Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (7): 1902-1910.doi: 10.13229/j.cnki.jdxbgxb.20210957

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Meshing stiffness calculation and vibration analysis of helical gear considering deflection

Guo-hui CHEN1(),Ye-yin XU2,Ying-hou JIAO1()   

  1. 1.School of Mechatronics Engineering，Harbin Institute of Technology，Harbin 150001，China
    2.School of Aerospace Engineering，Xi′an Jiaotong University，Xi′an 710049，China
  • Received:2021-09-23 Online:2023-07-01 Published:2023-07-20
  • Contact: Ying-hou JIAO E-mail:15b908046@hit.edu.cn;jiaoyh@hit.edu.cn

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Abstract:

Based on the change rule of the length of the contact line of the helical gear， the deflection moment under different load distributions along the axial direction is analyzed， and a novel model of the helical gear considering the time-varying stiffness and the deflection stiffness is proposed. The response of an example helical gear system with different tooth widths and torques is studied and compared with the existing experimental data. The lumped-parameter model accounting for backlash is also introduced to analyze the influence of torque and backlash. The results reveal that the proposed model is effective and advanced for general gear systems， especially at low and medium speeds. As the tooth width increases， the effect of the deflection stiffness becomes more significant. With increasing torque， the meshing stiffness of the helical gear increases， and the response of the gear system under parametric excitation caused by time-varying stiffness also increases. As the unbalanced force increases， the motion of the gear system considering backlash develops from periodic motion into pseudo-periodic motion and then back into periodic motion.

Key words: mechanical engineering, helical gear pair, meshing stiffness, deflection stiffness, backlash, dynamic response

CLC Number: 

  • TH113.2

Fig.1

Contact line in meshing plane of helical gear"

Fig.2

Dynamic model of a helical gear pair"

Fig.3

Meshing stiffness of a helical gear pair"

Fig.4

Dynamic model of a helical gear pair"

Fig.5

Dynamic model of experimental system inref.［5］"

Table 1

System parameter table"

参数数值
齿数50
法向模数/mm2.714
法向压力角/（°）18.224
节圆直径/mm150
基圆直径/mm140.954
螺旋角/（°）25.232
传递扭矩/（N·m）250

Fig.6

Comparison of predicted and measured DTE in ref ［6］ at 250 N·m"

Fig.7

Dynamic response of the system with different face width（left side of rotor 1）"

Fig.8

Dynamic response of system with differenttorque（left side of rotor）"

Fig.9

Geometric sketch of tooth position for drive-side contact and back-side contact"

Fig.10

Spectral analysis of gear's torsional vibration"

Fig.11

Poincaré map of gear's torsional vibration"

Fig.12

Time history diagrams and phase plots of the gear's torsional vibration under various speed"

Fig.13

Gear's torsional vibration under various torque"

Fig.14

Poincaré map of gear's torsional vibration with various backlash"

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