The time-varying mesh stiffness modeling of gear system with spalling defects in different positions

In this paper, A semi-physical method for calculating time varying mesh stiffness and the dynamic response of gear system based on experimental strain data is studied. In a previous work, it was reported that dynamic strain on gear tooth root can be measured under normal operating condition using fiber Bragg Grating (FBG) sensors. This paper aims to compute gear dynamic response using experimental strain data and give an explanation of the fault propagation process. Using the dynamic strain data from FBG sensors, a method for calculating the dynamic response of gear system is proposed. Based on the theory of potential energy and material mechanics, the relationship between the bending strain of the tooth root and the time varying mesh stiffness is established. The time varying mesh stiffness and dynamic response of healthy gear and pitted gear are then calculated respectively. The force transmission during gear mesh under the condition of surface pitting is analyzed. It is concluded that in the case of pitting fault, there will be a significant loss of torque in the power transmission process due to the loss of contact area. It is further inferred that the loss of meshing force andthedecreasing of Hertzian contact stiffness are the major contributing factors for pitting fault. In addition, the semi-analytical method of computing gear dynamic response is validated with experimental study ofacceleration signal in the perspective of dynamic response.

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

Applied Sciences ◽

10.3390/app10238379 ◽

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.

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Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220967693 ◽

2020 ◽

pp. 095440622096769

Author(s):

Wassim Lafi ◽

Fathi Djemal ◽

Dhouha Tounsi ◽

Ali Akrout ◽

Lassaad Walha ◽

...

Keyword(s):

Bevel Gear ◽

Gear System ◽

Uncertain Parameters ◽

Time Varying ◽

Mesh Stiffness ◽

Time Step ◽

Two Stage ◽

Straight Bevel Gear ◽

Potential Energy Method ◽

Process Method

A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.

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Dynamic Analysis of a Multi-Mesh Gear System With Mesh Stiffness Variation

Volume 5: 25th International Conference on Design Theory and Methodology; ASME 2013 Power Transmission and Gearing Conference ◽

10.1115/detc2013-12750 ◽

2013 ◽

Author(s):

Hanjun Jiang ◽

Yimin Shao

Keyword(s):

Numerical Simulation ◽

Dynamic Analysis ◽

Degrees Of Freedom ◽

Gear System ◽

Time Varying ◽

Mesh Stiffness ◽

Gear Teeth ◽

Linear Dynamic ◽

Complex Oscillation ◽

Stiffness Variation

Parameter excited oscillations induced by the varying tooth mesh stiffnesses of the gear pairs cause severe vibration in gear systems. The oscillations become more complex and serious in multi-mesh gear system because more mesh stiffnesses variation occur, which are necessary to be investigated in deeply. To illustrate the complex oscillation phenomena, a 8 degrees of freedom (DOF) non-linear dynamic model of a multi-mesh gear system is developed to study the responses of the system with considering time-varying mesh stiffnesses. Interactions between the mesh stiffness variations at the two meshes are examined. Seven different mesh phases are defined according to the alternating engagement of single and double gear teeth. The effects of different phases of the mesh stiffnesses between the two meshes on the typical multi-mesh gear system are identified by using numerical simulation. The results show that the oscillations of the multi-mesh gear system could be reduced by changing the phase of the mesh stiffnesses.

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A hybrid analytical-numerical method based on Isogeometric Analysis for determination of time varying gear mesh stiffness

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2021.104291 ◽

2021 ◽

Vol 160 ◽

pp. 104291

Author(s):

Andreas Beinstingel ◽

Michael Keller ◽

Michael Heider ◽

Burkhard Pinnekamp ◽

Steffen Marburg

Keyword(s):

Numerical Method ◽

Isogeometric Analysis ◽

Time Varying ◽

Mesh Stiffness ◽

Gear Mesh ◽

Gear Mesh Stiffness

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Research on dynamic characteristics of gear system considering the influence of temperature on material performance

Journal of Vibration and Control ◽

10.1177/10775463211002616 ◽

2021 ◽

pp. 107754632110026

Author(s):

Zhou Sun ◽

Siyu Chen ◽

Xuan Tao ◽

Zehua Hu

Keyword(s):

Elastic Modulus ◽

Dynamic Characteristics ◽

Poisson’S Ratio ◽

Gear System ◽

Poisson's Ratio ◽

Effect Of Temperature ◽

Time Varying ◽

Influence Of Temperature ◽

Meshing Stiffness ◽

Influence Of Temperature On

Under high-speed and heavy-load conditions, the influence of temperature on the gear system is extremely important. Basically, the current work on the effect of temperature mostly considers the flash temperature or the overall temperature field to cause expansion at the meshing point and then affects nonlinear factors such as time-varying meshing stiffness, which lead to the deterioration of the dynamic transmission. This work considers the effect of temperature on the material’s elastic modulus and Poisson’s ratio and relates the temperature to the time-varying meshing stiffness. The effects of temperature on the elastic modulus and Poisson’s ratio are expressed as functions and brought into the improved energy method stiffness calculation formula. Then, the dynamic characteristics of the gear system are analyzed. With the bifurcation diagram, phase, Poincaré, and fast Fourier transform plots of the gear system, the influence of temperature on the nonlinear dynamics of the gear system is discussed. The numerical analysis results show that as the temperature increases, the dynamic response of the system in the middle-speed region gradually changes from periodic motion to chaos.

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