Academic literature on the topic 'Limaçon technolog'

According to the meshing principle of non-circular gears, the meshing characteristic and digital manufacturing technology of Limacon type gears is studied. Based on analyzing the parameterized modeling of pitch curve, transmission characteristics and convexity-concavity analysis on Limacon type gears, the transmission feasibility of this type gear is proved. Through tooth shape design, CAM calculation and analysis with example, and processing simulation, the validity and manufacturability of theoretical design method on this type gear is proved. The research results can provide more systemic theory basis for the design, manufacture, measure and application of Limacon type gears.

Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) respectively are lying in the region bounded by the limaçon ( u − 1 ) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given.

Heart symbols are used as expressions of love. There are several mathematical explanations that can produce a curve in the shape of a heart symbol, the most famous of which is cardioid. Graphs that look exotic like cardioid and limacon can be solved using polar coordinates. Polar equations r = a ± b cos θ and r = a ± b sin θ, with a and b positive are called limacon curves, for the special case a = b is called the cardiod. Computer technology is an alternative that can be used to help this. One of the computer programs that can be utilized as a medium of mathematics learning especially in drawing the heart curve is GeoGebra. GeoGebra is a dynamic mathematical software that combines geometry, algebra, and calculus. GeoGebra program serves as a learning medium that provides a visual experience to students in interacting with the concept of polar coordinates in solving the problem of the heart curve.

The aim of this work is to describe the behavior of three-phase inverters connected to a faulty grid by means of a parametric approach which gives rise to limaçon of Pascal curves and 3D figures formed by the injected currents during the fault. The analytical study is given in the complex form of the transformed Park variables, and the simulation results are obtained by means of MATLABTM. The results show that the parametric analysis can be an easy and useful tool to predict the behavior of three-phase inverters operating under voltage sags, with the aim of achieving fault ride-through (FRT) capability.

Modern science operates with various methods, among which modeling is one of the most popular. The development of information technology allows the study of analogues (models) with the most significant characteristics of the real object. Modeling activities have been considered as useful teaching method in STEM education. Cloud services (like GeoGebra) are effective means for STEM education. The paper features a methodology of forming modeling skills based on STEM projects, which is grounded on modeling interesting curves of Analytic Geometry course. The content of the methodology is a course in Computer Modeling, which includes a module "STEM education and modeling". The module idea is based on the formation of skills required to model interesting curves (ellipse, hyperbola, parabola, conchoid of Nicomedes, limaçon of Pascal, strophoid, cissoid of Diocles, lemniscate of Bernoulli, Cassini oval, cycloidal curves, folium of Descartes, witch of Agnesi, logarithmic spiral). The methodology provides 4 steps (Step 1 – the teacher offers an example of a STEM project, which is discussed in class and solved by the teacher using GeoGebra; Step 2 – students are divided into groups of 3-4 people; Step 3 – the teacher offers a short STEM project (7-10 days), in which students model the curve; Step 4 – students offer their own STEM project (15-20 days), the solution of which is based on the modeling of an interesting curve). To test the effectiveness of the developed methodology, a pedagogical experiment was organized (2019-2021), which was joined by Master's students majoring in "Secondary Education (Mathematics)" and "Secondary Education (Computer Science)". Makarenko Sumy State Pedagogical University (Ukraine) was the experimental base. The effectiveness of the proposed methodology is proved by the sign test at the significant level of 0.05.

Annotation: This article highlights the rich history of irrigation and irrigation in the beautiful Fergana Valley in the snowcapped mountains, as well as interesting historical facts in its study. You can also learn about the findings and conclusions of the leading researchers of their time, as well as a brief description of the ancient irrigation structures. Keywords: Irrigation, Liman method, Panjaatan (fan-like) method, nevillerovka, sepoya, tanob, labgardon, wooden molds, evolution.

The limaçon positive displacement machine is characterised by its internal geometry and unique mechanical motion; both based on a mathematical curve known as the limaçon of Pascal. The limaçon technology offers many advantages, such as compact size and double‐acting functionality, and its great potential for fluid processing applications has been proven by a number of patents and innovative designs in engines, expanders, and pumps. However, no commercial application of the limaçon technology in the field of positive displacement compressors has been reported in the literature. This could be attributed to the fact that the potential of the limaçon technology for gas compression has not been established as yet. The process of establishing potential is necessary before funds and resources are dedicated to investing in prototyping and testing. This process entails a considerable amount of modelling, coding and analysis as one must ensure the embodiment is geometrically capable of delivering suction and compression strokes, ports can be arranged to support the workings of these strokes, a number of measurable parameters can be identified as impacting compressor performance and it is possible to calculate a set of parameters which optimise this performance. To achieve this objective, a comprehensive mathematical model of a limaçon machine, implemented as a compressor,was first developed. The model, which is multi‐physical in nature, spans such domains as kinematics, fluid dynamics, characteristics of the port flow, internal leakage due to seal vibration, dynamics of the discharge valve, and thermodynamics. Subsequently, the simulation of the model has been performed to numerically study the operational characteristics of the limaçon compressor and to investigate the effect of various parameters on the compressor performance. It was found that the increase in the operating speed and pressure ratio would lead to negative effects on machine performance, especially on volumetric efficiency. Additionally, the results of simulations indicated that the level of fluid over‐compression is influenced by the characteristics of the discharge valve. To ensure the suitability of limaçon technology for use in positive displacement compressors, a study was undertaken to determine whether such an embodiment lent itself to optimisation efforts. For this purpose, the thorough mathematical model which has been developed to simulate compressor workings was then used for optimisation purposes whereby a Bayesian optimisation procedure was applied. The optimisation procedure was conducted in a two‐stage fashion where the first stage optimises the machine dimensions to meet volumetric requirements specified by the designer; and the second stage focuses on revealing the optimum combination of port geometries that improves machine performance. A numerical illustration was presented to prove the validity of the presented approach, and the results show that considerable improvements in the isentropic and volumetric efficiencies can be attained. Moreover, the optimised design was tested under different operating speeds and pressure ratios to investigate its robustness. It was found that the optimised design can exhibit relatively stable performance when the working conditions vary within a small bandwidth around that used in the optimisation procedure. The limaçon technology has three embodiments, namely the limaçon‐to‐limaçon (L2L), the limaçon‐to‐circular, and the circolimaçon. The circolimaçon embodiment features using circular arcs, rather than limaçon curves, to develop profiles for the rotor and housing. This embodiment simplifies the manufacturing process and reduces the production cost associated with producing a limaçon technology. A feasibility study of the circolimaçon embodiment was conducted by comparing its performance with that of the L2L type device. The machine dimensions and port geometries obtained from the optimisation procedure were used in the comparative study. A nonlinear three‐degree of freedom model was presented to describe the dynamic behaviour of the apex seal during the machine operation. Additionally, the leakage through the seal‐housing gap was formulated by considering the inertia and viscous effects of the flow. The results from the case study suggest that the circolimaçon embodiment exhibits comparable performance to the L2L‐type machine, despite having more significant seal vibrations. Moreover, it was also discovered that the circolimaçon compressor with a small capacity undergoes a lower level of seal dynamics, indicating better machine reliability.
Doctor of Philosophy