## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2021-12-01

PAPER REVISED: 2022-06-18

PAPER ACCEPTED: 2022-06-18

PUBLISHED ONLINE: 2023-06-11

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 3**, PAGES [2119 - 2125]

- 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
- 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
- Moncada, M., et al., Torque Analysis of a Gyratory Crusher with the Discrete Element Method, Minerals, 11 (2021), 8, 878
- Edilboyev, U., Cone Vibration Crusher for Grinding Grain Materials, IOP Conference Series: Materials Science and Engineering, 1030 (2021), 1, 012157
- 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
- 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
- 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
- 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
- Dalmau, R., Stressed Volume and Fluid Responsiveness, European Journal of Anaesthesiology, 38 (2021), 1, pp. 86-88
- Gelman, S., Reply to: Stressed Volume and Fluid Responsiveness, European Journal of Anaesthesiology, 38 (2021), 1, pp. 88-89
- Tyukalov, Y. Y., Arbitrary Quadrangular Finite Element for Plates with Shear Deformations, Magazine of Civil Engineering, 107 (2021), 7, 10707
- Zubov, A., et al., Numerical Modeling of Viscoelasticity in Particle Suspensions Using the Discrete Element Method, Langmuir, 35 (2019), 39, pp. 12754-12764
- He, J.-H., A Tutorial Review on Fractal Space Time and Fractional Calculus, Int. J. Theor. Phys., 53 (2014), 11, pp. 3698-718
- 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
- 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
- He, J.-H., Li, Z.-B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
- 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
- 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
- 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
- He, J.-H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
- Sun, J. S., Approximate Analytic Solutions of Multi-Dimensional Fractional Heat-Like Models with Variable Coefficients, Thermal Science, 23 (2019), 6B, pp. 3725-3729
- Sun, J. S., Approximate Analytic Solution of the Fractal Klein-Gordon Equation, Thermal Science, 25 (2021), 2B, pp. 1489-1494
- Cao, X. Q., et al., Variational Principle for (2+1)-Dimensional Broer-Kaup Equations with Fractal Derivatives, Fractals, 28 (2020), 7, 2050107
- Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics，Fractals, 29 (2021), 7, 2150182
- 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
- Sun, J. S., Traveling Wave Solution of Fractal KDV-Burgers-Kuramoto Equation within Local Fractional Differential Operator, Fractals, 29 (2021), 7, pp. 1-10
- He, C. H., et al., A Modified Frequency-amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046
- Wu, P. X., et al., Solitary Waves of the Variant Boussinesq-Burgers Equation in a Fractal Dimensional Space, Fractals, 30 (2022), 3, 2250056
- 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
- Sun, J. S., Approximate Analytic Solutions of Multi-Dimensional Fractional Heat-Like Models with Variable Coefficients, Thermal Science, 23 (2019), 6B, pp. 3725-3729
- He, J.-H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
- He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals, 28 (2020), 1, 2050011
- Li M., et al., Finite Integration Method for Solving Multi-Dimensional Partial Differential Equations, Applied Mathematical Modelling, 39 (2015), 17, pp. 4979-4994
- He, J.-H., Exp-Function Method for Fractional Differential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366
- 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
- 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
- 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