Effective Computational Model for Determining the Geometry of the Transition Zone of End Coils of Machined Springs, Enabling Efficient Use of the Spring Material.

This paper presents an analysis of the effect of the geometry of the end-coil transition zone on the material stress state of a machined compression spring with a rectangular wire cross-section. The literature relationships for determining the stresses in rectangular wire compression springs neglect the effects associated with the geometry of this zone. A series of non-linear numerical analyses were carried out for models of machined compression springs with a wide range of variation in geometrical parameters. The results of these analyses were used to develop a computational model to estimate the minimum value of the rounding radius ρmin, which ensures that the stresses in this zone are reduced to the level of the maximum coil stresses. The model is simple to apply, and allows the radius ρmin to be estimated for springs with a spring index between 2.5 and 10, a helix angle between 1° and 15°, and a proportion of the sides of the wire section between 0.4 and 5.

Kinetic Energy-Based Indicators to Compare Different Load Models of a Mobile Crane.

This paper presents a proposal for the use of energy indicators to evaluate the load modelling methods on the dynamics of a mobile crane. Three different variants of mathematical models of a load carried were examined and compared: as a lumped mass on one hook-sling, as a sphere on one hook-sling, and as a box on four hook-slings. The formalism of joint coordinates and homogeneous transformation matrices were applied to define the kinematics of the system. The equations of motion were derived using the Lagrange equations of the second kind. These equations were supplemented by the Lagrange multipliers and constraint equations formulated for the cut-joints and drives. The energy indicators were proposed to evaluate the behavior of the crane and the carried load. The authors proved that modeling a load in the form of a lumped mass is a great simplification in the analysis of crane dynamics.

On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals technique. In some special cases the exponential estimates are constructed. On the basis of numerical modeling complex chaotic solutions of the model are obtained. Their investigation is performed with help of nonlinear characteristics, namely bifurcation maps based on Poincare sections and the maximal Lyapunov exponent were obtained.