Research on dynamic load sharing characteristics of double input face gear split-parallel transmission system

The face gear power-split system has huge superiorities over the traditional transmission form in the application of modern rotorcraft, and it has become the research trend of the industry in recent years. Thus this paper took the double input face gear split-parallel transmission system used in the rotorcraft as the research target, and established its dynamics model through the lumped parameter theory. Based on the Newtonian second law, the dynamics equations were built and solved to gain the meshing forces and load sharing coefficients of the transmission system. Simultaneously, the impacts of the eccentric errors, support stiffness, and torsional stiffness on the load sharing characteristics were studied. The results show that the meshing forces and load sharing coefficients of each gear pair have periodic changes; the eccentric errors of each drive stage gear have only a significant effect on the corresponding drive stage. Moreover, the changes in the support stiffness of the split-torque shafts and double gear shafts mainly affect the load distribution of the parallel stage, and the shaft torsional stiffness is less sensitively to maintain load balance. In addition, the increment of the shaft stiffness increases the load sharing coefficients of the corresponding gear pairs.

Experimental investigation of the dynamic load sharing of planetary gearboxes

Due to their compactness and power density, planetary gearboxes are used for a wide range of high-performance applications in the automotive, aviation and marine sector. Aerospace applications in particular benefit from a full use of the load capacity potential to meet the requirements for lightweight construction and efficiency. Against this background, the load sharing between the individual planetary gears plays a decisive role. A uniform load sharing enables the design of the single tooth meshes without load increases and oversizing. However, due to manufacturing and assembly deviations, a perfect load sharing is technically not feasible. These load increases are taken into account in the standard calculation of the load capacity of planetary gearboxes by the mesh load factor Kγ. The load sharing in planetary gearboxes is influenced by a number of factors, such as the rigidity of shafts, housing and bearings, the number of planets, the quality of the gear wheels and the operating conditions. Detailed simulations or extensive experimental measurements are required to determine the exact load sharing. For new designs of planetary gearboxes, there are only simplified assumptions available, based on the number of planets and a rough estimation of the operating range. Especially additional dynamic forces, due to operation in high-speed ranges or near resonance frequencies, can lead to a considerable change of the dynamic load sharing compared to the static load sharing and cause an uncertainty in the design. Thus, in this paper the dynamic load sharing behaviour is investigated from 0 to 6800 rpm sun speed for different loads. Based on the experimental data recommendations for the design of planetary gearboxes under consideration of the operating conditions are derived.

Study on dynamic load-sharing characteristics of face gear dual-power split transmission system with backlash, support and spline clearance

The dynamic load-sharing characteristics of aircraft face gear dual-power split transmission system (FGDPSTS) are taken as the research object. Considering the factors of time-varying meshing stiffness, comprehensive error, backlash, support clearance, spline clearance, torsional stiffness, and support stiffness, the dynamic load-sharing model was constructed based on the lumped-parameter method. The loaded tooth contact analysis (LTCA) simulation method was used to calculate the time-varying meshing stiffness. The dynamic load-sharing coefficient (DLSC) is obtained by using Runge–Kutta method. The influences of errors, backlash, support clearance, spline clearance, torsional stiffness and support stiffness on DLSC were analyzed, and the biggest factors affecting dynamic load-sharing performance were found out. The results show that the influence of the backlash of the two-stage herringbone gear pair on the DLSC is more sensitive. The influence of support clearance on the DLSC is less. The load-sharing coefficient increases with the increase of the installation error and eccentricity error, and the influence of the error of the two-stage gears on the system load-sharing performance is the most sensitive. The torsional stiffness has little effect on the load-sharing coefficient of one stage but has great effect on the two-stage load-sharing coefficient. The influence of support stiffness on the DLSC of two-stage is stronger. It provided a theoretical basis for the dynamic stability optimization design of the system.

Dynamic Load Sharing Behaviours of Planetary Gear Trains and Parameter Study through Perturbation Analysis

In this paper, an analytical solution on the dynamic mesh forces of planetary gear trains (PGTs) is proposed by investigating a lumped-parameter model. By using the method of multiple-scales (MMS), closed-form expressions of mesh force under the effects of manufacturing and assembly errors are obtained. From these expressions, the effects of several key factors such as the tooth thickness error, pin position error, applied torque, support stiffness of sun gear, and tooth profile modifications (TPM) on dynamic load sharing behaviours are explored. Numerical integration is carried out to verify the validation of the proposed method, and the developed expressions are also validated by comparing the results with previously published predictions. The results for several examined PGT systems show that the key factors abovementioned affect the dynamic load sharing behaviours as both static and dynamic factors. An important new conclusion obtained by this work is that proper tooth profile modifications keep the dynamic load sharing factors almost equal to the results obtained under static conditions. This conclusion provides the possibility to simplify the dynamic analysis to the static analysis on the dynamic load sharing problems.

Dynamic Load Sharing of Combined Pile Raft Foundation (CPRF) for Reinforced Concrete Structures

Combined pile raft foundation (CPRF) is one of the emerging concepts for providing a cost-effective and efficient solutions for heavily-loaded structures. However, predicting the behaviour of such foundations, especially the load sharing between raft and pile is a challenge due to its inherent complex interactions. Existing analysis methods are either bound within a range of simplifying assumptions or sometimes computationally demanding. Hence, an attempt has been made to evolve a simple and easily implementable methodology, considering non-linear degrading behaviour of soil in a rational manner. The approach has first been validated with measured response during an experimental centrifuge testing of a CPRF in soft Malaysian kaolin clay and an instrumented bridge (Impulsora) founded in soft clayey soil. Subsequently, a range of comparative parametric evaluation of load sharing and settlement characterstics has been carried out which has indicated the importance of pile layout, length and numbers to arrive at a safe and economic design.