| dc.description.abstract | In typical cycloidal planetary gear mechanisms, the K-H-V type and 2K-H type are two primary configurations. Among them, the K-H-V type, commonly known as the Cyclo type cycloidal planetary gear mechanism, has been developed for a long time and is widely utilized in transmission systems requiring compact volume and high reduction ratios. These transmission mechanisms are commonly found in various industrial applications ,including assembly line conveyors, automated guided vehicles, and industrial chemical mixers. As the demand for precision increases, the analysis of the transmission mechanism becomes more complex. Under strict conditions, such as machining and assembly errors, modified tooth cycloid profile, backlash, and bearing clearances, the impact on transmission performance and contact loads between components become crucial factors to consider. Especially, the roller bearings supporting the cycloidal discs bear the maximum load and are the weakest components in the mechanism. On the other hand, under the trend of sustainable decarbonization, the efficiency of transmission mechanisms must be considered. When analyzing these numerous factors, the cycloidal disc, treated as a planar mechanism, is regarded as having three degrees of freedom due to the bearing clearance. However, since the cycloidal disc simultaneously contacts multiple components, the contact analysis becomes even more complex.
The aim of the dissertation is thus to establish a comprehensive analytical model for the K-H-V type cycloid planetary gear mechanism, taking into account the influence of bearing clearance, errors, flank modification, and friction. The model includes meshing analysis of various contact pairs under different output conditions and a loaded tooth contact analysis model (LTCA), based on the influence coefficient method. These four contact pairs analyzed in this dissertation include: cycloid–pin, bearing roller–inner race and outer race, and cycloid–pinshaft. The contact analysis model considers both the presence and absence of bearing clearances, allowing for analysis of different objectives. In the absence of bearing clearance, deformation-displacement relationships of each contact pair under given external loads, as well as force and torque balance equations, are formulated using the influence coefficient method. These equations can be assembled into a matrix form and then iteratively solved to obtain the distributed loads of each contact pair, displacements of the cycloid disc, and angular displacement of the crankshaft. This calculation model is also applied to the design of cycloid tooth profile modification. However, when accounting for bearing clearance, the positions of each contact pair cannot be determined solely through angular relationships. Therefore, this study assumes three directions of displacement of the cycloid disc and the rotational displacement of the crankshaft to derive a loaded tooth contact analysis model considering clearances. Initially, the final positions of each component and the interference or clearance of each contact pair are calculated based on the given displacements. Subsequently, the loads of each contact pair are computed using the stiffness map established by the influence coefficient method. The frictional influence is then incorporated into the force and moment balance equations as the convergence condition for the iterative calculation. Displacement guess value for the next step needed is obtained by solving the tangent stiffness matrix based on the previous position.
The analysis model is then validated through a practical case study of a cycloidal speed reducer with a single-tooth difference. In the case study, the effects of bearing clearance, friction, crankshaft deformation, and errors on contact characteristics are investigated, and the impact of three different clearance values is compared. The analysis results indicate that bearing clearance has a significant impact on the load of the cycloid–pinshaft, and the findings are consistent with the ADAMS model, validating the feasibility of the numerical analysis model. Additionally, the frictional influence increases the input torque to achieve a constant ouptut torque, with an average mechanical efficiency of over 86.5% under normal operating conditions. Crankshaft deformation leads to significant fluctuations in loaded transmission error and loads of various contact pairs. However, bearing clearances have the capability to compensate for the effects of crankshaft deformation.
In the error analysis, the results reveal that the component eccentricity error and tangential error of pinshafts have a significant impact on loaded transmission error. The bearing clearances can compensate for the effects of errors in the load analysis of pin-wheel. In spectral analysis, the loaded transmission error values of each error for the first meshing frequency of pin-wheel are greater than those for the first meshing frequency of pinshaft. Finally, a comparative analysis of two different cycloid modification profiles in the context of all error conditions was conducted. The results show that, apart from noticeable differences in average mechanical efficiency, cycloid profile modifications have minimal influence on the contact load characteristics.
The results of the case study demonstrate that the cycloid planetary gear analysis model proposed in this dissertation not only solves the load analysis problem under bearing clearances but also simulates the impact of different primary component errors and friction on contact characteristics, and evaluates the mechanical efficiency. This analytical approach effectively simulates the transmission performance of the cycloid planetary gear mechanism under various actual operatinbg conditions. Consequently, it serves as a practical tool for assessing performance and optimizing the design of the entire mechanism. | en_US |