Three-dimensional integral dry friction model for the motion of a rectangular body

Introduction. A three-dimensional dry friction model in the interaction of a rectangular body and a horizontal rough surface is considered. It is assumed that there is no separation of the body from the horizontal surface. The body motion occurs under the conditions of combined dynamics when, in addition to the longitudinal movement, the body participates in twisting.Materials and Methods. Linear fractional Pade approximations are proposed, which replaced the cumbersome analytical expressions that most accurately describe the motion of bodies on rough surfaces. New mathematical models describing sliding and twisting of bodies with a rectangular base are proposed.Results. Analytical expressions of the principal vector and moment of friction for rectangular contact areas are developed and scientifically established. A friction model that takes into account the relationship between sliding and twisting speeds, which provides finding solutions for Pade dependences, is developed. After numerical solution to the equations of motion, the dependences of the sliding speed and angular velocity on time were obtained and constructed. Graphs of the dependences of the friction forces and their moment on two parameters (angular velocity and slip velocity) were constructed, which enabled to compare the integral and normalized models of friction. The comparison results showed good agreement of the integral model and the model based on Pade approximations.Discussion and Conclusions. The results obtained provide considering the dynamic coupling of components, which determines the force interaction of a rectangular body and a horizontal surface. These results can be used in mobile robotics. The analyzed motion of the body occurs through the motion control of a material point inside the body. Such mobile robots can be used when solving a wide class of problems: when creating autonomous robots for the exploration of outer space and planets; in the diagnosis and treatment in case of passing through complex structures of veins and arteries; in research under water, in places of large differential temperature; in underground operations.

Characteristic of Free-rolling Motion of Twodimensional Rectangular Body in the Regular Wave

his study investigated the characteristics of rolling motion of rectangular body for regular waves with a range of wave periods that are equal to and longer than its natural roll period. Using the volume of fluid (VOF) method based on the finite volume method with standard k-ε turbulence model, twodimensional (2D) incompressible viscous two-phase flow is simulated in a wave tank with the rectangular body. The present study introduces a wave period ratio (Tr=TW/TN) of an incident wave period (TW) to the roll natural period (TN) of body. The wide range of 1≤ Tr ≤2.5 is considered in this study. In the wave periods considered in this study, the roll motion shows two distinct patterns. One is the single oscillatory motion which appears in the period ratio of 1≤ Tr ≤1.7. The other is the double oscillatory motion in 1.8≤ Tr ≤2.5. In these two regimes, flow and the roll motion of the rectangular body, which are induced by the fluid flow-structure interaction for various wave periods, are carefully investigated to reveal the mechanism of two roll modes.

Variability of basic morphometric parameters in Posavatz hounds in Serbia

Introduction. By the number of litters and puppies per year, the Posavatz hound is the second most common hound breed in Serbia. This hound is intensively used for hunting in Serbia, since these dogs show very good working characteristics. The aim of this study was to determine the extent to which the external characteristics of the population in Serbia meet the norms prescribed by the official standard for the breed. Materials and Methods. A total of 251 Posavatz hounds, i.e. 134 adult males and 117 adult females, were included in a morphometric evaluation of the population sub-sample during 2017 and 2018. The basic parameters of height at the withers, body length, chest circumference and head length were measured. The variability of the results obtained was statistically analyzed by Student?s t-test for distribution of the frequencies, while the heterogeneity/homogeneity of the evaluated morphometric parameters within the Posavatz breed was estimated by coefficient of variation. Results and Conclusions. The results showed the studied Posavatz hounds in Serbia are characterized by a proper rectangular body shape. However, the average body height tended to be too low, i.e. more towards the lower limit of the prescribed height at the withers. The morphometric deviations established when comparing the Posavatz hound population in Serbia with the standard for the breed should enlighten the guidelines for sound selective breeding of the Posavatz hound by contributing to decision making by breeders and expert commissions of canine organizations. Overall, this should allow healthy breeding and welfare maintenance throughout generations for this hound breed.

Rectangular Body-centered Cuboid Packing Lattices and Their Possible Applications

We first introduce several sphere packing ways such as simple cubic packing (SC), face-centered cubic packing (FCC), body-centered cubic packing (BCC), and rectangular body-centered cuboid packing (recBCC), where the rectangular body-centered cuboid packing means the packing method based on a rectangular cuboid whose base is square and whose height is times the length of one side of its square base such that the congruent spheres are centered at the 8 vertices and the centroid of the cuboid. The corresponding lattices are denoted as SCL, FCCL, BCCL, and recBCCL, respectively. Then we consider properties of those lattices, and show that FCCL and recBCCL are the same. Finally we point out some possible applications of the recBCC lattices.

Differentiation of some Pramenka sheep breeds based on morphometric characteristics

For the purpose of the morphometric characterization and differentiation of local sheep breeds that belong to the group of breeds called Pramenka or Zackel, two Slovenian (Bela Krajina and Istrian Pramenka) and four Montenegrin sheep breeds (Bardoka, Sjenička, Pivska Pramenka, and Zeta Žuja) were studied. The variation of morphometric measures and nine morphometric indices were analysed. Principal component analysis (PCA) was applied in order to provide an easier description of body size and shape. Regarding body size, the Sjenička breed was one of the largest breeds (body weight 76.4 kg, wither height 72.7 cm, chest circumference 100.3 cm), while Zeta Žuja had the smallest body size (37.1 kg, 64.8, and 81.9 cm). On the other hand, Slovenian Istrian Pramenka had the largest body length, chest depth, chest width, and rump width among all included breeds (79.4, 33.6, 22.7, and 21.2 cm). Bela Krajina, Istrian Pramenka, and the Sjenička breed, according to the index of body frame (IBF) value (107–114), have a rectangular body frame, Bardoka and Pivska Pramenka have a square body frame (99.3–100), and Zeta Žuja has a short body frame (91.8). The PCA of all morphometric parameters extracted three components accounting for 96.6 % of the cumulative variance. An unweighted pair–group method with arithmetic mean (UPGMA) cluster analysis by Euclidian distance shows diversity among the studied breeds, through it grouped Pivska Pramenka with Sjenička and Istrian with Bela Krajina Pramenka in two clusters, while Bardoka and Zeta Žuja were clustered separately.

Combined Natural Convection and Thermal Radiation Heat Transfer in a Triangular Enclosure with an Inner Rectangular Body

In this paper, a numerical simulation was conducted to investigate the steady laminar natural convective heat transfer and surface radiation from a heated rectangular body in a triangular enclosure. The coupled equations of Navier-stockes and energy are both solved using the finite volume method. The velocity-pressure coupling is insured by the SIMPLER algorithm. The fluid used in this study is a dry air of Prandtl numberPr= 0.71.In such way that, the radiative exchanges are made only through solid walls and which are assumed to be gray and diffuse. The physical parameters characterizing the problem and influencing heat transfer are Rayleigh numberRa, aspect ratioA, heighthand widthwof the body. The results are presented in terms of isotherms, streamlines and average Nusselt number.

Analysis of Natural Convection Flow in a Trapezoidal Cavity Containing a Rectangular Heated Body in Presence of External Oriented Magnetic Field

The laminar natural convection flow and heat transfer inside a trapezoidal cavity filled with air and containing a rectangular block is investigated numerically. The left and right walls of the cavity are cold, the top and bottom walls are adiabatic and the rectangular body is heated uniformly. Finite Element Method of Galerkin’s weighted residual scheme is used to solve the transport equations with appropriate boundary conditions. The main objective of this study is to explore the influence of pertinent parameters such as Rayleigh number, Hartmann number and orientation of the magnetic field on the flow and heat transfer performance of the fluid while the Prandtl number is considered fixed. Results indicate that the heat transfer rate is significantly affected by increasing the mentioned parameters.