Coefficient Of External Friction Research Articles

Modelling of mined rock thin layer disintegration taking into consideration its properties changing during compaction

The aim of the work is modelling of stressed condition of the loose mined rock thin layer between two parallel working plates of disintegrator, taking into consideration the dependences of the layer porosity and its side thrust coefficient on the main stress value with hereditary model of deformation accumulation. The equation of extreme balance of mined rock compactable thin layer is obtained for the case of its compression with partial sliding on working surfaces. It is shown, that there is no sliding in the central area of deformed zone, unlike the peripheral area. The iterative algorithm for parameters calculation of the layer stressed condition for the hypothesis of symmetric parabolic distribution of the axial normal stresses in the directions being perpendicular to the plates is developed. The distributions of the side thrust coefficient in the layer, the effective coefficient of external friction and the stresses of disintegrators working surfaces are grounded. The practical value of the research is the possibility to determine precisely the contact forces while crushing of fine-grained material taking into consideration its compactibility.

Optimum Profile of Chisel Front Surface

Cultivators for fallow and intertilled crops cultivation have several tipes of chisel. The key design data of a chisel are a tip overhang, radius of curvature of the front surface, an angle between a tangent to the tip and the furrow bottom. The radius of curvature of the front surface consists of two parts. The first one is in the form of a logarithmic spiral, the another is as a straight line. The angle between the tangent to the top and the furrow bottom depends on the angle of internal friction. It is in an interval of 35-40 degrees. The curvature radius and a lateral form of chisel generally depend on the size of an internal angle of friction of the deformable soil. (Purpose of research) To obtain an analytical dependence o of the front surface profile of the chisel working body, which allows to work on soils with different granulometric composition and angle of internal friction. (Materials and methods)The authors assumed that the condition of steady sliding of soil layer with various aggregate-size distribution on the chisel surface is feasible if the product of the projections of the tangential reactions of the elemental area of the surface and projections of the movement trajectory is less than zero. The projection of the tangential reactions of the elemental area of the surface depends on the concordance of the rotation angle to the size of digging-in, also on the deepening of the elementary area, the coefficient of external friction of the soil, and the first derivative of the function curve of the surface. The curve coefficient of a quadratic parabola outlining the surface of a chisel was estimated considering its smoothness and continuity. (Results and discussion) At the same time the current value of vertical coordinate of chisel lateral surface changed when the fixed values of tip overhang and running depth. The lateral profile of the as-designed chisel does not depend on soil characteristics. The size of the initial angle corresponds to the requirement that the deformation does not extend below the tip, and elementary reactions cross the surface of the field. (Summary) The angle of grade of the lateral profile surface of the chisel makes 26 degrees and 50 minutes. The curved surface of the wedge-shaped mouldboard is described by the function square parabola. The coefficient of the curve parabola describing a profile of a chisel surface, being negative, is equal to ratio of chisel overhang to the doubled parameter of the running depth.

Engineering properties of peeled and unpeeled garlic cloves

Garlic (Allium sativum L.) is widely used as a condiment and for medicinal and pharmaceutical preparations. The present study was undertaken to evaluate the engineering properties of garlic in both peeled and unpeeled form. The physical properties of whole garlic segments such as length, width, thickness were measured to estimate their geometric mean diameter and sphericity. Other properties such as bulk volume, bulk density, true density and porosity were also determined for both types of cloves. The experiments were also conducted to assess the frictional properties. Angle of repose and coefficient of external friction were determined against two surfaces, namely plywood and galvanized iron (GI) sheet. The average values of geometic mean diameter, sphericity, bulk density and true density for unpeeled and peeled cloves were measured as 11.820 mm, 0.494, 0.471 g/cc, 1.077 g/cc and 11.004mm, 0.526, 0.556g/cc, 1.169 g/cc, respectively. The coefficient of external friction for unpeeled cloves for plywood and GI surface were calculated as 0.366 and 0.772 and for peeled cloves as 0.664 and 0.812, respectively. The coefficient of internal friction for the unpeeled and peeled cloves were found to be 0.570 and 0.826, while the angle of repose values were calculated as 39.88 and 23.52 degrees, respectively. These properties are important for carrying out further operations of storage, transportation, design and development of peeling and other processing equipments.

Engineering properties of cotton stalks (<italic>Gossypium hirsitum</italic> L.)

Different physical and thermal properties of chaffed and ground cotton stalks were evaluated. The moisture content of chaffed and ground cotton stalk was 10.01 and 12.31% respectively. The size of chaffed cotton stalk was 40.3 mm, whereas the equivalent diameter of chaffed and ground cotton stalk was estimated as 30.5 and 4.5 mm respectively. The mean value of bulk density of chaffed and ground cotton stalks was 206.16 and 217.30 kg/m<sup>3</sup>, whereas true density varied between 727.70 and 313.60 kg/m<sup>3</sup>. The porosity of chaffed cotton stalks was estimated to be greater than ground cotton stalks. Angles of repose for chaffed and ground cotton stalks were 43.18 and 34.35<sup>o</sup> respectively. The coefficient of internal friction for ground cotton stalks was 0.85, whereas coefficient of external friction for chaffed and ground cotton stalks was estimated to be 0.54 and 0 .68 respectively. The calorific value of chaffed and ground cotton stalks came out to be 16.70, 16.79MJ/kg respectively. Ash content of both chaffed and ground cotton stalks were almost same i.e. 6.93 and 6.87 % respectively.

Tribomechanical analysis of interlayer shear and surface crack nucleation processes in compacted disperse materials

The effect of the internal (interparticle) and external friction on the limiting state generation has been analyzed in terms of the shear-induced failure criterion of the surface layers in the compacted disperse materials. The proposed design scheme based on the Mohr-Coulomb combined diagram has made it possible to develop an original method and derive analytic dependences for determining the normal and tangential stresses in the interlayer shear sites along with the orientation angles of these sites. It has been shown that, with increasing coefficient of external friction, the pressure in the interlayer shear sites reduces until tensile stresses are generated. This is accompanied by the nucleation of the crack at a right angle close to the side surface perpendicular of the formed item.

Effective parameters on angle of repose, internal and external friction coefficient in two wheat varieties (Behrang and Shirudi)

Effective parameters on angle of repose, internal and external friction coefficient in two wheat varieties (Behrang and Shirudi)

Analysis of frictional properties of cereal seeds

The thickness, width, length and weight of cereal seeds (wheat, rye, barley, oats and triticale) and their external friction angles on three types of surfaces – steel, methyl polyacrylate and rubber – were determined. The experiment was performed with the use of a new device that measures the angle of external friction and the time taken by seeds to travel a given distance, which supports the determination of the coefficient of kinetic friction. The measured parameters were used to calculate arithmetic and geometric mean diameter, aspect ratio, sphericity index, specific weight, volume and density of seeds. The correlations between the analyzed parameters were evaluated by analysis of variance, correlation analysis and linear regression analysis. The dimensions, weight and the calculated indicators of the examined seeds did not affect their angles of friction or the coefficients of static and kinetic friction. The studied parameters were significantly influenced by the type of friction surface, and significantly lower average values were reported for the steel surface. An inversely proportional correlation between static and kinetic friction coefficients was also observed for the steel surface. Key words: Physical attributes, coefficient of external friction, correlation.

Flow properties of particles in a model annular shear cell

In order to quantitatively investigate the mechanical and rheological properties of solid flow in a shear cell under conditions relevant to those in an annular cell, we performed a series of discrete particle simulations of slightly polydispersed spheres from quasi-static to intermediate flow regimes. It is shown that the average values of stress tensor components are uniformly distributed in the cell space away from the stationary walls; however, some degree of inhomogeneity in their spatial distributions does exist. A linear relationship between the (internal/external) shear and normal stresses prevails in the shear cell and the internal and external friction coefficients can compare well with each other. It is confirmed that annular shear cells are reasonably effective as a method of measuring particle flow properties. The so-called I-rheology proposed by Jop et al. [Nature (London) 441, 727 (2006)] is rigorously tested in this cell system. The results unambiguously display that the I-rheology can effectively describe the intermediate flow regime with a high correlation coefficient. However, significant deviations take place when it is applied to the quasi-static regime, which corresponds to very small values of inertial number.

Effect of high hydrostatic pressure on the external friction coefficient

Experiments are carried out to determine the molecular and mechanical components of the specific friction force under the effect of hydrostatic pressure of up to 140 MPa. The molecular component of the friction coefficient declines by up to two times under the effect of the hydrostatic pressure in various fluids. It is found that the combined influence of the temperature and hydrostatic pressure on the mechanical properties and the contact pressure leads to considerable variations in the deformation component of the static friction coefficient in plastic contact at temperatures of up to 200°C and under pressures of up to 140 MPa. The dependence of the hardness of structural materials on the hydrostatic pressure is analyzed to predict the effect of the latter on the deformation component of friction. It is shown that with increasing pressure within the above range the hardness grows in proportion to the square of the pressure and is inversely proportional to the initial hardness. The formula for calculating the dependence of the indentation depth of a spherical indenter in elastic contact on the hydrostatic pressure is derived.

Study of physicomechanical properties of solid domestic waste during compaction by an unbound method into large blocks

Technology is considered for compaction of solid domestic waste into large blocks, excluding subsequent stitching and binding with wire, in order to avoid arbitrary breakage during lifting and transport operations. As a result of calculation and theoretical studies, and laboratory experiments for determining the dependence of side pressure coefficient, static and dynamic coefficients of external friction due to compaction pressure, and also calculation of limiting state parameters, it is shown that the stated aim is achieved with compaction of solid domestic waste with a conical punch. Model blocks are obtained by experiment that have adequate strength during shipment and disposal at a landfill site. In view of the imperfection of existing technology for compacting solid domestic waste (SDW), it is necessary to carry out research for selection of a compaction regime in order to obtain a strong briquette without additional binding. The aim of this work is development of a procedure for determining the physicomechanical parameters of SDW briquettes, establishment of their quantitative values for use in designing compaction, and creation of unbound SDW briquetting technology. During compaction there is a change in the shape and dimensions of a dispersed body, such as SDW, as a result of a reduction in pore volume and deformation of the material structure [1]. The capacity of solid dispersed material to increase its density under the action of pressure and to form a briquette of prescribed shape and dimensions is called “compaction” [2]. These production properties of SDW taking account of dimensions and configuration of finished objects, physiochemical, and mechanical properties of its structural elements, i.e., particles, should be considered in the choice of production parameters for compaction. Several methods exist for SDW compaction [3]. In contemporary enterprises for SDW processing by compaction, pressing devices are used whose operating cycle consists of the following operations:

The effect of interparticulate and external friction on the orientation of shear planes when brittle dispersed materials undergo compaction

A method of calculating the position of shear planes in clusters of a deformable brittle dispersed material with account of interparticulate and external friction is advanced. It is assumed that friction occurs over the planes where the tangential stresses reach value specific forces of interparticulate friction. The ranges of variations of the angles of orientation of planes with different combinations of interparticulate and external friction coefficients are determined.

Quality Evaluation of Mechanically Washed and Polished Turmeric Rhizomes

The quality of turmeric powder depends upon the initial quality of rhizomes and the practices adopted in various post harvest operations. Washing and polishing are two primary processes for quality enhancement. Turmeric rhizomes were mechanically washed in a rotary machine at varied speed and time and evaluated for microbiological washing efficiency and bruising. For optimized parameters such as 2.2 min washing time at 47.2 rpm rotational speed of the machine, the microbiological efficiency was 87.2% with negligible bruising. At optimum polishing (78%) performance parameters of40 rpm rotational speed for 20 min, the color improved from dark yellowish brown to desirable olive yellow color (2.5 YR 6/6, Munsell color chart rating), with increase in the surface smoothness (Coefficient of external friction on G.I sheet reduced from 0.487 to 0.436), and also resulted in improvement in the microbiological quality. Mechanical polishing reduced the surface microtlora by half. The total fungi reduced from 7050 to 3220 cfu/g, bacterial count decreased from 1500to 770 cfu/g and coli-forms reduced from 200 to 110 cfu/g, thus enhancing the final quality of turmeric rhizomes.

Friction and compression characteristics of chickpea flour and components

Chemical composition and selected physical properties of chickpea flour, the starch fraction and the protein fraction were determined. Coefficient of internal friction, coefficient of external friction (on steel, concrete, Teflon and polypropylene), cohesion and adhesion of samples were measured. Chickpea flour and starch fraction had the highest coefficient of internal friction and cohesion, respectively. The coefficient of external friction of chickpea flour and components on concrete was markedly higher than other surfaces. The starch fraction had the highest compressibility and asymptotic modulus at most of the preset loads. The compressibility and asymptotic modulus increased with porosity. Chickpea flour with the lowest porosity had the lowest asymptotic modulus. All samples underwent particle rearrangement during compression.

Shear stresses and material slip in high pressure roller mills

The compaction of the particle bed in a high pressure roller mill causes pressure and shear forces on the rollers, which have been measured simultaneously with a sensor. As known, the pressure peak arises short above the gap neck, the shear is firstly orientated against and then in the rotation direction. However, the zero point does not coincides with the pressure peak as often said but lies before it. In the entire compression zone and in the first part of the relaxation zone, the shear–pressure ratio is smaller than the coefficient of external friction μ, slip, therefore, does not exist in this region. This ratio exceeds μ only near to the outlet and indicates slip there. Based on a force balance on a differential strip and with the assumption of proportionality between the transversal pressure in the bed and the normal pressure on the roller, an equation arises relating shear to pressure. Only one property of the granular material remains in this equation, the stress ratio coefficient λ defined as in powder mechanics. The calculated shear agrees well with the measured value in the compression zone until to the shear minimum but is clearly smaller further down. The analysis of the measurements in view of the theoretical considerations leads to the conclusions that slip only exists in the region near to the outlet. Here, the material is extruded, which causes a tensile force acting on the material above and increases by that the shear over the calculation. This effect ceases further up, therefore, the calculation approaches the measured values.

A revised method of determining lateral-pressure and external-friction coefficients for powder pressing

There are basic parameters of granular and loose fibrous materials used in pressing: the lateral pressure coefficient ~, which is equal to the ratio of the pressure on the side of the die to the axial pressure, and the external friction coefficient f on the side surface, These parameters are needed to design tools in which powdered materials are pressed (milling and briquetting presses, tableting machines, and so on). Experiments have been made [1-4] to determine the lateral pressure and external friction by reference to the elastic strain in the wall of the pressing chamber and the strain in a special elastic element, which are recorded by strain gauges. For example, in [1] the combination ~.fwas determined from the measured external forces on displacement of the charge in a pressing chamber for a given distribution of the axial pressing force along the charge. In that method, it is fairly difficult to determine the distribution of the axial load and consequently of the lateral load along the material, and additional research is needed to determine the external friction coefficient. In [4], experiments were done on the distribution of the lateral pressure Px along a column of pressed powder, and estimates were made of ~ andf. Figure 1 shows the working scheme. The cylindrical die 3 containing plungers 6 and 1 was mounted on the elastic component 4. The free space between the plungers was filled with the powder. At the outer surface of the die in the powder zone, there were strain gauges 2 used to estimate the deformation of the wall due to the lateral pressure. The external friction was estimated with the strain gauges 5 cemented to the elastic element 4. During the pressing, the speed of the powder in contact with the upper plunger 1 is equal to that of the plunger itself; the speed of the powder at the lower plunger 6 is zero (neglecting axial deformation), The displacement of" the powder with respect to the inner surface of the die produces a frictional force, under which the die moves downwards and deforms the elastic element. Consequently, the displacements or velocities of the die and elastic element are identical. The displacement of the powder in the vertical direction during pressing ranges from maximal (at the upper plunger) to zero (at the lower one), so at a certain height, the speeds of the powder and die will be equal, so the frictional force in that zone will be zero. Below that zone, the frictional force changes direction and resists the displacement of the plunger 6 and the deformation of the elastic element 2. Figure 1 shows the variation in the relative velocity of the plunger 6 and powder. The residual frictional force is recorded by the strain gauges 5 in the elastic element 4 (if the external friction coefficient is constant over the height of the powder and one knows the distribution of the lateral pressure Px) and is given by

The baroeffect and an appropriate momentum boundary condition

As disparate molecular weight gases isothermally diffuse between two ends of a capillary tube, they can support a pressure gradient. The magnitude of this pressure gradient depends critically on viscous wall stress and becomes a measure of the boundary condition. This baroeffect has been used to test the state of a gas surface layer. Specifically, it allows one to quantify whether a binary gas has a finite wall velocity (diffusive slip). Here, a one-dimensional analytical model is proposed that allows for specular gas reflection from the wall. It explains anomalous (4/3) correction factors required previously to match experiment to baroeffect models. It predicts a new physical phenomenon, a surface-driven baroeffect for equal molecular weight gases. Diffusive slip contributions exceed the order of convective diffusion for Peclet number Pe<1 and approximately equal convective diffusion for 1<Pe<4. For binary gases, this model further extends the baroeffect experiment as a means to find momentum accommodation coefficients (MAC), slip lengths, and external friction coefficients. A corrected binary diffusion coefficient is defined. Analogous arguments can be made to explain corrections to thermal and viscous slip.

Slip effect for thin liquid film on a rotating disk

A flow for thin liquid films on rotating disks has been theoretically and experimentally studied. Liquid depletion behavior during a spin-coating process is calculated by solving the Navier–Stokes equation, taking into account interface slip between liquid and disk. Excellent agreement is seen between the model prediction and experimental data. According to observed depletion behavior on thin liquid films for various spin-coating parameters, half life falls off at the inverse square of rotational speed, and increases when viscosity increases, although the increasing rate falls off. The interface slip, represented as an external friction coefficient, is thermodynamically explained by the different (Δrc) in critical surface tension (rc) values between the liquid and the disk, which will be proportional to the solubility parameter. An infinite external friction coefficient, representing nonslip flow, may be given, when Δrc is zero. Spin-off experiments for liquids of various rc values, prepared by differing surface treatments, support this consideration.

Assessment of the coefficient of external friction in powder rolling

Assessment of the coefficient of external friction in powder rolling

Calculated coefficient of external friction in the pressing of metal powders

On the basis of the molecular-mechanical theory of friction of solids a relationship has been obtained which makes it possible to utilize the known frictional parameters of dense metals and determine by calculation coefficients of external friction in the pressing of metal powders. A check revealed good agreement between data yielded by the theoretical relationship between the coefficient of friction and pressing pressure and experimental results for PO2 tin and PMS-2 copper powders.

Coefficient of external friction in the pressing of metal powders

Experimental data on the external friction in the pressing of copper and iron powders have been processed graphicoanalytically, using Deryagin's binomial law, and the mechanical and adhesional components of the coefficients of friction in the pressing of these powders have been determined. A rise in pressing pressure decreases the static coefficient of friction by reducing its adhesional component.