航空混交面齿轮分流传动系统非线性动力学

莫帅; 唐旭; 陈科任; 张伟; 张以都

doi:10.13224/j.cnki.jasp.20230265

航空混交面齿轮分流传动系统非线性动力学

doi: 10.13224/j.cnki.jasp.20230265

莫帅^{1, 2, 3, 4, 5,},
唐旭²,
陈科任²,
张伟^3,*, ,,
张以都⁶

1.
广西大学特色金属材料与组合结构全寿命安全国家重点实验室，南宁 530004
2.
广西大学机械工程学院，南宁 530004
3.
广西大学工程力学研究中心，南宁 530004
4.
华中科技大学数字制造装备与技术国家重点实验室，武汉 430074
5.
直升机传动技术国防科技重点实验室，南京 210016
6.
北京航空航天大学虚拟现实技术与系统国家重点实验室，北京 100191

基金项目: 国家自然科学基金（52265004）；直升机传动技术国防科技重点实验室开放基金（HTL-0-21G07）；华中科技大学数字制造装备与技术国家重点实验室开放基金（DMETKF2021017）；广西科技重大专项（2023AA19005）

详细信息

作者简介:
莫帅（1987-），男，教授、博士生导师，博士，研究方向为高端装备振动控制与故障动力学、关键核心基础零部件设计制造（高性能齿轮/轴承）。E-mail：moshuai2010@163.com

通讯作者:
张伟（1960-），男，教授、博士生导师，博士，研究方向为非线性动力学。E-mail：sandyzhang9@163.com

中图分类号: V233.1；TH113.1
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出版历程
- 收稿日期: 2023-04-21
- 网络出版日期: 2024-10-01

Nonlinear dynamics of aircraft blended face gear split transmission system

MO Shuai^{1, 2, 3, 4, 5
,},
TANG Xu²,
CHEN Keren²,
ZHANG Wei^{3,*
, ,},
ZHANG Yidu⁶

1.
State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures，Guangxi University，Nanning 530004，China
2.
School of Mechanical Engineering，Guangxi University，Nanning 530004，China
3.
Scientific Research Center of Engineering Mechanics，Guangxi University，Nanning 530004，China
4.
State Key Laboratory of Digital Manufacturing Equipment and Technology，Huazhong University of Science and Technology，Wuhan 430074，China
5.
National Key Laboratory of Science and Technology on Helicopter Transmission，Nanjing 210016，China
6.
State Key Laboratory of Virtual Really Technology and Systems，Beihang University，Beijing 100191，China

摘要

摘要:
在考虑支撑刚度、时变啮合刚度、齿侧间隙、综合传动误差、轴承刚度等多种因素的前提下，建立混交面齿轮分流传动系统的非线性动力学模型，研究混交面齿轮分流传动系统的非线性动力学特性。采用Runge-Kutta积分方法对系统微分动力学方程进行求解，系统的非线性特征通过相平面图、时域图、频域图和庞加莱截面图小波分析图来描述，并用分分岔图描述外部激励频率和刚度对系统的非线性行为的影响。结果表明：在不同的外部激励和刚度作用下，系统将会呈现周期-混沌交替的运动特性。
- 非线性动力学 /
- 混交 /
- 面齿轮 /
- 分流传动 /
- 小波分析
Abstract:
On the premise of considering many factors, such as support stiffness, time-varying meshing stiffness, tooth backlash, comprehensive transmission error, bearing stiffness, etc, the nonlinear dynamic model of blended face gear split transmission system was established. The nonlinear dynamic characteristics of mixed face gear split transmission system were studied. The differential dynamic equation of the system was solved by Runge-Kutta integral method. The nonlinear characteristics of the system were described by phase plane diagram, time domain diagram, frequency domain diagram and Poincare section wavelet analysis diagram, and the bifurcation diagram was used to describe the influences of external excitation frequency and stiffness on the nonlinear behavior of the system. The results showed that under the action of different external excitation and meshing stiffness, the system could present periodic-chaotic alternating motion characteristics.
- nonlinear dynamics /
- blended /
- face gear /
- split transmission /
- wavelet analysis

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图 1 混交面齿轮分流传动系统三维模型

Figure 1. Three-dimensional model of blended face gear split transmission system

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图 2 混交面齿轮分流传动系统动力学模型

Figure 2. Dynamic model of split transmission system of blended face gear

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图 3 轴承的运动学模型

Figure 3. Kinematic model of bearings

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图 4 内外圈曲率中心几何关系图

Figure 4. Geometric relation diagram of curvature center of inner and outer circles

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图 5 x_n1量纲-频率分岔图

Figure 5. x_n1 dimensional-frequency bifurcation diagram

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图 6 x_n2量纲-频率分岔图

Figure 6. x_n2 dimensional-frequency bifurcation diagram

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图 7 ω_e=0.40时x_n1的非线性响应

Figure 7. Nonlinear response of x_n1 when ω_e=0.40

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图 8 ω_e=0.55时x_n1的非线性响应

Figure 8. Nonlinear response of x_n1 when ω_e=0.55

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图 9 ω_e=0.40时x_n2的非线性响应

Figure 9. Nonlinear response of x_n2 when ω_e=0.40

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图 10 ω_e=0.55时x_n2的非线性响应

Figure 10. Nonlinear response of x_n2 when ω_e=0.55

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图 11 等效位移x_n1的三维频域图

Figure 11. Three-dimensional FFT of equivalent displacement x_n1

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图 12 等效位移x_n2的三维频域图

Figure 12. Three-dimensional FFT of equivalent displacement x_n2

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图 13 x_n1的三维相空间图

Figure 13. Three-dimensional phase space diagram of x_n1

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图 14 x_n2的三维相空间图

Figure 14. Three-dimensional phase space diagram of x_n2

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图 15 x_n1量纲-啮合刚度分岔图

Figure 15. x_n1 dimension-meshing stiffness bifurcation diagram

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图 16 x_n2量纲-啮合刚度分岔图

Figure 16. x_n2 dimension-meshing stiffness bifurcation diagram

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图 17 κ_m=0.25时x_n1的非线性响应

Figure 17. Nonlinear response of x_n1 when κ_m=0.25

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图 18 κ_m=0.40时x_n1的非线性响应

Figure 18. Nonlinear response of x_n1 when κ_m=0.40

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图 19 κ_m=0.25时x_n2的非线性响应

Figure 19. Nonlinear response of x_n2 when κ_m=0.25

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图 20 κ_m=0.40时x_n2的非线性响应

Figure 20. Nonlinear response of x_n2 when κ_m=0.40

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图 21 x_n1量纲-支撑刚度分岔图

Figure 21. x_n1 dimension-brace stiffness bifurcation diagram

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图 22 x_n2量纲-支撑刚度分岔图

Figure 22. x_n2 dimension-brace stiffness bifurcation diagram

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图 23 系统非线性响应特性

Figure 23. System nonlinear response characteristic

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表 1 混交面齿轮分流传动系统参数

Table 1. System parameters of blended face gear split transmission system

参数	数值
圆柱齿轮齿数 z₁	23
正交面齿轮齿数 z₂	179
非正交面齿轮齿数 z₃	179
圆柱齿轮质量 m₁/kg	1.7
正交面齿轮质量 m₂/kg	42
非正交面齿轮质量 m₃/kg	48
模数 m/mm	2.5
压力角 α_n/（°）	25
圆柱齿轮转动惯量 J₁/10⁻³ （kg·m²）	0.14
正交面齿轮转动惯量 J₂/（kg·m²）	2.06
非正交面齿轮转动惯量 J₃/（kg·m²）	2.39

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表 2 轴承技术参数

Table 2. Bearing technical parameters

参数	数值
参数	面齿轮级	圆柱齿轮级轴承
质量/kg	1	0.5
内径/m	0.10	0.04
外径/m	0.18	0.08
宽度/m	0.034	0.018

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