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Article(id=1241049259827581324, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241049258309251153, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.06.001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1699113600000, receivedDateStr=2023-11-05, revisedDate=1701532800000, revisedDateStr=2023-12-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1773818801122, onlineDateStr=2026-03-18, pubDate=1749916800000, pubDateStr=2025-06-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773818801122, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773818801122, creator=13701087609, updateTime=1773818801122, updator=13701087609, issue=Issue{id=1241049258309251153, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='6', pageStart='1', pageEnd='158', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773818800761, creator=13701087609, updateTime=1773819014967, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241050156821434987, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241049258309251153, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241050156821434988, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241049258309251153, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1, endPage=10, ext={EN=ArticleExt(id=1241049260309926285, articleId=1241049259827581324, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Analysis of vibration characteristics of gear system during start-stop process, columnId=1228282191914926752, journalTitle=Journal of Mechanical Strength, columnName=Vibration·Noise·Monitoring·Diagnosis, runingTitle=null, highlight=null, articleAbstract=

When the gear system starts or stops in non-stationary working conditions, a sharp change of the speed can cause it to exhibit complex vibration characteristics which has a significant impact on the performance and lifespan of the gear. Considering the influence of time-varying meshing stiffness, backlash and gear meshing error, a dynamics model of spur gear system was established. The influence of external load and angular acceleration on the vibration characteristics of the start-stop process was studied. At the same time, the time-frequency analysis of the non-stationary vibration signal of the gear system was carried out by using the short-time Fourier transform. The results show that increasing the load and angular acceleration during the start and stop processes will exacerbate the degree of vibration and impact of the gear pair, and both will make the unstable motion process in the early start period end earlier, and the unstable motion process in the late stop period appear later, but the impact components in the late start period (the early stop period) will increase (decrease). In the frequency domain, increasing the external load will enhance the energy of the harmonic component of the gear system’s meshing frequency, but it has no effect on the fundamental energy of the meshing frequency. However, increasing the angular acceleration will enhance the energy of both the fundamental and harmonic components of the meshing frequency.

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CAO Zheng, E-mail：
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当齿轮系统启动或者停止处于非平稳工况时，转速的急剧改变会使其表现出复杂的振动特性，从而对齿轮使用性能和寿命产生重要影响。综合考虑时变啮合刚度、齿侧间隙及齿轮啮合误差的影响，建立直齿轮系统动力学模型，研究了外部载荷和角加速度两个工况参数对其启停过程振动特性的影响。同时，利用短时傅里叶变换对齿轮系统的非平稳振动信号进行了时频分析。结果表明，在启停过程中，增大载荷、增大角加速度均会加剧齿轮副振动与冲击的程度，并且均会使启动前期的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现，但启动后期（停止前期）的冲击成分却会分别增多和减少；在频域中，增大外部载荷会增强齿轮系统啮合频率的倍频成分能量但对啮合频率的基频能量没有什么影响，而增大角加速度会使啮合频率的基频和倍频成分能量都增强。

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曹正（通信作者），男，1988年生，安徽六安人，博士，讲师；主要研究方向为齿轮动力学；E-mail：。
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涂文兵，男，1983年生，江西南昌人，博士，副教授；主要研究方向为机械动力学、振动噪声与结构有限元分析；E-mail：。

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涂文兵，男，1983年生，江西南昌人，博士，副教授；主要研究方向为机械动力学、振动噪声与结构有限元分析；E-mail：。

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涂文兵，男，1983年生，江西南昌人，博士，副教授；主要研究方向为机械动力学、振动噪声与结构有限元分析；E-mail：。

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journalId=1227999626482147330, articleId=1241049259827581324, language=CN, orderNo=3, keyword=启停过程), Keyword(id=1241049286989894562, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, language=CN, orderNo=4, keyword=短时傅里叶变换), Keyword(id=1241049287103140776, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, language=CN, orderNo=5, keyword=振动特性)], refs=[Reference(id=1241049299606360152, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2014, volume=29, issue=7, pageStart=1543, pageEnd=1555, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=李朝峰, 周世华, 刘文明, journalName=航空动力学报, refType=null, unstructuredReference=李朝峰，周世华，刘文明，等.齿轮-转子-滚动轴承传动系统的弯扭耦合振动[J].航空动力学报，2014，29（7）：1543-1555., articleTitle=齿轮-转子-滚动轴承传动系统的弯扭耦合振动, refAbstract=null), Reference(id=1241049299807686746, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2014, volume=29, issue=7, pageStart=1543, pageEnd=1555, url=null, language=null, rfNumber=[1], rfOrder=1, authorNames=LI Chaofeng, ZHOU Shihua, LIU Wenming, journalName=Journal of Aerospace Power, refType=null, unstructuredReference=LI Chaofeng，ZHOU Shihua，LIU Wenming，et al. Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system[J].Journal of Aerospace Power，2014，29（7）：1543-1555.（In Chinese）, articleTitle=Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system, refAbstract=null), Reference(id=1241049300080316511, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2016, volume=38, issue=4, pageStart=667, pageEnd=674, url=null, language=null, rfNumber=[2], rfOrder=2, authorNames=程言丽, 肖正明, 王旭, journalName=机械强度, refType=null, unstructuredReference=程言丽，肖正明，王旭.直齿圆柱齿轮动力学特性分析与ADAMS仿真研究[J].机械强度，2016，38（4）：667-674., articleTitle=直齿圆柱齿轮动力学特性分析与ADAMS仿真研究, refAbstract=null), Reference(id=1241049300243894373, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2016, volume=38, issue=4, pageStart=667, pageEnd=674, url=null, language=null, rfNumber=[2], rfOrder=3, authorNames=CHENG Yanli, XIAO Zhengming, WANG Xu, journalName=Journal of Mechanical Strength, refType=null, unstructuredReference=CHENG Yanli，XIAO Zhengming，WANG Xu. Investigation on dynamic characteristic of cylinder gears and simulation based on ADAMS[J].Journal of Mechanical Strength，2016，38（4）：667-674.（In Chinese）, articleTitle=Investigation on dynamic characteristic of cylinder gears and simulation based on ADAMS, refAbstract=null), Reference(id=1241049300449415273, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2019, volume=38, issue=23, pageStart=246, pageEnd=252, url=null, language=null, rfNumber=[3], rfOrder=4, authorNames=魏维, 郭文勇, 吴新跃, journalName=振动与冲击, refType=null, unstructuredReference=魏维，郭文勇，吴新跃，等.考虑滑动轴承时变动力学参数的齿轮系统建模及分析[J].振动与冲击，2019，38（23）：246-252., articleTitle=考虑滑动轴承时变动力学参数的齿轮系统建模及分析, refAbstract=null), Reference(id=1241049300717850732, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2019, volume=38, issue=23, pageStart=246, pageEnd=252, url=null, language=null, rfNumber=[3], rfOrder=5, authorNames=WEI Wei, GUO Wenyong, WU Xinyue, journalName=Journal of Vibration and Shock, refType=null, unstructuredReference=WEI Wei，GUO Wenyong，WU Xinyue，et al. Gear system modeling considering sliding bearings’ time-varying dynamic parameters[J].Journal of Vibration and Shock，2019，38（23）：246-252.（In Chinese）, articleTitle=Gear system modeling considering sliding bearings’ time-varying dynamic parameters, refAbstract=null), Reference(id=1241049300810125424, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2019, volume=41, issue=5, pageStart=1211, pageEnd=1216, url=null, language=null, rfNumber=[4], rfOrder=6, authorNames=万志国, 李锁斌, 窦益华, journalName=机械强度, refType=null, unstructuredReference=万志国，李锁斌，窦益华，等.齿轮传动系统的参数稳定性及振动特性分析[J].机械强度，2019，41（5）：1211-1216., articleTitle=齿轮传动系统的参数稳定性及振动特性分析, refAbstract=null), Reference(id=1241049300940148850, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2019, volume=41, issue=5, pageStart=1211, pageEnd=1216, url=null, language=null, rfNumber=[4], rfOrder=7, authorNames=WAN Zhiguo, LI Suobin, DOU Yihua, journalName=Journal of Mechanical Strength, refType=null, unstructuredReference=WAN Zhiguo，LI Suobin，DOU Yihua，et al. Parameter stability and vibration characteristics analysis of gear transmission system[J].Journal of Mechanical Strength，2019，41（5）：1211-1216.（In Chinese）, articleTitle=Parameter stability and vibration characteristics analysis of gear transmission system, refAbstract=null), Reference(id=1241049301401522297, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2017, volume=50, issue=null, pageStart=569, pageEnd=584, url=null, language=null, rfNumber=[5], rfOrder=8, authorNames=XIANG L, GAO N, journalName=Applied Mathematical Modelling, refType=null, unstructuredReference=XIANG L，GAO N. Coupled torsion-bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation[J]. Applied Mathematical Modelling，2017，50：569-584., articleTitle=Coupled torsion-bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation, refAbstract=null), Reference(id=1241049301577683068, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2016, volume=29, issue=2, pageStart=281, pageEnd=292, url=null, language=null, rfNumber=[6], rfOrder=9, authorNames=ZHOU S H, SONG G Q, REN Z H, journalName=Chinese Journal of Mechanical Engineering, refType=null, unstructuredReference=ZHOU S H，SONG G Q，REN Z H，et al. Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations[J]. Chinese Journal of Mechanical Engineering，2016，29（2）：281-292., articleTitle=Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations, refAbstract=null), Reference(id=1241049303075049601, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2017, volume=39, issue=5, pageStart=1001, pageEnd=1006, url=null, language=null, rfNumber=[7], rfOrder=10, authorNames=时培明, 赵娜, 梁凯, journalName=机械强度, refType=null, unstructuredReference=时培明，赵娜，梁凯，等.变载荷激励下齿轮传动系统齿根裂纹故障动力学特性分析[J].机械强度，2017，39（5）：1001-1006., articleTitle=变载荷激励下齿轮传动系统齿根裂纹故障动力学特性分析, refAbstract=null), Reference(id=1241049303259598980, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2017, volume=39, issue=5, pageStart=1001, pageEnd=1006, url=null, language=null, rfNumber=[7], rfOrder=11, authorNames=SHI Peiming, ZHAO Na, LIANG Kai, journalName=Journal of Mechanical Strength, refType=null, unstructuredReference=SHI Peiming，ZHAO Na，LIANG Kai，et al. Analysis on dynamic characteristics of tooth root crack of gear drive system under variable load excitation[J].Journal of Mechanical Strength，2017，39（5）：1001-1006.（In Chinese）, articleTitle=Analysis on dynamic characteristics of tooth root crack of gear drive system under variable load excitation, refAbstract=null), Reference(id=1241049303465119881, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2020, volume=56, issue=17, pageStart=108, pageEnd=115, url=null, language=null, rfNumber=[8], rfOrder=12, authorNames=孟宗, 石桂霞, 王福林, journalName=机械工程学报, refType=null, unstructuredReference=孟宗，石桂霞，王福林，等.基于时变啮合刚度的裂纹故障齿轮振动特征分析[J].机械工程学报，2020，56（17）：108-115., articleTitle=基于时变啮合刚度的裂纹故障齿轮振动特征分析, refAbstract=null), Reference(id=1241049303616114830, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2020, volume=56, issue=17, pageStart=108, pageEnd=115, url=null, language=null, rfNumber=[8], rfOrder=13, authorNames=MENG Zong, SHI Guixia, WANG Fulin, journalName=Journal of Mechanical Engineering, refType=null, unstructuredReference=MENG Zong，SHI Guixia，WANG Fulin，et al. Vibration characteristic analysis of cracked gear based on time-varying meshing stiffness[J].Journal of Mechanical Engineering，2020，56（17）：108-115.（In Chinese）, articleTitle=Vibration characteristic analysis of cracked gear based on time-varying meshing stiffness, refAbstract=null), Reference(id=1241049303955853462, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2022, volume=44, issue=2, pageStart=369, pageEnd=375, url=null, language=null, rfNumber=[9], rfOrder=14, authorNames=曹正, 夏杨, 徐博宇, journalName=机械强度, refType=null, unstructuredReference=曹正，夏杨，徐博宇，等.基于动态啮合力刚度的剥落齿轮动力学建模及动态特性研究[J].机械强度，2022，44（2）：369-375., articleTitle=基于动态啮合力刚度的剥落齿轮动力学建模及动态特性研究, refAbstract=null), Reference(id=1241049304220094619, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2022, volume=44, issue=2, pageStart=369, pageEnd=375, url=null, language=null, rfNumber=[9], rfOrder=15, authorNames=CAO Zheng, XIA Yang, XU Boyu, journalName=Journal of Mechanical Strength, refType=null, unstructuredReference=CAO Zheng，XIA Yang，XU Boyu，et al. Research on dynamic modeling and dynamic characteristics of peeling gear based on dynamic mesh force stiffness[J].Journal of Mechanical Strength，2022，44（2）：369-375.（In Chinese）, articleTitle=Research on dynamic modeling and dynamic characteristics of peeling gear based on dynamic mesh force stiffness, refAbstract=null), Reference(id=1241049304316563616, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2014, volume=33, issue=18, pageStart=221, pageEnd=226, url=null, language=null, rfNumber=[10], rfOrder=16, authorNames=高洪波, 李允公, 刘杰, journalName=振动与冲击, refType=null, unstructuredReference=高洪波，李允公，刘杰.基于动态侧隙的齿轮系统齿面磨损故障动力学分析[J].振动与冲击，2014，33（18）：221-226., articleTitle=基于动态侧隙的齿轮系统齿面磨损故障动力学分析, refAbstract=null), Reference(id=1241049304425615521, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2014, volume=33, issue=18, pageStart=221, pageEnd=226, url=null, language=null, rfNumber=[10], rfOrder=17, authorNames=GAO Hongbo, LI Yungong, LIU Jie, journalName=Journal of Vibration and Shock, refType=null, unstructuredReference=GAO Hongbo，LI Yungong，LIU Jie. Dynamic analysis on spur gear system with wear fault based on dynamic backlash[J].Journal of Vibration and Shock，2014，33（18）：221-226.（In Chinese）, articleTitle=Dynamic analysis on spur gear system with wear fault based on dynamic backlash, refAbstract=null), Reference(id=1241049304576610468, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2022, volume=38, issue=6, pageStart=2921, pageEnd=2938, url=null, language=null, rfNumber=[11], rfOrder=18, authorNames=YANG L T, CHEN Q Y, YIN L, journalName=Quality and Reliability Engineering International, refType=null, unstructuredReference=YANG L T，CHEN Q Y，YIN L，et al. Dynamic characteristic of spur gear system with spalling fault considering tooth pitch error[J].Quality and Reliability Engineering International，2022，38（6）：2921-2938., articleTitle=Dynamic characteristic of spur gear system with spalling fault considering tooth pitch error, refAbstract=null), Reference(id=1241049304786325671, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2022, volume=41, issue=11, pageStart=225, pageEnd=234, url=null, language=null, rfNumber=[12], rfOrder=19, authorNames=代鹏, 王建平, 鲁珏, journalName=振动与冲击, refType=null, unstructuredReference=代鹏，王建平，鲁珏，等.变工况下裂纹故障直齿轮副振动特性分析[J].振动与冲击，2022，41（11）：225-234., articleTitle=变工况下裂纹故障直齿轮副振动特性分析, refAbstract=null), Reference(id=1241049304907960490, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2022, volume=41, issue=11, pageStart=225, pageEnd=234, url=null, language=null, rfNumber=[12], rfOrder=20, authorNames=DAI Peng, WANG Jianping, LU Jue, journalName=Journal of Vibration and Shock, refType=null, unstructuredReference=DAI Peng，WANG Jianping，LU Jue，et al. Vibration characteristics analysis of spur gear pair with crack fault under variable working conditions[J].Journal of Vibration and Shock，2022，41（11）：225-234.（In Chinese）, articleTitle=Vibration characteristics analysis of spur gear pair with crack fault under variable working conditions, refAbstract=null), Reference(id=1241049305054761132, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2014, volume=333, issue=24, pageStart=6498, pageEnd=6515, url=null, language=null, rfNumber=[13], rfOrder=21, authorNames=LIU C Z, QIN D T, LIM T C, journalName=Journal of Sound and Vibration, refType=null, unstructuredReference=LIU C Z，QIN D T，LIM T C，et al. Dynamic characteristics of the herringbone planetary gear set during the variable speed process[J].Journal of Sound and Vibration，2014，333（24）：6498-6515., articleTitle=Dynamic characteristics of the herringbone planetary gear set during the variable speed process, refAbstract=null), Reference(id=1241049305331585199, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2011, volume=25, issue=8, pageStart=3089, pageEnd=3101, url=null, language=null, rfNumber=[14], rfOrder=22, authorNames=KHABOU M T, BOUCHAALA N, CHAARI F, journalName=Mechanical Systems and Signal Processing, refType=null, unstructuredReference=KHABOU M T，BOUCHAALA N，CHAARI F. Study of a spur gear dynamic behavior in transient regime[J]. Mechanical Systems and Signal Processing，2011，25（8）：3089-3101., articleTitle=Study of a spur gear dynamic behavior in transient regime, refAbstract=null), Reference(id=1241049305658740915, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2004, volume=null, issue=null, pageStart=18, pageEnd=49, url=null, language=null, rfNumber=[15], rfOrder=23, authorNames=TIAN X H, journalName=null, refType=null, unstructuredReference=TIAN X H. Dynamic simulation for system response of gearbox including localized gear faults[D].Edmonton：University of Alberta，2004：18-49., articleTitle=Dynamic simulation for system response of gearbox including localized gear faults, refAbstract=null), Reference(id=1241049305935564980, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2004, volume=126, issue=4, pageStart=748, pageEnd=752, url=null, language=null, rfNumber=[16], rfOrder=24, authorNames=SAINSOT P, VELEX P, DUVERGER O, journalName=Journal of Mechanical Design, refType=null, unstructuredReference=SAINSOT P，VELEX P，DUVERGER O. Contribution of gear body to tooth deflections：a new bidimensional analytical formula[J].Journal of Mechanical Design，2004，126（4）：748-752., articleTitle=Contribution of gear body to tooth deflections：a new bidimensional analytical formula, refAbstract=null), Reference(id=1241049306044616888, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, doi=null, pmid=null, pmcid=null, year=2019, volume=40, issue=1, pageStart=135, pageEnd=153, url=null, language=null, rfNumber=[17], rfOrder=25, authorNames=LI X, CHEN K K, HUANGFU Y F, journalName=Journal of Low Frequency Noise，Vibration and Active Control, refType=null, unstructuredReference=LI X，CHEN K K，HUANGFU Y F，et al. Vibration characteristic analysis of spur gear systems under tooth crack or fracture[J].Journal of Low Frequency Noise，Vibration and Active Control，2019，40（1）：135-153., articleTitle=Vibration characteristic analysis of spur gear systems under tooth crack or fracture, refAbstract=null)], funds=[Fund(id=1241049296510963770, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, awardId=51965018, language=EN, fundingSource=National Natural Science Foundation of China(51965018), fundOrder=null, country=null), Fund(id=1241049296884256831, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, awardId=51965018, language=CN, fundingSource=国家自然科学基金项目(51965018), fundOrder=null, country=null), Fund(id=1241049297161080903, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, awardId=GJJ2200603, language=EN, fundingSource=Education Department Science and Technology Project of Jiangxi 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Main parameters of the spur gear pair

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参数
Parameter		主动轮
Driving gear		从动轮
Driven gear
齿数 Number of teeth2525
模数 Modulus/mm6
压力角 Pressure angle/（°）20
齿宽 Tooth width/mm16
轮毂半径 Hub radius/mm28
齿顶高系数 Addendum coefficient1
顶隙系数 Tip clearance coefficient0.25
弹性模量 Modulus of elasticity/GPa212
泊松比 Poisson ratio0.3
啮合误差常值
Meshing error constant/μm		0
啮合误差幅值
Meshing error amplitude/μm		15
), ArticleFig(id=1241049296271888438, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241049259827581324, language=CN, label=表1, caption=

直齿轮副主要参数

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参数
Parameter		主动轮
Driving gear		从动轮
Driven gear
齿数 Number of teeth2525
模数 Modulus/mm6
压力角 Pressure angle/（°）20
齿宽 Tooth width/mm16
轮毂半径 Hub radius/mm28
齿顶高系数 Addendum coefficient1
顶隙系数 Tip clearance coefficient0.25
弹性模量 Modulus of elasticity/GPa212
泊松比 Poisson ratio0.3
啮合误差常值
Meshing error constant/μm		0
啮合误差幅值
Meshing error amplitude/μm		15
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启停过程齿轮系统振动特性分析
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涂文兵 1 , 胡登亮 1 , 王浩 1 , 刘晨露 1 , 曹正 2
机械强度 | 振动·噪声·监测·诊断 2025,47(6): 1-10
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机械强度 | 振动·噪声·监测·诊断 2025, 47(6): 1-10
启停过程齿轮系统振动特性分析
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涂文兵1 , 胡登亮1, 王浩1, 刘晨露1, 曹正2
作者信息
  • 1.华东交通大学 机电与车辆工程学院，南昌　330013
  • 2.安徽大学 电气工程与自动化学院，合肥　230601

    • 涂文兵，男，1983年生，江西南昌人，博士，副教授；主要研究方向为机械动力学、振动噪声与结构有限元分析；E-mail：。

通讯作者:

曹正（通信作者），男，1988年生，安徽六安人，博士，讲师；主要研究方向为齿轮动力学；E-mail：。
Analysis of vibration characteristics of gear system during start-stop process
Wenbing TU1 , Dengliang HU1, Hao WANG1, Chenlu LIU1, Zheng CAO2
Affiliations
  • 1.School of Mechatronic and Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China
  • 2.School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China
出版时间: 2025-06-15 doi: 10.16579/j.issn.1001.9669.2025.06.001
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摘要
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当齿轮系统启动或者停止处于非平稳工况时，转速的急剧改变会使其表现出复杂的振动特性，从而对齿轮使用性能和寿命产生重要影响。综合考虑时变啮合刚度、齿侧间隙及齿轮啮合误差的影响，建立直齿轮系统动力学模型，研究了外部载荷和角加速度两个工况参数对其启停过程振动特性的影响。同时，利用短时傅里叶变换对齿轮系统的非平稳振动信号进行了时频分析。结果表明，在启停过程中，增大载荷、增大角加速度均会加剧齿轮副振动与冲击的程度，并且均会使启动前期的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现，但启动后期（停止前期）的冲击成分却会分别增多和减少；在频域中，增大外部载荷会增强齿轮系统啮合频率的倍频成分能量但对啮合频率的基频能量没有什么影响，而增大角加速度会使啮合频率的基频和倍频成分能量都增强。

齿轮系统  /  动力学  /  启停过程  /  短时傅里叶变换  /  振动特性

When the gear system starts or stops in non-stationary working conditions, a sharp change of the speed can cause it to exhibit complex vibration characteristics which has a significant impact on the performance and lifespan of the gear. Considering the influence of time-varying meshing stiffness, backlash and gear meshing error, a dynamics model of spur gear system was established. The influence of external load and angular acceleration on the vibration characteristics of the start-stop process was studied. At the same time, the time-frequency analysis of the non-stationary vibration signal of the gear system was carried out by using the short-time Fourier transform. The results show that increasing the load and angular acceleration during the start and stop processes will exacerbate the degree of vibration and impact of the gear pair, and both will make the unstable motion process in the early start period end earlier, and the unstable motion process in the late stop period appear later, but the impact components in the late start period (the early stop period) will increase (decrease). In the frequency domain, increasing the external load will enhance the energy of the harmonic component of the gear system’s meshing frequency, but it has no effect on the fundamental energy of the meshing frequency. However, increasing the angular acceleration will enhance the energy of both the fundamental and harmonic components of the meshing frequency.

Gear system  /  Dynamics  /  Start-stop process  /  Short-time Fourier transform  /  Vibration characteristic
涂文兵, 胡登亮, 王浩, 刘晨露, 曹正. 启停过程齿轮系统振动特性分析. 机械强度, 2025 , 47 (6) : 1 -10 . DOI: 10.16579/j.issn.1001.9669.2025.06.001
Wenbing TU, Dengliang HU, Hao WANG, Chenlu LIU, Zheng CAO. Analysis of vibration characteristics of gear system during start-stop process[J]. Journal of Mechanical Strength, 2025 , 47 (6) : 1 -10 . DOI: 10.16579/j.issn.1001.9669.2025.06.001
正文
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0　引言
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齿轮传动因传动比稳定、传动精度高、平稳性较好及传动效率高等优点而被广泛地应用于动力机械、船舶、航空航天等工业领域。齿轮系统经常处于启动或者停止等非平稳工况，转速的急剧改变会恶化齿轮轮齿之间的接触状态，致使轮齿之间发生频繁碰撞，从而对齿轮系统的振动特性产生重要影响，进而影响齿轮传动系统的运行精度和运行平稳性。因此，研究齿轮系统在启停过程中的振动特性显得尤为重要。
目前有关齿轮系统振动响应特性的研究有着较为丰硕的研究成果。李朝峰等[1]1543-1555构建了齿轮-转子-滚动轴承系统的弯扭耦合动力学模型，研究了转速、偏心量与轴承游隙等因素对系统振动响应的影响。程言丽等[2]考虑时变啮合刚度、啮合阻尼、齿面摩擦等因素，深入地研究了齿轮系统的动力学特性。魏维等[3]246-252将动压润滑轴承模型与齿轮啮合模型相结合，提出了一种齿轮-滑动轴承耦合系统的求解方法，研究了轴承间隙、齿侧间隙及转速对系统振动响应的影响。万志国等[4]考虑时变啮合刚度与齿侧间隙，建立了齿轮副非线性动力学模型，研究了参数激励作用下系统的振动稳定性及非线性振动特性。XIANG等[5]考虑时变啮合刚度、齿轮偏心和滚动轴承非线性接触特性，构建了弯扭耦合的齿轮-转子-滚动轴承系统的动力学模型，讨论了系统的振动响应。ZHOU等[6]建立了包含间隙、传动误差、偏心距和重力的8自由度非线性直齿圆柱齿轮-转子-轴承模型，研究了其横扭耦合振动特性。齿轮在运行过程中不可避免地会发生故障，从而直接影响机械设备的使用。时培明等[7-8]建立了含齿根裂纹故障的齿轮系统多自由度动力学模型，研究了轮齿裂纹对系统振动响应的影响。曹正等[9]考虑轮齿接触的非线性、啮合刚度和动态啮合力的相互作用，分析了剥落故障时齿轮的动态特性。高洪波等[10-11]考虑时变啮合刚度和齿间滑动摩擦，建立了单级齿轮传动系统6自由度啮合耦合型动力学模型，分别对含磨损和剥落故障的齿轮系统动力学行为进行了分析。
随着齿轮传动系统向着高速、重载等方向发展，其运行状况变得愈发复杂，齿轮在复杂变工况下的动力学问题日益突出。代鹏等[12]建立了裂纹故障齿轮副的啮合刚度模型和齿轮副动力学模型，分析了变工况下齿轮系统的振动特性。LIU等[13]分析了人字形行星齿轮变速过程的动力学特性，研究了齿廓误差激励对齿面分离现象的影响。KHABOU等[14]将时变啮合刚度简化为变频率的矩形波，研究了单级直齿圆柱齿轮减速器在不同转速下的动态响应，证实了瞬态工况对齿轮动态行为的显著影响，特别是在发动机不可靠工况下。
因此，现有的齿轮系统振动特性研究主要集中在稳定运行工况，对齿轮系统启停过程等非平稳工况下振动特性的研究却相对较少。然而，启停工况在齿轮服役期间是普遍存在的。此外，虽然部分学者在变速工况下齿轮系统振动特性方面的研究取得了一些成果，但大多将变速过程中的时变啮合刚度简化为变频率的矩形波，不能较好地描述齿轮旋转过程中啮合刚度的变化。鉴于此，本文基于势能法计算出时变啮合刚度，通过傅里叶级数进行了拟合，同时考虑齿侧间隙和齿轮啮合误差，建立了直齿轮系统动力学模型，分析了齿轮系统变速过程中各激励的特点，研究了外部载荷和角加速度两个工况参数对齿轮系统启停过程振动特性的影响规律，讨论了齿轮系统启动与停止过程中运动稳定性和冲击成分的变化，从而为改善齿轮系统的运行平稳性提供参考。
1　动力学模型的建立
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利用集中参数法建立的考虑时变啮合刚度、齿侧间隙及齿轮传递误差的直齿轮系统动力学模型如图1所示，以啮合线方向为y轴建立坐标系，每个齿轮均具有y方向的平移自由度和绕轴向的旋转自由度。
本文中下标p表示主动轮，下标g表示从动轮。设广义坐标为｛yp，θp，yg，θg｝，其中，yp、θp分别为主动轮y方向的平移自由度和旋转自由度；yg、θg分别为从动轮y方向的平移自由度和旋转自由度。图1中，mp、mg分别为主、从动轮的质量；zp、zg分别为主、从动轮齿数；Ip、Ig分别为主、从动轮的转动惯量；Rp、Rg分别为主、从动轮基圆半径；kpy、kgy分别为主、从动轮y方向径向支承刚度；km为齿轮副间的时变啮合刚度；cpy、cgy分别为主、从动轮y方向径向支承阻尼；cm为齿轮副间的啮合阻尼；b为齿轮副的半齿侧间隙；ωp、ωg分别为主、从动轮角速度。
1.1　启停过程转速与载荷分析
根据齿轮系统在启停过程的实际运行状况，假设输入转速即主动轮转速按线性规律变化，该假设具有很强的代表性。启停过程输入转速变化曲线如图2所示。启动过程中，输入转速从零时刻开始加速，由0线性上升至最大转速nm，终止时间为tm；停止过程中，输入转速从零时刻开始减速，由最大转速nm线性下降至0，终止时间为tm。
运行过程中主动轮角加速度αp（启动过程为“+”，停止过程为“-”）可表示为
本文假设变速工况下的外部载荷为一恒定值，根据给定的负载转矩Tg，可用式（2）求解出输入转矩Tp：
式中，αp、αg分别为设定的主、从动轮的角加速度；Fm为作用在轮齿上的动态啮合力。
在式（2）中，消除Fm后，可得输入转矩Tp的表达式，即
1.2　时变啮合刚度计算
啮合刚度是由齿轮啮合过程中啮合综合刚度时变性引起的动态激励。本文根据文献[15]18-49和[16]748-752基于势能法对齿轮副时变啮合刚度进行求解。由于齿轮在啮合时是以单齿和双齿交替啮合的方式进行的，所以要分单齿啮合和双齿啮合两种情况来计算齿轮副的综合啮合刚度。
对于单齿啮合区
对于双齿啮合区
式中，j=1表示主动轮；j=2表示从动轮；i=1表示第1对轮齿啮合；i=2表示第2对轮齿啮合。各参数的定义及计算式详见文献[15]18-49和[16]748-752。
针对上述计算出的时变啮合刚度结果，利用傅里叶级数对其进行拟合，具体形式为
式中，a0为齿轮副的平均啮合刚度；aj、bj为谐波项啮合刚度的幅值；ωm为齿轮啮合角频率，ωm=ωpzp。
根据式（6）拟合出一定转速下的时变啮合刚度，得到傅里叶级数各个系数的值及函数表达式。在变速工况下，啮合刚度的幅值大小并不会随转速的变化产生明显的影响，但是啮合刚度曲线的变化频率却会随之变化，因此需对拟合出的傅里叶函数表达式里的齿轮啮合角频率ωm进行修正。
若匀变速工况下主动轮的初始角速度为ω0，则有
积分后，得到ωm修正后的表达式为
根据参考文献[3]248-249可以得到啮合阻尼cm表达式，即
式中，ζ为啮合相对阻尼比，一般在0.03~0.17，本文中ζ取0.07。
1.3　啮合误差分析
轮齿啮合误差是由齿轮加工误差和安装误差引起的，是轮齿啮合过程的主要动态激励之一。本文根据轮齿精度等级要求的齿面误差，用简谐函数模拟齿轮误差，表达式[1]1545-1546为
求导后，可得
式中，e0为啮合误差的常值；er为啮合误差的幅值；ωm为变速工况下的啮合频率，用式（8）计算；φ为初相位，取φ=0。
1.4　系统微分方程
由动态激励引起的齿轮动态传动误差δ可表示为
于是，作用在轮齿上的动态啮合力的表达式为
f(δ)为与齿侧间隙有关的非线性函数，可表示为
根据图1所示的模型，对齿轮系统应用拉格朗日方程得到4自由度系统的动力学微分方程，即
采用吉尔方法解其动力学微分方程，设置工作步长为10−5 s，求解后可得到齿轮系统的振动信号。
2　模型验证
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本文选用的直齿轮副主要参数如表1所示。为了验证所建齿轮系统动力学模型的有效性，设置负载转矩为500 N·m、输入转速np为1 200 r/min，将从动轮角速度和轮齿啮合力的仿真值分别与对应的理论计算值进行对比，对比结果如图3、图4所示。
根据齿轮相关知识可得下述理论计算式：
从动轮角速度为
齿轮啮合时作用在基圆切线上的力为
由于齿轮啮合运动时，作用在基圆切线上的力和轮齿啮合力是1对大小相等、方向相反的相互作用力，所以取作用在基圆切线上的力作为轮齿啮合力理论值。
由图3、图4可以看出，从动轮角速度与轮齿啮合力仿真值均在对应的理论计算值上下波动，并且存在明显的谐波成分，其频率为啮合频率（500 Hz）。这是由齿轮系统的内部激励造成的，因此将仿真的平均值与对应的理论值进行比较，来验证模型的有效性。经计算，仿真得出的从动轮角速度与轮齿啮合力的平均值与理论值较为一致，相对误差都小于0.01%，由此证明了本文所建立的直齿轮副动力学模型的有效性。
为了进一步验证模型的有效性，将仿真得出的主动轮y方向振动加速度时域与频域信号与文献[17]135-153给出的试验结果进行对比。采用与试验中相同的工况参数，设置负载转矩为100 N·m、输入转速为1 490 r/min，则输入轴转频为24.83 Hz，啮合频率为620.8 Hz。图5所示为仿真得出的主动轮y方向振动响应结果，图6所示为文献[17]135-153给出的试验结果。
通过对比图5、图6可以看出，仿真获得的振动响应幅值与试验结果相比偏大。可能的原因是试验方法中信号传感器是置于齿轮箱体上，多个接合面导致振动能量有一定程度的耗散，而仿真提取的是齿轮内部的信号。比较仿真与试验信号的频域特征可以发现，两者主要频率成分基本一致，均存在啮合频率成分。其产生原因与同样具有啮合频率成分的轮齿啮合力密切相关，这说明在齿轮系统动力学模型中考虑非线性效应是十分必要的。此外，还有一系列啮合频率的谐波频率，符合理论的频率分析特征。不同的是，试验结果中还包含了啮合频率及其谐波成分与转频的调制频率，并且有明显的转动频率，该转动频率是由试验中两个齿轮的齿距累积误差和安装偏心导致的，但是本文的动力学模型没有考虑这些因素，因此频域中没有转动频率成分。将啮合频率及其高阶倍频的仿真值分别与对应的理论值、试验值进行对比，结果基本吻合，相对误差均在0.2%以内，由此进一步证明了本文所建立模型的有效性，为后续的分析奠定了良好的基础。
3　振动特性时域分析
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3.1　载荷的影响
为了分析载荷对齿轮系统在启动与停止过程中振动特性的影响规律，取nm=1 200 r/min、tm=0.5 s，通过设置负载转矩分别为60、20、10 N·m，对齿轮副启停过程进行动力学仿真后可得到不同转矩下齿轮系统的振动信号。
图7所示为不同转矩下启停过程中主动轮y方向振动加速度随时间变化的曲线。由图7可知，在启停过程中，振动加速度曲线的振动幅度大体上分别呈现出增大与减小的变化趋势，并且随着时间的推移，其脉冲冲击幅值也在分别增大与减小，齿轮系统处于不稳定状态。此外，随着载荷的增大，齿轮副的振动和脉冲冲击幅值整体上都在增大。
由图7还可以观察到，启动前期齿轮副的振动过程相较于后期更加不稳定，冲击成分十分混乱，随时间变化的随机性较强。这可能是由于启动前期齿轮转速较低，惯性作用力较小，齿面较启动后期更易脱啮，齿侧间隙影响较大，从而使齿轮运动稳定性较差，停止后期相较于前期同样如此。
为了进一步定量描述启停期间齿轮振动信号的差异性，选取均方根（Root Mean Square, RMS）值与峰值因子这两个常用的时域评价指标对齿轮的振动进行评价。
均方根值反映了信号能量的大小，其计算式为
峰值因子可以敏感捕捉和检测信号中的冲击成分，其计算式为
式中，x（n'）为信号的时域序列；n'=1，2，…，N；N为样本点数。
为了不失一般性，采用主动轮y方向振动加速度信号进行分析，由于仿真过程中齿轮转速非平稳变化，故本文取t0=0.01 s为单位时间间隔变量，分别计算了整个启停过程中不同时间间隔内主动轮y方向振动加速度信号的均方根值与峰值因子。
图8、图9所示分别为提取的不同转矩下启停过程中主动轮y方向振动信号的均方根值与峰值因子随时间变化的曲线。在图8（a）中，受转速不断增加的影响，加速过程中齿轮副轮齿之间接触碰撞频繁发生，齿轮运动状态变化频率不断加快，其振动信号均方根值曲线整体上呈现出不断上升的变化规律；随着转速的升高，齿轮副振动能量不断增加且增加速度越来越快。停止过程中均方根值曲线呈现出与此相反的趋势，如图8（b）所示。启停过程中均方根值随着载荷的增加而增大，这表明增大载荷会增强齿轮副的振动能量。但在启动前期这些变化规律不明显，均方根值曲线有所波动。这说明这一期间齿轮副振动能量的变化十分不稳定，停止后期同样如此。随着载荷的增大，启动前期与停止后期波动过程的持续时间增长。这表明增大载荷会使启动前期齿轮系统的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现。这可能是由于载荷的增大使齿面更不易脱啮，齿侧间隙影响变小，从而在一定程度上抑制了齿轮的不稳定运动进程。
由图9可以看出，启动过程中，齿轮振动信号峰值因子前期较大且曲线有剧烈波动，而后期较小且曲线有不断下降的趋势；停止过程中，峰值因子后期较大且曲线有剧烈波动，而前期较小且曲线有不断上升的趋势。这说明启动前期齿轮副的冲击成分较后期更加明显，并且冲击过程的随机性更强；停止后期相较于前期同样如此。另外，载荷越大，启动前期与停止后期波动过程的持续时间越长。这进一步表明，增大载荷会使启动前期齿轮系统的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现。启动后期峰值因子随着载荷增加有所增大，说明在此期间载荷的增大在一定程度上促进了齿轮冲击成分的产生；停止前期同样如此。
3.2　角加速度的影响
为了分析角加速度对齿轮系统在启动与停止过程中振动特性的影响规律，取负载转矩为20 N·m、tm=0.5 s，通过设置nm分别为1 950、1 200、750 r/min，此时主动轮角加速度分别为408.41、251.33、157.08 rad/s2，对齿轮副启停过程进行动力学仿真后可得到不同角加速度下齿轮系统的振动信号。
图10所示为不同角加速度下启停过程中主动轮y方向振动加速度随时间变化的曲线。由图10可以看出，在齿轮启停过程中，振动加速度曲线的振动幅度与脉冲冲击幅值整体上是随角加速度的增大而增大的。这表明角加速度的增大在一定程度上加剧了齿轮在启停过程中的振动与冲击程度。这是因为加减速过程中角加速度的增大使得齿轮速度变化加快，受力状态改变频率加快，从而加剧了齿轮的振动程度。
图11、图12所示分别为提取的不同角加速度下启停过程主动轮y方向振动信号的均方根值与峰值因子随时间变化的曲线。由图11可知，在启停过程中，随着角加速度的增大，齿轮振动信号均方根值整体上增大。这表明增大角加速度会增强齿轮副的振动能量。在启动前期与停止后期，随着角加速度的增大，均方根值曲线波动过程的持续时间变长。这表明增大角加速度会使启动前期齿轮系统的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现。这可能是因为高角加速度下转速变化较快，惯性作用较强，齿面不易脱啮，齿侧间隙影响较小，导致齿轮不稳定运动进程受到一定阻碍。
由图12可以看出，在启动前期与停止后期，随着角加速度的增大，峰值因子曲线波动过程的持续时间变长。这进一步表明，增大角加速度会使启动前期齿轮系统的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现，启动后期峰值因子随着角加速度增大而有所减小。这说明，在此期间角加速度的增大在一定程度上抑制了齿轮冲击成分的产生，停止前期同样如此。对比图12（a）与图12（b）可以看出，停止后期齿轮系统整个不稳定运动进程的峰值因子较启动前期整体上更大，这表明停止后期齿轮副的冲击成分较启动前期更加明显，这可能是因为停止过程中齿轮副更易发生齿背冲击。
4　振动特性频域分析
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由于变速工况下齿轮系统振动信号往往具有非平稳性并伴随调制现象的产生，所以本文利用短时傅里叶变换来处理齿轮系统的非平稳振动信号。选择nm=1 200 r/min、tm=0.5 s，设置负载转矩为20 N·m，分别对此工况参数下齿轮系统启动过程与停止过程主动轮y方向振动加速度信号进行时频分析，得到的对应时频分布图如图13所示。由图13可以看到，齿轮系统启停过程中啮合频率及其倍频非常明显，其中啮合频率占主导成分，表明内部激励在齿轮系统响应中起主要作用，系统的非线性特性使其产生了大量谐波成分。
另外，在启动工况下，齿轮副的啮合频率及谐波随时间不断增大，说明齿轮副转频不稳定，转速处于一直升高的状态，伴随而来的还有这些主要频率成分能量的增强，表明齿轮系统振动程度在增强；在停车工况下则具有相反的趋势，验证了时域分析所得出的结论。在转速很低的启动前期与停止后期，啮合频率及各倍频成分几乎不可见，能量很低，这说明这些阶段齿轮副振动较小。
为了对比不同转矩下和不同角加速度下齿轮系统主要频率能量的不同，提取启动过程不同工况参数下时频分布图中啮合频率的基频fe和倍频成分2fe～6fe的功率谱密度（Power Spectral Density，PSD）最大值并绘制图14与图15（停止过程的PSD最大值与此相当）。由图14可以看出，随着外部转矩的增大，啮合频率的倍频成分2fe～6fe的PSD最大值升高但其基频fe的PSD最大值几乎不变。表明在其他参数一定的情况下，增大外部载荷会增强齿轮系统启停过程中啮合频率的倍频成分的能量，但对啮合频率的基频能量没有什么影响。由图15可知，随着角加速度的增大，啮合频率的基频和倍频成分的能量都增强。
5　结论
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建立了直齿轮副系统动力学模型，针对主动轮y方向振动加速度对启停过程齿轮系统振动特性进行了研究，并且选择均方根值与峰值因子对齿轮振动进行了评价，进一步分析了外部载荷和角加速度两个工况参数对齿轮系统启停过程振动特性的影响规律，得到主要结论如下：
1）在启停过程中，齿轮系统振动响应曲线的振动幅度大体上分别呈现出增大与减小的变化趋势，启动前期齿轮副的振动过程相较于启动后期更加不稳定，冲击成分更明显，停止后期相较于停止前期同样如此。此外，停止后期齿轮副的冲击成分较启动前期更加明显。
2）增大载荷、增大角加速度均会加剧齿轮副启停过程中振动与冲击的程度，并且均会使启动前期齿轮系统的不稳定运动进程提前结束，停止后期的不稳定运动进程延后出现，但启动后期（停止前期）的冲击成分却会分别增多和减少。
3）启停过程中齿轮系统啮合频率及其倍频非常明显。在启动工况下，齿轮副的啮合频率及谐波随时间不断增大；在停止工况下则具有相反的趋势。增大外部载荷会增强启停过程中齿轮系统啮合频率的倍频成分的能量，但对啮合频率的基频能量没有什么影响；角加速度越大，启停过程中啮合频率的基频和倍频成分的能量都越强。
基金
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  • 国家自然科学基金项目(51965018)
  • 江西省教育厅科技项目(GJJ2200603)
  • 安徽省自然科学基金项目(2108085QE224)
文献
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参考文献 引证文献
排序方式：
[1]
李朝峰，周世华，刘文明，等.齿轮-转子-滚动轴承传动系统的弯扭耦合振动[J].航空动力学报，2014，29（7）：1543-1555.
LI Chaofeng，ZHOU Shihua，LIU Wenming，et al. Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system[J].Journal of Aerospace Power，2014，29（7）：1543-1555.（In Chinese）
[2]
程言丽，肖正明，王旭.直齿圆柱齿轮动力学特性分析与ADAMS仿真研究[J].机械强度，2016，38（4）：667-674.
CHENG Yanli，XIAO Zhengming，WANG Xu. Investigation on dynamic characteristic of cylinder gears and simulation based on ADAMS[J].Journal of Mechanical Strength，2016，38（4）：667-674.（In Chinese）
[3]
魏维，郭文勇，吴新跃，等.考虑滑动轴承时变动力学参数的齿轮系统建模及分析[J].振动与冲击，2019，38（23）：246-252.
WEI Wei，GUO Wenyong，WU Xinyue，et al. Gear system modeling considering sliding bearings’ time-varying dynamic parameters[J].Journal of Vibration and Shock，2019，38（23）：246-252.（In Chinese）
[4]
万志国，李锁斌，窦益华，等.齿轮传动系统的参数稳定性及振动特性分析[J].机械强度，2019，41（5）：1211-1216.
WAN Zhiguo，LI Suobin，DOU Yihua，et al. Parameter stability and vibration characteristics analysis of gear transmission system[J].Journal of Mechanical Strength，2019，41（5）：1211-1216.（In Chinese）
[5]
XIANG L，GAO N. Coupled torsion-bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation[J]. Applied Mathematical Modelling，2017，50：569-584.
[6]
ZHOU S H，SONG G Q，REN Z H，et al. Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations[J]. Chinese Journal of Mechanical Engineering，2016，29（2）：281-292.
[7]
时培明，赵娜，梁凯，等.变载荷激励下齿轮传动系统齿根裂纹故障动力学特性分析[J].机械强度，2017，39（5）：1001-1006.
SHI Peiming，ZHAO Na，LIANG Kai，et al. Analysis on dynamic characteristics of tooth root crack of gear drive system under variable load excitation[J].Journal of Mechanical Strength，2017，39（5）：1001-1006.（In Chinese）
[8]
孟宗，石桂霞，王福林，等.基于时变啮合刚度的裂纹故障齿轮振动特征分析[J].机械工程学报，2020，56（17）：108-115.
MENG Zong，SHI Guixia，WANG Fulin，et al. Vibration characteristic analysis of cracked gear based on time-varying meshing stiffness[J].Journal of Mechanical Engineering，2020，56（17）：108-115.（In Chinese）
[9]
曹正，夏杨，徐博宇，等.基于动态啮合力刚度的剥落齿轮动力学建模及动态特性研究[J].机械强度，2022，44（2）：369-375.
CAO Zheng，XIA Yang，XU Boyu，et al. Research on dynamic modeling and dynamic characteristics of peeling gear based on dynamic mesh force stiffness[J].Journal of Mechanical Strength，2022，44（2）：369-375.（In Chinese）
[10]
高洪波，李允公，刘杰.基于动态侧隙的齿轮系统齿面磨损故障动力学分析[J].振动与冲击，2014，33（18）：221-226.
GAO Hongbo，LI Yungong，LIU Jie. Dynamic analysis on spur gear system with wear fault based on dynamic backlash[J].Journal of Vibration and Shock，2014，33（18）：221-226.（In Chinese）
[11]
YANG L T，CHEN Q Y，YIN L，et al. Dynamic characteristic of spur gear system with spalling fault considering tooth pitch error[J].Quality and Reliability Engineering International，2022，38（6）：2921-2938.
[12]
代鹏，王建平，鲁珏，等.变工况下裂纹故障直齿轮副振动特性分析[J].振动与冲击，2022，41（11）：225-234.
DAI Peng，WANG Jianping，LU Jue，et al. Vibration characteristics analysis of spur gear pair with crack fault under variable working conditions[J].Journal of Vibration and Shock，2022，41（11）：225-234.（In Chinese）
[13]
LIU C Z，QIN D T，LIM T C，et al. Dynamic characteristics of the herringbone planetary gear set during the variable speed process[J].Journal of Sound and Vibration，2014，333（24）：6498-6515.
[14]
KHABOU M T，BOUCHAALA N，CHAARI F. Study of a spur gear dynamic behavior in transient regime[J]. Mechanical Systems and Signal Processing，2011，25（8）：3089-3101.
[15]
TIAN X H. Dynamic simulation for system response of gearbox including localized gear faults[D].Edmonton：University of Alberta，2004：18-49.
[16]
SAINSOT P，VELEX P，DUVERGER O. Contribution of gear body to tooth deflections：a new bidimensional analytical formula[J].Journal of Mechanical Design，2004，126（4）：748-752.
[17]
LI X，CHEN K K，HUANGFU Y F，et al. Vibration characteristic analysis of spur gear systems under tooth crack or fracture[J].Journal of Low Frequency Noise，Vibration and Active Control，2019，40（1）：135-153.
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文章信息
doi: 10.16579/j.issn.1001.9669.2025.06.001
  • 接收时间：2023-11-05
  • 首发时间：2026-03-18
  • 出版时间：2025-06-15
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出版历史
  • 收稿日期：2023-11-05
  • 修回日期：2023-12-03
基金
National Natural Science Foundation of China(51965018)
国家自然科学基金项目(51965018)
Education Department Science and Technology Project of Jiangxi Province(GJJ2200603)
江西省教育厅科技项目(GJJ2200603)
Natural Science Foundation of Anhui Province(2108085QE224)
安徽省自然科学基金项目(2108085QE224)
作者信息
    1.华东交通大学 机电与车辆工程学院，南昌　330013
    2.安徽大学 电气工程与自动化学院，合肥　230601

通讯作者:

曹正（通信作者），男，1988年生，安徽六安人，博士，讲师；主要研究方向为齿轮动力学；E-mail：。
参考文献
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https://castjournals.cast.org.cn/joweb/jxqd/CN/10.16579/j.issn.1001.9669.2025.06.001
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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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