Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Guang-jian, Wang; Luo, Qing; Zou, Shuaidong

doi:10.1007/s12206-021-0819-2

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…Therefore, the comprehensive meshing stiffness of the gear-pair changes periodically. References (Wang et al, 2012;Marafona et al, 2021;Wang et al, 2021) show that the meshing stiffness excitation is one of the main internal excitations that causes the vibration of the gear transmission system, which plays a decisive role in the basic characteristics of the system dynamics to a certain extent. Therefore, the basic function of the gear system vibration analysis is to accurately calculate the meshing stiffness of the gear pair (Zhou et al, 2022b).…”

Section: Introductionmentioning

confidence: 99%

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Ma,

Jiang,

et al. 2024

Mech. Sci.

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Abstract. Stiffness excitation is one of the important excitations for the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear system. Accurate calculation of the gear meshing stiffness is of great significance to investigating dynamic characteristics of the VH-CATT cylindrical gear system. Firstly, based on the forming theory of the modified tooth surface, the modified tooth surface equation of the VH-CATT cylindrical gear was deduced, and the 3D reconstruction was realised. Next, the load tooth contact analysis (LTCA) model of the VH-CATT cylindrical gear was developed to calculate the meshing stiffness of the VH-CATT cylindrical gear, and it was verified by the finite-element calculation. Finally, the influence of the load and modification parameters on the VH-CATT cylindrical gear stiffness was investigated. Research shows that the stiffness calculation method of the VH-CATT cylindrical gear based on LTCA is accurate. The meshing stiffness of the VH-CATT cylindrical gear in the double-tooth meshing area is large, and the meshing stiffness of the VH-CATT cylindrical gear in the single-tooth meshing area is small. The stiffness of the VH-CATT cylindrical gear increases with an increase in the load and cutter inclination angle, the stiffness of the VH-CATT cylindrical gear only in the double-tooth meshing area decreases with an increase in the parabolic coefficient, and the stiffness of the VH-CATT cylindrical gear increases with a decrease in the blade parabolic vertex position value. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising design.

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Section: Introductionmentioning

confidence: 99%

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Ma,

Jiang,

et al. 2024

Mech. Sci.

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“…[18][19][20] investigated the TVMS model containing different tooth damages (e.g., pitting, spalling and cracking). Considering the multi-tooth contact problem for internal meshing gear pair with the small tooth difference, Wang et al [21] developed two methods to calculate the TVMS and compared them with finite element method (FEM). However, these calculation models of TVMS and backlash are based on the assumption that the tooth surface is absolutely smooth.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics

et al. 2023

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The microscopic topography of tooth surface affects the nonlinear dynamic characteristics of the gear system. However, few studies have fully taken into account the effects of microscopic topography on time-varying meshing stiffness (TVMS) and backlash in gear dynamics. In this context, this study derives TVMS and timevarying backlash with fractal characteristics based on fractal theory, and introduced them into a 6-DOF nonlinear dynamic model. With various nonlinear dynamics analysis tools, the dynamic characteristics of the gear system under different fractal parameters are investigated. The results indicate that the increase of the fractal dimension or the decrease of the characteristic scale coefficient leads to a smoother tooth surface, larger TVMS, and smaller amplitude of backlash. The effect of fractal dimension is more sensitive than characteristic scale coefficient. Furthermore, in the low-speed region, the increase of fractal dimension has a positive effect on the dynamic response of the system, and can reduce the amplitude of transmission error. In the high-speed region, the opposite is true. It is worth pointing out that the influence of fractal dimension on gear dynamic characteristics is nonlinear. Considering the machining cost and dynamic response of gear, the fractal dimension of 1.5 is the best choice. The influence of characteristic scale coefficient on system dynamics is similar to that of fractal dimension but weak.

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“…Wang et al (2013) takes this algorithm further by incorporating the factor of tooth root circle correction into the calculation, while Meng et al (2013) addresses the phenomenon of crack-induced reduction in the time-variant meshing stiffness of gears. The methodology for calculating the time-variant mesh stiffness of existing gears is further refined by Wang et al (2021), who studied small differential internal gear pairs with multiple tooth contact problems. However, this method of calculating the time-variant mesh stiffness of gears using Weber's method is too tedious.…”

Section: Introductionmentioning

confidence: 99%

Study on the method of analyzing the time-variant internal mesh stiffness of helical gears considering the flexibility of the gear ring

WU,

ZHOU,

ZHAO

et al. 2023

JAMDSM

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In a 9-speed transmission, as a key participant of a planetary wheel system, the gear ring will be subjected to elastic deformation as a result of the meshing action, affecting the smoothness of the transmission. Firstly, the time-variant stiffness of helical gears is calculated using the potential energy method, the time-variant characteristics of bending rigidity, shear rigidity and compression rigidity are analyzed; secondly, the timevariant gear ring stiffness is computed using the bending beam theory, in which the change in gear ring rigidity is incorporated into the simplified model of the gear ring, and the circumferential displacement, radial displacement and bending angle of the gear ring is used to calculate the gear ring deformation variables and the time-variant stiffness of the internal gear ring; finally, the time-variant stiffness of planetary helical gear is calculated according to parallel connection theory. Finally, based on parallel theory, the comprehensive timevariant mesh stiffness of planetary helical gears was computed, and the ring stiffness influence on the comprehensive time-variant mesh stiffness of planetary helical gears was analyzed in meshing with single and double teeth. The average difference in the zone is 8.9%. The experiment shows that there are two peak values of tooth ring deformation in a meshing period between tooth ring and gear, and the peak value of tooth ring deformation near the meshing point is larger. At low rotational speed, the predicted strain value of the tooth surface of the gear ring has an average difference of 10.6% and 8.6% from the measured value of strain measuring point No. 1 and No. 2.

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Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Cited by 6 publications

References 25 publications

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics

Study on the method of analyzing the time-variant internal mesh stiffness of helical gears considering the flexibility of the gear ring

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