An Upper Bound Solution for the Compression of an Orthotropic Cylinder

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

Admissible velocity propagation: Beyond quasi-static path planning for high-dimensional robots

Path-velocity decomposition is an intuitive yet powerful approach to addressing the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler steps: first, a path is found in the configuration space that satisfies the geometric constraints (path planning), and second, a time-parameterization of that path satisfying the kinodynamic constraints is found. A fundamental requirement is that the path found in the first step must be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints during the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm – Admissible Velocity Propagation – which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path, while respecting the system’s kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

Computing Model for Vibratory Digging-Out of Sugar Beet Roots

The new design mathematical model of the sugar beet roots vibration digging-out process with the plowshare vibration digging working part has been created. In this case the sugar beet root is simulated as a solid body , while the plowshare vibration digging working part accomplishes fl uctuations in the longitudinal - vertical plane with the given amplitude and frequency in the process of work . The aim of the current research has been to determine the dependences between the design and kinematic parameters of the sugar beet roots vibra- tion digging-out technological process from soil , which provide the ir non-damage. Methods . For the aim ac- complishment, the methods of design mathematical models constructing based on the classical laws of me- chanics are applied. The solution of the obtained differential equations is accomplished with the PC involve- ment. Results . The differential equations of the sugar beet root’s motion in course of the vibration digging-out have been comprised . They allow to determine the admissible velocity of the vibration digging working part’s forward motion depending on the angular parameters of the latter. In the result of the computational simula- tion i.e., the solution of the obtained analytical dependence by PC, the graphic dependences of the admissible velocity of plowshare v ibration digging working part’s forward motion providing the extraction of the sugar beet root from soil without the breaking-off of its tail section have been determined. Conclusions . Due to the performed analytical research , it has been established that γ = 13 ... 16 ° , β = 20 ... 30 ° should be considered as the most reasonable values of γ and β angles of the vibration digging working part providing both its forward motion optimum speed and sugar beet root digging-out from the soil without damage . On the ground of the data obtained from the analytical rese arch, the new vibration digging working parts for the sugar beet roots have been designed; also the patents of Ukraine for the inventions have been obtained for them.

Velocity Field in Direct, Indirect and Friction Assisted Extrusion of Al

This study investigates the velocity fields that are descriptive for the forward, backward and friction assisted extrusion of axisymmetric rods. The Avitzur theory was used to calculate the velocity field and strain rate in extrusion of Al alloys. Several simulations have also been performed by using finite element analysis (FEA) with DEFORM 2D, in order to find the admissible velocity field for different conditions of friction including high and low friction. The results from FEA and theory of axisymmetric extrusion are compared to see if there is good agreement. The correlation between the data obtained by theory and FEA is discussed.

A Generalized Velocity Field for Plane Strain Extrusion Through Arbitrarily Curved Dies

In this paper, plane strain extrusion through arbitrarily curved dies is investigated analytically, numerically, and experimentally. Two kinematically admissible velocity fields based on assuming proportional angles, angular velocity field, and proportional distances from the midline in the deformation zone, sine velocity field, are developed for use in upper bound models. The relative average extrusion pressures for the two velocity fields are compared to each other and also with the velocity field of a reference for extrusion through a curved die. The results demonstrate that the angular velocity field is the best. Then, by using the developed analytical model, optimum die lengths which minimize the extrusion loads are determined for a streamlined die and also for a wedge shaped die. The corresponding results for those two die shapes are also determined by using the finite element code and by doing some experiments and are compared with upper bound results. These comparisons show a good agreement.

Three Dimensional Upper Bound Modelling for Extrusion of Round-to-Octagon Section Using Linearly Converging Die

The extrusion of section from round billet poses a great challenge for theoretical modeling of the process using upper bound method. The greatest difficulty in three-dimensional upper bound method is to determine kinematically admissible velocity field. The SERR (Spatial Elementary Rigid Region) technique is fairly applicable for analyzing extrusion of sections having re-entrant corners. A modified version of SERR technique has been used for extrusion of octagon sections from round billet through a linearly converging die. The circular cross section of the round billet is approximated by a regular polygon of equal area. The extrusion pressure has been computed for different boundary condition at the die billet interface. The optimum die geometry has been determined.