analysis and simulation of the grinding process. part iv: effects of wheel wear

~ Pergamon Int. J. Mach. Tools Manufact. Vol. 38, No. 1-2, pp. 41--49, 1998 © 1997 Elsevier Science Ltd. All fights reserved

Printed in Great Britain 0890-6955/98519.00 + .00

PII : S0890-6955(97)00041-2

A N A L Y S I S A N D S I M U L A T I O N O F T H E G R I N D I N G P R O C E S S .

P A R T IV: E F F E C T S O F W H E E L W E A R

XUN CHEN,t:~ W. BRIAN ROWE,t B. MILLSt and D. R. ALLANSONJ"

(Received 2 February 1997)

Abst rae t - -A method of simulating dressing and grinding was described in Parts I and II of this paper. In Part IV, the effects of wheel wear and wheel characteristics on grinding performance are simulated and compared with experimental results. The results show that grinding performance is strongly affected by dressing conditions immediately after dressing. As grinding continues, the grinding power, and also the surface roughness, tends to converge towards similar values for all dressing conditions when the same grinding conditions are employed. Results from the simulation show that the influence of wheel wear is affected by the wheel fracture characteristics. The convergence of the grinding behaviour shown in the simulation and experiments suggests that stable grinding performance in a wheel redress life cycle may be achieved by selecting dressing conditions, taking account of the grinding behaviour. © 1997 Elsevier Science Ltd

1. INTRODUCTION

The wear of a grinding wheel in grinding has a direct effect on workpiece quality and efficiency. Grinding wheel wear is evidenced by attritious wear and fracture wear. Attri- tious wear produces flats on the grain cutting edges and results in a loss of cutting ability of the wheel. Fracture wear is the removal of part or the whole of abrasive grains as a result of fractures in either the grains or the bond posts. Fracture in a grain creates new sharp cutting edges and may benefit the wheel cutting ability. This is called self-sharpening. Severe fracture wear of a wheel causes the wheel cutting surface to deteriorate so that a dressing operation is required to restore the wheel cutting ability and accuracy.

A commonly used parameter to express resistance to wheel wear is the G ratio, which is defined as the volumetric ratio of material removal to the whe~ wear. A high G ratio indicates a low wheel consumption. A very high G ratio is not necessarily the best condition, since self-,;harpening wear maintains cutting efficiency. For typical precision grinding operations with vitrified aluminium oxide wheels, the wheel consumption cost in grinding is usually small or even insignificant. More of the wheel is consumed by the dressing operation than by the grinding operation. A high G ratio may mean a poor self-sharpening ability. This can cause high grinding forces and poor workpiece quality.

Radial reduction of a wheel is a measure of the progress of the wheel wear during grinding. Wheel wear occurs in three stages, rapid primary wear, steady secondary wear and more rapid tertiary wear. The grinding behaviour in the primary and tertiary stages is unstable due to the high wheel wear rate, The relationship between grinding behaviour and radial reduction of the wheel is not well understood. This is due to the absence of a suitable description of grain shape variation and grain distribution during the wear process.

Computer simulation is a useful technique to test and demonstrate various aspects of wheel wear behaviour in grinding. In this paper, the simulation of grinding wheel wear is developed from the simulation framework of the basic grinding process described previously [1-3]. The physical behaviour of grinding is analysed with respect to the effect of wheel wear. A model is proposed for simulation of the influence of wheel wear on the grinding process. The results from simulation are compared with experimental results.

fSchool of Engineering, Liverpool John Moores University, Liverpool, UK *Author to whom correspondence should be addressed.

41

42 X. Chen et al.

2. EFFECTS OF THE WHEEL WEAR ON THE GRINDING PERFORMANCE

Previous investigations [4] showed that grinding performance is influenced by dressing conditions and by grinding conditions. The effects of dressing conditions dominate the grinding performance in the initial wheel wear stage and decline thereafter. The effects of grinding conditions, however, are evidenced throughout the wheel redress life. This behaviour is indicative of the nature of wheel wear in the grinding process.

The topography of the grinding wheel cutting surface is created initially by the dressing operation. The grain shape and cutting edge distribution can vary greatly depending on the dressing conditions employed. Therefore, the effect of dressing on grinding is very strong in the primary wear stage. In the secondary stage, the topography of the wheel surface tends to progressively change towards a condition which depends on the grinding conditions and the structural characteristics of the wheel. Fig. 1 shows an example of how grinding behaviour changes due to wheel wear and dressing conditions employed. With different dressing conditions the grinding performance varies greatly immediately after

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o a d = 0.005 mm, fd = 0.05 mm/r o ad = 0.015 mm, fd = 0.15 mm/r a - - ad=0.025mm , fd=0.25mrn/r

Grinding conditions: v s = 33 m/s, v w = 0.25 m/s, vf = 10 I.tm/s,

Grinding wheel: A465-K5-V30W, Grinding with 5 seconds spark out.

260 360 Stock removed (mm3/mm)

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0.3

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0 ad = 0.005 mm, fd = 0.05 rnrn/r o----- ad = 0.015 mm, fd = 0. 15 mm~ a----- ad=0.025mm , fd=0.25mm/r

Grinding conditions: v s = 33 m / s , v w = 0 . 2 5 m / s , v f = 10 ~.m/s ,


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Fig. 1. Experimental results of grinding performance in a redress life cycle.

Analysis and simulation of grinding process. Part IV 43

dressing. As grinding continues, the effects of dressing conditions decline. No matter what dressing conditions are used, the grinding power and the surface roughness tend to converge towards similar values when the same grinding conditions are employed, although significant differences may remain throughout the wheel redress life cycle. The differences which remain can be explained by the effect of dressing on the density of grains in the wheel surface.

Differences in grinding power and surface roughness in the primary wheel wear stage can be attributed to the differences of grain shape and the different distribution of cutting edges after dressing. As illustrated in Fig. 2, if a coarse dressing condition is applied, the grain shape is sharp. The density of cutting edges is low due to macro fracture and breakout of grains. Accordingly the grinding power is low and surface roughness is high. As the grinding wheel wears, the grains on the wheel surface become blunt and new grains appear at the surface leading to a higher density of cutting edges. These changes increase grinding power and reduce surface roughness. However, a large amount of wear would be required to increase the ,density of cutting edges towards the same density evident after a fine dressing operation. Before this condition is reached, further grain breakout is experienced. Therefore the density of the cutting edges changes towards an equilibrium level that depends on the grinding conditions and wheel hardness. Conversely, a very fine dressing condition generates a high initial grinding power and low surface roughness. As grinding proceeds, grain fracture reduces grinding power and increases surface roughness.

A fine dressing condition leaves more grains on the wheel surface after dressing and tends to flatten the grain surface. This generates finer chips when grinding with the same grinding conditions. Therefore a higher grinding power is expected due to the grain shape and the size effect [5]. Although a fine dressing condition may create several sharp cutting edges on a grain, the grain will not work as a sharp grain, because the space between these cutting edges is not large enough for efficient removal of the chips generated in grinding. The cracks in a grain due to the dressing operation make the grain susceptible to fracture when it engages with the workpiece. Tsuwa and Yasui [6] noticed that many of the non-directional micro-cracks on the flat streak of the grain were fragile. The fragile layer has a very low mechanical strength and cannot withstand even the 0.5 gram load of the diamond stylus of a profilometer. This implies that sharp edges on a grain may wear down very quickly after initial grinding. Deformed workpiece material squeezes into the space between cutting edges, which may lead to further fracture wear of grains or bonds. The fracture wear makes the wheel sharper and rougher. Therefore, the grinding power decreases and surface roughness increases. The steady increase of power during the stable phase of grinding is consistent with the increase of wear flat area on the tips of the abrasive grains. [7]

It is clear that grinding behaviour is strongly influenced by changes of grain shape and

Fig. 2. Effects of the topography of the wheel cutting surface.

44 x. Chen et aL

the cutting edge density in the course of wheel wear. Therefore a model for the influence of wheel wear needs to include the changes of grain shape and the density of cutting edges on the wheel surface.

3. A MODEL OF WHEEL WEAR

During grinding, the distribution of grains in the wheel changes and the shape of the grains is subject to the wear mechanisms which apply to each individual grain on the wheel surface. If the grinding load on an individual grain is small, the principal wear mechanism is attritious wear. As the load increases, the grain may fracture, sometimes called grain chipping. If the grinding load on a grain is too large for the strength of the retaining bond bridges, the grain will be pulled out. Bond fracture is the principal cause of the change of distribution of cutting edges on the wheel surface. Other wear mechanisms mainly change the grain shape. The model of grinding wheel wear therefore takes into account attritious wear, fracture of the grains and fracture of the bond.

The computer simulation of the generation of the grain cutting surfaces was discussed previously [1-3]. The shape of an abrasive grain is determined by dressing conditions, attritious wear and fracture wear in grinding. Here the emphasis is placed on attritious wear and fracture wear of the grains during the grinding process. Based on the assumption that one grain acts as one cutting edge, the density of cutting edges on the wheel surface is equal to the density of grains on the wheel surface. Multiple cutting edges on a single grain can be taken into account by a difference in grain shape. Under a load, grains of different shape will have a different interference area in contact with the workpiece. There- fore differences in the size of equivalent grains are expected. The methodology of rep- resenting the grain shape was described in a previous paper [2]. A large size of the equivalent grain indicates a blunt cutting edge. This methodology allows the effect of wheel wear to be represented. To determine the change in density of cutting edges, bond fracture is taken into account.

Fig. 3 shows a model of wheel wear used to account for attritious wear, grain chipping and bond fracture. The degree of attritious wear is determined from experiment by the reduction of wheel size in the radial direction. Grain fracture in grinding is represented by adding a sine wave to the attritious wear curve. As the attritious wear accumulates, the fracture of the grains also increases. The amplitude of the grain fracture curve was assumed to increase linearly with attritious wear. In order to retain the attritious wear feature when fracture wear is taken into account, the sine curve has two cycles within the attritious wear flat length. Based on this assumption, there are three points consistent with the attritious line for each attritious wear plateau. The initial phase angle of the sine wave was --tr/2 to ensure the continuity of the contour of the grain surface. Therefore the wear shape of a grain is expressed as

z(x) = hw + kwhwsin ~ - x - (1)

v

Fig. 3. Wheel wear model used in simulation.

hw


where z(x)is the grain surface position due to the grain wear, hw is the attritious wear plane, kw is the coefficient for the grain fracture wear, l is the wear plateau length and x is the distance from the plateau edge in the X direction. The coefficient k~ is chosen by trial and error so as to match the simulation results with the experimental grinding results. The length of each wear plateau is determined by the attritious wear depth and the grain profile after dressing as illustrated in Fig. 3.

Bond fracture !is determined by the strength of the bond retaining the grain and the force on the grain. Once the grinding force on a grain is higher than the maximum retention force of the grain, bond fracture occurs. The maximum retention force is determined [1] by

Fre~i n =gm,etain (2)

With this model it was found that it was possible to simulate and analyse grinding behaviour throughout the wheel redress life cycle.

4. PROCEDURE FOR SIMULATION OF WHEEL WEAR

To simulate the effects of wheel wear on grinding, the model of wheel wear was inte- grated into the models of the grinding process developed previously [1-3]. The grinding process as a whole includes dressing and grinding. The structure of the grinding process simulation including wheel wear is illustrated in Fig. 4.

The starting point for the simulation of the grinding process is the representation of the grain size, density of the grain distribution and wheel hardness within the sub-surface of the wheel. The wheel hardness is represented by a strength parameter which is related to the bond and grain material as well as the wheel structure. The strength parameter is determined from dressing experiments [ 1]. The kinematics and mechanics of grinding are simulated as each grain in the grinding wheel passes through the workpiece. Based on the structure of the simulation illustrated in Fig. 4, the geometrical relationships and physical behaviour of dressing and grinding are addressed. Wheel wear in the grinding process is addressed, taking into account attritious wear, grain fracture and bond fracture. The grinding wheel cutting surface is determined only after wheel wear is taken into account.

Four functions are represented in the simulation.

(i) Simulation of the grain locations and grain size; (ii) Simulation of wheel dressing which modifies the grain shape and distribution den-

sity; (iii) Simulation of grain wear and fracture; (iv) Simulation of workpiece generation and grinding force based on the actions of

individual grains.

In this way, it is possible to demonstrate various physical effects which can be related to real grinding behaviour, thus lending confirmation to the importance of the physical effects.

5. THE RESULTS OF THE SIMULATION

The conditions of the simulation were matched as closely as possible to the experiments. The wheel peripheral speed vs was 33 m/s. The workpiece peripheral speed Vw was 0.25 m/s. The plunge grinding cycle included an infeed stage and a dwell stage. The wheel infeed rate was 10/zm/s. The parameters vs, Vw and vf were checked and found to be controlled to an accuracy of approximately 1%. The stock removed in a grinding cycle was 300/,~m from the diameter. The dwell time was 5 seconds. The average grinding system time constant was estimated after grinding and found to be 0.87 seconds. The strength parameter of the wheel estimated by dressing was 724 N/mm 2 for the aluminium oxide grinding wheel type A465-K5-V30W. The following parameters were determined from the simulation by matching the results with experiment: the friction coefficient was assumed to be 0.4, the cutting efficiency ratio/3 to be 0.75, the constant of elastic deflection C to be 0.15, artd the coefficient for the grain fracture wear kw to be 0.5. The wheel

46 X. Chen et al.

I Input : specifications of the wheel and the workpiece, dressing and grinding conditions.

Distributing the grain centres

X(i= 1, 2, ...)

41,

I [:: Simulation based on a single ' .... grain in order k, j, i.

Generating the cutting /" "~ : i : : I surface of the grain ~ /

Simulating the wear f "~ i of the grain

n g i i Simulating the grindi action of the grain ~ 2 " ~ . ~ - - ~ '

i .///////// I

workpiece surface before grinding Z~

Accumulating the actions of the grains

Output results [

Fig. 4. Flow chart of the dressing and grinding simulation package.

attritious wear was determined from experiment by the reduction of the wheel radius hw at the wear stage under consideration.

Fig. 5 illustrates the differences of grinding performance immediately after dressing. The simulation results and the experimental results demonstrate similar trends which tends to confirm that the physical assumptions are consistent with reality. The variations in grinding behaviour represent the randomness of the grinding process. Case A illustrates typical grinding results using fine dressing conditions. Case B is for medium dressing conditions and ease C is for coarse dressing conditions. It earl be seem that experiments and simulations confirm that high power and low roughness are expected with fine dressing


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ad= 0.005 mm ad= 0.015 mm

fd = 0. 05 mm/r fd -- 0.15 mm/r

C

aa= 0.025 mm

fd = 0. 25 mm/r Dressing conditions:

Grinding conditions: v s = 33 m/s, V w= 0.25 m/s, vf-- 10 pro/s,

Grinding wheel: A465-K5-V30W, Grinding without spark out.

Fig. 5. Influence of dressing conditions on griming results.

conditions. As the dressing feed and dressing depth are increased, the power reduces and the roughness increases.

Fig. 6 shows a set of simulated grinding results including the effects of wheel wear. As grinding proceeds, the wheel wear tends to remove the features resulting from dressing on the wheel surface, although the effects of grain pull-out are not removed. Although the simulated results show large variability, the grinding behaviour in the simulation is similar in nature to that from experiments as shown in Fig. 1. The convergence phenomenon implies that if appropriate dressing conditions are applied, the grinding performance immediately after dressing can be adjusted so as to be similar to that at the end of the wheel redress life. The variation of grinding performance will then be minimised. Under stable grinding conditions, the density of cutting edges in the wheel surface immediately after dressing is approximately equal to the density after substantial wheel wear. The density therefore remains approximately constant. In Fig. 6, the medium dressing conditions, with ad : : 0.015 m m a n d f d = 0.15 mm/r, most closely achieve the required conditions. The result of grinding, such as power and surface roughness is also approximately constant.

It was found that the grain fracture coefficient is important for the grinding behaviour in a wheel redress life cycle. Fig. 7 shows how the grinding trends are affected by different values of grain fracture wear coefficient. When wheel wear is small, the effect of grain fracture is not significant. As the wheel wear accumulates, a small grain fracture coefficient, which means less grain fracture, leads to high grinding power and low surface roughness. Alternatively, a large grain fracture wear coefficient results in a higher surface roughness. Coincidentally, the grinding power tends to decrease due to the fracture sharp- ehing of the wheel. This phenomenon indicates that the selection of dressing conditions for stabilising grinding performance needs to take account of grinding conditions and wheel properties as evidenced by the grinding results. It was judged that the wheel used for the experiments was best characterised by a value kw = 0.5.

48 X. Chen et al.

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SIMULATION RESULTS

o..--- ad=0.005mm, fd=0.05mm/r A o------ ad = 0.015 mm, fa = 0.15 mm/r

= ~ r n m , f d ~ = 0. 25 mm/r

Grinding conditions: v s = 33 m/s, v w = 0.25 m/s, vf = 10 gin/s, Grinding wheel: A465-K5-V30W, Grinding with 5 seconds spark out.

= 0.87 second, kw = 0.5, [3 = 0.75,

i i i i i ' i

1 2 3 4 5 6 Radial wheel wear (lam)

o ad = 0.005 mm, fd = 0.05 nlm/r

o------ ad = 0.015 ram, fd = 0. 15 n'ml/r

a~ a d = 0.025 nun, fd ffi 0.25

Grinding conditions: v s = 33 m/s, v w = 0.25 m/s, vf= I0 ktra/s,


x = 0.87 second, kw = 0.5, [3 = 0.75, | i i ! | |

1 2 3 4 5 6 Radial wheel wear (~m)

Fig. 6. Effects of wheel wear on the grinding performance.

6. CONCLUSION

The results illustrate how grinding behaviour between redress operations is influenced by dressing conditions, grinding conditions and wheel characteristics. The grinding behaviour in a wheel redressing life cycle can be related to the nature of the wheel wear. Models of wheel wear developed in this paper enable the grinding behaviour during the wheel redress life cycle to be simulated. Because the models are developed on the basis of each individual grain action in grinding, the simulation takes into consideration the individual physical aspects involved.

The effect of wheel wear on the change of grinding behaviour in the initial grinding stage is found to be dominated by the changes of the density of cutting edges. The effects of attritious wear become more obvious in the steady stage of grinding. Convergence of grinding behaviour due to wheel wear suggests that a stable optimum grinding performance may be achieved if appropriate dressing conditions are selected. The simulation results also suggest that the characteristics of the wheel, including grain fracture, should be taken into account in the selection of dressing conditions.


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kw= 0.25

o--- kw= 0.5

, ~ m kw=l

Dressing conditions: ad= 0.015 ram, fd= 0. 15 mm/r

Grinding conditions: v s = 33 m/s, v w = 0.25 m/s, vf = 10 tlm/s,

Grinding wheel: A465-KS-V30W, Grinding with 5 seconds spark out.

o i ~ ~ ~ ~ Radial wheel wear (tim)

0 . 5 '

0.3

0.2.

0.1

0.0 0

e-

o kw= 0.25

-- -o---- kw = 0.5

-----D~ kw=l Dressing conditions: a d = 0.015 ram, fd-- 0.15 mm/r

Grinding conditions: v s = 33 m/s, v w = 0.25 m/s, vf = 10 lira/s,

Grinding wheel: A465-KS-V30W, Grinding with 5 seconds spark out.

i ~ ~ ~ ~ Radial wheel wear (tim)

Fig. 7. Effects of grain fracture in the wheel wear process.

REFERENCES

[1] Chen, X. and Rowe, W. B., Analysis and Simulation of the Grinding Process - Part I, Generation of the Grinding Wheel Surface. International Journal of Machine Tools and Manufacture, 1996, 36(8), 871-882.

[2] Chen, X. and Rowe, W. B., Analysis and Simulation of the Grinding Process - Part II, Mechanics of Grinding. International Journal of Machine Tools and Manufacture, 1996, 36(8), 883-896.

[3] Chen, X., Rowe, W. B., Mills, B. and Allanson, D. R., Analysis and Simulation of the Grinding Process - Part III, Comparison with Experiment. International Journal of Machine Tools and Manufacture, 1996, 36(8), 897-906.

[4] Chert, X., Strategy for the Selection of Grinding Wheel Dressing Conditions. PhD Thesis, Liverpool John Moores University, April, 1995.

[5] Rowe, W. B., Chen, X., Characterisation of the Size Effect in Grinding and the Sliced Bread Analogy. International Journal of Production Research, 1997, 35(3), 887-899.

[6] Tsuwa, H. and Yasui, H., Micro-Structure of Dressed Abrasive Cutting Edges. Proceedings of the Inter- national Grinding Conference. Pittsburgh, Pennsylvania, 1972, pp. 142-160.

[7] Maikin, S. and Cook, N. H., The Wear of Grinding Wheels, Part 1 - Attritious Wear. Journal of Engineering for Industry, Trans. ASME, 1971, 93(4), 1120-1128.

analysis and simulation of the grinding process. part iv: effects of wheel wear

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