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The load sharing characteristics of the herringbone planetary transmission system are a key indicator for evaluating the bearing stability and reliability of each planet gear in the transmission system. The value of the load sharing coefficient is closely related to the manufacturing error and the assembly error in gear processing and assembly process. Therefore, it is indispensable to study the influence mechanism of these errors on the load sharing characteristics of the transmission system. Nevertheless, researches on the multi-coupling transmission error to the load sharing characteristics of herringbone planetary transmission system did not receive enough attention, but much of the single errors. Based on the centralized parameters theory and the Lagrange method, this research establishes a dynamic model for herringbone planetary transmission system and creatively proposes a study of multi-coupling error which consists of eccentric error, tooth profile error, stagger angle and assembly error. This work shows that the changing regulation of the load sharing characteristics with any one of the above errors is different. However, the load sharing characteristics become worse with the increase of multi-coupling error, in which the eccentric error plays a main role. Therefore, the error control should focus on eccentric error.

In the field of mechanical engineering, involute helical gears are widely used. Compared with the involute spur gear, helical gears have a high bearing strength, more smooth transmission, less impact and less noise. The internal gear pairs have the features of large transmission ratio, low vibration, low noise and low wear and hence are widely used in planetary gear transmission systems. In order to meet the requirements of high strength, high speed of the modern gear transmission systems, a new type of asymmetric involute internal helical gears is designed based on conventional involute gears. This paper discusses the gear shaper cutter modeling for machining this new gear, analyzes the formation principle of asymmetric tooth profile and establishes a three-dimensional modeling by SolidWorks. Through MATLAB simulation, pressure angle, tooth number, coefficient of displacement and contact ratio of conventional and asymmetric gear are compared and analyzed. Using ANSYS, two types of gears are compared on strength in order to demonstrate superiority of asymmetric tooth and further study about the asymmetric internal helical gears.

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Face gear transmission is a kind of space-meshing mechanism that is mainly used in the field of aviation. Compared with traditional transmission, it has the advantages of stability, reliability, low noise, and strong carrying capacity. However, owing to its complex tooth surface, there are no means to accurately model the face gear. Likewise, research based on the geometry is difficult. Therefore, the tooth surface equation of the face gear is derived in this article based on the meshing theory. Based on the equations, the point cloud of the face gear tooth surface is calculated, the complex tooth surface is generated, and the face gear is accurately modeled. Moreover, taking tooth surface friction excitation into consideration, a multi-degree-of-freedom nonlinear dynamic model of face gear transmission system is established, using the adaptive variable step length Runge–Kutta method. As shown in the results, the bifurcation diagram, phase diagram, time history diagram, and Poincaré section diagram are combined to analyze the influence of tooth surface friction and meshing frequency on the dynamic characteristics of the system.

In this study, the dynamic model for the herringbone planetary gear transmission system is established by the lumped parameter method based on the system dynamics and the Lagrange equation, and the impact of the support stiffness and the torsional stiffness on dynamic characteristics is studied. The research results have a guiding significance for the design of the herringbone gear transmission system. In this model, the herringbone gear is treated as a special gear coupled by 2 opposite helical gears, where the stagger angle, comprehensive meshing error, support stiffness, support damping, and load inertia are considered in the analysis of dynamics. Moreover, the dynamic characteristic of the carrier is considered as well. By calculating the meshing force curve of the transmission system, the impact of the stagger angle, supporting stiffness, and the torsional stiffness on meshing force and load sharing coefficient is analyzed. The results show that the stagger angle has an obvious impact on load sharing coefficient while it has little impact on maximum meshing force. And the support stiffness has a more obvious impact on the dynamic characteristics of the system. The recommendary support stiffness of the system is that all of the support stiffness of the sun gear, planetary gear, ring gear, and carrier is 107 N/m. The torsional stiffness has little impact on the dynamic characteristics of transmission system, except the torsional stiffness of planetary gear, and carrier has an obvious impact on load sharing coefficient. The commercial software ADAMS carried out dynamics analysis of the transmission system to verify the necessity validity of the theoretical analysis.

This paper studies the multiple-split load sharing mechanism of gears in two-stage external meshing planetary transmission system of aeroengine. According to the eccentric error, gear tooth thickness error, pitch error, installation error, and bearing manufacturing error, we performed the meshing error analysis of equivalent angles, respectively, and we also considered the floating meshing error caused by the variation of the meshing backlash, which is from the floating of all gears at the same time. Finally, we obtained the comprehensive angle meshing error of the two-stage meshing line, established a refined mathematical computational model of 2-stage external 3-split loading sharing coefficient in consideration of displacement compatibility, got the regular curves of the load sharing coefficient and load sharing characteristic curve of full floating multiple-split and multiple-stage system, and took the variation law of the floating track and the floating quantity of the center wheel. These provide a scientific theory to determine the load sharing coefficient, reasonable load distribution, and control tolerances in aviation design and manufacturing. PrefaceTwo-stage external meshing planetary transmission system is widely used in aviation and special precision transmission field. The T53-L-11 turbo-axis aircraft engine produced by Lycoming (US Company) used two-stage external meshing planetary transmission system as its reducer. Located in the engine head and installed in the intake box, reducer transports the motivation from free turbine shaft to the second sun gear after decreasing speed and increasing torque. Two-stage star gear transmission has multiple duplicate gears with fixedaxes to share the load, its star gears do not revolve, and its characteristics are power split, high transmission power, and only one-side load bearing, and so on. Two-stage star gear transmission uses two-stage star gears, without the ring gear, directly output by two external gears, so that it overcomes the alternating load of planet gear in traditional planetary gear transmission, the difficulty in processing of ring gear, the centrifugal force caused by the rotation of carrier, and intermittent lubrication of planet gear. The system strength, stiffness, and working life and reliability of transmission system have greatly improved by using two-stage fixed-axis external meshing gears. In this paper, a precise load sharing characteristic analysis model is established for all gears with angular displacement compatibility, including bearing manufacturing errors, gear manufacturing errors (eccentricity error, tooth thickness error, and pitch error), installation error, and the meshing error caused by the variation of the meshing backlash resulting from simultaneous floating of all the gears. Research results can be used for aircraft engine and other precision special transmission systems in load sharing coefficients determination, vibration noise reduction, structure optimization, and error precision control. This paper provides sci...

Compared with the conventional gear, the asymmetric gear has better root bending stress and tooth contact stress. Taking a pair of asymmetric involute spur gears as the research object, a model of asymmetric gear considering the influence of friction and shear stress on root bending stress is established. Take the upper boundary point of single tooth meshing area as example, the formula for calculating root bending stress of asymmetric gear is deduced under friction, get the rule of root bending stress without neglecting the friction force and the shear stress by MATLAB. At the same time, we design the plane finite element model of conventional gear (20°/20°) and asymmetric gear (20°/35°) by using APDL. The upper and lower boundary points of the double tooth meshing area, the upper and lower boundary points of the single tooth meshing area, the meshing node are systematically studied, get the change rules of root bending stress in the meshing process under the condition that the friction force cannot be ignored.