Random vibration analysis of thin-walled elastic rings under multiple moving loads

2021 ◽  
pp. 095440622199640
Author(s):  
Jalal Taheri Kahnamouei ◽  
Jianming Yang
Keyword(s):  
Random Vibration ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Parameters ◽  
Ring Gear ◽  
Moving Loads ◽  
Newmark Scheme ◽  
Mean And Variance ◽  
Thin Walled ◽  
Bolt Connection

This paper investigates the random vibration of a thin-walled ring subjected to multiple moving loads from the inside of the ring. A ring gear in a planetary gear train with three equally-spaced planets is taken as an example. The ring is discretized with the finite element method of curved beam elements. The supports of the ring gear are treated as three linear springs to mimic a general bolt connection. The stochastic Newmark algorithm is used to solve the equations and obtain the response's mean and variance. Monte Carlo simulations are also conducted to verify the results from the stochastic Newmark scheme. A parametric study is conducted to examine the effect of design parameters on the responses.

Dynamic Analysis of Helical Planetary Gear Train

2013 ◽  
Vol 404 ◽  
pp. 312-317 ◽  
Author(s):  
Xian Zeng Liu ◽  
Jun Zhang
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Dynamic Model ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamic Responses ◽  
Design Parameters ◽  
Planetary Gear Train ◽  
State Dynamic ◽  
The Impact

A dynamic model for helical planetary gear train (HPGT) is proposed. Based on the model, the free vibration characteristics, steady-state dynamic responses and effects of design parameters on system dynamics are investigated through numerical simulations. The free vibration of the HGPT is classified into 3 categories. The classified vibration modes are demonstrated as axial translational and torsional mode (AT mode), radial translational and rotational mode (RR mode) and planet mode (P mode) followed by the characteristics of each category. The simulation results agree well with those of previous discrete model when neglecting the component flexibilities, which validates the correctness of the present dynamic model. The steady-state dynamic responses indicate that the dynamic meshing forces fluctuate about the average static values and the time-varying meshing stiffness is one of the major excitations of the system. The parametric sensitivity analysis shows that the impact of the central component bearing stiffness on the dynamic characteristic of the HPGT system is significant.

Electrostatically Actuated Surface Micromachined Offset Planetary Gear Pump Design

2001 ◽  
Author(s):  
Mohammad I. Kilani ◽  
Paul C. Galambos ◽  
Yousef S. Haik ◽  
Ching-Jen Chen
Keyword(s):  
Roller Bearing ◽  
Planetary Gear ◽  
Gear Train ◽  
Gear Pump ◽  
Ring Gear ◽  
Surface Micromachining ◽  
Eccentric Rotation ◽  
Pump Design ◽  
Electrostatically Actuated ◽  
Mechanical Elements

Abstract An offset planetary pump fabricated in five-level polysilicon surface micromachining is introduced. The pump consists of a ring gear enclosing two planetary gears and an offset sun gear, which generates pumping due to its eccentric rotation. The pump is driven by an electrostatically actuated comb-drive microengine and mechanical power is transmitted to the ring gear through a micro gear train. The paper presents a derivation of pump capacity and the detailed design of its mechanical elements, demonstrating the implementation of relatively advanced mechanical functions in multi-level surface micromachining, including axial roller bearing support, fluidic seal and planetary gear transmission.

A PLANETARY GEAR TRAIN WITH RING-INVOLUTE TOOTH

2008 ◽  
Vol 32 (2) ◽  
pp. 251-266
Author(s):  
Shyue-Cheng Yang ◽  
Tsang-Lang Liang
Keyword(s):  
Planetary Gear ◽  
Conjugate Problem ◽  
Gear Ratio ◽  
Gear Train ◽  
Tooth Surface ◽  
The Sun ◽  
Ring Gear ◽  
Planetary Gear Train ◽  
Envelope Method ◽  
Planet Gear

This paper proposes a planetary gear train with ring-involute tooth profile. Inherent in a planetary gear train is the conjugate problem among the sun, the planet gears and the ring gear. The sun gear and the planet gear can be obtained by applying the envelope method to a one-parameter family of a conical tooth surface. The conical tooth rack cutter was presented in a previous paper [5]. The obtained planet gear then becomes the generating surface. The double envelope method can be used to obtain the envelope to the family of generating surfaces. Subsequently the profile of a ring gear of the planetary gear trains can be easily obtained, and using the generated planet gear and applying the gear theory, the ring gear is generated. To illustrate, the planetary gear train with a gear ratio of 24:10:7 is presented. Using rapid prototyping and manufacturing technology, a sun gear, four planet gears, and a ring gear are designed. The RP primitives provide an actual full-size physical model that can be analyzed and used for further development. Results from these mathematical models are applicable to the design of a planetary gear train.

scholarly journals Random Vibration and Dynamic Analysis of a Planetary Gear Train in a Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jianming Yang ◽  
Ping Yang
Keyword(s):  
Random Vibration ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Gear Train ◽  
Premature Failure ◽  
Shaping Filter ◽  
Vibration Responses ◽  
Gear Trains ◽  
Dynamic Meshing

Premature failure of gearboxes is a big challenge facing the wind power industry. It highly depends on fully understanding the embedded dynamics to solve this problem. To this end, this paper investigates the random vibration and dynamics of planetary gear trains (PGTs) in wind turbines under the excitation of wind turbulence. The turbulence is represented by the Von Karmon spectrum and implemented by passing white noise through a 2nd-order shaping filter. Then, extra equations are formed and added to the original governing equations of motion. With this augmented equation set, a recursive numerical algorithm based on stochastic Newmark scheme is applied to solve for the statistics of the responses starting from initial conditions. After simulation, the variances of the vibration responses and the dynamic meshing forces at gear meshes are obtained.

Dynamic Analysis of Hybrid Gear Trains With Flexible Ring Gear Rim

2017 ◽  
Author(s):  
Xiangyang Xu ◽  
Junbin Lai ◽  
Yanfang Liu
Keyword(s):  
Dynamic Behavior ◽  
Planetary Gear ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Train ◽  
Gear Pair ◽  
Ring Gear ◽  
Gear Trains ◽  
Helical Gear Pair ◽  
Flexible Ring

In this paper, the dynamic behavior of a hybrid gear train (HGT), consists of a single-stage helical planetary gear set and a helical gear pair, is analyzed. A ring gear rim is connected with an internal gear in a helical planetary gear set and an external gear in a helical gear pair. Power flows from the helical gear pair to the helical planetary gear set. Therefore, loads in the external gear would cause additional axial force and radial force, which would lead to unexpected moment and force. As a result, deflections of ring gear rim must be taken into consideration. Under this condition, a three-dimensional dynamic model of a HGT with flexible ring gear rim is developed, in which six degrees of freedom including three translational motions and three rotational motions are employed. Coupling effects of the bearing support stiffness, gear mesh stiffness and time-varying transmission error are taken into consideration. The model also takes flexible supporting shafts and planet carrier into consideration by using finite element method. Then, the equations of motion in matrix form are established and solved to predict the forced vibration response due to the transmission error excitations. Subsequently, effects of positions of the helical gear pair relative to the planetary gear set and the thickness of ring gear rim on dynamic behavior of the HGT are discussed. The results show that the proposed model is potential and can be used to guide the design of hybrid gear trains.

Multi-Objective Optimization for the Efficiency and Weight of Helicopter Transmission Planetary Gear Train

2014 ◽  
Vol 635-637 ◽  
pp. 177-180
Author(s):  
Kang Huang ◽  
Xiao Hui Zhu ◽  
Xiang Chen ◽  
Gong Chuan Xia
Keyword(s):  
Planetary Gear ◽  
Optimization Method ◽  
Gear Train ◽  
Transmission Ratio ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Planetary Gear Train ◽  
Multi Objective ◽  
Critical Design ◽  
Helicopter Transmission

A multi-objective optimization method for the optimization of the efficiency and weight of helicopter transmission planetary gear train was established. Taking the transmission ratio, efficiency weight, and reliability as critical design parameters, taking the conditions of the planetary gear train itself and the strength check constraint for the gear train as constraint functions, making the weight and efficiency of the planetary gear train asoptimization targets and using the Matlab function fgoalattain, a multi-objective optimization has been made. Comparison between the initial and the optimized results showed the success of the optimized planetary gear train in reducing the weight and increasing the efficiency.

A multi-body dynamic study of vibration of a planetary gear train with the planetary bearing fault

2019 ◽  
Vol 233 (3) ◽  
pp. 677-695 ◽  
Author(s):  
Jing Liu ◽  
Linfeng Wang ◽  
Jinlei Ma ◽  
Wennian Yu ◽  
Yimin Shao
Keyword(s):  
Dynamic Model ◽  
Dynamic Modelling ◽  
Planetary Gear ◽  
Elastic Support ◽  
Gear Train ◽  
Radial Clearance ◽  
Ring Gear ◽  
Planetary Gear Train ◽  
Multi Body ◽  
Body Dynamic

Local faults including pits and spalls in any planet bearing can greatly affect the vibration of the planetary gear train, as well as the elastic support of the ring gear. However, the dynamic modelling methods in previous work can only formulate the local fault and the elastic support of the ring gear independently. To address this issue, a multi-body dynamic model for a planetary gear train with a local fault in the planet bearing and an elastic ring gear foundation are introduced to analyze the effect of local fault on the vibration. The local fault in the planet bearing is modelled as a rectangular one. Both the planet bearings including the radial clearance and ring gear with an elastic foundation are considered in the multi-body dynamic model. The contact stiffnesses and damping coefficients of gears and bearings are calculated by the methods reported in the literature. A Coulomb friction model is adopted to model the frictions between mating components of the system. In order to validate the proposed multi-body dynamic model, its simulation results are directly compared with those from theoretical methods as well as the experimental methods reported in the literature. Moreover, parameter studies are conducted to discuss the effects of local faults in the planet-bearing races, the sun gear speed, and the carrier moment on the vibration of the planetary gear train. The analyzing results of this study can provide some guidance for detection approaches of local faults in the planet bearings of planetary gear trains through vibration analysis.

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