Abstract
Conveyor’s belt with the drum contact task is paid a great researcher attention. It had solved in stresses with the mix boundary condition and Coulomb friction low action applies. Obtained solutions, as usual, do not satisfy to the displacement on drum surface boundary condition. The attempt to solve the system of Lamb equations in cylindrical coordinates in condition h/R<<1 values where h the belt thin and R drums radius is done. The Prandtl‘s technique and substitution methods are used to analytical solution obtain. As a result, the displacement expressions for rest and slide drum arcs are obtained. In search of rest arc length, radial and peripheral displacement equalities are used. Applied rest arc efforts are equal in values and have an opposite direction. The equality means the fact that traction efforts do not transfer under rest drum arc. The obtained results are coincided with the ones obtained by Zhukovskiy N.E. for flexible thread model. The fact to simultaneously satisfy to boundary conditions on inner and outer belt sides have to do the conclusion for boundary belt seam existing. Expressions for rest drum arc length without applied friction law are obtained. The displacement and corresponding stresses graphics are demonstrated.
Highlights
One of the effective ways to track drive effect increasing on drums surface is achieved with drums cover [1]
We find the boundary of the rest arc (RA) based on the conditions of radial and circumferential displacements at φ=φ*equality: urest=uslide ; vrest=vslide for φ=φ* or
There is some contradiction between the boundary conditions on the contact of the belt and the drum and on the free surface of the belt
Summary
One of the effective ways to track drive effect increasing on drums surface is achieved with drums cover [1] It is paid great attention by researchers [1 – 6] in the way of belt and cover drum interaction. O.V. Andreev [2], using the photo-elastic methods had confirmed slide and slide arc (SA) existing and track transmit on rest arc (RA). Sciences of Ukraine researches, non-experimental had confirmed RA track efforts transmit [5], but had made preposition for boundary layer being in contact zone [6]. The cover drums to belt efforts transmit task had solved under the boundary layer being [6]. Contact task solving for rigid drum and belt interaction in deflections under nonCoulomb friction law using allow explaining mechanism of high molecular (viscous) materials wear under boundary layer absence
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