Larionov G.I., Larionov M.G. Mathematical modeling of interrelation between conveyer belt and rigid drum with no friction considered

Details

Parent Category: Geo-Technical Mechanics, 2019

Category: Geo-Technical Mechanics, 2019, Issue 149

Geoteh. meh., 2019, 149, 186-197

https://doi.org/10.15407/geotm2019.149.186

MATHEMATICAL MODELING OF INTERRELATION BETWEEN CONVEYER BELT AND RIGID DRUM WITH NO FRICTION CONSIDERED

¹LarionovG.I., ¹Larionov M.G.

¹Institute of Geotechnical Mechanics named by N. Polyakov of National Academy of Sciences of Ukraine

UDC 004.926.8:622.647.2

Language: Ukrainian

Annotation.

One of the most effective methods to increase tractive force of the belt conveyer drive is to increase coefficient of cohesion between the conveyer belt and surface of the drum by way of its lining. The researches performed by the IGTM of the NAS of Ukraine not only experimentally confirmed the fact of transmission of tractive forces on the arc of rest, but also an assumption was made about existence of border layer in the area of the contact. During the researches, a problem of stresses was solved with the mix boundary condition and Coulomb friction low action. As a rule, the obtained solutions did not satisfy boundary conditions on displacements along the drum surface. An attempt was made to solve a system of the Lamb equations in cylindrical coordinates given that h/R<<1, where h was the belt thickness and R was the drum radius. By applying the Prandtl‘s technique and substitution methods, an analytical solution was obtain. As a result, the expressions for the displacements on the arc of rest and arc of sliding were obtained. In order to determine length of the arc of rest, the condition of equality of radial and peripheral displacements was used. On the basis of these solutions, the expressions were obtained for the tensile force. As it was established, the forces applied to the arc of rest and arc of sliding were equal in their values but oppositely directed. This equality means that tractive forces are not transferred by the arc of rest. The obtained results are coincided with the results shown by N.E. Zhukovskiy for flexible thread model. The fact of simultaneous satisfaction of boundary conditions both on inner and outer sides belt has led to the conclusion about existence of the belt marginal layer. Expressions were formulated for the length of arc of rest on the drum without using the condition of friction existing between the belt and the drum. In the article, graphic dependences between displacements and stresses are demonstrated. Saltatory behavior of radial and circuitous tensions is explained by dynamics of displacements at transition from the side of arc of rest to the arc of sliding. Expression for tensions contains partial derivatives of these displacements, and it results in jumps of tensions. Presence of jumps in the behavior of circuitous and radial tensions at transition from the arc of rest to the arc of sliding can be explained by existence of transitional area, where size of jumps is decreased.

Keywords:

mathematical model, belt, Lame problem, arc of rest

References

1. Strength and durability of mine mashine (2979), Ukraine postgraduate polytechnic institute, vol. 5, Moscow, SU.

2. Andreev A.V. (1967), “Some questions of belt conveyor work physics”, in Gornye mashiny I avtomatika. Raschet, konstruirovanie, ispytaniya, naladka [Mine machines and automatic .Design and construct, test, maintance] (Ed.), Moscow, SU.

3. Mossakovskiy V.I., Rudjakov G. Z. and Salitrenic V.B. (1967), “Contact belt and elastic drug cover research”, Mine mechanic and machine industry, Vol.18,  pp. 320-329.

4. Mossakovskiy V.I., Petrov V.B., Salitrenic V.B. and Grinevskiy A.G. (1977), “Flexible conveyor belt interaction with one direction elastic drum cover”, Applied mechanic, Vol.8, no. 7,  pp. 90-95.

5. Kiriya R.V. and Stakhovskiy Ye.A. (2000), “Experimental elastic belt and conveyor drum interaction research”, National Mining University: Sat scientific. tr., Dnepropetrovsk,  no. 5, pp.. 24-26 .

6. Kiriya R.V. and Stakhovskiy Ye.A. (2002), “Disturbing method application of Prundtl to eliminate N.E, Zhukovskiy paradox”, Systems Technology: Interagency .Regional Sat Nauchn. tr. Dnepropetrovsk, Vol. 4(21), pp. 33-46 .

7. Nayfeh Ali Hasan Perturbation methods, A Willey-Interscience Publication/John Wiley&Sons,New York. London. Sydney. Toronto, US.

8. Prochnost, ustoychivost, kolebaniya. Spravochnik v trekh tomakh [Strength, duarability, vibration. Handbook in 3 books] (1977), N.A. Birger, Ya.G. Panovko (ed.), Vol. 1, Moscow, SU.

About the authors

 Larionov Hrihorii Ivanovych, Doctor of Technical Sciences (D.Sc.), Senior Researcher, Senior Researcher in the Rock Mechanics Department, Institute of Geotechnical Mechanics named by N. Poyakov of National Academy of Sciences of Ukraine (IGTM NAS of Ukraine), Dnipro, Ukraine i This email address is being protected from spambots. You need JavaScript enabled to view it.

Larionov Mykola Hrihorovich, Candidate of Technical Sciences (Ph.D.), Junior Researcher of the Department of Geomechanics of Mineral Opencast Mining Technology, Institute of Geotechnical Mechanics named by N. Poyakov of National Academy of Sciences of Ukraine (IGTM NAS of Ukraine), Dnipro, Ukraine, i This email address is being protected from spambots. You need JavaScript enabled to view it.

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