• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.649-655
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• 2005

The universal mapping property and the Gelfand- Kirillov dimension of a skew enveloping algebra are studied and it is proved that every Poisson enveloping algebra is a homomorphic image of a skew enveloping algebra.

• Journal of the Korean Society for Precision Engineering
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• v.30 no.8
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• pp.785-789
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• 2013

Worm gear sets may be either single- or double-enveloping. In a single-enveloping set, the worm wheel is cut into a concave surface, thus partially enclosing the worm when meshed. The double-enveloping worm gear is similar to the single-enveloping gear; however, the worm envelopes the worm gear. Thus both are throated. The double-enveloping worm gear has more of the tooth surface in contact than the single-enveloping worm gear. The larger contact area increases the load-carrying capacity. For this reason, double-enveloping worm gearing is widely applied in heavy-duty machinery, for applications including construction and metallurgy. In this paper, we designed a compact reduction gear that is highly efficient using double-enveloping worm gears. We calculated the bearing load in the worm gearing to select the bearing and the housing surface area according to the recommended values from AGMA(American Gear Manufacturers Association). The finite element method was used to assess the structural integrity.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.87-91
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• 2002

This note consists of some efficient examples to support the notion of enveloping semigroup compactification and also employ this notion to obtain the universal reductive compactification.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.29-39
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• 2001

For a Poisson Hopf algebra A, we find a natural Hopf structure in the Poisson enveloping algebra U(A) of A. As an application, we show that the Poisson enveloping algebra U(S(L)), where S(L) is the symmetric algebra of a Lie algebra L, has a Hopf structure such that a sub-Hopf algebra of U(S(L)) is Hopf-isomorphic to the universal enveloping algebra of L.

• International Journal of CAD/CAM
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• v.3 no.1_2
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• pp.13-17
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• 2003

Hybrid method of representing geometric entities as combination of boundary (B-rep) and functional (F-rep) representations is presented which can be used as a basis of solid modeling kernel. It contains whole functionality of classic B-rep kernel, and also supports enveloping (sweep of solid body). Principles and keysolutions are considered. Example of a real task that comes from gearing is provided.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.253-254
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• 2006

In this investigation, the authors propose a novel method of Enveloping Helical gear generation by shaping operation and a math model to simulate its manufacturing process. The tooth geometry of the Enveloping Helical Gear is analytically determined by simulating the conjugate motion between the workpiece(Enveloping Helical gear) and cutting tool(shaper cutter) in the generation process. It is expected that such math modeling capability will give engineers an opportunity to correct manufacturing related issues in the design phase and thereby reduce the developing period.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.521-522
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• 2013

• Transactions of Materials Processing
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• v.28 no.4
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• pp.183-189
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• 2019

Cylindrical worm reducers are generally used in various fields and forms throughout the industry, and demand is increasing due to their role as an integral part of the industry. Market trends require high-load, high-precision components, and small-sized reducers with large loads. When using a cylindrical worm reducer, a reducer designed with a reduced center distance while maintaining the same output torque results in gear wear. To overcome this difficulty, an enveloping worm gear reducer is introduced and studied. In this paper, three types of end mill tools are used to evaluate the tooth profile accuracy for each tool shape during machining of the tooth profile for a non-developed surface worm thread. The effect of the endmill shape on the accuracy of the tooth profile was analyzed by performing 3D modeling of the surrounding worm tooth profile based on the Hindley method. In this study, we analyzed tooth profile accuracy, tooth surface roughness, and tooth surface machining time, etc. Through the study, efficient machining conditions for the enveloping worm gears and the influence of parameters on the process were presented.

• Transactions of Materials Processing
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• v.29 no.3
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• pp.144-150
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• 2020

In this paper, we propose the generation of a double enveloping worm thread profile with a non-developable ruled surface. Thread surface machining cuts all the way from the tip to the tooth root at one time, like full-face contact machining, rather than cutting several times like point machining. This cutting can reduce the cutting duration and achieve the smooth surface that does not require a grinding process for the threaded surface. The mathematical model of the cutting process was developed from theoretical equations, and the tooth surface was generated using two parameters and modeled in the CATIA using the generated Excel data. Additionally, the machining process of the worm was simulated in a numerical control simulation system. To verify the validity of the proposed method, the deviation between the modeling and the workpiece was measured using a 3D measuring machine.