طراحی مواد هدفمند از flyash پر کائوچو و مواد مرکب برای اصطکاک برنامه ترمز با استفاده از روش بهینه سازی رگرسیون غیر خطی

Targeted material design (TMD) following combinatorial engineering approach based on experimentally determined performance defining attributes (PDA) of a series of heterogeneous friction-composites is attempted via non-linear regression optimization (NLR-OPT) technique. The four key PDAs have been rigorously evaluated on a Krauss friction testing machine. The four selected performance defining attributes (PDA) are performance-friction, wear, friction-fade and friction-recovery. Based on the performance data two target-composite formulations are designed adhering to friction-maximization norms. The theoretically obtained formulation designs for a target set of PDA were later validated by fabricating actual composites followed by their performance assessment on identical testing set-ups and test-regulation. The two targeted composite formulations were also replicated for flyash derived cenospheres in addition to the raw flyash based composites. Finally, the deviations in PDA are critically analyzed from material composition point of view and the adopted approach gives rise to minimal deviation from the magnitude of theoretically estimated PDA. The study has successfully demonstrated that non-linear regression technique based optimization for targeted material design of heterogeneous composites with multiple performance goals may prove to be a sound and viable engineering approach for material designers. Graphical abstract Full-size image (26 K)

Designing of hybrid composite materials based on multiple and functionally disparate ingredients for heavy duty engineering applications such as in friction braking are a well known problem of multi-criteria objective optimization [1], [2] and [3]. Research in the area of friction material development is based on randomly chosen friction formulations with many chemically dissimilar ingredients [4] and [5]. These ingredients may broadly be of four classes that are binder, filler, fiber and friction modifiers [6]. Reaching at a successful friction formulation is often complex and involves tedious task of fabrication, characterization and performance evaluation of a large number of composites that may tentatively be equal to the possible permutations and combinations of the number of ingredients that are used. For example, a friction formulation with 15 ingredients may be optimized only by fabricating and tribo-evaluating 15! = 1.3 × 1012 number of composites, if one-variable-at-a-time (OVAT) experimental design is strictly followed. Therefore the conceptual issue of reaching at a desired formulation of friction material with a targeted set of performance defining attributes (PDA) may be tackled by resorting to several composite formulation optimization methods based on stochastic designs where the randomization of the performance attributes is deliberately carried out in order to generate a gray performance data base [7] and [8]. Such data base forms the basis of further analysis within the realms of several optimization theories, such as, multi-criteria decision making (MCDM) [2], multi-attribute decision making (MADM) [9], multiple objective decision making (MODM) [10], gray relational analysis (GRA) [7], gray target theory (GTT) [11], analytical hierarchy process (AHP) [12] and [13], technique for order preference by similarity to ideal solutions (TOPSIS) [3], elimination and choice translating reality (ELECTRE) [14], Golden section rule [15] and [16], Genetic algorithm [8], artificial neural network (ANN) [17], linear and non-linear regression methods [18] and Taguchi analysis [19]. Most of the decision support based models are subjectively evaluated. For example, Gray statistics theory involve relatively linear approximations [7] and [20], AHP and TOPSIS involve deviation/approaching degree with respect to an objective performance/formulation ideology [13] and [21] whereas GA and ANN models remain inherently sensitive from accuracy point of view, often due to the limited number of training data sets [8] and [17]. Non-linear approach has empirically been considered to be more appropriate though their realistic validation pertaining to friction materials is not yet attempted. An optimization method based on Chemometrics principles involving non-linear optimization has already been reported to be fairly successful in enabling the product designers to develop targeted materials with a pre-defined performance ideology [22]. Flyash with the ability to enhance the specific performance along with abrasion resistance, porosity serve as promising and cost-reducing functional filler for augmenting tribological performance of filled composites such as brake friction materials [23], [24], [25] and [26]. The relevance of flyash as a filler in friction materials becomes even more important considering the fact that these composites integrally consist of ∼50–60% of space filler/inert or non-functional filler such as barites and lime-stone [27]. The techno-commercial viability can only be realized when the performance requirements are not compromised, especially for a critical automotive component like brake. Because of the disparate nature of the quality of the coal that varies with mines and the differential combustion efficiency of the coal in the various thermal power plants, performance aspects always need to be assured [28]. Therefore multiple formulation designs will be the key to develop friction materials based on flyash that may vary in its composition either due to the geographical region-specificity or due to non-uniformity in the degree of combustion. Hence to address this problem of hitting at the formulation for a set of designed performance requirements the prior performance data dealing with influence of flyash in combination with other ingredients in various combinations need to be analyzed. Such an objective may theoretically be manipulated by resorting to standard statistical models/operation research principles where the closest possible performance criteria may be approximated though they need further validation by fabrication and real evaluation of the materials on the standard testing systems. Adding to the complications of performance prediction and analysis is the stochastic nature of tribological processes which may decisively alter PDA by inducing topographical variations [29] and other shear induced thermo-mechanical phase transitions at the braking interface [30] and [31]. However, efforts to systematically analyze the factors influencing the PDA including compositional variables and their interdependence while ensuring the performance-reliability is crucial to design a pre-defined targeted friction material. In this investigation, reaching at two sets of objective design alternatives (conforming to a set of fixed performance defining attributes) of friction material formulation via non-linear regression approach has been attempted. The validation of the designed composites based on optimization principles have also been carried out by developing and assessing the performance of real-time composites.

Non-linear regression optimization assisted targeted material design was attempted for a pre-defined set of performance defining attributes. The compositional ratio of the four ingredients based targeted flyash friction composite is obtained by solving non-linear optimization problem. The theoretically designed flyash friction composites were fabricated flowed by their real-time performance evaluation for validation. Two alternate design ideologies were realized by using raw flyash and refined flyash based cenospheres as the major ingredient. Our study has successfully demonstrated that non-linear regression technique based optimization for targeted material design of heterogeneous composites with multiple performance goals may prove to be a sound and viable engineering approach for material designers. Among the two classes of composites with variation in the nature of the flyash particles, it was observed that cenospheres lead to an enhanced fade-recovery performance as indicated from the self-similar nature of the friction-build-up and friction-decay plots. The presence of processed volcanic rock fiber-lapinus in combination with cenosphere particles was synergistic in terms of the overall performance and durability. However, addition of raw flyash has been observed to be useful to boost the performance-μ, μ-fade and μ-recovery level as compared to cenosphere based compositions though μmax–μmin remained comparable. The friction stability was superior for flyash based composites whereas variability coefficients remained unaffected by the nature of flyash incorporation. Flyash/cenosphere incorporation caused enhanced fade-reduction with flyash being more effective whereas the recovery remained dependent on the overall organic content in the composites. Cenosphere incorporation caused effective wear reduction irrespective of the design ideologies or the disparate nature of the multiple ingredients in the flyash friction composites.