Meccanica最新文献

This paper presents a detailed mathematical analysis of the effect of tooth distribution on the stability of broaching operations. Analytic and numeric techniques are employed to analyse a simplified one-degree-of-freedom mechanical model of variable pitch broaching, to assess its stability, and to find the optimal tooth distances maximizing robustness against harmful self-excited chatter vibrations. A novel modelling approach, considering a theoretical infinitely long broaching tool, draws parallels with variable pitch milling, and analytic formulas for tuning milling cutters are extended to broaching tools. For a further increase of robustness, and to take feasibility constraints into account, a goal function based on the semi-discretization and spectral collocation techniques is implemented in a direct numeric optimisation framework. A new, detailed derivation of the corresponding parameter gradients is presented to enable the use of gradient descent techniques. Since broaching is inherently a time-limited process, optimal parameters found in this manner are then validated via time domain simulations to show the desirable transient behaviours achievable by this ideal tuning of the tool geometry.

This research focuses on the stability analysis of an odd viscosity-induced shear-imposed Newtonian fluid flowing down an inclined slippery bed having an insoluble surfactant at the top of the liquid surface. The Orr-Sommerfeld boundary value problem is developed by applying the normal mode approach to the infinitesimal perturbed fluid flow and solved using the numerical method Chebyshev spectral collocation. The numerical results confirm the existence of Yih mode and Marangoni mode in the longwave zone. For the clean/contaminated surface of the film flow, the presence of an odd or Hall viscosity coefficient reduces the surface wave energy and delays the transition from laminar to perturbed flow. Also, it has stabilizing nature on the unstable Marangoni mode as well. The growth rate of both clean and contaminated liquid surfaces becomes more/less when the stronger external shear acts along the downstream/upstream direction of fluid flow. Further, the slip parameter leads to a lower critical Reynolds number and makes the liquid surface more unstable. An increase in the critical Reynolds number due to the stronger Marangoni force ensures that the insoluble surfactant has the potential to dampen the Yih mode instability. Moreover, the unstable shear mode occurs in the finite wavenumber regime with very high inertial force and a small angle of inclination. The two-fold variation of the shear mode instability is possible with respect to the imposed shear. However, the inclusion of the odd viscosity coefficient in the viscous falling film may advance the shear mode instability.

Thick origami structures are considered here as assemblies of polygonal panels hinged to each other along their edges according to a corresponding origami crease pattern. The determination of the internal actions in equilibrium with the external loads in such structures is not an easy task, owing to their high degree of static indeterminacy, and the likelihood of unwanted self-balanced internal actions induced by manufacturing imperfections. Here, we present a method for reducing the degree of static indeterminacy which can be applied to several thick origami structures to make them isostatic. The method utilizes sliding hinges, which allow relative translation along the hinge axis, to replace conventional hinges. After giving the analytical description of both types of hinges and describing a rigid folding simulation procedure based on the integration of the exponential map, we present the static analysis of a series of noteworthy examples based on the Miura-ori pattern, the Yoshimura pattern, and the Kresling pattern. Our method, based on kinematic-static duality, provides a novel design paradigm that can be applied for the design and realization of thick origami structures with adequate strength to resist external actions.

Variable stiffness (VS) composite laminates provide larger freedom to design thin-walled structures than constant stiffness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed shell element, MISS-4C, to the postbuckling analysis of VS composite laminate structures. MISS-4C has a linear elastic closed-form solution for the stress interpolation of symmetric composite materials. Its stress field interpolation is obtained by the minimum number of parameters, making it an isostatic element. Moreover, its kinematic is only assumed along its contour, leading to an efficient evaluation of all operators obtained through analytical integration along the element contour. MISS-4C uses a corotational approach within a fast multi-modal Koiter algorithm to efficiently obtain the initial post-buckling response of VS composite laminate structures.

First, the element performance is investigated by analysing a carbon fibre VS composite laminate plate subjected to compressive stresses. Numerical results obtained with MISS-4C are compared with those obtained with the MISS-4 element, showing good accuracy and a high convergence rate. Subsequently, the structural response of a glass fibre VS composite laminate girder of a short-length bridge is optimised through a multi-objective optimisation that exploits the robustness of the MISS-4C element and the efficiency of the multi-modal Koiter algorithm.

Tensegrity structures are prestressed structures consisting of compressed members connected by prestressed tensioned members. Due to their properties, such as flexibility and lightness, mobile robots based on these structures are an attractive subject of research and are suitable for space applications. In this work, a mobile robot based on a tensegrity structure with two curved members connected by eight tensioned strings is analyzed in terms of deformation in the curved members. Further, the difference in locomotion trajectory between the undeformed and deformed structure after the prestress is analyzed. For that, the theory of large deflections of rod-like structures is used. To determine the relationship between acting forces and the deformation, the structure is optimized using minimization algorithms in Python. The results are validated by parameter studies in FEM. The analysis shows that the distance between the two curved members significantly influences the structure’s locomotion. It can be said that the deformation of the components significantly influences the locomotion of tensegrity structures and should be considered when analyzing highly compliant structures.

This study proposed a unique texture type with parabolic grooves inspired by the parabolic grooves on the surface of a cuttlebone to improve the load-carrying capacity of lubricated sliding bearings. A hydrodynamic lubrication model was used to systematically analyze the effect of parabolic groove parameters on the lubrication properties. The load-carrying capacity of the grooved texture was determined by a precise balance between hydrodynamics and cavitation effects. Parabolic grooves exhibited a higher load-carrying capacity than that of conventional straight grooves owing to the fluid collection effect of the parabolic shape texture and narrowing cavitation region around the divergent wedge; the optimal groove depth was typically in the range 5–7 μm. The load-carrying capacity increased at greater sliding velocities and thinner initial film. Consequently, this study provides valuable insights into a new shape configuration and design guidelines for surface texture in sliding bearings, offering potential advancements in the lubrication technology.

The existence of backlash causes de-meshing and reverse impact in the gear system, and the influence of the working lubrication conditions of the gear on the dynamics is ignored. This study focused on the impact of the coupling characteristics of gear system based on the multi-meshing state model and the gear lubrication model on the evolution of nonlinear dynamic behavior. Firstly, the transition of the meshing state was considered, and the time-varying parameters such as contact radius, load distribution ratio, meshing stiffness, entrainment speed, and slip-to-roll ratio were analyzed under meshing and reverse impact conditions. Then, the elastohydrodynamic lubrication model of the gear was analyzed, the coupling effect between the lubrication model and the gear system was reflected by two factors. One was the comprehensive meshing stiffness obtained by coupling the gear meshing stiffness and the lubricating oil film stiffness, and the other was the lubrication state transition of the system determined by the oil film thickness. Further, the gear dynamics model considering the above factors was established, and the influence of the coupling characteristics of lubrication and gear systems on the dynamic behavior was analyzed on the torque–speed parameter plane. The research results have theoretical guiding significance for the parameter selection, optimization design of gear system and the optimization of meshing characteristics.

The structure of natural biomaterials such as mollusk shells, conch shells, fish scales, and sea turtles, serves as a basis for inspiration in this study. We designed two composites with octahedral structures which can preferentially hinder the propagation of stress waves through the material. Mechanical properties and damage mechanisms of bionic octahedral structural composites under high-velocity impact were investigated employing experiments and finite element methods. The results show that under high-velocity impact, the crack damage of the traditional structure is divergent. In contrast, the damage mode of the bionic octahedral structure is progressive, and the damage is mainly concentrated in the central region. This improvement mainly arises from the interface of multiple unit blocks in the bionic octahedral structure, which effectively reduces the strength of tensile and shear stress waves on the surface of the composite glass plate. Therefore, the bionic octahedral structure can improve the impact resistance of composite materials significantly. This study provides valuable insights for the design of bionic structural composite materials with excellent impact resistance.

This paper presents a semi-analytic solution for the continued quasi-static compression of a thin rigid/plastic layer between two rigid, parallel rough plates. The constitutive equations of isotropic material postulate that the shear yield stress depends on the equivalent strain rate, the equivalent strain, and other internal variables. No restriction is imposed on this dependence. The general solution is valid for any finite number of internal variables. This solution reduces to several simple differential equations and one transcendental equation in Lagrangian coordinates. The solution is based on the standard assumptions in formulating the boundary value problem for simpler material models. More straightforward particular cases of the constitutive equations that are important for applications are considered separately. The solution reduces to a single differential equation in the most straightforward cases. A transcendental equation should be solved to find the initial condition of this differential equation. The friction factor’s effect on the solution’s qualitative behavior is discussed in detail. A numerical example illustrates the solution for an uncoupled material model. An applied aspect of this research is that its results can be used to analyze the plane-strain compression of thin metal strips, an essential metal-forming process.