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Article(id=1149779600261210135, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, articleNumber=null, orderNo=null, doi=10.19562/j.chinasae.qcgc.2025.02.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1716134400000, receivedDateStr=2024-05-20, revisedDate=1725206400000, revisedDateStr=2024-09-02, acceptedDate=null, acceptedDateStr=null, onlineDate=1752058418573, onlineDateStr=2025-07-09, pubDate=1740412800000, pubDateStr=2025-02-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752058418573, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=1755587704001, onlineFirstDateStr=2025-08-19, sourceXml=null, magXml=null, createTime=1752058418573, creator=13701087609, updateTime=1752058418573, updator=13701087609, issue=Issue{id=1149779599254581563, tenantId=1146029695717560320, journalId=1146120084050784272, year='2025', volume='47', issue='2', pageStart='201', pageEnd='390', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752058418334, creator=13701087609, updateTime=1753780722751, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1157003467609956875, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1157003467609956876, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=281, endPage=291, ext={EN=ArticleExt(id=1149779600458342424, articleId=1149779600261210135, tenantId=1146029695717560320, journalId=1146120084050784272, language=EN, title=Torsional Vibration Characteristic Analysis of Diesel Engine Range Extender Under Electromechanical Coupling, columnId=null, journalTitle=Automotive Engineering, columnName=null, runingTitle=null, highlight=

Torsional vibration of power system is a hot and difficult problem in NVH field of extended range electric vehicles. In order to investigate the torsional vibration characteristics of the range extender under electromechanical coupling，taking a diesel engine range extender as the research object，systematic quantification of the shaft system is carried out and a torsional vibration mechanical model of the eight-degree-of-freedom shafting system is established. A non-contact measurement method is used to conduct torsional vibration tests on the range extender platform to verify the accuracy of the model. The method of obtaining shafting structure parameters，electromagnetic parameters and excitation torque is discussed. The coupling calculation of the range-extender shafting is carried out and the comparison analysis with the original machine is made. It is concluded that the addition of the motor rotor system will reduce the natural frequency of shafting by 27.6Hz and the maximum amplitude by about 21%. The resonant speed is shifted forward by about 200 r/min on the basis of the original machine，and a natural frequency is increased in the first 12 steps. The influence of electromagnetic parameters on torsional vibration characteristics of shafting is analyzed according to the particularity of range extender working condition. The results show that the electromagnetic damping is linearly and negatively correlated with torsional vibration amplitude，but it does not change the natural frequency and resonant speed of shafting. The electromagnetic stiffness has no obvious effect on the amplitude of torsional vibration，and mainly affects the size of zero frequency，which will lead to low frequency rolling vibration of shafting.

, articleAbstract=

Torsional vibration of power system is a hot and difficult problem in NVH field of extended range electric vehicles. In order to investigate the torsional vibration characteristics of the range extender under electromechanical coupling, taking a diesel engine range extender as the research object, systematic quantification of the shaft system is carried out and a torsional vibration mechanical model of the eight-degree-of-freedom shafting system is established. A non-contact measurement method is used to conduct torsional vibration tests on the range extender platform to verify the accuracy of the model. The method of obtaining shafting structure parameters, electromagnetic parameters and excitation torque is discussed. The coupling calculation of the range-extender shafting is carried out and the comparison analysis with the original machine is made. It is concluded that the addition of the motor rotor system will reduce the natural frequency of shafting by 27.6Hz and the maximum amplitude by about 21%. The resonant speed is shifted forward by about 200 r/min on the basis of the original machine, and a natural frequency is increased in the first 12 steps. The influence of electromagnetic parameters on torsional vibration characteristics of shafting is analyzed according to the particularity of range extender working condition. The results show that the electromagnetic damping is linearly and negatively correlated with torsional vibration amplitude, but it does not change the natural frequency and resonant speed of shafting. The electromagnetic stiffness has no obvious effect on the amplitude of torsional vibration, and mainly affects the size of zero frequency, which will lead to low frequen-

, correspAuthors=Jilin Lei, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Jilin Lei, Xiongzhuan Yang, Weichao Wang, Yue Qiu, Zhaoqian Yang, Yuhua Bi, Rui Mo), CN=ArticleExt(id=1149779626555302250, articleId=1149779600261210135, tenantId=1146029695717560320, journalId=1146120084050784272, language=CN, title=柴油机增程器机电耦合作用下的扭振特性分析*, columnId=null, journalTitle=汽车工程, columnName=null, runingTitle=null, highlight=

动力系统扭振问题是增程式电动汽车NVH领域研究的热点和难点。为了探讨增程器机电耦合作用下的扭振特性，以某款柴油机增程器为研究对象，对轴系进行系统当量化，建立了8自由度轴系扭振动力学模型，并采用非接触式测量方法在增程器台架上进行扭振试验验证了模型的准确性。讨论了轴系结构参数、电磁参数以及激励力矩的获取方法，对增程器轴系进行了解耦计算并与原机进行对比分析得出电机转子系统的加入使轴系固有频率降低了27.6 Hz，最大振幅降低约21%，共振转速在原机的基础上整体向前推移了约200 r/min，且在前12阶内会增加一个固有频率。并根据增程器工况的特殊性重点分析了电磁参数对轴系的扭振特性影响，结果表明电磁阻尼与扭振振幅呈线性负相关，但其并不改变轴系的固有频率和共振转速；电磁刚度对扭振振幅影响不明显，主要影响零频的大小，会导致轴系出现低频滚振现象。

, articleAbstract=

动力系统扭振问题是增程式电动汽车NVH领域研究的热点和难点。为了探讨增程器机电耦合作用下的扭振特性,以某款柴油机增程器为研究对象,对轴系进行系统当量化,建立了8自由度轴系扭振动力学模型,并采用非接触式测量方法在增程器台架上进行扭振试验验证了模型的准确性。讨论了轴系结构参数、电磁参数以及激励力矩的获取方法,对增程器轴系进行了解耦计算并与原机进行对比分析得出电机转子系统的加入使轴系固有频率降低了27.6Hz,最大振幅降低约21%,共振转速在原机的基础上整体向前推移了约200r/min,且在前12阶内会增加一个固有频率。并根据增程器工况的特殊性重点分析了电磁参数对轴系的扭振特性影响,结果表明电磁阻尼与扭振振幅呈线性负相关,但其并不改变轴系的固有频率和共振转速;电磁刚度对扭振振幅影响不明显,主要影响零频的大小,会导致轴系出现低频滚振现象。

, correspAuthors=雷基林, authorNote=null, correspAuthorsNote=
雷基林，教授，博士，E-mail：。
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参数 数值
活塞直径D/mm 80
曲柄半径R/mm 38.439
皮带轮端等效转动惯量I 1/（kg · mm2） 8.097 × 103
4个曲拐转动惯量I 2-I 5/（kg · mm2） 7.003 × 103
曲轴和飞轮间梯形轴转动惯量I 6/ （kg · mm2） 2.315 × 103
飞轮转动惯量I 7/（kg · mm2） 1.816 × 105
扭转减振器转动惯量I 8/（kg · mm2） 5.346 × 103
发电机转子转动惯量I 9/（kg · mm2） 6.150 × 104
各曲拐之间轴段扭转刚度K 2-K 5 /（N·mm·rad-1） 1.185 × 109
皮带轮与第1曲拐间扭转刚度K 1 /（N·mm·rad-1） 5.860×108
第4曲拐与飞轮端轴段扭转刚度K 6 /（N·mm·rad-1） 8.396×108
电机输出端扭转刚度K 7 /（N·mm·rad-1） 1.050× 109
扭转减振器扭转刚度K 8 /（N·mm·rad-1） 5.856×105
发电机外阻尼系数 0.02[13]
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增程器轴系相关机械参数

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参数 数值
活塞直径D/mm 80
曲柄半径R/mm 38.439
皮带轮端等效转动惯量I 1/（kg · mm2） 8.097 × 103
4个曲拐转动惯量I 2-I 5/（kg · mm2） 7.003 × 103
曲轴和飞轮间梯形轴转动惯量I 6/ （kg · mm2） 2.315 × 103
飞轮转动惯量I 7/（kg · mm2） 1.816 × 105
扭转减振器转动惯量I 8/（kg · mm2） 5.346 × 103
发电机转子转动惯量I 9/（kg · mm2） 6.150 × 104
各曲拐之间轴段扭转刚度K 2-K 5 /（N·mm·rad-1） 1.185 × 109
皮带轮与第1曲拐间扭转刚度K 1 /（N·mm·rad-1） 5.860×108
第4曲拐与飞轮端轴段扭转刚度K 6 /（N·mm·rad-1） 8.396×108
电机输出端扭转刚度K 7 /（N·mm·rad-1） 1.050× 109
扭转减振器扭转刚度K 8 /（N·mm·rad-1） 5.856×105
发电机外阻尼系数 0.02[13]
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参数 数值
额定电压（AC）/ V 380
额定转矩/ （N·m） 250
额定功率/ kW 60
额定转速/ （r·min-1） 2 400
极对数p 10
永磁体磁链ψf/Wb 0.126
直轴电感（定子绕组d轴等效电感）Ld/mH 0.492
交轴电感（定子绕组q轴等效电感）Lq/mH 0.495
), ArticleFig(id=1170299603896246405, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600261210135, language=CN, label=表2, caption=

ISG电机主要参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 数值
额定电压（AC）/ V 380
额定转矩/ （N·m） 250
额定功率/ kW 60
额定转速/ （r·min-1） 2 400
极对数p 10
永磁体磁链ψf/Wb 0.126
直轴电感（定子绕组d轴等效电感）Ld/mH 0.492
交轴电感（定子绕组q轴等效电感）Lq/mH 0.495
), ArticleFig(id=1170299603975938182, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600261210135, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
设备仪器 型号 主要技术参数
冷却水箱 ET4900-DJ

控制精度：±2 ℃

最高进水温度：≤32 ℃

温控范围：循环水温5-80 ℃

电池模拟器 BPDC1000D-EV

10%-90%负载上升/

下降时间：<5 ms

数据采集系统 NI PXI-1050

槽数：12

频率：47-63 Hz

功率：最大960 V·A

编码器 LF-102.4BM-C24F

光栅齿数：360

电源电压：5 V

工作原理：增量式

), ArticleFig(id=1170299604055629959, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600261210135, language=CN, label=表3, caption=

试验装置关键设备技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设备仪器 型号 主要技术参数
冷却水箱 ET4900-DJ

控制精度：±2 ℃

最高进水温度：≤32 ℃

温控范围：循环水温5-80 ℃

电池模拟器 BPDC1000D-EV

10%-90%负载上升/

下降时间：<5 ms

数据采集系统 NI PXI-1050

槽数：12

频率：47-63 Hz

功率：最大960 V·A

编码器 LF-102.4BM-C24F

光栅齿数：360

电源电压：5 V

工作原理：增量式

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柴油机增程器机电耦合作用下的扭振特性分析*
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雷基林 1 , 杨雄专 1 , 王伟超 1 , 邱越 1 , 杨钊乾 1 , 毕玉华 1 , 莫瑞 2
汽车工程 | 2025,47(2): 281-291
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汽车工程 | 2025, 47(2): 281-291
柴油机增程器机电耦合作用下的扭振特性分析*
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雷基林1 , 杨雄专1, 王伟超1, 邱越1, 杨钊乾1, 毕玉华1, 莫瑞2
作者信息
  • 1 昆明理工大学，云南省内燃机重点实验室，昆明 650500
  • 2 云内动力股份有限公司，昆明 650500

通讯作者:

雷基林，教授，博士，E-mail：。
Torsional Vibration Characteristic Analysis of Diesel Engine Range Extender Under Electromechanical Coupling
Jilin Lei1 , Xiongzhuan Yang1, Weichao Wang1, Yue Qiu1, Zhaoqian Yang1, Yuhua Bi1, Rui Mo2
Affiliations
  • 1 Kunming University of Science and Technology，Yunnan Key Laboratory of Internal Combustion Engine，Kunming 650500
  • 2 Kunming Yunnei Power Co. ，Ltd. ，Kunming 650500
出版时间: 2025-02-25 doi: 10.19562/j.chinasae.qcgc.2025.02.008
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摘要
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动力系统扭振问题是增程式电动汽车NVH领域研究的热点和难点。为了探讨增程器机电耦合作用下的扭振特性,以某款柴油机增程器为研究对象,对轴系进行系统当量化,建立了8自由度轴系扭振动力学模型,并采用非接触式测量方法在增程器台架上进行扭振试验验证了模型的准确性。讨论了轴系结构参数、电磁参数以及激励力矩的获取方法,对增程器轴系进行了解耦计算并与原机进行对比分析得出电机转子系统的加入使轴系固有频率降低了27.6Hz,最大振幅降低约21%,共振转速在原机的基础上整体向前推移了约200r/min,且在前12阶内会增加一个固有频率。并根据增程器工况的特殊性重点分析了电磁参数对轴系的扭振特性影响,结果表明电磁阻尼与扭振振幅呈线性负相关,但其并不改变轴系的固有频率和共振转速;电磁刚度对扭振振幅影响不明显,主要影响零频的大小,会导致轴系出现低频滚振现象。

增程器  /  扭转振动  /  机电耦合  /  动力学

Torsional vibration of power system is a hot and difficult problem in NVH field of extended range electric vehicles. In order to investigate the torsional vibration characteristics of the range extender under electromechanical coupling, taking a diesel engine range extender as the research object, systematic quantification of the shaft system is carried out and a torsional vibration mechanical model of the eight-degree-of-freedom shafting system is established. A non-contact measurement method is used to conduct torsional vibration tests on the range extender platform to verify the accuracy of the model. The method of obtaining shafting structure parameters, electromagnetic parameters and excitation torque is discussed. The coupling calculation of the range-extender shafting is carried out and the comparison analysis with the original machine is made. It is concluded that the addition of the motor rotor system will reduce the natural frequency of shafting by 27.6Hz and the maximum amplitude by about 21%. The resonant speed is shifted forward by about 200 r/min on the basis of the original machine, and a natural frequency is increased in the first 12 steps. The influence of electromagnetic parameters on torsional vibration characteristics of shafting is analyzed according to the particularity of range extender working condition. The results show that the electromagnetic damping is linearly and negatively correlated with torsional vibration amplitude, but it does not change the natural frequency and resonant speed of shafting. The electromagnetic stiffness has no obvious effect on the amplitude of torsional vibration, and mainly affects the size of zero frequency, which will lead to low frequen-

range extender  /  torsional vibration  /  electromechanical coupling  /  dynamics
雷基林, 杨雄专, 王伟超, 邱越, 杨钊乾, 毕玉华, 莫瑞. 柴油机增程器机电耦合作用下的扭振特性分析*. 汽车工程, 2025 , 47 (2) : 281 -291 . DOI: 10.19562/j.chinasae.qcgc.2025.02.008
Jilin Lei, Xiongzhuan Yang, Weichao Wang, Yue Qiu, Zhaoqian Yang, Yuhua Bi, Rui Mo. Torsional Vibration Characteristic Analysis of Diesel Engine Range Extender Under Electromechanical Coupling[J]. Automotive Engineering, 2025 , 47 (2) : 281 -291 . DOI: 10.19562/j.chinasae.qcgc.2025.02.008
正文
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前言
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“双碳”政策下，交通行业减碳压力增大，对传统燃油汽车市场造成了巨大的冲击。世界各国都在尝试向纯电动汽车转型，但目前纯电动汽车还存在续航里程短、成本高、充电桩数量少等缺点。而在这种情况下增程式电动汽车应运而生，以提供一种经济有效、可靠、高效和动态的解决方案来应对当前转型中遇到的问题[1-2]。
柴油增程器具有稳定性高、经济性好、环境适应性强等特点，因此发展柴油增程器在军用、船舶、工程机械和商用车领域具有广阔的前景[3]。然而柴油机增程器是一个复杂的机电耦合模型，由于电磁参数的介入，必将会使轴系的扭振特性变得更为复杂[4]。所以对增程器轴系的扭振特性进行分析研究对提升整个动力系统的安全可靠性及NVH性能具有重要的意义。
增程器轴系主要由发动机机械系统和集成启动发电机ISG（integrated started generator）电气系统组成，目前国内外学者对单个发动机轴系扭振的研究主要集中在分析发动机曲轴系在承受周期性的缸内爆发压力及回转部件惯性力等外载作用力下的扭振特性。Lu等[5]针对某中速柴油机提出了考虑扭转振动与提前喷油角之间耦合效应的创新模型，并进行试验验证，结果表明，耦合模型能有效预测带边频率处的振动峰值。曲俊龙等[6]采用调整离合器和半轴的刚度，以及在传动轴加装惯量盘的方法，将传动系轴系固有频率移除到发动机常用转速范围外，避免了轴系发生扭转共振。方健[7]、李亚南[8]、魏超[9]等均建立了发动机轴系的集总参数模型，通过仿真与试验相结合的方法分析了结构参数和扭转减振器对轴系扭振的影响。对于电机系统的扭振研究，Pindoriya等[10]提出了永磁同步电机和直流发电机之间端到端同轴耦合轴的等效集总参数模型以及有效模态质量和模态参与因子精度增强技术，以预测扭振。Arkkio等[11]采用时间离散有限元分析方法，研究了受振荡扭矩和线路电流谐波约束的感应电机在扭转振动下的损耗。
在考虑增程器机电耦合作用下的扭振研究方面，大部分研究集中在机械参数及机械激励对整个轴系的影响，对于电磁参数对轴系扭振的影响研究较少。Chen等[12]建立了增程器系统的仿真模型，分析了轴系结构参数对振动结果的影响，并采用遗传算法对设计参数进行了优化。张立军等[13]建立了某商用车增程器的扭转振动模型，并对典型工况下增程器系统的激励力矩和扭转振动进行了时域和频域特性分析。Wang等[14]建立了行星齿轮混动总成（PGHT）的扭振模型，并采用多目标优化控制策略，有效降低了轴系的扭转振动。黄中华等[15]对混合动力挖掘机轴系进行了解耦状态与耦合状态的有限元模态分析，最终通过试验和仿真得出导致耦合状态下各阶模态频率下降的原因是电机转子系统刚度低于柴油机曲轴系统导致的。Uspensky等[16]建立了柴油机和电机联轴器的扭振数学模型，分析得到了曲柄的动态力矩和发电机转子上的动态力矩是导致轴系发生危险非线性振动的主要激励源。
本文在分析国内外研究成果的基础上，针对现有研究的不足，首先对轴系进行了系统当量化，建立了8自由度轴系动力学模型，讨论了轴系结构参数、电磁参数以及激励力矩的获取方法，并通过台架试验验证了模型的准确性。对增程器轴系进行了强迫振动计算，求解得到了轴系的固有频率和临界转速并与原机进行了对比，根据增程器的工作特点对轴系进行了解耦分析，并重点分析了电磁参数对轴系扭振特性的影响。
1 增程器轴系扭振动力学模型
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1.1 增程器轴系模型的构建及简化方法
柴油增程器轴系主要包括皮带轮、曲轴、飞轮、扭转减振器、发电机转子系统5部分。增程器的实际轴系是一个复杂的连续体，并且承受周期性变化的力矩，想要精确地对其进行扭振计算非常困难。为了便于求解，本文采用系统当量化的方法对轴系进行简化处理。将皮带轮、飞轮、ISG电机转子这种转动惯量大且形状相对规则的部分近似为刚体，且集中质量点选择在其回转中心上。以主轴颈中央界面为界将曲轴划分为若干轴段，每一段用一个集中的惯量去替代该段内所有连续体的惯量，离散轴段之间通过弹簧连接，并忽略惯量只考虑刚度和阻尼。同时假设每个气缸的激励力矩通过活塞连杆作用到曲拐的集中惯量上，发电机的激励力矩作用到转子的集中质量上。不考虑轴系纵向振动、回旋振动对轴系扭振特性的影响，建立的8自由度扭振模型如图1所示。
根据动量矩定理，可推导得到该轴系的扭振运动微分方程：
I1φ¨1+C1(φ˙1-φ˙2)+K1(φ1-φ2)=0I2φ¨2+C2(φ˙2-φ˙3)+K2(φ2-φ3)-      C1(φ˙1-φ˙2)-K1(φ1-φ2)+e2φ˙2=M1I3φ¨3+C3(φ˙3-φ˙4)+K3(φ3-φ4)-      C2(φ˙2-φ˙3)-K2(φ2-φ3)+e3φ˙3=M2I4φ¨4+C4(φ˙4-φ˙5)+K4(φ4-φ5)-      C3(φ˙3-φ˙4)-K3(φ3-φ4)+e4φ˙4=M3I5φ¨5+C5(φ˙5-φ˙6)+K5(φ5-φ6)-      C4(φ˙4-φ˙5)-K4(φ4-φ5)+e5φ˙5=M4I6φ¨6+C6(φ˙6-φ˙7)+K6(φ6-φ7)-      C5(φ˙5-φ˙6)-K5(φ5-φ6)=0I7φ¨7+C7(φ˙7-φ˙8)+K7(φ7-φ8)-      C6(φ˙6-φ˙7)-K6(φ6-φ7)=0I8φ¨8+C8(φ˙8-φ˙9)+K8(φ8-φ9)-      C7(φ˙7-φ˙8)-K7(φ7-φ8)=0I9φ¨9+e9φ˙9+K9φ9-C8(φ˙8-φ˙9)-      K8(φ8-φ9)=Tg
式中：I 1为皮带轮端的等效转动惯量；I 2 ~I 5为四缸柴油机各曲轴曲拐的等效转动惯量；I 6为曲轴和飞轮之间连接梯形轴的等效转动惯量；I 7为飞轮的等效转动惯量；I 8为扭转减振器的等效转动惯量；I 9为ISG转子的等效转动惯量；φ1~φ9为各个等效惯量间的角位移；C 1 ~ C 8为各个轴段的内阻尼系数；e 2 ~e 5，e 9分别为4个曲拐的外部阻尼系数以及电机定、转子间的电磁阻尼系数；K 1 ~ K 8分别为各个轴段之间的扭转刚度，K 9为ISG电机定、转子之间产生的电磁刚度；M 1 ~ M 4为发动机各缸的激励力矩；T g为发电机的输出转矩。
1.2 模型参数的确定
1.2.1 结构参数的确定
扭振模型计算结果的准确性主要取决于模型结构参数（转动惯量、扭转刚度、阻尼）的精确性以及考虑非线性特性的分段线性化。随着计算机技术的飞速发展，对一些机械性结构参数的确定较为方便，如轴系各段的转动惯量可在CAD软件中对各部件指派材料属性后测得。部件的扭转刚度可通过有限元的方法计算得到。具体方法为对被测物体一端进行全约束，在另外一个端面施加一个弯矩可求解出部件的位移云图，最终通过施加转矩与对应角位移的比值可计算出扭转刚度。图2所示为曲柄半拐的扭转刚度计算过程。
对轴系进行强迫振动计算时，须考虑系统阻尼。对于耦合的增程器轴系，阻尼主要包括内阻尼、外阻尼、电磁阻尼，内部阻尼是弹性连接轴的结构阻尼，可由式（2）计算得到；外阻尼主要作用于活塞，由活塞环、油膜和气缸接触产生，可由式（3）计算得到[17]。
Ci=ξriKi/ω
ei=ξoiJiω
式中：ξri为轴段内单位阻尼系数，也称为轴段结构阻尼系数，根据工程实际经验确定，轴段内单位阻尼系数取值范围为0.02 ~ 0.04[18-19]；ξoi为外单位阻尼系数，取值范围为0.04 ~ 0.06[20]。以此为据，本文取0.02、0.04分别作为轴段的内单位阻尼系数和外单位阻尼系数。
增程器轴系的相关机械参数如表1所示。
1.2.2 电磁参数的确定
电磁刚度和电磁阻尼是直接影响轴系扭振特性的电磁参数，不同于机械参数的是二者会随着工况的改变而改变，需要根据电机的特有性能计算其数值，表2为ISG电机的主要参数。
电磁刚度可用电磁转矩表达式中电转角的一次项系数来定义[21]，电磁刚度和定子、转子的基波磁势幅值成正比，而磁势幅值是激励电流的正比函数，一般永磁同步电机的电磁刚度可表达为
Km=∂Tg∂φm=p4SIdqoIdqoT
对上式进行坐标变换，并采用id=0的矢量控制方式，可得到：
Km=(Ld-Lq)Tg23pψf
式中：T g为发电机输出转矩；p为极对数； I dq o为电流向量；ψf为永磁体磁链；Ld为直轴电感；Lq为交轴电感。根据上述公式可得到ISG电机输出转矩与电磁刚度的变化关系，如图3所示。
电磁阻尼由定、转子之间的气隙磁场所产生，其受到诸多因素的影响，因此想要精确地计算电磁阻尼非常困难。邱家俊等[22]通过数学模型解析以及实验研究，得到了电磁阻尼系数与电压之间的变化关系曲线。本文根据电机电磁转矩与定子线圈电流成正比的特性，在参考上述文献中电磁阻尼的计算及实验结果取值50、100、150 和200 N·m·s/rad作为仿真计算的边界条件。
1.3 激励力矩的计算
激励力矩是导致轴系发生扭振的主要能量源，增程器轴系工作时同时受到周期性的缸内压力、回转运动部件的惯性力矩等组成的机械力矩和ISG电机定子和转子之间气隙磁场造成的电磁力矩的作用。当激励力矩的频率和轴系某一谐次下的固有频率相等时，就会使轴系发生共振。
1.3.1 发动机激励的合成
发动机曲轴系的激励力矩为缸内气体压力和往复惯性力二者的力矩合成，即
M(i)=Mp+Mw
式中：M p为气缸压力引起的激励力矩；M w为往复惯性力引起的激励力矩。
由气体压力和往复惯性力引起的第v谐次的激励力矩分别为
Mp=π4D2RCvsinv(wct+δ)+φ1
Mw=π4D2RGRn2D2dvsin[v(ωct+δ)+φ2]
式中：D为活塞直径；R为曲柄半径；G为发动机往复部分重力；Cv为v次简谐系数；ω为圆频率；n为发动机计算转速；δ为气缸发火间隔角产生的相位；dv为往复部分惯性力引起的激励力矩简谐系数；φ1为气体压力引起的第v谐次简谐激励力矩相位角；φ2为与dv相应的相位角。
发动机在工作过程中，主谐次的激励力矩较大，因此在主谐次下激起的共振峰值最明显，对于四缸四冲程发动机来说，2、4、6、8、10谐次为主谐次，图4（a）为发动机激励力矩合成图，图4（b）为发动机在各主谐次下的合成力矩。
1.3.2 ISG发电机激励的合成
本文选用的ISG电机为内置式永磁同步电机，电机通过定子与转子之间气隙磁场的耦合作用产生电磁转矩。忽略电机中的磁滞损耗、磁路饱和、涡流以及磁路中的高次谐波磁势，采用id=0的电流控制策略并通过CLARKE和PARK变换可得到永磁同步电机电磁转矩矢量方程：
Tg=32pψfIq
式中：p为极对数；Iq为q轴电流；ψf为永磁体磁链。由于电机具有低速恒转矩、高速恒功率的特性，再根据表1中提供的参数，可计算得到该款ISG电机的外特性曲线，如图5所示。
2 扭振测试
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为了验证多体动力学模型的准确性，需要对增程器轴系进行扭振测试试验，试验测试台架原理如图6所示。试验台架由APU系统、电池模拟器、冷却系统、控制系统、进排气系统、接线箱以及整流器等组成。试验装置关键设备技术参数如表3所示。由于增程器发动机与汽车驱动系统之间实现了机械解耦、功率解耦、转速解耦[23]。基于这些特征，增程器发动机只须在高效区内运行即可，消除了适应全工况的必要，因此须重点关注增程器高效区内的扭振特性。根据发动机台架标定试验和电机厂商提供的参数确定了该款柴油机增程器的高效区为1 800 ~ 2 600 r/min。
2.1 测点和测试装备的选择
根据新国标GB/T 15371—2023《往复内燃机曲轴轴系扭转振动评定方法》要求传感器应布置在轴系扭振振幅较大位置处，通过对曲轴进行自由模态分析发现，曲轴自由端的振幅最大，因此测点选择在曲轴自由端。采用型号为LF-102.4BM-C24F的增量型光电编码器对搭建好的增程器进行扭振测试，图7为台架实物图及编码器安装位置图，编码器通过特制的支架保证同轴安装在发动机自由端，避免传感器与轴系由于轴向误差导致测试的不准确性。采用NI PXI-1050采集卡以及LMS Test.lab软件平台进行数据的采集及分析。
2.2 试验数据分析及验证
基于建立的8自由度四缸柴油机增程器轴系的扭振动力学模型，运用AVL-EXCITE对轴系进行扭振仿真求解。为了便于与试验结果做对比，设置仿真工况与实际试验的工况保持一致。图8为发电机施加150 N·m转矩时，增程器自由端8谐次和10谐次下扭振振幅的仿真计算结果与试验结果对比图。从图中可以看出，8谐次下，试验测试时轴系在转速为2 600 r/min时发生了共振，共振振幅为0.172°，而在此转速下，仿真计算得到的轴系扭振振幅为0.164°，误差为4.7%。在10谐次下，试验测试时轴系在转速为2 100 r/min左右时发生了共振，共振振幅为0.037°，此转速下的仿真计算振幅为0.035°，误差为5.4%。在会发生共振的两个主谐次内试验值与仿真计算值之间存在一定偏差，但在合理范围内，仿真计算结果与试验测量结果基本吻合。分析出现偏差的主要原因如下：（1）仿真模型中不考虑柴油机前端附件驱动系统（FEAD）对增程器轴系的影响，而在实际运行过程中FEAD与整个增程器轴系扭振系统之间存在耦合振动，FEAD动态负载波动的增大将增大轴系的扭振[24]，所以导致试验值大于仿真值。（2）发动机实际运行时，缸内燃烧过程导致发动机转矩存在波动，仿真时输出的缸压数据是稳态计算拟合而成，因此仿真计算结果更加平滑[25]。（3）增程器发动机和电机通过螺栓和花键装配在一起，在试验时会存在一定的校准误差、噪声干扰，导致测得的振幅值偏大。
3 轴系扭振响应分析
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3.1 临界转速求解
图9和图10分别为原机和增程器在强迫振动下求解得到的临界转速图谱。图中垂线表示轴系固有频率，过原点的斜线为各个谐次下的简谐力矩，其中斜线与垂线的交点为共振点，对应的转速为临界转速。没有与垂线相交的简谐力矩认为不会与轴系发生共振，因此原机在7.5谐次以内，增程器在7谐次以内干扰力矩都不会激励轴系发生共振。根据临界转速计算结果可知，原机在前1 500 Hz内只存在一个固有频率为376.6 Hz，而增程器在前1 500 Hz内存在两个固有频率，其1阶固有频率为349 Hz，增加的2阶固有频率为617.4 Hz。
增程器轴系与原机相比，1阶固有频率降低了27.6 Hz。其原因一方面是电机转子系统的介入增加了轴系的长度和整个轴系的转动惯量，而更长的轴段在施加相同转矩时会产生更大的角位移，从而会降低整个轴系的扭转刚度。另一方面是在发动机和ISG电机之间装配了扭转减振器，提供的附加质量和弹性元件也会使轴系固有频率降低。
3.2 解耦分析
图11和图12分别为发动机原机与增程器在1 000-3 200 r/min内曲轴自由端的曲柄转角-转速-总振幅对应的三维颜色映射曲面图。不论是发动机原机还是整个增程器系统其扭振振幅在低转速时都较高，这是因为低转速时，发动机动力输出不稳定，电机转矩波动大，且低速时曲轴和连杆等部件旋转产出的离心力很难自我平衡而造成振动更明显。随着转速的升高且没达到临界转速发生共振的情况下，扭振振幅会逐渐降低。从图中可看出，增程器轴系低速时的最大相对振幅为-1.98°，比原机低速时的最大相对振幅-2.5°降低了0.52°，降幅约为21%。ISG电机在不对发动机施加转矩时（此时电磁参数还不介入）增程器与原机的轴系在4、6、8、10谐次下的扭振振幅如图13所示。2谐次为四缸发动机的最低主谐次，扭振振幅一般都是随着转速的升高而降低，这种现象属于“滚振”，并不会对轴系激起扭振应力，所以并不将其作为扭振分析的评价指标。本文主要分析4、6、8、10谐次下的扭振特性。
从图13中可以看出，电机系统介入以后，整个轴系的最大扭振振幅降低了，且共振转速都提前了约200 r/min，使得增程器在高效区内更容易发生共振。4谐次和6谐次下，轴系扭振振幅随着转速增加先下降后升高，没有出现向上的峰值，说明原机和增程器在4谐次和6谐次下不会出现共振现象，但振幅较大。在8谐次和10谐次下轴系皆发生了共振，在8谐次下，发动机原机在转速为2 800 r/min左右时发生了共振现象，振幅为0.225°，已经超出单阶谐次下的许用值0.20°，但不在常用转速区内。根据公式f=n·v/60可计算得到其共振频率为373.3 Hz。增程器在2 600 r/min左右发生了1阶共振，共振振幅为0.16°，共振频率为346.7 Hz。10谐次下发动机原机在2 300 r/min时发生了共振，振幅为0.057°，共振频率为383.3 Hz。增程器在2 100 r/min左右时发生了共振，共振振幅为0.42°，共振频率为341.7 Hz。通过对数据分析发现，原机与增程器在8、10谐次下的共振频率和临界转速图谱中计算得到的固有频率基本一致。
3.3 电磁参数对轴系扭振特性影响分析
3.3.1 电磁阻尼的影响
由1.3节可知，电磁阻尼和电磁刚度与电机输出转矩呈线性正相关，一般情况下电磁阻尼和电磁刚度是同步变化的。为了研究单一参数变化对轴系扭转特性的影响，采用参数分离法在模型中控制某一变量，单独改变其中一个参数去观察输出结果的变化。在研究电磁阻尼变化对轴系扭振特性影响时，控制电磁刚度保持为10 N·mm/rad，再去计算不同电磁阻尼下的扭振振幅。图14为轴系第8谐次、第10谐次在电磁阻尼分别为50、100、150和200 N·m·s/rad时的强迫振动扭振振幅计算结果。从图中可以看出，随着电磁阻尼的增加，轴系的共振振幅线性降低，且效果显著。在不同电磁阻尼下，轴系在第8谐次和第10谐次下依旧会发生共振，但共振点始终保持在一条垂线上，说明电磁参数能改变轴系的共振振幅，但并不会影响轴系的固有频率和共振转速。
3.3.2 电磁刚度的影响
分析电磁刚度对轴系扭振特性的影响时，忽略电磁刚度改变所带来的电磁阻尼的变化，将电磁阻尼设为定值50 N·m·s/rad，并根据1.2节中对电磁刚度的计算结果，分别取值100、200、300和394 N·mm/rad对轴系进行模态频率计算和扭振振幅计算。图15为电磁刚度为100 N·mm/rad时计算的临界转速图谱，从图中可以看出，当电磁参数介入时，增程器轴系会产生一个接近0 Hz的固有频率，称为“零频”，其数值为1.4 Hz。随着电磁刚度增大到394 N·mm/rad时，“零频”增加到1.5 Hz，但其它高阶固有频率并没有发生改变，这是由于电磁刚度值与各个轴段的扭转刚度值相比较小的缘故。因此在电磁刚度变化时对发动机轴系各节点的振型几乎没有影响，但电磁刚度的介入会使电机转子振幅增大，由此可判断出电磁刚度在耦合状态下会导致发动机轴系产生低频滚振现象。图16为不同电磁刚度下，8谐次的振幅计算，从图中可以看出，随着电磁刚度的增大，8谐次的共振振幅也随着增大，但增幅并不明显。
4 结论
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本文建立了一增程器扭振分析的动力学模型，并通过试验测试验证了模型对此类轴系进行扭振分析的可行性，对提高增程式电动汽车的NVH性能，具有一定的工程实际意义。通过对一款四缸柴油机增程器进行扭振特性分析得出主要结论如下。
（1）机电耦合作用下使得轴系的共振现象更加丰富，通过临界转速求解得出电机转子系统的加入，轴系的固有频率降低27.6 Hz，且会在前12阶内增加一个固有频率，这是因为转子系统的加入增加了轴系的长度，降低了整个轴系的扭转刚度导致。
（2）在ISG电机不对发动机施加负载时，增程器轴系与发动机原机相比，最大振幅下降了约21%，共振转速向前推移了约200 r/min，将共振转速推移到了增程器的高效区内。
（3）电磁刚度对增程器轴系的影响主要体现在会产生零阶（前10 Hz）固有频率，对高阶固有频率和振幅基本不产生影响，但零频会导致增程器轴系在低阶频率下发生共振，从而辐射到机体，因此需要对电磁刚度产生的零频共振引起重视；电磁阻尼对扭振振幅的衰减呈线性负相关的关系，但其并不影响轴系的固有频率和共振转速。
基金
收起
  • *云南省省市一体化专项项目(202202AC080004)
  • 云南省重大科技专项计划项目(202302AE090052)
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2025年第47卷第2期
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doi: 10.19562/j.chinasae.qcgc.2025.02.008
  • 接收时间：2024-05-20
  • 首发时间：2025-07-09
  • 出版时间：2025-02-25
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  • 收稿日期：2024-05-20
  • 修回日期：2024-09-02
基金
*云南省省市一体化专项项目(202202AC080004)
云南省重大科技专项计划项目(202302AE090052)
作者信息
    1 昆明理工大学，云南省内燃机重点实验室，昆明 650500
    2 云内动力股份有限公司，昆明 650500

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雷基林，教授，博士，E-mail：。
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species		 占总种数比例
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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