D.t.n. Kushnir V.G., k.t.n. Benyukh O.A., magistrant Komarov A.P.

Kostanay state university by A. Baitursynov, Kazakhstan

The water-pump belt working process at various speeds

 

          It is known that increasing the velocity of the driven roller conveyor starts to form the water-pump so-called "water wedge" between the drum surface and the tape. This causes slippage of the tape and substantially lowers productivity water lift. [1]

          In solving the problem of contact-hydrodynamic behavior of a rubber band on a metal drum is necessary to determine its deflection under the action of pressure resulting in a layer of water between it and the drum. Modulus material hundred times less than the modulus of elasticity of the steel drum, moreover, the thickness of the tape is less than ten times the radius of curvature of the drum at its coverage. Therefore, the approximate solution admits reversibly assume tape is a flat layer lying on a completely rigid base and firmly adherent to it.

          Contact-hydrodynamic theory in its most general formulation is a joint decision of 3 mutually independent tasks:  hydrodynamic - for fluid flowing through the gap; contact - for the rubbing surfaces; heat - for lubricant and friction surfaces. [2]

          Heat processes beyond the scope of our problem, so only the first two, with the offer to use the procedure for distribution calculations sliding bearings with non-metallic collar, while introducing the assumption that the role of the journal will play a leading drum, and the role of non-metallic clips - gummed tape.

          As is known, the basic equations of motion hydrodynamic solid compressible medium has the form:

                       ;

       ;                                                 (1)

                       ;

and the continuity equation:

                                                                        (2)

          Taking into consideration that as the intermediate layer in this case is water, which is a Newtonian fluid and it Stu law is valid: 

                                                                                                           (3)

 

wherein: m 0 - viscosity at atmospheric pressure;

               n - coefficient of viscosity.

          For compressible viscous Newtonian fluid using the generalized Newton's law for the relation between stress and strain rates:

                 ;

       ;                    (4)

                 ;

 

where                                                                                       (5)

          After substituting (4) into (1), for compressible Newtonian fluid basic hydrodynamic equations take the form:

           (6)

where: x - coordinate measured along a tangent to the bottom surface reverse side of  

                 the movement, m;

            y - coordinate measured across the lubricating layer, m;

            z - coordinate measured along a tangent to the bottom surface and directed  

                  perpendicular to the axes X and Y, m;

             k0 - hydrodynamic pressure at a given point, Pa/m2;

             px, py, pz - normal stress at a given point, N/m2;

             Jx, Jy, Jz - shear stresses at this point, N/m2;

             u, v, w - the corresponding components of the velocity of the element fluid in  

                           the direction of axes X, Y, Z, m/s;

             ρ - density of the liquid at a given point, kg/m3;

             μ0 - absolute viscosity of the fluid at a given point, kg/m;

             X, Y, Z - components of body force per unit mass;

             t - duration, with;

             λ1 - the second viscosity coefficient, which determines the dissipation  

                  (scattering) energy during compression and expansion.

          It is known that during compression-extension of liquid thermodynamic equilibrium is broken and the process of recovery is dependent on its properties and the conditions in which there is a liquid.

          Duration of the impact of external forces on several orders of magnitude greater duration of relaxation. When m is at least time to change the volume balance be restored. However, in some cases, the relaxation time increases significantly, and if the cycle time "tensile-compressive" becomes less than or of the same order with the relaxation time, a considerable dissipation occurs (dispersion) of energy which is a measure of viscosity to the second λ1, λ2 - it is not a constant but a function of frequency of motion, in which it manifests itself. For Newtonian fluids, λ1 = 1.

          The thickness of the lubricating layer is very small compared to the linear dimensions of the other layer, e.g. the width of the tape and the contact area, and the drive drum. Then we can assume that the pressure does not change across the lubricating layer, for fluid pressure at a given point of the lubricating layer is a normal mu voltage with the opposite sign.

          Thus, for a Newtonian fluid the systems of equations (6) will greatly simplified form:

                                   ;

                                    ;                                                                (7) 

                                                

wherein:     and     ,   equal to the product of the shear stresses on viscosity minute gradient shear rate.

          Tangential movement of the rubbing surfaces have a higher order of smallness compared with radial, so they can be neglected.

Then:                                              ;

                                              ;                                                      (8)

                                              .

          It is known that the basic differential equation of hydrodynamic lubrication theory does not change its structure regardless of the accounting change in viscosity across the lubricating layer. Homogenization temperature, viscosity and density of the liquid lubricant layer obtained across the velocity profile of fluid elements in the direction of the X and Z:

                         

                                              (9)

          The basics of Korovchinsky M.V equation hydrodynamic lubrication theory for the general case of motion surfaces offered written as:

  (10)

where: h - film thickness at a given point, m;

            Ua, Ub - velocity in the direction of the rubbing surfaces reverse X-axis, m/c;

            Wa, Wb - velocity of rubbing surfaces in e.g. a phenomenon reverse axis Z,

                           m/s;

            V0 - removal rate from each other rubbing surfaces measured normal to the  

                   surface, m/s.

          Axial pull friction area (axis Z) is much less than the length of the friction area of the X-axis, then, consequently, a three-dimensional flow of lubricant can be regarded as flat.

          With this in mind, the original system of equations (1) is simplified to a single expression:

                                                            (11)

where: h 0 - film thickness at the maximum pressure, m;

                  Õ0, x - coordinate of the end of the field of friction, m.

          In this example, the mode of movement of the rubbing surfaces is considered to be steady, V0 = 0, and taking into account (3), the expression  (11)

becomes:                                                            (12)

          Due to the fact that water pressure-viscosity coefficient n is 0, so equation (12) simplifies to: 

                                                                                   (13)

 

          Thus, as seen from the formula, the pressure in the water layer between the belt and pulley is directly proportional to their velocity and inversely proportional to the cube of the thickness of this layer.

                                                              

Literature

1. Kaplan R.M., Kaskarauov I.A. K isledovaniyu lentochnykh vodopodmnikov dlya pastbishchnykh skvazhin. Vestnik s/kh nauki.-Alma-Ata, 1971. ¹7. s 101-107.

2. Kulpin P.I., Nechaev V.A., NechaevB.V. Eksperimentalnye issledovaniya vodopodemnika s povyshennoy skorostyu dvizheniya lenty. / Mekhanizatsiya rabot v zhivotnovodstve. Sb. nauchnykh rabot. Saratovskiy SKhI. Saratov, 1975, vyp.43. s. 140-147.