An improved analytical method for calculating time-varying mesh stiffness of helical gears

Feng, Mengjiao; Ma, Hui; Li, Zhanwei; Wang, Qibin; Wen, Bangchun

doi:10.1007/s11012-017-0746-6

Cited by 97 publications

(34 citation statements)

References 29 publications

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“…Equations (16) and (17) constitute the distribution expression of contact force in beveloid gear pair meshing process. Based on Lagrange multiplier rule, U t takes the minimum value for the following required condition…”

Section: Contact Force Modelingmentioning

confidence: 99%

“…Han and Qi 15 developed an analytical method to incorporate the faults by combining the slicing method, discrete integral method, and potential energy method. Feng et al 16 adopted a slice method to calculate the time-varying mesh stiffness (TVMS) of helical gear pairs, where the tooth is divided into many individual sliced spur gears along the tooth width, and the stiffness of helical gear pairs is obtained by accumulating the TVMS of the sliced spur gear pairs. Rezaei et al 17 derived the analytical equations for the spur gear pair and then extracted the helical gear pair mesh stiffness by dividing a helical tooth into the several independent thin spur tooth slices.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Sun

Song

Zhu

et al. 2020

The Journal of Strain Analysis for Engineering Design

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Using minimum potential energy theory and slicing method, a computational approach to calculate the magnitude and distribution of contact force for paralleled beveloid gear pair was proposed in this article. The theoretical tooth contact model was built based on spatial gearing theory to calculate the mesh parameters including the coordinates, normal vectors, and equivalent radius for meshing points. Then, the analytical contact force model of paralleled beveloid gear pair was derived based on minimum potential energy theory. Finite element contact analysis was conducted to verify the proposed model. Finally, the influences of macro-geometry design parameters on the contact force distribution were investigated. Results show that the pressure angle has a limited influence on the contact force distribution. The increase in helix and cone angles will observably increase the asymmetry of contact force distribution as well as the fluctuation of contact force distribution for a single tooth. A good correlation was obtained between the proposed analytical model and the finite element model for the distribution and magnitudes of contact force.

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Section: Contact Force Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Sun

Song

Zhu

et al. 2020

The Journal of Strain Analysis for Engineering Design

View full text Add to dashboard Cite

show abstract

“…For example, Mao 11 introduced an accurate method for estimating STE in powertrain transmission systems through an accurate gear contact analysis. The analytical method 1,[14][15][16][17][18] has the advantages of fast calculation speed and good accuracy, but its application range is narrow. For example, analytical method is used in the literature 1 to calculate timevarying mesh stiffness.…”

Section: Introductionmentioning

confidence: 99%

Effects of lightweight gear blank on noise, vibration and harshness for electric drive system in electric vehicles

Hou

Lei

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, effects of lightweight gear blank on static and dynamic behavior for electric drive system in electric vehicles are studied. First, a hybrid finite element-analytical method is proposed in this paper to establish gear load contact analysis model considering the structure of lightweight gear blank, which can balance the computing speed and numerical accuracy. Second, this paper establishes a rigid-flexible coupled dynamic model of electric drive system considering shaft elasticity, bearing stiffness, and housing flexibility. Finally, aiming at the noise, vibration, and harshness problem of an electric drive system equipped on electric vehicles, effects of gear web and gear rim thickness on noise, vibration, and harshness excitation source such as static transmission error and dynamic meshing force as well as dynamic response at bearings and housing are analyzed. The results show that changing gear web and gear rim thickness can significantly reduce dynamic meshing force and dynamic response. Compared with solid gear, dynamic meshing force is reduced by 68.50%, and dynamic response is reduced by 66.70% after optimization, thereby significantly improving the noise, vibration, and harshness performance of gear transmission system in electric vehicles.

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“…Excitation source is mostly believed as transmission error (TE) which is caused by manufacture precision, assembly error, gear geometry deviation and time-varying mesh stiffness. 1–8 Several methods have been adopted to investigate the TE mechanism and calculate the TE value. In 1995, Palmer and Munro 7 confirmed that through measurement, the exact relationship of transmission noise corresponds to the TE.…”

Section: Introductionmentioning

confidence: 99%

Model-based transmission acoustic analysis and improvement

Cao

Chen

Zang

2020

Proceedings of the Institution of Mechanical Engineers, Part D:

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A model-based transmission acoustic performance has been studied. Both excitation source and structure-borne noise transfer are investigated. For excitation source, transmission error is the main cause. To reduce transmission error, the most effective method is gear micro-geometry modification. However, there is no direct mathematical model that could reveal the relationship between transmission error and gear micro-geometry parameters, especially in the context of transmission system with shafts, bearings and housings included. By using multiple variable linear regression method, the relationship between transmission error and gear micro-geometry parameters is connected. The optimised transmission error decreases from 9.34 to 5.65 μm at a typical working condition. For structure-borne noise transfer, the housing modal and transmission system modal have been analysed. Based on the simulation results, housing thickness around bearing assembly area is increased, and strengthen ribs are added at weak areas. As a result, the amplitude of housing vibration acceleration is reduced. Finally, the transmission noise sound pressure level at 0.3-m distance has decreased by 4.63 dB on average. The presented model-based transmission acoustic analysis work flow is demonstrated workable and effective.

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An improved analytical method for calculating time-varying mesh stiffness of helical gears

Cited by 97 publications

References 29 publications

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Effects of lightweight gear blank on noise, vibration and harshness for electric drive system in electric vehicles

Model-based transmission acoustic analysis and improvement

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