>s Strojniški vestnik Journal of Mechanical Engineering no. 10 year 2020 volume 66 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: Koštomaj printing office, printed in 275 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 Mitjan Kalin University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Bojan Dolšak University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: The flow chart of the proposed damage online evaluation. A comparison between cumulated real damage (Real) over time and the results of the proposed methodology (Estimated ). Image courtesy: Department of Engineering, University of Perugia, Perugia, Italy ISSN 0039-2480, ISSN 2536-2948 (online) International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, King Fahd U. of Petroleum & Minerals, Saudi Arabia Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, University of Ljubljana, Slovenia Filippo Cianetti, University of Perugia, Italy Janez Diaci, University of Ljubljana, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Jožef Duhovnik, University of Ljubljana, Slovenia Igor Emri, University of Ljubljana, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, University of Ljubljana, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, University of Maribor, 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, University of Ljubljana, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, University of Ljubljana, Slovenia Gorazd Lojen, University of Maribor, Slovenia Darko Lovrec, University of Maribor, Slovenia Thomas Lubben, University of Bremen, Germany Jure Marn, University of Maribor, Slovenia George K. Nikas, KADMOS Engineering, UK Tomaž Pepelnjak, University of Ljubljana, Slovenia Vladimir Popovič, University of Belgrade, Serbia Franci Pušavec, University of Ljubljana, Slovenia Mohammad Reza Safaei, Florida International University, USA Marco Sortino, University of Udine, Italy Branko Vasič, University of Belgrade, Serbia Arkady Voloshin, Lehigh University, Bethlehem, USA 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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We would like to thank the reviewers who have taken part in the peer-review process. © 2020 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Research Agency. Strojniški vestnik - Journal of Mechanical Engineering is available on https://www.sv-jme.eu. Strojniški vestnik- Journal of Mechanical Engineering 66(2020)10 Contents Contents Strojniški vestnik - Journal of Mechanical Engineering volume 66, (2020), number A Ljubljana, October 2020 ISSN 0039-2480 Published monthly Papers Filippo Cianetti: How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems? Adam Kulawik, Joanna Wrbe 1: Numerical Study of Stress Analysis for the Different Widths of Padding Welds Oscar Tenango-Pirin, Elva Reynoso-Jardn, Juan Carlos Garcia, Yaliir Mariaca, Yuri Sara Hernández, Raü Ñeco, Omar Dávalos: Effect of Thermal Barrier Coating on the Thermal Stress of Gas Microturbine Blades and Nozzles Yong Wang, Zilong Zhang, Jie Chen Houlin Liu, Xiang Zhang, Marko Hočevar: Effect of Blade Coating on a Centrifugal Pump Operation under Sediment-Laden Water Flow llyas Kacar, Fahrettin Ozturk, Serkan Toros, Suleyman Kilic: Prediction of Strain Limits via the Marciniak-Kuczynski Model and a Novel Semi-Empirical Forming Limit Diagram Model for Dual-Phase DP60 Advanced High Strength Steel Xihui Chen, Gang Cheng, Ning Liu, Xinliui Shi, Wei Lou: Research on a Noise Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10,557-566 © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6853 Original Scientific Paper Received for review: 2020-07-09 Received revised form: 2020-08-21 Accepted for publication: 2020-09-24 How to Ep erimentalljM onitor the Fatigue Behaviour of Vibrating Mechanical S^ tems? Filippo Cianetti* University of Perugia, Italy Fatigue damage and, in general, fatigue behaviour is not simple to observe or estimate during the operational life of a generic vibrating mechanical system. There area lot of theoretical or numerical methods that allow to evaluate it or by knowing a priori the loading conditions and obtaining output stress states by adopting numerical models of the mechanical system or by directly experimentally measuring and acquiring stress/strain states. A few examples of instruments (e.g. rain flow recorders) or measurement chains dedicated to estimate it in time domain or frequency domain are found in the literature but none that fully both observes the system dynamic behaviour and estimates the related actualized cumulated damage, and, thus, none that can estimate the residual life of the system itself. In this paper, a simple time-domain method, designed to monitor the instantaneous fatigue behaviour by definition of the instantaneous and cumulated potential damage or of equivalent damage signal amplitude is presented, based on rain-flow counting method and a damage linear cumulation law and starting from system dynamics signals. This methodology was designed to overestimate real damage to alert the system manager before any crack starts and to be simply translated into electronic boards that can be mounted on generic mechanical systems and linked to one of the sensors that usually monitor system functionality. Keywords: fatigue; damage; rain flow counting; random loads Highlights • A smart procedure to on-line evaluate the fatigue behaviour of mechanical systems is presented. • It is based on rain-flow counting method and a damage linear cumulation law. • It is designed to be simply translated into electronic boards. • This method allows placing fatigue among the phenomena to be controlled in feedback in any mechanical system. 0 INTRODUCTION Fatigue damage and, in general, fatigue behaviour is not simple to be observed or estimated during the operational life of a generic vibrating mechanical system (e.g. automotive [1] and [2], aeronautical [3] and naval applications [4] or wind turbines [5]). Many theoretical or numerical methods allow evaluating it by knowing a priori the loading conditions (i.e. force or acceleration) [6], expressed in time [6] to [10] or frequency domain [10] to [12], and obtaining output stress states by adopting numerical models of the mechanical system (i.e. multibody (MBS) [13], finite element (FE) [14], multibody with flexible elements (Flex/MBS) [15]) or by directly experimentally measuring and acquiring stress/strain states, knowing, by hypotheses, the fatigue strength (i.e. S-N Wohler or Basquin curve [16]). A few examples of instruments or measurement chains dedicated to evaluate it in time domain (rain flow recorder [17]) or in frequency domain [18] and [19] are available the in literature but none that fully observes the system dynamic behaviour (i.e. accelerations, internal loads, strains) and foresights the related actualized damage and, is thus able to estimate the residual life of the system itself. In this paper, a simple time-domain method (used in previous papers [20] and [21]), designed to monitor the instantaneous fatigue behaviour by definition of instantaneous and cumulated potential damage or equivalent damage signal amplitude is presented, based on the Rain Flow Counting (RFC) method [16], on a damage linear cumulation law (Palmegren-Miner's rule [16]), and starting from signals coming from system dynamics. This methodology was designed to overestimate real damage to alert the system manager before any crack starts and to be translated simply into an electronic board to be mounted on a generic mechanical system and linked to one of the sensors that usually monitor system functionality. To this aim, this paper presents its translation in a computing enviromnent dedicated to the dynamic multi-domain simulation of mechanical systems and to the design and verification of control systems. This passage made it possible to verify how the results, obtainable from the evaluation tool, can be obtained online both directly, by the physical measurements made on the turbine, and, in any case, by numerical measures, obtainable through more or less complex dynamic models of the generator itself. The fundamental hypothesis of this work is that many experimental measures are acquired online. *Corr. Author's Address: University of Perugia , Via G. Duranti, 93,06125 Perugia, Italy, filippo.cianetti@unipg.it 557 Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10,557-566 for various reasons, on generic machines (i.e. speed, accelerations, moments) and whose values are instantly used to control any condition without being affected by assessments related to the duration, fatigue or damage of the system itself. Assuming the linear behaviour of the machine and of the mechanical system, a relationship can always be established between these measures and the generic stress state in any location of the components, allowing to drive evaluations toward fatigue on such generic signals but adopting the classical evaluation tools adopted on stress state time histories. If the evaluation of the fatigue behaviour is made starting from a generic signal on which all the hypotheses and tools developed over the years for the evaluation of the damage starting from stress state cannot be directly adopted [16], the definition of fatigue Potential Damage and, therefore, the proposed method can be justified. 1 TIME DOMAIN FATIGUE ANALYSIS If a generic signal (i.e. acceleration force, moment) x is considered, to evaluate the mechanical system or component fatigue behaviour and to evaluate its durability performance, the fatigue strength curve related to it has to be known. Its expression is the following, similar to that of the Basquin [16] curve for stress signals: xf =a-N13, a where xf is the strength amplitude value of the signal related to an applied cycles number TV, a is the intercept of the curve on the amplitudes axis for N= I [1 is the curve slope considered constant in the whole cycles range. Its inverse representation is also valid: N = Í/—, a (2) where N represents the strength cycles number when an amplitude value xa of the alternating signal is applied. The choice to adopt a single slope curve is justified by the nature of the proposed method intended to monitor potential damage but not real damage. The most common evaluation method of the fatigue behaviour, i.e., of the damage, therefore, requires two further steps: to identify a damage model and to choose a counting and identifying method for the alternating cycles of the signal under examination. The adoptable damage model is the linear damage cumulation law of Palmegren-Miner [16], Regarding the cycles counting, the counting method considered as standard in this paper; however, the scientific community and international standards uses the RFC as standard [16], The RFC identifies the closed hysteretic cycles defined by the signal and, generally, the cycles are collected in bands (bins) to reduce the result dimensions of this evaluation. A load spectrum (i.e. a three-column matrix) can be obtained in which the number of counted cycles n. the associated mean value xm and amplitude value xa of the signal are represented in its generic row. All the counted cycles can also still be kept in memory, with relative amplitude and mean value, without to be sampled in bands, obtaining, in this case, a spectrum with as many rows as many cycles were counted, that is assuming for each row n = .1 The presence of a mean value would require a further step to adopt the previously mentioned damage model. By adopting, for example, the correction of Goodman or Gerber [16], it is possible to trace back to an equivalent amplitude value of the cycle by knowing ultimate static strength related to of the variable, xut. However, following the hypothesis introduced in the introduction and at the beginning of this sections, that the signal that is going to be analysed does not allow going back to parameters strictly related to the component strength, for example to the ultimate static strength, the first simplification hypothesis assumed is that the mean value of the generic cycle will be neglected. Assuming the above hypothesis, the load spectrum can be represented as shown below: (3) with, respectively, xl7 and n the vectors of amplitude and number of applied or counted cycles. By knowing spectrum (Eq. (} ), fatigue damage is évaluable by Palmegren-Miner rule, that is by the following: (4) where m is the total number of counted cycles, Dp the cumulated damage [16], Subscript p is used to remember that the damage, not being calculated necessarily starting from a stress value, is potential damage [22] and [23], very useful for comparative 558 C/anett/, F Strojniski vestnik ■ Journal of Mechanical Engineering 66(2020)10, 557-566 analysis but not to be analysed as the absolute value of the real damage Another definition, useful to better understand the subsequent steps proposed by the method object of the present paper, is that of damage equivalent signal (DES) [5], often used in the field of wind engineering. Under the hypothesis of the constant slope of the fatigue strength curve, by knowing the damage or equivalently the load spectrum, it is possible to define a stationary cyclic condition equivalent to the entire spectrum [23] in terms of damage. Given an arbitrary number of cycles, to which it is possible to assign the value of the total number of cycles m. it is always possible to evaluate the equivalent amplitude value of the signal that determines the same damage of the whole spectrum (xl7, n) by means of the following equation: = a ■ •z (I that can be also expressed as follows by adopting damage definition (Eq. (J ): = a 2 PROPOSED PROCEDURE FOR DAMAGE MONITORING To evaluate the cumulative damage at a given moment in the life of the mechanical system requires acquiring the whole history of the signal, considered representative of its behaviour, from the first use of the machine, seamlessly, to the moment of evaluation. Moreover, it is useful to instantaneously know if the dynamic condition is dangerous or critical for system fatigue behaviour. The evaluation of cumulated damage is difficult to be performed both for reasons of memory space allocation and for reasons related to computational times to perform cycles counting through RFC and then to damage evaluation. As concerns the second aim, an instantaneous damage definition does not exist, such as an instantaneous equivalent damage value of the reference signal to be adopted to control system dynamics actively. The author wants to demonstrate the possibility of monitoring the potential damage of a generic machine by evaluating it at any of the operating times without taking up all the memory space required by the ideal methodology, evaluating it by adopting a mobile window defined in the time domain, of appropriate characteristics, allowing by this approach to define the "instantaneous" damage such as the "instantaneous" equivalent damage signal. Let us imagine having a signal measured throughout its temporal extension T and on which it is, therefore, possible to evaluate the real potential damage by applying the RFC and Palmgren-Miner's rule (Eq. $ ) in increasing time intervals |0. i,\. with i, between 0 and T. This enables defining a time history of the damage Dp{t). Associated with this time history, the time history of the damage equivalent signal xaj (t) can also be obtained. Fig. 1 shows the flow chart of the process. Fig. 1. Flowchart of standard evaluation of damage time history [20] How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems? 559 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 557-566 The formulation of the RFC method is a function of the hypothesis that the signal time history is single or repeats itself several times, which introduces a dichotomy of the load spectrum and, therefore, of the damage and of the equivalent alternating value of the signal caused by the definition of residue [16] and [24] and its management within the counting method. The residues are the values of the signal that do not determine any closed hysteretic cycle and, therefore, are not considered in the evaluation of the damage for single signal time history. For signals that repeats several times, however, by adopting the rule of Cloonnan-Seeger or ASTM [24] and [25], all the cycles are forcibly closed, which determines a different assessment of the damage for the two aforementioned hypotheses. With the objective of monitoring fatigue in mechanical systems that are typically very long-term loaded with variable and random loads, the hypothesis of repeating signal is adopted in this paper and in this proposed approach. The first step of the proposed procedure is to define a moving window. Which sampling time tl should has to be taken? How long must the mobile window be A7? The answers to these two questions define the fundamental choices of the procedure. Answering these questions means analysing the mechanical system and the load conditions to which it is typically subjected and, therefore, presumably, to which it will be subjected in the future, during operating conditions. The analysis of the frequency content of the loads (accelerations or forces) and of the natural frequencies of the system and/or component constitutes the instrument with which to reach and define these two values. The sampling time must be such as to capture the maximum frequency /m;ix that is wanted to be observed, whether this is the maximum observable in the input or that represents the natural mode of maximum natural frequency that is to be considered. The sampling time ti must be k times lower than that corresponding to the maximum frequency value: The length of the mobile window AT must instead be such as to capture the minimum frequency fmm that is wanted to be observed, whether this is the minimum observable in the input or that represents the natural mode of minimum natural frequency that is to be considered. AT must be at least k times the value of the one corresponding to the minimum frequency: AT = k- — . (8) f J min These two limit values allow observing and, therefore, being able to count the cycles associated with both fast and slow phenomena in the mobile window, in an appropriate number that can represent a significant spectrum for the loading condition. Once the floating window lias been defined, this is the data buffer that is continuously filled in for the evaluation of fatigue behaviour. In Fig. 2, a flow chart of the proposed procedure is shown. Fig. 2. Flowchart of proposed evaluation of damage time history [20] 560 Cianetti, F. Strojniski vestnik ■ Journal of Mechanical Engineering 66(2020)10, 557-566 When the mobile 7th window is post-processed, the load spectrum obtained by RFC is: The Cloorman-Seeger hypothesis is followed without considering the cycle mean value. If a strength curve such as Eq. (J is adopted, it is possible to define the 7th potential damage dp, which is called instantaneous damage, meaning by instantaneous the one associated with the current mobile window: A-=l M, ((D) in which subscript i refers to 7th window and k to the generic spectrum cycle (Eq. (ty ), counted in the same window, nij is the total number of cycles counted in the window. The cumulated damage at the generic instant, that is at the generic 7th window, is: r=i Similarly, the DES related to the window is: = a • «vZ k=l ■ a m. (2) (I The value jc is strongly influenced by the number of cycles counted in the window, mh and therefore window by window, could vary in value, increasing or decreasing, without, however, meaning that the damage has increased or decreased. For example, if two windows 7th and (i + J th generate the same instantaneous damage dp but the two windows contain different numbers of cycles m, and m, ,. two different values of x occur for the same damage. To overcome this result and have a value of comparable among the various windows and, therefore, independent of the number of cycles, the value of the normalized DES has been defined x that is evaluated in the hypothesis of a number of cycles constant for all the windows. In the case of the number of cycles constant and equal to 1 its definition x -a Ad «de, L Pi J (J It has to be highlighted that the definition of the fatigue curve as previously done and the consequent damage evaluation procedure are strictly related. If we have to manage signals that are not stresses or strains and thus not directly related to the concept of the Basquin curve or of hot spot stress or of the damage rule, a virtual damage evaluation has to be accepted, which that means the definition of a strength curve that implicitly considers aspects such as stress concentration, mean effect, or reliability. As more these are well modelled into the curve, the potential damage and the instantaneous damage will be closer to the real one. 3 SIMPLE TEST CASE The example (signal) considered to test the goodness of the method is shown in Fig. 3 and relative to an accelerometric measurement carried out in a wind tunnel, on a mini-wind generator [20], [21] and [26]. It varies in a rage from 2 m/s2to 2 m /s2. Fig. 3. Time history of signal test case Figs. 4 and 5 show the rain flow matrix, the cumulative of the amplitudes of the cycles (Fig. ^ and the time histories of the equivalent signal (DES) and of the damage (Fig. j> . The calculation of the damage and of the equivalent signal was carried out by assuming a fatigue strength curve with parameters a = ffi3n /s2 and fi=0,2228 How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems? 561 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 557-566 a) 0 0.5 1 1.5 2 2.5 3 3.5 10° 101 102 103 104 range Cycles log [no units] Fig. 4. a) Rain flow counting matrix, and b) cycles amplitude cumulative of test case time history 0 1 0 20 30 40 50 60 70 80 0 1 0 20 30 40 50 60 70 &0 time [s] time [S) Fig. 5. a) Damage equivalent signal and b) cumulative damage time histories of test case signal 562 Cianetti, F. Strojniski vestnik ■ Journal of Mechanical Engineering 66(2020)10, 557-566 Fig. 7. Proposed method results; a) instantaneous damage d„ and b) cumulative damage D„ time histories Fig. 8. Proposed method results; a) damage equivalent signal amplitude xa x time histories and b) normalized damage equivalent signal amplitude Analysing the temporal profile of the wind speed, which in this case was constant (therefore without a defined frequency content), the minimum and maximum frequencies were defined exclusively starting from the natural frequencies of the tower [26], Considering as a minimum factor a factor k (Eqs. (J and ) equal to 5 a mobile time window has been defined, characterized by AT=D s and d =0.005 s, which satisfies both relations (Eqs. (J and ). Fig. 6 shows one of the moving windows (/' = p!d (Fig. V . A comparison between the equivalent signals (DES) is not possible since, by definition, while for the real signal the number of cycles m grows monotonously over time (see Fig. J in the sampled one (proposed How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems? 563 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 557-566 time [s time [s] , 9. Comparison between results obtained by proposed method (Estimated) and standard one (Real); a) cumulative damage Dp and b) instantaneous damage dp time histories 10 time [s] time [s] Fig. 10. Proposed method sensitivity analysis; potential damage cumulatives; a) comparison among results obtained by adopting windowing sizesofTable 1, b) detailed comparison (in linear scale) for the last 30 seconds of the signal Analysts no.l Analysis no 2 Analysis no.3 time [s] Analysis ro.1 Analysis no.2 Analysis rta.3 time s] Fig. 11. Proposed method sensitivity analysis; comparison among results obtained by adopting windowing sizes of Table 1; a) instantaneous damage and b) normalized DES 564 Cianetti, F. Strojniski vestnik ■ Journal of Mechanical Engineering 66(2020)10, 557-566 method) each window shows a number of increasing or decreasing variable cycles (see Fig. 2). The comparison between the cumulative damage time histories (Fig. )> shows how the proposed method is sufficiently accurate to estimate both the trend but also the absolute value of the damage. In the final part of the paper, how the choice of an incorrect sampling time rather than an incorrect size of the mobile window can negatively affect the obtainable results is shown. In Figs. ® and 11 the results previously obtained with A7 - .1) s and ti =0.005 s are compared with those obtained with other two pairs of values of AT and ti for which values too small of AT have been deliberately adopted, from not being able to count the low-frequency cycles accurately (in this test case the most important), and too large values of ti have also adopted, losing the small-amplitude cycles (in this test case, the greater number) (Table J . Table 1. Windowing parameters adopted for sensitivity analysis Mobile window parameters tl [s] Ar[s] Analysis no.l 0.005 1.00 Analysis no.2 0.005 0.10 Analysis no.3 0.020 1.00 Fig. ® compares the time histories of the cumulative damage, real and estimated by the proposed method (represented in a logarithmic scale on the left and in a linear scale and for the final part of the signal on the right). In Fig. 11 the trends of the instantaneous damage (Fig. li ) and of the normalized equivalent signal (Fig. lib) are instead compared. It can be noted that the choice of these two parameters significantly influences the results. 4 CONCLUSIONS In this paper, it lias been demonstrated how, starting from the online measurement of any representative signal of the behaviour of the mechanical system, it is possible to define and obtain an instantaneous evaluation of the potential damage of the signal in terms of damage (DES) in the time domain. This possibility provides the scientific and technical community the automatic control the possibility to insert the fatigue among the phenomena to be controlled in feedback in any mechanical system (i.e., automotive vehicles, aircraft, trains, ships, wind turbines) evaluating not only the maximum or minimum values in the signal but also their damaging potential. In this way, in addition to an instantaneous evaluation, a cumulative evaluation of the potential damage is also obtained, which becomes a further control parameter, given an admissible threshold for this signal. The author does not want to estimate the final damage related to an assigned time duration of the system by observing a single time window (in this case, that has to be sufficiently long to stabilize damage variance) but only to evaluate an "instantaneous" one and obtain the actual cumulated damage by cumulating these values, which is a characteristic of the approach that allows it to be used as a monitor. The proposed methodology highlights how particular attention must be paid to the choice of the characteristic parameters of the window, specifically, its time length and sampling time. 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Journal of the Society of Materials Science Japan, vol. 46, no. 10, p. 1217-1221, D0I:10.2472/ jsms.46.1217. (in Japanese) [18] Braccesi, C., Cianetti, F., Moretti, M., Rossi, G. (2015). Random loads fatigue. Experimental approach through thermoelasticity. Procedia Engineering, vol. 101, p. 312-321, D0I:10.1016/j.proeng.2015.02.038. [19] Zanarini, A. (2015). Full field experimental modelling in spectral approaches to fatigue predictions. Proceedings of IFToMM - ICoEV2015 International Conference on Engineering Vibration, p. 773- 782. [20] Cetrini, A., Cianetti, F., Corradini, M.L., Ippoliti, G., Orlando, G. (2019). On-line fatigue alleviation for wind turbines by a robust control approach. International Journal of Electrical Power and Energy Systems, vol. 109, p. 384-394, DOI:10.1016/j. ijepes.2019.02.011. [21] Cianetti, F., Cetrini, A., Corradini, M.L., Ippoliti, G., Orlando, G. (2018). Dynamic behavior of wind turbines. An onboard evaluation technique to monitor fatigue. Procedia Structural Integrity, vol. 12, p. 102-112, DOI:10.1016/j. prostr.2018.11.103. [22] Cianetti, F., Alvino, A., Bolognini, A., Palmieri, M., Braccesi, C. (2018). The design of durability tests by fatigue damage spectrum approach. Fatigue and Fracture of Engineering Materials and Structures, vol. 41, no. 4, p. 787-796, D0I:10.1111/ffe.12686. [23] Cianetti, F. (2012). Development of a modal approach for the fatigue damage evaluation of mechanical components subjected to random loads. SDHM Structural Durability and Health Monitoring, vol. 8, no. 1, p. 1-29. [24] Clormann, U., Seeger, T. (1986). Rainflow - HCM - Ein Zählverfahren für Betriebsfestigkeitsnachweise auf werkstoffmechanischer Grundlage. Stahlbau, vol. 55, p. 65117. [25] ASTM Standard E 1049 (1985). Standard Practices for Cycle Counting in Fatigue Analysis. ASTM International, West Conshohocken. [26] Castellani, F., Astolfi, D., Becchetti, M., Berno, F., Cianetti, F., Cetrini, A. (2018). Experimental and numerical vibrational analysis of a horizontal-axis micro-wind turbine. Energies, vol. 11, no. 2, art. ID 456, D0I:10.3390/en11020456. 566 Cianetti, F. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10,567-580 © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6771 Original Scientific Paper Received for review: 2020-07-583 Received revised form: 2020-08-21 Accepted for publication: 2020-09-24 Numerical Studjof Stress Anal^ is for the Different W dths of Padding W Ids Adam Kulaw ik -J oannaWrbe 1* Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Poland In the presented study, the cases of regeneration of the element made of C45 steel, using the MAG (Metal Active Gas) method are analysed. The base material is applied to the regeneration process. The analysis of the influence of the padding weld width (0.006 m, 0.01 m, 0.014 m) and the preheating temperature on the phase transformations and effective stresses of the regenerated layer are performed. A nonstandard approach to preheating (before each padding weld after the cooling to ambient temperature) is considered. Due to the possibility of simplifying the model from 3D to 2D (symmetry of calculations for long padding welds), calculations were performed using the finite element method in the transverse to the padding direction. Each new padding weld was included as an additional area in the finite element mesh. The developed numerical model includes a temperature model, phase transformations in the liquid and solid states, and the stress model in the elastic-plastic range. The aim of the regeneration is not only to obtain the original geometiy of the element, but it is also important that the filler material used (in the considered case identical to the base material) has appropriate properties. These properties largely depend on the phase composition. The used filler material affects not only the hardness, brittleness, and ductility of the material. Its kinetics and changes in the geometry can cause significant stresses and even cracks. Based on the obtained results, it can be concluded that increasing the width of the padding welds causes a decrease in the level of residual effective stress; however, it is technologically difficult to accomplish. The most unfavourable stresses occur in the initial area of the pad welding zone. For lower preheating temperatures and smaller welds, areas with possible cracks are identified. In these cases, lower preheating and tempering should be carried out, which leads to similar energy costs as at higher preheating temperatures. Due to the complex phase transformation process for medium carbon steels and the need for the process parameters control, proper regeneration is possible only in automated workstations. Keywords: computational mechanics, numerical simulation, padding weld, preheating, strain analysis, stress Highlights • Modelling of multiple mesh geometry in the padding weld process is presented. • The mathematical and numerical models of phenomena occurring during the regeneration process using the welding are applied. • The presented research allows for significantly reducing the number of technological treatments. • The presented paper concerns the shape of the padding weld with an angle of 90 • The developed numerical model enables the modelling of the various parameters of the regeneration process, such as: preheat temperature, pad geometry, selection of the cooling medium. 0 INTRODUCTION The medium CS carbon steel is suitable for annealing, weldable, and an easy-to-heat treatment. It is a durable steel with significant ductility [1]. CS steel is used for the moderately loaded and abrasion-resistant machine and equipment parts, such as spindles, axles, shafts, gear wheels, shafts of electric motors, discs, screws, wheel hubs, as well as for moulds in plastics processing. Because the range of regenerated CS steel parts is extensive, in this paper only the application of new layers to the thin-walled element is analysed. Due to the need to obtain hard coatings, especially during exposure to abrasion, it is necessary to control phase changes during cooling and reheating. Components made of the tested material make it possible to obtain high surface hardness (8 HRC). The modelling of the multi-pass pad welding process is not a common topic of research papers. Due to the experimental approach for solving these problems, expensive test stands are most often used. For example, thermal analyses obtained from thermovision cameras for process control are used [2], The data obtained from these analyses can be successfully used to calibrate much cheaper numerical models. Modelling in the field of thermal phenomena in the pad-welding process of a multilayer or multi-pass is performed even for the complex geometries. However, such models most often refer to the thermal phenomena and compare temperatures obtained from numerical analysis to results obtained from experiments, such as the heat-affected zone (HAZ), hardness, and phase compositions [3], In the welding or pad welding technology, a highly accurate process temperature is required (at different points of geometry). This approach allows one to, for example. *Corr. Author's Address: Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Czestochowa, Poland, joanna.wrobel@icis.pcz.pl 567 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 control the grain size as well as the temperature of the start and finish of martensite transformation [4], Existing works show that the multi-layer thermal cycle for some materials can have a weakening effect on mechanical properties [5], However, there are contraindications to the use of large cross-sectional welds or padding welds due to unfavourable segregation of dopant and excessive strains. In pad-welding technology, there are also interesting studies on cladding the parent material with several layers of different materials. However, due to the low thickness of the obtained coating and the depth of HAZ, the stress analysis of these examples cannot be referred to as typical padding welds [6], Thin layers of padding welds, in cases in which the area of the base material is much larger, are characterized by a small thermal influence on this area. With a significant level of heat dissipation from the padding welds, a martensitic transformation may take place in the case of thin padding layers. Due to the large volume changes during the martensitic transformation the padding of thin layers is made of materials without phase transformations in a solid state. The residual stress analysis is more often performed by the authors of papers on repair welds, in which the system of the next padding welds has a vertical direction [7] and [8], In these cases, it is necessary to use the next small cross-sectional layers of padding weld. The use of a large padding weld would be unfavourable, for example, due to higher thermal loads or segregation of the admixture. This fact applies especially to corrosion-resistant materials; however, the influence of phase changes is most often not analysed, which is justified by the fact that such materials have a small change in microstructure, which cannot be said about medium carbon steel analysed in the paper. Regenerative pad welding is a complex process, and the regeneration of even a geometrically simple surface may involve the necessity of different position and direction of padding welds [9]. In cases of modelling the pad welding processes for large areas with layers of welds with different orientations, three-dimensional (E) ) modelling should be performed. It is not possible to perform the analysis only in the cross-section. The presented research allows one to reduce the number of technological treatments significantly. Due to the need to obtain a specific hardness of the hardfacing for various applications of C4 steel (steel with high carbon equivalent), it is necessary to choose the appropriate preheating temperature range. The ease of formation of the hardening structures of C4 steel during the hardfacing/welding often leads to high 568 Kulawik, A. - stresses and, consequently, cracks. The basic method of preventing cold cracks is preheating, which allows for more flexible transition structures, e.g., bainite [10], The presented paper concerns the shape of the padding weld with an angle of 9 In accordance with the requirements of the norm EN ISO 8 [11] quality D, this weld toe is the worst of the technologically possible solutions. It is also necessary to choose the padding weld width for economic reasons and the obtained stress states (the possibility of surface cracks and on the entire height of the padding weld). In both experimental and numerical studies, the authors most often analyse the shape of the padding welds with a quality level higher than D [12] and [13], This paper is an extension of the analyses carried out in the research contained in the earlier work [14], The authors analysed different preheating temperatures for one width of the padding weld. However, they did not discuss the choice of the width of the padding weld for the regeneration process of medium-carbon steel. In this paper, distinct from previous research [14], the application of both smaller and larger padding weld widths (0.006 m, 0.01 m, 0.04 m) was analysed. In order to obtain the correct regenerative padding weld (PW) without any nonconformities 2 cases of combinations of different preheating temperatures and widths of the padding weld are analysed in this paper. The use of numerical simulations reduces the cost of experiments. Using them on a wider scale allows for multi-criteria analysis, based on which we can obtain optimal parameter values. All calculations were performed on a copyrighted application. This model contains appropriate relationships between elements regarding temperature modelling and phase transformation occurring in the range above and below liquidus temperature ('/, ) and solidus temperature (Ts). The relationships between the above models and the model of mechanical phenomena are also taken into account. 1 COMPUTATIONAL MODEL In this paper, the computational model of phenomena taking place during the regeneration of parts is the same as for welding modelling. The model is composed of a module of heat treatment modelling (Fig. J and a module taking into account mechanical phenomena (Fig. } . The phase transformations of austenite to ferrite, pearlite, bainite, martensite and reverse transformations were considered (Fig. 2). The solidification process was analysed in the model. Couplings between the elements of the model were also included. Wrobel, J. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 ( Geometry ^ ( S2X 1 H (n*—*) \ , f Temperature J ✓ N Heat sources S Initial conditions J -JF 7> V__/ _c ^ rThermophysical\ / Integration ^ properties J I scheme. At j Fig. 1. Elements of the thermal phenomena model for the regeneration process The process of regeneration of steel elements depends mainly on the temperature factor. Therefore, not including the main elements in the heat transfer model can lead to significant simulation errors (Fig. J . Large temperature changes over time required the solution of the non-steady-state heat transfer equation in the following form: r)T V-(A.VT)-pC— = 0, (J where T [K] is the temperature, t [s] the time, X [W/(mK)] is the thermal conductivity, p [kg/m3] is the mass density, and C [J/(kgK)] is the effective thermal capacity. The material properties assumed in the computation were dependent on temperature and the phase fractions [15], The use of constant material properties from temperature causes very large computation errors. The model of solidification process takes into account the heat of transformation as a change of the effective heat capacity Cef-of the material [16] and [17]: Cef=p(T)-C(T)-psL df,(T) dT (2) where L [J/(kgK)] is the latent heat of transformation, fs share of the solid phase, T, liquidus temperature, and Ts solidus temperature. In Eq. (2), the fs is resolved by the lever rule: T -T fs=fs(T)=f-f- Changes in the phase composition during the cooling and heating are calculated on the basis of the analysis of continuous cooling transformation (CCT) and continuous heating transformation (CHT) diagrams [18], The data obtained from the diagrams are input to the macroscopic model, in which the modified Koistinen-Marburger equation was used for the high-rate cooling process [19] and [20]: rjr(T,t) = l-exp 4.60517 T -T v 1*r fr 0 where fjr is the austenite fraction Ty/ is the austenite start temperature, Tly is the austenite finish temperature. (Heating and \ cooling J temperature s^;- (CCTdiagram A (discrete form) J a /— I Phase \ \ transformations ) ,V____y\ C Initial phase \ _ ^ ^ «»"Position J (AuslenitizationV^ Z. ^Y stresses ^ temperature J jj V stresses I f Thermophyslcal \ V properties J Fig. 2. Elements of the phase transformations model for the regeneration process The phase transformations described by Eq. take place only in the area where the padding welds reheat the element, ft is assumed that austenite is the first structure formed after solidification during the cooling process. In the model of phase transformations during the heating, the ferrite and pearlite are treated as a homogeneous mixture. The phase transformations of the cooling process ,(7,7) (except for the martensite phase) are determined on the basis of a macroscopic model based on the Avrami equation [21]: (l ¡^ \\ ( 0.01005 ^„u) ^ t"(T) In n(T)=- ln(l-77i In f tf{T)^ (f where ;/(,ob) is the final fraction of i phase, //,- is the phase during cooling, n{T) functions depending on the start and finish times of transformation (ts and tt). During the cooling process, the transformations of austenite—»ferrite, austenite—»pearlite are considered separately. Numerical Study of Stress Analysis for the Different Widths of Padding Welds 569 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 The kinetics of martensite transformation '/ -o oos--0.010 Fig. 6. The temperature field [K] for the third padding weld of width 0.014 m(T(l =573 Kj after timet = 9 s PW) (Fig. 5). Because the geometry of the padding weld is characterized by a significant predominance of length over width and usually a quite high pad welding speed, critical data concerning stresses, for example, can be obtained mainly from the cross-section. Pad welding with a single path (at one time) and starting subsequent paths after reaching a relatively low temperature of the previous padding weld additionally ensures the correctness of the analysed cross-section. The width of the analysed plate was 0.25 m, the thickness 0.01 m, while the padding weld height was 0.005 m (Fig. $ . Three cases were considered for a different padding weld width: 0.006 m, 0.01 m and 0.04 m (Table 1). To ensure a similar amount of welded material, it was adopted that the PW was composed by the 4 beads for the first case, 8 beads for the second, and 6 beads for the third. In all the analysed cases, the first padding weld is located 0.045 m to the edge. The geometry of the PW is approximated by a quads element (Fig. | . Finite element mesh with quads elements and bilinear approximation was used for calculations [27], The padding weld element was discredited by 28 elements in length and ® in height (element size 0.001 0.00J . Each padding weld was approximated with finite elements of the same size: analysis No. 1 6 5 analysis No. 2: ®x 5 and analysis No. 3 4 5 (Fig. | . According to the welding standard ISO 8 [11] the weld toe equally 0 0 was adopted (limit for imperfections for quality level D). The technological process was simplified; it was assumed that the padding weld appears as a rectangular element with a given height and width (constant height, 3 cases of width) and an initial temperature of 000 K (Fig. J . The constant initial temperature of the PW and its different cross-sectional area were assumed; from the technological side, it requires the delivery of different amounts of heat (different parameters of the welding arc). For all analysed padding weld widths, the four preheating temperatures: T0 =29 K, 3 K, 4 3 K, 3 K were considered. The cooling on the boundaries was modelled with the Newton condition (Fig. $ . Air cooling was modelled according to the equation [28]: i0.0668x7\ T„ 773 K Table 1. Numerical research plan Analysis Preheating PW width Number Field of the PW No. temperature [K] [m] of PW area [m2] 1.1 293 1.2 373 - 0.006 14 0.00042 1.3 473 1.4 573 2.1 293 2.2 373 - 0.01 8 0.0004 2.3 473 2.4 573 3.1 293 3.2 373 3.3 473 - 0.014 6 0.00042 3.4 573 571 Numerical Study of Stress Analysis for the Different Widths of Padding Welds Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 For each case, calculations were performed for many finite element method (FEM) meshes. Each subsequent geometry differed in the formation of one padding weld. The number of simulations depended on the number of PW in each case (Table J . The assumption of a small value of finite elements defining the padding weld allowed one to observe the changes in the analysed phenomena. 0.05 0.06 0.07 0.08 0.09 0.1 x[m] b) 0.05 0.06 0.07 0.08 0.09 0.1 x[m] C) 0.05 0.06 0.07 0.08 0.09 0.1 x[m] Fig. 7. Geometry with mesh and initial temperature for the next three padding welds (analysis No. 3): a) one padding weld, b) two padding welds, c) three padding welds The appearance of the next PW was dependent on the value of temperature. Subsequent weld passes occurred after reaching the ambient temperature of the previous PW. The next step was to set the preheating temperature for the next padding weld and the whole element. The analysed material for the assumed cooling conditions (after the cooling process) does not contain an austenitic structure. In the model of mechanical phenomena, appropriate degrees of freedom were removed for selected elements; therefore, the model could be solved numerically. The selected nodes and applied zero displacements did not of the obtained stress levels. Due to large changes in material properties, the average values of material properties were determined for each finite element in the mechanical model. These properties depend (among other factors) on temperature level, phase transformations in the solid state, and solidification (Fig. * . Each case is a series of a few successive simulations. The model assumes the continuity of values for phase transitions and stress state between successive simulations. 3 RESULTS AND DISCUSSION One of the main parameters, especially for the materials subject to phase transformations during the regeneration process, is the depth of the heat-affected zone (HAZ) and fusion zone (FZ). Figs. 8 to ® show the HAZ depth in the base material below the padding weld. The results of calculations for the four preheating temperatures for each of the three widths were presented. The size of the HAZ was determined assuming a temperature of.l6, for the steel C4 equal to (DOSC . 0(H 0.06 0.08 0.1 0.12 014 X [m] Fig. 8. Depth of HAZ for padding weld width of 0.006 m 0.04 0.06 0.0B 0.1 0.12 114 y[m] Fig. 9. Depth of HAZ for padding weld width of 0.01 m The change of HAZ depth depending on the preheating temperature in relation to the padding weld width was linearly correlated and increased with the size of the padding weld. In Figs. 8 to it can be 572 Kulawik, A. - Wrobel, J. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 observed that the first padding weld causes the deepest HAZ, which is because three walls are cooled by air, and most of the heat is absorbed by the regenerated material. In other cases, contact with the regenerated material was through two walls of the padding weld. The largest difference between the depths of the HAZ was observed for the smallest width of the padding weld (Figs. 8 to ®) . In this case, proportionally, the smallest length of the edge is in contact with the regenerated material. According to predictions, the greatest depth of HAZ occurs for the largest volume of the padding weld (Fig. ®) . On the basis of the obtained temperature distribution in the area of contact between the padding welds and the base material, the depth of the fusion zone was minimal, and only the nodes of the finite element mesh on the border of the base area exceed the temperature T, = ffi K 0.04 0.06 O.OB 0.1 0.12 0.1« y[m) Fig. 10. Depth of HAZ for padding weld width of 0.014 m OOd 0 06 O.DS or 0,12 0,14 xjm] Fig. 11. Sum offerrite and pearlite fraction (afterprocess), preheating temperature 293 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m It can be observed that for the smallest padding weld for the first two preheating temperatures, the cooling rate exceeds critical velocity (rate of obtaining the quenching phase), which also applies to the first Numerical Study of Stress Analysis for the 0.0 J 006 0.08 0.1 0.12 Old * [m] Fig. 12. Sum offerrite and pearlite fraction (after process), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m ooj 0.09 o.oa 0,1 oi2 0.1J x[m] Fig. 13. Sum offerrite and pearlite fraction (after process), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m 004 0.06 OOS 0,1 012 014 x[nn] Fig. 14. Sum offerrite and pearlite fraction (after process), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m padding weld, for which the cooling is the slowest (the longest air-cooled boundary) (Figs, li and 2a ). With the increase of the PW width and the preheating Different Widths of Padding Welds 573 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 temperature, the cooling rate decreases to such a value that in the last case 31 (see Table 1 Fig. 4 ) the first padding weld is composed only of a ferrite-pearlite mixture, whereas the others only in about 8 % (Figs. 11 o| . Fig. 15. Bainite fraction (afterprocess), preheating temperature 293 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 16. Bainite fraction (afterprocess), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 17. Bainite fraction (afterprocess), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m The big differences in the distribution of the bainite structure, between the first and the other padding weld, were obtained. It was due to the Fig. 18. Bainite fraction (afterprocess), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 19. Martensite fraction (afterprocess), preheating temperature 293 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 20. Martensite fraction (afterprocess), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m 574 Kulawik, A. - Wrobel, J. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 different cooling conditions. The amount of bainite increases with the increase of the preheating temperature in the range 29 K to 3 K and the padding weld width. The amount of bainite structure increases with the change of the PW width from 0.006 m to 0.01 m. Whereas for the width of 0.04 m (Figs. o.oa 0.1 *[m] Fig. 21. Martensite fraction (afterprocess), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 22. Martensite fraction (afterprocess), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 23. Tempered martensite (afterprocess), preheating temperature 293 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 24. Tempered martensite fraction (afterprocess), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m o.oa 0,1 * (ml Fig. 25. Tempered martensite fraction (afterprocess), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 26. Tempered martensite fraction (afterprocess), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Numerical Study of Stress Analysis for the Different Widths of Padding Welds 575 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 i to $ influence of the heat of the padding weld on the shape of the cooling curve on the CCT diagram, and thus a greater share of the ferrite-pearlite structure was noted (Figs. 11 to J . The high repeatability of the distribution of phase composition in the central part of the material occurs for all cases. The composition of the quenching phases (bainite, martensite, and tempered martensite; Table 2) indicates the lightness of using preheating in order to control the shape of cooling curves and the ferrite-pearlite structure (Figs. $ to 26). The control of cooling curves, especially for hardly weldable materials, may cause a lower value of effective stress and in consequence elimination of cold cracks. As indicated by the results presented in Tables 2 and 3 the application of preheating at the level of 3 K and 3 K causes a much higher fraction of the bainite structure, which consequently reduces the yield point and the maximum values of effective stresses. This difference is especially visible for small volumes of the padding welds, where between the highest and the lowest preheating temperature, the difference in effective stresses reaches 4 %. It is less visible for wider padding welds, which, due to their volume, cool down more slowly (the difference between the bainite fraction for the smallest and the largest width of the padding weld without preheating temperature is over 0 %). The use of preheating only increases the fraction of bainite at the expense of martensite, until a ferrite-pearlite structure appears during cooling. Table 2. T he maximum values of the quenching structures Analysis Bainite Martensite Tempered No. [%] [%] martensite [%] 1.1 1.82 99.00 99.00 1.2 9.49 97.89 97.87 1.3 25.25 90.62 90.54 1.4 59.25 53.58 53.26 2.1 20.12 96.58 96.58 2.2 37.07 82.80 82.83 2.3 72.21 46.53 46.57 2.4 85.52 0.42 1.13 3.1 41.89 84.72 79.80 3.2 61.17 60.42 56.16 3.3 79.99 18.14 12.77 3.4 63.60 0 0 The distribution of plastic strains (Figs. 3 to | correctly indicates the areas where cracks can occur. Including recrystallization and loss of stress during heating significantly changes the results of calculations. The plastic strains were taken into account only below Q % of the solidus temperature of 576 Kulawik, A. - Ci steel. The highest amount of tempered martensite occurred in the structure with a width of 0.006 m and a preheating temperature of 25C (Fig. 2â ). Table 3. Summary of the calculation results for the considered cases after the regeneration process Analysis No. Maximum effective stresses [MPa] Maximum effective plastic strain Yield point [MPa] 1.1 947.00 0.0066 314.12-1217.05 1.2 862.90 0.0057 312.68-1202.54 1.3 876.54 0.0044 312.12-1132.65 1.4 577.56 0.0044 311.87-844.20 2.1 827.53 0.0070 313.42-1210.20 2.2 605.72 0.0055 312.51-1088.32 2.3 659.55 0.0054 312.07-804.80 2.4 466.05 0.0057 294.01-472.88 3.1 451.99 0.0051 313.11-1089.22 3.2 421.45 0.0040 312.38-886.11 3.3 416.08 0.0034 312.00-582.29 3.4 403.88 0.0033 310.48-434.41 The stress distributions for the first three preheating temperatures, with the assumed cooling conditions, were similar to the maximum values (Figs. 27 to 2)> . The influence of the padding weld width on the stress level was observed. The differences between the maximum values of effective stresses for the case without preheating even reach 00 % (analysis No. 31 and .1) . This difference decreases for the analysis No. 3t o less than 5/o (Table } . The most favourable was the distribution for a 0.04 m of padding width. The effective stress value for temperature 3 K was caused by the yield point value for analysed material (Table } . The yield point value was due to the high proportion of the ferrite-pearlite structure in relation to martensite. Reduction in the level of effective stresses with an increased number of padding welds was observed. Along with the increase of the padding weld width, the stresses were initialized deeper in the base material (Figs. 21 o 0) . The distribution and kinetics of phase transformations in the solid state determines the distribution of the yield point. Higher values of yield point occurred for areas with the highest cooling rate and martensite transformation (Table } . The assumed yield point of tempered martensite, at the level of bainite, were caused by the reduction of the yield point in the interpass areas. The temperature-dependent yield point values for the individual phases are shown in Fig. 4 The level of plastic strains decreased when the preheating temperature and padding weld width were Wrobel, J. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 increased. The greatest plastic strains occurred for the smallest width of the padding weld. The plastic strains increase towards the padding weld surface. They decrease with the width of the padding weld (Table 3). The distribution of plastic strains suggests the formation of cracks between welds, especially for smaller widths of the padding weld and a lower preheating temperature. The influence of the -h - -11.01 Fig. 27. Effective stresses [MPa] (after process), preheating temperature 293 K and padding weld width of: a ) 0.006 m, b) 0.01m, c) 0.014 m Fig. 30. Effective stresses [MPa] (after process), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 31. Effective plastic strain (afterprocess), preheating temperature 293 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Fig. 28. Effective stresses [MPa] (after process), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01m, c) 0.014 m b) o.oos-f ~ -0.006 ■0,01 0,1 a) O.OOS- 0.04 0.06 0.08 0,1 0,12 0.14 x[ml Fig 29. Effective stresses [MPa] (after process), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01m, c) 0.014 m 0,04 0,06 0.08 0,1 0,11 0.14 Xlmj Fig. 32. Effective plastic strain (after process), preheating temperature 373 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m Numerical Study of Stress Analysis for the Different Widths of Padding Welds 577 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 martensite tempering and recrystallization process was observed (Figs. 1 o f . -0,01 -1-I-1-1-1 0.04 0.06 0,08 0,1 0,12 0.14 x[m] Fig. 33. Effective plastic strain (after process), preheating temperature 473 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m *[m] Fig. 34. Effective plastic strain (after process), preheating temperature 573 K and padding weld width of: a) 0.006 m, b) 0.01 m, c) 0.014 m 4 CONCLUSIONS In the present paper, the influence of padding weld width and preheating temperature on phase transformations and stresses of the regenerated layer were analysed. The obtained results indicate that the use of preheating in order to change the shape of cooling curve, even until complete cooling, makes it possible to control the fraction of individual phases. However, the economic analysis of this process indicates that it would be more convenient, cheaper and more effective to control cooling conditions than heating. The obtained results give answers to questions about structures in the regeneration process, during which we did not have full control over the process conditions (the process was not controlled by the interpass temperature). This is applicable if the cooling process has not been stopped when 578 Kulawik, A. - the interpass temperature is reached at the level of preheating temperature only at the level of the ambient temperature. An example of such a process may be the performance of the next long padding welds with a long technological break, where the beginning of the padding weld is cooled to ambient temperature before the next pad. On the basis of the presented results and taking into account the stress distribution, it can be concluded that the use of the widest padding weld is highly advantageous. The use of preheating for analysis No. 3 is not required to obtain a hard but also brittle surface (high fraction of martensite). The selection of the optimal preheating value is possible only when we define the conditions under which the pad welding surface will work. If we want to obtain a large amount of bainite structure and small amount of martensite, the lowest suggested preheating is between 3 K and 3 K. Obtaining areas of tempered martensite is beneficial for regenerated surfaces. However, due to the specificity of pad welding, the area of tempered martensite cannot, especially for small padding welds, reach too deep into the pad welding without additional treatment. Therefore, during pad welding, we should focus on obtaining a bainite structure with the addition of martensite, whereas the area of tempered martensite treat as an additional advantage. However, it should be noted that in choosing large cross-sectional padding welds, problems may occur with the segregation of the admixture, the influence of the temperature of the padding weld on the base material or the noticeable higher values of plastic strains and the stresses inside the regenerated material. The results obtained from the analysis of the phase transformations in the solid state and stresses suggest that it is unreasonable to use heating and cooling sequentially to ambient temperature: this is also not economically viable. Therefore, it is reasonable to consider the case in which the next padding weld is applied when the temperature of the previous padding has reached the preheating temperature. The differences between the obtained distributions of plastic strains result from the influence of the preheating temperature, before each padding weld, on the cooling rate. As previously mentioned, the analysed material is very difficult to regenerate. The presented analysis allows one to assess whether there may be defects after the regeneration process in the absence of appropriate supervision. With unfavourable distribution of structural and thermal strains, cracks may occur in the cross-section of the PW (this would require a 3D analysis). Wrobel, J. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 567-580 In this paper, a geometrically simple case that can be easily referred to in experimental research or other computer simulation models was considered. However, in practical applications, where the shape of the pad welding object may be very different, the presented results cannot be transferred. 5 ACKNOWLEDGEMENTS The research has been performed within a statutory research BS/PB-1 00- 0®/ 2020/P. 6 REFERENCES [1] Odebiyi, 0.S, Adedayo, S.M, Tunji, LA, Onuorah, M.O. (2019). A review of weidabiiity of carbon steel in arc-based welding processes. 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D0l:10.5545/sv-jme.2020.6883 Original Scientific Paper Received for review: 2020-07-597 Received revised form: 2020-08-21 Accepted for publication: 2020-09-24 Effect of Thermal Barrier Coating on the Thermal Stress of Gas Microturbine Blades and Nozzles Oscar Tenango-Pirin1 -E Iva Reynoso-Jardn 14 uan Carlos Garcia2 * -Yaliir Mariaca1 - Yuri Sara Hernández3 41 aü Ñeco1 -O mar Dávalos1 1 Departamento de Ingeniería Industrial y Manufactura, Universidad Autáom a de Ciudad Juárez, México 2 Centro de Investigaciá e n Ingeniería y Ciencias Aplicadas, Universidad Autáo ma del Estado de Morelos, México 3 Tecnolgi co Nacional de México/Campus Pachuca, Pachuca de Soto, Hidalgo, México Thermal barrier coatings play a key role in the operational life of microturbines because they reduce thermal stress In the turbine components In this work, numerical computations were carried out to assess new materials developed to be used as a thermal barrier coating for gas turbine blades The performance of the microturbine components protection is also evaluated. The new materials were 8YSZ, Mg2Si04! Y3Ce7Ta20235, and Yb3Ce7Ta2023 5. For testing the materials, a 3D gas microturbine model is developed, in which the fluid-structure interaction is solved using CFD and FEM. Temperature fields and stress magnitudes are calculated on the nozzle and blade, and then these are compared with a case in which no thermal barrier is used. Based on these results, the non-uniform temperature distributions are used to compute the stress levels in nozzles and blades. Higher temperature gradients are observed on the nozzle; the maximum temperature magnitudes are observed In the blades. However, it is found that Mg2SI04 and Y3Ce7Ta20235 provided better thermal Insulation for the turbine components compared with the other evaluated materials. Mg2Si04 and Y3Ce7Ta20235 presented the best performance regarding stress and thermal Insulation for the microturbine components. Keywords: thermal barrier coating, gas microturbine, turbine blade, thermal stress Highlights • An investigation of the effectiveness of novel ceramics for TBC applications is carried out for their use in gas microturbine blades. • The Mg2Si04 and Y3Ce7Ta2023 provided the best performance on thermal Insulation under operational environments of the turbine. • The Mg2Si04 and Y3Ce7Ta2023 showed similar thermal and mechanical stress magnitudes on the blades, which were the lowest among the materials studied. • The use of those ceramics led diminishing the temperature and stress developed on the blades, which In turn, enables an Increase in the operating life of the turbine. 0 INTRODUCTION Gas microturbines (GMT) are small turbomachines that work using gases at high temperatures, with power capacities ranging from J kW to 00 kW and offer variable speeds from 0,000 rpm up to 20,000 rpm [1], They operate with the same operation principle of all the conventional gas turbines; therefore, the efficiency of these devices depends on the gas temperature, which can become higher than 000 K [2] and [3], Blades and nozzles of the turbines are subjected to different loads like high temperature, corrosion, centrifugal forces, etc., which could lead to failures [4] and [5], Regarding high temperature, one of the main drawbacks of GMTs is their small size, which augments heat transfer among their components, leading to failures by burning out or highly stressed zones. Highly stressed zones are often located near the root of the blades as a consequence of non-uniform temperature fields because of sudden changes in geometry and restrictions at the root [6] to [9]. In conventional turbines, in order to cool the blades, internal cooling passages are manufactured; however, this method can not be implemented for microturbines, given the size of such machines [10], Therefore, the thermal barrier coating (TBC) is used to protect turbine blades and to resist high temperatures enviromnents. A TBC often has a cover that is composed of three layers: the first is a ceramic topcoat (TC) layer, which has direct contact with hot gases; the second is a bond coat (BC) layer, which offers corrosion resistance; the third is a thermally grown oxide (TGO) layer, which is frequently formed between the TC and BC. Ni-based superalloys are often used as a substrate in gas turbines where TBC provides them with thermal insulation. In this way, TBC allows reducing substrate temperature, prolonging the operation life of the turbine and improving turbine efficiency by increasing its operating temperature [11]. *Corr. Author's Address: Universidad Autonoma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Mor., Mexico, jcgarcia@uaem.mx 581 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 581-590 The design of proper TBC plays a key role in the operating life of turbine blades; as a consequence, several studies are focused on the study of TBC characteristics. Li et al. [12] studied the thickness of TBC for a gas turbine blade. The materials used were Zr02-8 wt% Y203 (8" SZ) as a TC layer, a-Al203 as TGO layer and NiCrAlY as a BC layer. TC thickness was varied from 00 |im to 000 |im. It was observed that when increasing the TC layer thickness, the thermal insulation capability and stress levels within the coatings are enhanced. Radwan & Elusta [13] performed one-dimensional (B ) calculations to assessing a four-TBC layer made of Zirconia. They concluded that the TBC layer allowed reducing the blade temperature, thus enhancing the blade durability. Also, the material influenced the temperature distribution. Thickness optimization of a barrier coating of partially stabilized zirconia (PSZ) of a turbine blade was executed by Sankar et al. [6], TBC thickness was varied from 00 |im to 80 |im. and they found a critical thickness that occurred when thickness reached 8 |im. where heat transfer rate was the lowest. In other research [14], the temperature distribution and thermal stress field of TBC were obtained by employing a 2D decoupled method. TBC included the BC, TGO and TC, where the TC was made of W SZ. Non-uniform temperature fields were obtained, and zones with high stress were detected at the suction and the leading edge of the blade. In another study, it was shown that the impact of foreign object damage (FOD) could cause erosion on blade samples with TBC, and was most dangerous as it becomes perpendicular to the surface [5], Several materials have been developed to be used as TBC and studies have been performed to compare their effectiveness of substrate protection. In a review of the main materials used as TC and TGO presented by Saliith et al. [15], it was concluded that the most common material used as substrate material and bond coat was nickel-based superalloys. Meanwhile, yttria-stabilized zirconia (YSZ) (7 %) was most commonly used as the topcoat. YSZ appears as one of the best options to thermally protect the substrate blade, given its thermo-physical and mechanical properties, such as low thermal conductivity. Regarding the gas microturbines, YSZ was also the preferred material to be used as TBC [16], In recent studies, some researchers have proposed new materials to be used as TBC for gas turbine applications. Chen et al. [17] proposed the synthesized forsterite-type Mg2Si04 material as an alternative to zirconia. They showed a comparison with zirconia (JT SZ) in terms of mechanical properties. The new material proved to have a lower thermal conductivity at (I 3 K (J5 W/(mK) and 2.2 W/(mK) for the new material and JT SZ, respectively) and better thermal-shock resistance than those made of JT SZ. Other mechanical properties, such as hardness, fracture toughness and Young's modulus were similar to those of zirconia. Shi-min et al. [18] also introduced two novel ceramics for thermal barrier coatings. The proposed synthesized materials, Y3Ce7Ta202S and Yb3Ce7Ta2022i , were new rare-earth tantalite oxides with thermal conductivities lower than that of JT SZ at 000 K. Beyond this temperature, the new materials showed good stability which makes them appropriate for high-temperature applications. In another study, Yang et al. [19] synthesized high-purity Dy0 02Gd0.02 sYbo.cQsYn.osZrn.s 0B (DZ), Ti0 02Dy0 02Gd0 Q25Yb 0.025Y:,05Zr0 8 0B (TZ), and the YSZ powder and coating. According to their results, the TZ TBCs could effectively protect the superalloy substrate at S K. Also, the thermal conductivity of the TZ coating was lower than both DZ and YSZ, showing its potential to be used as TBC. However, most of those new materials have been tested under controlled conditions in a laboratory, and their effectiveness under realistic turbine operating conditions need to be considered. Numerical methods are the preferred tools to predict the thermal and structural fields on blades coated with TBC. Abubakar et al. [20] performed a general review of some methods for predicting residual stress in thermal spray coatings, concluding that some finite element method (FEM) schemes provide results of those stresses reasonably close to experiments; thus, they can be used to predict them in coatings. In contrast, Zhu et al. [7], evaluated the effectiveness of three versions of the k-e turbulence model to predict temperature fields by means of computational fluid dynamics (CFD). The k-e realizable offered the most accurate results when modelling blades with one-layer TBC. Li et al. [12] employed the FEM to design the TBC for a gas turbine blade. They found that thermal insulation was enhanced with the increase of the TC. Also, as mentioned before. Tang et al. [14] carried out a fluid-structure interaction (FSI) coupling method to predict stress fields in a turbine blade. However, their model was restricted to a 2D model. In other works [12] and [21], the uniform temperature on blade surfaces and static blade boundary conditions were used. However, these simplified conditions could drive to imprecise results since temperature fields on blade surfaces, induced by high-temperature combustion gases and the blade, are highly three dimensional and non-uniform. 582 Tenango-Pirin, 0. - Reynoso-lardón, E. - García, J.C. - Mariaca, Y. - Hernández, Y.S. - Ñeco, R. - Dáva/os, 0. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10,581-590 In this work, a E) FSI decoupling method of a gas microturbine is carried out to assess novel TBC materials proposed in the technical literature for applications in turbine blades. The coating materials studied are taken from literature: JT SZ, Mg2Si04, Y3Ce7Ta2023 5 and YthCcyTibC^ . To accurately predict the non-uniform temperature fields, stationary guide vanes are taken into account for the numerical domain, giving rise to a single axial passage that includes a static guide vane (nozzle), a rotating blade and their corresponding fluid domains. Results in terms of temperature and stress are discussed to identify the most effective thermal barrier coating for the microturbine. 1 METHODS 1.1 Microturbine Characteristics The main components of a gas microturbine engine are the expansion microturbine, the combustion chamber and the compressor. The expansion turbine section is referred to here as the microturbine. Computational modelling of an axial gas microturbine is performed using Ansys (Fluent and Mechanical structural). The microturbine geometry is taken from the technical literature [22], which is designed to supply output power of about 29 kW at the rated speed of 3)00 rpm. The microturbine geometry consists of one stage with T guide vanes of the stator (nozzle) and 2 rotating blades. Given its axisymmetric geometry, one E) single passage that includes one nozzle and one blade is constructed for CFD and FEM computations. Nozzle hub Periodic Blade Fig. 1. Turbine geometry and boundary conditions In Fig. 1 the numeric domain is depicted; the shroud is hidden to provide better visualization of the components. The whole computational domain is integrated by both fluid and solid domains corresponding to air and substrate (and TBC) domains. The dimensions of the turbine are (8 tmn in nozzle height, 7 tmn in blade height, 2 mm in nozzle chord, 8 tmn in blade chord, and 7 T mm in maximum turbine diameter. 1.2 Methodology for the CFD and Mesh Characteristics The numerical domain is discretized to generate the mesh needed for calculations. A mesh dependence analysis is carried out to obtain the optimal mesh for the passage. Given that the nozzle and the rotor domains have meshed separately, an interface boundary condition is used to join both domains. It is noteworthy than both solid and fluid domains been have meshed to predict temperature fields and heat transfer flux. Element sizes of 0.1 mm and 0.2 lmn and hexahedral element types are used. A mesh refinement to model the boundary layer was used in the near-wall region of nozzles and blades. Refinement is defined using 5 to 20 layers with a growth rate of 12. As a result, nine different meshes with densities ranging from .0)4 to 353 elements are constructed. After the analysis, a mesh with (23 (Fig. 2) elements is selected to carry out all computations because it has a variation of about 1 % of the computed substrate temperature with respect to a finer mesh. It should be mentioned that the mesh region corresponding to substrates (nozzles and blades) is used for the FEM solution to solve the stress generation. Fig. 2. Computational mesh for flow field and substrate domains 1.3 Boundary Conditions of the CFD and Cases of Study As a consequence of modelling one single passage of the turbine (Fig. J , boundary conditions are defined as follows: periodic boundary conditions are used at lateral sides of passage, and an interface is created between the nozzle and blade domains to ensure fluid continuity through the passage. The hub and shroud Effect of Thermal Barrier Coating on the Thermal Stress of Gas Microturbine Blades and Nozz/es 583 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 581-590 are defined as walls with a no-slip condition. When modelling TBC, thickness and type of material are assigned at coupling walls to model the heat transfer through the coating material. Mass flow rate and pressure outlet conditions are assigned at the inlet and outlet of the passage, respectively. The total mass flow rate incoming to the turbine is equal to 0.23 kg/s at rated speed. Since one single passage is used, this flow rate is divided by the T guide vanes resulting in 0.05 kg/s per passage. The fluid is considered as high-temperature compressible air, and a temperature of 05 K is also specified at the inlet. The solid domain is defined according to the substrate material (nozzles or blades) and their corresponding TBC. The investigated TBCs are Mg2Si04, YiCcyTihC^ and YbyCcyTayOyy , which are compared to 8YSZ. Coating material properties are taken from [17] to [19], and their properties are defined based on a temperature range of 9 K to 03 K to match with the operating temperature of the microturbine. The TBC properties used to predict heat transfer by CFD are indicated in Table 1 which also contains substrate (nozzles and blades) properties [23], Coating thickness is considered uniform and constant for the whole cases with a value of 8 |im based on some investigations [6] and [12], and it is added as a virtual layer into the CFD software. This virtual technique uses the TBC properties (thermal conductivity, specific heat, density and thickness) to compute heat transfer to the blades. Table 1. Top coating and substrate properties Material Thermal conductivity [W/(mK)] Density [kg/m3] Specific heat [J/(kgK)] Nimonic 105 22.23 8010 628 (substrate) [23] 8YSZ [19] 2.2 3610 505 Mg2Si04 [17] 1.76 3210 177000 Y3Ce7Ta20235 [18] 1.78 7245 472.1 Yb3Ce7Ta20235[18] 1.4 6321 431.1 1.4 Governing Equations and Turbulence Model A numerical FSI analysis is conducted using Ansys Workbench commercial code, which is used to solve thermal (Ansys Fluent) and structural (Ansys-Structural) analyses. First, the steady-state Reynolds-averaged Navier Stokes equations (RANS) approach is used to solve governing equations using CFD. Then the FEM is employed to calculate thermal stresses. CFD is used to compute the flow and temperature fields at steady-state conditions, taking into account the turbine operating conditions, like mass flow, pressure, temperature, wall thermal condition and rotating speed. Governing equations of continuity and momentum, given by Eqs. (J and (2), are solved using Ansys Fluent. To compute the conjugate heat transfer (CHT), the energy equation depicted by Eq. (} , is also solved. f ♦(<">),-«. <■> dv. p~dt~+pVjjVi + Pj ~T'JJ ~pFj = (2) Ds P~dt + PS dx~ dv~ dz~ k a dx where q is the heat transfer rate, k is thermal conductivity, a is the thermal diffusivity of the material, T is the temperature, and x, y and z, are coordinate directions. The convection is solved using Newton law which is given by Eq. (J as follows: q = hA(Tw-Tm), (7 where h is the convection heat-transfer coefficient, A is the surface area, and Tw and T., are the surface and the free stream fluid temperature, respectively. In this case, h is highly influenced by the fluid motion driving to a forced convection case. In contrast, the thickness of the coating is specified on the walls to obtain the thermal insulation and temperature decrement on turbine components. Temperature fields are needed to calculate stress fields in the blades. Mechanisms for corrosion and erosion phase transformation of the ceramic coating or its fracture behaviour are neglected to simplify the computations of the effectiveness of thermal insulation of TBCs and the thermal stress induced on nozzles and blades. 1.5 Finite Element Procedure Once temperature fields are solved using CFD, FEM is employed to compute stress on the components using Ansys Mechanical software. A decoupling method is used, in which the temperature in the components computed by CFD is sent to FEM software. The surface and internal temperature fields of substrates are used as a boundary condition in conjunction with restrictions to elongation of turbine components. Constraints are specified as follows: the nozzle is fixed at the top and bottom surfaces, and the blade is fixed only at its root. The properties of nozzle and blade are assigned based on Nimonic alloy 05 substrate material, as indicated in Table 1 This material is assumed to be homogeneous, continuous, and isotropic. Other properties used are the Young modulus of 9 GPa, the Poisson's Ratio of 0.3 and the thermal expansion coefficient of B x® 6/K[23], The same solid meshes depicted in Fig. 2 are used to predict three-dimensional stress fields accurately. 1.6 Governing Equations Thermal stress distribution was calculated following Eqs. to ((B) ; non-uniform and tliree-dimensional stress fields were obtained. Those equations describe three thermal stress components in the tangential, radial, and longitudinal directions, respectively [26], The equations allow taking into account partial mechanical constraints and internal constraints due to differences in thermal expansion of elements due to different temperatures. Also, when solving them, it was assumed that thermal equilibrium is reached at the rated speed of the turbine. o, =- Ea 1 ( ..2 1-v f- r~ —r. V o i \\r'T-rdr+\rT-rdr-T-r2 C„ =- Ea 1 1-v r1 f 1 0 r~ +rr ~2 2 r -r v » • jr°T-rdr+jrT-rdr (9 cr_ = Ea 1-v 2 2 r -r. V o l fT.rd, -T where dr indicates that the definite integrals are solved through the radial direction from inner radius, r,, to the outer radius, r0 (or an arbitrary intermediate radius, r); E is the Young Modulus, a is the thermal expansion coefficient, v is the Poisson ratio, T is temperature, and t, r, and z are the tangential, radial and longitudinal directions, respectively. Results are represented using the equivalent stress or Von Mises stress, which is derived from the Cauchy stress tensor. The equivalent stress is defined by Eq. (1J : er„„ = ICF,2 + , are set as 0 mm, 1 mm, 2 mm, 3 mm, and the corresponding coating tliickness coefficients are K0 = 0, = I K2 = 2, and = 3 respectively. The impellers with different coating tliickness coefficients are shown in Fig. 5 flow under the same coating tliickness coefficient when the volumetric flow rate is below around 0.9 (9d. According to [24], at low volumetric flow rates, this can be explained by the solid particles slightly decreasing disturbances near the wet surface, which reduces the turbulent boundary layer tliickness and energy loss. However, the head under the sedimentladen flow decreases faster when the volumetric flow exceeds around 0.9 (2d, because the whole velocity field of two-phase flow is more aberrant relative to the clear water flow. The velocity gradient is much greater under the large flow rate, which increases the loss generated by the velocity difference between water and particles. The contribution of this loss is more than the head increase from the disturbance elimination of particle swarm. Thus, the pump head is slightly lower than that under sediment flow under the larger flow rate. In contrast, the head under both sediment-laden flow and clear water flow decreases significantly as the coating tliickness coefficient increases. The theoretical pumping head II, and efficiency // are derived from Euler equations, Eqs. (} to [24] and [25], Here, /./,. h2. vMl and v„2 are the circumferential components of the inlet and outlet circumferential speed and absolute velocity, respectively; fi2 is blade angle at the exit; 9>2 is extrusion coefficient at impeller outlet; ,v„2 is blade outlet tliickness; y is the angle between the impeller outlet axis line and the streamline; /?,, is slip coefficient; is the pump efficiency; is the pump hydraulic efficiency; //,, is the volumetric efficiency; //„, is the mechanical efficiency; P0 is the power of liquid energy increase; is the shaft power; 2 RESULTS AND ANALYSIS 2.1 Energy Characteristics Fig. 6 shows the energy characteristics of the model pump for four coating tliickness coefficients under sediment-laden and clear water flow. Fig. 6 shows that the head under sedimentladen flow is slightly larger than under clear water c) Fig. 5. Impellers with different coating thickness coefficients; a)K0;b)Khc)K2;d)K3 30 25 20 1" X 15 -d « £ 10 5 Q -«O (water) — — Kq (sediment) "-X, (water) — — K] (sediment) -K2 ( water i - — K; (sediment) - ( water) — - K-, (sediment) 0.6 0.8 a) 1.0 Q'Qd 1.2 1.4 Fig. 6. Energy characteristics for different coating thickness coefficients and working mediums; a) head; b) efficiency Effect of Blade Coating on a Centrifugal Pump Operation under Sediment-Laden Water Flow 595 Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10, 591-601 H. = - u2h0 - Qd nD2b2(p2 tan fi2 , zS , and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, Ministry of Education, Xihua University (szjj20$ 0$ . The authors would like to thank the research program Energy Engineering P2-O01 funded by the Slovenian research agency ARRS. 5 NOMENCLATURES Od nominal flow rate, [m3/h] O flow rate, [m3/h] H pump head, [m] II, theoretical head, [m] n rotational speed, [rpm] N sample number P rated shaft power, [kW] ns specific speeds // efficiency, [%] », circumferential velocity of impeller at blade inlet, [m/s] h2 circumferential velocity of impeller at blade outlet, [m/s] r„ i circumferential velocity of flow at blade inlet, [m/s] v„2 circumferential velocity of flow at blade outlet, [m/s] tp2 extrusion coefficient at impeller outlet .v„2 thickness of blade at impeller outlet, [m] y angle between section line on axial plane and streamline at impeller outlet, [°] /?,, slip coefficient D] impeller inlet diameter, [mm] D2 impeller outlet diameter, [mm] Z)3 inlet diameter of volute, [mm] D4 outlet diameters of volute, [mm] h, inlet width of volute, [mm] z number of blades p average static pressure, [Pa] Pi fluctuating static pressure, [Pa] Ô thickness of blade, [mm] e>, thickness of blade coating , [mm] p density, [kg/m3] b2 outlet impeller width, [mm] f„ axis rotating frequency, [Hz] Kj coating thickness coefficient, Cp pressure fluctuation coefficient 600 Wang Y. - Zhang, Z. - Chen, J. - Liu, H. - Zhang X. - Hočevar, M. 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Review of formulas for efficiency calculation of centrifugal pump. Pump technology, vol. 6, p. 24-27, D0I:CNKI:SUN:SBJS.0.2009-06-007. (in Chinese) Effect of Blade Coating on a Centrifugal Pump Operation under Sediment-Laden Water Flow 601 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10,602-612 © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6755 Original Scientific Paper Received for review: 2020-07-618 Received revised form: 2020-08-21 Accepted for publication: 2020-09-24 Prediction of Strain Limits via the Marciniak-Kuczji ski Model and a Novel Semi-Empirical Forming Limit Diagram Model for Dual-Phase DP600 Advanced High Strength Steel IlyasKacari* -F ahrettin Ozturk2 3 -S erkanToros1-S uleyman Kilic4 1 Nigde Ômer Halisdemir University, Turkey 2 Turkish Aerospace Industries, Inc., Turkey 3 Ankara Yildmm Beyazit University, Turkey 4 Kirsehir Ahi Evran University, Turkey The prediction capability of a forming limiting diagram (FLD) depends on how the yield strength and anisotropy coefficients evolve during the plastic deformation of sheet metals. The FLD predictions are carried out via the Marciniak-Kuczynski (M-K) criterion with anisotropic yield functions for DP600 steel of various thicknesses. Then, a novel semi-empirical FLD criterion is proposed, and prediction capabilities of the criterion are tested with different yield criteria. The results show that the yield functions are very sensitive to anisotropic evolution. Thus, while the FLD curves from the M-K model and the proposed model are not the same for each thickness, the proposed model has better prediction than the M-K model. Keywords: DP600, anisotropy, yield criterion, forming limit diagram, M-K failure criterion Highlights • The most popular failure criterion, the Marciniak-Kuczynski, is compared to a novel semi-empirical failure criterion presented for sheet metals. • The most appropriate and conservative yield function among anisotropic functions is the YLD2000-2d to be able to use with the failure criterion for DP600 sheet steel. • The YLD2000-2d model parameters are presented for DP600 steel. • Prediction capabilities for strain limits are presented on forming limit curves. 0 INTRODUCTION Some strategies on weight reduction have been developed for vehicles in transportation, one of which is to be able to use a thinner body without sacrificing strength requirements by using stronger sheet metal, known as advanced high strength steel (AHSS), which can provide weight saving due to its higher strength leading to thinner and lighter bodies. Therefore, its use in automobile body parts has been increased tremendously [1] to [3], In AHSS, dualphase (DP) steels are manufactured by holding low carbon steel at the austenite temperature for a while and then quenching. They include both ferrite and martensite, which come from the cooling of unstable austenite [4], AHSSs have been increasingly used in automotive structural components, such as floor panels [5] and the trunk lid [6] due to their corrosion resistance, toughness, and high resistance to impact. However, it should be taken into consideration that carbon and nitrogen alloying elements decrease their formability. Numerous research studies have been carried out to enhance their mechanical behaviour, especially formability [7] to [11]. The determination of formability limitations is one of the requirements to achieve safer forming for sheet metals [12], Using forming limit curves is one of the methods to determine necking initiation during deformation. These curves are based on stress (forming limit stress diagram (FLSD)) or strain (forming limit diagram (FLD)). This study focuses on the FLD and determines the formability limit and safe zone of the sheet material under various deforming conditions. It is also an efficient tool for diagnosing manufacturing defects. Sheet metals have their own specific FLD curves. Fig. Is hows a typical FLD. The FLD was introducedby Keeler and Backhofen [13], and Goodwin [14] developed their application to sheet metal forming problems. Although today an FLD consists of two curves known as right-left side curves, Keeler and Backhofen [13] first developed the right side of the FLD (positive minor strain side). Goodwin [14] extended the curve to the left side (negative minor strain side). Forming limit curves are determined by using a failure criterion based on necking. An accurate determination of neck initiation and propagation is not an easy task in sheet metals. Various deformation processes from uniaxial to biaxial loadings may 602 *Corr. Author's Address: Nigde Omer Halisdemir University, Department of Mechatronics Engineering, Nigde 51240, Turkey, ikacar@gmail.com Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 cause different strain combinations. Also, material anisotropy has a significant effect on the strain pattern besides loading conditions [15] to [17], Swift [18] and Hill [19] developed a failure criterion based on instability analysis to determine necking [18] and [19]. While Swift's criterion takes care of the maximum force's direction to determine diffuse necking. Hill's criterion, which is especially suitable for anisotropy in sheet metals, is based on discontinuity to determine localized necking. While the first has the ability to construct just the right-hand side of the FLD, which is useful when strains at all directions are positive, the other one constructs just its left-hand side. Thus, it is quite possible to take different results depending on the criterion. In recent years, one of the criteria is presented in the finite element codes to determine the FLD [20], Fig. 1. An example FLD from ASAME software Marciniak and Kuczynski [21] presented another instability criterion known as the M-K model, based on force equilibrium. It can take into account geometric imperfection or inhomogeneity. Banabic et al. [22] compared their model to a maximum force criterion [23], diffusion based criterion [18], and the localized necking approach [19] to predict the FLD for a stamping process with a linear strain path by combining the M-K criterion and their orthotopic yield function, known as BBC2003 [24], Later, it was developed as BBC2008 [25], For a deep drawing simulation, the onset of necking was predicted, and yield surfaces were obtained via the M-K criterion [26], Many comparative studies were collected on the FLD prediction [27], As a result, it is seen that the M-K model is a preferred failure criterion due to its closer results to experimental data. The present study shows FLD predictions from combined models of the M-K with some anisotropic yield criteria. The curves were evaluated through experimental data collected from DP60 steel. The most appropriate criterion to represent the anisotropy properly was determined. The model and its curves show its applicability and accuracy on various deformation types for DP60. 1 MATERIALAND METHOD DP steels are characterized by their microstructure where hard martensite grains are dispersed. Martensite grains provide high strength in the soft and ductile structure of the ferritic matrix. The strength is adjusted by the amount of martensite and carbon content. In this study, DP60 sheet was examined by means of uniaxial tensile tests with a 00 kN tensile test machine. Elongation was determined by its extensometer with two cameras. Specimens of 0.8 mm thickness were prepared from rolling in the diagonal (DD) and transverse (TD) directions, according to the ASTM E8 / E8 standard [28], The strain rate was 0.008 s1 . Initial yield point (<7n). anisotropy coefficients (r-values), strength coefficient (K), and, hardening exponent (;?) were obtained to use as plasticity model parameters explained in the subsequent sections in detail [29], The results were given in Table 1 Tensile curves were obtained, as seen in Fig. 2. Even small discrepancies were seen, all curves had similar shapes. Although the yield strength was approximately the same for all, the ultimate tensile strength and total elongations were different. 0.00 0.05 0.10 0.15 0.20 0.25 True strain [mm mml Fig. 2. Tensile properties at different orientations for DP600 steel An experimental FLD curve was drawn using the out-of-plane fonnability test with 0.8 mm sheet thickness. The values for J6 mm and 2 mm were used from the literature [30], The tensile test was done only for the thickness of 0.8 mm because mechanical properties were independent on the thickness. The experiments were repeated three times on a I'.tir.cr Strain Prediction of Strain Limits via the M-K Model and a Novel Semi-Empirical FormingLimit Diagram Model... 603 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 double-action special press machine with a 00 mm hemispherical punch. Before deformation, 2.5 mm x 2.5 mm square grids were printed on the sample surface. After deformation, strains on the deformed grids were detected by an image processing software ASAME° The results were shown in Fig. 3. An offsetting procedure to reduce the size of the safe zone on the experimental FLD curve was applied as dashed lines. It increases the reliability as depicted in the Fig. 3 Table 1. Tensile test results for DP600 sheet steel Yield Hardening Strength coefficient, Direction strength r-value exponent, K [MPa] /7 [MPa] RD (0°) 355 0.89 0.194 979.46 (R~=0.996) DD (45°) 362 0.85 0.191 994.25 (R~=0.996) TD (90°) 371 1.12 0.188 1014.44 (/?"=0.997) 2 YIELD CRITERIA A plasticity model consists of a yield criterion to define an elastic to the plastic boundary, a hardening rule to model the evolution of this boundary during plastic deformation, and a flow rule to define plastic strain increment vector. Also, a failure criterion can be used in the case of failure estimates. The yield criterion's function produces one equivalent stress from stress components. In this study, the plasticity models were derived by using the H il lit the BarlatS and the YLD2000-2d functions. 2.1 Hill48 A yield formula of the quadratic HillS was given in Eq.(J [33]: 2 f(av) = F(ay-az)2 +G(az-axf + H (ax - ay )2 + 2Lx; + 2Mr;x + 2Nt% =1.(1) where x, v, z axes are mutually orthogonal. Its coefficients represent the anisotropic behaviour. The coefficients N, M, L, H, G, and F can be calculated by using anisotropy coefficients r0, r4 . r„ . as inEq. (2). F = r90 (1 r90 , G = 1 (I" H = (1- N = (r0+r90) + (l + r45) 2^90 (1 + ro) Fig. 3. FLDs determined for various thicknesses (1.6 mm: [31], 2 mm: [32]; While the area under the curves of the FLDs depicts the safe zone where the dashed line limits the safer zone, its size gives the material's forming ability. The more area under the FLD curve leads to a bigger safe zone for deformation. Strain limits depend on thickness and strain signs. While the bigger thickness leads to the more formability when the strain e2 has a positive sign, the formability decreases in the negative region contrary to expectations, especially for thicknesses 16 îmn or 2 mm. Experiments with the 16 îmn sample were carried out under in-plane deformation conditions while the other two were tested under out-of-plane conditions. The strain limit depends on the test method performed in-plane or out-of-plane deformation. Thus, a safety margin is used to eliminate the difference in practice. 2.2 Barlat89 Another widely used anisotropic yield function in sheet metal deformation simulations was proposed by Barlat and Lian [34] (denoted as the Barlat$ : 0 = a|À'1+À': r+bl^-Kf + C\2KT = 2 . Its coefficients; p, a, c, h characterize the anisotropic behaviour. c, -ha,. k2=. c, -ha,. (4) a=2-c=2-2 l + r0 1 + r90 (I 604 Kacar, I. - Ozturk, F. - Toros, S. - Kilic, S. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 h = 1 + r„. 1 + r„ P = - — M a 2a+ 2 c where /?, c, and a can be computed based on r-values. However, p cannot be calculated directly but using some ways explained in [34], rv, is yield point from shear stress test and rv, = rjxv while r>xx=rTvv = (). 2.3 YLD2000-2d Barlat et al. [35] presented another function known as the YLD2000-2d, which is more powerful to represent the anisotropy. It is described as follows: identification technic based on error minimization by referring to experimental yield strengths (a,,. crs , <7b , ab) and anisotropy coefficients (r0, r4 . r„ . rh) are applied to detennine them. Tliis method was explained in detail in [36], To detennine the YLD2000-2d yield function model's parameters, theoretical calculation of anisotropics and yield stresses, at different orientation angles were used. In the theoretical calculation of the biaxial stress and similarly in biaxial anisotropy calculation, it was assumed that ab = au = a22- Equi-biaxial yield strength rjh = SB MPa was determined via the bulge test and biaxial anisotropy as rb = 03 is then determined with the help of hole expansion test [37], where & is the equivalent stress and I -, -, I M I -, ~„ IM I ~„ ~„ IM + pj +25", +25"; +S2\ , where M is an exponent the same that of Barlat8 [24], and Sl: (k =12) are principal stresses in the transformed domain when ,v and .v are stress deviators. Transfonnations are linear based on ,v = CS. = C S = La, s =C S = L<7, (9 («) where C" and C" are matrices providing transfonnations. The ' and " superscripts mean two different transfonnations. a shows the stress state. T is a matrix including constants. The explicit fonns of /. ' and L " matrices are given in Eqs. (1J and (2) . (U ¿11 "2/3 0 o" A 2 -1/3 0 0 L2l = 0 -1/3 0 a2 L22 0 2/3 0 a7 4. 0 0 1 "-2 2 8 -2 o" a, A 2 1 -4 -4 4 0 a4 L2l = 4 -4 -4 1 0 a, L22 -2 8 2 -2 0 «6 .4. 0 0 0 0 1 _as_ (2) where «, to a8 are the YLD2000-2d function's parameters providing anisotropic effects. No direct fonnula to calculate them exists, so an inverse 2.4 Application of the M-K Failure Criterion This criterion assumes that the sheet metal includes a pre-existing thickness imperfection on the surface lying along the rolling direction. An imperfection factor is defined as f0 = (t" j where i defines thickness. The imperfection free zone and imperfection's zone are denoted by 'a' and '6' superscripts, respectively. Subscript 0 means anything at the beginning. If any biaxial stress increment is applied to a sheet metal, it leads to a strain increment in a and b sections. Necking initiates if the strain increment in section b is ten times higher than that of section a [38] to [41], Force exerted in a and b must be in balance during loading, as explained in Eq. (J Fa = F Fa = F (J where F is the force and n t shows the nonnal and tangential axes. Similarly, both equations can be rewritten in tenns of stresses as in Eq. (J . o\„ ■ taes' =a l0c u)j, ■te i0 e CT„ .fe3 =o l0c u,i ■tbeE3 l0 c (I where t0 is initial sheet tliickness. an and ant are nonnal and tangential stresses. The strain component exerted through tliickness in the nonnal axis is e3. The imperfection factor/can be generalized as in Eq. (J . / = /o (J where ({, is initial imperfection factor. e3 can be detennined by using incompressibility condition [42], The stress components C)hnn. a''n. C)hni. and effective strain increment dëb can be solved by means of simultaneous solution of four equations in Eq. (¡J> . Prediction of Strain Limits via the M-K Model and a Novel Semi-Empirical FormingLimit Diagram Model... 605 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 p _ d£n,Pnn + ds„a„ + y _ Q dsboY dsb 2 ds" p = s-S'jEL-1 = 0, J _a ■ CF nn b F, = f-m—1 = 0. 4 J a <3nt Although these equations depend on the groove angle, the M-K model can be used without the groove angle by following the flowchart in [43], The flowchart has been followed in this study. The To parameter of the M-K model was taken as 0.9 The other parameters of the model depend on the strain and f0. 2.5 The Proposed Failure Criterion The FLD consists of two curves and one intersecting point depending on three deformation modes such as uniaxial, biaxial, and plane strain deformations. While uniaxial strains give points on the curve in the left-hand side, biaxial strains give points on the other curve in the right-hand side with respect to zero strain point in the horizontal axis. Both curves are intersected at a point corresponding to zero strain in the horizontal axis leading to one strain component, which causes to plane strain deformation. In the study, a novel semi-empirical FLD model was proposed, which was created via regression analysis of the experimentally obtained FLD diagrams of the several materials that were obtained by the other researches of the authors. During the modelling of the FLDs, the general mechanical properties that affect the FLDs of the materials were defined. As is well-known from the experiences and literature, the thickness and anisotropic features of the materials are the main characters that can change the FLDs. During the fitting analysis of the simple mathematical formulations, the constants were then constrained with the given experimental properties. The model consists of three formulas corresponding two curves and one intersecting point. The formulas are based on normal anisotropy r, biaxial anisotropy rh. sheet thickness t. and strains as seen in Eq. (J . -rs2 + FLD0, -r.srF2 +FLD„. where FLD0=smg,f" s2 < 0 s2 > 0. (J FLD0 is the major strain at the point corresponding zero strain in the horizontal axis (f;2 = 0). It depends on the engineering strain percentage eeg% , sheet thickness I and hardening exponent n. Although there are many experiment types to determine the biaxial anisotropy, such as disk compression test [44], biaxial stretching test [45], or hole expansion test [46], it can also be calculated by using a flow rule, as in Eqs. ($ ) to (20), which gives the strain increment relation. , 3/ da dsn = dX^-— = ds ■ dan dau ds22 = dX df dcr,. da = ds - dan. da da22 da dan (9 ) (20) where A is a multiplier, ds gives true plastic strain increment. / is a scalar function defining "plastic potential". When the plastic potential function is a , this formula becomes the associated flow rule. au and 022 are plane stress states at the longitudinal and transverse axes with respect to the rolling axis. 2.6 Hardening Rule An isotropic hardening rule presented by Hollomon as in Eq. (2J is used [47], Thus the evolution on the stress (j;, due to hardening during plastic deformation is obtained. ah=Ks" (21) where K is the strength coefficient, n stands for the strain-hardening exponent, and h means the isotropic hardening function. These are determined from curve fitting of tensile data. 3 RESULT AND DISCUSSIONS While the parameters of the HillS and the Barlat89 can be determined from r-values, the YLD2000-2d's coefficients were determined by optimization based on the nonlinear least-squares method. Kilic et al. [48] explained an application of this optimization method in detail. The coefficients were calculated as in Table 2 for various thicknesses. In any plastic deformation process, it is expected that the plasticity model should give the yield point 606 Kacar, I. - Ozturk, F. - Toros, S. - Kilic, S. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 Table 2. Coefficients of the yield functions Thickness F G H N HÜI48 0.8 mm 0.4204 0.5291 0.4709 1.2819 1.6 mm 0.46 0.5754 0.4246 1.5304 2 mm 0.4035 0.5977 0.4023 1.5369 Thickness a c h P Barlat89 0.8 mm 1.0024 0.9976 0.9441 0.95 1.6 mm 1.0971 0.9029 0.9406 1.015 2 mm 1.1037 0.8963 0.8979 1.015 Thickness ax a2 CC3 as a6 Cty Ctg YLD2000-2d ■ 0.8 mm 1.0221 0.9387 1.0668 0.9766 0.9992 0.9806 0.9719 0.9778 1.6 mm 1.011 0.9162 1.0651 0.9793 1.0048 0.9653 0.9729 0.9356 2 mm 0.98 0.9431 1.078 0.9767 1.0075 0.951 0.9766 0.9281 and anisotropy predictions as accurately as possible. Therefore, the model performances were evaluated by their predictions on the yield strength and anisotropy coefficients depending on plane angle toRD [deg] Fig. 4. Yield stress predictions 90 Prediction of Strain Limits via the M-K Model and a Novel Semi-Empirical FormingLimit Diagram Model... 607 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 done by the models combined with the HillS and the YLD20002d, none of them provided a good fit for the left side. The YLD20002d gave conservative predictions on the right side curves for all cases. r^ïf \ -HMI48 Bar1at89 • YLD2000-2d * Expérimental • 0 45 90 Angle pto RD [—YLD2000 •— Experimental -o— Hill48 a Barlat89 <— YLD2000 Fig. 11. FLD curves from the proposed model and the yield criteria for thickness; a) 2 mm, b) 1.6mm, and c)0.8mm Fig. 10. FLD curves from the M-K model and the yield criteria for thickness; a) 2 mm, b) 1.6mm, and c) 0.8 mm a) 2 mm —•— Experimental —o—Hill48 —a— Barlat89 \ —ft— YLD2000 X v • ■ .I. ■0.4 -0.2 0.0 0.2 0.4 £ both models. Finally, the following conclusions were drawn: The estimated yield locus, the anisotropy coefficients, and the normalized yield strengths for DP60 fit well with the experimental data for the YLD2000-2d criterion. It can simulate almost entire amsotropy coefficient and stress distribution depending on a plane angle between 0 and 9 It works regardless of sheet thickness. Also, it is the most conservative one because it draws the smallest safe zone leading to the most reliable decision. The fact that it has more Prediction of Strain Limits via the M-K Model and a Novel Semi-Empirical FormingLimit Diagram Model... 609 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 602-612 parameters gives more nonlinearity to be able to represent the cases with complex loading, such as biaxial deformation for which material anisotropy plays a significant role on the fonnability and defect occurrences. Therefore, this criterion is suitable for sheet metal deformation simulations. Fig. 12. Comparison of the M K and the proposed criteria for thickness; a) 2 mm, b) 1.6 mm, and c) 0.8 mm The YLD2000-2d represents the most suitable curve in the positive deformation zone of FLDs, which means that it can be preferred for failure predictions of DP60 sheet metals. Its consistency continues for all thickness for the sheet. When the sheet thickness is 2 mm, the HillS and the Barlat8 criteria show bigger deviation from the experimental curve. Thus, both criteria were consistent up to 2 mm sheet thickness. The proposed model combined with the YLD2000-2d gives the most precise failure predictions for DP60 s heet steels. Within the scope of this study, a failure criterion was presented for sheet metals. Further work for this research should be evaluated for the sheets thicker than 2 mm of DP60 a nd other AHSSs. 5 REFERENCES [1] Kleiner, M, Chatti, S, Klaus, A. (2006). Metal forming techniques for lightweight construction. 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[47] Hollomon, J.R. (1945). Tensile deformation. Transaction of AIME, vol. 162, no. 1, p. 268-277. [48] KiIiq, S., Toros, S., Kacar, i., Ozturk, F. (2018). Luy, O.T.M., Qam, E., Bari§gi, N., Demirba§, M.D., Gugyetmez, M. (eds.). Scientific and Professional Studies-Engineering and Technology in the World of the Future, Ekin press, Bursa, p. 271-290. [49] Banabic, D., Carleer, B., Comsa, D.-S., Kam, E., Krasovskyy, A., Mattiasson, K., Sester, M., Sigvant, M., Zhang, X. (2010). Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation. Springer-Verlag Berlin Heidelberg. 612 Kacar, I. - Ozturk, F. - Toros, S. - Kilic, S. Strojniški vestnik - Journal of Mechanical Engineering 66(2020)10,613-626 © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6704 Original Scientific Paper Received for review: 2020-07-629 Received revised form: 2020-08-21 Accepted for publication: 2020-09-24 Research on a Noise Reduction Method Based on DTCW and the C^ lie Singular EnergjD ifference Spectrum Xihui Chen12 ® -G ang Cheng2-4 ing Liu3 inliui Slii1 - Wei Lou1 1 Hohai University, College of Mechanical and Electrical Engineering, China 2 China University of Mining and Technology, School of Mechatronic Engineering, China 3 China Coal Technology and Engineering Grope Shanghai Co., Ltd., China 4 Shandong Zhongheng Optoelectronic Technology Co., Ltd., China The gear is the most important part of the transmission system of mechanical equipment, and the monitoring and diagnosis of it can improve the reliability of mechanical equipment However, mechanical equipment generally works in harsh working conditions. The gear vibration signal is subjected to strong noise interference in working conditions, which brings great challenges for the effective diagnosis of gear faults. This paper proposed a noise reduction method based on the dual-tree complex wavelet transform (DTCWT) and cyclic singular energy difference spectrum. First, the gear vibration signal containing strong noise interference is decomposed into a series of signal components with different frequency characteristics by using the time-frequency analysis ability of DTCWT. Then, cyclic singular energy difference spectrum is proposed based on the idea of a cascaded cycle and the successive elimination of noise interference to process each signal component with different frequency characteristics, and the termination conditions of cyclic singular energy difference spectrum can be set according to the noise interference distribution characteristics in different frequency bands. The final noise reduction of the original gear vibration signal can be realized based on signal reconstruction after the noise reduction processing of each signal components with different frequency bands. Finally experiments are carried out to verify the effectiveness of the proposed method, which is effective and suitable for the noise reduction of the vibration signal. Keywords: noise reduction, DTCWT, singular value decomposition, cyclic singular energy difference spectrum, vibration signal Highlights • A noise reduction method based on dual-tree complex wavelet transform and cyclic singular energy difference spectrum is proposed. • The cyclic singular energy difference spectrum is proposed based on the idea of a cascaded cycle and the successive elimination of noise interference. • The adaptive selection methods of some parameters are applied to the proposed cyclic singular energy difference spectrum. • The simulated signals and experimental signals are used to verity the proposed method, which proves that the proposed method can effectively eliminate noise interference. 0 INTRODUCTION The gear is the most important part of mechanical equipment and is mainly responsible for the transmission of motion and power. On-line monitoring and fault diagnosis of gear is crucial in ensuring the safe operation of mechanical equipment [1] and [2], At present, the vibration signal analysis is the mainstream of gear fault diagnosis. However, the actual operation condition of mechanical equipment is generally harsh, the result of which is that the collected vibration signal contains a large amount of noise interference [3] and [4], The vibration signals obtained under harsh working conditions generally contain strong noise interference, which conceals the weak fault feature produced by the gear fault and greatly affects the accuracy of the vibration signal. The difficulty of obtaining useful information from the collected vibration signals is increased under such operation conditions [5], Therefore, the pre-processing of noise reduction is essential for the vibration signal in real working conditions. The commonly used traditional noise reduction method includes low-pass, high-pass, and bandpass filters, but for the noise interference generated in real working conditions, no matter which filter is used, the integrity of the useful signal components will be affected [5], With the development of signal-processing technology, more noise reduction methods have been proposed. Wavelet transform and singular value decomposition (SVD) are more commonly used in modern signal processing. Wavelet transform can decompose the original vibration signal into several signal components with different frequency bands and different resolutions [6]; the noise reduction is then processed for each signal components with different frequency bands. Generally, noise reduction methods based on wavelet transfonn include wavelet modulus maximum denoising, wavelet threshold denoising, wavelet correlation denoising and similar. However, *Corr. Author's Address: College of Mechanical and Electrical Engineering, Hohai University, Changzhou, China, chenxh@hhu.edu.cn 613 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 613-626 wavelet threshold denoising needs to determine the threshold value, and an accurate threshold setting has a great influence on noise reduction effect. Wavelet correlation denoising uses the correlation of wavelet coefficients at corresponding points on different scales to distinguish the useful signal coefficients and noise coefficients to achieve the purpose of noise reduction. However, wavelet correlation denoising has the disadvantage of a complex algorithm, and its noise reduction effect is generally limited by the judging of correlation of wavelet coefficients. The noise reduction based on SVD can eliminate noise interference according to the different contribution of useful signal and noise interference to singular values, and that has been applied in the noise reduction of vibration signal [7], However, the noise reduction methods based on SVD are faced with the problems of phase space matrix construction and denoising order selection. The noise interference generated in real working condition is more complex, which has the characteristics of irregularity, wide frequency distribution, and similar. In order to eliminate the strong noise interference in real work conditions, combining the advantages of the noise reduction ideas based on wavelet and SVD provides a new idea for the pre-processing of noise reduction of the gear vibration signal. The strong noise interference can be decomposed into a series of signal components with different frequency bands, and the corresponding denoising criteria based on SVD can be built to eliminate the noise interference in each frequency band according to its distribution characteristics. Nevertheless, the general wavelet transform has some shortcomings, such as frequency leakage, frequency aliasing, translation sensitivity and less direction selection, and there are also some problems such as phase space matrix construction and denoising order selection in SVD [8], With the development of the general wavelet transform, DTCWT has been proposed. Compared with the general wavelet transform, DTCWT has the characteristics of translation invariance, small frequency aliasing and multi-direction selection [9] and [10], Meanwhile, the selections of embedding dimension, delay parameters and denoising order involved in the noise reduction based on SVD also need to be further studied [11], In this paper, a noise reduction method based on DTCWT and cyclic singular energy difference spectrum is proposed. The gear vibration signal with strong noise interference is decomposed into a series of signal components by DTCWT, and the strong noise interference in each frequency band can be eliminated by cyclic singular energy difference spectrum. The noise reduction of the gear vibration signal can be realized by reconstructing the signal components of each frequency band after noise reduction. Finally, the validity of the proposed method is verified by experimental signal analysis. However, it should be noted that most equipment is not equipped with the suitable vibration sensors for state monitoring and matching acquisition systems in existing large equipment, such as shearers, heading machines, shield machines, and so on. Therefore, it is impossible to realize the long-time continuous acquisition of vibration signal in the working process of equipment. Only the external vibration sensors and acquisition system can be used for short-term experiments. However, the gear fault in the real working condition usually occurs suddenly and has a certain probability, so it is very difficult to obtain the vibration signal of gear fault in the short-term acquisition process. Therefore, this paper uses the mechanical fault simulation bench to simulate the vibration signal of the gear fault. Meanwhile, the strong noise interference in real working condition is collected. Then, the strong noise interference after energy conversion is added into the vibration signal of the gear fault, which provides a way to obtain the gear fault vibration signal under strong noise interference in real working conditions. 1 MODEL BUILDING 1.1 Dual-Tree Complex Wavelet Transform The basis function of DTCWT consists of two distinct real wavelets, and they constitute the Hilbert transform pair. The basis function of DTCWT is shown as [12] and [13]: V(.t) = 2 ry(r)) = 2J,2iy(t)i) CI7 (*) = X g„a- - 2p)C\%(p) + X &(* " 2p)m%(p) (f where h0 and h, are the low-pass filter and high-pass filter of real tree wavelet, and g0 and g, are the low-pass filter and high-pass filter of complex tree wavelet. 111 is the length of the filter of real tree wavelet, and p is the length of the filter of complex tree wavelet, k is the number of data points. h0, h,. go and A2> ...>A;,>0 is a diagonal matrix with (\+(d ) r) x/?/ dimension, and they are the singular values of phase space matrix A. U is the left singular matrix of A, and V is the right singular matrix of A. Next, the singular values contributed by the useful signal are retained, and that contributed by noise interference are set to zero. The singular value diagonal matrix is converted to S = (A1,/l2,...,/lt,0,...,0) kA2>...>Ah>0, and the energy of singular value can be expressed as follows: E,. = A; (U where E, is the energy of the ;th singular value. The difference spectrum of singular energy can be expressed as follows: b,.= A:-A,= 1,2,...,/7. (2) The average of the difference spectrum of the singular energy is calculated. (J The extreme value point />, of singular energy difference spectrum represents the mutation of the signal components at the ;th singular value. The singular value sequence numbers of all extreme points that are is greater than the average value are found. The maximum singular value sequence number of the extreme point with greater than the average value p is taken as the denoising order of one-time cycle. It can be found that the denoising order is a mutation point of singular value, which represents the signal component mutation. It is not the biggest mutation point, and it is obtained according to the average value. The singular values smaller than the denoising order can be determined to be essentially contributed by noise interference. Algorithm process The proposed cyclic singular energy difference spectrum is introduced on the basis of selection methods of delay parameter, embedding dimension and denoising order. Step 1 According to the characteristics of vibration signal under strong noise interference, the delay parameter and embedding dimension are selected by Eqs. ()> and ((B) , and the phase space matrix can be constructed; Step 2: The singular energy difference spectrum can be obtained according to Eqs. (1J and (2) , and the average value of those can be further obtained; Step 3 The singular value sequence numbers whose abrupt extreme values are greater than their average value in singular energy difference spectrum Research on a No/se Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum 617 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 613-626 are obtained, and the maximum sequence number is defined as the denoising order, and the singular values whose sequence number are greater than denoising order are replaced by zero; Step 4 The inverse process of SVD is carried out, and the noise reduction signal can be reconstructed, and one-time noise reduction is completed, and there is still a part of noise interference that has not been eliminated. Step 5 The signal after one-time noise reduction is regarded as a new signal, and it is treated as a new processed object to replace the original vibration signal. Then, the process of Steps 1 to 4 is cycled until the termination condition of noise reduction of cyclic singular energy difference spectrum is satisfied. Step 6 In the proposed cyclic singular energy difference spectrum, the termination condition is that the maximum sequence number of the singular values whose abrupt extreme values detected in Step 3 are greater than the average value of those is less than a certain value. When the termination condition is satisfied, the noise reduction process will be terminated after this time noise reduction. The flowchart of the proposed cyclic singular energy difference spectrum is shown in Fig. 2. Double tree filters Fig. 2. The flowchart of the proposed cyclic singular energy difference spectrum T Decomposition layer Original vibration signal DTCWT X The signals with different frequency bands Inverse reconstruction ofDTCWT Noise reduction in each frequency band 5 Cyclic singular energy difference spectrum Fig. 3. The flowchart of the proposed noise reduction method 2.1 The Analysis of the Simulated Signal Based on the characteristics of the vibration signal generated by gears, the simulated signal is shown as Eq. (J , and its time-domain signal and frequency spectrum are shown in Fig. 4 Fig. 4. The simulated signal a) time-domain signal, and b) its frequency spectrum It can be seen from Fig. 4 that the simulated time-domain signal is more regular and have more obvious periodic components. The main frequency components are outstanding. The Gaussian white noise is used to simulate strong noise interference, and which are added into the simulated signal. The simulated signal added noise interference and its frequency spectrum are shown in Fig. 5 y0 (i) = (1 + 0.8 + 0.4cos(20^r))Gsin(0.1siii(20^r)) yi(f) = (1 + 0.6 + 0.5cos(20 Kt) + 0.1cos(40/rf)) ■ cos(600/zt + 0.1sin(20/rf)) y2(r) = 0.5(1 + 0.5 + 0.3cos(20/rf)) . (4 ) ■ sin(1200/rf + 0.5siii(20/rf) + 0.2siii(40/rf)) y =y0+yi+y2 t = 0:0.0005: 2 2 EXPERIMENTAL ANALYSIS The overall analysis flowchart of the proposed method is shown in Fig. 3 and MATLAB software is used for the following analysis and processing of signals. It can be seen from Fig. 5 that the simulated signal is completely submerged by the added noise interference. Except for the very prominent frequency points of ® Hz and GO Hz, the other frequency components are disturbed by the noise interference. The proposed noise reduction method is used to deal 618 Chen, X. - Cheng, G. - Liu, N. - S hi, X. - Lou, W. Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10,613-626 with the simulated signal added noise interference. Firstly, DTCWT is used, and the number of the decomposition layers is important for the subsequent noise reduction effect. If the number of decomposition layers is large (more than $ , the frequency band of some decomposed signal components will be too narrow, and it is easy to cause signal loss and signal distortion. If the number of decomposition layers is small (less than J , it will cause the similar wavelet coefficients of useful signal and noise interference can not be separated, which cause the noise reduction effect of the subsequent process to be reduced. Therefore, through multiple experiments of the decomposition effect of DTCWT, the number of decomposition layer is determined to 6 The decomposition result of DTCWT is shown in Fig. 6 Frequency {HkJ Fig. 5. The simulated signal added noise interference and its frequency spectrum Fig. 6. The decomposition result of DTCWT The simulated signal added noise interference is decomposed into seven signal components by DTCWT, and the corresponding noise interference is also decomposed into each signal component. For each signal component with different frequency bands, the cyclic singular energy difference spectrum is carried out. Meanwhile, the termination condition is that the denoising order determined by the last cyclic noise reduction is less than a certain value. In this way, the corresponding termination conditions can be set according to the noise distribution of each frequency band. Due to the space limitation, the noise reduction process in frequency band dl is illustrated as an example, and the termination condition of this signal component is set as the denoising order being determined by the last cyclic process of noise reduction being less than The noise reduction result of the signal component of frequency band dl is shown in Fig. 7 Frequency [I l/| Fig. 7. Cyclic noise reduction result of the signal component of frequency band dl As can be found in Fig. 7 for the signal component of frequency band dl a total of four-cycle processes of noise reduction are used. With each cycle process of noise reduction, the noise interference is filtered out step by step, and the effective signal after noise reduction can be obtained. It can be found from the reduction result that the main frequency components in the frequency spectrum are § Hz, 60 Hz, 90 Hz, and 8 Hz, which are merely the frequency components of the simulated signal (Fig. J . It is illustrated that the proposed method can eliminate noise interference better. Furthermore, 9 0 Hz and 8 Hz are regarded as the useful signal and not filtered out in the final noise reduction. However, comparatively speaking, the proposed method can eliminate the most of noise interference, it has a good noise reduction effect. For other signal components obtained by DTCWT, noise reduction is carried out according to the cyclic singular energy difference spectrum, and the final noise reduction results of the simulated signal can be obtained, and they are shown in Fig. 8 Research on a No/se Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum 619 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 613-626 F rcqu cney [Hz] Fig. 8. Final noise reduction result of the simulated signal It can be seen from Fig. 8 that the proposed method can effectively eliminate the strong noise interference comparing with Fig. 5 In the final noise reduction result, the main feature frequency components of the simulated signal are ® Hz, 20 Hz, 28 Hz, 20 Hz, 8 Hz, 60 Hz, and ffi Hz, and they are completely retained, indicating that the above method can better eliminate noise interference and retain the useful signal. Comparing Figs. 4 and 8 it can be found that some frequency components are not filtered out; however, the amplitude of those frequency components are relatively low, and their interference with the useful signal is limited. Next, the validity of the proposed method is verified by the processing of the gear vibration signal under strong noise interference in real working condition. 2.2 Analysis of the Experiment Signal The acquisition experiment of the strong noise interference in real working conditions is carried out in the gear system of rocker arm of electric haulage shearer. The vibration signals generated by the gear system are collected when it is running under no-load and normal cutting and the strong noise interference in real working condition can be extracted, and the acquisition experiment is shown in Fig. 9 and the strong noise interference in real working conditions is shown in Fig. (I . rr™ i TH'r"TTT Wfff f »Ff^TH"" W II"1 Fig. 10. The strong noise interference in the real working conditions The SNR can be estimated after extracting strong noise interference in real working conditions, and its calculation process is shown in Eq. (J . EPR = 10 lg(SE / NE) = 10 lg(£ s; /£ ), (5 ) i-l / i-1 where EPR is the SNR in real working condition, K the energy of useful signal, NE the energy of strong noise interference, and / the number of data points. The gear fault vibration signal in strong noise interference is obtained by adding strong noise interference after energy conversion into the vibration signal collected from the mechanical fault simulation bench. In this paper, the mechanical fault simulation bench is composed of motor, planetary gearbox, spur gearbox, load system and vibration sensors, and vibration sensors are arranged on the housing of a planetary gearbox. In the experimental process, the broken tooth fault of sun gear in the planetary gearbox is simulated, and the broken tooth fault is processed by wire-cutting technology. The length of the broken tooth is 7 mm, and the broken gear is installed in the planetary gearbox. The motor speed is set to 0 Hz, and the load is set to .15 Nm by control software. The acquisition system works in synchronous sampling mode, and the sampling frequency is set to 280 Hz. The collected experiment with the mechanical fault simulation bench is shown in Fig. 11 and the collected gear fault vibration signal is shown in Fig. 2. 636 Chen, X. - Cheng, G. - Liu, N. - S hi, X. - Lou, W. Fig. 9. The acquisition experiment of strong noise interference According to the SNR in real working conditions, the energy conversion coefficient can be confirmed. The noise interference in real working conditions converted by energy conversion coefficient is added Dila qllKtlkiJi _ Biokrn Fig. 11. The collected experiment and gear state Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10,613-626 into the gear fault vibration signal collected from the mechanical fault simulation bench. The gear fault vibration signal under strong noise interference is shown in Fig. 3 from which it can be seen that the gear fault vibration signal is all submerged after adding the strong noise interference in real working conditions, and its frequency spectrum is shown in Fig. i Fig. 12. Vibration signal of broken gear fault collected from mechanical fault simulation bench Fig. 13. The gear fa ult vibration signal under strong noise interference in real working condition a) b) Fig. 14. The frequency spectrum of gear fault vibration signal in strong noise interference; a) detail frequency spectrum, and b) full frequency spectrum It can be seen from Fig. 4 that the prominent frequency points in the detail frequency spectrum are 0 Hz, 79 Hz, and 1$ Hz, which are the output frequency of the motor and its double frequency and triple frequency, respectively. However, there are also high amplitude frequency components around these frequencies, which cause interference to these feature frequencies. Furthermore, 6 Hz corresponds approximately to the meshing frequency of the gear system, which is the installation part of the fault gear, and 8 Hz, 2« Hz, 9 Hz and 4 Hz correspond to the triple frequency, fourfold frequency, fivefold frequency, and sevenfold frequency, respectively. Although some frequency points are prominent in the frequency spectrum but the gear fault vibration signal suffers from strong noise interference in the low-, middle-, and high-frequency bands. Next, the gear fault vibration signal is decomposed by DTCWT, and the decomposition layer is set to 6 In the decomposition process of DTCWT, the applied filters are as follows: The high-pass filter h, of real tree is [0.005 0.001 0.0(12, 0.023, OJ$ 0.01 « 0.« OJ 0.219 0.120, 0.08 O.OS 0.008 0.00 2f , the low-pass filter h0 of real tree is [0.0025 0.008 O.OS O.OS 0.1 2, 0.2739 0.9 0.« 0.01« OJ® 0.028, 0.0(12, 0.001 O.OOp . The high-pass filter gi of complex tree is [0.0025 0.008 O.OS 0.08 0.120, 0.219 OJ 0.6 $ 0.01 « OJ® 0.028, 0.0QI2, 0.001 O.OOp , and the low-pass filter g0 of complex tree is [O.OOS O.OOS 0.0QI2, 0.028, 0.1 00 0.01« 0.« OJ 0.219 0.1 120, 0.08 O.OS 0.008 0.002J . The decomposition result of DTCWT is shown in Fig. J Ci.O 0.2 0.4 0.6 0.8 1.0 Time [s] Frequency [Hz] Fig. 15. The decomposition result of DTCWT With DTCWT, seven signal components with different frequency bands and different resolution attributes are obtained. Meanwhile, the strong noise interference is also decomposed into different band signals according to their attributes. For the obtained signal components with different frequency bands, the noise reduction based on cyclic singular energy difference spectrum is carried out. Because the termination condition of the proposed noise reduction method is that the denoising order determined by the last cyclic is less than a certain value, different cycle termination conditions can be set for different band signals. In this paper, by comparing several experiments, the termination condition of noise reduction of frequency band c6 to dl is that the denoising order determined by the last cycle is less Research on a No/se Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum 621 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 613-626 than [0, 0, 0, 8, 00, 00, 20] , respectively. Due space limitations, the noise reduction process of frequency band d2 layer is illustrated as an example. The noise reduction process is shown in Fig. 6 l ime Is) Frequency [Hz] Fig. 16. Noise reduction process of frequency band d2 It can be seen from Fig. 6 that the noise reduction process of frequency band d2 is completed after 5 cycles of noise reduction. Compared to the signal of frequency band d2 layer between Figs. 5 and 16 the signal of frequency band d2 layer in Fig. J contains more noise interference, and the noise interference submerges most of the original signal frequency components. Based on the idea of the cascaded cycle and successive elimination of noise interference, the proposed cyclic singular energy difference spectrum is used, and the signal components determined to be noise interference are filtered out step by step in the process of each cycle noise reduction. It can also be seen from Fig. 16 that the noise interference can be eliminated step by step with the increasing of the cycle number of noise reduction; then, the strong noise interference in frequency band d2 layer can be eliminated, and the useful signal can be retained. To analyse the effect of different delay parameters on the noise reduction result, and the mutual information function method is proved to be effective in selecting the delay parameter, some qualitative and quantitative analyses are carried out. Similarly, the vibration signal of frequency band d2 is taken as the analysis object, and the delay parameters are set as 2. 4 6 8 ® and 2, respectively, where the delay parameter is equal to 6 which is selected by the mutual information function method in this paper. In addition, for different delay parameters, the same methods are used to select the embedding dimension and denoising order. For the vibration signal of frequency band d2, the noise reduction results using different delay parameters are shown in Fig. I 0.5 I IOOO 2000 3000 4000 S000< Timeisl Frequency III. Fig. 17. The noise reduction results using different delay parameters In the analysis process, except for different delay parameters, the other processing methods are all consistent. As can be seen from Fig. I with the increase of the value of the delay parameter, more signal components are retained. Compared with the ideal vibration signal without noise interference, when the delay parameter is selected 2 or 4 although their noise reduction results retain the main signal components, some useful signals are eliminated as noise interference. When the delay parameter is selected as ® or 2, it can be found that there is too much noise interference at both ends of the signal frequency band, and the noise interference can not be effectively eliminated. By comparison, when the delay parameter is selected 6 or 8 they have a better noise reduction effect, in addition, the noise interference 622 Chen, X. - Cheng, G. - Liu, N. - S hi, X. - Lou, W. Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10,613-626 Table 1. Some feature indexes of the noise reduction results of different delay parameters and the ideal vibrations signal without noise interference Delay parameter 2 4 6 8 10 12 Vibration signal without noise interference Energy 3.30 4.96 9.04 11.01 13.83 14.27 9.22 Average value (x1CT6) 1.18 9.87 4.20 9.7 4.2 3.45 6.87 Root mean square 1.82 2.23 3.01 3.32 3.72 3.93 3.04 Kurtosis 5.11 3.23 3.45 3.55 3.76 3.84 5.23 Waveform factor 143.3 144.1 145.3 146.1 146.6 147.1 146.28 Kurtosis factor (xlO-3) 1.4 2.7 7.2 10 14.9 16.4 8.3 results of different delay parameters are quantitatively analysed. Some feature indexes of the noise reduction results of different delay parameters and the ideal vibrations signal without noise interference are calculated, and they are shown in Table 1 It can be seen from Table 1 that the quantization indexes of noise reduction results are the closest to the vibration signal without noise interference when the delay parameter is 6 or 8 Because of the better symmetry of the vibration signal, the magnitude of average values is smaller. When the delay parameter is 2, only the most prominent signal components are retained, and their kurtosis indexes are the largest. When the delay parameter is selected as other values, some abrupt signal components are eliminated by mistake, so the kurtosis index is relatively small, which is also the key issue to be studied in the future. When the delay parameter is set to 12, it can be found that the energy of the noise reduction signal is higher approximately by 4 % from the vibration signal without noise interference, because when the delay parameter is 2 or another large value, the data in the (//+} th row always lags behind more data points compared with the data in the ;?th row. This phenomenon causes the dimension of the phase space to decrease, and the size and number of extreme points of the singular energy difference spectrum is also reduced. However, the termination condition in the proposed method is that the maximum sequence number of the singular values whose abrupt extreme values are greater than the average value of those is less than a certain value, so the cycle noise reduction process stops prematurely when the delay parameter is large, and some noise interference is not eliminated. Then when the delay parameter is 2, the noise reduction signal still contains some noise interference, so the energy of the noise reduction signal is significantly higher than that of the vibration signal without noise interference. In this paper, the delay parameter selected by the mutual information function method is 6 which also proves that it is feasible to apply mutual information function method for delay parameter selection. For other frequency band signals obtained by DTCWT, the noise reduction is carried out according to the above process, and the signals after noise reduction of each frequency band are inversely reconstructed to obtain the final noise reduction result. The final noise reduction results of the gear fault vibration signal and its frequency spectrum are shown in Fig. $ Fig. $ is the comparison of the detailed spectrums of the vibration signal without noise interference and the vibration signal with noise interference after noise reduction. Meanwhile, the effectiveness of the proposed method is proved by combining the comparison analysis of the above Fig. i which is the frequency spectrums of the vibration signal in strong noise interference. a) b) Fig. 18. Final noise reduction result of gear fault vibration signal and its frequency spectrum; a) gear fault vibration signal after noise reduction, and b) frequency spectrum after noise reduction To compare and analyse the above results comprehensively, it can be found that gear fault vibration signal is disturbed by strong noise interference seriously, main features of gear fault vibration signal are completely submerged by strong noise interference, and the low-, middle-, and high-frequency bands are full of noise interference (Fig. J . After the processing of the proposed method, the gear fault vibration signal after noise reduction shows the regularity similar to the gear fault vibration signal Research on a No/se Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum 623 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)10, 613-626 without noise interference, and the noise interference in low-, middle-, and high-frequency bands are greatly reduced (comparison between Figs. 4 and $ . That is because DTCWT is used for signal decomposition, and each signal component obtained by DTCWT is denoised separately. Meanwhile, to compare the detailed spectrums between the vibration signal without noise interference and the vibration signal with noise interference after noise reduction (Fig. J , it can be found that they have the same main frequency components, and the main composition of signal components is also similar. Most noise interference can be eliminated, main signal features can be represented, and the useful signal components can be obtained. However, it also can be found that the proposed noise reduction method does not completely eliminate the strong noise interference in real working condition, and there is still a small amount of noise interference. However, relatively speaking, any noise reduction method can not eliminate all noise interference. Compared with the strong noise interference in real working conditions, the proposed noise reduction method lias a relatively effective noise reduction effect. a) b) Fig. 19. The comparison of detailed spectrums; a) the detailed spectrum without noise interference, b) the detailed spectrum with noise interference after noise reduction In order to further illustrate the effectiveness of the proposed method, the proposed method is compared with the existing technologies, and the Butterworth low-pass filter and one-time noise reduction method based on SVD are used to process the same vibration signal under strong noise interference, respectively. When the Butterworth low-pass filter is applied, the cut-off frequencies are set as [8 Hz, 200 Hz, 00 Hz, 00 Hz, 90 Hz, 000 Hz, 800 Hz] for the signal components of frequency band c6 dl obtained by DTCWT after many experiments, and the final noise reduction result processed by Butterworth low-pass filter is shown in Fig. 20. When the one-time noise reduction method based on SVD is applied, the denoising order orders are set as [0, 0, 0, 8, 00, 00, 20] for the signal components of frequency band cé dl obtained by DTCWT, which is consistent with the proposed method in this paper. The final noise reduction result processed by one-time noise reduction method based on SVD is shown in Fig 21 a) bj Fig. 20. Final noise reduction result processed by Butterworth low-pass filter; a) time-domain signal after noise reduction, and b) frequency spectrum after noise reduction Fig. 21. Final noise reduction result processed by one-time noise reduction method based on SVD; a) time-domain signal after noise reduction, and b) frequency spectrum after noise reduction It can be seen from Fig. 20 that the time-domain signal processed by the Butterworth low-pass filter has no characteristic to follow. From the frequency spectrum, there is still more noise interference in the low-, middle-, and high-frequency bands. Among the frequency salient points marked in Fig. 20, some of them are the feature information contained in the original signal, but most of them are not included in the original signal. The noise reduction effect processed by Butterworth low-pass filter is worse than that of the proposed method. The main reason is that the low-pass filter eliminates all signal components lower than the cut-off frequency, and retains all signal components higher than the cut-off frequency. The strong noise interference in real working conditions exists in all frequency bands, so it is inevitable that the noise interference in some frequency bands cannot be eliminated. Furthermore, it is very difficult to set the cut-off frequency reasonably when dealing with the actual noise interference. It can be seen from Fig. 21 that 624 Chen, X. - Cheng, G. - Liu, N. - S hi, X. - Lou, W. Strojnlskl vestnik - Journal of Mechanical Engineering 66(2020)10,613-626 the time-domain signal processed by one-time noise reduction method based on SVD does not reflect the regular shock waveform similar to that in Fig. $ In the frequency spectrum of Fig. 21 the main features of the vibration signal (marked in Fig. 21) are retained, but their clarity is far less than that in Fig. $ there are still more noise interferences in the low-, middle-, and high-frequency bands of the whole frequency spectrum, which will interfere with these main feature information points. Moreover, it also can be found that the signal components in the frequency band from 0 00 Hz to 900 Hz are eliminated as noise interference, and the main features from 000 Hz to 900 Hz are also mistaken as noise interference, which is a bad result. It can be seen that the noise reduction result processed by one-time noise reduction method based on SVD is far worse than that processed by the proposed method. The above comparison and analysis can also show that the proposed method has better noise reduction effect. In this paper, the proposed method can be used to eliminate the strong noise interference of the vibration signal of equipment. It is a pre-processing for gear fault diagnosis process, which ensured that the further feature extraction and fault recognition can be conducted effectively and smoothly. Also, the proposed noise reduction method can also be applied to the detection of gear quality for production process. The authors of the present paper assert that the proposed method can be successfully applied to gear production process through two ways: The first way is that the proposed noise reduction method is applied to the condition monitoring of gear cutting machine. The vibration signal of the gear cutting machine can be obtained, and the proposed method can eliminate the noise interference contained in the vibration signal. The feature information that can reflect the operating state of the gear-cutting machine can be retained, and the operating state of the gear-cutting machine can be evaluated. The cutting quality of gear production process can be further guaranteed. Another way is that the proposed noise reduction method is applied to the gear quality test after the gear is machined. A special test bench for testing the quality of gears can be built, and the machined gears can be run on the test bench. The vibration signal of the test bench can be obtained, and the proposed noise reduction method can be used to process the vibration signal, the useful signals which can be reflected in the gear quality being obtained by using the proposed method to eliminate the external interference. Further combined with other signal-processing technologies, the gear machining defects, such as excessive radial runout, tooth surface defects, tooth profile asymmetry and tooth profile periodic error, can be detected. Through the above two ways, the noise reduction method proposed in this paper can be applied to the gear production process to ensure the quality of the gear. 3 CONCLUSIONS A pre-treatment noise reduction method based on DTCWT and cyclic singular energy difference spectrum is proposed in this paper. DTCWT can be used to decompose the gear fault vibration signal under strong noise interference, and the noise interference with different frequency attributes can be decomposed into different signal components. Based on the noise reduction principle of SVD, cyclic singular energy difference spectrum is proposed. According to the characteristics of each signal components obtained by DTCWT, the noise interference can be purposefully eliminated successively. Furthermore, the termination condition of cyclic singular energy difference spectrum can be set according to the noise interference distribution characteristics in different frequency bands, and it has a better noise reduction effect than the one-time noise reduction idea. The final noise reduction of gear fault vibration signal under noise interference can be realized on the basis of reducing noise for all signal components obtained by DTCWT. The experiment results show that the proposed method can effectively eliminate the strong noise interference in real working condition, and the useful vibration signal components can be retained. 4 ACKNOWLEDGEMENTS This research was funded by National Natural Science Foundation of China (8J , Changzhou Sci & Tech Program (CJ20®0| , the Fundamental Research Funds for the Central Universities (B20020222ji> , and the Special project of science and technology innovation of Tiandi Science & Technology (20$ TD-MS0J , and is gratefully acknowledged. 5 REFERENCES [1] Pang, X.Y., Cheng, B.A., Yang, Z.J. (2019). A fault feature extraction method for a gearbox with a composite gear train based on EEMD and translation-invariant multiwavelet neighbouring coefficients. 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Strojniški vestnik- Journal of Mechanical Engineering 66(2020)10 Vsebina Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 66, (2020), številka A Ljubljana, oktober 2020 ISSN 0039-2480 Izhaja mesečno Razširjeni povzetki (extended abstracts) Filippo Cianetti: Eksperimentalno spremljanje utrujenostnih lastnosti vibrirajočih mehanskih sistemov SI 71 Adam Kulawik, Joanna Wróbel: Numerična analiza napetosti za različne širine varkov pri navaijanju SI 72 Oscar Tenango-Pirin, Elva Reynoso-Jardn, Juan Carlos García, Yaliir Mariaca, Yuri Sara Hernández, Raü Ñeco, Omar Dávalos: Vpliv tennobariernih prevlek na toplotne napetosti v lopaticah in šobah plinskih mikroturbin SI 73 Yong Wang, Zilong Zhang, Jie Chen, Houlin Liu, Xiang Zhang, Marko Hočevar: Učinek prevlek lopatic na delovanje centrifugalnih črpalk pri toku z usedlinami SI 74 Ilyas Kacar, Fahrettin Ozturk, Serkan Toros, Suleyman Kilic: Napovedovanje deformacijskih mej za napredno dvofazno visokotrdno jeklo DP60 z modelom Marciniak-Kuczynski in novim polempiričnim modelom krivulje mejnih deformacij SI 75 Xihui Chen, Gang Cheng, Ning Liu, Xinliui Shi, Wei Lou: Raziskava metode za zmanjševanje šuma na osnovi DTCWT in cikličnega spektra razlik singularnih energij SI 76 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 71 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Eksperimentalno spremljanje utrujenostnih lastnosti vibrirajočih mehanskih sistemov Filippo Cianetti Univerza v Perugii, Italija Opazovanje in vrednotenje utrujenostnih poškodb in v splošnem utrujenostnih lastnosti mehanskih sistemov (v vozilih, letalih, plovilih, vetrnih turbinah ipd.) med življenjsko dobo ni preprosta naloga. Za to obstajajo različne teoretične in numerične metode v časovni ali frekvenčni domeni na osnovi privzetih obremenitvenih pogojev (tj. sil in pospeškov). Do izhodnih napetostnih stanj pridejo z numeričnimi modeli mehanskega sistema (npr. sistem več teles - MBS, končni elementi - MKE, sistem več teles z gibkimi elementi - Flex/MBS) ali z neposrednimi meritvami napetostnih/deformacijskih stanj na osnovi hipotez o trajni dinamični trdnosti (tj. Wohleijeve krivulje ali Basquinove krivulje S-N). V literaturi je opisanih več inštrumentov oz. merilnih verig za vrednotenje v časovni domeni (snemalnik rainflow) ali v frekvenčni domeni, pri nobeni od metod pa ni zagotovljeno celovito opazovanje dinamičnega vedenja sistema (tj. pospeškov, notranjih obremenitev, deformacij) in napovedovanje dejanskih poškodb za ocenjevanje preostale življenjske dobe sistema. V članku je predstavljena preprosta metoda v časovni domeni za spremljanje trenutnih utrujenostnih lastnosti z opredelitvijo trenutnih in kumulativnih potencialnih poškodb oz. amplitude ekvivalentnega poškodbenega signala na osnovi metode štetja Rainflow (RFC), zakona linearne akumulacije poškodb (Palmgren-Mineijevo pravilo) in signalov, ki izhajajo iz dinamike sistema. Metoda precenjuje realne poškodbe, daje upravitelj sistema opozoijen še pred nastankom razpok, poleg tega pa jo je mogoče preprosto pretvoriti v elektronsko vezje, ki se pritrdi na mehanski sistem in poveže z enim od običajnih senzoijev za nadzor funkcionalnosti sistema. V članku je predstavljena realizacija metode v računalniškem okolju za dinamično večdomensko simulacijo mehanskih sistemov ter projektiranje in verifikacijo regulacijskih sistemov. Na ta način je bilo mogoče preveriti uporabnost analitičnega orodja s fizikalnimi meritvami na sami turbini in z numeričnimi analizami na osnovi bolj ali manj kompleksnih dinamičnih modelov generatorja. Osnovna hipoteza tega dela je, da obstajajo različni parametri, ki se že merijo na strojih zaradi različnih razlogov (npr. hitrost, pospeški, momenti) in katerih vrednosti je mogoče takoj uporabiti za nadzor stanja, ne glede na ocene v zvezi s trajnostjo, utrujenostjo ali poškodbami sistema. Na osnovi domneve o linearnem vedenju stroja in mehanskega sistema je vedno mogoče določiti odvisnosti med merjenimi parametri in splošnim napetostnim stanjem v poljubni komponenti in tako vrednotiti utrujanje na osnovi teh generičnih signalov s klasičnimi orodji za analizo časovne zgodovine napetostnih stanj. Če se vrednotenje utrujenostnih lastnosti izvaja na generičnem signalu, ki ne omogoča neposredne uporabe vseh hipotez in orodij, ki so bila razvita za vrednotenje poškodb iz napetostnih stanj, je upravičena opredelitev potencialnih utrujenostnih poškodb in s tem predlagane metode. Znanstvena in tehnična skupnost na področju avtomatskega vodenja bo tako lahko vključila utrujanje med tiste procese v poljubnem mehanskem sistemu (vozila, letala, vlaki, ladje, vetrne turbine), ki jih je mogoče upravljati s povratno zanko ter upoštevati njegove minimalne ali maksimalne vrednosti in potencial za poškodbe. Ključne besede: utrujanje, poškodbe, vibracije, metoda štetja rainflow, naključne obremenitve, regulacijski sistemi *Naslov avtorja za dopisovanje: Univerza v Perugii Italija, filippo.cianetti@unipg.it SI 71 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 72 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Numerična analiza napetosti za različne širine varkov pri navarjanju Adam Kulawik - Joanna Wrbe 1 Tehniška univerza v Čenstohovi, Fakulteta za strojništvo in računalništvo, Poljska V članku so predstavljene razlike v napetostnih stanjih po nanosu varkov s kotom 90° po standardu EN ISO 5817. Primeijava rezultatov numeričnega modela omogoča izbiro primerne širine varkov pri reparaturnem navaijanju elementov iz malolegiranega srednjeogljičnega jekla (C45). Cilj je obnovitev začetne geometrije elementa, pomembna pa je tudi izbira dodajnega materiala z ustreznimi lastnostmi (v danem primeru je ta enak osnovnemu materialu). Te lastnosti so v veliki meri odvisne od fazne sestave. Dodajni material vpliva na trdoto, krhkost in duktilnost. Zaradi dragih eksperimentov, ki jih zaradi geometrijskih omejitev pogosto niti ni mogoče izvesti, je bila sprejeta odločitev o numerični analizi problema. Model je bilo mogoče poenostaviti iz treh v dve razsežnosti (simetrija izračunov za dolge varke), zato so bili opravljeni izračuni po metodi končnih elementov v prečno postavljeni ravnini glede na smer nanosa. Vsak novi varek je bil upoštevan kot dodatna površina v mreži končnih elementov. Opravljena je bila analiza vpliva širine varkov (0,006 m, 0,01 m in 0,014 m) in temperature predgrevanja na fazne transformacije in efektivne napetosti obnovljenega sloja. Uporabljen je bil nestandarden način predgrevanja (pred nanosom vsakega varka, po ohladitvi na temperaturo okolice). V članku je analiziranih 12 različnih kombinacij temperatur predgrevanja in širin varkov za doseganje ustreznega navajenega sloja brez neskladnosti. Vsi preračuni so bili opravljeni z avtorsko zaščitenim programom. Model vključuje ustrezne odvisnosti med elementi za modeliranje temperatur in faznih transformacij nad oz. pod temperaturo likvidus ('/, ) in solidus (Ts). Upoštevane so tudi odvisnosti med zgornjimi modeli in modelom mehanskih lastnosti. Iz rezultatov sledi sklep, da povečanje širine varkov ugodno vpliva na zmanjšanje stopnje efektivnih preostalih napetosti, kar pa je težko izvedljivo v praksi. Napetosti so najmanj ugodne v prvi površini navara. Pri nižjih temperaturah predgrevanja in ožjih varkih so bila identificirana območja možnih razpok. V tem primeru je treba uporabiti nižjo temperaturo predgrevanja in popuščanje, kar je povezano s podobnimi stroški energije kot pri višjih temperaturah predgrevanja. Načrtovana je tudi eksperimentalna raziskava za potrditev teh rezultatov, konkretno metalografske preiskave za opredelitev doseženih faznih transformacij. To še zlasti velja za območja, kjer prihaja do ponovnega ogrevanja. Načrtovani so tudi preizkusi trdote materiala. Ti bodo lahko potrdili analizo sestave navara in osnovnega materiala, kakor tudi rezultate numeričnih simulacij. Analiza trdote je lahko tudi izhodišče za konstruiranje elementov, kijih je mogoče obnoviti ali so namenjeni abrazivni obdelavi. V inženirski praksi se pred opredelitvijo postopka navaijanja elementov iz težavnih materialov, kot so tisti z visoko vsebnostjo ogljika, opravi serija eksperimentalnih raziskav. V članku je predstavljen numerični model, ki lahko v veliki meri nadomesti te raziskave. Analiza napetostnega stanja, opredeljenega z numeričnimi simulacijami, bo omogočila izbiro ustreznih parametrov procesa za komponente zahtevnih oblik, ki niso primerne za eksperimentalne študije s poenostavljeno geometrijo. Predstavljena analiza faznih premen v trdnem stanju in nastalih napetosti omogoča napovedovanje vedenja obnovljene površine in samega navara, ne le v območju stabilnega procesa (središče navara), temveč tudi na njegovem začetku in koncu. Rezultati analize bodo uporabni za izbiro širine varkov pri reparaturnem navaijanju. Ključne besede: računalniška mehanika, numerična simulacija, navar, predgrevanje, analiza deformacij, napetost SI 72 *Naslov avtorja za dopisovanje: Tehniška univerza v Čenstohovi, Fakulteta za strojništvo in računalništvo. Poljska, joanna.wrobel@icis.pcz.pl Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 73 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Vpliv termobariernih prevlek na toplotne napetosti v lopaticah in šobah plinskih mikroturbin Oscar Tcnango-Pirin1 -E Iva Reynoso-Jardn 1 -J .C. García2* - Yaliir Mariaca1 -Yuri Sara Hernández3 41 aü Ñeco1-O marDávalos1 1 Avtonomna univerza Ciudad Juárez, Oddelek za strojnišvo, Mehika 2 Avtonomna univerza Estado de Morelos, Raziskovalni center za strojnišvo, Mehika 3 Pachuca tehnološki inštitut, Mehika Termobarierne prevleke (TBC) pomembno vplivajo na življenjsko dobo mikroturbin, saj omejujejo prenos toplote v komponente. Visokotemperaturne obremenitve lahko skrajšajo življenjsko dobo komponent s tem, da povzročijo nastanek območij visokih napetosti v lopaticah in šobah. V pričujočem članku so predstavljene numerične analize za vrednotenje novih materialov, ki so bili razviti za termobarierne prevleke lopatic plinskih turbin. Ocenjena je njihova zmogljivost za zaščito komponent mikroturbin. Preučeni so bili novi materiali 8YSZ, Mg2Si04, Y3Ce7Ta202S in Yb3Ce7Ta202i; . Ti materiali iz literature so bili do zdaj preizkušeni samo v nadzorovanih pogojih in zato so bila v pričujoči raziskavi simulirana okolja, ki so podobna pogojem obratovanja plinskih mikroturbin. Za substrat šobe in lopatic so bile uporabljene lastnosti zlitine Nimonic 05 Razvitje bil 3D-model plinske mikroturbine, model interakcij med fluidom in konstrukcijo paje bil razrešen s CFD in MKE. V izračunih CFD so bile za TBC na šobi in lopatici uporabljene lastnosti zgornjih materialov. Pri računanju prenosa toplote iz visokotemperaturnega plina na substrat sta bili upoštevani domeni kapljevinaste in trdne snovi. Izračunana so bila temperaturna polja in amplitude napetosti na šobi in lopatici, rezultati pa so bili nato primeijani z rezultati modela brez toplotnih barier. Neenakomerne temperaturne porazdelitve v šobah in lopaticah so bile v naslednjem koraku uporabljene za izračun napetosti v substratu. Za oceno učinkovitosti toplotne izolacije TBC so bile analizirane temperaturne vrednosti in gradienti v substratu. Maksimalne temperature so bile ugotovljene na sprednjem in na zadnjem robu šobe in lopatice, tako s prevlekami TBC kot brez njih. Višji temperaturni gradienti so bili ugotovljeni na šobi, maksimalne amplitude temperatur pa na lopaticah. Absolutna vrednost temperatur seje zmanjšala pri uporabi TBC. Ugotovljeno je bilo, da materiali Mg2Si04 in Y3Ce7Ta202S zagotavljajo boljšo toplotno izolacijo komponent turbine v primeijavi z drugimi materiali. Analiza napetosti je pokazala, da so se toplotne napetosti pri uporabi TBC zmanjšale v obeh komponentah, ne glede na uporabljen material. Razvoj napetosti v komponentah je bil v vseh primerih zelo podoben, ugotovljena pa je bila variabilnost njihove amplitude. Največje napetosti pri šobi in pri lopatici so se razvile v predelu korena, kar je mogoče pripisati temperaturnim gradientom in omejitvam. Materiala Mg2Si04 in Y3Ce7Ta2023 5 izkazujeta najboljše termoizolacijske lastnosti za komponente mikroturbin. V študiji je bila ovrednotena samo sposobnost materialov za zaščito lopatic in šob plinskih mikroturbin pred toplotnimi obremenitvami. Raziskava tako prinaša nova spoznanja na področju optimizacije plinskih mikroturbin in metod za zaščito teh izdelkov pred visokimi temperaturami in napetostmi. Znano je, da lahko povečanje amplitude napetosti nastopi tudi zaradi vpliva drugih obremenitev, kot so centrifugalne sile ali poškodbe zaradi tujkov. Te obremenitve v tukajšnji raziskavi niso bile zajete. Ključne besede: termobarierna prevleka, plinske mikroturbine, lopatica turbine, toplotne napetosti, računalniška dinamika fluidov, končni elementi *Naslov avtorja za dopisovanje: Avtonomna univerza Ciudad Juarez, Oddelek za strojnišvo, Av. Universidad 1001, Cuernavaca, Mor., Mehika, jcgarcia@uaem.mx SI 73 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 74 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Učinek prevlek lopatic na delovanje centrifugalnih črpalk pri toku z usedlinami Yong Wang1 -L ilong Zhang1 4 ie Chen2 -H oulin Liu1 -X iang Zhang3 * -Marko Hočevar4 1 Jiangsu univerza, Raziskovalni center za dinamiko fluidov, Kitajska 2 Tehnološki inštitut v Pekingu, Fakulteta za strojništvo, Kitajska 3 Xihua univerza, Laboratorij za fluide, Kitajska 4 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija Centrifugalne črpalke pogosto črpajo tok z usedlinami, npr. za namakanje, v metalurgiji, rudarstvu itd.. Trdna faza v sedimentu povzroči abrazijo omočenih površin, predvsem lopatic, kar vodi do povečanega hrupa, vibracij, puščanja in na koncu do odpovedi črpalke. Zaradi velike hitrosti vrtenja rotoija do odpovedi pride najpogosteje zaradi poškodb na tlačni površini lopatic rotoija. Poleg tega močne vibracije, nihanje tlaka in abrazija materiala poškodovane centrifugalne črpalke znatno zmanjšajo zanesljivost sistema črpališč in povzročajo onesnaževanje okolja s hrupom. Z nanašanjem trdih prevlek na površino lopatic centrifugalnih črpalk želimo podaljšati življenjsko dobo črpalk pri črpanju toka z usedlinami. Študij tokov v dvofaznih dvofaznih centrifugalnih črpalkah z zaščitnimi premazi na lopaticah je v nam dostopni literaturi malo. Trenutno se raziskave na tem področju izvajajo predvsem s pomočjo numeričnih simulacij. Čeprav je numerična simulacija učinkovita metoda za napovedovanje rezultatov, so natančni eksperimenti bistveni za raziskave delovanja. Da bi raziskali učinek trdih prevlek, smo eksperimentalno preučevali fluktuacije energije, vibracij in tlaka centrifugalne črpalke. Konstrukcijski parametri modelne črpalke so naslednji: nazivni pretok Od = 20 m3/h, višina H =22 m, izkoristek // = 48 %, nazivna moč gredi I' = .15 kW, hitrost vrtenja n = 2900 vrt/min in specifična hitrost ns = 81,46. Merilno postajo so sestavljali cevovodi, rezervoar za vodo, izstopni ventil, potopna črpalka, dovodni ventil, elektromagnetni merilnik pretoka, model črpalke s frekvenčnim pogonom, sistem za meijenje fluktuacij tlaka, sistem za meijenje vibracij in sistem za meijenje električne moči črpalke. V poskusu je bila uporabljena enostopenjska horizontalna centrifugalna modelna črpalka z ravnimi lopaticami. Kot zaščitni material, uporabljen na tlačni površini lopatic, je bil izbran poliuretan. Poliuretanska obloga je bila izdelana s tehnologijo 3D tiska. Debelino prevleke smo predstavili v brezdimenzijski obliki, pri čemer je Ki koeficient debeline prevleke, ; = 0, 1, 2, 3. Debeline prevleke so znašale 0 mm, 1 mm, 2 mm, 3 mm, ustrezni koeficienti debeline prevleke pa znašajo K0 = 0, /J, =1 K2 = 2 in K3 = 3 Rezultati kažejo, daje dobavna višina pri črpanju vode z usedlinami nekoliko večja kot pri čisti vodi z enakim koeficientom debeline prevleke, kadar je volumetrični pretok pod približno 0,9 nazivnega pretoka. Pri večjih pretokih je dobavna višina v primeru črpanja čiste vode višja. Če vstopni in izstopni kot ter oblika lopatic ostanejo nespremenjeni, se višina H in izkoristek r) pri črpanju čiste vode in vode z usedlinami znatno zmanjšata s povečanjem koeficienta debeline prevleke. Frekvenca vrtenja rotoija in frekvenca prehoda lopatic BPF sta glavni frekvenci vzbujanja vibracij črpalke in nihanja izhodnega tlaka. Amplituda hitrosti vibracij in nihanje izhodnega tlaka pri frekvenci 1 BPF sta največja, na drugem mestu pa sledi primer pri frekvenci vrtenja rotoija. Najvišje vrednosti amplitude hitrosti vibracij in nihanja izhodnega tlaka so sorazmerne s koeficientom debeline prevleke. Analiza je bila izvedena za več naraščajočih debelin prevlek, kar ustreza koeficientom od K0 do Pri koeficientih debeline prevleke K„. /J, in K2 je amplituda hitrosti vibracij pri črpanju toka z usedlinami večja od vrednosti pri črpanju čiste vode, medtem ko je pri koeficientu debeline prevleke razlika zelo majhna. Amplitude nihanj tlaka pri različnih pretokih se najprej zmanjšajo in nato povečajo s povečevanjem koeficienta debeline prevleke, najnižje vrednosti pa so pri koeficientu debeline prevleke Kh Ključne besede: centrifugalna črpalka, obraba, prevleka lopatic, vibracije, fluktuacije tlaka, tok z usedlinami SI 74 *Naslov avtorja za dopisovanje: Xlhua univerza. Laboratorij za fluide, Chengdu, Kitajska, 927340633@qq.com Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 75 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Napovedovanje deformacijskih mej za napredno dvofazno visokotrdno jeklo DP600 z modelom Marciniak-Kuczji ski in novim polempiričnim modelom krivulje mejnih deformacij Ilyas KacarJ* - Fahrettin 0/turk2 3. Serkan Toros4 - Suleyman Kilic5 1 Univerza Omeija Halisdemiija v provinci Nigde, Turčija 2 Turška letalska in vesoljska industrija, Turčija 3 Univerza Yildmma Beyazita v Ankari, Turčija 4 Univerza Nigde Omer Halisdemir, Turčija 5 Univerza Ahija Evrana v Kirsehiiju, Turčija Krivulja mejnih deformacij (KMD) je uporabno orodje za načrtovanje procesov preoblikovanja pločevine. V pričujočem članku je predstavljen nov polempirični model krivulje mejnih deformacij, ki določa mejo preoblikovalnosti in varno območje v različnih pogojih preoblikovanja pločevine, obenem pa je tudi učinkovito orodje za diagnosticiranje napak v izdelavi. V predstavljeni študiji je bila za napovedovanje krivulje mejnih deformacij uporabljena kombinacija modela Marciniak-Kuczynski in nekaterih anizotropnih kriterijev tečenja. Krivulje so bile ovrednotene z rezultati eksperimentov, opravljenih na jeklu DP60. Napredna visokotrdna jekla, med katera spada tudi dvofazno jeklo DP600, se uporabljajo za zmanjševanje teže vozil. Z določitvijo mejnih deformacij jekla DP600 je mogoče zagotoviti preoblikovanje brez napak, primeren model pa omogoča tudi točnost napovedi simulacij. Modeli plastičnosti so bili izpeljani s funkcijami Hill48, Barlat89 in YLD2000-2d. Modeli so bili kombinirani z modelom M-K in s predlaganim kriterijem porušitve, določen je bil najprimernejši kriterij za popis anizotropije. Model in iz njega izpeljane krivulje so uporabni in dovolj natančni za različne vrste deformacij jekla DP600. Predlagani kriterij porušitve je bil določen z regresijsko analizo eksperimentalno pridobljenih KMD. Pri modeliranju KMD so bile opredeljene splošne mehanske lastnosti, ki vplivajo na KMD materiala. Pri analizi prileganja s preprostimi matematičnimi formulami so bile konstante nato omejene z danimi eksperimentalno določenimi lastnostmi. Formula po Marciniaku in Kuczynskem kot najbolj priljubljeni porušitveni kriterij je bila primeijana z novim polempiričnim kriterijem porušitve za pločevino. Najbolj konzervativna in najprimernejša funkcija deformacije med funkcijami izotropije za kriterij porušitve pločevine DP600 je YLD2000-2d. Predstavljeni so parametri modela YLD2000-2d. Na krivuljah mejnih deformacij so predstavljene možnosti napovedovanja deformacij skih mej. Za jeklo DP600 so bile preučene deformacijske meje. Funkcije anizotropne deformacije so bile uporabljene z modelom M-K in z novim polempiričnim modelom. Za oba modela so bile določene zmožnosti napovedovanja deformacij skih mej. Zaključki so: Ocenjena krivulja plastičnosti, koeficienti anizotropije in normalizirane meje plastičnosti materiala DP600 se dobro ujemajo z eksperimentalnimi podatki za kriterij YLD2000-2d. YLD2000-2d je najprimernejša krivulja v območju pozitivnih deformacij KMD, zato ima prednost pri napovedovanju porušitve pločevine DP600. Uporabna je za vse debeline pločevine. Predlagani model v kombinaciji s krivuljo YLD20002d zagotavlja najbolj natančne napovedi porušitve pločevine DP600. Ključne besede: DP600, anizotropija, kriterij tečenja, krivulja mejnih deformacij, kriterij porušitve M-K *Naslov avtorja za dopisovanje: Univerza Omerja Halisdemirja v provinci Nigde, Nigde 51240, Turčija, ikacar@gmail.com SI 75 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)9, SI 76 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-03-11 Prejeto popravljeno: 2020-06-18 Odobreno za objavo: 2020-07-14 Raziskava metode za zmanjševanje šuma na osnovi DTCW in cikličnega spektra razlik singularnih energij Xihui Chen12 ® -G ang Cheng-4 ing Liu3 inliui Shii - Wei Loui 1 Univerza Hohai, Kolidž za strojništvo in elektrotehniko, Kitajska 2 Kitajska rudarska in tehniška univerza, Šola za mehatroniko, Kitajska 3 Kitajska tehnologija premoga in strojništvo, Kitajska 4 Shandong Zhongheng Optoelektronska tehnologija, Kitajska Zobniki so najpomembnejši del prenosnih sistemov v mehanski opremi, z nadzorom in diagnostično obravnavo delovanja zobnikov pa je mogoče izboljšati zanesljivost mehanske opreme. Mehanska oprema običajno obratuje v zahtevnih razmerah. Signal vibracij zobnikov je v realnih delovnih pogojih obremenjen z močnim šumom, to pa je velik izziv za učinkovito diagnosticiranje napak na zobnikih. Za razrešitev problema močnega šuma v signalu vibracij je predlagana metoda za zmanjševanje šuma na podlagi dvodrevesne kompleksne valčne transformacije in cikličnega spektra razlik singularnih energij. Signal vibracij zobnikov z močnim šumom se s pomočjo časovno-frekvenčne analize DTCWT najprej razstavi na vrsto signalnih komponent z različnimi frekvenčnimi karakteristikami. Sledi predlagana metoda cikličnega spektra razlik singularnih energij, ki sloni na pristopu s kaskadnim ciklom in postopno odpravo šuma za obdelavo posameznih signalnih komponent z različnimi frekvenčnimi karakteristikami. Pogoje za zaključek metode cikličnega spektra razlik singularnih energij je mogoče prilagoditi lastnostim porazdelitve šuma v različnih frekvenčnih pasovih. Končno zmanjšanje šuma v originalnem signalu vibracij se izvede z rekonstrukcijo očiščenih posameznih signalnih komponent z različnimi frekvenčnimi pasovi. Članek sodi v področje obdelave signalov elektromehanske opreme. Opravljeni so bili tudi eksperimenti za preveijanje učinkovitosti predlagane metode zmanjševanja šuma na podlagi DTCWT in metode cikličnega spektra razlik singularnih energij, ki je učinkovita in primerna za zmanjševanje šuma v signalu vibracij. V nadaljnjih študijah metode cikličnega spektra razlik singularnih energij bodo podrobneje preučeni pogoji za končanje cikla. Signali vibracij mehanske opreme, pridobljeni v realnih delovnih pogojih, so obremenjeni z močnim šumom, ki otežuje učinkovito izločanje značilk napak. Predstavljena je metoda za zmanjševanje šuma na osnovi DTCWT in cikličnega spektra razlik singularnih energij, ki sloni na ideji kaskadnega cikla in postopne odprave šuma. Uspešnost predlagane metode je bila dokazana s simulacijami in eksperimentalno. Metoda je uporabna v procesu preobdelave signalov mehanske opreme in je osnova za nadaljnje diagnosticiranje napak in napovedovanje življenjske dobe. 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Strojniški vestnik -Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu http://www.sv-jme.eu Contents Papers FiLippo Cianetti: How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems? Ada m Kulawik, Joanna Wróbel: Numerical Study of Stress Analysis for the Different Widths of Padding Welds Oscar Tenango-Pirin, Elva Reynoso-Jardón, Juan Carlos García, Yahir Mariaca, Yuri Sara Hernández, Raúl Ñeco, Omar Dávalos: Effect of Thermal Barrier Coating on the Thermal Stress of Gas Microturbine Blades and Nozzles Yong Wang, ZiLong Zhang, Jie Chen, Houlin Liu, Xiang Zhang, Marko Hocevar: Effect of Blade Coating on a Centrifugal Pump Operation under Sediment-Laden Water Flow Ilyas Kacar, Fahrettin Ozturk, Serkan Toros, Suleyman Kilic: Prediction of Strain Limits via the Marciniak-Kuczynski Model and a Novel Semi-Empirical Forming Limit Diagram Model for Dual-Phase DP600 Advanced High Strength Steel Xihui Chen, Gang Cheng, Ning Liu, Xinhui Shi, Wei Lou: Research on a Noise Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum 557 567 581 602 9770039248001