signiﬁcantly inﬂuence the

thickness of the interfacial layer that may become detrimental to the performance

of the grinding wheel. This is particularly important if the failure mode during

grinding is interfacial fracture between bond and abrasive grain.

The dissolution model derived by Jackson and Mills has been compared with

experimental data using sintering and fusible vitriﬁed bonding systems that are used

extensively with high performance grinding wheels. The results predicted by the

model compare well with the experimental results pres ented in this paper. How-

ever, over longer periods of isothermal vitriﬁcation, the model becomes less

accurate due to the assumptions made in the dissolution model. The model may

be of use when predicting the mass fraction of quartz using high temperature ﬁring

cycles that are characterised by short soaking periods. The models used are useful

where bond bridge fracture wear is the dominant mode of grinding wheel wear.

128 M.J. Jackson

Acknowledgements The author thanks Professor Givi Bockuchava for permission to use

micrographs of abrasive materials from his extensive works on the wear of grinding wheels and

grinding wheel structure. The author also thanks the late Professor David Tabor, FRS, for advice

and direction on the tribology of abrasive materials and the structure of diamond and cBN, whilst

the author was a research fellow at the Cavendish Laboratory, University of Cambridge.

References

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Report of Osako University, Japan, (1961), 11, 299–309.

20. Y. Tanaka and N. Ikawa, Behaviour of abrasive grains on the diamond wheel, Technical

Report of Osako University, Japan, (1962), 12, 345–354.

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22. H. Tsuwa, Trans. A.S.M.E. J. Eng. Ind., (1964), 86, 371–382.

23. G.K. Lal and M.C. Shaw, Wear of single abrasive grains in ﬁne grinding, Proceedings of the

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2 Heat Treatment and Performance of Vitriﬁed Grinding Wheels 129

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130 M.J. Jackson

Chapter 3

Grinding Wheel Safety and Design

Mark J. Jackson

Abstract Grinding wheels are designed to withstand a variety of loads during the

grinding of complex shapes. This chapter highlights the fundamental equations

that are applied to calculate the highest stresses that may be encountered should the

wheel rotate freely on its spindle. These are used to calculate the most conservative

safety factors that are required in order to protect the grinding machine operator

from wheel burst. The chapter focuses on new grinding wheel designs that are used

in processes such as creep freed and VIPER grinding in addition to plain, parallel

sided grinding wheels. Implications for safe practice during grinding are discussed.

Keywords Grinding wheels  Safety  Mechanical design  Analysis

3.1 Introduction

To achieve a high performance from a grinding wheel it must stay sharp, and must

have the ability to absorb a high volume of metal chips. Therefore, the grinding

wheel must be porous and must be able to withstand high grinding loads that are

placed on the abrasive grains and on the bonding bridges that hold the grains in

position. The nature of the properties of the grinding wheel at the interface between

the bonding bridge and the abrasive grains is very important when one considers

how forces are transmitted into the bonding bridges through the interfacial layer.

Vitriﬁed bonds are typicall y used for high performance grinding processes and in

comparison with other type s of bonds, vitriﬁed bonds permit easy dressing while at

M.J. Jackson (*)

MET, College of Technology, Purdue University, 401 North Grant Street,

West Lafayette, IN 47907, USA

e-mail: jacksomj@purdue.edu

M.J. Jackson and J.P. Davim (eds.), Machining with Abrasives,

DOI 10.1007/978-1-4419-7302-3_3,

Springer ScienceþBusiness Media, LLC 2011

131

the same time possess high levels of resistance to wear [1–3 ]. In recent years, the

development of high speed grinding wheels has been focused on high-speed creep

feed grinding processes, or high efﬁciency deep grinding processes [4–8]. These

studies have led to the development of novel designs of grinding wheels that

overcome the severe limitations that are presented when using plain grinding

wheels. In addition to vitriﬁed segmented wheel designs, single layer electroplated

wheels are also gaining popularity especially when applied to high-speed form

grinding applications. Therefore, special consideration must be spent on the design

of abrasive grinding wheels.

3.2 Rotational Stresses

Stresses that occur in rotating grinding wheels arise from six principal sources,

namely: centripetal forces as a result of rotation at a steady operating speed;

clamping loads at the bore of the wheel; grinding forces at the point of wheel-

workpiece contact; acceleration to normal operating speed, and subsequent retarda-

tion; residual out-of-balance forces in the wheel itself; and thermal stresses from

heat generated when grinding. The grinding wheel must grind without signiﬁcant

heat generation or the effects of vibration during precision grinding. This avoids

thermal and mechanical damage to the workpiece so that wheels must be selected in

order to minimize grinding forces and heat generation. The stresses of real concern

during high speed grinding results from centripetal loading at the maximum

operating speed. The application of Lame

’s equations to the solution of rotational

stresses in grinding wheels has been investigat ed by Munnich [9]. Munnich’s results

conﬁrmed the validity of using the equations of elasticity to solve the magnitude of

rotational stress in grinding wheels, especially for porous vitriﬁed wheels.

Vitriﬁed grinding wheels are brittle bodies and can be treated as perfectly elastic

until the point of fracture is reached. Stresses occurring during rotation are the same

for those in any rotating disc. Assuming that the rotational stresses do not vary over

the thickness of the wheel, the governing equation for radial displacement is,

þ r

 u þ

þ nu



¼

1  n

: ro

(3.1)

For parallel and trapezoidal shaped grinding wheels, the thickness at any radius is,

h ¼ A þ B : r (3.2)

The governing (3.1) simply becomes,

A þ 2Br

Ar þ Br



A þð1  nÞBr

þ Br

:u ¼

1  n

: ro

r (3.3)

132 M.J. Jackson

This equation can be solved using ﬁnite difference approximations to give radial

displacement and derivatives at any radius. The rotational radial and circumferen-

tial stresses are,

1  n

þ n



(3.4)

And,

1  n

þ n



(3.5)

These solutions are applied to plane stress conditions. For grinding wheels whose

peripheral diameters are less than ten times that of their thickness, (3.4) and (3.5)

can be modiﬁed by replacing n with

1n

to account for axial stress. These condi-

tions are known as plane strain conditions. It is usual in the design of grinding

wheels to assume the boundary condition of free radial displacement since this

condition gives the highest level of stress that is circumferential and acts at the bore.

This stress is tensile in nature and is used to ﬁnd the maximum operating speed of

the grinding wheel. Modiﬁcation of the governing equation for the relevant boun-

dary conditions for a parallel-sided disc produces,







u þ

1  n

ðÞ

r ¼ 0 (3.6)

For a parallel-sided disc, h is constant, therefore, dh/dr is equal to zero. Thu s, the

governing equation becomes,



1  n

ðÞ

r ¼ 0 (3.7)

The displacement is calculated by solving the second order differential in

(3.7), thus,

u ¼

: 1  nðÞC

 1 þnðÞ



1  n

ðÞ



(3.8)

Where C

and C

are constants found from applying the boundary conditions. The

resulting radial and circumferential stresses, for plane stress conditions, are,

¼ C



3 þ nðÞ

(3.9)

¼ C



1 þ 3nðÞ

(3.10)

3 Grinding Wheel Safety and Design 133

The solutions to (3.9) and (3.10) for free radial displacement at the bore for plane

stress conditions are,

3 þ nðÞ

þ r



 r



(3.11)

3 þ nðÞ

þ r



1 þ 3n

3 þ n



(3.12)

For plane strain conditions, the resulting radial and circumferential stresses are,

¼ C



3  2nðÞ

8ð1  nÞ

(3.13)

¼ C



1 þ 2nðÞ

8:ð1  nÞ

(3.14)

The solutions to (3.13) and (3.14) for free radial displacement at the bore for plane

strain conditions are,

3  2nðÞ

8:ð1  nÞ

þ r



 r



(3.15)

3  2nðÞ

8:ð1  n Þ

þ r



1 þ 2n

3  2n



(3.16)

If the radial displacement of the grinding wheel is restra ined from movement, the

circumferential stress is reduced while the radial stress increases until, with full

restraint, the radial stress exceeds the circumferential stress.

3.3 Factor of Safety

The calculation of the factor of safety for the grinding wheels discussed in this

paper is dependent upon the type of material that the wheel is composed of. In the

case of reinforced, or composite, wheels, the safety factor is calculated using a

number of different failure criteria. For brittle materials, the modiﬁed Mohr theory

is used as it produces the most conservative estimate of safety factor. This involves

considering the maximum level of stress that exists in an uneven material using a

number of Dowling factors to provide the most conservative factor of safety. For

ductile materials, the distortion-energy theory or von Mises–Hencky theory is used

to observe the most conservative value of safety factor in the material that takes

account of an effective stress as a function of the distortion energy experienced by

the stressed volume of material subjected to centripetal loading when dynamically

134 M.J. Jackson