Rational Angles Research Articles

Study on the stability for non-uniform helix angle tools in the milling process

ABSTRACT Uniform helix angle tools cannot effectively suppress the chatter in the high machining process. Consequently, cutters with non-uniform helix and pitch angles are more and more common in various milling operations. To suppress the regeneration chatter, it is crucial to study the stable behavior of the tools. Therefore, this paper considers the relationship between the pitch angle and the chatter stability defined by the regeneration factor (RF). Further, the governing equation of the machining system with non-uniform helix angle cutters is formulated. Based on this model, the Enhanced Multistage Homotopy Perturbation Method (EMHPM) is used to compute the stability lobes. To validate the theory in this paper, the stability lobes are predicted and compared with the results in the literature. The results show that the rational helix and pitch angle cutters exhibit increases stability in the milling process.

Підвищення ефективності використання ріжучих елементів спеціальних фасонних фрез до верстатів КЖ20

A significant part in the structure of production costs associated with restoring the current operability of locomotive wheels by processing on the KJ20 machine is amounted by tool costs. The cost of the tool, especially hard-alloy, is constantly increasing. The restoration of the working capacity of hard-alloy cutting elements is carried out by turning them in the tool holder (knife) at a certain angle around the axis of this element. The new technique for the effective use of special shaped mills is based on determining the rational angle of rotation of the cutting elements. A promising direction for the use of cutting elements is also the restoration of the properties of worn elements for their reuse. EDM processes are especially effective in tool production in the manufacture of special tools. The authors developed and proposed a technology for restoring the working capacity of cutting elements that have already worked out their resources. The technology proposed by the authors makes it possible to introduce a system of cost-effective and rational operation for the use of part of worn out, but suitable for restoration, replaceable cutting elements, for their reuse in the repair of the working surface of wheelsets of rail vehicles on KJ20 machines.

Geometric error compensation of five-axis ball-end milling based on tool orientation optimization and tool path smoothing

Geometric error compensation may affect the quality of the machined surface textures due to the arbitrary adjustment of cutter locations. This paper proposes one geometric error compensation of five-axis ball-end milling in order to reduce the influences on the machined textures, including the tool orientation optimization of single cutter location and the smoothing of the overall tool path. At first, tool center limitation method is introduced briefly with the construction of the new cutter location. Second, CSO (chicken swarm optimization)-based tool orientation optimization is proposed for geometric error compensation. The inclining angle and the rational angle around the nominal tool orientation are chosen as the chicken. The tool center limitation method is used for the calculation of the fitness of the chicken. Next, the smoothing of the whole tool path is established to avoid the mutation of rotation angles including the evaluation of the smoothness and the inserting and optimizing of the new cutter locations. Finally, simulation and cutting experiments are proposed on the SmartCNC500_DRTD machine tool to testify the effectiveness of the geometric error compensation.

Shiyan Taihe Hospital Brand Promotion Organizational Communication Strategy

Taihe Hospital, as the largest grade A class 3 hospital and regional medical center in Shiyan City, will face more opportunities and challenges in the future under the background of the gradual deepening of China’s medical and health system reform and the rapid development of China’s medicine. Facing severe external environment, taihe hospital must from the rational Angle analysis the current common way and the reason about its own brand, and can clearly identify the advantages and disadvantages of current communication, based on the actual situation of taihe brand, concrete improvement measures are put forward, and can understand why brand need to implement these improvements, to obtain the benefits of taihe hospital brand, plan for the future Organizational Communication about taihe hospital brand strategy.

Complete and computable orbit invariants in the geometry of the affine group over the integers

The subject matter of this paper is the geometry of the affine group over the integers, $${\mathsf {GL}}(n,{\mathbb {Z}})\ltimes {\mathbb {Z}}^n$$ . Turing-computable complete $${\mathsf {GL}}(n,{\mathbb {Z}})\ltimes {\mathbb {Z}}^n$$ -orbit invariants are constructed for rational affine spaces, angles, segments, triangles and ellipses. In rational affine $${\mathsf {GL}}(n,{\mathbb {Q}})\ltimes {\mathbb {Q}}^n$$ -geometry, ellipses are classified by the Clifford–Hasse–Witt invariant, via the Hasse–Minkowski theorem. We classify ellipses in $${\mathsf {GL}}(n,{\mathbb {Z}})\ltimes {\mathbb {Z}}^n$$ -geometry combining results by Apollonius of Perga and Pappus of Alexandria with the Hirzebruch–Jung continued fraction algorithm. We then consider rational polyhedra, i.e., finite unions of simplexes in $${\mathbb {R}}^n$$ with rational vertices. Markov’s unrecognizability theorem for combinatorial manifolds states the undecidability of the problem whether two rational polyhedra P and $$P'$$ are continuously $${\mathsf {GL}}(n,{\mathbb {Q}})\ltimes {\mathbb {Q}}^n$$ -equidissectable. The same problem for the continuous $${\mathsf {GL}}(n,{\mathbb {Z}})\ltimes {\mathbb {Z}}^n$$ -equidissectability of P and $$P'$$ is open. We prove the decidability of the problem whether two rational polyhedra P and $$P'$$ in $${\mathbb {R}}^n$$ have the same $${\mathsf {GL}}(n,{\mathbb {Z}})\ltimes {\mathbb {Z}}^n$$ -orbit.

Rationalization of parameters of hydraulic dampers of a carriage

The possibility of the car dynamic performance improvement is studied through structural changes (modernization) of the passenger bogie. Based on the calculations of the natural oscillations of the car, the critical values were determined and rational values of the damper resistance coefficient were chosen for vertical and lateral vibrations. It was concluded that with the forced spatial fluctuations of a carriages on KCCW-CRI bogies the required damping value of the vertical oscillations should be twice as large as for the lateral ones; important factors in damping of the car oscillations are the central suspension dampers. The rational angle of installation of the hydraulic damper in the central suspension and the use of separate action in the central suspension of hydraulic dampers are justified. The proposed version of the modernization of the bogie can improve the smoothness indicators of the car by 25-30%.

Spherical tetrahedra with rational volume, and spherical Pythagorean triples

We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast families, discovered by computational efforts, of positive examples that confirm this conjecture. As a by-product, we also obtain a classification of all spherical Pythagorean triples, previously found by Smith.

Analytical determination of the rational angle of lifting: the soil cooking organ

The aim of the study is to search for the analytical dependence of the force of resistance of the wedge on the lifting angle in the case of working with wet soil, which does not crumble into fragments, but slides along the wedge in the form of a continuous tape. Tillage tools can have front and rear sharpening angles. The front angle raises the soil layer, and this action is most common in tillage. The rear corner seals the bottom of the furrow, so it is undesirable in plows. To determine the rational angle of inclination of the entire working surface under working conditions with wet soil, an analytical equation has been obtained, which is applicable if the technological indicators of the soil are observed in a particular field, especially indicators of soil sticking to the working surfaces. In this equation, the traction resistance of the wedge depends on the density of the soil, friction coefficient, tensile strength and shear strength. In the calculations, the deformation of the soil layer was taken inherent in the wetted state with the presence of plant residues, that is, the soil retains the shape of a continuous ribbon in its movement along the working surface of the wedge. According to the results of field studies of the experimental and basic plows, it was determined that on loamy soil with a moisture content of 16 to 22%, an rational angle of elevation of the tillage tool can be taken as an angle of 18 °. An experimental plow with a plowshare angle of 18 ° compared to a basic plow with a lifting angle of 30 ° showed an increase in productivity by 19% and a reduction in specific fuel consumption by 17% due to a decrease in traction resistance and, as a result, by reducing the likelihood of sticking of the soil and rare stops for cleaning the working bodies.

Genetics of Malaria Inflammatory Responses: A Pathogenesis Perspective.

Despite significant progress in combating malaria in recent years the burden of severe disease and death due to Plasmodium infections remains a global public health concern. Only a fraction of infected people develops severe clinical syndromes motivating a longstanding search for genetic determinants of malaria severity. Strong genetic effects have been repeatedly ascribed to mutations and allelic variants of proteins expressed in red blood cells but the role of inflammatory response genes in disease pathogenesis has been difficult to discern. We revisited genetic evidence provided by inflammatory response genes that have been repeatedly associated to malaria, namely TNF, NOS2, IFNAR1, HMOX1, TLRs, CD36, and CD40LG. This highlighted specific genetic variants having opposing roles in the development of distinct malaria clinical outcomes and unveiled diverse levels of genetic heterogeneity that shaped the complex association landscape of inflammatory response genes with malaria. However, scrutinizing genetic effects of individual variants corroborates a pathogenesis model where pro-inflammatory genetic variants acting in early infection stages contribute to resolve infection but at later stages confer increased vulnerability to severe organ dysfunction driven by tissue inflammation. Human genetics studies are an invaluable tool to find genes and molecular pathways involved in the inflammatory response to malaria but their precise roles in disease pathogenesis are still unexploited. Genome editing in malaria experimental models and novel genotyping-by-sequencing techniques are promising approaches to delineate the relevance of inflammatory response gene variants in the natural history of infection thereby will offer new rational angles on adjuvant therapeutics for prevention and clinical management of severe malaria.

Predicting the producing well stability in the place of its curving at the underground coal seams gasification

The relevant issues have been studied of ensuring the stability of producing wells in the place of their curving when uncovering the mining extracted area for the underground gas generator operation. It is emphasized that the design planning of efficient operation of underground gas generators in downhole gasification technology is impossible without consideration of the stress state of the rock massif, which can lead to a danger of the wellbore cutting and emergency shutdown of the technological system operation. The parameters of geomechanical models have been developed and substantiated for the study of the stress state of the “rock massif – producing well” system under the conditions of the Lviv-Volyn coal basin. A computer simulation has been performed of change in the stress state of a laminal massif around a well with a curvature radius in the range of 5 – 25 m with the use of the finite element method. The exponential function has been revealed of the tensile stresses value in the roof of the seam from the angle of the producing well entry into the coal seam. It is recommended the rational angle of a well entry into the coal seam, which is in the range of 21 – 28 degrees, and an appropriate curvature radius will be 5 – 10 m.

Conformal amplitude hierarchy and the Poincaré disk

The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d O(n) model is studied as a function of n. For a generic value of n, the 4-point function has infinitely many amplitudes, whose landscape can be very spiky as the higher amplitude changes its sign many times at the simple poles, which generalize the unique pole of the energy operator amplitude at n = 0. In the stadard parameterization of n by angle in unit of π, we find that the zeros and poles happen at the rational angles, forming a hierarchical tree structure inherent in the Poincaré disk. Some relation between the amplitude and the Farey path, a piecewise geodesic that visits these zeros and poles, is suggested. In this hierarchy, the symmetry of the congruence subgroup Γ(2) of SL(2, ℤ) naturally arises from the two clearly distinct even/odd classes of the rational angles, in which one respectively gets the truncated operator algebras and the logarithmic 4-point functions.

Reflection of owner’s attributes in financing decisions of SMEs

ABSTRACTThe purpose of the study is to examine the influence of demand side factors on the financing preferences of small and medium-sized enterprises (SMEs). Demand side factors include SME owner/manager’s business goal, attitude towards risk and control over business, networking ties and their personal attributes. The study uses a structured questionnaire designed with the help of previous studies. A total of 309 valid responses are analysed to accomplish the research objectives. The study uses various statistical techniques namely k-means cluster analysis, exploratory factor analysis and hierarchical regression. The study uses a segmentation approach and classifies the respondents into three categories – risk avoiders, growth seekers and steady players. Furthermore, the results reveal the importance of personal attributes and networking ties of SME owner/manager with banks and suppliers. The study contributes to the extant literature of SME financing and highlights the influence of demand side factors on financing preferences of SMEs. The study also provides a new and rational angle of examining the financing preferences of SMEs. It highlights the need for awareness amongst SME owner/manager towards their behaviour and its impact on the financing decisions of firms.

Harmonic global parametrization with rational holonomy

We present a method for locally injective seamless parametrization of triangular mesh surfaces of arbitrary genus, with or without boundaries, given desired cone points and rational holonomy angles (multiples of 2π/ q for some positive integer q ). The basis of the method is an elegant generalization of Tutte's "spring embedding theorem" to this setting. The surface is cut to a disk and a harmonic system with appropriate rotation constraints is solved, resulting in a harmonic global parametrization (HGP) method. We show a remarkable result: that if the triangles adjacent to the cones and boundary are positively oriented, and the correct cone and turning angles are induced, then the resulting map is guaranteed to be locally injective. Guided by this result, we solve the linear system by convex optimization, imposing convexification frames on only the boundary and cone triangles, and minimizing a Laplacian energy to achieve harmonicity. We compare HGP to state-of-the-art methods and see that it is the most robust, and is significantly faster than methods with comparable robustness.

Modeling the operation of a screw L-shaped knife of a tiller

During the operation, standard L-shaped knives are exposed to various loads. The shape of the L-shaped knife blades does not meet the requirement of performing sliding cutting, which leads to an increase in the energy intensity of milling the soil. To ensure optimal cutting conditions without weed-covering and knife blocking, it is necessary that in any section of the blade (in the plane of rotation) the angle of its setting у (cutting) is constant. Therefore, the blade of the knife should be made on a screw line, which will ensure its smooth entry and sliding cutting when moving in the soil. The purpose of the study is to improve the quality and reduce the energy consumption of soil cultivation by selecting a rational angle for installing the blade and optimizing the parameters of the screwed L-shaped cutter blades. To study the work and the loading process of the screw L-shaped cutter knife, the finite element method was used from the APM FEM application library of the KOMPAS-3D system. The design of the knife was broken into elements to show their movements and deformations through the displacements of the boundary points (knots) of the element, then the nodal displacements, deformations and stresses were determined. In the course of the study, the dependence of the values of linear displacements and stress values was studied depending on the angle of installation of the knife blade (у = 35° ... 60°). The results of the study showed that as the angle of the blade was increased to у = 60 °, the total linear displacements decreased by 18 % reaching 0,6978 mm, compared to у = 35 ° (0,8455 mm) at a maximum load of 2000 N. The knife with an installation angle у = 60° has safety factor values higher than a knife with у = 35° for all load stages (500, 1000, 1500 and 2000 N). The screw knife with a large installation angle is most suitable for milling soil with slip, which is typical for sod processing. As a result of the research it was proposed to use knives with a screw working surface for milling the soil with high quality.

Spherical quadrangles with three equal sides and rational angles

When the condition of having three equal sides is imposed upon a (convex) spherical quadrangle, the four angles of that quadrangle cannot longer be freely chosen but must satisfy an identity. We derive two simple identities of this kind, one involving ratios of sines, and one involving ratios of tangents, and improve upon an earlier identity by Ueno and Agaoka. The simple form of these identities enable us to further investigate the case in which all of the angles are rational multiples of π and produce a full classification, consisting of 7 infinite classes and 29 sporadic examples. Apart from being interesting in its own right, these quadrangles play an important role in the study of spherical tilings by congruent quadrangles.

Embedding formulae for scattering in a waveguide containing polygonal obstacles

For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method.

Calculation of design relative density for rational sandwich structure with truss core

A technique of design analysis of the relative density of core and face sheets (skin) for rational sandwich structure with truss core is proposed. The examples of calculating the rational angle of truss core slope and design values of sandwich structure density are presented.

Forecasting of operational indicators of grinding tools with the controlled form and orientation of abrasive grains

The interconnection of the abrasive grain front angle parameter with the form, orientation and wear out parameters is investigated. The form of the abrasive grains was estimated by means of form coefficient which represents the relation of diameters of the spheres described around contours of grains, to diameters of the spheres entered in them. The spatial orientation angle of the abrasive grains was defined between main (i.e. the biggest) axis of the grains and the cutting plane. It is established that, depending on an orientation angle at increase in a form coefficient of the abrasive grains can be either an increase or a decrease in the values of their front angles. In most cases, with an increase in a form coefficient of the oriented grinding grains (at orientation angles Θ=10°÷125°) the growth of their front angles is fixed. At tangential orientation of grains (Θ=0°) and at the close directions of orientation (Θ=135°÷80°) the return picture is observed. Also established that the longer the abrasive grain wears along the main axis and located in the tool body, the larger is its front angle. Besides that, the front angles of the abrasive grains reach the maximum positive values at orientation angles Θ=22.5°÷45°.Dependence of tension in grains during the work with parameters of their form, orientation and depth of embedment in the bundle is investigated. It was found that for all orientation angles of grains their tension significantly increases with an increase in their form coefficient. Besides that it is confirmed that the deeper the grain is in the bundle, the lower the tension is there. Also found that tension is minimal when the grains are tangential orientated. Further on increase the option of the grains in the direction of action of the cutting force follows. Such option of orientation is the most rational both from the point of view of minimization of tension, and for ensuring rational sizes of front angles of the abrasive grains. The rational angle of grain orientation for cutting disc are in range Θ=65°÷75°.The joint analysis of dependences of front angles and tension in grains from factors of their form and orientation allows the prediction of operating characteristics of grinding tools at the design stage for specific tasks and processing conditions.

Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

The discrete Fourier slice theorem is an important tool for signal processing, especially in the context of the exact reconstruction of an image from its projected views. This paper presents a digital reconstruction algorithm to recover a two dimensional (2-D) image from sets of discrete one dimensional (1-D) projected views. The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise. A mapping of discrete projections is constructed to allow aperiodic projections to be converted to projections that assume periodic image boundary conditions. Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation. The discrete projection angles are selected so that the set of remapped 1-D slices exactly tile the 2-D DFT space. This permits direct and mathematically exact reconstruction of the image via the inverse DFT. The reconstructions are artefact free, except for projection inconsistencies that arise from any additive and remapped noise. We also present methods to generate compact sets of rational projection angles that exactly tile the 2-D DFT space. The improvement in noise suppression that comes with the reconstruction of larger sized images needs to be balanced against the corresponding increase in computation time.

A Riemannn surface approach for diffraction from rational wedges

This paper aims at the explicit analytical representation of acoustic, electromagnetic or elastic, time-harmonic waves diffracted from wedges in R3 in a correct setting of Sobolev spaces. Various problems are modelled by Dirichlet or Neumann boundary value problems for the 2D Helmholtz equation with complex wave number. They have been analyzed before by several methods such as the Malinzhinets method using Sommerfeld integrals, the method of boundary integral equations from potential theory or Mellin transformation techniques. These approaches lead to results which are particularly useful for asymptotic and numerical treatment. Here we develop new representation formulas of the solutions which are based upon the solutions to Sommerfeld diffraction problems. We make use of symmetry properties, which require a generalization of these formulas to Riemann surfaces in order to cover arbitrary rational angles of the wedge. The approach allows us to prove well-posedness in suitable Sobolev spaces and to obtain explicit solutions in a new, perhaps surprising, form provided the angle is rational, i.e., α = πm/n where m,n ∈ N . Mathematics subject classification (2010): 35J05, 78A45, 45E10, 47B35.