an investigation of the effect of machine loop stiffness on grinding of ceramics
TRANSCRIPT
An Investigation of the Effect of Machine Loop Stiffness on Grinding of Ceramics
Bi Zhang (2) University of Connecticut, Storrs, CT 06269, USA
Abstract This experimental study deals with the effect of machine structural loop stiffness on grinding of ceramics. The objective of the study is to investigate how the loop stiffness affects grinding forces, wheel actual depth of cut (ADOC) and workpiece strength. A compliant workholder is specifically designed and attached to a precision grinder to simulate grinding machines of various compliances so that the effect of machine loop stiffness can be isolated under otherwise identical conditions. Silicon nitride is used as workpiece material and ground with diamond wheels of two bond types and three grit sizes at machine loop stiffness of four different levels. The ground workpieces are assessed in terms of residual workpiece strength, grinding damage, grinding forces, and ADOC. Theoretical analyses are given to indicate that machine loop stiffness can affect on normal grinding forces and workpiece strength. A discussion is provided to reveal how residual workpiece strength is affected by residual stress and grinding-induced damage.
Keywords: machine loop stiffness, surface grinding, residual workpiece strength
1 INTRODUCTION
Ceramics are difficult to machine because of their extreme hardness and high brittleness. Grinding has been one of the primary methods used in machining ceramics. However, grinding of ceramics has encountered several problems, such as reduced material removal rate due to machine deflection, and strength degradation by grinding damage [I ] . Machine deflection can be one of the factors contributing to grinding damage, strength degradation, and dimensional inaccuracies of ground parts [2-31. In order to reduce grinding damage, high stiffness machines have been recommended for commercial grinding of ceramics in ductile mode to obtain 'damage-free' workpieces [4].
Although a significant amount of work has been conducted in grinding research of ceramics, very little is found on how machine stiffness affects ground parts. The objective of this study is to investigate the effect of machine loop stiffness on grinding of ceramics with specific concerns on workpiece strength, grinding forces, and ADOC. Theoretical analyses and experimental investigations are provided to show how machine loop stiffness affects grinding results. A recommendation is given for satisfactory grinding of ceramic materials.
2 THEORETICAL ANALYSES
The existing literature provides an experimentally verified relationship between normal grinding force F, and wheel ADOC a, that can be written as (e.g. [5])
where C, is a constant determined by grinding conditions. FO is the break-in force under which ADOC is zero. Eq. (1) shows that the normal grinding force has a threshold value FO that must be reached before material removal takes place. As soon as material removal starts, the normal grinding force is linearly proportional to the actual depth of cut of the grinding wheel. Wheel ADOC can be presented for the ith pass as [6]
F, = F, +C,a, (1 1
aui = a o { 1- [k:Jkw)] ~
where a0 is wheel set depth of cut (SDOC), k, is machine loop stiffness and k, is cutting stiffness. Substituting Eq. (2) into ( I ) , the normal grinding force F, in the ith pass is given as
F, =Fo +Cuao 1- ~ [ [ ks?kw ) ] (3)
For given grinding conditions, F,, C,, a, and k, are non- negative constants. The following relationship is obtained:
(4)
Eq. (4) shows that normal grinding force F,, monotonically increases with the increase of machine stiffness. However, as there exists k.J(kS+kJ<l, k.J(ks+k.J approaches zero for a highly stiff machine. In this case, normal grinding force F,, becomes a constant, Fz=Fo+C,ao. In addition, if the number of grinding passes i is large enough, i.e. [k.J(k,+k.J]' approaches zero, normal grinding force F,, can again become constant. Moreover, wheel ADOC approaches wheel SDOC if machine stiffness or the number of grinding passes is large enough. It should be noted that any difference between wheel ADOC and SDOC would directly contribute to the dimensional inaccurades of a ground workpiece. Based on the previous analyses [A and Eq. (3), the normal grinding force per grit in the ith pass can be expressed as
where 5 is a dimensionless constant, k, is a constant determined by grinding conditions, C is the number of active cutting points per unit area, exponent h is a constant related to contact frequency, and t is an exponent describing the influence of contact pressure. An analytical model is thus derived to predict the residual strength of a ground workpiece, based on the work reported by Malkin and Hwang [8]:
where q and M are non-negative constants. Thus, under general grinding conditions
J L ' ' J 1
(7)
Eq. (7) demonstrates that the residual strength of of ground workpieces decreases with the increase in machine stiffness. If the number of grinding passes i is large enough, k.J(k,+k.J approaches zero as k.J(ks+k&1. In this case, residual strength of becomes stabilized. In other words, as the number of grinding passes increases, residual strength of ground workpieces approaches a certain value and is not affected by machine stiffness.
3 EXPERIMENTATION
Grinding experiments were conducted in the mode of cup type surface grinding on a precision grinder. The machine loop stiffness was varied by adding compliance through a workholder (Fig. 1). The basic requirements for the workholder were adjustable compliance, high sensitivity, and high accuracy. Adjustable compliance was realized by sliding the two sliding blocks of the workholder along a flexural plate of 3 mm in thickness as shown in Fig. 1. High sensitivity was obtained through an appropriate design of the spring plate, and high accuracy was ensured by the rigid sliding blocks combining a rigid base, and by applying a large preload to all the mechanical interfaces of the workholder. A piezoelectric force transducer (Kistler 91 17A1.5) and a capacitance displacement sensor (Lion Precision) were included in the workholder. The objective for designing and using such a workholder was to isolate the effect of machine stiffness for a given grinding cycle. This approach eliminates the influences of motion errors and positioning characteristics that would result if different machines were used. The machine loop stiffness between the grinding head and the workholder was adjustable in the range of 5-40 Nlpm. At the machine loop stiffnesses of 10, 20, and 40 Nlpm, for example, the first-mode natural frequencies were 65, 75, and 95 Hz, respectively. On the other hand, the second-mode frequency response was found negligibly low for all the cases. Grinding coolant was supplied from a heat exchanger (Neslab model HX-75) to ensure a constant coolant temperature.
High pressure sintered silicon nitride (GS-44 of AlliedSignal) was used as workpiece material. Four diamond wheels of two bond types (vitrified and cast iron) and three grit sizes were used in the investigation. All diamond wheels were trued with a brake truer of a silicon carbide wheel. The vitrified bond wheels were dressed with alumina sticks, whereas the
cast iron bond wheels with an ELlD unit. After truing and dressing, the wheels were arranged to grind a cast iron block in 10 passes at a feed of 2 pmlpass to stabilize their cutting faces before they were actually used for grinding. After grinding, all the workpieces were tested using a four-point bending machine (Instron Model 8511) for their residual strength information per standard guidelines of American Society for Testing Materials (ASTM) C1161-94 Configuration B [9]. The experimental conditions were as follows:
Method Grinding wheel
Wheel notation
Workpiece
Wheel speed Feedrate Wheel SDOC Grinding width Coolant ELlD
Surface grinding with cup-type wheels SD120NIOOV (vitrified bond, 110 pm grit) SD600N100V (vitrified bond, 15 pm grit) SDIOOONIOOC (cast iron bond, 15 pm) SDIOOOONIOOC (cast iron bond, 1.5 pm) wheel 120Vfor SD120N100V wheel 6OOVfor SD600N100V wheel I k C for SDI OOONI OOC wheel 1 OkC for SDI OOOONI OOC High pressure sintered silicon nitride with dimensions 45x4x3.1 mm 25 mls 5 mmls 2-25 pm 4 mm Chemical solution type (electrolyte) Open voltage: 60 V; Peak current: 1 OA Onloff time: 2 ps; Pulse waveform: square
Fig. 1 Grinding arrangement with a workholder of adjustable compliance.
It should be noted that the vitrified bond wheels were American products while the cast iron bond wheels were Japanese. The mean grit size of the American wheel 600V is equivalent to that of the Japanese wheel IkC. The grinding wheels are then called in their respective notations.
4 EXPERIMENTAL RESULTS
Fig. 2 shows the correlations of wheel ADOC and normal grinding force with machine stiffness for wheel I k C at SDOCs of 3, 5 and 10 pm. At the respective SDOCs, both the wheel ADOC and normal grinding force showed a monotonic increase with machine stiffness. As an example, at an SDOC of 10 pm, a wheel ADOC of 4.7 pm was obtained when the stiffness of the machine was set at 5 Nlpm. The ADOC increased to slightly over 8 pm under the machine stiffness of 40 Nlpm. In addition, with an increase in machine stiffness, the ratio of ADOC with respect to SDOC became larger and larger. A possible explanation is that under low machine stiffness or at a small SDOC, rubbing and plowing of the grinding wheel against the workpiece become dominant. Conversely, micro- cutting due to abrasive actions becomes dominant.
Fig. 3 shows the effect of machine stiffness on the wheel ADOC and grinding force for the respective grinding wheels. It is observed that both ADOC and normal grinding force increase with machine stiffness although at a decreasing rate. Under all the machine stiffnesses tested, wheel I k C resulted in the largest ADOC, but the smallest normal grinding force, which was followed by wheels 120V, 600V, and 10kC. In addition, the wheel of a large grit size generated a small grinding force with a large ADOC compared to that of small grit
sizes under the same conditions. In contrast to the vitrified bond wheel, the cast iron bond wheel resulted in a much lower grinding force yet a much larger ADOC. The difference between ADOC and SDOC can be minimized using a high stiffness machine, or ELID, or a large depth of cut, or a combination of the above.
...
0
9 4 ii 2 0 0
- 8
- 6
- 4
- 2
0
a
SDOClOwn
z 6 ’O- 0
0 SDOC 5 p n
w SDOClOpn SDOC 5 p m
- SDOC 3 Frn
Machine stiffness, Nlpn
(a) Wheel ADOC vs. machine stiffness
10 w wheel 1kC
- 0 wheel 120V 0 wheel 6OOV 80%
Z 160- 6 2 P 120
._ c 80- L Ol ; 40-
Ol C U ._
-
0
0 wheel 1kC 0 wheel 120V 0 wheel 6OOV
,_____... n - wheel lOkC ._.___ ___..*-*-.- *-.--q
.p*.“*’ 9.--
-r-a-----------
o~ ----- .-
. r .
z o e - I I I
Fig. 4 presents the effect of machine stiffness on the residual strength of the workpieces ground with wheel 120V.
The residual strength showed a certain decrease as machine stiffness was increased from 5 to 40 Nlpm. The strength degradation can be attributed to increasing wheel ADOC with increased machine stiffness, as shown in Fig. 4.
1200 I I 1 0 Baseline strength 846 MPa 2 1000
Ol 600
c m
3 5 200 - 4001 6 ADOC + Strength
LL 01 10
0 10 20 30 40
Machine stiffness, Nlpn
Fig. 4 Residual strength and the corresponding ADOC vs. machine stiffness (wheel 120Vat 10 pm SDOC).
Wheel: 600V 0 SDOC: 15 pm
0 2 4 6 8 Time, second
Fig. 5 Normal grinding force under unstable grinding conditions.
A grinding process is after all a dynamic process that can become unstable if vibration occurs. Vibration may be induced in a number of reasons, such as insufficient machine stiffness, wheel wear, poor dressing and truing, and wheel unbalance. Fig. 5 shows an example of normal grinding force under an unstable grinding condition. A mean grinding force of approximately 65 N is super-imposed with a dynamic component of approximately 45 N in amplitude at the entry of wheellworkpiece contact. The dynamic component grows to nearly 60 N at the exit of the contact. The growing dynamic component depicts that the grinding process is unstable.
A correlation between residual strength and normal grinding force is constructed for wheels 600V and 1 OkC, and is presented in Fig. 6. Both the mean and variance of the force are provided to show the effect of grinding force and its dynamic component on the residual strength of ground workpieces. In Test 1 using wheel 600V, a mean force of 50 N with a variance of 15 N2 was obtained, which resulted in the residual strength of approximately 960 MPa. In Test 2, the mean and variance increased to 71 N and 83 N2, respectively, whereas the resulting residual workpiece strength reduced to about 900 MPa. It is difficult to conclude at this stage that the strength degradation was mainly due to the increase of the mean grinding force, or its dynamic component.
To confirm the dominant factor affecting workpiece strength, two more tests were further conducted. One was the addition of grinding disturbance to the grinding process. In this test, through the adjustments of the wheel unbalance and SDOC, the mean grinding force was maintained at 52 N while the variance was increased to 605 N2. Consequently, the residual strength of the ground workpieces was reduced to 470 MPa, a change of almost 50%. The other was the increase in the static component (mean) of the grinding force. In this test, wheel 10kC was used to investigate the effect of dynamic component on workpiece strength. With the application of wheel IOkC, a large grindin force of 113 N and a relatively small force variance of 54 N were obtained. As a result, the 9
residual workpiece strength remained around 900 MPa. Compared with the results of Tests 1 and 2 , Test 4 provided almost the same workpiece strength although an almost doubled mean grinding force. In comprehending the results presented in Fig. 6 , it is evident that the dynamic component, rather than the static component of the grinding force, is the predominant factor affecting the workpiece strength.
MeanIvariance of grinding force, NIN2
Fig. 6 Correlation of residual workpiece strength with meanlvariance of normal grinding force.
Fig. 7 Measurement results on residual strength and damage depth of silicon nitride subjected to grinding at SDOC 10 pm and machine stiffness 40 NIpm.
5 DISCUSSION
In this study, it is identified that the residual strength of ground workpiece can be enhanced by the compressive residual stress in the ground surface, but may be reduced by the introduction of grinding induced damage to the workpiece. It is therefore agreed that residual strength 0,. is expressed in the following equation,
where ob is the baseline strength; A o C is strength gain due
to compressive residual stress; AUd is the strength loss due to grinding damage.
Eq. (8 ) presents that the residual workpiece strength is determined by the baseline strength of the workpiece as well as possible strength gain A o C and strength loss A o d that are related to the grinding process, which is consistent with Xu et al. [ l o ] . If neither strength gain nor strength loss is induced in a workpiece, the workpiece should retain its baseline strength that can practically be obtained by lapping or polishing. Under a normal grinding condition, both strength gain and strength loss may occur simultaneously, which makes the prediction of residual workpiece strength or somewhat difficult.
To further address this point, Fig. 7 presents measurement results on residual strength and stress as well as damage depth of silicon nitride workpiece subjected to grinding at wheel SDOC 10 pm, and machine stiffness 40 NIpm. Under the same grinding conditions, wheel 600V bestowed the highest strength on the ground workpieces while wheels I k C and 120V resulted in the almost equally low strength, although wheels 600V and I k C shared the same mean grit size. Obviously, there must be some important factors other than grit size that affect workpiece strength. On
U,. = U b + AUc -AUd (8 )
the other hand, the measurement results on ground workpiece damage showed that wheel 600V results in a much smaller damage depth than did the other wheels. It may be speculated that strength loss AUd could be much less with wheel 600V than with the other two wheels due to possibly less damage induced. Furthermore, compressive residual stress of ground workpieces was the highest for wheel 120V and the lowest for wheel I k C . Strength gain A o C could be high for the workpieces ground by wheels 120 V and 600V, and low by wheel I k C . Ground workpiece strength is determined by the combined effect of strength gain and strength loss. Generally, more compressive residual stress can be induced with a dull grinding wheel, or a wheel with larger grit size, or a wheel with stiffer and stronger bond material, while less damage may be generated with smaller grit depth of cut. Since ELlD grinding allows a more aggressive cutting, it may not be beneficial to workpiece strength although it is good for workpiece dimensional accuracies. High workpiece strength can be obtained using a high compressive stress yet low damage grinding. In this regard, grinding wheels of a higher concentration and a larger grinding width are recommended for grinding ceramics. In addition, grinding machines of higher stiffness should be utilized.
CONCLUSIONS
In investigating the effect of machine stiffness on grinding of ceramics, the study has the following findings: As machine stiffness increases in single-pass grinding, ADOC and normal grinding forces increase, whereas the residual strength of ground workpieces decreases The residual workpiece strength is mainly affected by the dynamic component, rather than the static component, of the normal grinding force. The residual strength is determined by the baseline strength of the workpiece, the strength gain due to grinding-induced compressive residual stress, and strength loss due to grinding induced damage. For the same grinding conditions, ELlD helps generate a larger ADOC but a smaller grinding force compared to the vitrified bond wheel of the same mean grit size.
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