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

在创新的应用领域和对锥齿轮日益增长的需求的推动下，需要开发一种设计这种特殊齿轮的一致的分析方法。除了确定合适的主齿轮数据外，它的主要优点是直接进行解析优化以获得共轭啮合，而不需要迭代数值模拟。尽管有很大的优势，但许多适用于锥齿轮的应用是通过其他概念和附加设计元素来实现的。原因之一当然是缺乏技术诀窍，或者在设计过程中必要地使用迭代或模拟工具时需要付出很高的努力。因此，仍然缺乏一致的分析方法来确定合适的主齿轮数据并考虑到预定义的安装位置来优化微观几何形状。本研究项目旨在通过开发一种经济地、符合要求的设计小轴角和偏心的锥齿轮的方法来缩小这一差距。此外，数学方法的泛化允许转移到其他类型的齿轮。拟议的研究项目的起点是一个等效的圆柱齿轮，它是根据要求预先确定尺寸的。对于这些数据和所需的安装位置，提出了一种确定无侧隙啮合中心接触点的锥齿轮主齿轮参数的解析方法。在此基础上，可以通过局部适配主齿轮数据来实现共轭啮合或预定的接触图案位置和大小。最后，通过大量的参数研究和按该方法设计的典型锥齿轮的实验，从理论上验证了该计算方法的有效性。研究表明，该方法也可应用于其他类型的齿轮，该计算方法的发展和数学方法在其他类型齿轮上的可移植性具有显著的基础研究特点，可为渐开线齿轮的解释提供重要的研究成果。

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.