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Modular Dynamic Modeling Investigation of Multi-Stage Planetary Gears for Space Manipulator Joints

In order to overcome the shortcomings of the traditional modeling method, a modular modeling approach for the space manipulator joint transmission system in this paper is proposed. In the first place, the multi-stage planetary transmission system for the space manipulator joint is divided into several sub-modules, and the sub-modules of each level are established by considering the factors such as meshing stiffness, meshing errors and so on. In the second place, the dynamic differential equations of the multi-stage planetary transmission system for the space manipulator joint are obtained through the integration of each level modules. The proposed modular modeling approach is convenient for the dynamic behavior analysis and the quick choice of transmission scheme.


Introduction
The planetary gear transmission (PGT) joint has large capacity, high reliability and long service life. However, to achieve a higher transmission ratio, the multi-stage planetary gear transmission is required. Domestic and international research on the dynamic characteristics of the multi-stage planetary gear transmission system is concentrated in the aviation and marine fields [1][2][3][4][5].
All above literatures are based on the whole system, and the dynamic model of the system is established. If the system transmission form is changed, the corresponding dynamic model need be reestablished. The above modeling method is called the traditional integrated modeling. This modeling method is not convenient for quickly selecting the transmission scheme through dynamic performance analysis. The model is not universal, not only complicated and time consuming, but also prone to errors during the reconstruction of the model.
In order to overcome the shortcomings of the traditional modeling approach, the modular modeling idea in this paper is presented to establish a generalized modular dynamic model of the space manipulator joint transmission system, which is not limited to a certain transmission form and helpful for the rapid selection of transmission schemes and the study of dynamic characteristics.

Transmission Scheme of Gear trains for Space Manipulator Joints
The multi-stage 2K-H planetary transmission connected in series is adopted in this study. The schematic diagram of the transmission scheme is shown in Fig. 1. Each stage of the 2K-H planetary transmission consists of a sun gear s, Ni uniform planet gear p, a ring gear r and a planet carrier c. The planet carrier of the upper stage is connected to the sun gear of the next stage. The input and output members of the system are the sun gear of the first transmission stage and the planet carrier of the N-th stage, respectively. respectively. Since the composition of each transmission stage in the transmission scheme for space manipulator joints is the same, only a single-stage calculation model is given in Fig. 2.

Modular Modeling Approach
In this paper, the modular modeling method is adopted to divide the overall model of the transmission system into four-level modules. A generalized dynamic model of the planetary gear transmission system is established via the call of different levels of modules. The specific component of each module model is as following: 3.2.1. Construction of one-level module model. The one-level module is a pair of gear meshing, including internal meshing (i.e. ring and planet gear meshing) and external meshing (sun and planet gear meshing). Based on the torsional dynamic model presented in Fig. 2, considering time-varying mesh stiffness and comprehensive mesh errors, the dynamic model for a pair of gear is constructed.

3.2.2.
Construction of two-level module model. The two-level module includes multiple pairs of gear meshing module as well as the planet carrier and multi-planet module. The multiple pairs of gear meshing modules include the meshing of the sun gear with a plurality of planet gears as well as the ring gear and a plurality of planet gears, and the number of planet gears is limited by the assembly conditions. Taking the planet carrier and multiple planet gears as the whole research object, the dynamic model of the carrier and multi-planet module can be established. ( ) 3.2.4. Construction of four-level module model. Considering the coupling connection among each transmission stage, and calling the first three modules in turn, the four-level module model can be constructed, that is, the nonlinear dynamic differential equations of the multi-stage planetary gear transmission system is able to be set up as follows.