WEAR OF GRINDING WHEELS – SOFTWARE FOR THEIR SELECTION
A.A.Torrance,
Dept. of Mechanical & Manufacturing Engineering, Trinity College, Dublin 2
ABSTRACT
An existing model of the grinding process has been upgraded to predict grinding wheel
wear as G ratios. It has been successfully benchmarked against experimental results for several
combinations of coolant wheel and workpiece. As a Windows-based application, it offers a rapid
and versatile way of assessing the performance of grinding wheels and processes in a realistic
way. For the best results, it should be benchmarked before use against appropriate experimental
results.
KEYWORDS
Grinding; Software; Wear
1. INTRODUCTION
The key to a successful grinding process is the selection of the right wheel for the job. It
must be able to provide the finish and accuracy required, and it should also wear enough to keep
sharp, but not enough to lose its form and to grind unstably. Selection is normally empirical, and
whilst this often works, it can throw up unexpected results, which may degrade the accuracy and
integrity of the workpiece. A more scientific selection method would clearly be an advantage,
but has been hard to develop because of the complex interactions which determine grinding
performance.
A recent paper [1] is something of a breakthrough in this respect. A model is developed
which is robust enough to predict grinding forces, workpiece temperature, and roughness from
basic grinding data: machine settings, wheel and coolant specifications, dressing technique and
workpiece properties. It is built around an advanced model of abrasive mechanics [2,3], and
makes use of recent analysis of heat transfer effects in grinding [4] to calculate temperatures.
To calculate the effect of dressing on wheel topography. the model makes use of
published data on the mechanical strength of vitreous bonds and abrasive grits, and data on the
statistical variation of this strength. [5-7]. This allows the prediction of fracture pattern of the
wheel as it is dressed, to which its topography, and sharpness, are directly related.
Application of the same methods to the interaction of the wheel with the workpiece as it
grinds should allow the wear rate of the wheel to be calculated. In what follows, a method for
doing this is described. Combined with the force prediction model already developed, grinding
ratios can be calculated for a variety of grinding processes for which measurements have been
published allowing validation of the calculations. The resulting algorithms are incorporated into
a windows based application [8] which allows all the above parameters to be displayed as a
function of metal removal rate.
2. THEORY
A grinding wheel in contact with a workpiece deforms elastically. The stresses associated
with this deformation can conveniently be divided into two parts: those due to the compressive
radial stress (p), and those due to the tangential traction (q). The first are everywhere
compressive (see figure 1a) whilst the second give rise to a substantial tensile stress where the
grinding wheel leaves the arc of cut (figure 1b) [9]. Since a vitreous bonded grinding wheel is a
brittle body, we may expect the fracture processes leading to wear will be controlled by the
tensile stresses in the region of the arc of cut. The stress obviously varies greatly and is
determined at any point by the sum of the stresses due to traction and those due to compression.
In order to create a model of wheel wear, it is first necessary to define a critical stress for bond
fracture. This is usually the main mechanism of wear, since bond fracture leads to the removal of
a complete active grit[10]. Inspection of the stress field in the arc of cut reveals that the tensile
stress is a maximum at the surface of the wheel, and falls rapidly with depth into the wheel.
Since it is only the stress in the surface layer which will cause grit removal, it was decided to use
the mean tensile stress at the back of the arc of cut over a depth of one half a grit diameter as the
critical stress for grit wear. These stresses may be calculated from the grinding forces predicted
[1] and the length of the arc of cut using the equations given by Sackfield and Hills [11]
z/p
a) 1.5
1
b)
vs
2
1
x/q
compression
tension
Figure 1: Stresses on wheel surface a) due to normal force; b) due to tangential force.
The next step is to define the relevant bond strength, and the statistics of bond failure.
Peklenik et al. give details of the statistics of the force required for a special scratch tool to eject
a grit from the surface of a wheel as a function of wheel grade [12]. From this, it is possible to
deduce that the Weibull modulus of the fracture process is around 2. It is harder to deduce the
characteristic stress which would be appropriate to the wear process, since the stress field will be
rather different. An alternative approach is to use the bursting speed of grinding wheels as a
means of calculating their bulk strength. Using the data given by Malkin [13] this gives the
results shown in figure 2. It should be remembered that the strength of brittle solids is related to
the stressed volume through the Weibull equation, which gives the probability (Ps) of a stressed
volume V surviving a stress :
1
(1)
Ps 
 V    m 
exp    
 V0   0  
The curves in figure 2 can be fitted to equation 2, where the grade letters are replaced with
integers: A = 0 J = 9 K = 10 etc. The coefficients M and C vary with grit size as shown in
equations 3. The grit diameter (dg) is given in mm as dg = 15.2/N, where N is the mesh number.
 0  M log G   C
M  14.338 log d g   2.4017
C  22.4 log d g   0.384
(2)
(3)
In a wheel burst, the entire bore of the wheel is stressed, whereas the ejection of grits takes place
due to a stress field of similar size to the grit. For a 120 mesh grit, the stress field for ejection is
about 100 times smaller than for bursting, which, with m = 2.3 makes the characteristic stress for
grit ejection higher than the bursting stress by a factor of around 7.4. The factor gets smaller as
the grits get bigger. A Weibull modulus of 2.3 was a used in the predictions made in this work,
since it gave a good fit to experimental results. The effect of changing it is discussed below.
Each time a grit passes through the arc of cut, it will experience a stress , and will have
a probability of being ejected of 1 - Ps. The active grit density (ng) can be calculated using the
equations given in [1]. The overall wear rate due to grit fracture can then be found as:
Z sf  1000v s .n g 1  Ps .V g
(4)
where Vg is the volume associated with a grit: grit + bond + void.
Bursting stress
35
30
25
MPa
20
36
15
46
10
60
5
80
0
J
K
Wheel grade
60
L
M
N
36
Grit size
O
Figure 2. Bursting stress of vitreous wheels
At low metal removal rates, stresses may be too low to cause much wear by bond
fracture, so it is necessary also to calculate wear due to grit attrition. Brecker [6] and Shaw [7]
give much data on the statistics of fracture for abrasive grits of a wide range of size and
composition, and their data can be used, in much the same way as for bond fracture, to calculate
the rate of grit fracture, and the material removed by this means. The force applied to a grit, and
the resulting stresses, can be calculated from the equations in reference [1]. Then the assumption
is made that if the grit fractures, it will fracture at the edge of its area of contact with the work, in
accordance with the observations of Patterson and Mulhearn [14]. This allows the volume of
material removed in a fracture incident to be calculated, which completes the inputs needed for
wear calculation.
3. RESULTS
The software developed to implement this calculation technique [8] was used to predict
forces and grinding ratios for a large series of cooperative tests done under the auspices of the
CIRP. [15]. These were cylindrical plunge grinding tests on hard bearing steel and a softer, cast
steel, using different wheels and coolants. The results are expressed in terms of "equivalent chip
thickness (heq) rather than metal removal rate. Forces are expressed as force per mm width of
wheel (F't and F'n), and wheel wear as G ratio (metal removal rate/ wheel wear rate). If Z's is the
metal removal rate per unit width of wheel, then is heq given by:
Z'
heq  s
(5)
vs
100
10
10
1
0.01
G
F'n/F't N/mm
100
1
0.1
1
heq microns
100
100
10
10
1
0.01
G
F'n/F't N/mm
Figure 3: Predicted and measured values for F'n ( ),F't (x) and G(*). The workpiece was 4615
steel, the wheel 6A-54-L5-VA2, and the coolant 3% soluble oil in water.
1
0.1
1
heq microns
100
100
10
10
1
0.01
G
F'n/F't N/mm
Figure 4: Predicted and measured values for F'n ( ),F't (x) and G(*). The workpiece was 100Cr6
steel of 62 Rc, the wheel EK-60-L7VX, and the coolant 3% soluble oil in water.
1
0.1
1
heq microns
Figure 5: Predicted and measured values for F'n ( ), F't (x) and G(*). The workpiece was
100Cr6 steel of 62 Rc, the wheel EK-60-L7VX, and the coolant sulphurised EP oil..
Plotting grinding results against heq allows results from tests where different wheel sizes and
speeds are used to be compared more easily. In all the predictions run of the grinding tests, the
wheel speed ( vs) was taken to be 60 m/s, and the work speed to be 1 m/s. Data for the wheels,
dressing conditions, workpieces and coolants used were taken from the paper [15]. Space
prohibits repeating all this data here.
The results of the calculations made using the software [8] are shown in figures 3 to 5.
The lines are the predicted values, whilst the points are the values experimentally determined by
the CIRP. The agreement is quite good, and shows that such detailed predictions are now within
the compass of this technique.
4. DISCUSSION
100
100
10
10
1
0.01
G
F'n/F't N/mm
The results given here refer to the performance of the wheel immediately after it has been
dressed. As it is used, its topography will generally change with time: it may become blunter, or
it may become sharper. If it gets too blunt, it may become unstable. This arises when the contact
stress gets so high in the arc of cut that rapid bond wear ensues, leading to poor accuracy and
finish [16]. The grinding charts calculated by the software [8] can be used to decide in which
regime the wheel is likely to operate. If operation is to the left of the maximum in the G ratio
curve, the wheel will probably get blunter as it grinds. Provided this does not lead to a stress on
the arc of cut high enough to cause instability, the result will be a smoother workpiece, but with
more risk of burn. To the right of the maximum, there should be a tendency for the wheel to
sharpen initially. The workpiece will tend to get rougher, but there will be less risk of burn.
Accuracy may suffer too if the wheel wears too much, and re-dressing will be required.
1
0.1
1
heq microns
Figure 6: Predicted and measured values for F'n ( ),F't (x) and G(*), m = 2.8 The workpiece was
100Cr6 steel of 62 Rc, the wheel EK-60-L7VX, and the coolant 3% soluble oil in water.
Some comment on the choice of certain parameters for the calculations is also called for:
in particular, the Weibull modulus (m) for the bond fracture process. What data is available [6,7]
indicates that this probably lies in the range 2 – 3. The exact value will clearly depend on the
way the grinding wheel is made – how uniform was the grit size, how uniform are the bond
bridges, what was the exact bond composition etc. To show how changing m may alter the
results, figure 4 was re-calculated using m = 2.8. The result is given in figure 6. Raising m raises
the G ratio, and also raises the slope of the right hand part of the curve. The overall accuracy of
the prediction is not greatly affected. G is now slightly over-predicted rather than slightly underpredicted. If better data were available for the way m varies with wheel specification, the quality
of the prediction might be improved.
5. CONCLUSION
The capabilities of a model of the grinding process have been extended to predict wheel
wear, and benchmarked against published results in the literature. Its predictions can provide a
useful guide to wheel selection and the performance of the grinding process. It would be quite
straightforward to extend it to other combinations of wheel and workpiece if suitable
benchmarking data were acquired.
REFERENCES
1. A.A.Torrance and J.A.Badger The relation between the traverse dressing of vitrified
grinding wheels and their performance Intl. J of Machine Tool Manufacture Design and
Research 40 (2000) 1787-1811.
2. J.A. Williams and Y. Xie: The generation of wear surfaces by the interaction of parallel
grooves Wear 155 (1992) 363-379.
3. Y. Xie and J.A. Williams: The prediction of friction and wear when a soft surface slides
against a hard rough surface. Wear 196 (1996) 21-34.
4. W.B. Rowe, S.C.E. Black,B. Mills,M.N. Morgan & H.S. Qi , Grinding temperatures and
energy partitioning. Proc.R.Soc.Lond. A 453 (1997), 1083-1104.
5. J. Peklenik, R. Lane & M. C. Shaw: Comparison of static and dynamic hardness of
grinding wheels. Trans ASME 86 B (1964) pp.294-298.
6. J. N. Brecker: The fracture strength of abrasive grains. Trans ASME, J. Engng. for Ind.
96 (1974) pp.1253-1257.
7. M.C. Shaw. The Principles of Abrasive Processes, Oxford 1996.
8. http://www.mecheng.tcd.ie/~torrance/software.html
9. K.L. Johnson: Contact Mechanics Cambridge 1985.
10. S.Malkin and N.H. Cook: The Wear of Grinding Wheels Pt 1. Fracture Wear. Trans
ASME J. Engnrg for Industry 93 (1971) 1129-33.
11. A. Sackfield and D. Hills: Some useful results in the tangentially loaded Hertz contact
problem Journal of Strain Analysis 18 (1983) 107.
12. J. Peklenik, R. Lane & M. C. Shaw: Comparison of static and dynamic hardness of
grinding wheels. Trans ASME 86 B (1964) pp.294-298.
13. S. Malkin: Grinding technology - Theory and Applications of Machining with Abrasives.
Ellis Horwood, Chichester (1989).
14. G. W. Patterson and T. O. Mulhearn: The fracture of idealised abrasive particles, Wear
13 (1969) 175-182.
15. Peters J., Snoeys R., Decneut A. The significance of chip thickness in grinding. Annals
of the CIRP Vol. 23 No. 2 (1974) pp. 227-237.
16. Erasteel: “La réctification des aciers rapides” Les Guides Techniques. Erasteel, Paris 15
(2001).
APPENDIX
100
100
10
10
1
0.01
G
F'n/F't N/mm
It may also be of interest to see how changing the wheel specification might affect the results,
even if actual experimental results are not available for comparison. In the process described in
figure 4, a finer wheel might be chosen if smaller fillet radii were to be ground, or if a finer
finish were required. Figure 7 shows what might be expected with a WA80J5V wheel. G ratios
are lower, and the maximum of the curve is close to the left hand axis, indicating that feeds
should be reduced by a factor of around 3 to obtain a performance equivalent to the coarser
wheel used in figure 4.
1
0.1
1
heq microns
Figure 7: Predicted values for F'n,F't and G. The workpiece was 100Cr6 steel of 62 Rc, the wheel
WA80J5V, and the coolant 3% soluble oil in water.