THERMAL SCIENCE

International Scientific Journal

Chu-Han Shang

,

Huai-An Yi

A FRACTAL-FRACTIONAL MODEL ON IMPACT STRESS OF CRUSHER DRUM

ABSTRACT
In this paper, a fractal-fractional model of the impact stress on the crusher drum is established by using He's fractal derivative and the fluid-solid coupling vibration equation. The two-scale transform is used to obtain its solution, which can be used to improve the safety performance of beating machines.
KEYWORDS
He’s fractal derivative, the fluid solid coupling vibration equation, beating engine, Two-scale transform method, impact stress
PAPER SUBMITTED: 2021-12-01
PAPER REVISED: 2022-06-18
PAPER ACCEPTED: 2022-06-18
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303119S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE No. 3, PAGES [2119 - 2125]
REFERENCES
[1] Yang, R. Y., et al., Design of Highly Efficient NOx Storage-Reduction Catalysts from Layered Double Hydroxides for NOx Emission Control from Naphtha Cracker Flue Gases, Chemical Engineering Jour-nal, 326 (2017), Oct., pp. 656-666, 10.1016/j.cej.2017.06.016
[2] Garcia-Leon, R. A., et al., Application of the QFD Method to the Design of a Cocoa Pulping Machine, International Journal of System Assurance Engineering and Management, 12 (2021), 6, pp. 1199-1220, 10.1007/s13198-021-01416-0
[3] Moncada, M., et al., Torque Analysis of a Gyratory Crusher with the Discrete Element Method, Minerals, 11 (2021), 8, 878, 10.3390/min11080878
[4] Edilboyev, U., Cone Vibration Crusher for Grinding Grain Materials, IOP Conference Series: Materials Science and Engineering, 1030 (2021), 1, 012157, 10.1088/1757-899x/1030/1/012157
[5] Dolle, K., Bajrami, B., Beating of Eucalyptus Pulp Fibers under Neutral and Alkaline Conditions - A Valley Beater Study, Journal of Engineering Research and Reports, 20 (2021), 8, pp. 86-96, 10.9734/jerr/2021/v20i817362
[6] Sun, H. G., et al., LBM Simulation of Non-Newtonian Fluid Seepage Based on Fractional-Derivative Constitutive Model, Journal of Petroleum Science and Engineering, 213 (2022), June, 110378, 10.1016/j.petrol.2022.110378
[7] Cochennec, M., et al., Influence of the Fluid-Fluid Drag on the Pressure Drop in Simulations of Two-Phase Flows Through Porous Flow Cells, International Journal of Multiphase Flow, 149 (2022), Apr., 103987, 10.1016/j.ijmultiphaseflow.2022.103987
[8] He, C. H., et al., A Fractal Model for the Internal Temperature Response of a Porous Concrete, Applied and Computational Mathematics, 21 (2022), 1, pp.71-77
[9] Dalmau, R., Stressed Volume and Fluid Responsiveness, European Journal of Anaesthesiology, 38 (2021), 1, pp. 86-88, 10.1097/eja.0000000000001281
[10] Gelman, S., Reply to: Stressed Volume and Fluid Responsiveness, European Journal of Anaesthesiology, 38 (2021), 1, pp. 88-89, 10.1097/eja.0000000000001282
[11] Tyukalov, Y. Y., Arbitrary Quadrangular Finite Element for Plates with Shear Deformations, Magazine of Civil Engineering, 107 (2021), 7, 10707
[12] Zubov, A., et al., Numerical Modeling of Viscoelasticity in Particle Suspensions Using the Discrete Element Method, Langmuir, 35 (2019), 39, pp. 12754-12764, 10.1021/acs.langmuir.9b01107
[13] He, J.-H., A Tutorial Review on Fractal Space Time and Fractional Calculus, Int. J. Theor. Phys., 53 (2014), 11, pp. 3698-718, 10.1007/s10773-014-2123-8
[14] He, J.-H., El-Dib, Y. O., A Tutorial Introduction to the Two-Scale Fractal Calculus and Its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268, 10.1142/s0218348x21502686
[15] He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Phys. Lett. A, 376 (2012), 4, pp. 257-259, 10.1016/j.physleta.2011.11.030
[16] He, J.-H., Li, Z.-B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334, 10.2298/tsci110503068h
[17] He, J.-H., et al., A New Fractional Derivative and its Application to Explanation of Polar Bear Hairs, Journal of King Saud University Science, 28 (2016), 2, pp. 190-192, 10.1016/j.jksus.2015.03.004
[18] He, J.-H., Qian, M. Y., A Fractal Approach to the Diffusion Process of Red Ink in a Saline Water, Thermal Science, 26 (2022), 3B, pp. 2447-2451, 10.2298/tsci2203447h
[19] Qian, M. Y., He, J.-H., Two-Scale Thermal Science for Modern Life -Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412, 10.2298/tsci2203409q
[20] He, J.-H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276, 10.1016/j.rinp.2018.06.011
[21] Sun, J. S., Approximate Analytic Solutions of Multi-Dimensional Fractional Heat-Like Models with Variable Coefficients, Thermal Science, 23 (2019), 6B, pp. 3725-3729, 10.2298/tsci180612256s
[22] Sun, J. S., Approximate Analytic Solution of the Fractal Klein-Gordon Equation, Thermal Science, 25 (2021), 2B, pp. 1489-1494, 10.2298/tsci200301051s
[23] Cao, X. Q., et al., Variational Principle for (2+1)-Dimensional Broer-Kaup Equations with Fractal Derivatives, Fractals, 28 (2020), 7, 2050107, 10.1142/s0218348x20501078
[24] Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics，Fractals, 29 (2021), 7, 2150182, 10.1142/s0218348x21501826
[25] Sun, J. S., Approximate Analytic Solution of the Fractal Fisher's Equation via Local Fractional Variational Iteration Method, Thermal Science, 26 (2022), 3B, pp. 2695-2701, 10.2298/tsci2203699s
[26] Sun, J. S., Traveling Wave Solution of Fractal KDV-Burgers-Kuramoto Equation within Local Fractional Differential Operator, Fractals, 29 (2021), 7, pp. 1-10, 10.1142/s0218348x21502315
[27] He, C. H., et al., A Modified Frequency-amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046, 10.1142/s0218348x22500463
[28] Wu, P. X., et al., Solitary Waves of the Variant Boussinesq-Burgers Equation in a Fractal Dimensional Space, Fractals, 30 (2022), 3, 2250056, 10.1142/s0218348x22500566
[29] Liang, Y. H., Wang, K. J., A New Fractal Viscoelastic Element: Promise and Applications to Maxwell-Rheological Model, Thermal Science, 25 (2021), 2B, pp. 1221-127, 10.2298/tsci200301015l
[30] Sun, J. S., Approximate Analytic Solutions of Multi-Dimensional Fractional Heat-Like Models with Variable Coefficients, Thermal Science, 23 (2019), 6B, pp. 3725-3729
[31] He, J.-H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934, 10.1007/s10910-019-01048-7
[32] He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals, 28 (2020), 1, 2050011, 10.1142/s0218348x20500115
[33] Li M., et al., Finite Integration Method for Solving Multi-Dimensional Partial Differential Equations, Applied Mathematical Modelling, 39 (2015), 17, pp. 4979-4994, 10.1016/j.apm.2015.03.049
[34] He, J.-H., Exp-Function Method for Fractional Differential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366, 10.1515/ijnsns-2011-0132
[35] He, C. H., El-Dib, Y. O., A Heuristic Review on the Homotopy Perturbation Method for Non-Conservative Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 41 (2021), 2, pp. 572-603, 10.1177/14613484211059264
[36] Zhou, Z., et al., Analysis Of The Influence Of Fluid Impact On The Force Acting On The Bend Of Pipe (in Chinese), Chinese Journal of Applied Mechanics, 36 (2019), 3, pp. 674-676
[37] Alhamli, M., Boundary Effects on Streaming Flow Around a Pulsating Bubble Located at the Velocity Antinode of a Standing Wave, Bulletin of the American Physical Society, 61 (2016), 20, pp. 20-22
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A fractal-fractional model on impact stress of crusher drum

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