多维度耦合的弧齿锥齿轮干运转时间预测

陆凤霞; 李牟; 王经花; 朱如鹏

doi:10.13224/j.cnki.jasp.20230049

多维度耦合的弧齿锥齿轮干运转时间预测

doi: 10.13224/j.cnki.jasp.20230049

南京航空航天大学直升机动力学全国重点实验室，南京 210016

基金项目: 国家自然科学基金（52075241）；国家科技重大专项（J2019-Ⅲ-0023-0067）；直升机传动技术重点实验室基金（HTL-A-21G05）

详细信息

作者简介:
陆凤霞（1972-），女，副教授，博士，主要从事机械传动方面的研究

中图分类号: V275.1
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- 被引次数: 0
出版历程
- 收稿日期: 2023-02-03
- 网络出版日期: 2025-04-18

Prediction of dry running time multi-dimensionally coupled spiral bevel gears

National Key Laboratory of Helicopter Aeromechanics，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

摘要:
为预测弧齿锥齿轮干运转时间，提出一种齿面弹流润滑-轮齿啮合-齿轮系统热传递的耦合预测方法，以揭示微观弹流润滑与宏观流场/温度场间的演变机理。应用弹流润滑理论建立锥齿轮稳态热弹流润滑模型，获得齿面间摩擦因数；引入油膜保持参数，形成齿面时变摩擦因数计算方法；应用计算流体力学方法，仿真计算轮齿啮合稳态温度分布及齿轮系统瞬态温度分布；通过3个维度间的参数传递及耦合，预测锥齿轮干运转时间。结果表明：该模型时间尺度从齿面弹流润滑维度的微秒级至齿轮系统热传递维度的分秒级，空间尺度从齿面弹流润滑维度的微米级至齿轮系统热传递维度的分米级，耦合结构-力-润滑-热特征建立弧齿锥齿轮干运转时间预测方法，预测齿轮约在1.5 h失效。
- 弧齿锥齿轮 /
- 干运转 /
- 弹流润滑 /
- 计算流体力学 /
- 油膜厚度 /
- 温度分布
Abstract:
In order to predict the dry running time of spiral bevel gear, a coupling prediction method for tooth surface elastohydrodynamic lubrication tooth meshing gear system heat transfer was proposed to reveal the evolution mechanism between micro elastohydrodynamic lubrication and macro flow field/temperature field. The steady-state thermal elastohydrodynamic lubrication model of spiral bevel gear was established by using the elastohydrodynamic lubrication theory, and the friction coefficient of gear tooth surface was obtained. By introducing the oil film retention parameter, the calculation method of time-varying friction coefficient of tooth surface was formed; using computational fluid dynamics (CFD) method, the steady-state temperature distribution of gear meshing and the transient temperature distribution of gear system were simulated and calculated. The dry running time of spiral bevel gear was predicted by parameter transmission and coupling between three dimensions. The results showed that the time scale of the model was from O(10⁻⁶) s of the elastohydrodynamic lubrication dimension of the tooth surface to O(10⁻¹) s of the heat transfer dimension of the gear system, and the spatial scale was from O(10⁻⁶) m of the elastohydrodynamic lubrication dimension of the tooth surface to O(10⁻¹) m of the heat transfer dimension of the gear system. The coupled structure-force-lubrication-thermal characteristics were employed to set up a prediction method for the dry running time of spiral bevel gear, predicting the failure of gear within about 1.5 h.
- spiral bevel gear /
- dry running /
- elastohydrodynamic lubrication /
- CFD /
- oil film thickness /
- distribution of temperature

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图 1 不同维度间数据传递关系

Figure 1. Data transmission relationship of each scale

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图 2 多维度耦合预测模型示意图

Figure 2. Schematic diagram of multi-dimensional coupling prediction model

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图 3 弧齿锥齿轮的啮合过程

Figure 3. Meshing process of spiral bevel gear

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图 4 齿面摩擦因数

Figure 4. Tooth surface friction coefficient

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图 5 失油过程中的润滑状态演变

Figure 5. Evolution of lubrication state during oil loss

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图 6 失油状态下齿面时变摩擦因数

Figure 6. Time varying friction coefficient under oil loss

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图 7 轮齿啮合维度

Figure 7. Gear scale

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图 8 齿轮风阻仿真计算

Figure 8. Simulation calculation of gear windage

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图 9 齿轮系统热传递维度的温度场分布

Figure 9. Temperature field distribution in the thermal transfer dimension of gear systems

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图 10 3个维度耦合的参数传递关系

Figure 10. Parameter transfer relationships in three-dimensional coupling

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图 11 失油过程中的啮合摩擦热源

Figure 11. Frictional heat generation during gear meshing under starved lubrication conditions

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图 12 失油过程中齿轮系统温度场仿真结果

Figure 12. Simulation results of temperature field in gear systems under starved lubrication conditions

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表 1 多维度的时间尺度及空间尺度

Table 1. Multidimensional temporal and spatial scales

维度	齿面弹流润滑	轮齿啮合	齿轮系统热传递
时间尺度/s	10⁻⁶	10⁻⁴	10⁻¹
空间尺度/m	10⁻⁶	10⁻⁴	10⁻¹

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表 2 弧齿锥齿轮的主要结构参数

Table 2. Main structural parameters of spiral bevel gear

参数	小轮	大轮
轴交角/（°）	90
大端端面模数/mm	6.3
齿数	31	46
齿宽/mm	57.4
中点螺旋角/（°）	35
外锥距/mm	14.7327
分锥角/（°）	33.9767	56.0233
根锥角/（°）	32.2728	53.4411
面锥角/（°）	36.5589	57.7272
齿顶高/mm	6.696	4.014
齿根高/mm	5.198	7.88

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表 3 大轮的加工参数

Table 3. Machining parameters of the large wheel

参数	大轮
刀尖直径/mm	302.3
刀顶距/mm	3.048
压力角/（°）	20
轴向轮位/mm	0
床位/mm	0
垂直轮位/mm	0
切削滚比	1.2047
径向刀位/mm	138.9976
角向刀位/（°）	63.9142

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表 4 小轮加工参数

Table 4. Machining parameters of the small wheel

参数	小轮凹面	小轮凸面
刀尖直径/mm	276.0331	337.0620
压力角/（°）	18	22
轴向轮位/mm	−7.445	−7.7334
床位/mm	3.9748	3.91339
垂直轮位/mm	10.4092	−6.1197
切削滚比	1.7961	1.8230
径向刀位/mm	138.3450	144.9935
角向刀位/（°）	−64.5356	−63.7857
二阶变性系数	0.019	0
三阶变性系数	0	0

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表 5 椭圆长短轴及卷吸速度

Table 5. Long and short axis of the ellipse and the entrainment velocity

啮合点编号	短轴/m	长轴/m	卷吸速度 μ/（m/s）	μ与短轴夹角/（°）
1	0.00082	0.00146	6.98	86.06
2	0.00083	0.00147	6.76	86.03
3	0.00083	0.00147	6.54	86.01
4	0.00084	0.00148	6.31	85.99
5	0.00085	0.00149	6.06	85.98
6	0.00086	0.00149	5.79	85.97
7	0.00086	0.00150	5.52	85.96
8	0.00087	0.00151	5.24	85.95
9	0.00087	0.00151	4.94	85.94
10	0.00088	0.00152	4.64	85.93
11	0.00089	0.00153	4.32	85.92
12	0.00089	0.00153	4.30	85.97

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表 6 失油过程中齿轮箱零件表面最高温度

Table 6. Maximum surface temperature of the gearbox parts during oil loss

时间/s	大轮温度/℃	小轮温度/℃
600	95	108
1200	122	141
1800	152	176
2400	180	209
3000	205	239
3600	227	266
4200	246	289
4800	263	309

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参考文献(21)

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