scholarly journals Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

Machines ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Tingqiong Cui ◽  
Yinong Li ◽  
Chenglin Zan ◽  
Yuanchang Chen
Keyword(s):  
Planetary System ◽  
Lagrange Equation ◽  
Great Influence ◽  
Planetary Gear ◽  
Rotation Frequency ◽  
Rotational Inertia ◽  
Nonlinear Dynamic Model ◽  
Modeling And Analysis ◽  
Time Frequency ◽  
Meshing Stiffness

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Nonlinear Dynamic Model and Equations of RV Transmission System

2012 ◽  
Vol 510 ◽  
pp. 536-540 ◽  
Author(s):  
Li Jun Shan ◽  
Xue Fang ◽  
Wei Dong He
Keyword(s):  
Differential Equations ◽  
Lagrange Equation ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Transmission System ◽  
Dynamics Model ◽  
Nonlinear Dynamic Model ◽  
Restoring Force ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equations are transformed to identical dimensionless nonlinear differential equations in matrix form. The establishment of the nonlinear differential equations laid a foundation for The Solution of differential equations and the analysis of the nonlinearity characteristics.

A study on body sway of car-trailer combinations considering dry friction in steering subsystem

2021 ◽  
pp. 095440702110520
Author(s):  
Ning Zhang ◽  
Ke-Ke Geng ◽  
Tian Li ◽  
Jian-Hua Wu ◽  
Guo-Dong Yin
Keyword(s):  
Dynamic Stability ◽  
Dry Friction ◽  
Sliding Friction ◽  
Dynamic Instability ◽  
Lagrange Equation ◽  
Steering System ◽  
Body Sway ◽  
Rotational Inertia ◽  
Nonlinear Dynamic Model ◽  
Steering Characteristics

Considering the stability of vehicle system, static instability and dynamic instability are two different instability problems. Because of the dynamic coupling between car and trailer, the problem of dynamic stability of car-trailer combination (CTC) is more obvious. This instability is called body sway or flutter in engineering, its boundary is often described by dynamic critical speed ( vcrit). It has been proved by experiments that the steering system characteristics have an important impact on the dynamic stability of CTC, but the specific mechanism is not clear. In this paper, the characteristic and influence of steering subsystem are studied for the first time. Firstly, a 6-DOF nonlinear dynamic model of CTC is established by Lagrange equation. The steering subsystem characteristics, incl. stiffness, damping, rotational inertia, and dry friction, are considered in theoretical modeling. On this basis, the influences of steering characteristics, especially the dry friction, on vcrit and axle cornering stiffness of CTC are analyzed. Simulation results show that the vcrit can increase by 16% and 23.2% respectively via adjusting the steering stiffness and the sliding friction factor. Therefore, a fine selection of steering subsystem characteristics can effectively improve the dynamic stability and safety of CTC. The research results of this paper can provide reference for the design of steering system considering dynamic stability.

A nonlinear dynamic model for analysis of the combined influences of nonlinear internal excitations on the load sharing behavior of a compound planetary gear set

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1048-1068 ◽  
Author(s):  
Haibo Zhang ◽  
Shijing Wu ◽  
Zeming Peng
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Planetary Gear ◽  
Load Sharing ◽  
Nonlinear Dynamic Model ◽  
Meshing Stiffness ◽  
Bearing Clearance ◽  
Internal Excitation ◽  
Single Factor Analysis ◽  
Sharing Behavior

Nonlinear internal excitations, which include meshing stiffness, backlash, and bearing clearance, may cause nonuniform load distribution in compound planetary gear transmission. To quantify the influence of nonlinear internal excitations on load sharing behavior, and to study the combined effects of meshing stiffness, backlash, and bearing clearance on load sharing behavior, this paper develops a nonlinear dynamic model of a Ravigneaux compound planetary gear set with all members possessing translational and torsional vibration degrees of freedom, as an extend dynamic model to the prior research for compound planetary gear set. In detail, the dynamic model is derived on the basis of the second Lagrange equations, and the load sharing coefficients for different meshing pairs are defined and calculated. Single factor analysis is introduced to investigate the influence of each nonlinear internal excitation on load sharing coefficient ( LSC). On the basis of single factor analysis, Taguchi method is incorporated with the nonlinear dynamic model to study the combined effects of nonlinear internal excitation and figure out the most significant control factor affecting LSC among meshing stiffness, backlash, and bearing clearance. The calculation results are evaluated by using signal-to-noise ( S/ N) analysis and ANOVA method. The results indicate that backlash affects the load sharing behavior most significantly, compared with mean value of meshing stiffness and bearing clearance.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Analysis of Elastic Motion Stability of Flexible Manipulator Arm Based on Lyapunov Stability Theory

2014 ◽  
Vol 620 ◽  
pp. 321-329
Author(s):  
Guang Rui Liu ◽  
Wen Bo Zhou ◽  
Rong Fu Liu
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Lagrange Equation ◽  
Lyapunov Stability Theory ◽  
The State ◽  
Flexible Manipulator ◽  
Rotational Inertia ◽  
Control Input ◽  
Motion Stability ◽  
Manipulator Arm

In order to study the elastic motion stability of flexible manipulator arm , to compute the maximum dynamic allowable payload , the partial differential equation of elastic motion of the flexible manipulator arm is solved using the method of Laplace transformation , the dynamic model of flexible manipulator arm carried addition mass on its end position is established ,simplified and truncated using Lagrange equation . the state space expression is established with the state variable and control input and output variable designated , the elastic motion stability rule is built upon and simplified using Lyapunov stability theory . The influence of the end position addition mass and articulation rotational inertia of flexible manipulator arm on its elastic motion stability is analyzed using the stability rule , and the dynamic maximum allowable payload of flexible manipulator arm on its end position is computed in order to guarantee its elastic motion stability . this study is important to the design of robot mechanical manipulator and corresponding drive control system .

scholarly journals Improvement of Intake Structures in a Two-Way Pumping Station with Experimental Analysis

2020 ◽  
Vol 10 (19) ◽  
pp. 6842
Author(s):  
Yanjun Li ◽  
Rong Lu ◽  
Huiyan Zhang ◽  
Fanjie Deng ◽  
Jianping Yuan
Keyword(s):  
Frequency Domain ◽  
Great Influence ◽  
Operating Conditions ◽  
Stable Operation ◽  
Pressure Pulsations ◽  
Pump Unit ◽  
Measuring Point ◽  
Time Frequency ◽  
Pumping Station ◽  
Bell Mouth

Pumping stations are important regulation facilities in a water distribution system. Intake structures can generally have a great influence on the operational state of the pumping station. To analyze the effects of the bell mouth height of the two-way intake on the performance characteristics and the pressure pulsations of a two-way pumping station, the laboratory-sized model pump units with three different intakes were experimentally investigated. To facilitate parameterized control, ellipse and straight lines were used to construct the profile of the bell mouth. The frequency domain and time-frequency domain of the pressure pulsations on the wall of intakes were analyzed by the Welch’s power spectral density estimate and the continuous wavelet transform (CWT) methods, respectively. The results showed that the bell mouth height (H) has significant influences on the uniformity of the impeller inflow and the operation stability of the pump unit. When H = 204 mm, the data fluctuated greatly throughout the test process and the performance curves are slightly lower than the other two schemes. As the bell mouth height gradually decreases, the average pressure difference of each measuring point began to decrease, more homogeneous velocity distribution of impeller inflow can be ensured. The amplitude of blade passing frequency is obvious in the spectrum. While when (H) is more than 164 mm, the main frequency of pressure pulsations at three points fluctuates with the rotation of the impeller. When H decreases to 142 mm, pressure pulsations will be independent of the operating conditions and positions which contributes to the long-term stable operation of the pump unit.

Pseudo-rigid-body dynamic modeling and analysis of compliant mechanisms

2017 ◽  
Vol 232 (9) ◽  
pp. 1665-1678 ◽  
Author(s):  
Yue-Qing Yu ◽  
Qian Li ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
Dynamic Responses ◽  
Modeling And Analysis ◽  
Rigid Body Dynamic ◽  
Body Dynamic

An intensive study on the dynamic modeling and analysis of compliant mechanisms is presented in this paper based on the pseudo-rigid-body model. The pseudo-rigid-body dynamic model with single degree-of-freedom is proposed at first and the dynamic equation of the 1R pseudo-rigid-body dynamic model for a flexural beam is presented briefly. The pseudo-rigid-body dynamic models with multi-degrees-of-freedom are then derived in detail. The dynamic equations of the 2R pseudo-rigid-body dynamic model and 3R pseudo-rigid-body dynamic model for the flexural beams are obtained using Lagrange equation. Numerical investigations on the natural frequencies and dynamic responses of the three pseudo-rigid-body dynamic models are made. The effectiveness and superiority of the pseudo-rigid-body dynamic model has been shown by comparing with the finite element analysis method. An example of a compliant parallel-guiding mechanism is presented to investigate the dynamic behavior of the mechanism using the 2R pseudo-rigid-body dynamic model.

Investigation on Impact Response Feature of Railway Vehicles With Wheel Flat Fault Under Variable Speed Conditions

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yang Jianwei ◽  
Yue Zhao ◽  
Jinhai Wang ◽  
Yongliang Bai ◽  
Chuan Liu
Keyword(s):  
Fourier Transform ◽  
Variable Speed ◽  
Dynamic Features ◽  
Modeling And Analysis ◽  
Railway Vehicles ◽  
Safety Issues ◽  
Time Frequency ◽  
Wheel Flat ◽  
Short Time ◽  
Response Feature

Abstract Wheel faults are the main causes of safety issues in railway vehicles. The modeling and analysis of wheel faults is crucial for determining and studying the dynamic characteristics of railway vehicles under variable speed conditions. Hence, a vehicle–track coupled dynamics model was established for analysis and calculations. The results showed that the dynamic features of the wheel with a flat fault were more pronounced under traction and braking conditions, whereas the variations in the features under coasting conditions were insignificant. In this paper, a short-time fast Fourier transform and reassignment method was used to process the signals, because the results were unclear when the time–frequency graph was processed only by short time Fourier transform, especially under braking conditions. The variation in the fault frequency under variable speed conditions was determined. Finally, statistical indicators were used to describe the vibration behaviors caused by the wheel flat fault.

Hybrid dynamic modeling and analysis of the electric vehicle planetary gear system

2020 ◽  
Vol 150 ◽  
pp. 103860
Author(s):  
Changzhao Liu ◽  
Xiansong Yin ◽  
Yinghua Liao ◽  
Yuanyuan Yi ◽  
Datong Qin
Keyword(s):  
Electric Vehicle ◽  
Dynamic Modeling ◽  
Planetary Gear ◽  
Gear System ◽  
Modeling And Analysis ◽  
Planetary Gear System
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