Dynamic Analysis of Gear–Shaft–Bearing Coupled System Considering Bearing Waviness Defect

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Huan Bai ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Jianjun Tan ◽  
Xinzi Li
Keyword(s):  
Dynamic Response ◽  
Vibrational Energy ◽  
Coupled Model ◽  
Coupled System ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Mesh ◽  
Gear Transmission System ◽  
Dynamic Transmission Error

Abstract Using finite element and lumped parameter methods, a gear–shaft–bearing coupled vibration model was developed for a single-stage gear transmission system considering bearing waviness, bearing clearance, time-varying transmission error excitation, and shaft flexibility. Runge–Kutta algorithm was applied for solving the dynamic response of the coupled model. The influences of rotational speed, the number, and amplitude of bearing waviness on the dynamics were studied. Results show that any change in the number of bearing waviness has an obvious impact on the dominant frequency component of the dynamic transmission error. When the number of bearing waviness is equal to the number or multiples of the rolling element, the dynamic mesh force occurs peak response and the system vibrates violently. At low and medium speeds range, the gear transmission system with bearing waviness has larger vibrational energy than the gear transmission system without bearing waviness, leading to unstable dynamic response, which would potentially cause a significant chaotic response. The dominant frequencies of the dynamic transmission error for the gear transmission system with bearing waviness are the ball passage frequency (BPF) and its harmonic frequency. At high speeds range, the main excitation is the transmission error both for the gear transmission systems with and without bearing waviness. In addition, the increasing amplitude of bearing waviness would enlarge the dynamic mesh force and decrease the number of loaded rolling elements.

scholarly journals Non-Linear Dynamic Feature Analysis of a Multiple-Stage Closed-Loop Gear Transmission System for 3D Circular Braiding Machine

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1788
Author(s):  
Lingling Yao ◽  
Zhuo Meng ◽  
Jianqiu Bu ◽  
Yize Sun
Keyword(s):  
Closed Loop ◽  
Transmission Error ◽  
Mean Value ◽  
Transmission System ◽  
Gear Transmission ◽  
Random Disturbance ◽  
Symmetrical Structure ◽  
Linear Dynamic ◽  
Gear Transmission System ◽  
The Mean

Aiming at the particularity of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine, the model of gear transmission system in radial braiding machine was simplified. The non-linear dynamic equations of a n-elements closed-loop gear transmission system with symmetrical structure including static transmission error, the random disturbance of meshing damping and backlash were considered. For convenience of calculation n = 3, the equations were solved numerically by using Runge-Kutta. The dynamic transmission error(DTE) with different backlash, dynamic meshing forces with and without the random disturbance of meshing damping, the amplitude of dynamic transmission error at n = 1000 r/min and b = 2.65 × 10−5 m, root mean square(RMS) of DTE and the mean value of DTE of the first pair of gears were analyzed. The simulation results show that different backlash and the random disturbance of meshing damping have a great influence on the dynamic displacement error and meshing force of the gear pair, and RMS and the mean value of DTE changes at different rotational speeds. The results will provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine and have great practical significance for improving the braiding quality.

The Fault Characteristics of Planetary Gear System with Tooth Breakage

2013 ◽  
Vol 569-570 ◽  
pp. 489-496 ◽  
Author(s):  
Yong Gui ◽  
Qin Kai Han ◽  
Zheng Li ◽  
Zhi Ke Peng ◽  
Fu Lei Chu
Keyword(s):  
Dynamic Response ◽  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear System ◽  
Operation Conditions ◽  
Gear Transmission System ◽  
Planetary Gear System ◽  
Two Parameters

Tooth breakage is a typical failure form of wind-turbine planetary gear transmission system, it is important to study the influence of tooth breakage on vibration characteristics of planetary gear transmission system. In this paper, considering the tooth breakage defect, a lumped parameter vibration model of a planetary gear system with time-periodic mesh stiffness is established. Effects of the length and width of tooth breakage on meshing stiffness and dynamic response are discussed in detail. The relation between characteristic frequency of the tooth breakage fault and rotating speeds is pointed out. Several statistical indicators are utilized to show the influence of two parameters (length of planet tooth breakage and input speed) on the dynamic response of the system. Experiments are carried out to verify the simulation results. These results would be useful for fault diagnosis of wind turbine transmission system at different operation conditions.

scholarly journals Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Zhihui Liu ◽  
Hongzhi Yan ◽  
Yuming Cao ◽  
Yuqing Lai
Keyword(s):  
Excitation Frequency ◽  
Transmission Error ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Torsional Stiffness ◽  
System Response ◽  
Gear Mesh ◽  
Gear Transmission System ◽  
The Impact

A four-degree-of-freedom nonlinear transverse and torsional vibration model of spur gear transmission system for one-way clutch, two-shaft assembly was developed, in which the one-way clutch was modeled as a piecewise nonlinear spring with discontinuous stiffness, considering the factors such as the time-varying gear mesh stiffness, static transmission error, and nonlinearity backlash. With the help of bifurcation diagrams, time domain response diagrams, phase plane diagrams, and Poincaré maps, the effects of the excitation frequency and the torsional stiffness of one-way clutch on the dynamic behavior of gear transmission system for one-way clutch, two-shaft assembly are investigated in detail by using Runge-Kutta method. Numerical results reveal that the system response involves period-1 motion, multiperiodic motion, bifurcation, and chaotic motion. Large torsional stiffness of one-way clutch can increase the impact and lead to instability in the system. The results can present a useful source of reference for technicians and engineers for dynamic design and vibration control of such system.

scholarly journals Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Li Yinong ◽  
Li Guiyan ◽  
Zheng Ling
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Bevel Gear ◽  
Gear Transmission ◽  
Spiral Bevel Gear ◽  
Mesh Stiffness ◽  
Light Load ◽  
Gear Transmission System ◽  
Spiral Bevel ◽  
Asymmetric Mesh

An 8-DOF (degrees-of-freedom) nonlinear dynamic model of a spiral bevel gear pair which involves time-varying mesh stiffness, transmission error, backlash, and asymmetric mesh stiffness is established. The effect of the asymmetric mesh stiffness on vibration of spiral bevel gear transmission system is studied deliberately with numerical method. The results show that the mesh stiffness of drive side has more effect on dynamic response than those of the coast side. Only double-sided impact region is affected considerably by mesh stiffness of coast side while single-sided impact and no-impact regions are unchanged. In addition, the increase in the mesh stiffness of drive side tends to worsen the dynamic response of the transmission system especially for light-load case.

Rotordynamics analysis of a single helical gear transmission system for high speed applications

2020 ◽  
Vol 14 (3) ◽  
pp. 7040-7048
Author(s):  
Najeeb Ullah ◽  
C. Xi ◽  
T. Cong ◽  
H. Yucheng
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Transmission Error ◽  
Gear Transmission ◽  
Dynamic Mesh ◽  
Coupled Systems ◽  
Acceleration Response ◽  
Vibration Acceleration ◽  
Gear Transmission System ◽  
The Stability

Since the non-linear dynamic response under various high-speed conditions can directly affect the life of gear transmission systems. In addition, the transmission error and dynamic mesh force play a key role in noise and harshness analysis of gear bearing coupled systems. So, in this piece of work, a 12 degree of freedom dynamic model is developed to probe the vibration response by using finite element method and taking into account the bearing and flexible shafts in the first part. Subsequently, some meshing gear characteristics such as dynamic and vibration acceleration response under different rotational speeds (1000-9000 rev/minute) were analyzed whereas critical speed appeared at 6500 rev/minute. Then, the stability analysis is performed to investigate the dynamics behind the critical speed by using MASTA. It was observed that natural frequency of 0.45 kHz for a fourth harmonic order is analogous to critical speed which further causes sudden elevation in both dynamic mesh force and transmission error.

Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system

2013 ◽  
Vol 228 (7) ◽  
pp. 1108-1118 ◽  
Author(s):  
Jinyuan Tang ◽  
Zehua Hu ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Characteristics ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Factor ◽  
Gear Pair ◽  
Face Gear ◽  
Amplitude Variation ◽  
Gear Transmission System ◽  
Static Transmission Error

The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near [Formula: see text] . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zehua Hu ◽  
Jinyuan Tang ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System ◽  
The Face ◽  
Time Invariant ◽  
Backlash Nonlinearity

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

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