Dissertation Defense: A Dynamic Load Distribution Model for Helical Gear Pairs Having Various Manufacturing Errors

Michael Benatar

Abstract: This dissertation research focuses on developing and experimentally validating a three-dimensional load distribution model for helical gear pairs that is suitable for both quasi-static and dynamic conditions. As one phase of this research, the modeling work is carried out in two main steps. The first step focuses on quasi-static conditions by (i) developing a generalized procedure to define instantaneous contact lines along the gear mesh interface, (ii) formulating the flexibility introduced by the support structures such as bearings and shafts in a systematic way, and (iii) including gear blank related manufacturing errors such as eccentricity and wobble. The contact problem under these conditions, governed by compatibility and equilibrium equations, are solved by using an iterative elastic contact algorithm. In the second step, dynamic effects are included in the model of the first step to develop a dynamic load distribution model of a helical gear pair having the same novel features of the quasi-static model. For this, the compatibility equations of the quasi-static model are coupled to the equations of motion in the state-space representation and solved by using a backward Euler method. The other phase of this research is focused on validation of the quasi-static and dynamic load distribution models. As very little experimental helical gear data is available in the literature, an experimental study is conducted to generate an extensive database for validation of the models of this study as well as for guiding future helical gear modeling efforts. The experimental study considers a family of unity-ratio helical gear pairs having varying amounts of micro-geometry modifications as well as several spur gears having certain manufacturing errors. An encoder-based measurement system is devised to quantify the static transmission error at various transmitted torque levels to form Harris charts and define the design load values. An accelerometer-based measurement system is also incorporated with the same setup to evaluate the dynamic transmission error of the same test articles within wide speed ranges of operation. The predictions of the proposed models are compared to the experimental measurements to demonstrate that the models are accurate under both quasi-static and dynamic conditions, with or without gear blank related manufacturing errors. Given their computational efficiency, the proposed models with their novel capabilities are suitable for design optimizations studies.
 

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