The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

中文翻译：

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曲线面齿轮的数学模型及复合传动的时变啮合特性

曲面齿轮副是一种用于空间有限螺旋运动的变传动比的新型齿轮副。在本文中，一种新开发的曲面齿轮的数学模型被简化并由标准成形器直接获得。结合空间齿轮原理和丝杠理论，进一步分析了曲线面齿轮复合传动特性的后续研究。首先，导出了共轭齿面几何形状以及曲面齿轮的点接触轨迹。其次，通过瞬时丝杠、轴、收缩曲线、共轭节面等基本几何元素，对齿轮副之间的几何关系与相应的啮合特性进行了评价。基于这样的分析，结果表明，齿接触法向与瞬时扭转呈倒数关系，表明目前的曲面齿轮复合传动可以实现具有所需传动比的共轭运动。此外，还揭示了曲面齿轮副的时变滑动特性，即在齿面的所有接触处滚动和滑动作用并存。总之，这项工作为后续研究用标准成形器加工曲线面齿轮提供了理论依据。滚动和滑动作用在齿面的所有接触处并存。总之，这项工作为后续研究用标准成形器加工曲线面齿轮提供了理论依据。滚动和滑动作用在齿面的所有接触处并存。总之，这项工作为后续研究用标准成形器加工曲线面齿轮提供了理论依据。