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      저자 : FAN Shuqian (검색결과 2 건)
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      • Parametric Surface Defined on Parallelogrammic Domain and its Properties

        FAN Shuqian,ZOU Jinsong,SHI Mingquan (사)한국CDE학회 2013 한국CAD/CAM학회 국제학술발표 논문집 Vol.2010 No.8

        As essential components of many mechanical systems, tooth geometrical properties of spiral bevel gears greatly influence on the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show unique advantage in transmission due to their constant spiral angle property. However, mathematical model suitable for accurate digital modeling, differential geometrical characteristics and related contact analysis methods of tooth surface have not been deeply investigated, since such gears are not convenient to traditional cutting manufacture in gear industry. An accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry. Actually, the tooth surface is a parametric surface defined on parallelogrammic domain. Then, an equivalence proof of the tooth surface geometry is given in order to greatly simplify the mathematical model. As major factors affecting lubrication, surface fatigue, contact stress, wear and manufacturability of gear teeth, differential geometrical characteristics of the tooth surface is summarized employing classical fundamental forms. By using mentioned geometrical properties, manufacturability and its limitation of logarithmic spiral bevel gears is analyzed using precision forging and multi-axis freeform milling, instead of classical cradle-type machine tools based milling or hobbing. Geometry and manufacturability analysis result shows that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multi-axis freeform milling should be further solved.

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        Parametric surface and properties defined on parallelogrammic domain

        Fan, Shuqian,Zou, Jinsong,Shi, Mingquan Society for Computational Design and Engineering 2014 Journal of computational design and engineering Vol.1 No.1

        Similar to the essential components of many mechanical systems, the geometrical properties of the teeth of spiral bevel gears greatly influence the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show a unique advantage in transmission due to their constant spiral angle property. However, a mathematical model suitable for accurate digital modeling, differential geometrical characteristics, and related contact analysis methods for tooth surfaces have not been deeply investigated, since such gears are not convenient in traditional cutting manufacturing in the gear industry. Accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed in this study, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry; actually, the tooth surface is a parametric surface defined on a parallelogrammic domain. Equivalence proof of the tooth surface geometry is then given in order to greatly simplify the mathematical model. As major factors affecting the lubrication, surface fatigue, contact stress, wear, and manufacturability of gear teeth, the differential geometrical characteristics of the tooth surface are summarized using classical fundamental forms. By using the geometrical properties mentioned, manufacturability (and its limitation in logarithmic spiral bevel gears) is analyzed using precision forging and multiaxis freeform milling, rather than classical cradle-type machine tool based milling or hobbing. Geometry and manufacturability analysis results show that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multiaxis freeform milling also need to be solved in a further study.

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