高速履带车辆机电悬架惯量分析与滤振缓冲设计

doi:10.12382/bgxb.2021.0588

摘要/Abstract

摘要：

为解决高速履带车辆机电悬架在高频区性能恶化与结构可靠性的问题,分析基于扭杆的机电悬架刚度特性,求解悬架杆系复杂运动关系,计算机电执行器的等效惯性质量,建立考虑惯性质量与负重轮阻尼的2自由度机电悬架模型。量化分析惯性质量对悬架性能的不利影响,得到影响悬架平顺性、部件可靠性的惯性力的频域分布区间与功率谱密度分布区间。根据悬架惯性力的频域分布,以及悬架动挠度的幅频特性,提出滤振与缓冲的措施,建立带有滤振缓冲器的悬架模型。仿真和试验结果表明:滤振缓冲能够有效降低惯性质量影响,在D级路面40km/h行驶工况下,将原惯性力的均方根值由原2143N降低至175N。同时簧载质量加速度均方根值,由原3.5108m/s²降低至1.2682m/s²。台架测试证明齿圈应力在采用滤振缓冲措施后得到较大衰减,最大值由519.9MPa降低为110.1MPa。通过仿真和试验,验证了滤振与缓冲的措施能够提升机电悬架的性能,有助于解决惯性质量带来的高频区性能恶化的问题。

关键词: 惯性质量, 惯性力, 滤振, 缓冲, 机电悬架

Abstract:

In order to solve the problem of performance deterioration and ensure structural reliability of the electromechanical suspension of high-speed tracked vehicles in high-frequency zone, the stiffness characteristics of the electromechanical suspension based on the torsion bar are analyzed, the complex motion relationship of the suspension rod system is solved, the equivalent inertia mass of the electric actuator is calculated, and a two-degree-of-freedom electromechanical suspension model considering inertia mass and load wheel damping is established. We quantitatively analyze the adverse impact of inertia mass on suspension performance, and obtain the frequency domain distribution interval and power spectral density distribution interval of inertia force affecting suspension's ride comfort and component reliability. According to the frequency domain distribution of suspension inertia force and the amplitude frequency characteristics of the suspension's dynamic deflection, the measures of vibration filtering and buffering are put forward, and a suspension model with the vibration filtering buffer is established. The simulation and test results show that vibration filtering and buffering can effectively reduce the influence of inertial mass. Under the driving condition of 40km/h on class D Road, the root mean square value of the original inertial force is reduced from 2143N to 175N, and the root mean square value of sprung mass acceleration is reduced from 3.5108m/s² to 1.2682m/s². The bench test shows that the gear ring stress is greatly attenuated after the vibration filtering and buffering measures are adopted, and the maximum value is reduced from 519.9MPa to 110.1MPa. Through simulation and test, it is verified that the measures of vibration filtering and buffering can improve the performance of the electromechanical suspension and help to solve the problem of performance deterioration in the high frequency zone caused by inertial mass.

Key words: inertial mass, inertia force, vibration filtering, buffer, electromechanical suspension

中图分类号:

TJ81⁺0.1

宋慧新, 顾亮, 张进秋, 董明明, 王利明. 高速履带车辆机电悬架惯量分析与滤振缓冲设计[J]. 兵工学报, 2023, 44(2): 380-393.

SONG Huixin, GU Liang, ZHANG Jinqiu, DONG Mingming, WANG Liming. Inertia Analysis and Vibration Filtering Buffer Design of Electromechanical Suspension of High Speed Tracked Vehicle[J]. Acta Armamentarii, 2023, 44(2): 380-393.

图/表 33

图1 机电悬架能量耗散或回收原理

Fig.1 Energy dissipation or recovery principle of electromechanical suspension

表1 悬架参数

Table 1 Suspension parameters

参数	数值
m_s/kg	2400
非簧载质量m_u/kg	235
单元履带质量m_l/kg	170
扭杆材料剪切弹性模量G/MPa	78300
扭杆工作长度l/mm	1940
扭杆工作直径d_T/mm	48
平衡肘初始安装角α₀/(°)	-43.56
负重轮垂向刚度k_f/(N·m)	2160
履带垂向刚度k_l/(N·m)	40000
车辆底甲板距地高度h/mm	406.5
扭杆中心距车底甲板高度h₀/mm	95
履带板厚度h_b/mm	80
平衡肘旋转半径R_d/mm	360
负重轮直径D_f/mm	600
悬架静行程f_j/mm	135
悬架动行程f_d/mm	293

图2 单轮机电悬架总成与运动关系

Fig.2 Single wheel's electromechanical suspension assembly and motion relationship

图3 悬架变形量与悬架刚度、簧载质量固有频率关系

Fig.3 Relationship between suspension deformation and suspension stiffness/sprung mass natural frequency

图4 机电悬架系统杆系运动关系分析图

Fig.4 Analysis of linkage motion relationship for the electromechanical suspension system

表2 悬架杆系参数

Table 2 Suspension linkage parameters

参数	数值
平衡肘与摇臂旋转点水平间距AF/mm	566
平衡肘与摇臂旋转点垂直间距DF/mm	70
摇臂旋转半径CD/mm	260
连杆长度CE/mm	240
平衡肘旋转点至连杆安装点长度AE/mm	300
平衡肘与负重轮旋转点至连杆安装点长度BE/mm	60

图5 悬架变形量与摇臂旋转角度对应关系与拟合直线

Fig.5 Relationship between suspension deformation and rocker arm rotation angle as well as the fitted straight line

图6 执行器内部结构原理

Fig.6 Internal structure principle of actuator

表3 机电执行器参数

Table 3 Parameters of electromechanical actuator

参数	数值
J_r/(kg·m²)	0.32019
J_x/(kg·m²)	0.05316
J_d/(kg·m²)	0.02335
i_r	1
i_x	9.4
i_d	5.2
摇臂的旋转半径R_y/mm	260

图7 2自由度机电悬架模型

Fig.7 Two-degree-of-freedom (2DOF) electromechanical suspension model

表4 2自由度悬架模型参数

Table 4 Parameters of 2DOF electromechanical actuator

参数	数值
m_s/kg	2400
m_l/kg	235
m_r/kg	526
k_s/(N·mm^-1)	154
c_s/(N·s·m^-1)	9612
k_u/mm	1940
c_u/(N·s·m^-1)	800
μ	0.098
β	2.1
γ	13.3
ξ	0.25
ε	0.083
f_s₀/Hz	1.27
f_s/Hz	1.15
f_u₀/Hz	15.41
f_u/Hz	8.57

图8 惯性力与簧载质量加速度随车速的变化

Fig.8 Variations of inertia force and sprung mass acceleration with vehicle speed

表5 频域内D级路面车速40km/h时悬架特性对比

Table 5 Comparison of suspension characteristics at 40km/h on class F road in the frequency domain

悬架状态	均方根值
悬架状态	$σ F m r$ /N	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
惯性质量为0kg	0	2.15	0.4212	17.47
惯性质量为526kg	2216	5.17	0.5561	17.31

表5 频域内D级路面车速40km/h时悬架特性对比

Table 5 Comparison of suspension characteristics at 40km/h on class F road in the frequency domain

悬架状态	均方根值
悬架状态	$σ F m r$ /N	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
惯性质量为0kg	0	2.15	0.4212	17.47
惯性质量为526kg	2216	5.17	0.5561	17.31

图9 不同惯性质量时簧载质量加速度的功率谱密度

Fig.9 Power spectral density of sprung mass acceleration with different inertial masses

图10 D级路面车速40km/h时惯性力

Fig.10 Inertia force at 40km/h on Class D road

图11 惯性质量为526kg时惯性力的功率谱密度

Fig.11 Power spectral density of inertial force under the inertial mass of 526kg

图12 滤振起始频率与滤振区域的图示

Fig.12 Diagram of the initial frequency of vibration filtering and the vibration filtering region

图13 滤振起始频率随簧载质量变化关系

Fig.13 Variation of the initial frequency of vibration filtering with sprung mass

表6 滤振幅值7mm以下对应的不同路面行驶速度

Table 6 Different speeds on road corresponding to the amplitude value less than 7mm

内容	路面等级
内容	A	B	C	D	E	F
动挠度均方根值/mm	1.9	3.8	7.0	7.0	6.9	5.6
行驶速度不小于/(km·h)	120	120	100	26	7	2

图14 增加滤振缓冲器的2自由度悬架模型图

Fig.14 Diagram of 2DOF suspension model with vibration filtering buffer

图15 滤振缓冲器结构

Fig.15 Vibration filtering buffer structure

表7 电机与缓冲器参数表

Table 7 Motor and buffer parameters

参数	数值
电机的感应电动势常数k_e/(V·s·rad^-1)	0.6
电机的扭矩常数k_i/(N·m·A^-1)	10
电机负载电阻R/Ω	100
电机内阻r/Ω	1.3
缓冲器刚度k_hs/(N·m·rad^-1)	259
缓冲器阻尼系数c_hs/(N·m·s·rad^-1)	0.01
缓冲器转动惯量J_h/(kg·m²)	0.005

图16 执行器力-位移特性

Fig.16 Actuator force-displacement characteristics

图17 执行器力-速度特性

Fig.17 Actuator force-speed characteristics

图18 各频率阻尼力标准差均值与缓冲器刚度关系

Fig.18 Relationship between mean value of standard deviation of damping force at each frequency and buffer stiffness

表8 D级路面40km/h时3种状态的悬架特性对比

Table 8 Comparison of suspension characteristics for the three states at 40km/h on Class D road

悬架状态	均方根值
悬架状态	$σ F u i$ /N	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
无惯性质量	0	0.8609	0.3076	31.70
惯性质量为526kg	2143	3.5108	0.5568	32.20
惯性质量为526kg (带滤振缓冲器)	175	1.2682	0.4104	34.03

表8 D级路面40km/h时3种状态的悬架特性对比

Table 8 Comparison of suspension characteristics for the three states at 40km/h on Class D road

悬架状态	均方根值
悬架状态	$σ F u i$ /N	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
无惯性质量	0	0.8609	0.3076	31.70
惯性质量为526kg	2143	3.5108	0.5568	32.20
惯性质量为526kg (带滤振缓冲器)	175	1.2682	0.4104	34.03

图19 有无滤振缓冲惯性力的功率谱密度对比

Fig.19 Comparison of power spectral density of inertial force with or without vibration filtering and buffering measures

图20 机电悬架的台架试验

Fig.20 Bench test of electromechanical suspension

图21 内齿圈的测点分布

Fig.21 Measuring point distribution of inner gear ring

图22 有无滤振缓冲措施的内齿圈应力对比

Fig.22 Stress comparison of inner gear ring with or without vibration filtering and buffering measures

表9 多频点台架试验悬架特性对比

Table 9 Comparison of suspension characteristics in multi-frequency bench test

悬架状态	簧载质量振动加速度均方根值/(m·s^-2)
悬架状态	频率3Hz, 振幅30mm	频率7Hz, 振幅8mm	频率10Hz, 振幅5mm	频率15Hz, 振幅3mm
无滤振缓冲	1.8609	8.1693	12.4382	16.3824
有滤振缓冲	0.3881	0.6153	0.3998	1.0373
降低百分比/%	79.14	92.47	96.79	93.67

图23 有无滤振缓冲器的簧载质量加速度对比

Fig.23 Comparison of sprung mass acceleration with and without vibration filtering buffer

表10 D级路面台架试验悬架特性对比

Table 10 Comparison of suspension characteristics in bench test of Class D road

悬架状态	均方根值
悬架状态	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
无滤振缓冲	5.8215	0.8324	35.43
有滤振缓冲	2.5243	0.7121	38.32

表10 D级路面台架试验悬架特性对比

Table 10 Comparison of suspension characteristics in bench test of Class D road

悬架状态	均方根值
悬架状态	$σ z · · s$ /(m·s^-2)	$σ F d / G s$	$σ f d$ /mm
无滤振缓冲	5.8215	0.8324	35.43
有滤振缓冲	2.5243	0.7121	38.32

参考文献 23

[1]	WEEKS D A, BRESIE D A, GUENIN A M, et al. The design of an electromagnetic linear actuator for an active suspension[C]// Proceeding of SAE International Congress and Exposition.Detroit,MI, US:SAE, 1999.
[2]	WEEKS D A, BENO J H, GUENINA M, et al. Electromechanical active suspension demonstration for off-road vehicles at the university of texas center for electromechanics[C]// Proceeding of SAE International Congress and Exposition.Detroit,MI, US:SAE, 2000.
[3]	HAYES R J, BENO J H, WEEKS D A, et al. Design and testing of an active suspension system for a 2-1/2 Ton military truck[C]// Proceeding of SAE World Congress. Detroit,MI, US:SAE, 2005.
[4]	BYLSMA W, GUENIN A M, BENO J H, et al. Electromechanical suspension performance testings[C]// Proceeding of SAE World Congress. Detroit,MI,US:SAE, 2001.
[5]	毛明, 张亚峰, 杜甫, 等. 高机动履带车辆行驶系统中的5个科学技术问题[J]. 兵工学报, 2015, 36(8):1546-1555. doi: 10.3969/j.issn.1000-1093.2015.08.024
	MAO M, ZHANG Y F, DU F, et al. Five scientific and technological problems on running system of High mobility tracked vehicle[J]. Acta Armamentarii, 2015, 36(8):1546-1555. (in Chinese) doi: 10.3969/j.issn.1000-1093.2015.08.024
[6]	HAMID T. A novel energy harvesting approach for hybrid electromagnetic-based suspension system of off-road vehicles considering terrain deformability[J]. Mechanical Systems and Signal Processing, 2021, 146(1):106988-107006. doi: 10.1016/j.ymssp.2020.106988 URL
[7]	寇发荣, 陈晨, 李阳康, 等. 电磁复合式馈能悬架半主动控制研究[J]. 中国科技论文, 2020, 15(2):167-173.
	KOU F R, CHEN C, LI Y K, et al. Research on semi-active control of electromagnetic hybrid energy-fed suspension[J]. China Science Paper, 2020, 15(2):167-173. (in Chinese)
[8]	ZHAO Z H, GUAN Y L, CHEN S A. Experimental research on PMSM ball screw actuator and structural design suggestion of featured active suspension[J]. IEEE Access, 2020, 99(8):66163-66177.
[9]	喻凡, 张勇超. 馈能型车辆主动悬架技术[J]. 农业机械学报, 2010, 41(1):1-6.
	YU F, ZHANG Y C. Technology of regenerative vehicle active suspensions[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(1):1-6. (in Chinese)
[10]	黄昆, 喻凡, 张勇超. 基于能量流动分析的电磁式馈能型主动悬架控制[J]. 上海交通大学学报, 2011, 45(7):1068-1073.
	HUANG K, YU F, ZHANG Y C. Active control of energy-regenerative electromagnetic suspension based on energy flow analysis[J]. Journal of Shanghai Jiao Tong University, 2011, 45(7):1068-1073. (in Chinese)
[11]	殷珺, 罗建南, 喻凡. 汽车电磁式主动悬架技术综述[J]. 机械设计与研究, 2020, 36(1):161-168.
	YIN J, LUO J N, YU F. The-state-of-art review on automotive electromagnetic active suspension technolog[J]. Machine Design and Research, 2020, 36(1):161-168. (in Chinese)
[12]	曹民, 刘为, 喻凡. 车辆主动悬架用电机作动器的研制[J]. 机械工程学报, 2008, 44(11):224-228.
	CAO M, LIU W, YU F. Development on electromotor actuator for active suspension of vehicle[J]. Chinese Journal of Mechanical Engineering, 2008, 44(11):224-228. (in Chinese)
[13]	张进秋, 彭志召, 岳杰, 等. 车辆馈能悬挂技术综述[J]. 装甲兵工程学院学报, 2012, 26(5):1-7.
	ZHANG J Q, PENG Z Z, YUE J, et al. Review of regenerative suspension technology for vehicle[J]. Journal of Academy of Armored Force Engineering, 2012, 26(5):1-7. (in Chinese)
[14]	张进秋, 王兴野, 贾进峰, 等. 主动悬架有限频域H∞时滞控制参数影响分析及优化[J]. 兵工学报, 2018, 39(9):1850-1857. doi: 10.3969/j.issn.1000-1093.2018.09.023
	ZHANG J Q, WANG X Y, JIA J F, et al. Parameter analysis and optimization of finite frequency H_∞ control with time delay for active suspension[J]. Acta Armamentarii, 2018, 39(9):1850-1857. (in Chinese)
[15]	王兴野, 张进秋, 刘义乐, 等. 作动器惯性质量对主动悬架幅频特性的影响[J]. 汽车工程, 2018, 40(9):1083-1088.
	WANG X Y, ZHANG J Q, LIU Y L, et al. Influence of inertia mass in actuator on amplitude-frequency characteristics of active suspension[J]. Automotive Engineering, 2018, 40(9):1083-1088. (in Chinese)
[16]	彭虎, 张进秋, 张建, 等. 并联复合式电磁悬挂模型参考多模式切换控制研究[J]. 兵工学报, 2019, 40(1):19-28. doi: 10.3969/j.issn.1000-1093.2019.01.003
	PENG H, ZHANG J Q, ZHANG J, et al. Research on model reference multi-mode switching control of parallel composite electromagnetic suspension[J]. Acta Armamentarii, 2019, 40(1):19-28. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.01.003
[17]	汪若尘, 谢健, 叶青, 等. 直线电机式主动悬架建模与试验研究[J]. 汽车工程, 2016, 38(4):495-499.
	WANG R C, XIE J, YE Q, et al. Modeling and experimental study of active suspension with linear motor[J]. Automotive Engineering, 2016, 38(4):495-499. (in Chinese)
[18]	汪若尘, 钱禹辰, 丁仁凯, 等. 基于LQG的混合电磁悬架阻尼-刚度设计及试验研究[J]. 振动与冲击, 2018, 37(3):61-65.
	WANG R C, QIAN Y C, DING R K, et al. Design and tests for damping-stiffness of a hybrid electromagnetic suspension based on LQG[J]. Journal of Vibration and Shock, 2018, 37(3):61-65. (in Chinese)
[19]	王庆年, 刘松山, 王伟华, 等. 滚珠丝杠式馈能型减振器的结构设计及参数匹配[J]. 吉林大学学报(工学版), 2012, 42(5):1100-1106.
	WANG Q N, LIU S S, WANG W H, et al. Structure design and parameter matching of ball-screw regenerative damper[J]. Journal of Jilin University:Engineering and Technology Edition, 2012, 42(5):1100-1106. (in Chinese)
[20]	段国柱, 宋慧新, 陈宇, 等. 基于MATLAB 软件的机电悬挂连杆机构的运动学分析[J]. 机械工程师, 2020(2):103-104,109.
	DUAN G Z, SONG H X, CHEN Y, et al. Kinematics analysis of mechatronic suspension linkages based on MATLAB software[J]. Mechanical Engineer, 2020(2):103-104,109. (in Chinese)
[21]	余志生, 夏群生. 汽车理论[M]. 北京: 机械工业出版社, 2019.
	YU Z S, XIA Q S. Automobile theory[M]. Beijing: China Machine Press, 2019. (in Chinese)
[22]	宋慧新, 李翠芬. 基于频率分析的半主动悬架模糊控制方法研究[J]. 汽车工程, 2008, 30(6):518-522.
	SONG H X, LI C F. Study on the fuzzy control method of semi-active suspension based on frequency analyses[J]. Automotive Engineering, 2008, 30(6):518-522. (in Chinese)
[23]	LI Z J, ZUO L, LUHRS G, et al. Electromagnetic energy-harvesting shock absorbers:design,modeling,and road Tests[J]. IEEE Transactions on Vehicular Technology, 2013, 62(3):1065-1074. doi: 10.1109/TVT.2012.2229308 URL