Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

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

10.1177/09544062211049860 ◽

2021 ◽

pp. 095440622110498

Author(s):

Ruxin Lu ◽

Wencheng Tang

Keyword(s):

Analytical Calculation ◽

Calculation Model ◽

Tooth Profile ◽

Thermal Time ◽

Time Varying ◽

Mesh Stiffness ◽

Profile Error ◽

Gear Teeth ◽

Influencing Mechanism ◽

Torque Load

The temperature has a great contribution to the mesh stiffness and backlash of the gear pair. Presence of thermal deformation caused by temperature will complicate the gear teeth interaction. In this paper, the thermal time-varying stiffness model and thermal time-varying backlash model are proposed with the consideration of tooth profile error and total thermo-elastic deformation consists of the teeth deformation, teeth contact deformation, and gear body-induced deformation. The key parameters of thermo-elastic coupling deformation affected by temperature are calculated. Based on the proposed models, the influencing mechanism of temperature on the tooth profile error, mesh stiffness, total deformation, and backlash are revealed. The effects of shaft radius and torque load on the thermal stiffness and thermal backlash are studied. The proposed thermal stiffness and backlash calculation model are proven to be more comprehensive and the correctness is validated.

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Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

Journal of Tribology ◽

10.1115/1.4052941 ◽

2021 ◽

pp. 1-16

Author(s):

Siyu Wang ◽

Rupeng Zhu

Keyword(s):

Dynamic Response ◽

Hydrodynamic Lubrication ◽

Helical Gear ◽

Calculation Model ◽

Tooth Surface ◽

Time Varying ◽

Gear Pair ◽

Surface Wear ◽

Mesh Stiffness ◽

Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

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Analysis of tooth stiffness of nutation face gear

Engineering Computations ◽

10.1108/ec-11-2019-0522 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Guangxin Wang ◽

Lili Zhu ◽

Peng Wang

Keyword(s):

Gear Transmission ◽

Time Varying ◽

Mesh Stiffness ◽

Face Gear ◽

Content Type ◽

Gear Teeth ◽

Meshing Stiffness ◽

Single Tooth ◽

Tooth Stiffness ◽

External Face

Purpose The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission. Design/methodology/approach From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear. Findings The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained. Originality/value Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

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Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2020.103838 ◽

2020 ◽

Vol 149 ◽

pp. 103838 ◽

Cited By ~ 16

Author(s):

Zaigang Chen ◽

Ziwei Zhou ◽

Wanming Zhai ◽

Kaiyun Wang

Keyword(s):

Analytical Calculation ◽

Spur Gear ◽

Calculation Model ◽

Tooth Profile ◽

Gear Mesh

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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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