车用高速机电复合传动系统固有振动特性及共振转速研究

doi:10.12382/bgxb.2023.1149

摘要/Abstract

摘要：

车用高速机电复合传动系统(Electro-Mechanical Transmission,EMT)结构高紧凑、零部件高转速,导致系统机电耦合效应显著,易产生共振。针对串联式EMT系统进行机电耦合固有振动特性分析,推导系统的机电耦合固有振动模型,研究其固有频率及模态振型,基于各阶模态的振型特点,总结系统的6种典型振动模式。研究高速运行工况和机电磁耦合效应对系统固有频率和模态振型的影响,并基于坎贝尔图和模态能量法研究宽速域运行范围内系统的共振转速。研究结果表明,机电磁耦合效应改变了系统的低频振动特性,高速运行工况可显著改变系统的某些固有频率,在动力学建模中应对二者进行充分考虑,共振转速研究为系统动力学调控和优化提供了参考。

关键词: 高速机电复合传动系统, 机电耦合效应, 固有振动特性, 高速运行工况, 共振转速

Abstract:

The high-speed electromechanical transmission(EMT) system for vehicle is characterized by a highly compact structure and high-speed components,leading to significant electromechanical coupling effects and susceptibility to resonance.This paper analyzes the electromechanical coupling inherent vibration characteristics of a series EMT system.An inherent vibration model of the system is derived,its natural frequencies and mode shapes are studied,and six typical vibration modes of the system are summarized based on the characteristics of each mode shape.The influences of high-speed operating conditions and electromechanical coupling effects on the system’s natural frequencies and mode shapes are investigated.The resonance speeds of the system within a wide operating speed range are studied using Campbell diagrams and modal energy method.The results indicate that the electromechanical coupling effects alter the low-frequency vibration characteristics of the system,and the high-speed operating conditions can significantly change the certain natural frequencies of the system.Both factors should be fully considered in dynamics modeling.The research of resonance speed provides a reference for the dynamic regulation and optimization of system.

Key words: high-speed electromechanical transmission system, electromechanical coupling effect, inherent vibration characteristics, high-speed operating condition, resonance speed

解云坤, 刘辉, 高普, 吴云豪, 李新毅, 周如意. 车用高速机电复合传动系统固有振动特性及共振转速研究[J]. 兵工学报, 2025, 46(1): 231149-.

XIE Yunkun, LIU Hui, GAO Pu, WU Yunhao, LI Xinyi, ZHOU Ruyi. Study on Inherent Vibration Characteristics and Resonance Speed of High-speed Electromechanical Transmission System for Vehicle[J]. Acta Armamentarii, 2025, 46(1): 231149-.

图/表 19

图1 车用高速机电复合传动系统构型

Fig.1 Configuration of EMT used in high-speed HEV

图2 EMT系统横扭耦合动力学模型

Fig.2 Trans-ftorsional coupling dynamics model of EMT system

图3 EMT系统参考坐标系

Fig.3 Coordinate system of EMT system

图4 PMSM定-转子偏心示意图

Fig.4 Schematic diagram of PMSM with stator-frotor eccentricity

表1 EMT系统振动模式(1挡)

Table 1V ibration mode of EMT system(1st clutch)

阶数	频率/Hz	模式	阶数	频率/Hz	模式
1	0	A	12	914	E
2	187	B	13	914	E
3	398	B	14	914	E
4	400	D	15	914	E
5	654	C	16	2220	E
6	654	C	17	2220	E
7	701	C	18	2220	E
8	701	C	19	2220	E
9	772	B	20	2905	B
10	821	C	21	2979	B
11	821	C	22	3134	F

图5 机电复合传动系统典型振动模式

Fig.5 Typical vibration mode of EMT system

表2 机电磁耦合对固有频率的影响(1挡)

Table 2 Effect of electro-mechanical-magnetic coupling on natural frequency(1st clutch)

固有频率阶数	固有频率/Hz
固有频率阶数	考虑机电磁耦合	不考虑机电磁耦合
1	25	0
2	189	187
3	398	398
4	400	400
5	626	654
6	626	654
7	667	701
8	667	701
9	772	772
10	821	821

图6 机电磁耦合对振型矢量的影响

Fig.6 Effect of electro-mechanical-magnetic coupling on vector of mode shape

图7 振动模式B固有频率曲线(1挡)

Fig.7 Natural frequency of vibration mode B (1st clutch)

图8 振动模式C固有频率曲线(1挡)

Fig.8 Natural frequency of vibration mode C(1st clutch)

图9 振动模式D固有频率曲线(1挡)

Fig.9 Natural frequency of vibration mode D(1st clutch)

图10 振动模式E固有频率曲线(1挡)

Fig.10 Natural frequency of vibration mode E(1st clutch)

图11 振动模式F固有频率曲线(1挡)

Fig.11 Natural frequency of vibration mode F(1st clutch)

图12 振动模式C固有频率曲线(2挡)

Fig.12 Natural frequency of vibration mode C(2nd clutch)

图13 振动模式E固有频率曲线(2挡)

Fig.13 Natural frequency of vibration mode E(2nd clutch)

图14 机电复合传动系统坎贝尔图

Fig.14 Campbell diagram of EMT system

图15 机电复合传动系统模态动能分布

Fig.15 Modal kinetic energy of EMT system

表3 机电复合传动系统共振转速点(1挡)

Table 3 Resonance speed of EMT system(1st clutch)

共振转速/(r·min^-1)	固有频率/Hz	激励频率成分
750	ω₁	2f_s1、2f_s3
950	ω₉,ω₁₀,ω₁₁	2f_m-PG1、2f_m-PG3
1500	ω₁	f_s1、f_s3
1900	ω₉,ω₁₀,ω₁₁	f_m-PG1、f_m-PG3
2300	ω₃,ω₄	2f_m-PG5、2f_m-PG6
3450	ω₂₀	2f_m-PG1、2f_m-PG3
4550	ω₃,ω₄,ω₉,ω₁₀,ω₁₁	f_m-PG5、f_m-PG6 2f_m-PG5、2f_m-PG6
5250	ω₁₂,ω₁₃,ω₁₄,ω₁₅	2f_m-PG5、2f_m-PG6
5650	ω₂	2f_s1、2f_s3
6900	ω₂₀	f_m-PG1、f_m-PG3
9150	ω₉,ω₁₀,ω₁₁	f_m-PG5、f_m-PG6
10450	ω₁₂,ω₁₃,ω₁₄,ω₁₅	f_m-PG5、f_m-PG6
11350	ω₂	f_s1、f_s3

表4 机电复合传动系统共振转速点(2挡)

Table 4 Resonance speed of EMT system(2nd clutch)

共振转速/(r·min^-1)	固有频率/Hz	激励频率成分
225	ω₄	2f_m-PG1、2f_m-PG3
450	ω₄	f_m-PG1、f_m-PG3
750	ω₁,ω₅~ω₁₂	2f_m-PG1、2f_m-PG3
950	ω₁₃,ω₁₄,ω₁₅	2f_m-PG1、2f_m-PG3
1500	ω₁,ω₅~ω₁₂	f_m-PG1、f_m-PG3
1900	ω₁₃,ω₁₄,ω₁₅	f_m-PG1、f_m-PG3
3500	ω₁₆,ω₁₇	2f_m-PG1、2f_m-PG3
4600	ω₂₀	2f_m-PG1、2f_m-PG3
4950	ω₂₃	2f_m-PG1、2f_m-PG3
7000	ω₁₆,ω₁₇	f_m-PG1、f_m-PG3
9200	ω₂₀	f_m-PG1、f_m-PG3
9900	ω₂,ω₃,ω₂₃	2f_PG5、2f_PG6 f_m-PG1、f_m-PG3

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