Three-dimensional flow state analysis of microstructures of porous graphite restrictor in aerostatic bearings
Introduction
Aerostatic bearings are widely used in ultraprecision machine tools, integrated circuit manufacturing equipment, and precise measurement instruments. It offers many advantages, including high accuracy, low friction, and no pollution [1]. A porous aerostatic bearing is a novel bearing that effectively improves the load capacity and dynamic behavior.
A porous restrictor can yield a more even pressure distribution; however, the static and dynamic performances of porous bearings are still being investigated primarily because of their small opening and throat with complex and irregular distributions, which increase the difficulty in constructing three-dimensional (3D) material modeling [2,3]. In a previous study, a porous material was treated as an entire block on a two-dimensional (2D) plane with isotropic permeability. Such approaches, however, have failed to address the flow state inside the porous material as well as the development of the flow state in a 3D space. Therefore, it is essential to reconstruct the 3D porous model and analyze the 3D flow field.
Porous materials have been studied in geological structures, such as porous soil and porous rock. Many equivalent simplified models that do not require destructive measuring instrument have been proposed, such as the pore network model, capillary model, and volume packing model, to accommodate the characteristics of small openings and throat [4]. The solid part of the materials is fitted by simple geometries such as spheres and cylinders, which are stacked together to build a general framework. The throat part is fitted by a simple tube such as circular, square, and capillary tubes [5]. These reconstruction methods are unsatisfactory because they are merely idealized models for qualitative analysis.
In the manufacturing of porous materials, the pore and throat tend to be randomly distributed. Therefore, numerous studies regarding porous material reconstruction based on various stochastic methods have been conducted. In 1975, Joshi [6] proposed the Gaussian analysis. Subsequently, Quiblier [7] used this method in a 3D space and obtained the first 3D porous material model. In 1953, the simulated annealing algorithm was developed by Metropolis et al. to establish a rock structure that is highly similar to a real one [8]. In 1997, Bakke and Oren [9] presented a process simulation analysis for the simulation of the 3D pore network of sandstone. In 2004, Wu Kejian et al. [10] used an efficient Markov chain Mont- Carlo analysis method (MCMC) for simulating soil structure.
The methods above have their own applications, merits, and disadvantages. The Gaussian analysis affords a fast 3D reconstruction but not universal applicability and translatability. The simulated annealing algorithm enables the reconstruction model to contain more information regarding the character of a real sample. However, it cannot realize the structure of a high-connectivity porous framework and requires a significant amount of processing time. The process simulation is complicated and only applied for reconstructing simple porous materials. The MCMC method is a simple and efficient method for building a model; however, it poses challenges when used for 3D heterogeneous materials. In general, stochastic models only contain features that are similar to those of a real sample and do not reflect the actual and individual structure of the porous material.
The only method to obtain the actual structure of a porous material is by experiments. To date, X-ray industrial computed tomography (CT) is the best measuring instrument to reconstruct 3D models in nondestructive testing. Nikles et al. [11] built a 3D porous model using a CT scanning image and introduced Avizo software into the 3D reconstruction. Hu et al. [12] used CT to study the effects of pore microstructures on the anti-clogging performance of porous asphalt concrete. Khormani et al. [13] estimated the mechanical properties of concrete via CT scanning. However, it is costly to obtain micron-scale pore distributions via high-precision CT scanning. Furthermore, it is unrealistic to scan each porous material while constructing a 3D model. Focused ion beam (FIB) or scanning electron microscopy (SEM) is another affordable method for measuring microscopic structures; however, it can only capture the scanning image from the surface. Tomutsa and Radmilovic [14] optimized the accuracy of the slice reconstruction method using FIB. Lu et al. [15] analyzed the fluid lubricating film of a lubricant on the porous composite surface by SEM. Li et al. [16] obtained the composition and microstructure of a composite coatings using SEM. Xin et al. [17] used SEM to detect the microstructure of sandstone and obtained the evolution law of the surrounding rock microstructure of underground coal gasification. Occasionally, ion beams can destroy the microstructure of the porous material. However, SEM does not damage the surface and satisfies the measurement requirements of the pores. However, without the scanning images of internal layers, accuracy will be degraded in 3D reconstruction modeling.
Currently, deep learning is effective for image recognition. The standard convolutional neural network (CNN) contains an input layer, a convolution layer, a pooling layer, a fully connected layer, and an output layer. In 2012, Alex Krizhevsky [18,19] won the first rank of the Image Net competition using the Alex Net network model with an 84% precision rate. Subsequently, the CNN model became popular worldwide and has been widely used in feature extraction and image identification. In 2014, Ian Goodfellow reported the use of the generative adversarial network (GAN) [20,21]. This network comprises two main parts: the discriminant module D and the generating module G. The two modules compete with each other to produce optimized results, i.e., the image produced by G is sufficiently good and cannot be recognized by D. Combining the CNN network with the GAN yields the deep convolutional generative adversarial network (DCGAN), which will automatically obtain features from porous scanning images and then produce high-quality internal layer images that exhibit the features of the real porous material.
The purpose of reconstructing the 3D model is to obtain an accurate 3D flow state in a porous material. Permeability is a critical parameter that depicts the macroscopic reflection of microscopic pore structure characteristics. Wang et al. [22] obtained the permeability of the porous material of aerostatic porous bearing by the experiment. However, discrepancies in permeability exist between theoretically calculated and experimental results. Wang et al. [23] revised the formula for calculating permeability coefficient by including the effect of tortuosity without using an empirical constant. It improved the accuracy of calculations and is easy to popularize.
After obtaining the 3D structure model, the precision of the permeability calculation can be further improved and the anisotropy permeability quantitatively described. By applying flow analysis software such as Fluent and Avizo, the 3D simulation of flow fields in porous materials can be achieved. Sun et al. [24] used Avizo to reconstruct a multiscale and multi-mineral digital core model of low-permeability uranium-bearing sandstone, as well as characterized macroscopic and microscopic pore–throat structures of low-permeability uranium-bearing sandstone. Fan et al. [25] used Avizo to quantitatively identify the pores, coal matrix, and minerals in coal. However, the analysis of flow state inside materials is insufficient. Based on the computational fluid dynamic (CFD) method and dynamic mesh technology, Cui et al. [26,27] quantitatively studied the effects of manufacturing errors on the static characteristics and running accuracy of aerostatic porous bearings. Similar to Cui, most authors only solved the pressure distribution at the outlet and did not divulge the flow state inside porous materials. Hence, it is difficult to accurately predict the performances of bearings without knowing the physics inside the material.
Hence, we herein propose a high-accuracy, low-cost, and a few-sample method to reconstruct 3D porous models and obtain the 3D flow state inside porous materials. Section 2 describes the 3D reconstruction process using the DCGAN deep learning algorithm. In Section 3, the microcosmic parameters of the porous material and the permeability are calculated using a 3D model, which was verified experimentally. The gas flow in a porous material along different directions obtained using CFD software is presented in Section 4. Finally, the flow rate and pressure distribution in 3D flow fields with different inlet pressures are analyzed.
Section snippets
Obtaining surface scanning images
Although micro-CT affords a high precision of 1 nm and no damage to the material, it requires a precise instrument and is hence an expensive method. In comparison, SEM affords nanoscale resolution ratios and can be applied in high-vacuum, rough-vacuum, and humid environments. Furthermore, it provides simple 3D information of samples with different gray values. Fig. 1 shows the SEM equipment used in this paper.
The NeoScope JCM-5000 was used in this study. The voltage used in the experiment was
Diameter of pores and porosity
The porous material was built by sintering tiny graphite particles. The pore channel was the interspace between the particles. The best approach to learn the distribution of the pore channel is to separate the solid body from the pore of the model. In Avizo, this is achieved using an invert process. The pore space is defined as the “solid” body and the real solid is reduced. The original and pore space models are shown below in Fig. 16.
After isolating the pore space, the diameter of the pore
Analysis of flow field in 3D model
Although Avizo can simulate the flow state of the microstructure, the details of results and the varieties of boundary and calculation condition setting are not enough for further analysis. Therefore, such model need to be imported and analyzed in Fluent. Fluent is currently the most popular CFD software, which is widely used in the simulation analysis of fluids, heat transfer and chemical reactions. It is based on a finite volume method, using multiple solution methods and multi-grid
Conclusion
An innovative method for constructing the 3D model of a porous material and analyzing the internal flow field was presented herein. Cross-sectional images were obtained via SEM. After performing binarization and noise reduction, the images were input to a DCGAN system to generate intermediate images. The 3D model was built by combining stretching slices. Microcosmic morphology parameters and the internal flow field of porous materials were calculated. Some interesting conclusions are obtained,
CRediT authorship contribution statement
Chaoqun Zeng: Writing – original draft. Wei Wang: Writing – review & editing, Supervision. Xuhao Cheng: Software. Rui Zhao: Validation. Hailong Cui: Data curation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to thank the Fundamental Research Funds for the Central Universities (ZYGX2019J032), NSAF(U1830110), National Natural Science Foundation of China (52075506), Sichuan Provincial Science and Technology Development Special Fund Guided by the Central Government (2020ZYD019).
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2022, Materials Today CommunicationsCitation Excerpt :The scanning electron microscopy (SEM) is another alternative method. Zeng et al. [15] processed SEM images via convolutional deep learning neural network to construct a 3D microscopic model of porous graphite. The internal fluid flow state was simulated and the calculated permeability of the established 3D model was compared to the experimental values, verifying the model feasibility.