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Radtnko GLIGORIJEVIC jeremua JEVTIC Djuro BORAK Abstract. Materials and process selection are key issues in optimal design of industrial products. Substituting and selecting materials for different machining parts is relatively common and often. Material selection is a difficult and subtle task, due to the immense number of different available materials. From this point of view paper deal with a set of major gear design criteria which are used for gear material selection.

The main gear design criteria are: surface fatigue limit index, bending fatigue limit index, surface atigue lifetime index, bending fatigue lifetime index, wear resistance of toots flank index and machinability index. Using computer allows a large amount of information to be treated rapidly. One the most suitable model, for ranking alternatives gear materials, is ELECTRA, which using a multiple criteria, which all material performance indices and their uncertainties are accounted for simultaneously. Key words: gear, material, selection 1.

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INTRODUCTION Materials and process selection are key issues in optimal design of industrial products. Recently many materials which have long been used in industry are being replaced y newer materials in order to meet demands of cost reduction and better performance [1 In the manufacture of mechanical parts, knowledge of material properties, cost, design concepts and their interactions is required. The large number of available materials, together with the complex relationships between the various selection parameters, often makes the selection process a difficult task.

When selecting materials, a large number of factors must be taken into account. These factors are mechanical properties, physical and electrical properties, corrosion resistance, envlronmenta I Trlenallness ana economy. In mecnanlcal design, however, mechanical properties are the most important. The most important mechanical material properties usually encountered in material selection process are fatigue strength, tensile strength, yield point, hardness, stiffness, toughness, creep resistance and density.

The first step in the material selection is to specify the performance requirements of the component and to broadly outline the main materials characteristics and processing requirements [4-8]. Accordingly, certain classes of materials may be eliminated and other chosen as probable candidates for making the component. Then, he relevant material properties are identified and ranked in order of importance. Then, optimization techniques are used to select the best material.

There are a few strategies for material selection: on the base experience, on the base trial and error, Ashby method [4-8], which is advanced Grenoble team [6], graph theory and matrix approach. Ashby introduced materials selection charts which allow the identification, from among the full range of available materials, the subset most likely to perform best in a given application. He has used a multi-obJective optimization method to compromise between several onflicting objectives in material selection.

Using computer allows a large amount of information to be treated rapidly. One the most suitable model, for ranking alternatives gear materials, is ELECTRE (Elimination and Choice Expressing the Reality) [6-8]. ELECTRE (l, II, Ill, and ‘V) is a method for dealing with the problem of ranking alternatives from the best to the worst. This method is suitable for gear material selection. 2. GEAR MATERIAL SELECTION MODELS Optimal design of gears requires the consideration of the two type parameters: Material and geometrical parameters.

The choice of stronger material parameters may allow the choice of iner geometrical parameters and vice versa. Very important difference among these two parameters is that the geometrical parameters are often varied independently. On the other hand, material parameters can be inherently correlated to each other and may not be varied Independently. An example 0T wnlcn Delng tne varlatlon of the bending fatigue limit (Sbf) with the core hardness (HB) for some steel materials. If these parameters would be varied independently in an optimization case, it may result in infeasible solutions.

Therefore, the final choice of material may not be possible within available data base. If gear material and geometrical parameters are optimized simultaneously then it is common to assume empirical formulas approximating a relation between material parameters for example the bending fatigue limit (Sbf) and ultimate tensile strength (Rm) as a function of hardness. If the choice of material is limited to a list of pre-defined candidates, then two difficulties can be appeared. First, a discrete optimization process should be followed against material parameters.

Second, properties of different alternatives materials may not indicate any obvious correlation in the given list. The main goal is to choose aterial with best characteristic among alternatives. Table 1 . shows suggested nine materials with their characteristics in a gear material selection process. 389 Table 1 . Characteristics of alternative materials for gear selection To choose the best materials, it is recommended [4-8] that individual material characteristics be grouped into a set of characteristics indices to reflect particular design goals.

The base of this model [5,7] is material characteristics charts for a wide range of material selection cases. Two main features of the charts are: fundamental relationships between material haracteristics and the ability to choose an optimal material for a particular application based on predefined performance. Therefore, this model taking into account a large number of designs and manufacturing alternatives. It is the reason for introducing a computer aided methodology for the selection of a Joining procedure [7,8]. here, asl – is the service life factor (for 107 cycle it is unity), Dr – Is rellaDlll unity) and ty Tactor (Tor rellaDlllty Ssf – is the nominal surface fatigue limit measured in a laboratory condition for 107 cycle lifetime, 99% reliability. asl and br are dimensionless design factors. 3. MATERIAL PERFORMANCE INDICES The main characteristics considered in the design of gears are: -surface fatigue limit (Ssf), -root bending fatigue limit (Sbf), -wear resistance of tooth’s flank and -machinability. Therefore, definition of material characteristics indices should be based on relationships characterizing these criteria.

From a material selection aspect, the surface fatigue failure is pitting when due to excessive Hertzain stress, is cyclic loading, relatively smooth – bottomed cavities appear or near contact surfaces. Another form of surface fatigue failure is spalling when areas of the skin flake away due to a ontinuation of pitting. When gears have surface hardened, this failure can occur due to the formation of cracks in sub-surface or on surface of case [9,11]. The relationship between modified surface limit (Sm) and surface fatigue limit of material can be express as: Sm= Ssf a sl br 390 Fig. . The failed gear due to surface fatigue (a), root bending fatigue (b) Estimating of a sl is performed dependence on material and number of cycles (Fig 2), [12]. It is shown that ultimate gear failure in service is begun: 1) when once or more teeth have completely broken away or 2) the gear unit has been damaged that the vibration nd noise levels are not acceptable. It can be seen from fig. 2 that for a given service life Tactor N I ,tne nlgner tnen Rm/ SST ratlo, tne nlgner tne service life factor (asl), and the higher the modified endurance limit (Ssm).

When Rm/ Ssf ratio is higher it means that the crack initiation phase is longer (constant horizontal line). On the base for Sm to be optimal (eq. l) two materialrelated performance indices should be maximized: fl = Ssf (8) and f2 = Rm/ Ssf Fig. 2. Basquin S-N curve dependence of material and cycle life factor It can be seen from eq. (9) that optimization of the two indices should ideally yield a higher Ssf and Rm. Another very important material characteristic for gears is bending fatigues. Figure 3 and 4 show the value of bending fatigue limit of picies for two group gear steels [15].

When a crack on the root or surface of a tooth is initiated, a gear may still continue working for a few more cycles until the final breakage occurs. In dependence on a given material and stress magnitude, the total number of cycles (N) before final bending fatigue [13] of surface fatigue failure [14] can be defined: N=Ni+NP where Ni and Np are the number of cycles required for the crack initiation phase and the crack propagation phase respectively. It is important to hoose materials with higher resistance to crack initiation. It means that Ni Np .

For a given stress magnitude of oi , Ni can be estimated by Basquin S-N low (fig. 3), [13,14]: Ni = ND (Oil OD)-k where: – k is a material constant, (and when the k is smaller the crack initiation phase is the longer), – ND and OD correspond to the number of cycles and the stress level at the endurance limit. If we know that the tooth fails under a cyclic load with an amplitude equal to Rm and the corresponding the number of cycles N Rm (fig. 2) then the simile is for Ssf which corresponding Nsf (107 cycles), then follows: Ni = NSf (oil oSf)-k , where Ni

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