A new platform for the prediction of field-dependent yield stress and plastic viscosity of magnetorheological fluids using particle swarm optimization
Introduction
Magnetorheological (MR) fluids are made by dispersing micron-sized magnetic particles in a non-magnetic carrier fluid. The yield stress and viscosity can be changed by the external stimulus of the magnetic fields [1]. The yield stress can be defined as the minimum force or pressure that is required to change a non-Newtonian fluid from an elastic to a plastic form [2]. The yield stress is an important parameter that is used to indicate the performance of an MR fluid, primarily, to identify the effect of a magnetic field on its material properties. Although the existence of yield stress is debatable [3], it has been adequately defined and has undeniably become an important parameter in the design of MR devices and the characterization of MR fluids. Meanwhile, viscosity is an equally essential parameter for gauging the internal friction of a moving MR fluid. In general, there are a few ways of classifying viscosity, namely, apparent [4] and plastic viscosity [5]. While the apparent viscosity is easy to obtain and is calculated from the data collected from flow curves [6], the plastic viscosity concept can be easily utilized for designing MR devices since it is defined based on a well-known rheological Bingham plastic model [5], [7], [8], [9].
The Bingham plastic model has an advantage over other rheological models in terms of its simplicity as it only consists of two adjustable parameters, namely plastic viscosity and yield stress [7]. However, as the plastic viscosity is not constant under conditions of different flow velocities and magnetic fields, the phenomenon of shear thinning or thickening exists in the flow of MR fluids. In this condition, the Bingham plastic model may be deficient in predicting the behaviour of MR fluids. There are two types of yield stress, namely, the yield stress in low [10], [11] and high [4], [12], [13] shear rate regions, as illustrated in Fig. 1. The yield stress () in a low shear rate region, also known as the dynamic yield stress, can be calculated using any of the rheological models [7], except bi-viscous model, while the yield stress in a high shear rate region (), also known as the apparent yield stress, can be determined by using the Bingham plastic model, when only considers data in the high shear rate region [14], [15]. The low and high shear rate regions can be connected using parameter namely critical shear rate, that is defined as the limit between both regions in the Bingham biplastic model [14]. Any change in the would have a significant effect on the plastic viscosity and yield stress. Based on the existence of the , four other parameters can be identified, namely, the yield stress and plastic viscosity ( at the low and high shear rate regions. Some possible values of the critical shear rate or the intersection between the low and high shear rate regions are illustrated in Fig. 2. This means that four other parameters also have more than one possible magnitude.
Very few researchers have discussed the calculation of which is generally carried out by arbitrarily selecting the data or by making the value static at all the applied magnetic fields [13], [16], [17], [18]. Because Fig. 2 shows that values of can be more than one, this case can be considered as an optimization problem. The existing optimization works tried to fit the Bingham plastic and Herschel Bulkley models into the experiments with using the least mean square (LMS) method and genetic algorithm (GA) [19], [20]. However, the objective functions of the mentioned metaheuristic methods were simply used to fit the existing rheological model to the experimental data without considering the critical shear rate. In terms of the objective function, the cost or objective functions of the existing LMS and GA consist of two or three decision variables. Meanwhile, to consider the , four or five decision variables and shear rate regions need to be included in the cost function. In terms of the optimization method, although the GA is capable of overcoming the LMS or the gradient descent method [19], [21], another similarly well-known optimization method, i.e. particle swarm optimization (PSO), can also be considered. PSO has shown better performance than the genetic algorithm [22], [23] and has a lower running time compared to the genetic algorithm [24]. Although PSO is easy to implement, the computation of the critical shear rate, yield stress and plastic viscosity of MR fluids in low and high shear rate regions is a new area of application for PSO.
As evident from the above literature survey, the existing models for the prediction of field-dependent rheological characteristics are faced with difficulties in standardizing the calculation of the critical shear rate, yield stress and plastic viscosity in various shear rate regions and magnetic fields. Consequently, the development of a new platform to resolve the limitations of conventional prediction models is required. This work presented a new platform for the prediction of the magnetic field and shear rate region-dependent rheological properties of MR fluids with high accuracy. To achieve this target, a set of rules associated with an optimization tool were formulated for the standardization of the critical shear rate selection as well as to maintain the least error of the model. In other words, the prediction model proposed in this work was capable of carrying out meta-heuristic optimization as a means of determining the magnetic field-dependent dynamic and apparent yield stress simultaneously. The proposed platform consisted of a machine learning algorithm and PSO. The machine learning algorithm was used to predict the shear stress in various magnetic fields, while the optimization method was used to ensure that the parameter determined on the basis of the objective function was the optimized value. In the optimization procedure, the calculation was performed on the basis of the objective function, which considered the amount of data at lower and higher shear rates. To validate the effectiveness of the proposed platform, several comparative works between the measured data and predicted values of the yield stress and the plastic viscosity were undertaken, and these showed a high prediction accuracy at various magnetic field intensities.
Section snippets
Shear stress model
Fig. 3 shows the usual flow curve pattern of an MR fluid as the basic data for building a model to predict shear stress with variations of the magnetic fields (, , , ). The conventional methods prefer to build a model for each magnetic field. Therefore, if the magnetic fields have five values, the model number will also be five for each known magnetic field [20]. This kind of model can be utilized to design an MR device by assuming that the magnetic field values are the same. As the
Overview
The proposed platform was designed to predict and optimize the dynamic yield stress, apparent yield stress, critical shear rate, and plastic viscosity by considering the shear rate regions. The block diagram of the proposed platform is depicted in Fig. 4. The platform consisted of the shear stress model and the parameter optimization section. The shear stress model provided the shear stress values in a desired shear rate range and a magnetic field value. As for the parameter optimization, the
Tested MR fluid
The training data were based on a steady-state experiment using MRF 132 DG, an MR fluid from Lord Corporation, with its properties listed in Table 2. The rotational rheometer used for the test was produced by Anton Paar, Physical, MCR 302, GmbH, Austria. The MR fluid was tested using a twin parallel-plate rheometer (MCR 304 Anton Paar) and the magnetic fields were adjusted at 0, 100, 200, 300, 400, and 500 mT. The shear rate varied from 0.01 to 2000 s−1 with a logarithmic ramp pattern.
Model parameters
Since the
Results and discussion
This section discusses the evaluation of the platform with regard to (1) the performance of the PSO method, the tuning of the proposed search space identification, and its comparison with other optimization methods, and (2) the performance of the proposed objective functions and the predicted rheological parameters. The performance of the PSO was evaluated based on the accuracy of the shear stress, which could be correlated with the output of the objective function. Firstly, the optimization
Conclusion
In this work, a new platform that can predict the dynamic yield stress, apparent yield stress, critical shear rate, and plastic viscosity of MR fluids was developed. The platform consisted of a shear stress model and an optimization method. The shear stress model was a single-hidden layer feed-forward neural network obtained by using an extreme learning machine, while the optimization method was developed based on the PSO theory. The principal results are summarized as follows.
(1) The proposed
Acknowledgements
The authors gratefully acknowledge the financial funding of Universiti Teknologi Malaysia under TDR (Vot No: 06G77) and also Universitas Sebelas Maret (UNS), Indonesia through hibah PPKGR 2019.
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