.» Since 1955 _ \ Strojniški vestnik Journal of Mechanical Engineering ■ » M J4 ж™ « * w ««an i » >■ T ш Tl* .Vi * ij В Strojniški vestnik - Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Grafex, d.o.o., printed in 310 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Branko Širok University of Ljubljana, Faculty of Mechanical Engineering, Slovenia International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, University of Engineering and Technology, Pakistan Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, UL, Faculty of Mechanical Engineering, Slovenia Franci Čuš, UM, Faculty of Mechanical Engineering, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Igor Emri, UL, Faculty of Mechanical Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, UL, Faculty of Mechanical Engineering, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, UM, Faculty of Mechanical Engineering, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, UL, Faculty of Mechanical Engineering, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, UL, Faculty of Mechanical Engineering, Slovenia Gorazd Lojen, UM, Faculty of Mechanical Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mechanical Engineering, Slovenia George K. Nikas, KADMOS Engineering, UK José L. Ocana, Technical University of Madrid, Spain Miroslav Plančak, University of Novi Sad, Serbia Vladimir Popović, University of Belgrade, Faculty of Mech. Eng., Serbia Franci Pušavec, UL, Faculty of Mechanical Engineering, Slovenia Bernd Sauer, University of Kaiserlautern, Germany Rudolph J. Scavuzzo, University of Akron, USA Arkady Voloshin, Lehigh University, Bethlehem, USA Vice-President of Publishing Council Jože Balič University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: Image depicts the entire technology chain for inspection of periodically corrugatted plate heat exhangers (CPHE): a fabricated corrugated plate for fluid flow visualization, a checkerboard pattern distorsion introduced by corrugation, it's estimation by image processing algorithm and streamlines obtained by particle tracking and distortion compensation algorithm. In foreground: a steel-mould for hot-embossing of transparent corrugatted plate. Courtesy: Jaka Pribošek, University of Ljubljana, Faculty of Mechanical Engineering, Slovenia ISSN 0039-2480 General information Strojniški vestnik - Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue). 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Strojniški vestnik - Journal of Mechanical Engineering is available on http://www.sv-jme.eu, where you access also to papers' supplements, such as simulations, etc. Contents Strojniški vestnik - Journal of Mechanical Engineering volume 62, (2016), number 1 Ljubljana, January 2016 ISSN 0039-2480 Published monthly Papers Jaka Pribošek, Miha Bobič, Iztok Golobič, Janez Diaci: Correcting the Periodic Optical Distortion for Particle-Tracking Velocimetry in Corrugated-Plate Heat Exchangers 3 Grzegorz Budzik, Jan Burek, Anna Bazan, Pawel Turek: Analysis of the Accuracy of Reconstructed Two Teeth Models Manufactured Using the 3DP and FDM Technologies 11 Ning Zhang, Minguan Yang, Bo Gao, Zhong Li, Dan Ni: Investigation of Rotor-Stator Interaction and Flow Unsteadiness in a Low Specific Speed Centrifugal Pump 21 Veysel Alankaya, Fuat Alargin: Using Sandwich Composite Shells for Fully Pressurized Tanks on Liquefied Petroleum Gas Carriers 32 Tomaž Pepelnjak, Mladomir Milutinović, Miroslav Plančak Dragiša Vilotić, Saša Randjelović, Dejan Movrin: The Influence of Extrusion Ratio on Contact Stresses and Die Elastic Deformations in the Case of Cold Backward Extrusion 41 Marek Magdziak: An Algorithm of Form Deviation Calculation in Coordinate Measurements of FreeForm Surfaces of Products 51 Jixin Wang, Hongbin Chen, Yan Li, Yuqian Wu, Yingshuang Zhang: A Review of the Extrapolation Method in Load Spectrum Compiling 60 Strojniški vestnik - Journal of Mechanical Engineering 62(2016)1, 3-10 © 2016 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2015.3125 Original Scientific Paper Correcting the Periodic Optical Distortion for Particle-Tracking Velocimetry in Corrugated-Plate Heat Exchangers Jaka Pribošek1* - Miha Bobič2 - Iztok Golobič1 - Janez Diaci1 1 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2 Danfoss Trata, Slovenia To improve current methods for the experimental validation of numerical simulations in corrugated-plate heat exchangers (CPHEs), a full-field quantitative velocimetry of fluid flow is required. This paper investigates the application of particle-tracking velocimetry (PTV) to modified CPHEs. For this, an experimental CPHE unit with a transparent, corrugated upper plate was built. We show that by viewing through a corrugated, refractive interface, a complex periodic optical distortion is introduced, that affects and corrupts the estimated particle trajectories. As this problem cannot be addressed using existing calibration techniques, we propose a novel calibration algorithm for periodic optical distortion. The algorithm relies on the automatic detection of nonlinear distortion using a checkerboard target place within the CPHE unit. The calibration is first made on a coarse grid and subsequently refined by a set of low-order periodic basis functions in order to seize the periodic nature of the deformation field. The proposed algorithms have been applied to a test case with known, uniform particle velocities in order to demonstrate the performance. When applied to a real case, a reduction in the systematic positional error by 35 % was demonstrated. Keywords: optical distortion, corrugated-plate heat exchanger, particle-tracking velocimetry Highlights • We modified corrugated-plate heat-exchanger units to allow fluid-flow visualization and applied a particle-tracking velocimetry to measure the flow. • We addressed the problem of periodic optical distortion due to the view through corrugated refractive interfaces. • A novel calibration method allowing for periodic optical distortion has been introduced. • Experimental results using the proposed algorithms show a reduction in the systematic error by 35 %. 0 INTRODUCTION Plate heat exchangers (PHEs) have recently been gaining more attention owing to their high overall heat-transfer coefficient, compactness and implementation flexibility. As such, they are finally replacing the traditional tubular designs in various process applications [1]. Recent improvements to heat-transfer efficiency, a higher heat-transfer-area-to-volume ratio and a lower pressure drop have been achieved by the micro-corrugation of PHE surfaces -the so-called corrugated PHE (CPHE) [2]. Design optimization of the corrugated surface is crucial for tailoring this technology for various applications. So far, very few studies have addressed the optimization problem. Such optimizations of PHEs were mainly studied using CFD simulations [3]. However, the validation of these CFD simulations has mainly been limited to the overall pressure drop and to inlet/outlet temperature measurements [4]. To further extend the validation possibilities, the pressure distribution has recently been measured in a CPHE unit [5]. IR thermography has been applied to obtain a deeper understanding of the temperature fields and flow patterns inside the PHE [6] and [7]. In terms of a CFD validation, the existing methods still have a very limited scope. The lack of experimental systems aimed at an internal flow inspection was first addressed by Focke and Knibbe [8]. In this study one of the plates of a plate heat exchanger was replaced by its transparent acrylic equivalent, enabling the visualization of the flow patterns inside the PHE. This pioneering study was able to draw many important conclusions and influenced many others that utilized similar experimental setups for the purpose of optimizing CFD codes [9] and [10] or experimental studies on fluid-flow phenomena [11] to [13]. Although most of the reported experimental units enable fluid-flow monitoring, no studies on the velocity fields inside PHEs can be found in the literature. One of the main reasons for this is the challenging system calibration due to the complex optical distortion that occurs in such situations. Up to now, different optical setups, such as telecentric lenses and Scheimpflug camera configurations [14] to [16], have been exploited to minimize the distortion and compensate for the projection error. In this way, the calibration of a PTV system is fairly straightforward and simple image registration or scaling may be needed. This approach, however, does not allow for the compensation of the errors that arise from viewing through refractive interfaces. An analytic study of viewing through a refractive freeform optical interface is presented in [17], while others employ ray-tracing techniques. A generalized system-calibration procedure for optical setups used in particle velocimetry was proposed by Soloff et al. [18], followed by various improvements [19] to [22], as well as various self-calibrating schemes [23]. Existing techniques exploit either polynomial or rational models to model the optical distortion, which is generally sufficient to account for the distortion introduced by either the camera optics or the refractive interfaces, such as optical flats or cylindrical pipes. In the case that more complex, arbitrary distortion occurs, the refractive-matching technique is usually employed to avoid the distortion-compensation problem [24] and [25], since no general optical-distortion models accounting for such cases exist. Extending the work of Soloff et al. in this direction has also been suggested as a further desirable improvement to the PIV and PTV methods [26], although no further studies could be found, to the best of our knowledge. In an experimental CPHE system, the upper plate is transparent and corrugated periodically, which results in periodic, freeform optical distortion. In our study, we provide experimental evidence that the results from the PTV in the CPHE are highly erroneous when left uncalibrated. In such a situation, the corrugation of the CPHE is small, implying that extremely dense calibration patterns are to be used for the calibration in order to provide sufficient sampling. This often has many practical limitations in regions where total internal reflection due to oblique interfaces occurs, which significantly limits the maximum density of the calibration pattern. This paper provides a novel method for estimating the periodic optical distortion using a coarse grid pattern, subsequently refined using a discrete cosine transform. This allows us to capture the periodic nature of the deformation fields and still keep a coarse calibration pattern. We believe the proposed study is a first step towards a quantitative fluid-flow inspection inside a CPHE, which would be of great help in the validation of the CFD corrugation optimization. surface is first fabricated from 0.5-mm stainless-steel sheet by means of microforging technology. The corrugation of the plate is two-dimensional with an amplitude of 1.5 mm and a period of 7 mm in both the X and y directions fabrication of its transparent counterpart, avoiding the need for costly master-tool fabrication. The master, together with the PMMA sheet, is then preheated to 150 °C in a ventilated oven. The hot PMMA is then sandwiched between the negative master, on the one side, and the additional glass plate, on the other, and then pressed in a manual clamping press with a 35-kN clamping force and left for 25 min to cool. Next, the corrugated stainless-steel plate is inserted into the CNC-cut aluminum holder with integrated inlet and outlets and glued with an epoxy that has a high level of aluminum content for a better heat transfer. The pressure drop across the heat exchanger can be monitored with a pressure sensor (PS). The sensor data is acquired with an Agilent DS 34970A connected to a personal computer. Fig. 1. a) Experimental system for fluid-flow visualization inside the CPHE, and b) fabricated CPHE unit 1 METHODS Our experimental corrugated heat-exchanger unit (Fig. 1) is based on the experimental designs reported in [8], [10] and [11], where the fluid flow is inspected at the cold side of the heat exchanger, and the flow is visualized through a transparent plate. A corrugated The fluid flow is monitored using a high-speed camera (Camelopard EVO, Optomotive L.t.d.), featuring 360 FPS streaming for an image size of 2048^1088 pixels and a pixel size of 5.5 ^m. The camera was equipped with a standard 16-mm C-mount lens. Special attention was given to ensure the proper lighting conditions for the corrugated plate, which seems to be a problem that has not received much attention in previous studies [8] and [27]. In order to prevent unwanted shadows and reflections as much as possible, we use homogenous lightning conditions. This was achieved using an improvised lightning tunnel as a variation of the classic Ulbricht Sphere illuminated with eight high-power LED diodes (LD), yielding a high-quality image. The corrugated, transparent plate in contact with the fluid beneath the plate is a composite optical element that refracts the incident light. If the effects of pressure and temperature are neglected, the light travels in straight rays. ®hmin Fig. 2. a) Three particles at different lateral positions along the same optical ray b) Error reduction by distortion compensation Fig. 2 depicts three particles, Ph0 , Phmax and Phmin , along the same optical ray, that all correspond to the same image position on the camera. Regarding their actual position, the errors Em , E^ and ЕШп are present in the case of Phmax and Phmin , respectively. The error curve is linear, given by E (h) = kh + eh0, and represented by the upper linear curve in Fig. 2b. By subtracting the displacement of Ph0 , the error curve is shifted to zero (see the lower linear curve of Fig. 2b) modelled as E (h ) = kh + eh0. What interests us the most, however, is how the calibration affects the total error. This is formulated as an integral of the product of E(h) and the probability p(h) that a particle can be found at one particular height hmax Etot = J E(h)p (h)dh. Under the assumption of hmin uniformly spread particles in the fluid, the probability p(h) equals the normalized velocity distribution. By inserting the error functions, we estimate the difference between the corrected and uncorrected total hmax errors E,0, - EM = J ehcVnom (h )dh , which for a hmin positive definite function Vnorm (h) is always greater than zero. In highly distributed, turbulent flows, such as in a CPHE with Re > 4000, the effects of surface friction are less significant and the velocitydistribution function can be approximated using a uniform function (Fig. 2), for which the corresponding probability function sums to a unit one. As such, by means of a single plane planar calibration we reduced the total error of all the particles, regardless of their height, at least for the term eh0 (hmax-hmin), or greater in the case of less turbulent flows. 1.1 Optical Distortion Correction Given the two different domains, the Image domain 1 (observed) and the Cartesian domain С (hidden state), we refer Jo the mapping I ^ C as direct mapping, and C ^ I as the inverse mapping between both domains. We estimate the unknown mappings by observing a fiducial checkerboard pattern through the corrugation plate placed at the middle of the cavity, formed by both plates of the corrugated-plate heat exchangers, yielding exact point-to-point correspondences between both domains. 1.2 Image Processing We have developed a custom algorithm for an automatic mapping estimation based on image processing of the distorted view of a fiducial pattern (Fig. 3). For this a checkerboard pattern was employed, since by considering both white and black regions, a four-times-higher information density is obtained compared to conventional dot patterns. First, an adaptive threshold is applied in order to binarize the image and to eliminate the effects of the illumination gradient that may occur. This was achieved with a 10*10 window, where the local threshold was set according to the average intensity of that region. After the binarization we apply a morphological erosion to isolate the connected white regions. Two-pass connected component labelling is then applied for their segmentation, allowing us to calculate the centroid point of each blob i. The very same procedure is then repeated for the segmentation of the black regions, whereas the morphological erosion was replaced by dilation. The detected feature points were then meshed using Delaunay triangulation. To each triangle, a circumcircle is calculated. The centroid of the circumcircle is then used to define the nearest neighboring triangle. The two triangles are combined to form a quadrilateral shape, which is then ordered in a grid using the recursive grid-finding algorithm. This grid-finding algorithm starts from an initial, randomly chosen 3x3 neighborhood, which is inserted into an empty matrix M. From the remaining neighborhoods in the set, the one with at least one matching node is chosen and inserted into M such that the matching elements overlap. We repeated this procedure in a recursive manner until all the neighborhoods were assigned to M. The result of the represented segmentation and meshing is the formation of point-to-point correspondences with a Cartesian uniform mesh required to estimate the optical distortion. Final mesh i Fig. 3. The complete calibration algorithm 1.3 Rigid-Body Registration By analyzing the point-to-point correspondences between both domains, we attempt to estimate the mapping between them. Fig. 4 shows the major steps of the nonlinear spatial deformation field estimation. Let p, be the observed vertices in the Image domain and qi the corresponding hidden vertices in the Cartesian domain of the same fiducial pattern, for i = 1, ..., N. We may then split the mapping T we are searching for into a rigid-body transformation term H (camera extrinsic parameters) and a nonlinear deformation field St induced by the optical distortion of the corrugated plate qi=H pi + Si . Using the homogenous coordinate notation for the given point-to-point correspondences pi and qi , i = 1, ..., N we have: 1xi C sx cosa -sy sina tx Pxi I C qyi = sx sina sy cosa ty Pyi + Syi . (1) i 0 0 1 1 0 Assuming an isotropic scaling sx=sy=s we can reformulate the following least-square system, minimizing the Si terms, yielding a rigid-body registration that accounts for the camera pose (a, tx, ty), and the optical magnification (s): Px1 Pyl Px 2 Py 2 Pxn Pyn - Pyl 1 0 Pxl 0 1 P y 2 1 0 Px 2 0 1 -Pyn 1 0 P„ 0 1 s cos(a) s sin(a) 4x1 qy1 4x 2 4y 2 Qxx 4yn The above system Ax = y is solved for x using the singular value decomposition (SVD) and yields the elements of the rigid-body transformation matrix H. This then allows the characterization of the nonlinear terms induced by the optical distortion as the difference between q and p': 1xi Pxi' Syi qyi Pyi' (3) where p' denotes the p being transformed to С : ^ xì C qxi C Sy, = qyi - 0 i 5 cosa -5 srna 5 sina 5 cosa 0 0 1 (4) where Sxi and Syi then represent the required deformation field, evaluated for the region i. 3.3 Parametrization of the Deformation Fields In order to ensure good sampling of the deformation field, we strive to keep the fiducial calibration pattern as dense as possible, while still maintaining good performance and robust segmentation. Regardless of all the efforts, the obtained sampling frequency of the optical distortion remains very low. However, since the structures of the corrugated plate have a periodic geometry, the deformation field induced by the optical distortion will be periodic. Since we sample the displacement field with a sampling frequency that is a non-integer multiple of the fundamental frequency of the periodic structures, we may exploit this fact to further improve the estimation of the optical distortion. We do this by modelling a spatial deformation vector field as a linear combination of some periodic basis functions. The basis function used here are a few frequency components (< 300) of the two-dimensional direct cosine transform (2D DCT) of the input deformation field. The transform of the variable (kj,k2) in the Cartesian domain to F(k1,k2) in the frequency domain for the 2D DCT is given in [28]: t x t y N1-IN1 -1 { } F(kPk2)=a(k)a(k2)(ki,k2) « =0 «2 =0 cos n(2n1 + l)k1 ^ ( n(ln2 + l)k2 —---— cos —---— 2 N1 2 N (5) for k = 0, 1, ..., N1 -1 and k2 = 0, 1, ..., N2-1 and a(k) defined as: a (k ) = (n' fork = 0 (6) -, fork = N -1 Analogously to Eq. (6), we write the same for the transformation of sj0*1 (kp k2). Using the 2D DCT, we enforce the periodicity on the estimated "sparse" deformation field by blocking some of the lowest and highest frequency components. Using the filtered F (k1, k2) we reproduce the filtered deformation field as: ~ {C} -1 - Sx ( к2 )=ZI«(k1 )«(k2 )F (k1, к2 ) cos n(2n1 + 1)k1 Л (n(2n2 + 1)k2 —---— cos —---— 2 N 2 N (7) for n1 = 0, 1, ..., N1 -1 and n2 = 0, 1, ..., N2-1. In addition to this, knowing the deformation field as an linear combination of some basis functions allows us to upsample the original deformation field (Fig. 5b), while maintaining the smoothness and periodicity constraints. Since the parametrization was made in the Cartesian domain, we apply a backward transform to the image domain, and interpolate it over the entire domain to prepare the look-up table for an efficient implementation. Fig. 5. a) Original and b) upsampled and smoothed deformation field; the magnitude of the deformation field on right was scaled down for the sake of clarity After the calibration we acquire an image stream of the particles flowing through the CPHE section. The outcome of the general PTV algorithm is a state vector built from particle positions and velocities in the image domain J : Sk{I]=[xXyy]Г . (8) where k runs through all the detected particles. To allow an estimation of the true physical quantities in the Cartesian domain, the trajectories are corrected by the mapping build from the deformation fields 8x and Sy : (C) ^ 0 0 0 8x (x, y) 0 sx 0 0 xt,y+ y t)-8x(x, y) 0 0 Sy 0 Sy(x, y) 0 0 0 s, 5>+ xt,y+ yt) - 53.0.CO;2-G. Strojniški vestnik - Journal of Mechanical Engineering 62(2016)1, 11-20 © 2016 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2015.2699 Original Scientific Paper Analysis of the Accuracy of Reconstructed Two Teeth Models Manufactured Using the 3DP and FDM Technologies Grzegorz Budzik - Jan Burek - Anna Bazan - Pawel Turek The Rzeszow University of Technology, Department of Mechanical Engineering, Poland This paper presents results of the research focused on the accuracy of the manufacturing process of biomedical models, specifically tooth models. A patient's head was scanned with cone-beam computer tomography (CBCT). The best effect of tooth geometry reconstruction was obtained using the isotropic dimensions of voxel 0.2 mm x 0.2 mm x 0.2 mm. The same Hounsfield value was used (1254HU) and the method of segmentation (region growing) applied for the models of the teeth in the process of 3D reconstruction. The marching cubes algorithm, a method of surface rendering, allowed fully reconstructing the 3D geometry. The models were manufactured using two additive techniques (3DP and FDM). They were similarly aligned in the work space of both printers to maintain similar conditions of printing, and similar layer thicknesses of 0.1 mm and 0.13 mm were used. The printed models were scanned using a focus variation (FV) microscope. The scanned geometry of the models of the two teeth was compared with the geometry of the teeth after their segmentation and filtering. A fitting process was carried out using the best fit algorithm with a fitting condition of 0.001 mm. The achieved accuracy of the FV measurements was significantly higher than the accuracy of the used printing methods. FV can be applied to performing 3D scans of complex shapes such as the crown and roots of a tooth. 3DP models have more homogenous structure, whereas layer structure is easy to recognize for FDM models. Due to that, the 3DP models have to be strengthened using infiltration, which makes it more difficult to predict the final dimensions and to achieve required accuracy. Keywords: dental model, reverse engineering, rapid prototyping, focus variation Highlights • The accuracy of FDM and 3DP techniques were examined in terms of manufacturing dental models such as tooth models. • The infiltration applied to the 3DP models reduced in accuracy compared to FDM models. • For the FDM models, the values of mean deviation were negative and met the accuracy specified by the printer's manufacturer. • Due to infiltration the values of mean deviation of 3DF models were positive. • The infiltration also caused the models manufactured with the FDM to be more accurate than the 3DP ones. • It was determined that the focus variation method can be applied to measure parts with a complex shape, such as the crown and roots of a tooth. 0 INTRODUCTION Traditional computer modelling is performed using CAD systems. Everything starts with a constructor idea. They present their concept on a technical drawing and then perform it in a virtual environment of a 3D model. This model may then be manufactured with the use of available methods. The problem arises when technical documentation of an object, for example, a tooth model, is not available. 2D images are the traditional way of presenting anatomical structures; unfortunately, this method is sometimes ineffective. In advanced cases of dental conditions, there are difficulties in the recognition and proper interpretation of 2D images of the affected area. This is why other ways to show the shape of the complex internal structures have been researched, such as the Marching Cube [1] and [2] and Splitting Box algorithm [3]. With the development of computer tomography systems, it has become possible to obtain volumetric data. Thanks to processing the volumetric data, a 3D computer model of a scanned part can be created as a result. Next, medical models can be manufactured using subtractive [4] or additive techniques [5] and [6]. Due to the complexity of the reconstruction process of medical models, the accuracy of an output model is dependent on a 3D scanning method, such as structure light [7], MDCT [8] and [9], CBCT [10] and [11], and MRI systems [12]. Scientists also present work about a comparative evaluation of CBCT and MDCT at the stage of image reconstruction [13] and [14] and accuracy reconstruction 3D model [15]. The reconstruction process is also dependent on spatial and contrast resolution of computer tomography systems [16] and [17] method of segmentation [18] software algorithms [19] and [20], and a manufacturing technology [7] and [21]. Additive techniques are based on the incremental building of objects. They are the opposite of subtractive methods of manufacturing, often described as conventional, where an object is shaped via mechanical removal of material. Rapid prototyping (RP), i.e. additive manufacturing of physical models *Corr. Author's Address: The Rzeszow University of Technology, Department of Mechanical Engineering, Poland, pturek@prz.edu.pl 11 [22] and [23] rapid tooling (RT) [24] and machining [25] are currently used to fabricate dental models. These models help a surgeon to diagnose, plan a treatment [26] and [27] and perform surgery [28] and [29]. In the field of biomedical applications, additive manufacturing (AM) has great advantages over subtractive methods when it comes to building intricate shapes matching human anatomy as well as constructing complex porous micro structure s [30]. There is a broad variety of devices using the additive methods currently on the market. Each device has specific characteristics and requirements regarding material, environmental conditions, the temperature of the process, the and stage of the final model preparation. Due to the diversity of properties and the varied availability of the RP technologies, none of these dominates in the field of medical applications; this applies to dental surgery as well [25]. The RP technologies are open to new possibilities for the development of customized applications such as the manufacture of dental models. Scientists are still conducting research to obtain reasonable accuracy at the stage of processing 2D data [10] and [11], as well as to improve the quality of dental models manufactured using the RP [31] and [32],working on material properties [33] and to find an optimal measurement system for inspecting dimensions [34] and [35]. The purpose of this investigation is to analyse the accuracy of the models of two teeth manufactured with the use of different RP methods. Because 3D printing (3DP) and fused deposition modelling (FDM) are one of the most widely used RP methods, as well as due to the relatively low cost of these processes, they were chosen for this research. An additional aim of this paper is to evaluate a focus variation (FV) microscope as a measuring system for inspecting small parts with complex geometry, such as dental models. 1 METHOD Three-dimensional computer models of 2 teeth were obtained by scanning the patient's mandible with the cone beam computer topography method and subsequent segmenting the teeth from measured data. After performing geometry reconstruction, the models were printed using the two RP methods, i.e. FDM and 3DP. Next the printed models were measured using an FV microscope. The measured geometries of the models of the two teeth were compared with geometries of the teeth after their segmentation and filtering. 1.1 Reconstruction of Geometries of the Teeth from DICOM Data All measurements of the mandible were made with a cone bean computer tomography system - Gendex CB500 3D by a medical partner. The maximum resolution of Gendex is 0.125 mm; however, parameters are set up for each patient individually. Table 1 presents parameters used during the measurements. To minimize artefacts associated with discontinuous interpolation, the isostructure of the voxel (0.2 mm x 0.2 mm x 0.2 mm) was used. The obtained data included a stack of individual images. Each image represented a thin slice of the scanned body part and was composed of individual pixels. Those pixels were arranged on a two-dimensional grid. The scanned data of the patient's mandible obtained using the cone-beam computed tomography (CBCT) and stored as images in the digital imaging and communications in the medicine (DICOM) format were subsequently processed in software 3D Doctor to reconstruct the geometry of the two separated teeth. Table 1. Parameters used in measurements with Gendex CB500 3D Parameter Value/Type Voxel size 0.2 mm X 0.2 mm x 0.2 mm Type of sensor Amorphous silicon flat panel Line of Pairs 14 lp/cm Grayscale (BIT) 14 bit Shades of grey 16384 shades of grey Field of view 8 cm X 8 cm - standard mode Scan times 23 s To increase accuracy, the images were subjected to filtration, reducing noisy and blurred edges. Noise reduction and sharpening parameters were chosen empirically to obtain the best results. To separate a tooth from the mandible, a region-growing algorithm was used. The region-growing algorithm allows to select pixels with similar Hounsfield units (HU) and classify them into a group defining the given tissue [18]. The threshold value was set above 1254HU to select only the tissue that represented a segmented tooth. After the 3D image was segmented, i.e. after every voxel was assigned to some material, a polygonal surface model was created. To reconstruct the surface, the marching cubes algorithm was used [1] and [2] (Fig. 1). This algorithm guarantees that the resulting surfaces are free from cracks and holes, that no facet (single surface build on three nearest points) intersects one another, and that all regions assigned to different materials are well separated from one another. A disadvantage of this technique is that small details of a segmented data set may be lost. a) b) I Fig. 1. Tooth models reconstructed from the DICOM data: a) tooth 1, b) tooth 2 1.2 Manufacturing Models of the 2 Teeth Using Rapid Prototyping Technologies The models were manufactured using the two rapid prototyping technologies: FDM and 3DP. These methods are cheaper than others used in the dental industry such as PolyJet or SLS. Furthermore, the accuracy of FDM models is comparable to those of PolyJet or SLS. FDM and 3DP were also chosen for the reason of testing an FV microscope as a measuring system for printed models. The authors were curious about the results of measuring white powder and white/cream plastic, which are materials with different optical properties. FDM is the most widely used additive technique in manufacturing medical replicas after stereolithography [21]. An FDM model is built of thin layers of thermoplastic wire similar to filaments (Fig. 2a). Filaments of heated thermoplastic wire are extruded from a tip that moves in the xy-plane. The platform is maintained at a lower temperature so that the thermoplastic hardens quickly. After the platform descends, an extrusion head deposits a second layer on the first. Along the way, support is built and fastened to a printed part either with a second, weaker material or with a perforated linkage. Support structures are fabricated for overhanging geometries and are later removed by breaking them away from the object. A water-soluble support material that can be easily washed away is also available. Several types of materials are available for building models, e.g. acrylonitrile butadiene styrene (ABS) which offers good strength, or polycarbonate and polysulfide materials that have recently increased the capability of the FDM method in terms of strength and temperature range. The advantage of the FDM method is that there is no need for untidy liquid photopolymers, powders and lasers [36]. A 3D printing system uses print heads to selectively disperse a binder onto powder layers (Fig. 2b). A thin layer of powder is spread over a tray with a roller. A print head scans the powder tray and delivers continuous jets of a solution that binds powder particles (mostly gypsum powder) as it touches them. After one layer of a model is built, the powder bed is lowered, and the next layer of powder is spread. No support structure is required while a prototype is fabricated because surrounding powder supports unconnected parts. When the process is completed, the surrounding powder is aspirated. a) Powder feed piston Build piston Fig. 2. a) FDM technology diagram b) 3D printing technology (3DP) diagram In the finishing process, prototype surfaces are infiltrated with epoxy resin or a salt solution to harden the structure. An advantage of the 3DP technology is the low cost of a printed model [36]. The sets of the process parameters used to manufacture the models of the two teeth are presented in Table 2. In both the printers, the models were similarly aligned in the work space to maintain similar conditions of production. Table 2. Parameters used in manufacturing the models of the 2 teeth the sample was in focus can be determined (Fig. 4). This allows to relate the vertical position of the optical system to Z coordinates of the points on the scanned surface [41]. Printer Fortus 360 mc Accuracy Parts are produced with the (p = 99.7%) accuracy of ± 0.2 mm [37] FDM .. . . . Material ABS Layer thickness 0.127 mm Manufacturing time Tooth 1 to 15 min Tooth 2 to 30 min Printer ZPrinter 650 Accuracy Parts are produced with the accuracy (p = 99.7%) of ± 0.18 mm (with no infiltration) [38] 3DP Material gypsum powder Infiltrating material epoxy resin Layer thickness mm Manufacturing time Tooth 1 to 20 min Tooth 2 to 35 min 1.3 Measurement of the Printed Models Measurements of the printed elements were carried out using the Alicona InfiniteFocus microscope based on a measurement method called FV. The operating principle of an FV microscope combines the small depth of focus of the optical system with the vertical scanning of a specimen. Focus variation is an area-based method in which many points are measured with one vertical scan. In the FV method, information on image sharpness of a measured surface is used to determine surface height as a function of position (x, y) [39] and [40]. The construction and operating principle of an FV microscope are shown in Fig. 3. The optical system is moved in the vertical direction along the optical axis in the range in which all points of a scanned surface are shown as sharp. In certain positions from this range, white light, emitted by a light source, is delivered through a semi-transparent mirror and lenses and illuminates the sample. The light reflected by the scanned surface is projected through the semitransparent mirror and the lenses to a charge-coupled device (CCD) sensor. During the vertical movement of the optical system, contrast on the CCD sensor is changing relative to the change of focus. A contrast curve is calculated for every lateral position (pixel) on the CCD sensor and for the whole vertical scanning range. With the contrast curve, the Z position where Fig. 3. Diagram of the focus variation scanning method: 1 CCD sensor, 2 lenses, 3 white light source, 4 semi-transparent mirror, 5 objective lens with limited depth of field, 6 sample, 7 vertical movement with a driving unit, 8 light rays from the white light source, 9 optional analyzer, 10 optional polarizer and 11 optional ring light Sharp position Z position Fig. 4. Change of focus with respect to Z position For each vertical position of the optical system, several scans of contrast are carried out. Consequently, it is possible to calculate the repeatability of measurement for each point. Due to the complexity of the geometry of the measured models, they were scanned in parts. The FDM and 3DP models of Tooth 1 were scanned in two parts - side surface and top surface (Fig. 5), and Tooth 2 models were scanned in three parts - side surface, top surface, and roots (Fig. 6). In the case of an FV microscope, there are several objectives with different magnification capabilities that can be used. For each objective, a specific range Fig. 5. Scanned point clouds of the FDM model of the tooth 1: a) side surface, b) top surface, and of the 3DP model of the tooth 1: c) side surface, d) top surface Fig. 6. Scanned point clouds of the FDM model of the tooth 2: a) side surface, b) top surface c) roots, and of the 3DP model of the tooth 2: a) side surface, b) top surface c) roots of vertical and lateral resolution can be set. Each objective is also characterized by the field of view. Additionally, the distance between the objective lens and a measured surface varies for each objective; the higher magnification, the smaller the distance between the lens and a sample. In the studied case, where complex geometry was measured, especially for the roots and the side surface of Tooth 2, it was essential to choose an objective for which the working distance would be long enough to avoid collision during the measurement. This is why the 2.5x objective was chosen. The vertical resolution for this objective can be set in the range from 2.3 pm to 132.51 pm, and the lateral resolution from 6.92 pm to 58.71 p.m. During the research, several sets of resolutions' values were used at testing stage. The set that offers the best quality was chosen for the final measurements. Measurement settings (i.e. vertical and lateral resolution) for each scan are presented in Table 3. Information regarding the repeatability of measurements of the tooth 1 and the tooth 2 are shown in Table 4. Table 3. Infinite focus scan setting Tooth Scanned Vertical resolution Lateral resolution part [pm] [pm] Tooth 1 side surface 15.5 19.57 Tooth 1 top surface 15.5 19.57 Tooth 2 side surface 26.76 27.86 Tooth 2 top surface 15.22 19.57 Tooth 2 Roots 7.08 16.27 Scanned geometries of the models of the 2 teeth were compared with the geometries of the teeth after their segmentation and filtering. The fitting process was carried out using the best fit algorithm with a fitting condition of 0.001 mm. Table 4. Repeatability information of scanned point clouds FDM 3DP Scanned part Repeatability threshold [^m] Mean repeatability [^m] Median repeatability [^m] Repeatability threshold [^m] Mean repeatability [^m] Median repeatability [^m] „ , , side surface 5.39 2.32 2.13 1.63 0.59 0.51 top surface 11.5 3.39 1.87 10.02 1.47 1.07 side surface 7.75 3.0 2.43 2.33 0.44 0.33 Tooth 2 top surface 59.1 9.21 4.01 29.8 8.89 3.62 roots 76.6 11.9 5.8 13.2 3.23 1.96 Table 5. Results of comparison between the CAD models reconstructed from the DICOM data and the printed models (Tooth 1) Tooth 1 (FDM) Tooth 1 (3DP) Part Mean deviation [^m] SD [p.m] Mean deviation [^m] SD [p.m] side surface -25 59 41 129 top surface -59 47 145 80 assembly -43 30 98 68 The comparison was made for all the scanned parts of the teeth as well as for the scanned parts assembled into complete tooth geometries. The assembly and the process of comparison were made using Focus Inspection software. As a result, the deviation for each point was calculated. Values of mean deviation of an inspected part, standard deviation (SD) for these values, and distribution of deviations of the printed models are shown in Table 5 for Tooth 1 and in Table 6 for Tooth 2. 3 RESULTS AND DISCUSSION The models of the two teeth manufactured using the FDM and 3DP technologies were compared with their CAD models to examine their accuracy. Basic statistics (mean value and SD) and distributions of the printed models are gathered in Tables 5 and 6. The accuracy of the fabricated models was influenced by errors of scanning, manufacturing, and the best-fit algorithm used. Repeatability (Table 4) is the standard deviation of a series of the same measurements. Knowing the vertical resolution (Table 3) and the mean repeatability of scanning, it is possible to calculate a confidence interval at a specific level of significance. The confidence interval reflects the quality of scanning. The smaller the confidence interval, the better measurement. The smallest 95 % confidence interval was calculated for the 3DP side surface, and it equalled to ±9 ^m. The biggest 95 % confidence intervals were calculated for the FDM roots, the FDM top surface, and the 3DP top surface and they were ±27 ^m, ±26 ^m, and ±25 ^m respectively. Comparing the values of scanning resolutions and the scanning mean repeatability with the distributions of models' deviations, it can be assumed that measurement errors have negligible influence on the results. The values of deviations far more exceed the scanning confidence intervals. For all the inspected parts of the models of the two teeth and for the complete models, values of mean deviation were negative for FDM and positive for 3DP. In every case, except roots, the absolute value of the mean deviation was significantly higher for the 3DP models than for the FDM models. Higher and positive values of the 3DP models' deviations were caused by infiltration of the models with an epoxy resin that increased their dimensions. For all the parts and the complete models, the standard deviation of the deviations' values was also much bigger for the 3DP than the FDM. For the top surface and roots of the Tooth 2 models manufactured using the FDM and the 3DP, and the side surface of the FDM model of Tooth 2, a bimodal distribution of the deviations could be recognized. To perform the evaluation of these parts, each original distribution was separated into two distributions using the peak fit function available in OriginPro 9.1. The mean value and the standard deviation of the components are presented in Table 7. For all the above-mentioned parts, it can be observed that one mean value of components' distributions is positive and the second is negative, and the modes are symmetrical with respect to 0. Also in each case, the antimode is near 0. It can be then assumed that the observed bimodal distributions are composed of distributions of the positive and negative deviations. That implicates low and similar values of mean deviation when the distributions are evaluated as unimodal (Table 6). The observed bimodality may indicate an error during the fitting process, specifically the rotation/ translation of the measured models with respect to nominal shape (reconstructed CAD models). All the calculated statistics of the components are significantly smaller for the FDM models than for the 3DP ones, as was previously observed for all unimodal distributions. The values of mean deviations for the assemblies are approximately equal to the mean values calculated from the mean deviations of the scanned parts. Standard deviations for the assemblies are lower than the SD of the single parts, except the side surface of Tooth 2 manufactured with the 3DP. The greater number of points in the assemblies' files allowed for a better fit to nominal, that is to CAD models. It can be stated that FDM models are manufactured with the accuracy specified by the printer's manufacturer (Table 2). In the case of the 3DP models, there is a lack of information on model accuracy after the infiltration. That is why the comparison with the data presented by the 3D printer's manufacturer cannot be made. 4 CONCLUSIONS The geometry of patient's tooth crowns and roots can be obtained by scanning the patient's mandible using CBCT. At the stage of acquiring and processing the data to create a 3D CAD model of a tooth, the voxel size and the Hounsfield value are the most significant parameters. The 3D CAD model saved as the standard template library (STL) file can be used to fabricate a physical model by one of the additive techniques. This paper asserts that small complex models, such as the crown and roots of a tooth, can be manufactured using the 3DP and FDM technologies. The fabricated models were examined in terms of their accuracy. They were compared with their CAD models, and that is why their accuracy is the result of Table 6. Results of comparison between the CAD models reconstructed from the DICOM data and the printed models (Tooth 2) Tooth 2 (FDM) Tooth 2 (3DP) Part Mean deviation [^m] SD [p.m] Mean deviation [^m] SD [p.m] side surface -30 67 137 101 top surface -8 82 77 135 roots -10 83 11 168 assembly -11 58 71 111 errors of scanning, manufacturing, and the used best- Recognizable errors during the fitting process fit algorithm. occurred especially in the case of the top surface and Table 7. Statistics of components' evaluated bimodal distributions Part Tooth 2 (FDM) Tooth 2 (3DP) Mean 1 [)um] SD 1 [um] Mean 2 [um] SD 2 [um] Mean 1 [um] SD 1 [um] Mean 2 [um] SD 2 [um] side surface -59 31 52 29 - - - - top surface -65 25 61 21 -82 29 116 57 roots -56 27 49 26 -120 52 109 49 the roots of the Tooth 2 models. Better fitting results were achieved for the assemblies rather than for the separate parts. Upon comparing the mean deviations and their standard deviations, it can be concluded that the models manufactured with the FDM are more accurate than the 3DP ones. This is caused by the infiltration applied to the 3DP models. To be able to predict final dimensions and meet required accuracy of the 3DP models, it would be necessary to carry out further studies. The focus variation method can be applied to measure parts with a complex shape, such as the crown and roots of a tooth. The achieved accuracy of measurement is significantly higher than the accuracy of the printing methods used. This means that measurement errors can be regarded as negligible. The focus variation method can be an alternative to the current measurement methods that are used in case of relatively small and complex dental models. 5 REFERENCES [1] Lorensen, W., Cline, H. (1987). Marching cubes: a high resolution 3D surface construction. 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CIRP Annals - Manufacturing Technology, vol. 63, no. 1, p. 545-548, DOI:10.1016/j.cirp.2014.03.086. [41] Helmli, F. (2011). Focus variation instruments. Leach, R. (ed.) Optical Measurement of Surface Topography. Springer, Berlin, Heidelberg, p. 131-166, DOI:10.1007/978-3-642-12012-1. Strojniški vestnik - Journal of Mechanical Engineering 62(2016)1, 21-31 © 2016 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2015.2859 Original Scientific Paper Investigation of Rotor-Stator Interaction and Flow Unsteadiness in a Low Specific Speed Centrifugal Pump Ning Zhang* - Minguan Yang - Bo Gao - Zhong Li - Dan Ni Jiangsu University, School of Energy and Power Engineering, China Instantaneous flow dynamics induced by rotor-stator interaction are detrimental to the stable operation of centrifugal pumps. In this study, unsteady rotor-stator interaction and flow structures within a low specific-speed centrifugal pump are analysed using the Large Eddy Simulation (LES) method. For that purpose, pressure pulsations and the evolution processes of vortical structures are combined to investigate rotor-stator interaction in order to clarify the inherent correlation between pressure amplitude and vorticity distribution. The results show that distinct peaks at blade passing frequency (fBPF) are closely associated with the positions of the monitoring point due to rotor-stator interaction. An unsteady vortical structure at the near tongue region is related to the relative position of the impeller with respect to the tongue, and the upstream effect of the volute tongue significantly affects the vorticity distribution on the blade pressure side. Rotor-stator interaction is dominated by vortex shedding in the wake of the blade trailing edge and their impingement on the volute tongue with subsequent cutting and distortion. Moreover, the high-pressure amplitude is generated with the corresponding high vorticity magnitude observed as well. Therefore, it is confirmed that pressure amplitude is significantly associated with the corresponding vorticity magnitude. Keywords: centrifugal pump, large eddy simulation, flow unsteadiness, rotor-stator interaction, pressure pulsation, vortical structure Highlights • Numerical investigation of rotor-stator interaction and flow unsteadiness in a centrifugal pump. • Vortical structure within the pump and its shedding from the blade trailing edge. • Evolutionary process of vortical structure at the near tongue region. • Correlation between pressure amplitude and vortical structure. 0 INTRODUCTION Unsteady pressure pulsation due to fluid-structure interaction significantly affects the stable and safe operation of the centrifugal pump. Due to the intense rotor-stator interaction between the impeller and the volute, severe vibration can be generated causing some unexpected damage to the mechanical components, for instance, the bearing and seal of the pump [1]. Some studies have been carried out to investigate unsteady rotor-stator interaction, either by the numerical or experimental method, but most of them only focus on the unsteady pressure pulsation at blade passing frequency (fBPF) [2] and [3]. According to the classic theory, it is well known that flow discharged from the impeller exit, showing a jet-wake pattern, has a significant impact on rotor-stator interaction in centrifugal pumps, as well as to the unsteady pressure pulsation characteristics [4] and [5]. Therefore, it is essential to analyse unsteady flow structure, especially vorticity distribution within the pump, to clarify the influence of wake dynamics shedding from the blade trailing edge on pressure pulsations. Posa et al. [6] and [7] numerically investigated unsteady flow distribution in a mixed flow pump using LES, especially the instantaneous vorticity distribution, and numerical results were validated with experiments. As for rotor-stator interaction, many studies only concentrate on distinct peaks in pressure spectra, especially pressure amplitude at fBPF. Parrondo et al. [8] analysed pressure pulsations in a centrifugal pump for various conditions, and particular emphasis was placed on pressure amplitude at fBPF. With the development of non-contact and nonintrusive measuring techniques in recent years, unsteady particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) measuring techniques are often applied to investigate complex rotor-stator interaction in pumps so that no external disturbance would be imposed on the flow field. Keller et al. [9] used PIV to analyse unsteady flow field around the near tongue region at high flow rates, and consecutive contours of vorticity sheet shedding in the wake of the blade trailing edge were attained to observe the details of flow evolution at the tongue region. Wu et al. [10] and [11] also applied the PIV technique to investigate the internal flow field in a centrifugal pump. Stress was laid on the flow distribution at a nominal flow rate, and an unsteady velocity field together with principal Reynolds normal stress and the principal Reynolds shear stress were revealed. Feng et al. [12] successfully used LDV to periodically measure unsteady flow in a radial flow pump, and complex flow structures in the interaction region *Corr. Author's Address: Jiangsu University, Xuefu road 301, Zhenjiang, China, zhangningwlg@163.com 21 between the rotating impeller and stationary diffuser were captured. To alleviate the intense rotor-stator interaction, some effective approaches could be implemented, for instance increasing the radial gap between the impeller and volute [13], optimal design of the impeller and the volute and some specially devised structures of the pump [14]. However, in these studies, most simply concentrate on pressure amplitude at fBPF or unsteady flow structure individually, and a combination analysis has rarely been conducted. As a result, a comprehensive understanding of rotorstator interaction, especially the correlation between instantaneous flow dynamics and pressure pulsation, has not been thoroughly illustrated. In this study, unsteady rotor-stator interaction in a low specific speed centrifugal pump is analysed using a numerical method. Pressure pulsation signals together with vorticity distribution are attained. Special attention is laid on the vortical structure shedding in the wake of the blade trailing edge and the interaction with the volute tongue. The detailed evolution process of vortical structures at the near tongue region and within the blade channel are focused and analysed. Finally, the correlation between pressure amplitude and vorticity distribution is discussed. 1 NUMERICAL INVESTIGATION 1.1 Governing Equations After adding a filter to Navier-Stokes (N-S) and continuity equations, LES governing equations can be described in the following form: dui dx. = 0, (1) du. д ,__. —- +--(u.u. ) = dt дх,. ' 1 1 dp p дх. д дх - ^du. д— — + —- дх - дх. \ 1 ' у дт + -1 + St, (2) дх where u (i = 1, 2, 3) is the grid-scale velocity component, p is the grid-scale static pressure, p is the density and v is the kinematic viscosity. Si is the source term, and T.. is the subgrid-scale (SGS) stress tensor having the form of т = uiuj -uu. . From comparisons with conventional Navier-Stokes (N-S) equations, it is found that an additional SGS stress tensor T term is introduced in the LES governing equations. In the present study, SGS model Smagorinsky-Lilly is applied to close the equations and T term is solved in Eq. (3). T --S^kk = -2vTS, 3 (3) where S.. is the strain rate tensor and vT is the SGS j T stress viscosity having the form of Eq. (4). vr = (C A)2 \S\, |S| =\J2SijSij, (4) (5) where Д is the filter scale and Cs is a dimensionless parameter called the Smagorinsky coefficient. Moreover, during numerical calculation, Cs is usually a constant 0.1. 1.2 Mesh Generation A low specific speed ns = 69 centrifugal pump, incorporating a two-dimensional impeller with six backward-curved blades, is designed for investigation. Moreover, the main parameters of the model pump are presented in Table 1. During numerical simulation, the front and back chambers of the model pump are usually neglected for simplification. However, in low specific speed pumps, the leakage flow from the wear ring clearance is normally more than 5 % of the total flow rate, and it would have a significant effect on the unsteady flow structure inside the model pump. Therefore, in this paper, the entire computational domain, containing inlet suction, impeller, volute, pump outlet, front and back chambers, is established for calculation as shown in Fig. 1. Moreover, the wear ring clearance is 0.5 mm. Table 1. Main design parameters of the model pump Parameters value Nominal flow rate Qd 55 m3/h Designed head Hd 20 m Nominal rotating speed nd 1450 r/min Specific speed ns = 3.65 n^^JQd / Hd075 69 Blade number Z 6 Angle of volute tongue 20° Impeller suction diameter Dx 80 mm Impeller outlet diameter D2 260 mm Impeller outlet width b2 17 mm Volute inlet diameter D3 290 mm Volute outlet diameter D4 80 mm Tangential velocity at impeller exit u2 19.6 m/s Impeller rotating period AT 0.0414 s Fig. 1. Computational domain of the model pump Structured grids of the model pump are generated using the Ansys-ICEM mesh generation tool for high precision calculation. Fig. 2 shows partially structured grids at the mid-span of the impeller. In the near-wall region, a fine grid is required by LES, so grid cells near the wall are refined to satisfy the requirement [15] to [17]. At the near wall region, the mesh cell size is lower than 0.5mm. Finally, the averaged y+ value of the whole computational domain is approximately 4.5, which would provide adequate resolution in the critical regions of the computation domain. After the independent mesh check, the performance of the model pump does not change more than 0.5 % when the overall mesh element exceeds 2*106. Finally, the overall mesh element used in the calculation is about 2.5*106. The mesh element of each part, i.e. inlet and outlet suctions, impeller, volute casing, front chamber, back chamber, is 58,240; 56,128; 1,298,386; 752,361; 270,668; 127,372, respectively. The same mesh is used for steady and transient simulation. 1.3 Solution Parameters Commercial software Ansys-Fluent 13.0 is used for numerical simulation. For transient LES calculation, steady numerical simulation results achieved by the RNG k-e model are set as the initialization condition. Velocity inlet boundary condition is imposed at the pump inlet suction, where a spectral synthesizer is chosen for fluctuating velocity algorithm. A constant pressure p = 1*105 Pa boundary condition is imposed at the pump outlet. To achieve adequate resolution of pressure signals, the time step is set as At = 1.15X10-4 s. During numerical simulation, when the continuity residual is lower than 3*10-5, the result is considered to be converged. Nearly 30 impeller revolutions are calculated to enable periodic pressure pulsation results. Moreover, the inside faces of the front and back chambers rotate synchronously with the rotating impeller. It is well accepted that even at a nominal flow rate, flow field distribution along the volute periphery tongue casing is not circumferentially uniform leading to pressure pulsating [18] and [19]. Therefore, it is essential to have a comprehensive understanding of pressure pulsation along the volute. For this purpose, twenty monitoring points are evenly mounted on the volute casing near the impeller exit, as seen in Fig. 3. The angle between two adjacent monitoring points is 18 deg. The angle of the volute tongue is 20 deg, and it is located between Point B and Point C. Pressure pulsation signals are processed with a FFT (Fast Fourier Transform) algorithm to investigate pressure spectrum characteristics under various flow rates. Fig. 2. Structured grids at the mid-span of the impeller Fig. 3. Details of the monitoring point on the volute casing 2 EXPERIMENTAL SETUP To validate the accuracy of the current numerical method, experimental investigation of the model pump was conducted on a closed test rig as shown in Fig. 4. An electronic flowmeter was applied to obtain flow rates of the model pump at various operating conditions; meanwhile, the head was measured using the pressure gauges located at the pump inlet and outlet pipes. The measuring errors are lower than 1% of the measured values. During experiments, the rotating speed of the model pump was ensured to be at the design value of 1450 r/min by adopting a frequency inverter. Meanwhile, one pressure transducer (PCB113B27 series) is mounted at Point C to achieve the pressure spectrum. During experiments, the inlet static pressure is about atmospheric pressure. Even at 1.4 Qd, the critical NPSH is about 3.3 m, which means that cavitation could not occur during pump operations. Fig. 4. Closed test platform 3 RESULTS AND DISCUSSIONS 10% of the total flow rate at the design flow rate, and it increases to 19 % of the total flow rate at 0.2 Qd. Therefore, it is unreasonable to exclude the front chamber in low specific speed centrifugal pumps, since the disturbance flow at the impeller inlet leaking from the wear ring clearance would generate apparent influence on the unsteady flow field. 26 22- 20- T^ TEXP LHS H-LES H- EXP o\ -0.2 o!o 0^2 04 о!б o!e 10 1.2 1.4 1.6 1 0.8 0.6 0.4 0.2 0.0 -0.2 Fig. 5. a) Performance comparison between experimental and numerical results, b) comparison of pressure spectra 3.1 Validation of the Numerical Method To validate the accuracy of the current numerical method, Fig. 5a shows a performance comparison between numerical and experimental results. The best efficiency point is around 1.1 Qd. The predicted results exhibit good agreement with the experimental results. From 0.4 Qd to 1.4 Qd, calculation errors are lower than 2%. At flow rates lower than 0.4 Qd, numerical error increases, rising to 3.5 % from head curve at 0.2 Qd. It remains a satisfactorily precise calculation. As observed from Fig. 5b, the calculation error at fBPF is relatively small: normally lower than 10 %. As for pulsation pressure prediction, it is a fairly good result [20] and [21]. Numerical result shows that leakage flow from the wear ring clearance is almost From the comparison results, it indicates that the current numerical method could effectively capture the main flow structures within the model pump. 3.2 Unsteady Pressure Pulsations Fig. 6a shows the time domain pressure signals of Point C for numerical simulation, and the corresponding pressure spectra are shown in Fig. 6b. It is found that pressure signals fluctuate significantly, and pronounced peaks at blade passing frequency fBPF (145 Hz) dominate the pressure spectra under different flow rates. Meanwhile, the high harmonic frequency 2fBPF could also be identified. According to Fig. 6b, discrete peaks at fBPF are the predominant components in pressure spectra inferred from the numerical results. Due to the asymmetry of the spiral volute and jet-wake flow pattern at the blade exit, flow field is not circumferentially uniform, and it would affect pressure spectra at different monitoring points along the volute casing. To clarify the correlation, Fig. 7 presents angular distributions of pressure amplitudes at fBPF under various flow rates. It is observed that angular distribution of pressure amplitude at fBPF exhibits a modulated pattern characterized by the presence of six local peaks and valleys. The modulation pattern is closely associated with rotor-stator interaction inside the model pump [22] and [23]. At off-design conditions, especially at flow rates of 0.2 Qd and 1.4 Qd, pressure amplitudes are much larger than that at the rated condition. Frequency [ Fig. 6. a) Time domain pressure pulsation signals at point C under three flow rates, b) the corresponding pressure spectra From Fig. 7, it is also noted that pressure amplitudes at the near tongue region, Points A, B, and C, show great discrepancy, and Fig. 8 presents the enlarged configuration of pressure amplitudes at fBPF for a nominal flow rate. As observed, pressure amplitude at Point B (в = 18 deg ahead of the volute tongue) is quite small. In contrast, pressure amplitude at the point after the volute tongue, around Point C (в Fig. 7. Angle distributions of pressure amplitudes at fBPF along the volute casing under various flow rates Fig. 8. Pressure amplitudes at fBPF for nominal flow rate = 54 deg), achieves maximum, indicating that rotorstator interaction is more intense around this region. This phenomenon is more obvious when the model pump operates at low flow rates of 0.2 Qd and 0.4 Qd. At a great distance from the volute tongue (в > 54 deg), rotor-stator interaction is less intense due to the increasing radial gap between the impeller and volute. As shown in Fig. 8, it is evident that pressure amplitudes (в > 54 deg) show a decreasing tendency due to the less significant rotor-stator interaction. In these regions, pressure pulsation is mainly induced by the unsteady flow structure shedding from the blade trailing edge (jet-wake pattern). 3.3 Instantaneous Flow Dynamics Based on the results of Fig. 7 and Fig. 8, it is clear that pressure amplitudes on the periphery of the spiral volute casing show a significant difference. Around the volute tongue region, pressure amplitude at Point C is much larger than that at Point B, as means that flow induced pulsation pressure mechanisms at these regions are obviously different. Therefore, it is essential to clarify flow structures inside the model pump and its influence on pressure amplitude, particularly around the volute tongue zone, where intense fluid-structure interaction is expected. Fig. 9 shows relative velocity distributions on the mid-span of the impeller for four flow rates, namely 0.2 Qd, 0.6 Qd, 1.0 Qd and 1.4 Qd. As observed, at a high flow rate of 1.4 Qd, flow mainly concentrates on the blade suction side due to the increasing blade inlet angle, and the high-velocity region almost covers the whole blade passage, extending to the blade exit. At almost half chord of the blade pressure side, a significant low relative velocity region is formed. Meanwhile, a small portion of the flow detaches from the blade surface in this region. At a low flow rate of 0.6 Qd, the separate flow region on the blade pressure side expands, forming a significant counter-clockwise rotating vortex. At the blade exit, the velocity of the flow near the blade pressure side is much larger than that near the blade suction side. Hence, flow at the impeller outlet is characterized by a jet-wake pattern, which results in pressure pulsating at any position along the spiral volute casing. At 0.2 Qd, due to the reverse flow at the blade exit, a large scale vortex occurs on the blade pressure side in Channel 2 causing partial blade channel blockage. In general, at low flow rate, flow separation may easily occur inside the blade channels due to the inlet flow deviating seriously from the rated condition. As observed in Channel 1, flow distribution is in a disorderly status characterized by many small scale vortices developed. At a nominal flow rate, flow distribution is more uniform than that at off-design conditions, especially at the blade outlet region. However, the separate flow region on the blade pressure side could still be observed. Due to the high incident angle, flow tends to move towards the blade suction side, and low-velocity magnitude on the blade pressure side is expected. Furthermore, the curvature of the blade may be larger, and fluid could not move along the blade streamlines. Consequently, a high-pressure gradient occurs, leading to secondary flow forming. Finally, a separate flow structure develops on the blade pressure side due to the combination effects. (dv.. - л Vorticity = 2az = (6) dv _x_ \ dx dy j Having investigated relative velocity inside the blade channels at four flow rates, vorticity distribution would be further analysed to illustrate instantaneous flow dynamics. Fig. 10 shows the vorticity magnitude at the mid-span of the impeller for a nominal flow rate. As observed, four typical vorticity regions with high magnitude developed inside the model pump, specifically regions a, ß, у, and S. At the blade pressure side of each channel, high vorticity magnitude region ß is observed, in accordance with the flow detachment region as shown in Fig. 9. The vorticity value in the central zone of the impeller is quite small indicating that the flow field is relatively uniform. On the blade suction side, another strong vorticity region у is generated, and it almost starts from the blade leading edge covering the whole blade chord. This high vorticity region is probably caused by the boundary layer developed on the blade suction side, and a high-velocity gradient is usually expected in this region. The vorticity sheet shows good coherence on the blade before approaching the blade trailing edge. At the blade outlet, it is evident that the vortical structure in region у starts to detach from the blade suction side, consequently shedding in the wake. Then the shed vortical structure moves into the volute casing; therefore, a high vorticity magnitude region S is generated inside the volute casing. The periodic shedding effect of the vortical structure would cause intense pressure changes and pulsations, as characterized by the modulated pattern shown in Fig. 7. At the near tongue area, it is noted that a rather strong vorticity region a is generated. It is caused by the impingement effect between the shedding vortex from the blade trailing edge and the volute tongue. Due to the impingement effect, turbulence activity in this region is more intense, as manifested by the increase of vorticity magnitude, and it would have a significant influence on pressure pulsations in this region. Due to the intense impeller-tongue interaction, the flow structure around the near tongue region is rather complicated and distorted. As observed in Fig. 7, pressure amplitudes at the near tongue region, Points A, B, and C, show significant discrepancy. The pressure magnitude at Point C is almost 4 times that at Point B. Besides, in Fig. 10, vorticity magnitudes 10 Qd \AQd Fig. 9. Relative velocity distributions on mid-span of the impeller for different flow rates in the areas before and after the volute tongue differ obviously, and a high vorticity magnitude area is generated at the after tongue region. Therefore, the emphasis is placed upon the vorticity distribution at the interested near tongue region to investigate instantaneous flow dynamics and clarify the correlation between vortical structure and pressure amplitude. Fig. 10. Vorticity distribution at the mid-span of the impeller under nominal flow rate Fig. 11 shows instantaneous vorticity distributions for four consecutive positions of the impeller at the rated condition. At tx = 0 (Fig. 11a), it is evident that two vortical structures, denoted as VS1 and VS2, are generated around the volute tongue. These vortical structures are closely associated with the wake shedding from the trailing edge of Blade 3. When approaching the volute tongue, the vortical structure impinges on the tongue, and it is cut into two parts (VS1 and VS2). Then the two resultant vorticity zones continue their motion towards the pump exit and the narrow side of the tongue respectively. In Fig. 11b, when Blade 2 aligns with the tongue, the torn-off portion, VS1 moves to the pump outlet and experiences a reduction in magnitude. It is more significant that seen in Fig. 11d, and VS1 becomes progressively weaker, while undergoing some distortion. This is due to the combination effect of the bending and streamwise stretching of the vortical structure near the volute tongue and its mixing effect with the external flow with lower vorticity magnitude in the diffuser section. Finally, with the impeller rotating, VS1 would dissipate in the diffuser section. It is also noted that the magnitude of VS2 undergoes a rapid decrease at this moment. This is due to the increasing of the radial distance between the impeller and the volute when VS2 continues its motion to the narrow side of the volute tongue. In Fig. 11c, with the impeller continuously rotating, Blade 2 moves away from the volute tongue. However, the wake shedding from the trailing edge of Blade 2 has not reached to the tongue; therefore, the intense impingement effect does not occur. Consequently, the low vorticity magnitude around Point B is always observed. According to the results of Fig. 11, vortical structures around the volute tongue that show obvious differences, which cause different pressure amplitudes at Points B, and C. Due to the impingement effect of vortical structure on the tongue, a high magnitude of C) d) Fig. 11. Configurations of vorticity distributions around the volute tongue at the mid-span of the impeller for four consecutive positions at nominal flow rate; a) t1 = 0, b) t2 = 18/360 AT, c) t3 = 28/360 AT, d) t4 = 38/360AT c) d) Fig. 12. Detailed analysis of vorticity distributions inside the blade channels for four consecutive positions at nominal flow rate; a) t=0, b) t2=28/360 AT, c) t3=48/360 AT, d) t4=78/360 AT the vorticity region VS2 is generated. It also means that strong turbulence activity is expected in this region as indicated by the high value of vorticity magnitude, and the corresponding Point C coincidentally is located in this area. As a contrast, Point B would always undergo lower vorticity magnitude with the impeller rotating periodically. Therefore, it is certain that the pressure amplitudes of the monitoring point are closely associated with the corresponding vorticity magnitudes, and high vorticity magnitude would generally result in high-pressure amplitude. The unsteady rotor-stator interaction has two kinds of effects, as discussed by Feng et al. [12]. The first is the downstream effect of the impeller acting on 0.2& 1.4g, Fig. 13. Vorticity magnitudes at off-design flow rates of 0.2 Qdand 1.4 Qd 0.2 Qd 1 AQd Fig. 14. Absolute velocity distributions around the volute tongue for flow rates of 0.2 Qd and 1.4 Qd the stator characterized by the unsteady effects due to flow discharged from the impeller and the jet-wake flow pattern. The second is the upstream effect of the stator acting on the flow distribution inside the impeller channels. Moreover, in this study, the upstream effect of the volute tongue is significant from vorticity distribution inside the different blade channels. From Fig. 12, it is found that vorticity distribution in blade Channel 2 facing the volute tongue is different from that at other channels as shown in Fig. 10. In Fig. 10, vorticity region ß shows good coherent on the blade pressure side, however, in Fig. 12a, vorticity region ß1 detaches from Blade 2, extending into the central zone of the blade channel. In Fig. 12b, with Blade 2 moving away from the volute tongue, vorticity region ß1 separates completely from Blade 2. Moreover, it experiences a reduction in magnitude due to the mixing effect of the low vorticity magnitude fluid in the central zone of the blade channel, as shown in Fig. 12d; finally, it would be shed in the wake of the blade trailing edge into the volute casing. With Blade 1 moving close to the volute tongue, the upstream effect of the volute tongue would significantly affect the vorticity distribution inside Blade channel 1. As shown in Fig. 12b, vorticity region ß2 starts to detach from the pressure side of Blade 1. With Blade 1 rotating further, vorticity region ß2 separates and stretches into the central zone of the channel. Finally, it would also undergo a decrease in magnitude and be shed in wake into the volute casing. Therefore, it is concluded that the vorticity distributions in different blade channels show great discrepancy due to the upstream effect of the volute tongue acting on the impeller. When the blade channel passes the volute tongue, the vorticity region on the blade pressure side would detach into the central zone of the channel. However, in other blade channels, the vortical structure shows coherent characteristics on the blade pressure sides. As observed in Fig. 9, it is evident that flow structures at off-design conditions show great discrepancy compared with that at the nominal condition. Fig. 13 presents vorticity distributions at flow rates of 0.2 Qd and 1.4 Qd. At the high flow rate of 1.4 Qd, the blade inlet angle is much larger than that at the nominal flow rate leading to flow deviating to the blade suction side. Due to the impacting effect of the inflow on the blade suction side, vorticity region у differs significantly from that at a nominal flow rate. At 1.0 Qd, vorticity region у develops from the blade leading edge almost covering the whole blade channel. However, at 1.4 Qd, vorticity region у starts to develop at the blade downstream covering half of the blade chord. At the blade trailing edge, vortical structure sheds in the wake, which is in coincidence with that at a nominal flow rate. At a low flow rate of 0.2 Qd, in contrast with that at 1.4 Qd, the blade inlet angle is much smaller than that at a nominal flow rate. Flow at the blade leading edge would deviate to the blade pressure side. As observed, high vorticity region e develops at the blade leading edge due to the deviating effect of the inflow. Vorticity sheets, at blade pressure and suction sides, are not significant compared with that at the rated condition. As presented in Fig. 9, many small-scale vortices are generated in the central zone of the blade channel, resulting in vorticity magnitude increasing rapidly. Furthermore, it is found that vortical structures show a significant difference for flow rates 0.2 Qd and 1.4 Qd at the near tongue region. At 1.4 Qd, vortical structure shedding from the blade outlet is eventually cut by the volute tongue and interacts with the tongue intensely. One portion of the vortical structure continues to move to the diffuser exit. However, at a low flow rate of 0.2 Qd, the cut effect of the volute tongue is not significant, and the whole wake approaching the volute tongue moves to the narrow side of the tongue. The vortical structure at the near tongue region is closely associated with the corresponding absolute velocity distribution as presented in Fig. 14. At a low flow rate of 0.2 Qd, a significant portion of the fluid leaks from the wide side of the tongue to the narrow side of the volute tongue. In contrast, at a high flow rate of 1.4 Qd, all fluid tends to move into the diffuser section of the volute casing. Thus, the vortical structure at the near tongue zone is associated with absolute velocity distribution and is significantly affected by the leakage flow direction at the volute tongue region. 4 CONCLUSIONS Rotor-stator interaction and unsteady flow in a low specific speed centrifugal pump are investigated in this study, and some conclusions are carried out. Angular distributions of pressure amplitudes at fBPF show a typical modulated pattern due to the intense rotor-stator interaction. At nominal flow rate, pressure amplitudes at fBPF along the volute casing show a decreasing tendency in the distant region of the volute tongue, and it is attributed to the increasing gap between the impeller and volute. Four different patterns of vorticity regions are captured on the mid-span of the impeller. It is evident that the vortical structure, shedding in the wake from the blade exit, interacts intensely with the volute tongue. From a combination analysis of pressure pulsation and vortical structure, it is found that the pressure pulsation amplitude is determined by the corresponding vorticity magnitude. When the blade passes the volute tongue, it is also evident that the upstream effect of the volute tongue has a significant influence on vorticity distribution on the blade pressure side. At off-design flow rates, vortical structures on the blade suction side at 1.4 Qd, blade leading edge and around the tongue region at 0.2 Qd exhibit great discrepancy from that at a nominal flow rate. 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D0l:10.5545/sv-jme.2015.2611 Short Scientific Paper Using Sandwich Composite Shells for Fully Pressurized Tanks on Liquefied Petroleum Gas Carriers Veysel Alankaya1* - Fuat Alargin2 Turkish Naval Academy, Department of Naval Architecture, Turkey 2Yildiz Technical University, Department of Marine Engineering Operation, Turkey The growth of shipping as the main link of the seaborne gas supply chain results from the growing demand for liquefied petroleum gasses due to their various uses, such as fuel for cooking/heating, automotive power, and numerous applications. This study investigates the structural suitability of sandwich composite materials for pressurized tanks, which can be used in on-board carriers or barges for transportation, as well as inland for industrial or residential storage needs. The analytical solution methodology for analysing stresses and deformations is based on higher order shear deformation theory (HSDT). A boundary discontinuous generalized double Fourier series approach is used to solve highly coupled linear partial differential equations. The complementary boundary constraints are introduced through boundary discontinuities, generated by the selected boundary conditions for the derivation of the complementary solution. Numerical solutions are presented for laminated sandwich shells having both cylindrical and spherical forms, which are the preferred geometries for pressurized tanks. Keywords: sandwich composites, pressurized tanks, boundary-discontinuity, doubly curved shell, liquefied petroleum gas carriers Highlights • HSDT with arbitrary boundary conditions was studied. • Laminated sandwich composite shells are analysed with the presented mathematical model. • Results are in good agreement with FEA counterparts. • Effect of core layer and geometry using stress distribution is presented. 0 INTRODUCTION Petroleum gases, an alternative to fuel oil with lower prices, are preferred for numerous uses, which can be briefly listed as (i) in-house basic needs, such as cooking and heating, (ii) industrial needs for power plants, plastic and chemical applications, and (iii) propulsion fuel for transportation. This large operational suitability causes the configuration of a distribution network depending on pipelines for the areas with infrastructure, storages for field usage, or shipping solutions for seaborne supply. The U.S. Energy Administration estimates energy consumption, which was approximately 825 million barrels in 2013, to increase by 0.6 % annually from 2012 to 2040 while the natural oil resources are declining [1]. Since many world oil resources are difficult to reach, growth in sea gas transport capacity and the construction of new gas transport pipelines are expected. As indicated by Fujitani et al. [2], while pipelines on land and in the sea can deliver the gas in gaseous form only over relatively short distances, another means of transporting the gas in larger quantities over longer distances is required. The most cost efficient way of transporting gas between continents is to carry it in liquid form using ships. Further transport cost reductions can be achieved by decreasing the weight of the ship using composite materials rather than steel, since composites have a higher weight-to-stiffness ratio. The aim of this study is to investigate the suitability of sandwich composite shells as structural members of cylindrical or spherical tanks by analysing stress distribution through the shell thickness and the shell deformations under pressure loading. 1 PRESSURIZED LIQUEFIED GAS TANKS Liquefied gasses are defined as consisting of a broad range of petroleum gas mixtures, which, as listed in the rules of Turkish Lloyd [3], include: acetaldehyde, ammonia, butane, carbon dioxide, ethane, ethylene, nitrogen, refrigerant gasses, sulphur dioxide, etc. Liquefied gas transportation distinguishes three major gas conditions: (i) fully pressurized (pressurized at ambient temperature), (ii) semi-refrigerated (pressurized and refrigerated at optimum temperature and pressure), (iii) fully refrigerated (refrigerated at or near atmospheric pressure). The loads associated with these liquefied gas conditions are one of the main characteristics that determine the pressurized tank design. For refrigerated tanks, the tank material's low-temperature toughness becomes the most important property to consider, since most materials become 32 *Corr. Author's Address: Turkish Naval Academy, Department of Naval Architecture, , Tuzla, 34942 Istanbul, Turkey, valankaya@dho.edu.tr brittle below a certain temperature. Some liquefied gasses, such as ammonia, butane, propane, propylene and vinyl chloride, can be transported at ambient temperatures. Although the storage temperature is not considered for liquefied gasses, operating temperature caused by environmental conditions shall be taken into account in terms of stationary thermal loads. The operating temperature may give rise to significant thermal stresses. Therefore, each cargo tank is fitted with at least one liquid level gauging device, designed to operate at pressures not less than the maximum allowable relief valve setting at the temperatures within the cargo operating temperature range [3]. These liquefied gasses are transported via cylindrical or spherical cargo tanks at a vapour pressure of maximum 18 MPa, as indicated by Fujitani et al. [2]. In this study, the main loading is considered to be the maximum vapour pressure, ignoring thermal stresses caused by operating temperature and environmental conditions. In addition to the liquefied gas storage temperature, tank design is also done according to the cargo tank arrangement restrictions from the International Code for the construction and equipment of ship carrying liquefied gasses in bulk (ICG code), incorporated into the Safety of life at sea (SOLAS) convention. According to the ICG code, liquefied gasses that do not need to be refrigerated, are restricted to Type C tanks, which are structurally independent of the ship's hull. Fig. 1 shows a generic mid-ship section view of a hull and cargo tank. LNG tanks are cylindrical and spherical in shape, the present methodology also could be applied to these tanks. Fig. 1. Mid-ship section of the hull and cargo tank Type C cargo tanks are completely self-supporting and do not form part of the ship's hull, nor do they contribute to the hull strength [2]. Similar applications of independent tanks are also common at liquefied natural gas (LNG) ships, as presented in Fig. 2. However LNG tanks, which store the gas at -162 °C, are not investigated in this study, because the refrigeration temperature effect on the tank material is beyond the scope of this study. Nevertheless, since Fig. 2. Hull-independent tank on an LNG carrier [4] 2 COMPOSITE MATERIALS As presented by Mouritz et al. [5], composite materials can be chosen for several functional components of ships, such as hull (complete or partial as for bulkheads), superstructure (complete for small crafts, or partial for bigger crafts), for the mast, for the propulsion system components, and even for propellers. One major reason for these choices is the composites' high stiffness-to-weight ratio, which reduces the components weight; another reason is the lower cost of moulding complex geometry parts rather than machining them. Moreover, the design flexibility inherent in composite laminates, which is described as tailoring by Kabir et al. [6], makes composites a reasonable choice for obtaining optimum specific design requirements through a combination of structural/ material concepts, stacking sequence, ply orientation, choice of the component phases, etc. These allow composites to provide modern solutions for thermal and acoustic insulation, stealth capabilities, shock resistance, etc. When Liquefied Petroleum Gas (LPG) is in a hull-independent type C tank, no thermal insulation is required. Therefore, the design of the material can be tailored to be non-flammable and to bear the load while minimizing weight. Utilization of composite materials, however, also brings difficulties to the analyst, such as the interlaminar or transverse shear stress due to mismatch of material properties among layers, bending-stretching coupling due to lamination asymmetry, and in-plane orthotropy. The transverse stress and strain components are ignored in classical or thin shell theories, which makes these theories inadequate for the analysis of thicker shells. Hence, reliable prediction of deformations and stresses for thicker structures require the use of higher order shear deformation theories, which are based on a cubic or higher expansion of the in-plane displacements. Higher order theories introduce additional unknowns that are difficult to interpret in physical terms and require more mathematical computations for finding solutions [7] and [8]. As indicated by Youssif [9], to analyse the effects of design sensitivities efficiently and accurately, it is crucial to have the appropriate techniques associated with good structural models. Therefore, it is essential to develop a solution methodology considering the additional complexities arising by way of satisfying boundary conditions that cannot be handled by Navier's or Levy's traditional analytical approaches. Chaudhuri [10] provides the mathematical explanations for the boundary discontinuous type Fourier series approach for solving completely coupled system of partial differential equations, subjected to admissible general boundary conditions. In this particular study, static deflections of cylindrical and spherical shaped pressurized tanks made of sandwich composites are investigated by using the higher order shear deformation theory. The effects of boundary conditions on the solution functions are introduced as described by Oktem and Chaudhuri [11] and the presented solution methodology is developed to apply to sandwich composites. 3 DEFINITION OF THE PROBLEM The geometry of a composite shell, which consists of laminated plies with uniform thicknesses is shown in Fig. 3, where a and b represent the dimensions in the & axes respectively, while £3 is a line normal to the mid-surface defined at the centre going through the shell thickness h. The terms R1 and R2 are the mid-surface curvatures in the (£b £2) axes respectively. Fig. 4 shows the ply distance z from the mid-surface. The terms ф1 and ф2 are rotations about and £ axes, respectively. Details of the strain-displacement relations and other explanations are given by Reddy [12]. / Ply N - layers / Ply к ft*. i Z "4 h2 "V Ply 2 / Ply 1 ft, midsurface b) Fig. 4. Ply distances from the mid-surface for a laminated shell; a)without a core, and b) with a sandwich core The displacement field by considering the cubic terms and satisfying the conditions of transverse shear stresses (and hence strains) vanishing at a point (£b 4, ±h / 2) on the top and bottom surfaces of the shell, is given by Reddy [12] as follows: ui = u Лг ) = uo ( ) + +z(Pi Лг )- 3т mm 0 ; P ; a u(pp)=YLWm«%(PP) 0;b (юс) mm 0 < £ < a ъ (i'£2)=ZZад (i) 0 <1 < b (iod) m=0 n=1 0 — Ч2 — °> mm 0 < P < a Ъ (Pi P ) = YLYmn*2 (Pi P ) 0 IP ; b d0e) m=1 n=0 0 — b2 —°> U1,11 = 2 jj cmsin (föl ) + 1 m=1 where, (Il Č2 ) = COS (<*Šl ) Sin ß ), ( 11a) ^2 (1^2 ) = («1 )COS (ß2 ) , (11b) (i « I2 ) = ™ (« 0, o2 > 0, -1

umax or X , < umin. By POT, the maxima above the threshold umax and the minima below the threshold umin are randomly regenerated, and only these extreme values will be extrapolated. For the threshold, on one hand, the level must be high enough so that only true peaks, with Poisson arrival rates, are selected. Small values for the threshold will lead to a biased estimation [47]. On the other hand, the level must be low enough to ensure that sufficient data will be selected to guarantee an accurate estimation of the distribution parameters, and the variance of the parameters will be decreased [47]. Johannesson [40] suggested a simple method that sets the threshold equal to the square root of the cycle number in the signal and works well in many cases [48]. Other threshold-selection methods have also been proposed, for example, Davison [49], Ledermann et al. [50] and Walshaw [51]. Level upcrossings (LU): According to Johannesson and Thomas [17], LU is proposed to obtain the maxima and minima of the load cycles, then determine the limiting shape of the rainflow matrix (RFM) and estimate the limiting RFM G [17]: (5a) E[fj] (5b) gij= lim-(5b) z^rc z where the elements f of Fz are the number of rainflow cycles in distance z, with a minimum in class i and a maximum in class j. Fz is the rainflow matrix in distance z. This approach is based on an asymptotic theory for the crossings of extreme (high and low) levels. First, obtain a measured RFM F [17]: (6) where f is the number of the cycle with minimum i and maximum j. Then, calculate the LU from F and determine a suitable threshold. The level upcrossings spectrum is calculated as follows [17]: n=(n ^ (7) Time Fig. 1. Schematic diagram of BMM Time Fig. 2. Schematic diagram of POT A Review of the Extrapolation Method in Load Spectrum Compiling 63 where nk is the accumulative cycle number from the load level i below k to the load level j above k: nk = Z fij. i (12) where fij is the cumulative frequency number from the load level i to the load level j, fij = ni+1j-1 - nij-1 - ni+1j + nij ■ The main process of EVE has been sketched out and the practical operation is conducted based on the technical software package, for example, WAFO [57]. Johannesson [40] conducted the 100-fold extrapolation and compared the extrapolated load spectrum with the 100 repetitions of the measured load spectrum, then it was found that the extrapolation result was more reasonable because it agreed well with the observed load spectrum. Due to the uncertainty of wind conditions, the extreme load on a wind turbine is usually difficult to determine. In 2008, Collani et al. [58] put forward a reliable method named LEXPOL [59] to solve the problem. For the sake of different environments, Agarwal and Manuel [60] deduced the long-term loads with POT and a three-parameter Weibull distribution, then a good extrapolated result was obtained. A quadratic distortion of the Gumbel distribution was introduced by Natarajan et al. [61] and Natarajan and Holley [62] and it was used to fit the tail of the extreme loads on a wind turbine. Based on this method, the finite sample data was extrapolated to 50 years. In addition, an extrapolation method based on the mean and standard deviation of extreme values was proposed by Moriarty [63], where subjectivity of the parametric extrapolation was avoided. 1.2 Nonparametric Extrapolation Method (NPE) NPE, which was proposed by Dressler et al. in 1996 [64], uses a nonparametric statistical approach to get the statistical probability distribution. In NPE, the nonparametric density estimation reduces the subjectivity of empirical hypothesis because it makes no assumptions on the distribution of the sample data. As a result, the extrapolated load spectrum is not influenced by the characteristics of the sample data. The kernel estimation can be employed for nonparametric density estimation [65] and [66]. The estimation transforms a discrete histogram of sample data into a probability distribution. Suppose XbX2,■■■,Xn are observed samples from a common distribution with density f(). The kernel density estimation (KDE) off() is [64]: fh ( X) = 4 ±K (^ ), nh i=1 h (13) where K is the kernel function and h is the bandwidth. To assure the reasonability of the KDE function fh (x), kernel K satisfies [64]: K(x) > 0, \ K(x)dx = 1, J —го The main process of NPE is as follows [66]: 1. Transform the measured load time history into a rainflow counted histogram. 2. Select the appropriate kernel function and bandwidth, then use the nonparametric method in combination with the Monte Carlo method [67] to extrapolate the RFM that is obtained from the lifecycle one. 3. Reconstruct a new load spectrum from the RFM lifecycle. For NPE, a lot of research was conducted on the selection of the kernel function and bandwidth. Wang et al. [68] proposed a selection method for the kernel function and the multi-criteria decision making technique was successfully used to solve the problem of the kernel function selection. For the bandwidth selection, Heidenreich et al. [69] reviewed the bandwidth selections for the kernel density estimation and some of the methods can be used in NPE. Sheather [70] proposed two kinds of bandwidth determination methods: Sheather-Jones plug-in bandwidth and least squares cross validation. The Sheather-Jones plug-in bandwidth was widely used because of its overall good performance, but this method was prone to be over-smoothing in some situations. As a supplement, it was solved by the least squares cross validation. Besides, Bayesian methods [71] and [72] were used to estimate the adaptive bandwidth and adaptive bandwidth matrix in univariate and multivariate KDEs. For the applications of NPE, Dressler et al. [64] transformed the discrete rainflow matrix into a smooth function that is more accessible with a kernel density estimator. In the literature, the RFM is seen as two-dimensional histograms of the opening and closing points of hystereses, and can only be described by a nonparametric method due to its arbitrary shapes. Socie [73] employed nonparametric kernel smoothing techniques to transform the discrete rainflow histogram of cycles into a probability density histogram and extrapolated the short-term measured load to an expectedly long-term one. The key role of the bandwidth in KDE is also indicated in the literature. Johannesson [17] considered that kernel smoothing is a feasible smoothing technique and well-established statistical method for nonparametric estimation. A kernel smoother method is also proposed to estimate the RFM for the cycles with small and moderate amplitudes. Mattetti et al. [74] extrapolated the RFM by NPE in carrying out of accelerated structural tests of tractors. 1.3 Quantile Extrapolation Method (QE) Considering the influences of different working conditions and operating behaviours in engineering, load extrapolation is difficult. Under these circumstances, the quantile extrapolation method (QE) is capable of taking various conditions and behaviors into consideration and optimizing the extrapolation results. The main process of QE is as follows [64]: 1. Break the data set of the rainflow-counted histogram into a series of clusters B1, B2,..., Bm with similar variables and damages. 2. Compute the damage of each original RFM R by Miner's rule. Damage vectors [64]: ( Dl(Rl),..., Dm ( R) (D(R ),..., Dm ( R )) are obtained for all original RFMs, where Rj, R2, ..., Rn represent the influence of various conditions and behaviors. 3. Estimate the expected damage for the x% quantile. The quantile damage vector (q1 q2, ..., qm), which describes the damage distribution between the individual clusters of the rainflow matrix, is used to construct the rainflow matrix. The original rainflow matrix is superposed such that [64]: Rg = R +••• + Rn. (15) 4. Construct and extrapolate the corresponding RFM into a matrix, the extrapolation of the resulting matrix [64] is: Re = extrapol (RG ), (16) where RE represents the extrapolated result and is made up of the basic process and peak values. Socie and Pompetzki [66] described a method for statistically extrapolating a single measured service load time history to an expected long-term load spectrum. Because of the difference between operating behaviors, the extrapolation method was extended to combine data from several users. The extrapolated load spectrum would represent more severe users in the population and the optimization effect was obvious. Mattetti et al. [74] introduced a method for an accelerated test on tractors and employed QE to calculate rainflow matrices for 20 tasks repeated in five different working forms. In the selected sample, the 95th percentile of the most damaging conditions are considered. In load spectrum compiling, QE is usually combined with other extrapolation methods and it is also an important component in computer software. 1.4 Classification of the Extrapolation Methods The extrapolation methods are integrated into one figure for clarity. As shown in Fig. 3, the classifications and pivotal elements of the methods are reflected. 2 CASE ANALYSIS In this section, some illustrations and examples are displayed to evaluate and demonstrate the extrapolation methods. 2.1 Case Analysis of PEE In PEE, distributions of the sample data affect the extrapolation results [26]. In this section, the load on an axle shaft of a loader powertrain was taken as the research object. According to the obvious segment working characteristics of a loader, the operation process was divided into six sections. In this paper, the load on the axle shaft in the spading and the no load backward sections were illustrated to verify the characteristics of PEE. Amplitudes of the load with different characteristics and distributions were focused on. The Weibull distribution was employed, with the fitting results shown in Fig. 4 and Fig. 5. Compared with Fig. 4a, the fitting in middle of Fig. 5a diverges from the distribution function more remarkably. In Fig. 5b, the tail of the fitting seriously diverges from the skew line, as in Fig. 5c. Based on the comparison, the conclusion is that the fitting between the function and load in the spading section is better. So, when PEE is applied to extrapolating the load on an axle shaft with different characteristics, the repeatability of the result will be influenced. Therefore, the distributions of the sample data will influence the fitting error in PEE, and the fitting error will lead to an inaccuracy in the extrapolation results. 2.2 Case Analysis of EVE In EVE, both the data extracting and fitting function selection will affect the extrapolation results. During the data extracting process, selection of the threshold or block size is important [75] to [78], as this will influence the data utilization ratio and the distribution characteristics of the extreme values. Fitting precisions vary from each other due to different load characteristics, thus the extrapolation results of EVE are dependent on the fitting precisions. Several examples will illustrate the influences of different thresholds on the fitting precisions. In this section, the load on an axle shaft of a loader powertrain in the spading section was used. The automatic threshold selection method, which was proposed in Thompson [79], was adopted to determine the original threshold. In data processing, based on the sample data, 2897.3 Nm was set as the automatic threshold and the number of extreme values was 5734, thus 5734 exceedances were calculated. With GPD, the exceedances were fitted with the parameters estimated by the maximum likelihood method, and the results are shown in Fig. 6. In order to reflect the effects of thresholds on fitting precisions, 2000 Nm and 3500 Nm were selected as the other thresholds to extract values, thus Fig. 3. Classification of the extrapolation methods н Probability plot rIff - I Sample data -- Fitting function . — Boundary of the confidence interval 500 1000 1500 2000 2500 3000 3500 4000 4500 x a) Residual quantile plot Residual probability plot / / * _7 ~7 , to Sample data Reference curve Empirical b) Empirical c) Fig. 4. Fitting results between the distribution and load the in spading section 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Probability plot Residual quantile plot Sample data ----Fitting function ~ Boundary of the - confidence interval 1000 1200 1400 1600 a) Residual probability plot Л Sample data Reference curve 0 200 400 600 800 1000 1200 1400 Empirical b) 0.4 . , 0.6 Empirical Fig. 5. Fitting results between the distribution and load in the no load backward section 0.8 0.8 0.6 0.6 0.4 0.2 0.2 0 0 0 0 0.2 0.8 0 0.2 0.8 0 c) the values were fitted with the same distribution and parameter estimation method. The fitting results are shown in Fig. 7 and Fig. 8. Compared with Fig. 6, the deviations between the data points (the extreme values) and the fitting distribution in Fig. 7 and Fig. 8 are obvious, especially in plot a and b of the figures. So, with different thresholds, the fitting precisions are different, which will influence the results from EVE. On the basis of the comparison, the significance of selecting the threshold or block size is verified. The influence of the distribution function on the extrapolation results also needs to be considered. In Johannesson [17], GPD was used to extrapolate the simulated Markov load with the maximum likelihood estimation and the result was shown in Fig. 9a [17]. Thus, the exponential distribution was adopted to extrapolate the same load, the result was shown in Fig. 9b [17]. Making a comparison between the two parts in Fig. 9, the exponential tail in Fig 9b yields a straight line in the log-scale that tends to overestimate the intensity for extreme crossings [17]. Therefore, the conclusion can be drawn that GPD gives a better extrapolation and thus verifies the importance of selecting a suitable distribution function. There are two branches in EVE: EVET and EVER. Making a comparison of the two branches, it is easy to find some distinctions, such as the application domains, the fitting functions and the types of the extrapolation results. In Johannesson [40], EVET and EVER were both applied to extrapolate the load of a train and a car, respectively, and the results are show in Fig. 10. Fig. 10 allows some comparisons between EVET and EVER to be noted [40]: 1. EVET generates the extrapolated load cycle directly based on the measured load time history, so the outcome is more reliable; 2. EVET is more robust because it is only on the basis of EVT, while the EVER uses an additional extreme value approximation for the shape of the rainflow matrix; 3. The limitation in the extrapolation multiple of EVET is that the extrapolated result is an N-fold extrapolated load. In EVER, the extrapolated result is a limited rainflow matrix, which represents infinite repetitions. 4. Results extrapolated by EVET are usually adopted into a fatigue test or as the input load Probability plot Sample data Fitting distribution -Boundary of the confidence interval 600 800 x 1000 1200 1400 Residual quantile plot Residual probability plot đ a с T3 I04 200 400 600 800 1000 1200 a) Empirical b) Fig. 6. Threshold u = 2897.3, fitting results Empirical c) Probability plot Residual quantile plot Residual probability plot Sample data Fitting function Boundary of the confidence interval x a) 2500 0 500 1000 1500 Empirical b) Fig. 7. Threshold u = 2000, fitting results 0.4 0.6 0.8 Empirical c) Probability plot s'ir* .'/JS ■ МГ t'V *Y Sample data / Boundary of the / confidence interval Residual quantile plot Residual probability plot Sample data Reference curve 300 400 x a) 600 700 0 100 200 300 400 500 600 Empirical b) Fig. 8. Threshold u = 3500, fitting results 0.4 0.6 0.8 Empirical c) 0.8 0.8 0.6 0.6 0.4 0.2 0.2 0 0 0 0.8 0.6 0.4 0.2 0 0 0 0.2 0.8 0.6 0.4 0.2 0 0 0.2 0 for life prediction. However, if the target is to extrapolate a load spectrum and acquire the relationship between the load and frequencies over the whole life, EVER will be an appropriate selection because it has high efficiency and it can estimate the shape of the load spectrum for an infinitely long measurement. Sometimes, the extrapolation results can be transformed. Load in the time domain can be transformed into rainflow domain by RCM. The Markov method [80] can also be used to transform the load from the rainflow domain to the time domain. However, the accuracy of the results will be influenced during the transforming process. 2.3 Case Analysis of NPE In NPE, kernel estimation provides a convenient way to estimate the probability density [65] and [81]. In kernel estimation, both kernel function [68] and bandwidth [66] are of great concern. In Wang et al. [68], the selection of the kernel function was considered. Four kinds of kernel functions were illustrated; the extrapolation results are shown in Fig. 11 using these kernel functions. [68]. As shown in Fig. 11, the results based on different kernel functions vary from each other, especially the extrapolated extreme loads. When NPE was first proposed by Dressler et al. in 1996 [64], the importance of bandwidth was emphasized and this was also confirmed in the following research [64], [66] and [82]. Compared with the kernel function, extrapolation results are more sensitive to the bandwidth [64] and [66]. So far, only two kinds of bandwidths are commonly applied to data extrapolation. They are the fixed and the adaptive bandwidth [64] and [66]. In this section, level, и a) Fig. 9. Extrapolation of level in order to verify the influence of the bandwidths on the probability density, a fixed bandwidth with different values will be discussed. As shown in Fig. 12, the solid line represents the probability density based on the automatic fixed bandwidth hs = 0.5187, where the other two lines represent the densities with the bandwidths hs = 0.2 and hs = 1 respectively. As shown in Fig. 12, when the bandwidth equals 0.2, the double-peak occurred at the peak of the density and the fluctuation in the second half was obvious. When the bandwidth increases to 1, the maximum density declined to a large extent. So, with different bandwidths, the probability density, which is directly related to the extrapolation result, makes a big difference. 2.4 Case Analysis of QE Based on the former discussion on QE, the principle in Dressler et al. [64] is important and comprehensive. In Dressler et al. [64], based on four figures (Figs. 10 to 13 in K. Dressler et al. [64]), the importance and level, и b) ity; a) with GPD; b) with EXP [17] (a) Load spectrum - Train (b) Load spectrum - Car a) b) Fig. 10. 100 times extrapolation, comparing time andrainflowdomainmethods [40] -2296. Fig. 7 11. a) To [Nm] Comparison among extrapolated results based on different kernel functions; circular; b) mean-basedellipse; c) range-based ellipse; d) epanechekov Sample data Fig. 12. Probability density distribution with different bandwidths necessity of QE were confirmed, and determinations of the clusters were shown. The choice of the solution parameters in QE was also emphasized in Dressler et al. [64]. On one hand, the extrapolation results are highly dependent on the determination of the clusters B1, B2, ..., Bm , which can be adjusted according to different conditions or be defined invariant of the data analyzed. On the other hand, it is important to test the resultant vectors for Gaussian distribution and the determination of the x% matrix will be much easier with the vectors. 3 SUMMARIES OF THE EXTRAPOLATION METHODS 3.3 Application Ranges Characteristics of the extrapolation methods are summarized from three aspects (the critical factors, the advantages and disadvantages, and the application ranges of each extrapolation method) based on the previous sections. 3.1 Critical Factors Critical factors in each extrapolation method are summarized in Table 1. These factors are mentioned and emphasized in the preceding part based on the literature and illustrations. 3.2 Advantages and Disadvantages Based on the literature and illustrations, the advantages and disadvantages of each extrapolation method are summarized in Table 2. Table 1. Critical factors in each extrapolation method Extrapolation method Critical factor Distribution prediction of the sample data PEE Selection of the distribution function _Parameter estimation_ Threshold or block size determination Distribution prediction of the sample data Selection of the distribution function Parameter estimation EVE NPE Selection of the kernel function Bandwidth determination QE Data characteristics judgment and breaking Resultant vectors test Different extrapolation methods have their own application ranges. In practice, the application ranges of a certain extrapolation method are not categorical. A method has to be selected on the basis of the practical situation. Application ranges of the methods in this paper are mainly based on the load characteristics and extrapolation purposes, which are summarized as follows. PEE: For sample data, when the stationary test for a certain distribution is qualified, PEE will be an appropriate selection. However, when convenience and efficiency of data processing is required instead of the accuracy, PEE can be considered. For example, in Xiang [20], the distributions of the load amplitudes and mean values fit well with the fitting functions and they are independent, so PEE is adopted. EVE: EVE is a proper choice in circumstances where the sample data is composed of extreme load. For example, the data in the fields of wind speed and engineering machinery could be extrapolated by EVE. Furthermore, if the purpose is to produce a load time history for fatigue test and fatigue life evaluation, EVET is a better choice because it is capable of extrapolating the load time history directly. EVER is more applicable for accurate load spectrum extrapolation of large load cycles. EVER is also an appropriate choice in circumstances where the load spectrum can be modeled as a Gaussian or Markov model. NPE: NPE is limited by the sample size of large load cycles. If the sample size is enough, NPE may be a better choice. For extrapolating medium and small load cycles, NPE can be used. When it is difficult to Table 2. Advantages and disadvantages of each extrapolation method Extrapolation method Advantages Disadvantages PEE • Computes efficiently [20] and [7]; • Considers the influences of both mean value and • amplitude of the sample data [19] and [20]. Relies on the distribution of the measured data; There is subjectivity in selecting a parameter-estimate method [26]. EVET • Gets a load time history directly; • Generated sequence of cycles is realistic; Robust; • Considers the influence of extreme values. The block size and threshold selection has a great influence on the extrapolation accuracy. Relies on distributions of the sample data ; EVER • Estimates the shape of the load spectrum for an infinitely • long measurement; Available for large cycles. • Produces a rainflow matrix and needs to be converted into a time signal; Choice of the threshold is difficult. Relies on distributions of the sample data; NPE • Independent of the distributions of the sample data [64]; • Effective estimation of the load spectrum with arbitrary • shapes [64]. Large amount of sample data is needed [64] and [66]; The kernel function and bandwidth selection is influential. QE • The extrapolated samples consider the influence of • different conditions and operating behaviours. Influential step is breaking the sample data into a series of clusters [64]. define the model of the distribution accurately or there is little dependence on the distribution of the sample data, NPE may be a good choice. For example, in the field of vehicles, the load may be extrapolated by NPE [68]. QE: When different working conditions and operating behaviors are considered, QE will be useful in data processing. For example, due to the complex working conditions of engineering machinery, the load in the field may be extrapolated with QE [4]. 4 DISCUSSIONS Due to the limited paper length, there are some deficiencies in this review. For example, in PE, some other distribution functions should be reviewed, such as the logarithmic normal distribution in PEE and the Rayleigh distribution in EVE. In EVE, the importance of the threshold or block size is verified, but the selecting methods of the threshold or block size should be further discussed. In NPE, the influence of bandwidths on the density distribution is verified, but the difference between the adaptive and fixed bandwidth requires further comparison, and which one is better for a certain situation is not concluded. For QE, where different working conditions are concerned, the process and details of combining QE with other methods are not fully reviewed. Furthermore, one purpose of this review is to provide guidance on selecting an appropriate load extrapolation method for a certain case. In this review, only part of the guidance is involved, so further research on completing the guidance may be useful. 5 CONCLUSIONS Load extrapolation provides a feasible and reliable approach to obtaining a long-term load spectrum for fatigue analysis and life prediction in engineering. Several commonly used extrapolation methods are reviewed in this paper. Some conclusions are as follows: 1. PEE and EVE are both included in PE. PEE is based on the distributions of the sample data. Specific distribution functions are employed to fit and the parameters in the functions are estimated according to the sample data. The PEE process is simple and efficient, but some errors may arise in the results; 2. EVE is based on EVT. Extreme values obtained by extraction methods such as BMM, POT, and LU are extrapolated by a process similar to PEE, but the distribution functions are usually different. EVE is valid for the load time history with large load cycles, but selecting a proper threshold or block size usually requires further consideration; 3. For extrapolating small and moderate loads, NPE can be applied accompanied by kernel estimation. There is no need to predict the distributions of the sample data and estimate the parameters of the functions in NPE. The rationality of the results extrapolated by NPE is directly influenced by the kernel function and bandwidth, especially the latter; 4. The extrapolation methods mentioned above could be combined with QE when the influences of different working conditions and operating behavior are considered. In QE, determining the solution parameters is an important step. Some potential future research directions are also predicted: First, a difference between the extrapolated and measured load always exists, thus an evaluation criterion should be set to evaluate the difference, which may provide important guidance for selecting the appropriate method. Second, the references and applications are mainly about the field of engineering in this review. In fact, extrapolation is being used in many other fields, such as weather prognosis, hydrological forecasting, and financial analysis. Methods from other fields can be borrowed and adopted in another field. In addition, limited by the physical circumstances in engineering, many load spectra have maximum or minimum limits. Extrapolating the sample data appropriately within these limits is challenging. 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A bandwidth selection for kernel density estimation of functions of random variables. Computational Statistics & Data Analysis, vol. 47, no. 1, p. 4962, D0I:10.1016/j.csda.2003.10.013. List of reviewers who reviewed manuscripts in 2015 Boris Aberšek, Slovenia Bojan Ačko, Slovenia Mike Adams, UK Dragan Aleksendrić, Serbia Hafiz Muhammad Ali, Pakistan Luis F. Almeida, Brazil Abdullah Altin, Turkey Miha Ambrož, Slovenia Ciril Arkar, Slovenia Fausto Arpino, Italy Kamil Arslan, Turkey Viktor P. Astakhov, USA Ayyanar Athijayamani, India Csoban Attila, Hungary Önder Ayer, Turkey Aleš Babnik, Slovenia Tom Bajcar, Slovenia Ivan Bajsić, Slovenia Pedro P. Balestrassi, Brazil Jože Balič, Slovenia Serkan Balli, Turkey Sebastian Baloš, Serbia Mustapha Barakat, France Nilson Barbieri, Brazil Jani Barle, Slovenia Cemal Baykara, Turkey Bernd-Arno Behrens, Germany Josep M. 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Kursat Celik, Turkey Yikai Chen, China Peng Cheng, USA Simone Chiappino, Italy Chong-Du Cho, South Korea Christian Cierpka, Germany Snezana Ciric-Kostic, Serbia Franco Concli, Italy Mario Costa, Portugal Dario Croccolo, Italy Gregor Čepon, Slovenia Martin Česnik, Slovenia Mirko Čudina, Slovenia Franci Čuš, Slovenia Jos Darling, UK Marta Cristina Cardoso de Oliveira, Portugal Marco Dell'Isola, Italy Edvard Deticek, Slovenia Andrew J. Dick, USA Anselmo Eduardo Diniz, Brazil Norman E. 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Hecker, Argentina Niko Herakovič, Slovenia Philippus Stephanus Heyns, South Africa Marko Hočevar, Slovenia Petr Horak, Czech Republic Elžbieta Horszczaruk, Poland Tomislav Horvat, Switzerland Aleš Hribernik, Slovenia Matjaž Hriberšek, Slovenia Xiaoming Huang, China Gino Iannace, Italy Soichi Ibaraki, Japan Ayhan Ince, USA Hajro Ismar, BiH Mohammad Israr, India Juan Carlos Jauregui, Mexico Boris Jerman, Slovenia Marko Jerman, Slovenia Libin Jia, USA Juan-Carlos Jimenez-Munoz, Spain Dragica Jošt, Slovenia Sonja Jozić, Croatia Roman Kamnik, Slovenia Mitja Kastrevc, Slovenia Tomaž Katrašnik, Slovenia Iyas Khader, Germany Andrzej Kielbus, Poland Kadir Kiran, Turkey Turgay Kivak, Turkey Jernej Klemenc, Slovenia Milan Kljajin, Croatia Damjan Klobčar, Slovenia Davorin Kofjac, Slovenia Leon Kos, Slovenia Borut Kosec, Slovenia Kari Koskinen, Finland Igor Kovač, Slovenia Attila Kovari, Hungary Davorin Kramar, Slovenia Janez Kramberger, Slovenia Simon Krasna, Slovenia Živa Kristl, Slovenia Grzegorz M. Krolczyk, Poland Jan Kudlaček, Czech Republic Janez Kušar, Slovenia Lovro Kuščer, Slovenia Jože Kutin, Slovenia Karl Kuzman, Slovenia Panagiotis Kyratsis, Greece Pawel Andrzej Laski, Poland Andrej Lebar, Slovenia Yaguo Lei, China Hirpa G. Lemu, Norway Zhuang Li, China Xiangping Liao, China Yaoyao Liao, China Edward Lisowski, Poland Huibin Liu, USA Youyu Liu, China Zhong-Liang Liu, China Thomas Loeser, Germany Gorazd Lojen, Slovenia Andrew Peter Longstaff, UK Darko Lovrec, Slovenia Željan Lozina, Croatia Urban Lundin, Sweden Balazs Magyar, Hungary Franc Majdič, Slovenia Julio César Gómez Mancilla, Mexico Tamas Mankovits, Hungary Noah D. Manring, USA Leonardo Marini, Italy Angelos P. Markopoulos, Greece Jure Marn, Slovenia Gregory C. McLaskey, USA Giovanni Meneghetti, Italy Miran Merhar, Slovenia Miroslav S. Milutinovic, BiH Xu Ming, China Nagaraja Mohan, India Nikolaj Mole, Slovenia Dimitris Mourtzis, Greece Janez Možina, Slovenia Swarnajay Mukherjee, USA Hubertus Josef Murrenhoff, Germany Marko Nagode, Slovenia Kanthavelkumaran Natesan, India Balazs Nemeth, Hungary Andreas Nestler, Germany George K. Nikas, UK Saša S Nikolić, Serbia Anatolij Nikonov, Slovenia Ali Nikparto, USA Peter Nyhuis, Germany Ivan Okorn, Slovenia Remi Olatunbosun, UK Simon Oman, Slovenia Vytautas Ostasevicius, Lithuania Sabri Ozturk, Turkey Iztok Palčič, Slovenia Nikolakopoulos Pantelis, Greece Detlef Pape, Switzerland Dimitrios G Pavlou, Norway K. Pazand, Iran Stanislav Pehan, Slovenia Alexandra Pehlken, Germany Tomaž Pepelnjak, Slovenia J.M. Pérez, Spain Matjaž Perpar, Slovenia Rok Petkovšek, Slovenia Damian Pietrusiak, Poland Miha Pipan, Slovenia Miroslav Plancak, Serbia Vladimir Popovic, Serbia Antonio Posa, USA Primož Potočnik, Slovenia Iztok Potrč, Slovenia Ivan Prebil, Slovenia Radu-Emil Precup, Romania Andrej Predin, Slovenia Jurij Prezelj, Slovenia Ted Prodan, Slovenia Franci Pušavec, Slovenia Homer Rahnejat, UK Matjaž Ramšak, Slovenia Robert Randall, Australia Jure Ravnik, Slovenia Sunil J. Raykar, India Zlatko Rek, Slovenia Janko Remec, Slovenia Minodora Ripa, Romania Samuel Rodman Oprešnik, Slovenia Miroslaw Rodzewicz, Poland Fairuz I. Romli, Malaysia Klemen Rupnik, Slovenia Izidor Sabotin, Slovenia Mohammad Reza Safaei, Malaysia Elham Sahraei, USA Tadeusz Salacinski, Poland Mika Salmi, Finland Graziano Salvalai, Italy Bernd Sauer, Germany Robert Schmitt, Germany Hans-Peter Schulze, Germany Stephan Schuschnigg, Austria Hubert Schwarze, Germany Marcel Schweiker, Germany Tine Seljak, Slovenia Andrej Senegačnik, Slovenia Vladimir V. Serebryakov, Ukraine Luca Settineri, Italy Y. Shtessel, USA Marko Simic, Slovenia Anže Sitar, Slovenia Janko Slavič, Slovenia Mojca Slemnik, Slovenia Jussi Sopanen, Finland Knut Sorby, Norway Marco Sortino, Italy Philip Southey, UK Andrea Spagnoli, Italy Karsten Stahl, Germany Matteo Strano, Italy Uroš Stritih, Slovenia Kurra Suresh, India Bo Svensson, Sweden Željko Šitum, Croatia Boris Štok, Slovenia Roman Šturm, Slovenia Ulla Tapaninen, Finland Jože Tavčar, Slovenia Jouni Tervonen, Finland Roberto Teti, Italy Iztok Tiselj, Slovenia Jim Townsend, USA Enrico Troiani, Italy Gabrielle J.M. Tuijthof, The Netherlands Janez Tušek, Slovenia Toma Udiljak, Croatia Samo Ulaga, Slovenia Miran Ulbin, Slovenia Nicolae Ungureanu, Romania Janez Urevc, Slovenia Senthil Kumar V.S, India Joško Valentinčič, Slovenia Mien Van, Singapore James D. Van de Ven, USA Judy Vance, USA Edgar Ernesto Vera Cardenas, Spain Tomaž Videnič, Slovenia Gustavo da Silva Vieira de Melo, Brazil Jožef Vižintin, Slovenia Arkady Voloshin, USA Rok Vrabič, Slovenia Damir Vrančić, Slovenia Tomaž Vuherer, Slovenia Nikola Vukašinović, Slovenia Lin Wang, USA Xiaodong Wang, China Roman Zbigniew Wdowik, Poland Marian Wiecigroch, UK Kai Willner, Germany Yongbo Wu, Japan Zhang Xiaohong, China Liping Xu, UK Yusuf Yesilce, Turkey Matej Zadravec, Slovenia Michele Zazzi, Italy Dejan Zupan, Slovenia Samo Zupan, Slovenia Franc Zupanič, Slovenia Janez Žerovnik, Slovenia Uroš Župerl, Slovenia The Editorial would like to thank all the reviewers in participating in reviewing process. We appreciate the time and effort and greatly value the assistance as a manuscript reviewer for Strojniški vestnik - Journal of Mechanical Engineering. Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 62, (2016), številka 1 Ljubljana, januar 2016 ISSN 0039-2480 Izhaja mesečno Razširjeni povzetki (extended abstracts) Jaka Pribošek, Miha Bobič, Iztok Golobič, Janez Diaci: Kompenzacija periodične optične distorzije pri metodi sledenja delcev na valovitih ploščnih prenosnikih toplote SI 3 Grzegorz Budzik, Jan Burek, Anna Bazan, Pawel Turek: Analiza natančnosti dveh modelov rekonstruiranih zob, izdelanih s tehnologijo 3DP in FDM SI 4 Ning Zhang, Minguan Yang, Bo Gao, Zhong Li, Dan Ni: Raziskava interakcij med rotorjem in statorjem ter nestacionarnosti toka pri centrifugalni črpalki z majhno specifično hitrostjo SI 5 Veysel Alankaya, Fuat Alargin: Uporaba lupin iz sendvič kompozitov pri tlačnih posodah za tankerje za ukapljen naftni plin SI 6 Tomaž Pepelnjak, Mladomir Milutinović, Miroslav Plančak Dragiša Vilotić, Saša Randjelović, Dejan Movrin: Vpliv razmerja iztiskavanja na kontaktne napetosti in elastične deformacije matrice pri hladnem protismernem iztiskavanju SI 7 Marek Magdziak: Algoritem za izračunavanje odstopanja oblike pri koordinatnih meritvah površine izdelkov poljubnih oblik SI 8 Jixin Wang, Hongbin Chen, Yan Li, Yuqian Wu, Yingshuang Zhang: Pregled metod ekstrapolacije pri zbiranju spektrov obremenitev SI 9 Osebne vesti SI 10 Kompenzacija periodične optične distorzije pri metodi sledenja delcev na valovitih ploščnih prenosnikih toplote Jaka Pribošek1* - Miha Bobič2 - Iztok Golobič1 - Janez Diaci1 1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2 Danfoss Trata, Slovenija Optimizacija valovitih ploščnih prenosnikov toplote je bila dotlej omejena na numerične CFD simulacije, pri čemer pa spričo zaprte konstrukcije tovrstnih prenosnikov, eksperimentalna validacija teh simulacij ostaja nenaslovljena. Ker so tokovni pojavi v valovitih prenosnikih navadno kompleksne narave, je za uspešno validacijo nujna kvantitativno spremljanje celotnega tokovnega polja znotraj prenosnikov. V ta namen smo na valovitih ploščnih prenosnikih toplote vpeljali metodo sledenja delcev. Za neposredno vizualizacijo toka v prenosniku je bil izdelan lasten eksperimentalni sistem, kjer je bila ena od kovinskih plošč ploščnega prenosnika zamenjana s prozorno polimerno ploščo. Prozorna plošča je bila izdelana po postopkih vročega vtiskovanja in sicer tako, da njena geometrija popolnoma ustreza nadomeščeni kovinski plošči. Tak kompozitni sestav omogoča prosto vizualizacijo tokov znotraj prenosnika, vendar valovitost prozorne plošče in razlike v lomnem količniku vnesejo pojav kompleksne periodične optične distorzije. Optična distorzija močno popači trajektorije sledenih delcev, kar v meritev vnese veliko sistematično napako ter onemogoča direktno rabo obstoječih metod sledenja delcev. V pričujočem članku predstavljamo metodo eksperimentalne identifikacije optične distorzije s pomočjo vzorca v obliki šahovnice ter lastnega algoritma na osnovi obdelave slik. Algoritem detektira popačenost slike šahovnice, ter iz nje določi iskano polje deformacij. Za boljši popis deformacij vpeljemo nov model periodične distorzije na osnovi diskretne kosinusne transformacije, ki znatno izboljša krajevno ločljivost zaznanih deformacijskih polj. Razvita metoda nam omogoča kompenzacijo vpliva optične distorzije na popačitev trajektorij sledenih delcev ter s tem eliminacijo sistematično napako meritev položaja delcev. Pravilnost delovanja algoritmov smo preverili z vrsto simulacijskih eksperimentov na znanih enodimenzionalnih hitrostnih poljih, kjer smo lahko eksperimentalno ovrednotili sistematično položajno napako delcev pred in po kompenzaciji. Sistematična napaka položaja delcev je bila v teh primerih s pomočjo razvite metode zmanjšana za več kot 50 %. Razvite algoritme za kompenzacijo tokovnic smo aplicirali tudi na realnem primeru na prenosniku med obratovanjem. Pri tem je bila sistematična napaka v določanju položaja delcev zmanjšana za 35 %. Pričujoč članek predstavlja pionirsko delo na področju kvantitativne analize valovitih ploščnih prenosnikov toplote v svetovni javnosti. Naše nadaljnje delo bo naravnano v smeri uporabe obstoječih algoritmov za merjenje tridimenzionalnih velikostnih polj znotraj valovitih toplotnih prenosnikov za namene njihove eksperimentalne optimizacije ter validacije večjega števila obstoječih numeričnih analiz. Ključne besede: periodična optična distorzija, metoda sledenja delcev, valoviti ploščni prenosniki toplote, optimizacija ploščnih prenosnikov, eksperimentalna validacija numeričnih analiz Analiza natančnosti dveh modelov rekonstruiranih zob, izdelanih s tehnologijo 3DP in FDM Grzegorz Budzik - Jan Burek - Anna Bazan - Pawel Turek Tehniška univerza v Rzeszowu, Oddelek za strojništvo, Poljska Dodajalne izdelovalne tehnologije (AM) imajo na področju biomedicine pomembne prednosti pred postopki izdelave z odvzemanjem materiala, še posebej takrat, ko gre za gradnjo kompliciranih oblik človeške anatomije in kompleksnih poroznih mikrostruktur. Na trgu je veliko naprav, ki uporabljajo dodajalne izdelovalne tehnologije. Vsaka od njih ima posebne lastnosti in zahteve glede materialov, pogojev okolice, temperature procesa in korakov končne obdelave modela. Prav zaradi raznolikosti omenjenih lastnosti in različne razpoložljivosti tehnologij za hitro izdelavo prototipov (RP) danes še nobena od njih nima dominantnega položaja na področju aplikacij v medicini, kar velja tudi za dentalno kirurgijo. Tehnologije RP odpirajo nove priložnosti na področju razvoja aplikacij po meri, kot je izdelava dentalnih modelov. Znanstveniki še vedno raziskujejo, kako doseči zadostno natančnost v fazi obdelave podatkov, pridobljenih med skeniranjem pacientove anatomije, ter kako izboljšati kakovost dentalnih modelov, izdelanih po postopkih RP, iščejo pa tudi optimalen merilni sistem za kontrolo dimenzij. Namen te raziskave je analiza natančnosti modelov dveh zob, izdelanih z različnimi postopki RP. Za raziskavo sta bila izbrana 3D-tiskanje (3DP) in neprekinjeno ciljno nalaganje (FDM), ker spadata med najbolj razširjene postopke RP in sta povezana z razmeroma majhnimi stroški. Dodatni cilj tega članka je tudi ovrednotenje primernosti mikroskopa s spremenljivim goriščem (FV) za uporabo v funkciji merilnega sistema za kontrolo majhnih predmetov s kompleksno geometrijo, kot so dentalni modeli. Tridimenzionalni računalniški modeli dveh zob so bili pridobljeni s skeniranjem pacientove spodnje čeljusti po metodi računalniške tomografije s stožčastim snopom (CBCT), ki mu je sledilo segmentiranje zob na podlagi izmerjenih podatkov. Geometrija zob je bila najbolje rekonstruirana pri vokslih izotropnih dimenzij 0,2 mm x 0,2 mm x 0,2 mm. Pri 3D-rekonstrukciji sta bili za modele zob uporabljeni enaki Hounsfieldova vrednost (1254HU) in metoda segmentacije (rast območja). 3D-geometrija je bila popolnoma rekonstruirana z algoritmom Marching cubes, eno od metod za upodabljanje površin. Modeli so bili izdelani po postopkih 3DP in FDM. Modeli so bili analogno orientirani v delovnem prostoru obeh tiskalnikov, s čimer so bili zagotovljeni podobni pogoji pri tiskanju, prav tako pa je bila nastavljena podobna debelina slojev 0,1 mm oz. 0,13 mm. Natisnjeni modeli so bili nato poskenirani z mikroskopom s spremenljivim goriščem (FV), in sicer po delih zaradi kompleksne geometrije. Skenirana geometrija modelov dveh zob je bila primerjana s pripadajočimi CAD-modeli. Primerjava je bila opravljena tako za posamezne dele kakor tudi za sestavljene modele zob. Opravljen je bil proces iskanja najboljšega prilega s pogojem natančnosti prilega 0,001 mm. Natančnost izdelanih modelov je vsota napak pri skeniranju, napak pri izdelavi in uporabljenega algoritma za iskanje najboljšega prilega. Pri zobeh s kompleksnejšo geometrijo je med procesom iskanja prilega prišlo do prepoznavnih napak. Pri sestavih je bil dosežen boljši prileg kot pri posameznih delih. Modeli, izdelani po postopku FDM, so bili natančnejši od modelov, izdelanih po postopku 3DP. Vzrok je v infiltraciji, ki se uporablja pri modelih 3DP. Da bi bilo mogoče napovedovati končne dimenzije in doseči zahtevano natančnost modelov 3DP, bi bilo treba izvesti še dodatne študije. Metoda spreminjanja gorišča je uporabna za merjenje delov kompleksnih oblik, kot so zobne krone in korenine. Dosežena natančnost meritev je bila bistveno večja od natančnosti uporabljenih postopkov tiskanja in zato lahko privzamemo, da je merilna napaka zanemarljiva. Metoda spreminjanja gorišča je dobra alternativa za postopke, ki se trenutno uporabljajo pri merjenju razmeroma majhnih in kompleksnih dentalnih modelov. Ključne besede: dentalni model, vzvratno inženirstvo, hitra izdelava prototipov, spreminjanje gorišča Raziskava interakcij med rotorjem in statorjem ter nestacionarnosti toka pri centrifugalni črpalki z majhno specifično hitrostjo Ning Zhang* - Minguan Yang - Bo Gao - Zhong Li - Dan Ni Univerza Jiangsu, Šola za energetiko, Kitajska Nestacionami tlačni impulzi zaradi interakcij med fluidom in konstrukcijo pomembno vplivajo na stabilno in varno delovanje centrifugalnih črpalk. Zaradi intenzivne interakcije med kolesom in ohišjem (rotorjem in statorjem) nastajajo močne vibracije, ki lahko nepričakovano poškodujejo mehanske komponente. Zato je nujna analiza nestacionarnih tokovnih struktur, še posebej porazdelitve vrtincev v črpalki, za pojasnitev vpliva dinamike odlepljanja vrtincev na sprednjem robu lopatice na tlačne impulze. Predstavljena študija analizira nestacionarno interakcijo rotorja in statorja pri centrifugalni črpalki z majhno specifično hitrostjo. Pridobljeni so bili signali tlačnih impulzov skupaj s porazdelitvijo vrtincev. Posebna pozornost je bila posvečena odlepljanju vrtinčastih struktur v vrtinčni sledi na sprednjem robu lopatice ter interakciji z jezikom ohišja. Podrobno je bila analizirana evolucija vrtinčnih struktur v okolici jezika in v kanalu lopatice. Namen tega dela je ugotovitev povezav med tlačnimi impulzi in nestacionarnimi tokovnimi strukturami. V predstavljeni študiji so bile za ugotovitev notranjih povezav med tlačnimi impulzi in nestacionarnimi tokovnimi strukturami analizirane nestacionarne interakcije med rotorjem in statorjem ter tokovne strukture po metodi LES. Za zaključevanje enačb je bil uporabljen SGS-model Smagorinsky-Lilly. Numerična metoda je bila validirana z eksperimenti. Kotne porazdelitve amplitude tlaka v fBPF nakazujejo značilen moduliran vzorec zaradi intenzivne interakcije med rotorjem in statorjem. Amplituda tlaka v fBPF vzdolž ohišja pri imenskem pretoku kaže tendenco po zmanjševanju v območju, oddaljenem od jezika ohišja, kar lahko pripišemo širjenju reže med kolesom in ohišjem. V srednjem delu kolesa so bili ugotovljeni štirje različni vzorci območij vrtinčenja. Očitno je, da je vrtinčna struktura, ki se loči v vrtinčni sledi na izstopu lopatice, v intenzivni interakciji z jezikom ohišja. Kombinirana analiza tlačnih impulzov in vrtinčne strukture je pokazala, da je amplituda tlačnih impulzov odvisna od velikosti vrtinca. Ko lopatica prehaja mimo jezika ohišja, gorvodni učinek jezika ohišja pomembno vpliva na porazdelitev vrtincev na tlačni strani lopatice. Pri pretokih, ki se razlikujejo od projektiranih, se vrtinčne strukture na sesalni strani lopatice pri 1,4 x Qd, na sprednjem robu lopatice in v okolici jezika pri 0,2 x Qd močno razlikujejo od struktur pri imenskem pretoku. Podroben in natančen opis nestacionarnih tokovnih struktur v modelski črpalki je težavna naloga. V tej študiji ni bilo mogoče zajeti procesa evolucije odlepljanja vrtinca od sprednjega roba lopatice. V nadaljnjih študijah bi bilo zato treba uporabiti finejšo mrežo in več računskih zmogljivosti za razkritje procesa odlepljanja vrtinčne strukture na sprednjem robu lopatice in mehanizma interakcije z jezikom ohišja. Z eksperimentalno raziskavo tlačnih impulzov in nestacionarnimi meritvami PIV bi bilo mogoče validirati numerične rezultate ter pridobiti celovit pregled nad interakcijami med rotorjem in statorjem v centrifugalnih črpalkah. Razjasnitev interakcij med rotorjem in statorjem pri centrifugalnih črpalkah je klasičen raziskovalni cilj. Objavljene raziskave obravnavajo bodisi amplitudo tlaka v fBPF bodisi nestacionarne tokovne strukture. V splošnem velja, da je amplituda tlaka odvisna predvsem od interakcij med rotorjem in statorjem, sami vplivi na interakcijo med rotorjem in statorjem pa so le redko predmet raziskav. Članek razkriva evolucijo odlepljanja vrtinca na sprednjem robu lopatice in njegovo interakcijo z jezikom ohišja. Analizirani so tudi dejavniki, ki vplivajo na amplitudo tlaka, kar je v objavljeni literaturi redkost. Raziskava tako prispeva k izboljšanemu razumevanju interakcij med rotorjem in statorjem. Ključne besede: centrifugalna črpalka, simulacija velikih vrtincev, nestacionaren tok, interakcije med rotorjem in statorjem, tlačni impulzi, vrtinčna struktura Uporaba lupin iz sendvič kompozitov pri tlačnih posodah za tankerje za ukapljen naftni plin Veysel Alankaya1* - Fuat Alargin2 JTurška pomorska akademija, Oddelek za ladjedelništvo, Turčija 2Tehniška univerza Yildiz, Oddelek za ladijsko strojništvo, Turčija Naftni plin kot alternativa za kurilno olje je na voljo po nižjih tržnih cenah in je primeren za mnoge namene, med drugim: (i) za osnovne gospodinjske potrebe, kot sta kuhanje in ogrevanje, (ii) za industrijske potrebe v elektrarnah, industriji plastike in kemični industriji, (iii) kot pogonsko gorivo za transport. Izkoriščanje tega potenciala zahteva izgradnjo distribucijskih omrežij s plinovodi za infrastrukturna območja, skladiščne zmožnosti za terensko uporabo in rešitve za transport po morju. Rast trgovskih ladjevij zahteva tankerje z večjimi kapacitetami za transport plina, vendar z minimalno težo. Prednostna rešitev za izpolnitev te zahteve so kompozitni materiali, ki imajo veliko razmerje med togostjo in težo. Namen te študije je preučitev primernosti lupin iz sendvič kompozitov v vlogi konstrukcijskih delov cilindričnih ali sferičnih rezervoarjev, in sicer z analizo porazdelitve napetosti po debelini lupine in deformacij lupin pod tlačno obremenitvijo. Uporaba kompozitnih materialov je povezana z določenimi težavami pri analizi, kot so medslojne ali transverzalne strižne napetosti zaradi neujemanja materialnih lastnosti med sloji, sklapljanje upogibanja in natezanja zaradi asimetrične laminacije, in ravninska ortotropija. Transverzalne komponente napetosti in deformacij se v teoriji klasičnih ali tankih lupin zanemarijo, zato te teorije niso primerne za analizo debelejših lupin. Zanesljivo napovedovanje deformacij in napetosti v debelejših konstrukcijah tako zahteva uporabo strižno-deformacijskih teorij višjega reda na osnovi ekspanzije ravninskih odmikov tretjega ali višjega reda. Teorije višjega reda uvajajo dodatne neznanke, za katere je težje poiskati fizikalno interpretacijo, iskanje rešitev pa zahteva tudi več matematičnih izračunov. Za učinkovito in točno analizo podrobnosti zasnove so nujne ustrezne tehnike v povezavi z dobrimi strukturnimi modeli, zato obstaja potreba po razvoju metodologije reševanja, ki bi upoštevala dodatne kompleksnosti zaradi robnih pogojev, ki izključujejo tradicionalne analitične pristope po Navierju ali Levyju. Ta študija preučuje statični odklon cilindričnih in sferičnih tlačnih posod iz sendvič kompozitov z uporabo teorije strižnih deformacij višjega reda. Vplivi predpisanih robnih pogojev na funkcije za reševanje so dostopni v literaturi, v tej študiji pa so bili razviti posebej za sendvič kompozite. Metodologija za analizo napetosti in deformacij bazira na teoriji strižnih deformacij višjega reda (HSDT). Za reševanje visoko sklopljenih linearnih parcialnih diferencialnih enačb je bil uporabljen pristop mejno nezvezne posplošene dvojne Fourierjeve vrste. Dodatne robne omejitve so bile uvedene z mejnimi nezveznostmi, ustvarjenimi z izbranimi robnimi pogoji za izpeljavo komplementarne rešitve. Predstavljene so numerične rešitve za laminirane sendvič lupine cilindrične in sferične geometrije, ki prevladujejo pri tlačnih posodah. Nadaljnji rezultati so zbrani v nadaljevanju: • Prediktivna ocena razvite metodologije reševanja je predstavljena s primerjavo numeričnih rezultatov rešitev FSDT in MKE. • Čeprav je metoda končnih elementov v raziskovalnih sferah močno razširjena, je prednost predstavljene metodologije za cilindrične in sferične sendvič lupine v tem, da zahteva manjše računske zmogljivosti. • Vpliv debeline jedrne plasti na normalizirani centralni odklon lupine je signifikanten. Debelina jedrnega sloja, kot eden glavnih parametrov, je zato uporabna za spreminjanje geometrije rezervoarjev za ukapljen naftni plin. • Geometrija kot naslednji glavni parameter zasnove rezervoarjev ima velik vpliv na vrednosti odklona. Ukrivljenost lupine zmerno vpliva na centralni odklon. • Pomemben je tudi vpliv debeline jedrnega sloja na porazdelitev medslojnih napetosti. Povečanje debeline prinese občutno zmanjšanje porazdelitve medslojnih napetosti. Ključne besede: sendvič kompoziti, analiza po metodi končnih elementov, teorija strižnih deformacij višjega reda, mejna nezveznost, tlačne posode, dvakrat ukrivljena lupina, tankerji za ukapljen naftni plin Vpliv razmerja iztiskavanja na kontaktne napetosti in elastične deformacije matrice pri hladnem protismernem iztiskavanju Tomaž Pepelnjak1* - Mladomir Milutinović2 - Miroslav Plančak2 -Dragiša Vilotić2 - Saša Randjelović3 - Dejan Movrin2 1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenia 2 Univerza v Novem Sadu, Fakulteta tehniških znanosti, Serbia 3 Univerza v Nišu, Fakulteta za strojništvo, Serbia V članku je obravnavan problem elasto-plastičnega obnašanja sistema orodje-preoblikovanec za postopek protismernega iztiskavanja. Dobro poznavanje velikih tlačnih obremenitev orodja je neobhodno tako za konstrukcijo orodja kot tudi za opredelitev izdelovalne natančnosti samega preoblikovalnega procesa. V ta namen je potrebno združiti teoretska znanja, meritve opazovanih veličin in numerične analize s katerimi vnaprej napovedujemo pojave pri izdelovalnih procesih. V članku je predstavljena porazdelitev napetosti v kontaktu orodje-preoblikovanec kot tudi elastična deformacija orodja pri procesu hladnega protismernega iztiskavanja. Slednja se pojavi kot posledica obremenitev orodja zaradi plastične deformacije preoblikovanega jeklenega surovca. Analize kontaktnih tlakov in elastičnih deformacij so bile analizirane eksperimentalno in numerično z metodo končnih elementov. Za eksperimentalno določanje kontaktnih tlakov obstaja več merilnih metod. Pri predstavljenih rasziskavah je bila uporabljena meritev s palično tlačno merilno celico, ki meri obremenitve orodja neposredno na njegovi površini. Za zasledovanje kontaktnih tlakov na aktivni površini orodja za protismerno iztiskavanje je bilo zasnovano posebno orodje z vgrajenim zaznavalom, ki se ga vstavlja na različne lokacije v orodju. S tem je bil analiziran tlak pri različnih pomikih gibljivega dela orodja in ovrednoteno njegovo spreminjanje med preoblikovalnim postopkom. Raziskave so bile usmerjene v določitev vpliva razmerja iztiskavanja na porazdelitev kontaktnih tlakov. V ta namen je bilo uporabljenih pet različnih premerov pestičev, ki zagotavljajo različne stopnje protismernega iztiskavanja. V naslednjem koraku se je na osnovi izmerjenih kontaktnih tlakov in preračuna z Lamejevo enačbo določilo radialne pomike notranje stene matrice. Izvedena je bila primerjalna analiza dobljenih rezultatov in preračunov z metodo končnih elementov. Za analize z metodo končnih elementov je bil izbran komercialni računalniški program Simufact.forming. Na osnovi meritev kontaktnih tlakov in rezultatov numeričnih simulacij se je v prvi fazi primerjave preverilo natančnost numeričnih izračunov. Primerjava je pokazala, da numerični izračuni izkazujejo višje vrednosti maksimalnih radialnih napetosti v primerjavi z eksperimentalno določenimi za vse vrednosti razmerja iztiskavanja ep. Numerične vrednosti maksimalnih radialnih napetosti so od eksperimentalnih večje med 14,8 % in 23,7%. Elastična deformacija orodja vpliva tudi na natančnost izdelovalnega procesa. Z numeričnimi simulacijami se je ovrednotilo vpliv elastične obremenitve in radialne deformacije matrice na natančnost izdelovalnega postopka. Za protismerno iztiskavanje ob največji analizirani deformaciji prečnega preseka z vrednostjo ep = 2.11 so numerične simulacije pokazale, da se velikost odstopka zunanjega premera izdelka giblje v tolerančnih razredih od IT8 do IT11. Velikost tolerančnega razreda je odvisna od višine protismerno iztisnjenega dela - večja je globina iztiskavanja, večji je izdelovalni tolerančni razred. Primerjalne analize vseh treh raziskovalnih konceptov so pokazale njihove prednosti in slabosti. Pri tem se je analizirala predvsem primernost uporabe Lamejeve enačbe in uporabnost palične tlačne celice za merjenje kontaktnih tlakov pri postopkih iztiskavanja za vključevanje v nadaljnje raziskovalno delo. Razlika med izračunanimi radialnimi pomiki dobljenimi z Lamejevo enačbo in numerično izračunanimi vrednostmi je prečejšnja. Izkaže se, da je ta razlika precej večja kot primerjava eksperimentalnih in numeričnih izračunanih vrednost. Iz navedenega lahko povzamemo, da je izračun po Lamejevi enačbi pomanjkljiv in le omejeno uporaben pri analizah obremenitev in deformacij orodij za masivno preoblikovanje. Ključne besede: protismerno iztiskavanje, kontaktne napetosti, elastična deformacija matrice, palična tlačna merilna celica, metoda končnih elementov Algoritem za izračunavanje odstopanja oblike pri koordinatnih meritvah površine izdelkov poljubnih oblik Marek Magdziak* Tehniška univerza v Rzeszowu, Fakulteta za strojništvo in aeronavtiko, Poljska Glavni cilj predstavljene raziskave je bil razvoj nove metode za izračunavanje odstopanja oblik, ki bo uporabna pri koordinatnih meritvah površin izdelkov poljubnih oblik. Nova metoda mora biti primerna tudi za programsko opremo koordinatnih merilnih strojev. Predlagani algoritem za vrednotenje odstopanja oblik bazira na metodi interpolacije korigiranih merilnih točk po Lagrangeu in Čebišovu. Algoritem razdeli točke, ki jih izmeri koordinatni merilni stroj, v skupine po pet točk. Skupine se interpolirajo po obeh omenjenih metodah interpolacije in pri tem se oblikujejo skupine polinomskih krivulj četrtega reda, ki predstavljajo dejansko obliko merjenca. V članku so predstavljeni rezultati numeričnih in eksperimentalnih preiskav, povezanih s predlaganim algoritmom. Numerične preiskave vključujejo simulacijo kontaktnih koordinatnih meritev izdelkov na koordinatnem merilnem stroju. Merjeni izdelki so bili prostih oblik, za katere je značilna spremenljiva ukrivljenost in posledično stopnja geometrijske kompleksnosti. V simulacijah so bile generirane izmerjene točke na različnih oddaljenostih od imenskih profilov. Raztros merilnih točk je posledica nenatančnosti postopkov izdelave merjencev ter nenatančnosti koordinatnih meritev analiziranih predmetov. Rezultati simulacij so bili eksperimentalno preverjeni z realnimi kontaktnimi meritvami na koordinatnem merilnem stroju ACCURAII. Predstavljena metoda izboljšuje natančnost meritev površin izdelkov poljubnih oblik. Predlagani algoritem za izračunavanje odstopanja oblik zagotavlja boljše rezultate preizkusov kot metoda na podlagi nominalnih točk v programski opremi Calypso. Prednost predlagane metode je v možnosti izbire primernega algoritma za interpolacijo izmerjenih točk. Razviti algoritem je poleg tega mogoče implementirati v večini programskih paketov za meritve in programska oprema Calypso konkretno omogoča implementacijo s pomočjo modula PCM. Uporabnik lahko v tem okolju uporablja zunanje uporabniško definirane procedure in izvaja uporabniške programe. S takšnim pristopom so mu na voljo izboljšane možnosti za analizo rezultatov koordinatnih meritev. Predlagani algoritem se lahko v prihodnjih raziskavah podrobneje verificira z realnimi koordinatnimi meritvami. Meritve se lahko opravijo tudi z drugačnimi merilnimi parametri od tistih, ki so bili analizirani v študijah. Glavna inovacija novega algoritma za izračunavanje odstopanja oblik je v tem, da se interpolacija merilnih točk izvaja po metodah Lagrangea in Čebišova. Te interpolacijske metode niso na voljo v programski opremi uporabljenega koordinatnega merilnega stroja. Ključne besede: koordinatna merilna tehnika, poljubna oblika, interpolacija, odstopanje oblike Pregled metod ekstrapolacije pri zbiranju spektrov obremenitev Jixin Wang* - Hongbin Chen - Yan Li - Yuqian Wu - Yingshuang Zhang Univerza v Jilinu, Fakulteta za tehniške vede in strojništvo, Kitajska Spektri obremenitev predstavljajo osnovo za analizo utrujanja in napovedovanje življenjske dobe v strojništvu. Ekstrapolacija obremenitev je nepogrešljiv postopek za določanje dolgoročnega spektra obremenitev. V zadnjih desetletjih je bilo predlaganih več metod ekstrapolacije in izbiranje ustrezne med njimi je pomemben korak, ki zahteva več pozornosti. Članek podaja pregled pogosto uporabljenih metod ekstrapolacije ter povzetek njihovih načel in lastnosti. Podane so tudi smernice pri izbiri ter nekatere omejitve in smeri raziskav na tem področju. V tem pregledu se metode ekstrapolacije glede na to, ali je privzeta določena porazdelitev vzorčnih podatkov, delijo na parametrične metode ekstrapolacije (PE) in neparametrične metode ekstrapolacije (NPE). Metode PE se z ozirom na predmete ekstrapolacije in osnovno teorijo delijo tudi na metode ekstrapolacije z ocenjevanjem parametrov (PEE) in metode ekstrapolacije z ekstremnimi vrednostmi (EVE). Dodatno je pregledana še kvantilna metoda ekstrapolacije (QE). Po predstavitvi postopkov posameznih metod je podana pripadajoča literatura za nadaljnji študij. Metode in osnovna načela so nato strnjeni v obliki preglednega diagrama. Prikazanih je nekaj ilustracij ter primerov za vrednotenje in demonstracijo metod. Na podlagi ilustracij je preverjenih nekaj ključnih točk metod, kot so vpliv vzorčnih podatkov pri PEE, vpliv izbire praga pri EVE ter pomen pasovne širine pri NPE. Citirana literatura obravnava tudi nekatere druge lastnosti, vključno z vplivom porazdelitvenih funkcij v PE, različnimi uporabami EVE v različnih domenah, vplivom izbire jedrne funkcije v NPE ter pomenom in nujnostjo QE. Na podlagi pregleda, primerjav, literature in ilustracij je podan povzetek lastnosti posameznih metod, vključno s kritičnimi dejavniki, prednostmi, slabostmi in področji uporabe: 1. Postopek PEE je preprost in učinkovit, toda v rezultatih se lahko pojavijo določene napake. 2. EVE velja za zgodovino obremenitev z dolgimi cikli obremenitev, izbira ustreznega praga ali velikosti bloka pri ekstrahiranju podatkov pa je težavna. 3. Pri ekstrapolaciji manjših in zmernih obremenitev se lahko uporabi NPE v kombinaciji z oceno jedra. Na verodostojnost rezultatov, ekstrapoliranih z NPE, vplivata jedrna funkcija in še posebej pasovna širina. 4. QE se lahko uporabi takrat, ko vzorčni podatki zajemajo različne delovne pogoje in obratovalne režime. QE je mogoče kombinirati tudi z drugimi metodami ekstrapolacije. Ta pregled ima tudi nekaj pomanjkljivosti. Tako so bile v pregled vključene samo nekatere najbolj pogosto uporabljene metode ekstrapolacije v tehniki, dodati pa bi bilo treba tudi metode iz drugih področij. Uporaba metod ekstrapolacije ni popolnoma razdelana in zato bi bilo treba vključiti dodatno literaturo ter popolnejše smernice za izbiranje. Opraviti bi bilo treba tudi več eksperimentov za preverjanje lastnosti in ovrednotenje vpliva metod. Končno je podanih tudi nekaj smeri za nadaljnje raziskave. Postaviti bi bilo mogoče kriterij za vrednotenje razlike med ekstrapoliranimi in izmerjenimi obremenitvami. Ekstrapolacije se uporabljajo na mnogih področjih, od koder bi si jih bilo mogoče izposoditi in jih smiselno prilagoditi. Rezultati ekstrapolacije morajo biti znotraj zgornjih in spodnjih fizičnih meja tehniških obremenitev, kar daje raziskavam pravilne ekstrapolacije poseben pomen. Članek podaja izčrpen pregled pogosto uporabljenih metod ekstrapolacije v strojništvu, s tem pa prispeva k boljšemu razumevanju metod in njihovih lastnosti. V smernice za izbiro bi bilo mogoče vključiti tudi omembe uporabe metod, predlagane smeri nadaljnjih raziskav pa bi lahko pospešile razvoj na tem področju. Ključne besede: kratkoročni spekter obremenitev, dolgoročni spekter obremenitev, ekstrapolacija obremenitev, parametrična ekstrapolacija, neparametrična ekstrapolacija, kvantilna ekstrapolacija DOKTORSKE DISERTACIJE Na Fakulteti za strojništvo Univerze v Ljubljani so obranili svojo doktorsko disertacijo: • dne 9. decembra 2015 Igor PETROVIĆ z naslovom: »Določitev vpliva odcepljenega toka na aerodinamične lastnosti membranskega aeroprofila« (mentor: prof. dr. Franc Kosel); V nalogi je določen vpliv odcepljenega toka na aerodinamične lastnosti deformabilnega membranskega aeroprofila. Predlagan je numerični algoritem za reševanje dvojno povezane interakcije med fluidom in strukturo, ki je uporabljen za določitev vpliva geometrijskih in snovnih parametrov membrane ter vpliv presežne dolžine membrane na odcepitev in posledično aerodinamične lastnosti membranskih aeroprofilov. Razvit je aeroelastični model s tremi prostostnimi stopnjami, z vertikalnimi in horizontalnimi pomiki ter zasuki okoli prečne osi, ki v aerodinamičnem delu upošteva tudi vpliv odcepljenega toka in sile upora za določitev statičnih aeroelastičnih nestabilnosti krila, npr. divergenčne hitrosti. Rezultati numeričnih simulacij so primerjani z rezultati meritev v vetrovniku, za katere je izdelan merilni model. Ugotovljeno je dobro kvalitativno in kvantitativno ujemanje. Dobljeni numerični rezultati omogočajo razvoj modela majhnega brezpilotnega letala z membranskimi krili, katerega aerodinamične lastnosti so preverjene v vetrovniku; • dne 23. decembra 2015 Marko POLAJNAR z naslovom: »Vpliv zdrsa med mazivom in površino na tribološke lastnosti mazanih kontaktov« (mentor: prof. dr. Mitjan Kalin); V doktorskem delu smo preučevali vpliva zdrsa med površino in mazivom na trenje v mazanih inženirskih makro-kontaktih. V začetnem delu je predstavljeno teoretično ozadje obravnavanega problema in podan pregled dosedanjih raziskav na tem področju, ki pokaže, da je trenutno razumevanje zdrsa med inženirskimi površinami in mazalnimi olji slabo, tudi zaradi nerazumevanja vloge omočljivosti pri tem procesu. V rezultatih doktorske naloge smo tako predstavili medsebojne povezave površinskih lastnosti inženirskih površin in maziv z omočljivostjo, pri čemer smo ugotovili, da je za vrednotenje omočljivosti inženirskih površin z mazalnimi olji potrebno namesto kota omočljivosti uporabljati parameter razširjanja. Ta prameter je tudi ključno orodje za nadzor zdrsa in s tem trenja v mazanih kontaktih. Nadalje smo na podlagi ugotovitve, da vrsta medmolekulskih interakcij pomembno vpliva na omočljivost, predlagali okvirni model zdrsa, ki pojasni, da odsotnost trajnih polarnih interakcij med mazivom in površino povečuje zdrs. V nadaljevanju je predstavljen iterativni postopek za vrednotenje zdrsa v makro-kontaktih, pri čemer smo z vpeljavo novega parametra navideznega zdrsa, prikazali omejitve, doslej najpogosteje uporabljene zdrsne dolžine, za optimiranje tornih lastnosti v mazanih kontaktih, ki temelji na njeni odvisnosti od debeline mazalnega filma. Na koncu smo tudi prikazali, kako lahko s spreminjanjem površin kontakta in kontaktne kinematike, vplivamo na zdrs in trenje. Pri tem lahko podobne učinke znižanja trenja, kot v kontaktih z zdrsom na obeh kontaktnih površinah, pri določenih pogojih dosežemo že v kontaktih le z eno zdrsno površino, kar predstavlja pomemben tehnološki doprinos; • dne 30. decembra 2015 Klemen DOVRTEL z naslovom: »Vremensko pogojeno aktivno naravno ogrevanje in hlajenje stavb« (mentor: prof. dr. Sašo Medved); V doktorski nalogi je prikazan razvoj algoritma vremensko pogojenega delovanja sistemov aktivnega naravnega ogrevanja in hlajenja stavb. Na delovanje teh sistemov močno vplivajo meteorološke razmere, te pa vplivajo tako na potencial energijskega vira (sončno obsevanje, toplota in hlad okolja), ki ga izkoriščamo za ogrevanje in hlajenje stavb, kakor tudi na toplotni odziv sistemov in stavbe. Učinek in razpoložljiva moč energijskega vira sta zato odvisna ne le od trenutnega potenciala naravnih virov energije, temveč tudi od njihovega spreminjanja in pričakovanega toplotnega odziva stavbe v bližnji prihodnosti. Zato smo zasnovali scenarije delovanja sistema aktivnega naravnega ogrevanja in hlajenja ter razvili algoritem, s pomočjo katerega lahko njihovo delovanje optimiramo na podlagi vremenske napovedi. Algoritem vključuje tudi korekcijo vremenske napovedi, ki temelji na rekurzivni metodi korekcije vremenske napovedi z diskretnim Kalmanovim filtrom, s katerim napoved prilagodimo glede na lokalne, specifične lastnosti okolja. Na podlagi razvitega modela nestacionarnega toplotnega odziva sistema aktivnega naravnega ogrevanja in hlajenja ter modela nestacionarnega toplotnega odziva stavbe smo ob predvidenih vremenskih parametrih optimirali delovanje sistema. Na podlagi enokriterijske analize s Quazi-Newtonovo metodo in metodo Nelder-Maid ter večkriterijske analize na podlagi algoritma NSGAII in metode utežnih ostankov smo določili enokriterijski in večkriterijski optimum delovanja sistema. Algoritem vremensko pogojenega delovanja za primer hlajenja smo eksperimentalno preverili na modelu manjše bivalne enote. Information for Authors All manuscripts must be in English. Pages should be numbered sequentially. The manuscript should be composed in accordance with the Article Template given above. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide juastification in a cover letter. 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In this case we will kindly ask the authors to carefully read the Information for Authors and to resubmit their manuscripts taking into consideration our comments. COVER LETTER INSTRUCTIONS: Please add a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and their affiliations. 2. Type of paper: original scientific paper (1.01), review scientific paper (1.02) or short scientific paper (1.03). 3. A declaration that neither the manuscript nor the essence of its content has been published in whole or in part previously and that it is not being considered for publication elsewhere. 4. State the value of the paper or its practical, theoretical and scientific implications. What is new in the paper with respect to the state-of-the-art in the published papers? Do not repeat the content of your abstract for this purpose. 5. We kindly ask you to suggest at least two reviewers for your paper and give us their names, their full affiliation and contact information, and their scientific research interest. The suggested reviewers should have at least two relevant references (with an impact factor) to the scientific field concerned; they should not be from the same country as the authors and should have no close connection with the authors. FORMAT OF THE MANUSCRIPT: The manuscript should be composed in accordance with the Article Template. The manuscript should be written in the following format: - A Title that adequately describes the content of the manuscript. - A list of Authors and their affiliations. - An Abstract that should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions. - 4 to 6 significant key words should follow the abstract to aid indexing. - 4 to 6 highlights; a short collection of bullet points that convey the core findings and provide readers with a quick textual overview of the article. These four to six bullet points should describe the essence of the research (e.g. results or conclusions) and highlight what is distinctive about it. - An Introduction that should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated. - A Methods section detailing the theoretical or experimental methods used. - An Experimental section that should provide details of the experimental set-up and the methods used to obtain the results. - A Results section that should clearly and concisely present the data, using figures and tables where appropriate. - A Discussion section that should describe the relationships and generalizations shown by the results and discuss the significance of the results, making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve clarity.) - A Conclusions section that should present one or more conclusions drawn from the results and subsequent discussion and should not duplicate the Abstract. - Acknowledgement (optional) of collaboration or preparation assistance may be included. Please note the source of funding for the research. - Nomenclature (optional). Papers with many symbols should have a nomenclature that defines all symbols with units, inserted above the references. If one is used, it must contain all the symbols used in the manuscript and the definitions should not be repeated in the text. In all cases, identify the symbols used if they are not widely recognized in the profession. Define acronyms in the text, not in the nomenclature. - References must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript. - Appendix(-icies) if any. SPECIAL NOTES Units: The SI system of units for nomenclature, symbols and abbreviations should be followed closely. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.). Please also see: http://physics.nist.gov/cuu/pdf/sp811.pdf . Abbreviations should be spelt out in full on first appearance followed by the abbreviation in parentheses, e.g. variable time geometry (VTG). The meaning of symbols and units belonging to symbols should be explained in each case or cited in a nomenclature section at the end of the manuscript before the References. Figures (figures, graphs, illustrations digital images, photographs) must be cited in consecutive numerical order in the text and referred to in both the text and the captions as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats. If a figure is composed of several parts, please mark each part with a), b), c), etc. and provide an explanation for each part in Figure caption. The caption should be self-explanatory. Letters and numbers should be readable (Arial or Times New Roman, min 6 pt with equal sizes and fonts in all figures). Graphics (submitted as supplementary files) may be exported in resolution good enough for printing (min. 300 dpi) in any common format, e.g. TIFF, BMP or JPG, PDF and should be named Fig1.jpg, Fig2.tif, etc. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. Multi-curve graphs should have individual curves marked with a symbol or otherwise provide distinguishing differences using, for example, different thicknesses or dashing. Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the captions as Table 1, Table 2, etc. In addition to the physical quantities, such as t (in italics), the units [s] (normal text) should be added in square brackets. Tables should not duplicate data found elsewhere in the manuscript. Tables should be prepared using a table editor and not inserted as a graphic. REFERENCES: A reference list must be included using the following information as a guide. Only cited text references are to be included. Each reference is to be referred to in the text by a number enclosed in a square bracket (i.e. [3] or [2] to [4] for more references; do not combine more than 3 references, explain each). No reference to the author is necessary. References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. Please add DOI code when available. Examples follow. Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code. [1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, D0I:10.5545/sv-jme.2011.013. Journal titles should not be abbreviated. Note that journal title is set in italics. Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication. [2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken. Note that the title of the book is italicized. Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages. [3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553576. Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages. [4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied lean system in process industry. MOTSP Conference Proceedings, p. 422-427. Standards: Standard-Code (year). Title. Organisation. Place. [5] ISO/DIS 16000-6.2:2002. Indoor Air — Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva. WWW pages: Surname, Initials or Company name. Title, from http://address, date of access. [6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 200909-07. EXTENDED ABSTRACT: When the paper is accepted for publishing, the authors will be requested to send an extended abstract (approx. one A4 page or 3500 to 4000 characters). The instruction for composing the extended abstract are published on-line: http://www.sv-jme.eu/information-for-authors/ . COPYRIGHT: Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original work by the authors and not be published elsewhere in any language without the written consent of the publisher. The proof will be sent to the author showing the final layout of the article. Proof correction must be minimal and executed quickly. Thus it is essential that manuscripts are accurate when submitted. Authors can track the status of their accepted articles on http://en.sv-jme.eu/. PUBLICATION FEE: Authors will be asked to pay a publication fee for each article prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 240.00 EUR (for articles with maximum of 6 pages), 300.00 EUR (for articles with maximum of 10 pages), plus 30.00 EUR for each additional page. The additional cost for a color page is 90.00 EUR. These fees do not include tax. Strojniški vestnik - Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu http://www.sv-jme.eu Contents Papers Jaka Pribošek, Miha Bobič, Iztok GoLobič, Janez Diaci: Correcting the Periodic Optical Distortion for Particle-Tracking Velocimetry in Corrugated-Plate Heat Exchangers Grzegorz Budzik, Jan Burek, Anna Bazan, Pawet Turek: Analysis of the Accuracy of Reconstructed Two Teeth Models Manufactured Using the 3DP and FDM Technologies Ning Zhang, Minguan Yang, Bo Gao, Zhong Li, Dan Ni: Investigation of Rotor-Stator Interaction and Flow Unsteadiness in a Low Specific Speed Centrifugal Pump VeyseL ALankaya, Fuat ALarcin: Using Sandwich Composite Shells for Fully Pressurized Tanks on Liquefied Petroleum Gas Carriers Tomaž PepeLnjak, MLadomir MiLutinović, Miroslav PLančak Dragiša ViLotić, Saša RandjeLović, Dejan Movrin: The Influence of Extrusion Ratio on Contact Stresses and Die Elastic Deformations in the Case of Cold Backward Extrusion Marek Magdziak: An Algorithm of Form Deviation Calculation in Coordinate Measurements of Free-Form Surfaces of Products Jixin Wang, Hongbin Chen, Yan Li, Yuqian Wu, Yingshuang Zhang: A Review of the Extrapolation Method in Load Spectrum Compiling 3 9770039248001