Influence of Sliding Friction on the Dynamic Characteristics of a Planetary Gear Set With the Improved Time-Varying Mesh Stiffness

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Wei Luo ◽  
Baijie Qiao ◽  
Zhixian Shen ◽  
Zhibo Yang ◽  
Hongrui Cao ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Friction Forces ◽  
Basic Model ◽  
Internal Excitation ◽  
Improved Model

Abstract Acting as an important internal excitation, sliding friction can cause the vibration and noise of the planetary gear set. In this paper, a dynamic model is developed to study the influence of sliding friction on the dynamic characteristics of the planetary gear set by including the time-varying mesh stiffness (TVMS), sliding friction forces and torques. An improved analytical model is proposed to calculate the TVMS with sliding friction. The explicit analytical expressions of the sliding friction forces and torques are also derived. Three kinds of different models are applied to investigate the influence of sliding friction: (1) the basic model: sliding friction is neglected in the dynamic model; (2) the improved model I: only the sliding friction forces and torques are considered in the dynamic model; and (3) the improved model II: both the influence of sliding friction on the TVMS and the sliding friction forces and torques are introduced into the dynamic model. The planetary gear set with three equally spaced planet gears is applied to analyze the dynamic characteristics under sliding friction. The simulation results show that the dynamic characteristics can be enhanced or disturbed by sliding friction. In the end, the dynamic model is validated by the experiments. Therefore, the influence of sliding friction is non-negligible when investigating the dynamic characteristics of the planetary gear set. The developed dynamic model provides a feasible dynamic research scheme for the planetary gear set with sliding friction.

scholarly journals Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Wang ◽  
Lei Zhang ◽  
Yuan-Qing Luo ◽  
Chang-Zheng Chen
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Experimental Result ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

Effects of Temperature on the Time-Varying Mesh Stiffness, Vibration Response, and Support Force of a Multi-Stage Planetary Gear

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Hui Liu ◽  
Pengfei Yan ◽  
Pu Gao
Keyword(s):  
Temperature Change ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Thermal Deformation ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Displacement ◽  
Influence Of Temperature ◽  
Nonlinear Dynamic Characteristics

Abstract The thermal deformation of gears will affect the vibration of the planetary system; this research mainly studied the effect of thermal conditions on planetary systems nonlinear vibration under the thermal equilibrium state. To study the influence of gear temperature on the planetary gear system, a nonlinear dynamic model considering thermal deformation was established. The mathematical expression of the thermal time-varying mesh stiffness (TTVMS) varied with temperature, and the backlash caused by the temperature change was also computed. The influence of temperature on the TTVMS was investigated. The calculation results indicated that the methods used to determine the TTVMS and backlash of gear pairs were effective, and the trends of the change in the nonlinear dynamic characteristics with temperature were obtained. According to the fast Fourier transform (FFT) spectrums and root-mean-square (RMS) analysis, the influence of temperature change on the nonlinear dynamic characteristics of the system was analyzed. When the temperature was lower than 80 °C, the vibration displacement and the supporting shaft load remained unchanged or decreased. Once the temperature was higher than 80 °C, the vibration displacement and load of the system were strengthened.

scholarly journals An Improved Rigid Multibody Model for the Dynamic Analysis of the Planetary Gearbox in a Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Wenguang Yang ◽  
Dongxiang Jiang
Keyword(s):  
Dynamic Analysis ◽  
Transient Analysis ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Signals ◽  
Planetary Gearbox ◽  
Multibody Model ◽  
Improved Model ◽  
Rigid Multibody

This paper proposes an improved rigid multibody model for the dynamic analysis of the planetary gearbox in a wind turbine. The improvements mainly include choosing the inertia frame as the reference frame of the carrier, the ring, and the sun and adding a new degree of freedom for each planet. An element assembly method is introduced to build the model, and a time-varying mesh stiffness model is presented. A planetary gear study case is employed to verify the validity of the improved model. Comparisons between the improvement model and the traditional model show that the natural characteristics are very close; the improved model can obtain the right equivalent moment of inertia of the planetary gear in the transient simulation, and all the rotation speeds satisfy the transmission relationships well; harmonic resonance and resonance modulation phenomena can be found in their vibration signals. The improved model is applied in a multistage gearbox dynamics analysis to reveal the prospects of the model. Modal analysis and transient analysis with and without time-varying mesh stiffness considered are conducted. The rotation speeds from the transient analysis are consistent with the theory, and resonance modulation can be found in the vibration signals.

Time-varying mesh stiffness calculation of a planetary gear set with the spalling defect under sliding friction

Meccanica ◽  
2020 ◽  
Vol 55 (1) ◽  
pp. 245-260
Author(s):  
Wei Luo ◽  
Baijie Qiao ◽  
Zhixian Shen ◽  
Zhibo Yang ◽  
Xuefeng Chen
Keyword(s):  
Sliding Friction ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Spalling Defect

scholarly journals Dynamic Analysis of Planetary Gear with Root Crack in Sun Gear Based on Improved Time-Varying Mesh Stiffness

2020 ◽  
Vol 10 (23) ◽  
pp. 8379
Author(s):  
Jian Shen ◽  
Niaoqing Hu ◽  
Lun Zhang ◽  
Peng Luo
Keyword(s):  
Fault Diagnosis ◽  
Dynamic Model ◽  
Theoretical Basis ◽  
Planetary Gear ◽  
Vibration Response ◽  
Gear System ◽  
Transition Curve ◽  
Parameter Method ◽  
Time Varying ◽  
Mesh Stiffness

The time-varying mesh stiffness (TVMS) is the crucial parameter of the dynamic model of the gear system. Accurate calculation of TVMS is essential for effective fault diagnosis of the gear system. A mesh stiffness improved method considering both the gear tooth transition curve and deformation of the gear body is presented in this paper, and the stiffness calculation expressions under healthy and crack states are given, respectively. Based on the lumped parameter method, the dynamic model of planetary gear with crack in sun gear is constructed, and the vibration response is solved. The simulation results show when the tooth root cracks appear, the vibration response of the tooth has obvious shock response characteristics. The characteristic frequency and frequency multiplication of sun gear fault can be found obviously by envelope analysis. The simulation signal and the test signal obtained by the drivetrain dynamics simulator gearbox test rig are compared and verified. The comparison and verification results show that the proposed TVMS calculation method and the dynamic model are accurate, which can provide a certain theoretical basis for the fault diagnosis of planetary gear with crack fault. The test results are consistent with the numerical analysis results, which provides a theoretical basis for the fault diagnosis of tooth crack.

Construction of Semianalytical Solutions to Spur Gear Dynamics Given Periodic Mesh Stiffness and Sliding Friction Functions

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Song He ◽  
Todd Rook ◽  
Rajendra Singh
Keyword(s):  
Dynamic Models ◽  
Sliding Friction ◽  
Linear Time ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
System Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Friction Forces

Gear dynamic models with time-varying mesh stiffness, viscous mesh damping, and sliding friction forces and moments lead to complex periodic differential equations. For example, the multiplicative effect generates higher mesh harmonics. In prior studies, time-domain integration and fast Fourier transform analysis have been utilized, but these methods are computationally sensitive. Therefore, semianalytical single- and multiterm harmonic balance methods are developed for an efficient construction of the frequency responses. First, an analytical single-degree-of-freedom, linear time-varying system model is developed for a spur gear pair in terms of the dynamic transmission error. Harmonic solutions are then derived and validated by comparing with numerical integration results. Next, harmonic solutions are extended to a six-degree-of-freedom system model for the prediction of (normal) mesh loads, friction forces, and pinion/gear displacements (in both line-of-action and off-line-of-action directions). Semianalytical predictions compare well with numerical simulations under nonresonant conditions and provide insights into the interaction between sliding friction and mesh stiffness.

scholarly journals Experimental Investigations of Noise Control in Planetary Gear Set by Phasing

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. H. Gawande ◽  
S. N. Shaikh
Keyword(s):  
Experimental Work ◽  
Noise Level ◽  
Planetary Gear ◽  
Experimental Investigations ◽  
Mesh Stiffness ◽  
Gear Noise ◽  
Gear Drive ◽  
Internal Excitation ◽  
Key Factor ◽  
Set Up

Now a days reduction of gear noise and resulting vibrations has received much attention of the researchers. The internal excitation caused by the variation in tooth mesh stiffness is a key factor in causing vibration. Therefore to reduce gear noise and vibrations several techniques have been proposed in recent years. In this research the experimental work is carried out to study the effect of planet phasing on noise and subsequent resulting vibrations of Nylon-6 planetary gear drive. For this purpose experimental set-up was built and trials were conducted for two different arrangements (i.e., with phasing and without phasing) and it is observed that the noise level and resulting vibrations were reduced by planet phasing arrangement. So from the experimental results it is observed that by applying the meshing phase difference one can reduce planetary gear set noise and vibrations.

An Analytical Investigation of Rattle Characteristics of Powder Metal Gears

2019 ◽  
Author(s):  
Elizabeth Slavkovsky ◽  
Murat Inalpolat ◽  
Anders Flodin
Keyword(s):  
Transmission Error ◽  
Analytical Investigation ◽  
Time Varying ◽  
Evaluation Tool ◽  
Mesh Stiffness ◽  
Gear Design ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Gear Mesh Stiffness ◽  
Gear Rattle

Abstract This study employs an analytical model of a gear pair with transverse-torsional dynamics that allows analysis of single-sided, double-sided, and random rattle situations to contrast rattle characteristics of isotropic PM gears with a baseline steel gearset. This model utilizes time-varying gear mesh stiffness and transmission error as the internal excitation sources and time-varying operating torque as an external excitation. The gear rattle performance of PM gears is investigated under different torque conditions and operating speeds. The system kinetic and potential energy is assessed as an evaluation tool that can indicate the severity of different rattle conditions. The dynamic response of two different versions of an existing PM gear design are compared with a baseline traditional steel gear.

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