基于疲劳强度的RV减速器寿命计算与试验方法

张跃明; 李亿万; 纪姝婷

doi:10.13224/j.cnki.jasp.20220957

基于疲劳强度的RV减速器寿命计算与试验方法

doi: 10.13224/j.cnki.jasp.20220957

北京工业大学材料与制造学部，北京 100124

基金项目: 国家自然科学青年基金（51905009）；河北省重点研发计划项目（20311802D）

详细信息

作者简介:
张跃明（1965-），男，教授，博士，主要从事齿轮啮合原理、机构动力学、数字化设计及精密制造技术方面的研究

通讯作者:
纪姝婷（1988-），女，副教授，博士，主要从事工业机器人精密减速器数字化设计及齿廓修形理论研究。E-mail：jishuting@bjut.edu.cn

中图分类号: V233.7⁺2；TH132.46
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出版历程
- 收稿日期: 2022-12-15
- 网络出版日期: 2024-02-27

Life calculation and test method of RV reducer based on fatigue strength

Faculty of Materials and Manufacturing，Beijing University of Technology，Beijing 100124，China

摘要

摘要:
为准确计算实际工况下rotate vector（RV）减速器的寿命，缩减耐久性寿命试验的周期和成本，以工业机械臂用RV减速器为研究对象，提出了一种基于疲劳强度理论的RV减速器疲劳寿命计算方法，设计并搭建试验台进行加速寿命试验。结合材料stress-fatigue life（S-N）曲线及Palmgren-Miner线性损伤累积理论，建立了RV减速器的基本寿命模型；构建RV减速器额定寿命与使用寿命的数学表达式，系统研究RV减速器负载与使用寿命之间的规律，设计基于S曲线加减速控制算法的加速寿命试验；搭建试验台试验并进行数据分析，验证RV减速器疲劳寿命计算方法的准确性。结果表明：利用该疲劳寿命计算方法所得RV减速器寿命与试验结果相对误差仅为6.3%，试验加速系数为20.7，试验周期与成本缩减效果显著。
- 工业机器人 /
- RV减速器 /
- 疲劳强度理论 /
- 疲劳寿命 /
- 加速寿命试验
Abstract:
To accurately calculate the life of rotate vector (RV) reducer under actual operation and reduce the cycle and cost of durability life test, taking RV reducer for industrial manipulator as research object. A fatigue life calculation method of RV reducer based on fatigue strength theory was presented, and a device was designed and built for accelerated life test. Combined with stress-fatigue life (S-N) curve and Palmgren-Miner rule, the basic life model of RV reducer was established. The mathematical expression of the RV reducer’s rated life and service life was constructed, the law between the load and service life of the RV reducer was systematically studied, and the accelerated life test based on the S curve acceleration and deceleration control algorithm was designed. The test device was set up and the data were analyzed to verify the accuracy of the life calculation method. The results showed that the relative error between the life obtained by the fatigue life calculation method and the test results was only 6.3%, the acceleration factor was 20.7, and the test cycle and cost reduction effect were remarkable.
- industrial robot /
- RV reducer /
- fatigue strength theory /
- fatigue life /
- accelerated life test

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图 1 多级载荷应力幅与循环次数

Figure 1. Multi-level load stress and cycle life

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图 2 曲轴轴承与摆线轮间的力

Figure 2. Force between needle roller bearing and cycloidal gear

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图 3 曲轴轴承与摆线轮之间力的分析

Figure 3. Analysis of force between needle roller bearing and cycloidal gear

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图 4 曲轴轴承的力随转臂旋转角度的变化曲线

Figure 4. Variation of force of needle roller bearing with rotation angle of rotating arm

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图 5 曲轴轴承当量载荷随输出转矩变化曲线

Figure 5. Variation of equivalent load of needle roller bearing with output torque

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图 6 单周期曲轴轴承力变化曲线

Figure 6. Variation of force of needle roller bearing in single cycle

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图 7 曲轴轴承参数

Figure 7. Parameters of needle roller bearing

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图 8 RV减速器使用寿命数学表达式计算程序框图

Figure 8. Calculation procedure of RV reducer life

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图 9 实际工况下减速器运行姿态

Figure 9. Posture of reducer under actual working condition

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图 10 加速阶段S曲线

Figure 10. Acceleration phase S curve

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图 11 摆动一周期的S加速曲线图

Figure 11. S acceleration curve of swing cycle

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图 12 摆臂模型

Figure 12. Swing arm model

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图 13 加速寿命试验台

Figure 13. Accelerated life test device

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图 14 加速寿命试验数据

Figure 14. Accelerated life test data

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图 15 曲轴表面金属剥落失效

Figure 15. Metal spalling failure on crankshaft surface

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表 1 RV-80E减速器基本参数

Table 1. Basic parameters of RV-80E

参数	数值
偏心距e/mm	1.45
针齿半径R_p/mm	76.5
针轮齿数Z_p	40
摆线轮齿数Z_c	39
曲轴分布圆半径r₀/mm	42
额定转矩T/（N·m）	784
曲轴数λ	3

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表 2 RV-80E用曲轴轴承基本参数

Table 2. Basic parameters of needle roller bearing of RV-80E

参数	数值
滚子公称直径$ {D}_{{\mathrm{we}}}$/mm	5
滚子有效长度$ {l}_{{\mathrm{we}}} $/mm	9
滚子数Z	14
轴承节圆直径$ {D}_{{\mathrm{m}}} $/mm	31
轴承外径$ {D}_{{\mathrm{u}}} $/mm	36
轴承内径$ {D}_{{\mathrm{l}}} $/mm	26

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表 3 减速器摆动信息

Table 3. Reducer swing information

参数	加速	匀速	减速	静止
$ \Delta t/ $s	0.3	1.7	0.3	1
$ \Delta \omega $/（rad/s）	$ \dfrac{{\text{π}} }{2} $	0	$ \dfrac{{\text{π}} }{2} $	0
$ \Delta \varphi / $rad	$ \dfrac{3{\text{π}} }{40} $	$ \dfrac{17{\text{π}} }{20} $	$ \dfrac{3{\text{π}}}{40} $	0

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表 4 各阶段加速度

Table 4. Acceleration at each stage

历程	重力加速度/ （m/s²）	向心加速度/ （rad/s²）	平均角加速度/ （rad/s²）
加速段	g	0	$ \dfrac{5{\text{π}} }{3} $
匀速段	g	ω²l_i	0
减速段	g	0	$ -\dfrac{5{\text{π}} }{3} $
静止段	g	0	0

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表 5 各阶段转矩与转速大小

Table 5. Torque and speed at each stage

历程	重力矩T	惯性矩Q	平均转速n_m
加速段	$\displaystyle\sum {{m_{{\mathrm{a,}}i}g{l_i}\cos\; {\varphi _i}}} $	$ \dfrac{5{\text{π}} }{3}J $	$ \dfrac{{\text{π}} }{4} $
匀速段	$\displaystyle\sum {{m_{{\mathrm{a,}}i}g{l_i}\cos\; {\varphi _i}}} $	$ J{\omega }^{2}l $	$ \dfrac{{\text{π}} }{2} $
减速段	$\displaystyle\sum {{m_{{\mathrm{a,}}i}g{l_i}\cos\; {\varphi _i}}} $	$ -\dfrac{5{\text{π}} }{3}J $	$ \dfrac{{\text{π}}}{4} $
静止段	${m_{{\mathrm{a,}}i}g{l_i}}$	0	0

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表 6 RV减速器的试验参数

Table 6. Test parameters of RV reducer

参数符号	数值
额定转矩T₀/（N·m）	784
额定输出转速n_out/（r/min）	15
额定寿命L₀/h	6000
启、停许用转矩T_s1/（N·m）	1 960
瞬时最大许用转矩T_s2/（N·m）	3920
摆臂长度r/mm	850

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