Planetary Gear Profile Modification Design Based on Load Sharing Modelling

In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.

Load Sharing Behavior of Star Gearing Reducer for Geared Turbofan Engine

Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.

Load Sharing Performance of the Main Drive System in the Shield Machine and Improvement of Control Method

Shield machine is the major technical equipment badly in need in national infrastructure construction. The service conditions of shield machine are extremely complex. The driving interface load fluctuation caused by geological environment changes and multi field coupling of stress field may lead into imbalance of redundant drive motors output torque in main driving system. Therefore, the shield machine driving synchronous control is one of the key technologies of shield machine. This paper is in view of the shield machine main driving synchronous control, achieving the system＇s adaptive load sharing. From the point of view of cutterhead load changes, nonlinear factors of mechanical transmission mechanism and the control system synchronization performance, the authors analyze the load sharing performance of shield machine main drive system in the event of load mutation. The paper proposes a data-driven synchronized control method applicable to the main drive system. The effectiveness of the method is verified through simulation and experimental methods. The new method can make the system synchronization error greatly reduced, thus it can effectively adapt to load mutation, and reduce shaft broken accident.

Distributed Event-triggered Secondary Control for Average Bus Voltage Regulation and Proportional Load Sharing of DC Microgrid

This paper proposes a novel distributed event-triggered secondary control method to overcome the drawbacks of primary control for direct current(DC)microgrids.With eventtriggered distributed communication,the proposed control method can achieve system-wide control of parallel distrubted generators(DGs)with two main control objectives:①estimate the average bus voltage and regulate it at the nominal value;②achieve accurate current sharing among the DGs in proportion to their power output ratings.Furthermore,the proposed control strategy can be implemented in a distributed way that shares the required tasks among the DGs.Thus,it shows the advantages of being flexible and scalable.Furthermore,this paper proposes a simple event-triggered condition that does not need extra state estimator.Thus,limited communication among neighbors is required only when the event-triggered condition is satisfied,which significantly reduces the communication burden at the cyber layer.

Interaction behavior and load sharing pattern of piled raft using nonlinear regression and LM algorithm-based artificial neural network

In the recent era,piled raft foundation(PRF)has been considered an emergent technology for offshore and onshore structures.In previous studies,there is a lack of illustration regarding the load sharing and interaction behavior which are considered the main intents in the present study.Finite element(FE)models are prepared with various design variables in a double-layer soil system,and the load sharing and interaction factors of piled rafts are estimated.The obtained results are then checked statistically with nonlinear multiple regression(NMR)and artificial neural network(ANN)modeling,and some prediction models are proposed.ANN models are prepared with Levenberg-Marquardt(LM)algorithm for load sharing and interaction factors through backpropagation technique.The factor of safety(FS)of PRF is also estimated using the proposed NMR and ANN models,which can be used for developing the design strategy of PRF.

Numerical Method on Load Sharing Problem of Thick Laminate Joints

Accurately and efficiently predicting the load sharing of multi^bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional （2D） finite element method （FEM） is introduced to meet such a demand. The deformation contributions of the joint zone are analyzed and calculated separately, including the shearing deformation of the fasteners shank, the bending deformation of the fasteners shank, and the bearing deformation of the fasteners and joint plates. These deformations are all transferred and incorporated into the components of the fastener＇s flexibility. In the 2D finite element model, the flexibilities of the beam elements and bush elements are used to simulate different components of the fastener＇s flexibility. The parameters of the beam elements which include the bending moment of inertia and intersection area, and the parameters of the bush elements which include the stiffness in different directions, are all obtained through equalizing the fasteners flexibilities. In addition, the secondary bending effect introduced by the single-lap joints is also taken into account to verify the flexibilities of the fasteners in practical application. The proposed FEM is testified to be more accurate than the traditional 2D FEMs and more efficient than the three-dimensional （3D） FEM in solving load sharing problem of multi-bolt single-lap thick laminate joints. With the increase of joint plates＇ thickness, the advantages of the proposed method tend to be more obvious. The proposed 2D FEM is an effective tool for designing bolted joints in large-scale composite structures.

Droop control method for load share and voltage regulation in high-voltage microgrids

When the line impedance is considered in the microgrid, the accuracy of load sharing will decrease. In this paper, the impact of line impedance on the accuracy of load sharing is analyzed. A robust droop control for a highvoltage microgrid is proposed based on the signal detection on the high-voltage side of the coupling transformer. For a high-voltage microgrid, the equivalent impedance of coupling transformer connecting distributed generator with the grid is usually the dominate factor. Compared with the conventional droop control strategy, the proposed control method in this paper detects the feedback signal from the high-voltage side of the coupling transformer. The impact of line impedance on the load sharing accuracy can be mitigated significantly. The proposed droop control only changes the detection point of the feedback signal, thus it is easy to be implemented. The PSCAD/EMTDC simulation results show the effectiveness of the proposed robust droop control concept in load sharing and voltage regulation with highly accuracy.