减速器滞回模型及其应用

程慧明; 石照耀

doi:10.13700/j.bh.1001-5965.2023.0055

减速器滞回模型及其应用

doi: 10.13700/j.bh.1001-5965.2023.0055

程慧明,
石照耀^,

北京工业大学北京市精密测控技术与仪器工程技术研究中心，北京 100124

基金项目: 深圳市技术攻关重点项目(JSGG20220831104001002)

详细信息

通讯作者:
E-mail：shizhaoyao@bjut.edu.cn

中图分类号: TH89
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- 被引次数: 0
出版历程
- 收稿日期: 2023-02-15
- 录用日期: 2023-04-23
- 网络出版日期: 2023-05-10
- 整期出版日期: 2025-02-28

Hysteresis model of reducer and its application

CHENG Huiming,
SHI Zhaoyao^,

Beijing Engineering Research Center of Precision Measurement Technology and Instruments，Beijing University of Technology，Beijing 100124，China

Funds: Shenzhen Techmical Key Projects (JSGG20220831104001002)

More Information

Corresponding author: E-mail：shizhaoyao@bjut.edu.cn

摘要

摘要:
减速器是典型的滞回系统，滞回影响传动性能。现有减速器滞回模型会忽略几何误差的滞回特性，而将其当成常量，导致模型不能完整反映其滞回特性。为此，探究了减速器滞回的产生机理，从理论上分析了几何误差、摩擦和弹性变形对减速器滞回的影响，建立了考虑几何误差滞回特性的减速器滞回模型。在模型的实际应用中，发现了减速器回差的动态性，并推导了动态回差公式。通过实验研究，验证了几何误差对减速器滞回的影响，证实了滞回模型的有效性；通过改变回差测试时的加载速率，验证了回差的动态性；发现材质不同，受加载速率的影响不同，加载速率每增加0.05 (N·m)/s，模数为0.22 mm的小型金属和塑料齿轮减速器的回差测试结果分别下降约3′和10′。
- 减速器 /
- 滞回模型 /
- 回差 /
- 动态性 /
- 加载速率
Abstract:
A reducer is a typical hysteresis system, and the hysteresis affects its transmission performance. The existing hysteresis models of reducers usually ignore the hysteresis characteristics of geometric errors and treat them as constants, which results in the inability of these models to fully reflect the hysteresis characteristics of reducers. In order to better understand the mechanism behind gear reducer hysteresis, this paper theoretically analyzes the effects of friction, elastic deformation, and geometric errors on the phenomenon. Additionally, it develops a new model for gear reducer hysteresis that takes geometric error hysteresis characteristics into account. The model's practical application reveals the dynamic characteristics of the lost motion in the reducer, and a dynamic lost motion formula is deduced. Experimental research verifies the influence of geometric errors on the reducer hysteresis and confirms the effectiveness of the hysteresis model. By changing the loading rate during the lost motion test, the dynamic characteristics of the lost motion are verified. It was found that different materials have different effects on the loading rate. For every 0.05 (N·m)/s increase in the loading rate, the lost motion test results of the small metal gear reducer and the small plastic gear reducer with a modulus of 0.22 mm decrease by about 3′ and 10′, respectively.
- reducer /
- hysteresis model /
- lost motion /
- dynamic characteristics /
- loading rate

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图 1 减速器的输入-输出关系

Figure 1. Input and output relationship of reducer

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图 2 减速器滞回模型结构

Figure 2. Hysteresis model structure of reducer

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图 3 考虑几何误差的减速器滞回模型

Figure 3. Hysteresis model of reducer including geometric error

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图 4 输入转角与输出转角的关系

Figure 4. Relationship of input angle and output angle

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图 5 几何误差的滞回曲线

Figure 5. Hysteresis curve of geometric error

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图 6 摩擦产生的滞回曲线

Figure 6. Hysteresis curves of friction

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图 7 理想的刚度曲线

Figure 7. Ideal stiffness curve

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图 8 实际的刚度曲线

Figure 8. Actual stiffness curve

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图 9 减速器滞回曲线的组成

Figure 9. Composition of hysteresis curve of reducer

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图 10 几何回差、弹性回差和总回差之间的关系

Figure 10. Relationship among geometric lost motion, elastic lost motion and total lost motion

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图 11 减速器输入端固定时的几何误差滞回曲线

Figure 11. Geometric error hysteresis curves with fixed inputs to the reducer

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图 12 实验用减速器

Figure 12. Experimental reducer

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图 13 实验用减速器结构

Figure 13. Structure of experimental reducer

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图 14 测试设备

Figure 14. Testing machine

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图 15 测试步骤^[16]

Figure 15. Test step^[16]

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图 16 加载力矩为0.01 N·m时的测试曲线

Figure 16. Test curve when the loading torque is 0.01 N·m

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图 17 加载力矩0.02 N·m时的测试曲线

Figure 17. Test curve when the loading torque is 0.02 N·m

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图 18 加载力矩在0.1 N·m时的测试曲线

Figure 18. Test curve when the loading torque is 0.1 N·m

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图 19 叠加的曲线

Figure 19. Superimposed curve

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图 20 减速器1以加载速率为0.01 (N·m)/s时的测试曲线

Figure 20. Test curve of reducer 1 at a loading rate of 0.01 (N·m)/s

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图 21 减速器1以加载速率为0.01 (N·m)/s时的测试曲线

Figure 21. Test curve of reducer 1 at a loading rate of 0.01 (N·m)/s

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图 22 减速器1以加载速率为0.01 (N·m)/s时的测试曲线

Figure 22. Test curve of reducer 1 at a loading rate of 0.01 (N·m)/s

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图 23 减速器2以加载速度0.01 (N·m)/s时的测速曲线

Figure 23. Test curve of reducer 2 at a loading rate of 0.01 (N·m)/s

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图 24 减速器2以加载速率为0.05 (N·m)/s时的测速曲线

Figure 24. Test curve of reducer 2 at a loading rate of 0.05 (N·m)/s

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图 25 减速器2以加载速率为0.1 (N·m)/s时的测速曲线

Figure 25. Test curve of reducer 2 at a loading rate of 0.1 (N·m)/s

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表 1 减速器参数

Table 1. The parameters of reducer

减速器	材料	传动比	额定转速/(r·min⁻¹)	峰值转速/(r·min⁻¹)	额定力矩/(N·m)	几何回差/(′)	工作效率/%
减速器1	Fe、Cu、Ni	1296	6.0	23.0	0.1	180.0	56
减速器2	POM	1296	6.0	23.0	0.1	190.0	58

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表 3 减速器1的几何回差测试结果

Table 3. Experiment results of geometric lost motion of reducer 1

加载速率/ (N·m·s⁻¹)	δ_g/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	88.32	88.97	87.29	88.19
0.05	88.68	88.46	88.77	88.64
0.1	87.96	87.69	88.54	88.06

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表 2 减速器1的总回差测试结果

Table 2. Experiment results of total lost motion of reducer 1

加载速率/ (N·m·s⁻¹)	δ/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	261.23	260.32	260.28	260.61
0.05	258.72	257.29	258.91	258.31
0.1	255.89	255.27	254.37	255.18

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表 4 减速器1的弹性回差测试结果

Table 4. Experiment results of elastic lost motion of reducer 1

加载速率/ (N·m·s⁻¹)	δ_e/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	172.91	171.35	172.99	172.42
0.05	170.04	168.83	170.14	169.67
0.1	167.93	167.58	165.83	167.11

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表 6 减速器2的几何回差测试结果

Table 6. Experiment results of geometric lost motion of reducer 2

加载速率/ (N·m·s⁻¹)	δ_g/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	261.25	260.42	260.61	260.76
0.05	260.31	260.39	260.82	260.51
0.1	259.91	260.30	260.77	260.33

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表 5 减速器2的总回差测试结果

Table 5. Experiment results of total lost motion of reducer 2

加载速率/ (N·m·s⁻¹)	δ/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	620.86	619.37	621.33	620.52
0.05	607.23	608.11	608.92	608.09
0.1	587.47	589.23	588.26	588.32

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表 7 减速器2的弹性回差测试结果

Table 7. Experiment results of elastic lost motion of reducer 2

加载速率/ (N·m·s⁻¹)	δ_e/(′)			平均值/(′)
加载速率/ (N·m·s⁻¹)	0°	180°	360°	平均值/(′)
0.01	359.61	358.95	360.72	359.76
0.05	346.92	347.72	348.10	347.58
0.1	327.56	328.93	327.49	327.99

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