Tangential Surface Research Articles

Impacts of different characteristics of marine biofouling on ship resistance

Ship resistance research on marine biofouling is an old but hot topic which invokes plenty of studies recently. Previous studies on the surface roughness of ship hulls mainly focus on the height of micro-organisms or macro-organisms adhered to ship hulls without considering other components which may indeed play an important role in generating additional resistance. Many authors attempt to use a single parameter, for example, height of the biofoulers, to describe the hull roughness. Our research indicate that any single factor affecting ship hull roughness can not completely reflect the compositions of ship resistance. Here we propose a novel numerical model which enables more precise estimates of the contribution of each single component involving in the marine biofouling.The standard k−ε model of FLUENT is modified by considering the possible rotating, jetting, surging and swirling of fluid flowing over ship hulls due to characteristics of the marine biofoulers. Simulated results using the modified model at various speeds are compared with that using the original model, and an improvement of ship resistance is evident, quantitatively consistent with measured, indicating that the modified model behaves in a reasonable manner in simulating the relationship between ship resistance and ship surface roughness.The marine biofoulers affect ship resistance primarily by increasing the tangential surface shear stresses. Simulated results demonstrate that additional resistance caused by height, shape, hardness and density of the biofoulers accounts for up to ∼80% of total resistance in the heavy fouling condition (taking vessel “YOURIXX” as an example), implying an economic demand for good hull performance.

Sweeping Surfaces according to Type-3 Bishop Frames in Euclidean 3-Space

The aim of this work is to investigate sweeping surfaces and their local singularities due to type-3 Bishop frames in Euclidean 3-space, E3. A sweeping surface a is surface that is designed from a section curve positioned along a path, which acts as the vertebral column or spine curve, and it has symmetrical characteristics. In this work, we have specified a sweeping surface and have examined its geometry and singularity. Thereafter, we deduced the circumstances required for this surface to be a developable surface. In great detail, we concentrated on the fundamental discussion on whether the resulting developable surface is a cylindrical, cone or tangent surface. Meanwhile, examples are detailed to explain the applications of the notional outcomes.

Accurate optimal power flow for active distribution networks via floating tangent surface

Accurate optimal power flow for active distribution networks via floating tangent surface

B-Lift curves and its ruled surfaces

In this paper, we have described the B-Lift curve in Euclidean space as a curve obtained by combining the endpoints of the binormal vector of a unit speed curve. Subsequently, we have explored the Frenet frames of the B-Lift curves. Moreover, we have introduced the tangent, normal and binormal surfaces of the B-Lift curve and examined the geometric invariants of these surfaces. Finally, we have investigated the singularities of these surface and visualized the surfaces with MATLAB program.

Cargo carrying with an inertial squirmer in a Newtonian fluid

We numerically investigate the hydrodynamics of a spherical swimmer carrying a rigid cargo in a Newtonian fluid. This swimmer model, a ‘squirmer’, which is self-propelled by generating tangential surface waves, is simulated by a direct-forcing fictitious domain method (DF-FDM). We consider the effects of swimming Reynolds numbers (Re) (based on the radius and the swimming speed of the squirmers), the assembly models (related to the cargo shapes, the relative distances (ds) and positions between the squirmer and the cargo) on the assembly's locomotion. We find that the ‘pusher-cargo’ (pusher behind the cargo) model swims significantly faster than the remaining three models at the finite Re adopted in this study; the term ‘pusher’ indicates that the object is propelled from the rear, as opposed to ‘puller’, from the front. Both the ‘pusher-cargo’ and ‘cargo-pusher’ (pusher in front of the cargo) assemblies with an oblate cargo swim faster than the corresponding assemblies with a spherical or prolate cargo. In addition, the pusher-cargo model is significantly more efficient than the other models, and a larger ds yields a smaller carrying hydrodynamic efficiency η for the pusher-cargo model, but a greater η for the cargo-pusher model. We also illustrate the assembly swimming stability, finding that the ‘puller-cargo’ (puller behind the cargo) model is stable more than the ‘cargo-puller’ (puller in front of the cargo) model, and the assembly with a larger ds yields more unstable swimming.

Study of frictional properties, long-term (cyclic) strength of materials of brake pads of motor vehicles

Fractogram analysis shows that deep scratches, particles of titanium and chromium carbides and other elements were found on the friction surfaces. Moreover, in the braking devices there was damage to the large size of the brake pads of trucks. The transfer of particles of borides and carbides to the surface of the wheels can be explained by the processes of metal flooding with their subsequent embrittlement, which inevitably leads, as a rule, to the destruction of friction wheel pairs. It is established that such types of wear as fretting corrosion significantly (by 1.5-2 times) reduce the fatigue limit of parts. Also significantly reduce the cyclic strength of metal friction pairs oxide films on their surface in the absence of lubricant. The service life of friction wheel pairs has a particularly strong impact on fatigue strength. The main reason for the decrease in endurance due to the processes of setting on the working surfaces of friction units is a high concentration of stresses caused by deep tears, cuts, microcracks. The process of destruction of brake pads from fatigue begins from the surface of the part. In this regard, the quality of the surface, its structural-phase composition, physical and mechanical properties of the surface layer in most cases are decisive for the intensity of the development of wear processes of parts from fatigue of the tribosystem (friction wheel pairs), which are operated under cyclic loads. The peculiarity of the influence of friction and wear processes on the fatigue strength of metal is that at the time of running-in there is a change in surface roughness, structure and properties of surface layers. As the analysis of literature sources has shown, the effectiveness of the influence of friction and wear processes on the characteristics of fatigue resistance in the case of repeatedly alternating (cyclic) loads is essential, and therefore ignoring this effect during the traditional assessment of the reliability of parts by individual criteria, for example, wear resistance, often leads to an incorrect assessment of the operational durability of the elements of the tribological system of road or rail transport. The long-term (cyclic) strength of brake pads was determined on a specialized unit model 1251 by Instron company (Great Britain). The basis for spraying and surfacing of different types of coatings was normalized steel 35. Tensile-compressive deformations at zero average stress and a cycle frequency of 20 Hz were studied on the laboratory unit. Most of the tests were carried out in salt solutions (NaCℓ of industrial purity was used).The process of destruction of brake pads from fatigue begins with the surface of the part. In this regard, the quality of the surface, its structural-phase composition, physical and mechanical properties of the surface layer in most cases are decisive for the intensity of the development of wear processes of parts from fatigue of the tribosystem (friction wheel pairs), which are operated under cyclic loads. Endurance limits in the case of simultaneous exposure to friction forces and cyclic loads will depend on the sliding speed of the tangent surfaces of the normal contact load, which determines the friction force, and the composition of the environment.

Nonlinear vibration analysis for bolted CFRC plates based on displacement-dependent surface spring-damping model of bolted joint

Under the effect of external excitation, bolted structures are prone to stiffness weakening and damping energy dissipation at the bolted joint, which makes the structures show nonlinear vibration behavior. In this paper, the displacement-dependent surface springs and tangential surface damping expressed by the S-curve model are proposed to simulate the nonlinear mechanical properties of the bolted joint. The non-uniform distribution of the mechanical parameters for the bolted joint is given to simulate the actual joint interface pressure distribution. Based on these, a nonlinear semi-analytical model for bolted carbon fiber reinforced composites (CFRC) plates considering the nonlinear mechanical characteristics of the bolted joint is established. Combined with the experimental results for a bolted CFRC beam, the specific S-curve expressions for the relevant mechanical parameters of the bolted joint are obtained by the inverse identification technology and numerical fitting method. After that, the bolted joint model is transplanted to the dynamic model of a bolted CFRC plate for numerical calculation. The comparison with the corresponding measured results shows that the proposed modeling method can well reproduce the soft nonlinear vibration of the actual bolted CFRC plate, which verifies the correctness and applicability of the proposed modeling method.

Predictive modelling for enhanced scratching of brittle ceramics with magneto-plasticity

The micro-cutting of brittle ceramics starts with elastic-plastic deformation followed by severe brittle fracture, which significantly restricts the machinability and application of these materials. Magnetic field-enhanced plasticity (i.e., magneto-plasticity) has shown a positive potential to augment the ductile-brittle transition and machinability but the material removal mechanism of brittle ceramics with magneto-plasticity and its dependence on strain rate remains unclear. In this study, a deformation energy-based model was developed to bring light to the deformation mechanisms affecting the ductile-brittle transition under magneto-plasticity and the corresponding dependency on strain rate. MD simulations assisted the analytical modeling by deriving the orientation-dependent dislocation movement and stress distribution that contribute to single-crystal anisotropy in the surface formation and ductile-brittle transitions during scratching. The proposed model accurately predicted the improvement in ductile-brittle transition under various magnetic field intensities and orientations as confirmed in the experimental magnetic field-enhanced micro-scratching tests on single-crystal calcium fluoride (CaF2). Scratched surface morphologies, acoustic emission (AE) signals, and critical loading conditions demonstrated the improvements in ductile-brittle transition with magneto-plasticity. Additionally, the progression of lateral slip trace and tangential surface pile-up under various magnetic field conditions confirm the direct influence of magneto-plasticity on dislocation mobility and the change in surface formation mechanism of brittle ceramics. This study not only deepens the understanding of the manifestation of magneto-plasticity during the deformation of brittle ceramics, but also opens new avenues for the integration of magnetic field-assisted technology in manufacturing processes.

Computational analysis of conductive fluid flow with tangential components of magnetic flux density and electric field in metallic and non-metallic circular pipe

This paper has focused on the study of flow characteristics of a steady conductive fluid through a circular pipe in the presence of an applied transverse uniform magnetic field. A numerical simulation of the fluid flow was performed using a multi-physics computational tool. The radial velocity distribution due to the effect of the tangential component of induced magnetic flux density and electric fields at various axial positions is examined in metallic and non-metallic surfaces of the circular pipe. This simulation study helps to analyse the effect of drag force on the variation in axial velocity close to the metallic and non-metallic walls. The induced electric potential is directed along the normal to the Laplacian tangential surface of the pipe. In addition to that, sigmoidal-shaped field profiles are observed when the fluid flow crosses from the upstream to downstream of the magnet edge and vice versa along the axial length of the circular pipe. Simultaneously, it is observed that the average velocity of the fluid flow decreases for a laminar and increases for turbulent Reynolds number. Streamline plots pertinent flow variable such as flow velocity are presented for non-conducting and conducting walls.

Erratum to “Navier–Stokes equations in a curved thin domain, Part III: thin-film limit”

There are two flaws in the third part [3] of our study on the Navier--Stokes equations in a curved thin domain. The first one is that the form of Ladyzhenskaya's inequality on a closed surface taken from the arXiv version [2] of the second part of our study is incorrect. The second one is that a wrong claim is used in the proofs of lemmas in [3, Section 6.3] which give estimates for the weighed potential part of a tangential surface vector field. This erratum corrects these flaws.

Revisiting surfaces with a common null geodesic curve in Minkowski 3-space 𝔼13

In this paper, we study the problem of constructing a surface family from a given null geodesic curve in Minkowski 3-space [Formula: see text]. Using the Cartan frame of the given null curve, we present the surface tangent plane is coincident with the curve rectifying plane, and analyze the necessary and sufficient condition for that curve to be null geodesic. Then, the extension to ruled, and developable surfaces are also outlined. As an application, we derive an explicit solution of the Da Rios vortex filament equation lying in the B-scroll.

Sweeping surface due to rotation minimizing Darboux frame in Euclidean 3-space $ \mathbb{E}^{3} $

<abstract><p>In this paper, we address a new version of Darboux frame using a common tangent vector field to a surface along a curve and call this frame the rotation minimizing Darboux frame (RMDF). Then, we give the parametric equation due to the RMDF frame for a sweeping surface and show that the parametric curves on this surface are curvature lines. Consequently, necessary and sufficient conditions for sweeping surfaces to be developable ruled surfaces are derived. Also, we analyze the conditions when the resulting developable surface is a cylinder, cone or tangential surface. We also provide some examples to illustrate the main results.</p></abstract>

Helical surfaces with a constant ratio of principal curvatures

We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio \(a:=\kappa _1/\kappa _2\) of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC surfaces beyond the known rotational ones. Our approach is based on the involution of conjugate surface tangents and on well chosen generating profiles such that the characterizing differential equation is sufficiently simple to be solved explicitly. We analyze the resulting surfaces, their behavior at singularities that occur for \(a>0\), and provide an overview of the possible shapes.

A new construction for harmonic evolute surfaces of quasi tangent surfaces with quasi frame

In this paper, we study a harmonic evolute surface of quasi tangent surface associated with quasi frame. We construct quasi tangent surface with first and second fundamental forms. Moreover, we determine harmonic evolute surface of quasi tangent surface by using these fundamental forms. Finally, we obtain some new results about these new surfaces.

Mold growth on spruce and pine samples in steady state conditions: Time of germination and maximum coverage

Wood is a material that is environmentally friendly and has minimal carbon impact. The durability of wood depends on ambient environmental conditions. This article deals with mold growth on wood samples under constant relative humidity (75 %; 87 %; 95 % RH) and temperature (23 °C). Pine and spruce samples with surfaces oriented along the three principal anatomical directions of wood were prepared. The occurrence of mold was studied by regular microscopic observations. The mold consortium was a mixture of Penicillium sp., Aspergillus sp., and Alternaria sp.The first signs of mold growth on pinewere observed after 7 days for 87 % RH and 12 days for 95 % RH, regardless the surface orientation. Molds on spruce began to grow in 12 to 26 days at 95 % RH in dependence on surface orientation: at first on tangential surface, then on transversal surface, and finally on radial surface. The lower relative humidity of 87 % resulted in a shorter germination time: 7 days for tangential and radial surfaces, and 21 days for transversal surface.

Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram

We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surfacic restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surfacic RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes.

Tangential Ultrasonic-Vibration Assisted Forming Grinding Gear: An Experimental Study.

This study used a forming grinding wheel to machine an involute spur gear with ultrasonic vibration applied to the gear in order to improve the gear processing technology and enhance the gear processing effect. Conventional grinding and ultrasonic vibration-assisted forming grinding gear (TUVA-FGG) tests were carried out. The effects of grinding parameters, such as spindle speed, feed rate, radial grinding depth, and ultrasonic amplitude, on grinding force, grinding temperature, residual stress, surface roughness, and surface morphology were analyzed. The TUVA-FGG significantly improved processing efficiency. With the increase in spindle speed, the maximum reductions in the normal and tangential grinding forces, grinding temperature, and surface roughness reached 33.6, 24.5, 23.9, and 21.6%, respectively. With the increase in feed rate, the respective maximum reductions were 21.4, 19.7, 20.3, and 16.1%. With the increase in radial grinding depth, these values attained 24.6, 20.3, 21.5, and 17.6%, respectively. Finally, with the increase in ultrasonic amplitude, these reductions reached 21.4, 19.7, 21.5, and 19.4%. The maximum residual compressive stress grew by 30.3, 27.5, 30.9, and 27.5% with the increase of wheel rotation speed, feed speed, radial grinding depth, and ultrasonic amplitude, respectively. TUVA-FGG changed the conventional continuous cutting mechanism between the abrasive grain and workpiece into intermittent cutting, reducing grinding forces, grinding temperature, and surface roughness. Moreover, it increased residual compressive stress and improved the micromorphology of the tooth surface, thus enhancing gear machining efficiency.

Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves

In this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the osculating developable surface of the timelike surface along the curve. The ruling of the osculating developable surface is parallel to the osculating Darboux vector field. The main goal of this paper is to classify the singularities of the osculating developable surface. To this end, two new invariants of curves are defined to characterize these singularities. Meanwhile, we also research the singular properties of osculating developable surfaces near their lightlike points. Moreover, we give a relation between osculating Darboux vector fields and normal vector fields of timelike surfaces along curves from the viewpoint of Legendrian dualities. Finally, some examples with symmetrical structures are presented to illustrate the main results.

On derivations of evolving surface Navier–Stokes equations

In recent literature several derivations of incompressible Navier–Stokes-type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling approach and in the coordinate systems in which the resulting equations are represented. This is an overview paper in the sense that we put five different derivations of surface Navier–Stokes equations into one framework. This then allows a systematic comparison of the resulting surface Navier–Stokes equations and shows that some, but not all, of the resulting models are the same. Furthermore, based on a natural splitting approach in tangential and normal components of the velocity, we show that all five derivations that we consider yield the same tangential surface Navier–Stokes equations.

Ray Optical Scattering From Uniform Reflective Cylindrical Metasurfaces Using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction (UTD) is proposed to model electromagnetic (EM) field scattering from curved metasurfaces (MSs). The problem addressed is the illumination of a purely reflective uniform cylindrical MS by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [Kim and Wang (1989)]. The approach is fundamentally based on a representation of the MS using the generalized sheet transition conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction (EF) description of the MS problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [Kim and Wang (1989)]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous EF solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.