Selection of process parameters in grinding ceramics.

Dobrescu, Tiberiu ; Enciu, George ; Nicolescu, Adrian 等

1. INTRODUCTION

In a grinding process, each protruding abrasive grain on a grinding wheel generates an intense local stress field upon contacting the workpiece surface. This stress field causes irreversible material deformation in the form of dislocations, cracks and voids. The material-removal mechanisms are usually classified into two categories: brittle fracture and plastic deformations. Brittle fracture, analogous to indentation of a brittle material by a hard indenter, involves two principal crack systems: lateral cracks which are responsible for material removal, and median cracks, for strength degradation. In brittle fracture, material-removal is accomplished through void and crack nucleation and propagation, chipping or crushing. Plastic deformation is similar to the chip formation process in metal grinding, which involves scratching, plowing, and chip formation. The material is removed in the form of severely sheared machining chip. The strength, hardness, and fracture toughness of the work material are the governing factors that control the extent of brittle fracture and plastic deformation. Grinding process is an inherently damaging process since the abrasive grains are forced into the surface. It is therefore not surprising that the grinding operation causes decreased mechanical strength of the machined components, an effect frequently reported in the literature (Zhang & Howes, 1994).

Owing to variations of the grinding wheel topography and microgeometry of abrasive grains, in grinding the impacts of cutting edges are statistically distributed. Thus, grinding processes are characterized by probabilistic mechanisms of influencing parameters and resulting effects. In addition the grinding system, consisting of grinding wheel, workpiece and machine tool, causes a dynamic process behavior with fast changes of the cutting conditions in the contact zone. Moreover an instationary process behavior arises during grinding of ceramic materials, as the wheel topography is steadily subjected to changes caused by specific wear mechanisms. Without self-sharpening effects occurring, the wheel constantly loses its grinding performance. These three basic modes of interaction make it difficult to analyze the grinding process and to determine the optimum process conditions as it is frequently discussed in the literature (Inasaki, 1987). Therefore a kinematic model of the cutting edge engagement is derived for the evaluation of uncut chip thickness in connection with single grain scratch tests in order to determine parameter limits to prevent surface damage.

2. PRINCIPLE OF DUCTILE MATERIAL REMOVAL

The term "ductile regime" has been used to describe the material-removal mechanisms in the grinding of ceramics. A hypothesis has been advanced according to which all materials, regardless of their hardness and brittleness, will undergo a transition from a brittle to a ductile regime below a critical depth of cut. The hypothesis is based on the energy consumption in different material-removal processes. The energy required for brittle fracture is proportional to the square of a characteristic dimension, which can be depth of cut, the energy required for plastic deformation is proportional to the cube of the characteristic dimension: the energy ratio of plastic flow to fracture is therefore proportional to the characteristic dimension. As the scale of machining decreases, plastic flow becomes an energetically more favorable material-removal mechanism; the material-removal mechanism at a reduced scale thus is based on the ductile regime (Zhang & Howes, 1994).

In the grinding of ceramics, material-removal may however, be based on such mechanisms as crushing, chipping of fracture, pulverization, and ductile deformation. In dealing with precision grinding processes, where the depth of cut is normally in the submicrometer range, crushing and chipping or fracture mechanisms can be excluded from this list. Material pulverization occurs when ceramic grains sized in micrometers are pulverized during grinding into finer grains in submicrometer range or even smaller. In a material-removal process, the response of the material is to generate the highest possible resistance to the external machining system in order to maintain its natural structure. The highest possible resistance corresponds to the highest possible energy consumption by the material, which determines the most favorable material-removal mechanisms in a machining process. Based on this energy argument, pulverization is considered to be the most favorable material-removal mechanism in grinding of ceramics at minute depth of cut. Material removal can be due mainly to the material pulverization rather than ductile deformation.

Single grain scratch tests represent a theoretically and experimentally idealized model with one grain on the outer diameter of the grinding wheel (Toenshoff, 1992). They allow a theoretical computation of the kinematic conditions and a phenomenological view of surface formation without stochastic superposition of different effects during the engagement of numerous cutting edges. Contrary to ductile metallic materials the brittle ceramic materials show cracks in the surface and in depth, to the sides and in tangential direction when a limiting uncut chip thickness is exceeded, depending on the workpiece material. A surface featured by such brittle mechanisms influences the tribological properties of slide face as well as the components tensile strength under static and dynamic stress conditions (Dobrescu & Anghel, 2008).

3. MODELLING THE KINEMATICS OF AN INTRUDING CUTTING EDGE

Based on single grain scratch tests a kinematic model of the intrusion of a cutting edge is developed considering limiting uncut chip thickness hg for each workpiece material. This model intends to determine process parameters effecting mainly plastic deformation along surface relevant areas of the grain path, thus minimizing the number of induced microcracks. During modeling of the kinematic grain path creep feed grinding and reciprocating grinding conditions are separated by their different characteristic courses of uncut chip thickness leading to different mechanisms of surface generation as show in Figure 1 (Dobrescu, 1998).

Creep feed grinding is characterized by a comma-shaped course of grain path (Figure 1.a) caused by the superposition of two subsequent cycloid arches. The uncut chip thickness h versus the grinding wheel rotation angle [phi] starts at zero in the moment of contact at point B, growing almost linearly until the maximum uncut chip thickness [h.sub.max] is reached at point M, and then decreasing arch-shaped towards point A, where the grain leaves the workpiece again (Figure 1.c). In the shown system of coordinates with the workpiece speed [v.sub.w] related to the center of the grinding wheel the trajectory of the single grain is computed:

x([phi]) = [r.sub.s] x (([phi]/q + sin [phi]) (1)

y([phi]) = [r.sub.s] - (1 - cos [phi]) (2)

With q=[v.sub.s]/[v.sub.w]. The x coordinate of contact point B results from:

[x.sub.B] = [pi] x [r.sub.s]/q (3)

Where [r.sub.s] are grinding wheel radius and [v.sub.s] is circumferential speed of grinding wheel.

[FIGURE 1 OMITTED]

Caused by the superposition of the grain path cycloids a wavy surface profile with sharp ridges arises. The uncut chip thickness correlated to the peaks of these ridges is defined as the surface relevant uncut chip thickness [h.sub.0], representing the maximum of crack inducing stress along the arising workpiece surface. In order to avoid rim and sub-surface damages, kinematic process parameters are consequently chosen in a way, that the surface relevant uncut chip thickness [h.sub.0], which can be adjusted by these kinematic parameters, does not exceed the limiting uncut chip thickness hg for a specific material. These definitions and kinematics are valid for uncut as well as downcut conditions.

Reciprocating grinding (Figure 1.b) is defined by single grain paths of subsequent revolution not intersecting inside the workpiece. Theoretically a small web of the original surface remains, reducing to a ridge under limit conditions. The maximum uncut chip thickness [h.sub.max] at reciprocating grinding equals the selected depth of cut ae. This maximum is reached in the middle of the contact arch (Figure 1.c) and represents the surface relevant uncut chip thickness [h.sub.0] as well.

4. COMPARISON OF KINEMATIC MODELING AND REAL GRINDING PROCESS

The superposition of multiple kinematic cutting edges on one circumferential line can be taken into account by correcting the speed ratio corresponding to the number of cutting edges, i.e. 10 equidistant kinematical cutting edges on a circumferential line can be compared to a wheel speed increased by ten times. In a real grinding process small deviations of shape and roundness of the grinding wheel, an eccentricity of the wheel fixture and influences caused by vibrations and deflection are to be taken into consideration.

5. CONCLUSION

The following guidelines and general rules should be considered for the selection of process parameters in grinding of ceramics:

* Creep feed grinding results in low uncut chip thickness and therefore minimum surface damage. Following the presented definition of creep feed grinding, not necessarily a great depth of cut is assumed. Even a spark-out process can be implemented under creep feed conditions.

* An increased removal rate should be realized by increased depth of cut more than high workpiece speeds, as long as sufficient coolant supply is guaranteed.

* Increased cutting speeds reduce the uncut chip thickness at the single grain and improve surface quality.

* During finishing, one single depth of cut with respectively reduced workpiece speeds should be preferred in order to obtain low cutting forces.

6. REFERENCES

Dobrescu, T. (1998). Cercetari privind optimizarea masinilor de superfinisat materiale fragile, PhD Theses, University "Politehnica" of Bucharest, Romania

Dobrescu, T.; Anghel, F. (2008). Surface grinding method of silicon wafers, Annals of DAAAM for 2008, 22 - 25th October 2008, Tarnava, Slovakia, pp. 0395-0396

Inasaki, I. (1987). Grinding of Hard and Brittle Materials, CIRP Annals, no. 36, pp. 463-471

Toenshoff, H. K.; Peters, J.; Inasaki, I. & Paul, T. (1992). Modeling and Simulation of grinding Processes, CIRP Annals, no. 41, pp. 677-688

Zhang, B. & Howes, T. D. (1994). Material Removal Mechanisms in Grinding Ceramics, CIRP Annals, no. 43, pp. 305-308