• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.

• Transactions of the Korean Society of Automotive Engineers
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• v.10 no.3
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• pp.218-226
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• 2002

This study was carried out to develop continuously variable-speed transmission(CVT) fur an agricultural tractor. The full-toroidal variator mechanism with flour discs and six rollers was utilized as a device fur changing speed ratio continuously. In system layout design, the sizes of the roller cylinders and the end-load cylinder, which were critical factors for controlling the variator, were designed. The planetary gear unit and six pairs of the gear assemblies were designed to establish the maximum speed of the vehicle at 30 ㎞/hr. In addition, the hydraulic clutch, the silent chain, the hydraulic manifold and the electronic controller were designed. Based on the design, a prototype CVT was developed and tested. Test results show that the CVT developed in this study could successfully provide variable speed of the tractor.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2000.11b
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• pp.162-169
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• 2000

This study was carried out to develop a continuously variable-speed transmission(CVT) for agricultural tractor. A full-toroidal CVT mechanism with four discs and six rollers was selected as a device for changing speed ratio continuously. In the step of system layout design, the sizes of roller cylinders and end-load cylinder, which were critical factors for controlling the variator, were designed. Also the control pressure range was designed to limit the contact pressure of variator. In order to make the maximum speed of vehicle as 30km/h, the planetary gear and the six pairs of gears were designed. Also the hydraulic clutch, silent chain, hydraulic manifold and electronic controller were designed. After the design, a prototype with CVT controller was developed and tested. The speed of vehicle was changed continuously to the speed set by driver and the settling time was about 0.52 second at the step-response test (reduction ratio of variator 2.0 to 1.0), which was acceptable as a response time for working with tractor.