Development of a method to determine the main gear data of involute gears with a small shaft angle and offset

受创新的应用领域和对锥齿轮的需求增加的推动，将开发一种一致的分析方法来设计这种特殊的齿轮传动装置。除了确定合适的主齿轮数据外，它的主要优点是直接分析优化，以获得共轭啮合，而无需迭代数值模拟。尽管有很大的优势，但许多适用于锥齿轮的应用都是通过其他设计元素的概念来实现的。其中一个原因当然是缺乏专门知识，或者在设计过程中需要使用迭代或模拟工具。因此，仍然缺乏一种一致的分析方法，该方法确定合适的主齿轮数据并考虑预定义的安装位置来优化微几何形状。本研究项目旨在通过开发一种方法来经济地设计具有小轴角和偏移的变厚齿轮，并根据要求来缩小这一差距。此外，数学方法的推广允许转移到其他类型的gearing.The出发点的建议的研究项目是一个等效的圆柱齿轮，这是预先确定尺寸的要求。对于这些数据和所需的安装位置，开发了一种分析方法，以确定具有无侧隙啮合和接触中心点的变截面齿轮的主齿轮数据。在此基础上，通过局部调整主齿轮数据，可以实现共轭啮合或预定的接触图案位置和尺寸。最后，通过大量的参数研究和根据该方法设计的典型变截面齿轮的实验，从理论上验证了该计算方法。研究表明，该方法也可应用于其它类型的齿轮传动，其显著的基础研究特点是，这种计算方法的发展和数学方法对其它类型齿轮的可移植性，可为渐开线齿轮的解释提供重要的发现。

Motivated by innovative fields of application and an increased demand for beveloid gears, a consistent analytical method to design this special gearing is to be developed. In addition to the determination of suitable main gear data, its key benefit is the direct analytical optimization to obtain a conjugated meshing without iterative numerical simulations.Despite great advantages, many applications suitable for beveloid gears are implemented by other concepts with additional design elements. One of the reasons is certainly the lack of know-how or the high effort involved in the necessary use of iterative or simulative tools in the design process. Thus, a consistent analytical method is still lacking that determines suitable main gear data and optimizes the microgeometry in consideration of a predefined mounting position. This research project aims to close this gap by developing a method to design beveloid gears with a small shaft angle and offset economically and in accordance with the requirements. In addition, the generalization of the mathematical approach allows transferability to other types of gearing.The starting point of the proposed research project is an equivalent cylindrical gear, which is pre-dimensioned with respect to the requirements. For these data and the required mounting position, an analytical method is developed to determine the main gear data for beveloid gears with backlash-free meshing and centered point of contact. Based on this, a conjugated meshing or a predetermined contact pattern position and size can be realized by locally adapting the main gear data. Finally, this calculation method is validated theoretically by an extensive parameter study and experimentally by exemplary beveloid gears designed according to this method. In addition, a study shows that the method can also be applied to other types of gearing.The development of this calculation method for beveloid gears and the possible transferability of the mathematical approach to other types of gears are marked by a significant basic research character, from which important findings for the interpretation of involute gears can be gained.