Finite Element Analysis of Internal Gear in High-Speed Planetary Gear Units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.

Analysis of the Relationship Between the Meshing Stiffness and the Inherent Characteristics of Planetary Gear Transmission Mechanism

According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism,a equivalent concentrated mass dynamics model of the planetary transmission mechanism is established.The natural frequency of the planetary gear train at a specific gear is calculated and extracted.The relationship between the meshing stiffness of each row and the natural frequency of the system is analyzed,thereby avoiding possible resonance behavior by changing the meshing stiffness.These results show that the meshing stiffness,in its range of possible values,has nearly no effect on the low order natural frequency(<4.000.Hz),and that the time-varying meshing stiffness mainly affects the natural frequencies of the higher-and middle-order parts of the system.Changes of the natural frequencies lead to the change of the system's corresponding vibration mode,which will change the vibration situation of the system.

Non-undercutting condition and parameter optimization for cycloid ball planetary transmission

The transmission performance of cycloid ball planetary transmission(CBPT) is affected by cycloid tooth undercutting directly, and the design of CBPT can be optimized by the non-undercutting condition. Firstly, the theoretical equation of cycloid tooth is given, and the curvature radius of cycloid tooth profile is derived. Secondly, according to the relationship between the curvature radius and the distribution circle of balls, the non-undercutting condition of cycloid tooth profile is established, and the non-undercutting critical condition is deduced. Finally, the validity of the non-undercutting critical condition is verified by simulation. The result shows that the non-undercutting critical condition can be used to optimize the design of CBPT.

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Planet pin position errors significantly affect the mechanical behavior of planetary transmissions at both the power-sharing level and the gear tooth meshing level,and its tolerance properties are one of the key design elements that determine the fatigue reliability of large aviation planetary systems.The dangerous stress response of planetary systems with error excitation is analyzed according to the hybrid finite element method,and the weakening mechanism of large-size carrier flexibility to this error excitation is also analyzed.In the simulation and analysis process,the Monte Carlo method was combined to take into account the randomness of planet pin position errors and the coupling mechanism among the error individuals,which provides effective load input information for the fatigue reliability evaluation model of planetary systems.In addition,a simulation test of gear teeth bending fatigue intensity was conducted using a power flow enclosed gear rotational tester,providing the corresponding intensity input information for the reliability model.Finally,under the framework of stress-intensity interference theory,the computational logic of total formula is extended to establish a fatigue reliability evaluation model of planetary systems that can simultaneously consider the failure correlation and load bearing time-sequence properties of potential failure units,and the mathematical mapping of planet pin positional tolerance to planetary systems fatigue reliability was developed based on this model.Accordingly,the upper limit of planet pin positional tolerance zone can be determined at the early design stage according to the specific reliability index requirements,thus maximizing the balance between reliability and economy.

Design and Dynamics Simulation of a Novel Double-Ring-Plate Gear Reducer

A patented double-ring-plate gear reducer was designed and its dynamic performance was simulated. One unique characteristic of this novel drive is that the phase angle difference between two parallelogram mechanisms is a little less than 180 degree and four counterweights on two crankshafts are designed to balance inertia forces and inertia moments of the mechanisms. Its operating principle, advantages, and design issues were discussed. An elasto-dynamics model was presented to acquire its dynamic response by considering the elastic deformations of ring-plates, gears, bearings, etc. The simulation results reveal that compared with housing bearings, planetary bearings work in more severe conditions. The fluctuation of loads on gears and bearings indicates that the main reason for reducer vibration is elastic deformations of the system rather than inertia forces and inertia moments of the mechanisms.

Finite element modeling and analysis of planetary gear transmission based on transient meshing properties

Planetary gear trains are widely applied in various transmission units.Whether strengths of all gears are accurately calculated or not can affect reliability of the entire system significantly.Strength calculation method for planetary gear trains usually follows the method for cylindrical gears,in which the worst meshing positions for both contact stress and bending stress cannot be determined precisely,and calculation results tend to be conservative.To overcome these shortcomings,a kinematics analysis for a planetary gear train is firstly performed,in which the influence of relative speed is investigated.Then the finite element strength analysis of a planetary gear train based on its transient meshing properties is carried out in ANSYS.Time–history curves of contact and bending stresses of sun gear,planetary gears and ring gear are respectively obtained.Also the accurate moment and its corresponding position of the maximum stress are precisely determined.Finally,calculation results of finite element method(FEM)and traditional method are compared in order to verify the effectiveness.Simulation and comparison show the stability of the proposed method in this paper.Researches in this paper establish the foundations for fatigue analysis and optimization for a planetary gear train.