Article ID: 1003-6326(2005)02-0243-04

Machinability evaluation of machinable ceramics with fuzzy theory

YU Ai-bing(ÓÚ°®±ø)¹, ZHONG Li-jun(ÖÓÀû¾ü)¹, TAN Ye-fa(Ì·Òµ·¢)²

(1. Key Laboratory of Advanced Ceramics and Machining Technology, Education Ministry,Tianjin University, Tianjin 300072, China;

2. Nanjing Engineering Institute, PLA University of Science and Technology, Nanjing 210007, China)

Abstract: The property parameters and machining output parameters were selected for machinability evaluation of machinable ceramics. Based on fuzzy evaluation theory, two-stage fuzzy evaluation approach was applied to consider these parameters. Two-stage fuzzy comprehensive evaluation model was proposed to evaluate machinability of machinable ceramic materials. Ce-ZrO₂/CePO₄ composites were fabricated and machined for evaluation of machinable ceramics. Material removal rates and specific normal grinding forces were measured. The parameters concerned with machinability were selected as alternative set. Five grades were chosen for the machinability evaluation of machnable ceramics. Machinability grades of machinable ceramics were determined through fuzzy operation. Ductile marks are observed on Ce-ZrO₂/CePO₄ machined surface. Five prepared Ce-ZrO₂/CePO₄ composites are classified as three machinability grades according to the fuzzy comprehensive evaluation results. The machinability grades of Ce-ZrO₂/CePO₄ composites are concerned with CePO₄ content.

Key words: Ce-ZrO₂/CePO₄; ceramics; machinable ceramics; machinability; fuzzy theory CLC number: TQ174.15; TG113.26

Document code: A

1 INTRODUCTION

By controlling microstructural modifications, weak interfaces on the microstructural scale can be introduced into ceramics^[1-5]. Material removals are finished due to the formation and linking of cracks at the weak interfaces between two phases. Machinable ceramics, which can be machined with conventional metal-cutting tools such as high-speed steel and tungsten carbide, show insensitivity to strength degradation from machining operations^[3]. The fabrication of machinable ceramics provides an essential way to solve the machining problems of advanced ceramics. Oxide ceramics containing rare earth phosphates^[5-10], such as Ce-ZrO₂/CePO₄, and mullite/LaPO₄, are machinable. There exist weak interfaces between phosphates and oxides^{[5, 7]}.

More attentions have been paid to material design, fabrication and property studies of machinable ceramics. However, machinability of material is an important factor for evaluation and design of ceramics. The optimum machining technologies can be determined according to the machinability of ceramics. And in order to obtain better machinability of ceramics, the rational property parameters might be designed before fabrication of materials. So, the chemical composition and preparation processes can be intentionally designed to meet the needs for ceramics machining. Therefore, through the research of machinability, we might design compatible advanced ceramics, which simultaneously meet the needs of both applications and machining operations^[11]. Usual criteria for machinability assessment of machinable ceramics include material removal rate, tool life, brittleness index, etc. Mostly, machinability of machinable ceramics is evaluated considering any one of the above criteria^{[12, 13]}. Recently, fuzzy evaluation approach was applied to study the machinability of ceramics^{[7, 11]}. And the property parameters of materials were selected as alternative set. In this study, two-stage fuzzy evaluation model was used to analyze the machinability of machinable ceramics, in which both property parameters and machining output parameters were considered simultaneously. Machinabilities of five fabricated Ce-ZrO₂/CePO₄ composites were evaluated as the example.

2 EXPERIEMNTAL

Two-phase composites consisting of CePO₄ and Ce-ZrO₂ were fabricated. Powders were ball-milled in an aqueous slurry for 7h, dried, uniaxially dry-pressed at 100MPa, cold iso-statically pressed at 200MPa, then sintered for 2h in air. The hardness was measured using Vickers indentations. The fracture toughness was measured using single edge notched beams loaded in three-point bending. Elastic modulus was estimated from rule of mixtures for two-phase materials.

Samples were drilled with water coolant at a fixed drilling load of 22.87N and spindle rotating speed of 3700r/min. The diameter of tungsten-cobalt carbide drill bits was 1.5mm. The material removal rates were calculated as the material removal volume per unit time. Surface grinding tests were conducted on horizontal spindle precision grinder. A resin-bonded diamond wheel had grit size of 270/325 and content of 100%. Grinding tests were done in the down mode at a peripheral cutting velocity of 22.6m/s, workpiece velocity of 5.5m/min and grinding depth of 50¦Ìm. Grinding coolant was water-soluble synthetics. Normal grinding forces were measured using a piezoelectric platform dynamometer. The machined surfaces of ceramics were observed with SEM.

3 EVALUATION METHODOLOGY

Machinability means machining difficulty for certain material. Usually, machinability is estimated with two-type parameters, material property parameters and machining output parameters^{[11, 14, 15]}. During machining processes, removal of materials is closely concerned with the deformation and fracture of material, which can be reflected by property parameters, including elastic modulus E, hardness H_v, fracture toughness K_¢ñC, etc. Machining output parameters are defined as variables measured in or after machining operations, such as material removal rate, cutting force and tool life.

There exists uncertainty in linguistic notions about machinability, such as ¡°easy to machine¡± and ¡°very easy to machine¡±. The characteristic of machinability assessments lies in the lack of precise boundaries. The machinability of material is a comprehensive factor, which could not be accurately described with single parameter. So, one system covering some parameters is needed to evaluate the machinability. Fuzzy theory is particularly appropriate to deal with the uncertain linguistic notions. Many parameters can be taken into account together through fuzzy multi-criteria decision-making method^[16]. Relations between parameter and parameter are considered without missing of any information. The machinability of machinable ceramics can be completely reflected by two-stage fuzzy comprehensive evaluation method, which contains the following steps.

1) Let U={u₁, u₂, ¡­, u_n} be a set of available alternatives

The machinability of machinable ceramics is regarded as evaluated objective. The mechanical property parameters and machining output parameters are selected to constitute alternative set U. To avoid too many alternatives on one set, we divide set U into two subsets U₁ and U₂. Then, U= {U₁, U₂}, where U₁ denotes the subset of alternatives containing mechanical property parameters, U₂ denotes the subset of alternatives containing machining output parameters. Let V= {v₁, v₂, ¡­, v_m} be a set of evaluation criteria, usually conflicting, by which the performance of an alternative is evaluated. The machinabilities are classified as some grades represented by fuzzy terms using linguistic variables, such as ¡°easy¡± and ¡°medium¡±.

2) First-stage fuzzy comprehensive evaluation

Fuzzy matrices R₁ and R₂ are constituted through evaluation of each alternative on subsets U₁ and U₂, respectively. Set of weights, represented as one vector A, is assigned. For a given material with alternative subset U₁ and U₂, the fuzzy operations are

B₁=A₁¡ðR₁; B₂=A₂¡ðR₂(1)

where ¡°¡ð¡± is fuzzy operator. The weighted average fuzzy model^[16] is chosen for considering all alternatives in terms of the assigned weights, so the fuzzy operation model in Eqn.(1) becomes M(¡¤, «Ý), where ¡°¡¤¡± denotes ordinary real multiplication, ¡°«Ý¡± denotes bounded sum. Vector B₁ represents result evaluated with mechanical property parameters, and vector B₂ represents result evaluated with machining output parameters. A₁ is corresponding to U₁, and A₂ to U₂.

3) Second-stage fuzzy comprehensive evaluation

For alternative set U, two first-stage evaluation results constitute fuzzy matrix R. Then, final evaluation result is

As for the maximum element b_{j, max} on vector B, there will be corresponded to one grade. Then, the machinability grade of machinable ceramic material is determined.

4 RESULTS AND DISCUSSION

4.1 Surface and parameters

The transgranular and intergranular fractures of grains were observed on machined surfaces. Take Ce-ZrO₂/50%CePO₄ for example, the SEM micrographs of ground surface is shown in Fig.1. Some grains are in cleavage fracture mode indicated by arrows A. The layered microstructures indicate that these grains are CePO₄. There exists transgranular fracture of CePO₄ grains during machining processes of Ce-ZrO₂/CePO₄. Arrows B shows integrated grains without breakage, which suggests intergranular fracture between ZrO₂ and CePO₄ grains. When composite are exerted with loads, fracture will occur along weak boundaries between ZrO₂ and CePO₄ grains. Similar phenomena can be observed on other composites machining surfaces. Moreover, ductile deformation of Ce-ZrO₂/CePO₄ material can be observed in Fig. 1 indicated by arrow C. Fig.2 shows a lower magnification SEM image of Ce-ZrO₂/15%CePO₄ surface drilled with metal cutting tools. Obviously ductile machining marks, similar to metal drilled surfaces, can be observed in Fig.2.

Fig.1  Ground surface of Ce-ZrO₂/50%CePO₄

Fig.2  Drilled marks of Ce-ZrO₂/15%CePO₄

   The properties of composites, material removal rates Q and specific normal grinding forces F_n are listed in Table 1. The Ce-ZrO₂/CePO₄ composites were prepared with different CePO₄ content ¦Á and sintering temperature t. If only single parame- ter in Table 1 is selected to evaluate machinability, it is impossible to have correct and complete estimation. By fuzzy method, all parameters in Table 1 can be taken into account together to have a comprehensive evaluation result.

4.2 Evaluations

The set of alternatives is composed of H_v, K_¢ñC, E, Q and F_n. Then, we have U= {u₁, u₂, u₃, u₄, u₅}={H_v, K_¢ñC, E, Q, F_n}, U₁={u₁, u₂, u₃}={H_v, K_¢ñC, E}, U₂={u₄, u₅}={Q, F_n}. The set of evaluation criteria is V={v₁, v₂, v₃, v₄, v₅}={very easy, easy, medium, difficult, very difficult}. Suppose effects of each parameter on machinability are similar, and suppose effects of two type parameters on machinability are similar. Therefore, the weighting coefficient vectors in Eqn.(2) are assigned as A₁=(0.334, 0.333, 0.333), A₂=(0.5, 0.5), A=(0.5, 0.5). Suppose material property values and machining output parameter values meet normal distribution. The fuzzy normal distribution is selected as the membership function:

where ¦Ò and c_i are constants corresponding to v_i. Here, constants are determined on basis of the value range in Table 1. Five evaluated grades of machinability are corresponding to five values in c_i. With the increase of H_v, K_¢ñC, E, and F_n values, the machinable ceramics become difficult to machine. Higher Q value means the easiness of material removal. According to the influences of those parameters on material removal, the constant values for every parameter are as follows. H_v: ¦Ò=2, c₁=3, c₂=5, c₃=7, c₄=9, c₅=11; K_¢ñC: ¦Ò=2, c₁=0, c₂=3, c₃=6, c₄=9, c₅=12; E: ¦Ò=10, c₁=150, c₂=160, c₃=170, c₄=180, c₅=190; Q: ¦Ò=0.1, c₁=0.4, c₂=0.3, c₃=0.2, c₄=0.1, c₅=0; F_n: ¦Ò=5, c₁=35, c₂=40, c₃=45, c₄=50, c₅=55.

When taking Ce-ZrO₂/50%CePO₄(1450¡æ) for example, let every parameter value in Table 1 be the value of x in Eqn.(3), repeatedly substituting ¦Ò and c_i(i=1, 2, ¡­, 5) values for every pa rameters into Eqn.(3), the evaluated result of every alternative can be calculated. Evaluated results of alternatives on subset U₁ constitute fuzzy matrix R₁, and evaluated results of alternatives on subset U₂ constitute matrix R₂. Thus, we have

Substituting A, A₁, A₂, R₁ and R₂ into Eqn.(2), the comprehensive evaluation result B of Ce-ZrO₂/50%CePO₄(1450¡æ) materials is B=(0.533, 0.584, 0.389, 0.040, 0.001). In the same way, we have the comprehensive evaluation results of other composites listed in Table 2.

Table 1 Property and machining parameters

Table 2 Evaluation results of machinable ceramics

As for Ce-ZrO₂/50%CePO₄ (1450¡æ), the maximum element on set B is b₂=0.584, which corresponds to v₂=¡°easy¡± on set V. Thus, its machinability grade is ¡°easy to machine¡± among five materials. From Table 2, five Ce-ZrO₂/CePO₄ composites are classified as three machinability grades, ¡°easy to machine¡±, ¡°difficult to machine¡± and ¡°very difficult to machine¡±. The machinabilities of Ce-ZrO₂/CePO₄ composites increase with the increase of CePO₄ content.

From the experimental results of specific material removal rates Q listed in Table 1, we can estimate the machinability of five composites with single parameter criterion. Values of specific material removal rates can be classified as three grades. Among five composites, Ce-ZrO₂/15%CePO₄ has the lowest value of removal rates, two Ce-ZrO₂/25%CePO₄ ceramics have medium values of removal rates, and higher removal rates belong to two Ce-ZrO₂/50%CePO₄ ceramics. The evaluation results with fuzzy approach are consistent with the comparison of single parameter in machining experiments.

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Foundation item: Project(50305023) supported by the National Natural Science Foundation of China

Received date: 2004-11-25; Accepted date: 2005-01-18

Correspondence: YU Ai-bing, Associate professor; Tel:+86-22-27406951; E-mail: yuaibing@126.com

(Edited by YANG Bing)