Makine Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.11779/1944

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Assessment of the Models for Predicting the Responses of Spherical Objects in Viscoelastic Mediums and at Viscoelastic Interfaces
(IOP Publishing Ltd, 2021) Körük, Hasan
Spherical objects, such as bubbles and spheres, embedded in mediums and atviscoelastic interfaces are encountered in many applications, including the determination ofmaterial properties. This paper assesses the models for predicting the responses of sphericalobjects in viscoelastic mediums and at viscoelastic interfaces used in various applications. Themodels are presented very compactly, and evaluations are performed based on the analyses ofthe models for the spherical objects in viscoelastic mediums and at viscoelastic interfaces. First,the models for predicting the static displacements of spherical objects are presented andassessed. After that, the models for predicting the dynamic responses of spherical objects arepresented and their dynamic behaviours are compared. Then, the models for the deformation ofthe medium around spherical objects and stress distribution are presented and evaluated. Themodels and evaluations presented in this study can be exploited in various applications,including biomedical applications.
The Minimum Variance Distortionless Response Beamformer for Damage Identification Using Modal Curvatures
(Association of American Publishers, 2023) Eroğlu, Uğurcan; Pau, A.
This study presents a damage identification procedure in beams based on the use of beamforming algorithms, which are mostly utilized in inverse problems of source identification and image reconstruction. We choose the modal curvatures as observed quantities and compare the performance of the Bartlett beamformer, minimum variance distortionless response (MVDR) processor, and of a conventional objective function based on the modal curvatures. By means of a set of experiments, we show that the MVDR processor can overcome some of the difficulties encountered with other estimators, especially in cases of slight damage, or damage located between two sensors. © 2023, Association of American Publishers. All rights reserved.
Citation - Scopus: 6
On the Difficulties in Manufacturing of Luffa Fibers Reinforced Biocomposites and Variations in Their Dynamic Properties
(Institute of Noise Control Engineering, 2016) Genç, Garip; Körük, Hasan
Defects in raw bio materials such as luffa plant effect the characteristics of the composites of these materials. These defects results in structural differences and large scattering mechanical properties such as density, damping and elasticity modulus. There are difficulties during the manufacturing of the composites from bio materials inherent to their nature. The major problems and restrictions encountered with the use of green luffa materials as reinforcement are studied in this study. First, the structural differences in the raw luffa plants are presented and the difficulties in their manufacturing are discussed. After that, the variations in measured modal parameters of luffa composites such as natural frequencies and loss factors and mechanical properties such as density and elasticity modulus are presented. Some solutions are provided to minimize the problems in manufacturing and identifying properties of luffa composites. The results show that the luffa composites can be produced with similar properties without any special selection of fibers to homogenize the batches of fibers for controlling the defects. However, a preliminary selection of fibers is required if the mechanical or dynamic properties of the luffa composites are desired to have small variations.
Technology of Mental Functional Representations as a First Stage of Conceptualization and Implementation of Complex Scientific Knowledge in Innovation Processes
(Transfer-Innovations, 2019) Dorantes-Gonzalez, Dante Jorge; Balsa-Yepes, Aldrin
In innovation processes, it is common to deal with highly cross-multidisciplinary topics. For example, an innovation process may integrate psychological, neuroscientific, biological and engineering disciplines, among many others dealing with bio-cybernetic systems. One specific type of those theories is related to cognitive processes, knowledge representation, and self-learning systems. Therefore, there is a need to easily and rapidly understand, as well as apply and share knowledge of complex theories by innovation managers, engineers, scholars, training practitioners, computational modelers, managers, and stakeholders, among others. In this regard, the present article provides with a graphical tool to represent complex cross- multidisciplinary theories, concepts and processes in a simple, concise, and logical manner, by using functional principles and graphical representations that have been successfully used in engineering and technology areas such as adaptive control systems, algorithmic flow charts, and computational cognitive neuroscience. Once described the models that have been typically used to represent and model knowledge and cognition, functional cognitive modeling is introduced, and then applied to represent and model complex cognitive theories from psychology and neuroscience such as Jean Piaget’s Theory of Intellectual Growth, Antonio Damasio’s Somatic Marker Hypothesis, and Dante Dorantes’ Soft Skills Model.
A Novel Business Model Frame for Innovative Startups - (may 12-14, 2017)
(World Conference on Technology, Innovation and Entrepreneurship, 2017) Dorantes-Gonzalez, Dante Jorge
The business model canvas has been used in business and entrepreneurship to sketch and frame the key points behind the development of a startup, and it was meant to strategically analyze and develop startups or documenting existing businesses. The business model canvas describes the firm’s value proposition, partners, resources, activities, customer relationships, distribution channels, customers, revenue streams and cost structure. However, when it comes to innovative startups, this template does not explicitly include innovation measures, no problem/opportunity formulation, or even such a basic component of a business model, as the profit formula. The present paper proposes a novel business model frame to visually and concisely sketch, besides accurately state traditional business concepts, key innovation concepts that any startup should integrate to be a game-changer in a competitive market. This new model is based on a combination of key principles of the theory of inventive problem solving (TRIZ) applied to business and management, such as multi-screen analysis of value-conflict mapping, trends of ideality of business system evolution positioning, among others; but also intellectual property, disruptive strategies, and open innovation, as well as startup metrics to describe the business differentiation and attractiveness to potential investors, incubators and accelerators.
Tri̇bi̇ne Vertical Axis Wind Turbine Efficiency Analysis
(TÜBİTAK, 2019) Dorantes-Gonzalez, Dante Jorge; Layegh Khavidaki, Seyed Ehsan
Proje konusu, savonius tip dikey eksenli rüzgar türbini verim kıyaslamasıdır. Proje kapsamında dört farklı yarim cembersel tasarimli model tasarlanmış ve karşılaştırılması yapılmıştır. Bu modeller bıçaklar arası açıklık ve bıçak sayısının model üzerindeki verim etkisini gözlemlemeyi hedef almıştır.
Citation - WoS: 7
Citation - Scopus: 9
Displacement of a Bubble Located at a Fluid-Viscoelastic Medium Interface
(Acoustical Society of America, 2019) Körük, Hasan; Choi, James J.
A model for estimating the displacement of a bubble located at a fluid-viscoelastic medium interface in response to acoustic radiation force is presented by extending the model for a spherical object embed- ded in a bulk material. The effects of the stiffness and viscosity of the viscoelastic medium and the amplitude and duration of the excitation force on bubble displacement were investigated using the proposed model. The results show that bubble displacement has a nonlinear rela- tionship with excitation duration and viscosity. The time at which the steady state is reached increases with increasing medium viscosity and decreasing medium stiffness.
Citation - Scopus: 4
Investigation of the Motion of a Spherical Object Located at Soft Elastic and Viscoelastic Material Interface for Identification of Material Properties
(Academic Enhancement Department, King Mongkut's University of Technology North Bangkok, 2024) Körük, Hasan; Pouliopoulos, A.N.
Measuring the properties of soft viscoelastic materials is challenging. Here, the motion of a spherical object located at the soft elastic and viscoelastic material interface for the identification of material properties is thoroughly investigated. Formulations for different loading cases were derived. First, the theoretical models for a spherical object located at an elastic medium interface were derived, ignoring the medium viscosity. After summarizing the model for the force reducing to zero following the initial loading, we developed mathematical models for the force reducing to a lower non-zero value or increasing to a higher non-zero value, following the initial loading. Second, a similar derivation process was followed to evaluate the response of a spherical object located at a viscoelastic medium interface. Third, by performing systematic analyses, the theoretical models obtained via different approaches were compared and evaluated. Fourth, the measured and predicted responses of a spherical object located at a gelatin phantom interface were compared and the viscoelastic material properties were identified. It was seen that the frequency of oscillations of a spherical object located at the sample interface during loading was 10–15% different from that during unloading in the experimental studies here. The results showed that different loading cases have immense practical value and the formulations for different loading cases can provide an accurate determination of material properties in a multitude of biomedical and industrial applications. © 2023 King Mongkut’s University of Technology North Bangkok. All Rights Reserved.
Citation - WoS: 8
Citation - Scopus: 9
Identification of Crack Noises in Household Refrigerators
(Elsevier, 2015) Körük, Hasan; Arısoy, Ahmet
The crack noises propagating from a refrigerator disturb residents in a household; however, the reasons behind the mechanisms of such noises have not been identified yet. In this study, the crack noises in modern household refrigerators are identified and their root causes are explored. The appropriate parameters for overall and Fourier analyses are first determined and the noise characteristics of typical household refrigerators under various conditions are presented. Then, a special test rig providing remote control of the subcomponents including the compressor, fan and heater is designed and structural acceleration and sound pressure measurements inside and outside the test rig in a quiet room are performed. The acoustic and vibration measurements are conducted under various conditions by separately controlling each subcomponent. The crack noises in typical household refrigerators are identified and their root causes are explored by using the results of the overall and Fourier analyses. Some solutions to minimize the crack noises in household refrigerators are also summarized.
Citation - WoS: 4
Citation - Scopus: 4
Application of Ultrasonic Vibrations for Minimization of the Accumulation of Limescale in Steam Irons
(Elsevier, 2018) Körük, Hasan; Şanlıtürk, Kenan Yüce; Serenli, Muzaffer
The accumulation of limescale in steam irons can significantly reduce the ironing efficiency. It is this problem that inspired us to introduce ultrasonic vibrations to irons in order to minimize limescale accumulation. This study describes a methodology for designing, modelling and optimizing an iron fitted with an ultrasonic exciter in an attempt to minimize limescale accumulation. In our methodology, first, an experimental demonstration of the potential benefits of ultrasonic vibrations in steam irons was conducted, using two existing irons, one of which was equipped with an ultrasonic exciter. Having confirmed the benefits, an experimental iron was designed and then optimized to maximise ultrasonic vibrations using finite element analyses within a predefined frequency range. To validate the results of the finite element analyses, a prototype iron base was built, and forced vibrations of this prototype, at ultrasonic frequencies ranging from 35 to 40 kHz, were measured using a laser vibrometer. The results of the theoretical and experimental vibration analyses as well as the physical experiments on the steam irons indicate that it is possible for ultrasonic vibrations to be utilized in irons to minimize the accumulation of limescale.
Citation - Scopus: 2
Strong Transient Effects of the Flow Around a Harmonically Plunging Naca0012 Airfoil at Low Reynolds Numbers
(Springer, 2015) Yücel, S. Banu; Şahin, Mehmet; Ünal, M. Fevzi
Abstract The flow pattern around a NACA0012 airfoil undergoing harmonic plunging motion corresponding to the deflected wake phenomenon reported by Jones and Platzer (Exp Fluids 46:799–810, 2009) is investigated in detail using direct numerical simulations. An arbitrary Lagrangian–Eulerian formulation based on an unstructured side-centered finite volume method is utilized in order to solve the incompressible unsteady Navier–Stokes equations. The Reynolds number is chosen to be 252, and the reduced frequency of plunging motion (k = 2?fc/U?) and the plunge amplitude non-dimensionalized with respect to chord are set to be 12.3 and 0.12, respectively, as in the experimental study of Jones and Platzer (2009). The present numerical simulations reveal a highly persistent transient effect, and it takes two orders of magnitude larger duration than the heave period to reach the time-periodic state. In addition, the three-dimensional simulation reveals that the flow field is three-dimensional for the parameters used herein. The calculation reproduces the deflected wake and shows a good agreement with the experimental wake pattern. The instantaneous vorticity contours, finite-time Lyapunov exponent fields and particle traces are presented along with the aerodynamic parameters including the lift and thrust coefficients.
Citation - WoS: 12
Citation - Scopus: 12
Mechanics of Milling 48-2 Gamma Titanium Aluminide
(Elsevier, 2020) Layegen, S. Ehsan; Lazoğlu, İsmail; Hussain, Abbas; Arrazola, Pedro-J.; Subaşı, Ömer; Yavaş, Çağlar; Lazcano, Xabier; Öztürk, Çağlar; Yiğit, İ. Enes; Aristimuno, Patxi-X.
Accurate and fast prediction of cutting forces is important in high-performance cutting in the aerospace industry. Gamma titanium aluminide (gamma-TiAl) is a material of choice for aerospace and automotive applications due to its superior thermo-mechanical properties. Nevertheless, it is a difficult to machine material. This article presents the prediction of cutting forces for Ti-48Al-2Cr-2Nb (48-2-2) gamma-TiAl in milling process using orthogonal to oblique transformation technique. The novelty of this paper lies in reporting the orthogonal database of 48-2-2 gamma-TiAl. Fundamental cutting parameters such as shear stress, friction angle and shear angle are calculated based on experimental measurements. Friction coefficients are identified for two different coating conditions which are AlTiN, and AlCrN on carbide tools. Predicted results are validated with the experimental cutting forces during end milling and ball-end milling operations for different cutting conditions. The simulated results showed good agreement with the experimental results, which confirms the validity of the force model
Citation - WoS: 19
Citation - Scopus: 26
Jute and Luffa Fiber-Reinforced Biocomposites: Effects of Sample Thickness and Fiber/Resin Ratio on Sound Absorption and Transmission Loss Performance
(Taylor & Francis, 2021) Şanlıtürk, Kenan Y.; Genç, Garip; Körük, Hasan; Özcan, Ahmet Cihan
The acoustic properties of natural fiber-reinforced composites should be identified before using these materials in various engineering applications including sound and vibration isolation. This study investigates the effects of sample thickness and fiber/resin ratio on the acoustic performance of jute and luffa fiber-reinforced biocomposites. For this purpose, jute and luffa composite samples with different thicknesses and fiber/epoxy ratios are manufactured and their sound absorption coefficients (SACs) and transmission losses (TLs) are determined using impedance tube method. Thickness-dependent tendencies of the SACs and TLs of jute and luffa composites for low-, medium-, and high-frequency ranges are identified. The effect of fiber/epoxy ratio on the acoustic properties of jute and luffa composites as a function of frequency are determined. Furthermore, the SACs and TLs of some natural fiber-based samples with different thicknesses are predicted using mathematical models and the theoretical and experimental results are compared and evaluated.
Citation - WoS: 3
Citation - Scopus: 3
Characterization of Viscoelastic Materials Using Free-Layered and Sandwiched Samples: Assessment and Recommendations
(Polish Physical Society, 2015) Özer, Mehmet Sait; Körük, Hasan; Şanlıtürk, Kenan Yüce
Viscoelastic materials are widely used in many applications in practice. However, determination of the elastic and damping properties of these materials is quite difficult in the sense that the identified results may contain high degree of uncertainty. The characterization of viscoelastic materials using the Oberst beam method, based on non-contact excitation and response measurements, is revisited in this paper. The effects of signal processing parameters such as frequency resolution in Frequency Response Function (FRF) measurements, as well as the effects of various single-degree-of-freedom modal analysis methods, including circle-fit, half-power and line-fit are investigated first. Then, the modal loss factors, Young's modulus and shear modulus of some sample viscoelastic materials are identified using both the free-layered and sandwiched samples. The results obtained from different tests are compared, discussed and some recommendations are made so as to identify the damping and elastic properties of typical viscoelastic materials with better accuracy. Analyses of a large number of FRF measurements show that the selection of the appropriate signal processing parameters and the use of appropriate modal analysis method can be very significant during the identification of viscoelastic materials. By following the approach presented in this paper, the damping and elastic properties of viscoelastic materials can be identified with better accuracy using either free-layered or sandwiched samples. The material properties obtained by this approach can be used for developing valid structural models and/or for damping optimization purposes.
Citation - WoS: 11
Citation - Scopus: 14
Modelling Small and Large Displacements of a Sphere on an Elastic Half-Space Exposed To a Dynamic Force
(IOP Publishing, 2021) Hasan Körük
Spheres at medium interfaces are encountered in many applications, including in atomic force microscopy or indentation tests. Although the Hertz theory describes the contact mechanics between an elastic sphere and an elastic half-space for static loading and small deformations very well, there is a need to consider the density of the medium, the mass of the sphere and the radiation damping for dynamic loading to obtain reliable results. In this study, an analytical model for predicting the small and large displacements of a sphere on an elastic half-space exposed to a dynamic force is developed. For this purpose, after summarizing a mathematical model that has recently been proposed for the sphere at a medium interface, a finite element model for the sphere at an elastic interface is developed. Based on the comparison of the mathematical and finite element models, an improved analytical model for the sphere at an elastic interface is developed. In addition to considering the elastic properties of the medium and the size of the sphere, the model developed here takes into account the density of the medium, the mass of the sphere, and the radiation damping, and the model is valid for small and large sphere displacements. The developed model can be used to understand the dynamic responses of spherical objects at medium interfaces in practical applications. Furthermore, the proposed model is a remarkable tool for undergraduate and graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres at medium interfaces. © 2021 European Physical Society.
Citation - WoS: 24
Citation - Scopus: 26
Acoustic Particle Palpation for Measuring Tissue Elasticity
(American Institute of Physics, 2015) El Ghamrawy, Ahmed; Körük, Hasan; Choi, James J; Pouliopoulos, Antonios N
We propose acoustic particle palpation—the use of sound to press a population of acoustic particles against an interface—as a method for measuring the qualitative and quantitative mechanical properties of materials. We tested the feasibility of this method by emitting ultrasound pulses across a tunnel of an elastic material filled with microbubbles. Ultrasound stimulated the microbubble cloud to move in the direction of wave propagation, press against the distal surface, and cause deformations relevant for elasticity measurements. Shear waves propagated away from the palpation site with a velocity that was used to estimate the material’s Young’s modulus.
Study of Tuned Mass Damper for Attenuating Skyscraper Oscillations Through Project-Based Learning
(Filodiritto Publisher, 2019) Şengül, Özden; Dorantes-Gonzalez, Dante Jorge
The intention of the project was to introduce a complex real-life engineering problem in an easy manner to sophomore students, namely, the topic of a tuned mass damper (TMD). Even though TMD is a multiple-degree-of-freedom vibration problem seen only in advanced university courses, the phenomenon of earthquake effects on buildings is easy to understand. In order to ease the complexity, the multi-degree-of-freedom mathematical problem was converted into a single degree of freedom, such as the behavior of a vertical single-mass cantilever beam. Through a do-it-yourself project to be done in home conditions, students are introduced to the topic of mechanical vibrations via seismic action on tall buildings. Two sections of the "Engineering Mechanics: Dynamics" course, with an overall number of 58 students, participated in the project. The project develops critical thinking and inquiry skills by designing and constructing the physical prototype of a building-like structure and its corresponding tuned mass damper; conducting an experiment under certain restrictions to test the stabilizing effect of the damper after an initial displacement; learning a proper software application to graph and measure underdamped oscillations; calculating corresponding vibration parameters; as well as analyzing and discussing experimental results. Students approach the problem of mass-damper tuning by means of trial and error, an on-purpose strategy to add fun and gambling to the process, to enthusiastically compete for the best performance in terms of efficiency of attenuation. Data were collected from direct observation, surveys, reports and presentations. The results showed that students positively and enthusiastically responded at all project stages and with a better understanding of the phenomenon and engagement in comparison with previous students of the same course without project. The impact of the project on students’ engagement and implications for engineering education are discussed.
Biyomalzemelerin Akustik ve Mekanik Özelliklerinin Arastırılması
(2020) Genç, Garip; Körük,Hasan
Bu proje kapsamında, jüt lifleri ve çesitli luffa lifleri kullanılarak, farklı kalınlıklarda reçinesiz (hiçbir reçine kullanılmayan) homojen ve hibrit jüt ve luffa yapılar ve yine farklı kalınlıklarda ve farklı lif/reçine oranlarında reçineli homojen ve hibrit jüt ve luffa yapılar üretilerek, bu yapıların akustik ve mekanik özellikleri ile ilgili kapsamlı bir resmin ortaya konulması hedeflenmistir. Bu kapsamda kullanılan yöntemler/sonuçlar su sekildedir: (i) Akustik testler için farklı kalınlıklarda hem reçinesiz hem de farklı lif/reçine oranlarına sahip reçineli homojen ve hibrit numuneler üretilmistir. Empedans tüp yöntemi kullanılarak bu akustik numunelerin ses yutma ve ses iletim kaybı gibi akustik özellikleri deneysel olarak belirlenmistir. Homojen ve hibrit kompozit yapıların akustik performansları karsılastırılmıstır. Sonuçta, kalınlık ve lif/reçine oranın bu yapıların akustik özellikleri üzerindeki etkisi ortaya konulmustur. (ii) Farklı frekans aralıkları için kalınlıgın ve lif/reçine oranının bir fonksiyonu olarak ölçülen akustik verilere egriler uydurularak, malzemelerin akustik özelliklerini belirlemeye yönelik basit ampirik modeller ortaya konulmustur. Dahası, malzemelerin ses yutma katsayıları Delany-Bazley ve Johnson- Champoux-Allard gibi teorik modeller kullanılarak tahmin edilmis ve sonuçlar deneysel sonuçlarla karsılastırılmıstır. Benzer sekilde, numunelerin ses iletim kayıpları teorik olarak hesaplanmıs ve deneysel sonuçlarla karsılastırılmıstır. Sonuçta, bu yapıların tasarımında akustik amaçla kullanılabilecek ampirik ve teorik modeller ortaya konulmustur. (iii) Titresim testleri için farklı kalınlık ve lif/reçine oranlarına sahip reçineli homojen ve hibrit numuneler üretilmis, üretilen bu yapılar üzerinde akustik ve yapısal frekans tepki fonksiyonları ölçülmüs ve aynı yapıların teorik modellerinden yararlanılarak malzemelerin elastik ve sönüm gibi mekanik özellikleri belirlenmistir. Homojen jüt ve luffa kompozit yapıları hem izotropik varsayılarak hem de bu yapıların yöne baglı elastik özelliklerinin olması durumu dikkate alınarak modellenmislerdir. Sonuçta, kalınlık ve lif/reçine oranın mekanik özellikler üzerindeki etkisi ortaya konulmus ve pratikte bu yapıların tasarımı için kullanılabilecek bazı yaklasımlar ortaya konulmustur.
Citation - Scopus: 9
Investigation of the Sound Absorption and Transmission Loss Performances of Green Homogenous and Hybrid Luffa and Jute Fiber Samples
(King Mongkut’s University of Technology North Bangkok, 2021) Genç, Garip; Şanlıtürk, Kenan Y.; Körük, Hasan; Özcan, Ahmet Cihan
In order to promote the use of natural fibers in noise and vibration applications, the properties of these structures should be fully identified. The sound absorption coefficients (SACs) and transmission losses (TLs) of green luffa fiber samples are thoroughly investigated and their acoustic performances are compared with the acoustic performances of green homogenous jute and hybrid jute/luffa fiber samples in this study. For this purpose, green homogenous luffa and jute fiber samples and their green hybrid fiber samples with different thicknesses (10, 20, 30, and 40 mm) are produced and their SACs and TLs are determined using the impedance tube method. First, the methods for the experimental identification of acoustic properties are presented and the variations in the measured acoustic properties are identified. After that, the effects of sample thickness on the acoustic performances of homogenous luffa as well as jute samples and their hybrid fiber samples as a function of frequency are explored. The thickness-dependent tendencies of the SACs and TLs of homogenous and hybrid luffa and jute fiber samples for low, medium and high frequency ranges are determined. Then, the acoustic performances of the homogenous and hybrid luffa and jute samples are compared and evaluated. The results and analyses for the acoustic properties of homogeneous luffa and jute fiber samples and their hybrid fiber samples for a variety of thicknesses and different frequencies presented here can be used to design homogenous as well as hybrid luffa and jute fiber structures in practical applications.
Citation - WoS: 10
Citation - Scopus: 20
Assessment of the Measurement and Prediction Methods for the Acoustic Properties of Natural Fiber Samples and Evaluation of Their Properties
(Taylor & Francis, 2021) Körük, Hasan
Although some studies have been conducted to show how natural fibers canreplace synthetic materials, the use of many natural fibers is still limited. Onthe other hand, the use of natural fibers can become very common in manyapplications once their performance is fully understood. This paper aims topresent a critical assessment of the acoustic properties of natural fibersamples. First, the methods commonly used for the measurement and prediction of the acoustic properties of natural fiber samples are determined.Second, the common techniques for measuring sound absorption coefficients (SACs) and sound transmission losses (STLs) are presented, and theiradvantages and limitations are evaluated. After that, the models commonlyused for the prediction of acoustic properties are presented. Then, the SACsof many natural fiber samples are presented along with the thickness, bulkdensity and flow resistivity of the samples. Furthermore, the SACs of thesamples are normalized using sample thickness and bulk density, and thesound absorption performance of the fiber samples is evaluated. Based onthe results of many natural fiber samples, an empirical model for estimatingthe SACs of natural fiber samples is presented. Finally, the STLs of someporous natural fiber samples are presented.