analysis and simulation of the grinding process. part ii: mechanics of grinding

14
~ Pergamon Int. J. Mach. Tools Manufact. Vol. 36, No. 8, pp. 883-896, 1996 Copyright © 1996 Elsevier Science lad Printed in Great Britain. All rights resctwed 0890-6955/96515.00 + .00 0890-6955(96)00117-4 ANALYSIS AND SIMULATION OF THE GRINDING PROCESS. PART II: MECHANICS OF GRINDING XUN CHEN and W. BRIAN ROWE (Original received i September 1995) Abstract--This paper is the second of three parts which describe the analysis and simulation of the grinding process. Generation of the workpiece surface depends on the interactions between the grains of the wheel and the workpiece. The grinding wheel surface generated by dressing was simulated by the method described in Part I. This part describes a method to investigate the process of grinding by simulating the cutting action of every grain which engages with the workpiece. Grinding forces are analysed by simulating the force on each grain which passes a section of the workpiece. The simulated workpiece surface shows features which are similar in nature to the experimental results. A more extensive comparison of simulated and experimental grinding behaviour is presented in Part III. Copyright © 1996 Elsevier Science Ltd I. INTRODUCTION Grinding performance of a wheel depends on the grain-workpiece interactions. The nature of the interactions depends on the grain distribution and the kinematic conditions of dress- ing and grinding. A quantitative description of these interactions is therefore used to pro- vide a basis for the simulation. With the help of computer simulation, the various phenom- ena in grinding can be visually represented, leading to a better understanding of their consequences. In Part I, a method of simulating the dressing process was discussed. The topography of the wheel surface was generated based on the specification of the wheel and the dressing conditions. In this part, a method of simulating the grinding process is described. The generation of workpiece profiles in grinding is illustrated and investigated in relation to the fundamental parameters associated with the topography of the working surface of the grinding wheel. The nature of the interactions between the wheel and the workpiece is based on the shape and spacing of the effective cutting edges and chip cross- sectional area. The mechanics of grinding is analysed from a consideration of the energy consumption of every grain involved in grinding a section of the workpiece. 2. MECHANICS OF THE GRINDING PROCESS In the grinding process, the kinematic relationship between the grinding wheel and the work- piece motions applies to each cutting grain. Early studies of the grinding process were based on the mechanics of an average individual grain in the wheel surface [2, 3]. Some aspects of the process by which a grain grinds can be illustrated by the geometrical relationship between a grain and the workpiece during the grinding process. The geometry of the undeformed chip is shown in Fig. 1. The undeformed chip shape is characterized by the cutting path length of the grain lk and the maximum undeformed chip thickness hm. The grinding process can be distinguished into three phases, including rubbing, ploughing and cutting. When the grain engages with the workpiece in up-cut grinding, the grain slides without cutting on the workpiece surface due to the elastic deformation of the system. This is the rubbing phase. As the stress between the grain and workpiece is increased beyond the elastic limit, plastic deformation occurs. This is the ploughing phase. The workpiece material piles up to the front and to the sides of the grain to form a groove. A chip is formed when the workpiece material can no longer withstand the tearing stress. The chip formation stage is the cutting phase. From the point of view of the energy required to remove material, cutting tLiverpool John Moores University, Liverpool, U.K. 883

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Page 1: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

~ Pergamon Int. J. Mach. Tools Manufact. Vol. 36, No. 8, pp. 883-896, 1996 Copyright © 1996 Elsevier Science lad

Printed in Great Britain. All rights resctwed 0890-6955/96515.00 + .00

0890-6955(96)00117-4

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 II: M E C H A N I C S O F G R I N D I N G

XUN CHEN and W. BRIAN ROWE

(Original received i September 1995)

Abstract--This paper is the second of three parts which describe the analysis and simulation of the grinding process. Generation of the workpiece surface depends on the interactions between the grains of the wheel and the workpiece. The grinding wheel surface generated by dressing was simulated by the method described in Part I. This part describes a method to investigate the process of grinding by simulating the cutting action of every grain which engages with the workpiece. Grinding forces are analysed by simulating the force on each grain which passes a section of the workpiece. The simulated workpiece surface shows features which are similar in nature to the experimental results. A more extensive comparison of simulated and experimental grinding behaviour is presented in Part III. Copyright © 1996 Elsevier Science Ltd

I. INTRODUCTION

Grinding performance of a wheel depends on the grain-workpiece interactions. The nature of the interactions depends on the grain distribution and the kinematic conditions of dress- ing and grinding. A quantitative description of these interactions is therefore used to pro- vide a basis for the simulation. With the help of computer simulation, the various phenom- ena in grinding can be visually represented, leading to a better understanding of their consequences. In Part I, a method of simulating the dressing process was discussed. The topography of the wheel surface was generated based on the specification of the wheel and the dressing conditions. In this part, a method of simulating the grinding process is described. The generation of workpiece profiles in grinding is illustrated and investigated in relation to the fundamental parameters associated with the topography of the working surface of the grinding wheel. The nature of the interactions between the wheel and the workpiece is based on the shape and spacing of the effective cutting edges and chip cross- sectional area. The mechanics of grinding is analysed from a consideration of the energy consumption of every grain involved in grinding a section of the workpiece.

2. MECHANICS OF THE GRINDING PROCESS

In the grinding process, the kinematic relationship between the grinding wheel and the work- piece motions applies to each cutting grain. Early studies of the grinding process were based on the mechanics of an average individual grain in the wheel surface [2, 3]. Some aspects of the process by which a grain grinds can be illustrated by the geometrical relationship between a grain and the workpiece during the grinding process. The geometry of the undeformed chip is shown in Fig. 1. The undeformed chip shape is characterized by the cutting path length of the grain lk and the maximum undeformed chip thickness hm.

The grinding process can be distinguished into three phases, including rubbing, ploughing and cutting. When the grain engages with the workpiece in up-cut grinding, the grain slides without cutting on the workpiece surface due to the elastic deformation of the system. This is the rubbing phase. As the stress between the grain and workpiece is increased beyond the elastic limit, plastic deformation occurs. This is the ploughing phase. The workpiece material piles up to the front and to the sides of the grain to form a groove. A chip is formed when the workpiece material can no longer withstand the tearing stress. The chip formation stage is the cutting phase. From the point of view of the energy required to remove material, cutting

tLiverpool John Moores University, Liverpool, U.K.

883

Page 2: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

884 Xun Chen and W. Brian Rowe

..Z~..:.5.~; 5:

N .'....~',??&'&

• : -•~ .....:

vh~l vl ¢ ;~" 7 , •

';~?., C~" f i : . ~ ?'-";?¢' •

"' '".' :4':':"

Fig. 1. Three stages of chip generation.

is the most efficient phase• Rubbing and ploughing are inefficient, since the energy is wasted in deformation and friction with negligible contribution to material removal. Furthermore a high temperature may result, producing an excessive rate of wheel wear and the workpiece surface may suffer metallurgical damage•

An abrasive grain is a cutting tool of irregular shape. However, Shaw modelled a grain on the wheel surface as a sphere [4]. This is not altogether unreasonable, considering the large negative rake angles presented by the grains• The normal force applied to a grain was assumed to be similar to the force in the Brinell hardness test or the Meyer hardness test. The defor- mation process is constrained by an elastic-plastic boundary. As the sphere moves horizontally, the plastically deformed zone beneath the surface becomes inclined• The workpiece material is squeezed upwards, forming a chip which is subsequently sheared from the surface. The model is illustrated in Fig. 2, where the horizontal movement of a sphere at a cutting depth t is equivalent to a sphere indented into the surface to the same depth t.

In the absence of friction at the surface between the sphere and the workpiece, the magnitude of the force required to indent the workpiece is constant and independent of the direction in which it is loaded. This implies that the projected area of the indentation is a constant irrespec- tive of the direction of the force• Therefore the radius, b, of the projected area is given by

where R is the indentation force, C' is a constraint factor, which is defined as the ratio of the

chip

Fig. 2. Action of a spherical grain in grinding.

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Analysis and simulation of the grinding process. Part II 885

average pressure p on the contact area to the uniaxial flow stress oh. In most cases, C' is about 3 [4]. The specific energy may be expressed as

ec =f/A; (2)

where ft is the tangential grinding force and A is the cross-sectional area of an unreformed chip. If A, illustrated in Fig. 2, is approximated to

4 A = ~ bt (3)

then the specific energy related to the cutting action is given by [4]

3Rsin0 ec¢- 4bt (4)

where 0 defines the line of action of the indentation force. The specific energy due to cutting may therefore be expressed as

e= = -~- t H sine (5)

The friction force is gRcose, where g is the mean coefficient of friction at the contact surface. The specific energy due to friction is

ef = ~- I.t t H cos0 (6)

Therefore the total specific energy for a single grain is

eg = -~- t H (sin0 + gcos0) (7)

Generally only a portion of the workpiece material engaged with a grain is removed in grinding. Shaw defined an upward flow ratio 13 to take account of the ploughing action, where

Volume rising above original surface (8) [~ = Total volume displaced

Considering ploughing action and where the average diameter of the grains ag is much larger than the average grain cutting depth/, equation (7) can be simplified to

e s = ~ - 1 + ~ -~- (9)

3. SIMULATION OF GRINDING

A grinding process can be expressed as a process where the workpiece material is removed by grains on the wheel surface as a consequence of the grinding kinematics. Therefore the analysis of the total grinding process needs to take account of both dressing and grinding. In Part I of the paper, the topography of the grinding wheel was generated as the output of a

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886 Xun Chen and W. Brian Rowe

dressing process, which was affected by the characteristics of the wheel, the shape of the dressing tool and the motion of the dressing tool.

The relationships between the inputs and the outputs of the total process, which includes dressing and grinding, are illustrated in Fig. 3. The basic inputs to the total grinding process include the characteristics of the wheel and the workpiece, the shape of the dressing tool and the kinematics of dressing and grinding. Figure 3 shows that first the topography of the grinding wheel is generated, then the chip geometry, followed by calculation of the single grain loads. Finally the outputs of the grinding are predicted. The parameters which are predicted include grinding forces and surface texture.

The cross-sectional area of the undeformed grinding chips is determined by simulating the kinematics of the grains of the wheel and their action on the workpiece. The grinding load on each individual grain is determined based on the characteristics of the workpiece material. From Fig. 3, the load on each single grain in the wheel is found to be the key point of a grinding process. Therefore the simulation is based on the behaviour of each individual grain in dressing and grinding. The final grinding behaviour is obtained by aggregation of the behav- iour of all the grains involved in grinding. The dressing and grinding process is simulated and used to predict the surface roughness and the grinding force. There is the potential to extend the simulation to predict further parameters such as wheel wear behaviour with stock removal.

3.1. Simulation of the workpiece surface During grinding, the grains on the surface of the wheel pass through the workpiece and cut

a portion of the workpiece material, as shown in Fig. 4. When the workpiece passes through the grinding contact zone of length lo the distance travelled by the surface of the wheel is l~.

l~ = v~ l~ (10) Vw

This means that all the active grains over a length l~ (ACDD'C'A') engage with the cross section of the workpiece ABB'A'. When a cutting edge passes through a cross section of the grinding zone the material of the workpiece higher than the cutting edge is removed. Assuming the grit Gij.k passes through the grinding zone at abb'a', the shaded area will be removed. After

grindingwh~l [~IH dressingtool H kincmaficsdressing ~ Kmematms" ~ndin.g ~ work'pi~

grinding wheel topography

chip geome~

t single grain load

Fig. 3. Process relationships in grinding.

Page 5: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

Analysis and simulation of the grinding process. Part II 887

D t

b' (B') b (B)

Fig. 4. Kinematic relation between grinding wheel and workpiece.

the grinding wheel passes through the cross section ABB'A' , the remaining surface contour is the ground surface of the workpiece. The simulation is carried out for each grain in turn.

Local elastic deflection of a grain reduces the real cutting depth. The local deflections of the wheel when a grain is in contact with steel are of the same order of magnitude as the undeformed chip thickness [5]. Saini et aL [5] assumed that the elastic deflection consists of four components. The four components are local workpiece deformation 8w, grain tip defor- mation 8 v variation of deflection of the grain centre 8c and rotation 8,, as shown in Fig. 5. From their results, it was concluded that grain tip deformation 8g and rotation 8~t are relatively small. The local workpiece deformation 8,~ was said to be just a little more than 2 ~tm and might be considered as a part of the total workpiece deflection. The deflection of the grain centre 8c was found to be up to 3 I.tm. The variation of the deflection of the grain centre 8c has a trend and scale similar to the total deflection [5]. Therefore the deflection of the grain centre is considered as the local deflection in the simulation of both the dressing and the grinding process. Nakayama et al. [6] described the deflection of the grain centre as following the form of a Hertz distribution,

5, = c ~ ~ (11)

t i

fso Fig. 5. Grit deflection in grinding.

Page 6: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

888 Xun Chen and W. Brian Rowe

where ~5c is expressed in ~tm and C is a constant in the range 0.08 to 0.25 and average value 0.15. F, is the normal force acting on the grain.

In grinding, only a portion of the undeformed chip material is removed by a grain. The remaining material is removed by successive grains. The remaining plastically deformed material piles up at the sides of the grain as shown in Fig. 6. It was therefore assumed that the area of the material removed is proportional to the undeformed cutting area of the grain. The ratio of the volume of the material removed to the volume of the undeformed chip is defined as the cutting efficiency ratio 13. The remaining material piled up alongside the grain will be a proportion (1 - 13) of the volume of the undeformed chip. Therefore the area of the remaining material on each side of the grain trace is

(1 - ~ Ap - 2 (12)

The shape of the displaced material was approximated by a parabola expressed as follows.

a 2

x ~ = ~ ( h - z ) (13)

The area of the pile-up material is

4 Ap = ~ah (14)

3.2. Simulation of the grinding forces

The grinding force F can be separated into a tangential component Ft and a normal compo- nent/7, or into a horizontal component Fh and a vertical component Fv, as illustrated in Fig. 7. When the diameter of the grinding wheel is much larger than the depth of cut, the angle cx is very small. Under these conditions the horizontal component can be assumed to be identical to the tangential component and the vertical component identical to the normal component.

The total grinding force was obtained by summing the grinding force for each individual grain in the grinding zone. Due to the random distribution of the grains in a grinding wheel, it is difficult to know the real number or the orientation of the grits in the grinding zone. An alternative method to obtain an expression for the total grinding force is by consideration of the energy consumption of the grinding process. When the area ABCD is removed, as illustrated in Fig. 7, the grinding energy consumption is

E=F,.I~ (15)

The energy consumption to remove area AC.Ax is

Fig. 6. Plastic pile-up due to ploughing.

Page 7: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

Analysis and simulation of the grinding process. Part II

• . .. """ • ;', ' : .

. . . , . . . . . .:,!..::~:;~.~

1 C workpiece BI_ lc _

~.?..?.~ ?..,,?#:.

..%?/..

....//.

V W D

A x

Fig. 7. Relationship between grinding force components.

n n

a e = E f,, sat = E f,., ax ' V w i i

889

(16)

where ft.~ is the tangential grinding force on a grain i as it passes the section AC and At is the time for a grain to travel a distance Ax. To remove the area ABCD the energy consumption is

E = E A E = E f~., v_~ Ax = E ft.i v~.~ lc P w i V w

(17)

Combining equation (10), equation (15) and equation (17), the tangential grinding force is

F ! = ~ f t , i ( 1 8 )

i

The grinding force can therefore be simulated by considering the action of each individual grain as it passes a section such as AC. This is a very useful conclusion which enables the grinding force to be simulated by considering each individual grain as it passes a single section.

The specific energy using a single sphere grain approach is given by equation (9). The cutting depth was assumed to be much smaller than the diameter of the grain, an assumption which is suitable for the case where the grain is not dressed. After dressing, the cutting edges on a grain were still assumed to be equivalent to a spherical cutting edge based on the assump- tion that one grain only acts as one cutting edge [7]. As in Fig. 8, the interface area was assumed to be equivalent to the shaded oval area, which was expressed as

Ao = ~ acbc (19)

where a¢ is the maximum contact length of the grain in cutting direction and bc is the cutting width of the grain. The equivalent spherical grain was assumed to have the same interface area with the workpiece as the shaded oval area. So the diameter of the equivalent grain contact circle is

,/o = ~ (20)

When the maximum cutting depth of a grain tm~, is available, the diameter of the equivalent grain dg,~ can be determined from the geometry illustrated in Fig. 8.

Page 8: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

890 Xun Chen and W. Brian Rowe

grin

/ tmax

(cutting width)

d~

,"1~7 v,,! t ' 7;;L ~':"', ~ t I / /

' ~ , ~

Fig. 8. The equivalent grain.

equivalent contact circle

dg~q - (21 ) /max

The size of the dressed grain is smaller than the original one, but the equivalent diameter of the cutting edge may be larger or smaller than the original diameter of the grain. The equivalent grain diameter depends on the shape of the grain and the depth of cut of the grain, as illustrated in Fig. 9.

f

/ \ / equivalent cutting edge for at \

/ \

/ Y ~ ,, I ~ ~ " equi~Talent cutting edge for a2

', V . - ' - - ' - ( \ / '1 / ' , / , , ~I ^! - I^ I

' , ""-'.._ Y.d'""/"1 1 \ #

N / N, t "

Fig. 9. Equivalent spherical cutting edge varying with depth of cut.

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Analysis and simulation of the grinding process. Part II 891

After the diameter of the equivalent grain has been determined, the grinding force on a grain can be determined. If the action of a grain in grinding is idealized, as in Fig. 2, the indentation force of the grain R can be expressed by equation (1). The cutting force on a grain is assumed to be the indentation force R acting in the direction O as shown in Fig, 10. The tangential cutting force on a grain is

ftc.i = - - - H A sin0 (22) 4 t

and the normal cutting force on a grain is

3rtbH(-~)AcosO (23) f.c.i- 4 t

If the friction coefficient is g, the tangential and normal friction forces will be

3X b H (~)laA cos0 (24)

3~ b H (~ ) lxA sin0 (25) f .f,i = --~

Combining the cutting and friction actions, the forces for each grain are

f " = 4 - t H ~ (sin0 + ~tcos0)A (26)

C' 3rtb (~-)(cos0 - lasin0)A f . . i = ~ t H (27)

4. SIMULATION PROCEDURE

Three functions were represented in the total grinding simulation program. The first was the simulation of the dressing process, which provides the location of the grains and the shape of the cutting edges. The second was the simulation of the grinding process by the grains accord- ing to the kinematics and the deformations in the process. The third function in the simulation

Fig. 10. Grinding force on a spherical grain.

Page 10: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

892 Xun Chen and W. Brian Rowe

was to represent the action of each individual grain as it contributed to the total grinding forces. The basic steps of the simulation are shown in Fig. 11.

After the input parameters have been specified as closely as possible to measured experimen- tal conditions, the shapes and distribution of the grains in the wheel are determined as described in Part I. The co-ordinate axis system for the grains in the grinding operation is set up as in Fig. 4. The chip to be cut by a grain was determined from the kinematic relationships of grinding as shown in Fig. 4. When a grain Gij.~ passes across the section AA'B'B, the grain centre rises by a distance Ai.j. k in the workpiece co-ordinate system.

_ to 2 (28)

Therefore the z' value for the centre of the grain in the workpiece co-ordinate system is

Z' = Z..G~jj, + A i j , , + Az. z

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

Simulation of dressing and grinding process based on a single grain in order k. j, i.

Ir ,

w~cpi~ sm'hc~ be~o~ ~

Accumulating the Z I ~ actions of the grains no@

Fig. 11. Float chart of the dressing and grinding simulation package.

(29)

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Analysis and simulation of the grinding process. Part II 893

where z%k is the position of grain centre in the wheel co-ordinate system and Az,z is the distance between the two system origins. Figure 12 shows the grinding action of the grain under the combination of the workpiece co-ordinate system and the wheel co-ordinate system. Cutting, elastic deflection and plastic pile-up are considered. As illustrated in Fig. 13, the initial work- piece surface was set into an array z ' ( i ' ) , i" = 0, 1, 2, 3 ..... where i' represents the positions of the workpiece to be simulated. The value of each element in the array represents the z" value of the workpiece point i'. The number of elements in the array depends on the precision required of the simulation. A larger number of elements gives more precision. The interval between elements used in the simulation was 1 ~t.

The cutting process was simulated by comparing the cutting surface of the grain with the relevant surface points of the workpiece. If a grain Gu. k passes through the grinding zone, the surface points of the workpiece in the area [x%k - ds/2, x%k+ds/2] are involved in the cutting simulation. The material higher than the cutting face of the grain is removed. Values of elastic recovery and plastic pile-up were assigned to the relevant workpiece points after each grain passed through the workpiece. Once the grinding force on a grain was calculated, the deflection of the grain centre was determined from equation (11). The material piled up along the sides of the grain path is given by the cutting efficiency ratio ~. Since the cutting efficiency ratio varies with the cutting depth and grain shape [4], a practical value of [~ was not available. 13 was therefore assumed to be 0.75 in the simulation. Consequently 25% of the undeformed chip remains on the workpiece surface. The determination of the contour of the piled up material is detailed in Fig. 14. The material was assumed to pile up in the direction of ¢t at both sides of the grain path, where the angle ¢t is determined by the equivalent diameter and the maximum depth of cut of the grain. After the area of piled up material was determined from equation (12), the parameters for determination of the contour of the piled up material were given from equation (13) and equation (14) as

•/ 3Av--

a = 2 tan ct

z . z " /

-g

Fig. 12. Simulation of the grinding action of a grin.

Z' z'(i')

i'-I i' i'+l

Plastic pile-up

,~io~ of the undeformed chip

X

x"

x"

(30)

Fig. 13. Workpiece surface array in simulation.

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894 Xun Chen and W. Brian Rowe

It . Initial workpiece surface ~ 2b

Fig. 14. Simulation of the plastic pile-up of the workpiece material.

and

h=%/3Ap? °t (31)

Therefore, the z values of the piled-up material may be expressed as z' corresponding to the position x'.

2 tan ot ,2~ ~ tan ot Z'= 1 - 3Ap x ~ (32)

tmax Since tantz = ~ - then

Z' = 1 3 - - ~ X '2 - x /

(33)

The final workpiece topography is the surface shape of the material remaining on the work- piece after the passage of all the engaged grains through the grinding zone. The generation of the workpiece surface is sketched in Fig. 15, where the numbers represent the sequence of the grains passing through the section under consideration. A simulated ground surface is illustrated in Fig. 16 and is compared with an experimental result. It can be seen that the simulated surface contains features which hear a resemblance to the experimental surface.

The total grinding force was determined by summing up the loads for all grains involved in grinding, as expressed in equation (18). The forces on each grain were calculated from equation (26) and equation (27). There were five parameters to be determined, the grain shape ratio b/t, the material hardness, the factor C', the friction coefficient Ix and the direction of the chip flow 0. The grain shape ratio was determined from the kinematic relationship between

Z' workpiece surface before grinding _

g I

x'

Fig. 15. Generation of the workpiece during grinding.

Page 13: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

Analysis and simulation of the grinding process. Part II 895

3"

2 -

N I

0

3'

2

N I

Grinding wheel: A465-K5-V30W. Dressing conditions: ad~0.014 mm,fth= O . 1 8 ~ v , bd= 0.330 ram. Grinding conditions: v s 33 m/s, v w 0.25 m/s, vf 10 Ixm/s.

x (ttm) I I I I

0 200 400 600 800 1000

X ¢tm) I I I I

0 200 400 600 800 1000

Fig. 16. Comparison of ground surface from experiment and simulation.

the grain and the workpiece in the simulation. The material hardness was determined from a Rockwell hardness test and was HRC 61. In most cases the cutting depth was much smaller than the diameter of the grain. Following Shaw's assumption [4], the factor C' was assumed to be 3. The friction coefficient was assumed to be 0.4 for a reasonable value of F , IFt. T h e chip flow direction determined by Shaw's spherical grain model is shown in Fig. 10. Using the diameter and the cutting depth of a grain, the direction of the chip flow 0 was calculated from

f 2b ~t(d~ - t)

0 = arcsin ~ = arcsin 2 dg (34)

The effects of dressing conditions on specific grinding force based on the simulation are illustrated in Fig. 17. The effects of dressing depth on grinding force are found to be stronger

v, = 33 m/s, Vw = 0.25 m/s, vf ffi 10 tm)/s

ds = o.293 ram, v t - o..~. ~ = 7 u N / , m ;

H =HRC 61, [3 =0.75, C =0.15 " ~ ' ~ ~ -- 3 7 0 _ ~ , ram, dw = 17 mm

o---- fd = 0.05 mm/r ----o--- fd = 0.15 mm/r - - , ' , - - fd - 0.25 mm/r

0 ad (~tm)

0 113 2]3 3b

Fig. 17. Simulated effects of dressing conditions on grinding force.

Page 14: Analysis and simulation of the grinding process. Part II: Mechanics of grinding

896 Xun Chen and W. Brian Rowe

1.5, R, (l.tm)

, 0

/ .,oo~,6 ~" ~ ad = 5 ttm / _.--"2" . . . . -15 m

/ . . . . * / ' - - - . , , - - . , :zsi / /;.,'< oO ~,, 0.5 / ./,,~"" v , = 33 m/s, vw = 0 .25 m/s, vf = 10 lml/s

J~,f,~,~f d s =0.293 ram, V s = 0.54, oi, = 724 Nhnm 2 St.,i,,- _.- ____-_. _'__ ooo ° H = HRC 61, 13 =0.75, C =0.15

d, = 370 mm, d,, = 17 mm 0.0 ~1 (ram/r)

' ' 0'. 0.0 0.1 0.2 3

Fig. 18. Simulated effects of dressing conditions on surface roughness.

than the effects of dressing lead. This is a consequence of macro fractures and grain pull-out, as described in Part I. The effects of dressing conditions on surface roughness are shown in Fig. 18. The surface roughness increases with increase of dressing lead. This is a consequence of the reduced overlap ratio as described in Part I. The dressing depth has a relatively weak influence on surface roughness and the nature of the influence is less clear.

5. CONCLUSION

The simulation results are consistent with previous experimental observations [1, 8]. Although, clearly, this is not a proof that the underlying assumptions are correct, it is clear evidence that the assumptions are consistent with the facts in so far as the investigation went. This is evidence that a reasonable working model has been obtained for the effects of dressing on the grinding process. Further experimental results will be compared with simulation results in Part III. It is tentatively concluded that the understanding of causation achieved so far provides a reasonable basis for the investigation of the dressing and grinding process.

REFERENCES

[1] X. Chen, Strategy for the selection of grinding wheel dressing conditions, Ph.D. Thesis, Liverpool John Moores University (1995).

[2] J. J. Guest, Grinding MachineD'. Edward Arnold, London (1915). [3] G. I. Alden, Operation of grinding wheels in machine grinding, ASME Trans. 36, 451-460 (1914). [4] M. C. Shaw, A new theory of grinding, Int. Conf. Proc. Science in India, Monash University, Australia, pp.

i-16 (1971). [5] D. P. Saini, J. G. Wager and R. H. Brown, Practical significance of contact deflections in grinding, Ann.

CIRP 31, 1, 215--219 (1982). [6] K. Nakayama, J. Brecker and M. C. Shaw, Grinding wheel elasticity, Trans. ASME J. Engng Ind. 93(5),

609--4514 (1971). [7] J. Verkerk, Final report concerning CIRP cooperative work on the characterization of grinding wheel topogra-

phy, Ann. CIRP 26(2), 385-395 (1977). [8] W. B. Rowe, X. Chen and B. Mills, Towards an adaptive strategy for dressing in grinding operations, Proc.

31st Int. MATADOR Conf. Vol. 31, pp. 415-420. Macmillan, New York (1995).