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Article(id=1153756965126791957, tenantId=1146029695717560320, journalId=1152916057816748034, issueId=1153756963994329869, articleNumber=null, orderNo=null, doi=10.3969/j.issn.2095‒1469.2025.02.04, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1706889600000, receivedDateStr=2024-02-03, revisedDate=1713715200000, revisedDateStr=2024-04-22, acceptedDate=null, acceptedDateStr=null, onlineDate=1753006696254, onlineDateStr=2025-07-20, pubDate=1742400000000, pubDateStr=2025-03-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1753006696254, onlineIssueDateStr=2025-07-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1753006696254, creator=13701087609, updateTime=1753006696254, updator=13701087609, issue=Issue{id=1153756963994329869, tenantId=1146029695717560320, journalId=1152916057816748034, year='2025', volume='15', issue='2', pageStart='125', pageEnd='262', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1753006695984, creator=13701087609, updateTime=1757654146268, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1173249783352410923, tenantId=1146029695717560320, journalId=1152916057816748034, issueId=1153756963994329869, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1173249783352410924, tenantId=1146029695717560320, journalId=1152916057816748034, issueId=1153756963994329869, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=155, endPage=163, ext={EN=ArticleExt(id=1153756965550416665, articleId=1153756965126791957, tenantId=1146029695717560320, journalId=1152916057816748034, language=EN, title=Temperature Field Analysis and Cooling Structure Optimization of Wheel Hub Motors for Specialized Vehicles, columnId=1153756965466530584, journalTitle=Chinese Journal of Automotive Engineering, columnName=Green and Low-Carbon Technologies Section, runingTitle=null, highlight=null, articleAbstract=

To address the heat dissipation issue of hub motor in a specialized vehicle, a serpentine flow channel was chosen as the cooling structure. CFD simulations were performed to analyze the temperature rise, temperature distribution, and radial temperature variation of the hub motor. Subsequently, the effects of the number and width of flow channels on the motor's temperature and flow fields were investigated. The appropriate number of flow channels was determined and an initial selection of channel width was decided. Furthermore, taking the flow channel height and width as optimization variables, a multi-objective optimization was conducted, with the maximum motor temperature and flow channel pressure drop as the optimization targets. The results show that after optimization, the highest motor temperature increased by 0.22℃, while the flow channel pressure drop decreased by 904.19 Pa, effectively reducing energy loss and improving the heat dissipation efficiency of the cooling system.

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针对某特种车辆轮毂电机散热问题，选择蛇形水道为冷却结构，通过CFD仿真方法对轮毂电机温升、温度分布和径向温度变化趋势进行了分析，接着研究了水道数目、水道宽度对轮毂电机温度场和流场的影响，得到了合适的水道数目并初步确定水道宽度。进一步以水道高度b和水道宽度a为优化变量，以电机最高温度和水道压降为优化目标，对水道进行多目标优化，结果表明，优化后的冷却水道，电机最高温度提高了0.22 ℃，而水道压降降低了904.19 Pa，有效降低了冷却系统能量损耗，提高了冷却系统散热效率。

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娄华语（1998-），男，贵州遵义人，硕士研究生，主要研究方向为轮毂电机热管理。 E-mail：

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娄华语（1998-），男，贵州遵义人，硕士研究生，主要研究方向为轮毂电机热管理。 E-mail：

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娄华语（1998-），男，贵州遵义人，硕士研究生，主要研究方向为轮毂电机热管理。 E-mail：

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figureFileBig=x52U3MVqWux75DjsoLfDvg==, tableContent=null), ArticleFig(id=1175545920771998497, tenantId=1146029695717560320, journalId=1152916057816748034, articleId=1153756965126791957, language=CN, label=图14, caption=Pareto最优解集, figureFileSmall=bniExbcji85kNqCLjsSaQg==, figureFileBig=x52U3MVqWux75DjsoLfDvg==, tableContent=null), ArticleFig(id=1175545920839107362, tenantId=1146029695717560320, journalId=1152916057816748034, articleId=1153756965126791957, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
参数 值
额定功率/kW 15
额定转速/（r/min） 2 000
额定电压/V 120
铁芯长度/mm 60
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电机基本参数

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参数 值
额定功率/kW 15
额定转速/（r/min） 2 000
额定电压/V 120
铁芯长度/mm 60
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铁芯损耗系数 值
kh 2.05×10-2
ke 3.54×10-4
x 1.662
kex 4.42×10-7
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铁芯损耗系数参考值

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铁芯损耗系数 值
kh 2.05×10-2
ke 3.54×10-4
x 1.662
kex 4.42×10-7
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部件 产热率/（W/m3）
定子铁芯 53 043
转子铁芯 3 020
绕组 2 730 122
永磁体 101 626
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各部件产热率

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部件 产热率/（W/m3）
定子铁芯 53 043
转子铁芯 3 020
绕组 2 730 122
永磁体 101 626
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水道宽度/mm 温度/℃
13 114.51
17 114.84
21 115.24
25 114.87
27 115.22
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不同水道宽度时电机最高温度

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水道宽度/mm 温度/℃
13 114.51
17 114.84
21 115.24
25 114.87
27 115.22
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设计变量 a/mm b/mm
水平1 19 7.0
水平2 20 7.5
水平3 21 8.0
水平4 22 8.5
水平5 23 9.0
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水道设计变量及水平

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设计变量 a/mm b/mm
水平1 19 7.0
水平2 20 7.5
水平3 21 8.0
水平4 22 8.5
水平5 23 9.0
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项目 a/mm b/mm ΔP /Pa Tmax/℃
变化幅度/% 0.95 6.25 -16.03 0.19
初始值 21 8 5 640.26 115.24
优化后 21.2 8.5 4 736.07 115.46
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优化前后结果对比

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项目 a/mm b/mm ΔP /Pa Tmax/℃
变化幅度/% 0.95 6.25 -16.03 0.19
初始值 21 8 5 640.26 115.24
优化后 21.2 8.5 4 736.07 115.46
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特种车辆轮毂电机温度场分析及冷却结构优化
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娄华语 1 , 杨晓光 1 , 张明 1 , 邹小俊 2 , 宋伟 2 , 王良模 1
汽车工程学报 | 绿色低碳技术专栏 2025,15(2): 155-163
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汽车工程学报 | 绿色低碳技术专栏 2025, 15(2): 155-163
特种车辆轮毂电机温度场分析及冷却结构优化
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娄华语1 , 杨晓光1, 张明1, 邹小俊2, 宋伟2, 王良模1
作者信息
  • 1 南京理工大学，南京 210094
  • 2 南京依维柯汽车有限公司，南京 210037

    • 娄华语（1998-），男，贵州遵义人，硕士研究生，主要研究方向为轮毂电机热管理。 E-mail：

Temperature Field Analysis and Cooling Structure Optimization of Wheel Hub Motors for Specialized Vehicles
Huayu LOU1 , Xiaoguang YANG1, Ming ZHANG1, Xiaojun ZOU2, Wei SONG2, Liangmo WANG1
Affiliations
  • 1 Nanjing University of Science and Technology，Nanjing 210094，China
  • 2 Nanjing IVECO Automobile Co.，Ltd.，Nanjing 210037，China
出版时间: 2025-03-20 doi: 10.3969/j.issn.2095‒1469.2025.02.04
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摘要
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针对某特种车辆轮毂电机散热问题，选择蛇形水道为冷却结构，通过CFD仿真方法对轮毂电机温升、温度分布和径向温度变化趋势进行了分析，接着研究了水道数目、水道宽度对轮毂电机温度场和流场的影响，得到了合适的水道数目并初步确定水道宽度。进一步以水道高度b和水道宽度a为优化变量，以电机最高温度和水道压降为优化目标，对水道进行多目标优化，结果表明，优化后的冷却水道，电机最高温度提高了0.22 ℃，而水道压降降低了904.19 Pa，有效降低了冷却系统能量损耗，提高了冷却系统散热效率。

轮毂电机  /  温度场  /  流场  /  冷却水道  /  多目标优化

To address the heat dissipation issue of hub motor in a specialized vehicle, a serpentine flow channel was chosen as the cooling structure. CFD simulations were performed to analyze the temperature rise, temperature distribution, and radial temperature variation of the hub motor. Subsequently, the effects of the number and width of flow channels on the motor's temperature and flow fields were investigated. The appropriate number of flow channels was determined and an initial selection of channel width was decided. Furthermore, taking the flow channel height and width as optimization variables, a multi-objective optimization was conducted, with the maximum motor temperature and flow channel pressure drop as the optimization targets. The results show that after optimization, the highest motor temperature increased by 0.22℃, while the flow channel pressure drop decreased by 904.19 Pa, effectively reducing energy loss and improving the heat dissipation efficiency of the cooling system.

hub motor  /  temperature field  /  flow field  /  cooling flow channel  /  multi-objective optimization
娄华语, 杨晓光, 张明, 邹小俊, 宋伟, 王良模. 特种车辆轮毂电机温度场分析及冷却结构优化. 汽车工程学报, 2025 , 15 (2) : 155 -163 . DOI: 10.3969/j.issn.2095‒1469.2025.02.04
Huayu LOU, Xiaoguang YANG, Ming ZHANG, Xiaojun ZOU, Wei SONG, Liangmo WANG. Temperature Field Analysis and Cooling Structure Optimization of Wheel Hub Motors for Specialized Vehicles[J]. Chinese Journal of Automotive Engineering, 2025 , 15 (2) : 155 -163 . DOI: 10.3969/j.issn.2095‒1469.2025.02.04
正文
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轮毂电机具有体积小、结构紧凑的优点，有助于提高车辆的操纵稳定性，减少能量损耗和提高传动效率[1]。同时，轮毂电机可实现多种复杂的驱动方式，提高汽车行驶安全性和稳定性[2]。但轮毂电机内部空间有限、运行工况复杂，在工作过程中面临严重的散热问题，同时，温度过高会对电机各部分材料性能造成影响[3]，因此，需要合理设计冷却系统，将电机温升控制在合理范围内。
目前对电机温升的研究主要有两种方法，包括等效热网络法和数值计算法[4]。王晓远等[5]、XU Yongming等[6]、王英杰等[7]通过热网络法建立电机温度场模型，并开展了电机温升试验，通过仿真值与试验值的对比，验证了电机等效热网络模型的有效性。龚浩文[8]、CHEN Peng等[9]通过CFD方法，对电机温升模型进行数值求解，该方法求解结果与试验结果比较接近，验证了电机温升CFD模型的合理性。GUO Changbo等 ［10]、张璐璐等[11]采用磁-热耦合分析方法，考虑到了温度与损耗之间的相互影响，通过电机温升试验，验证了电磁-热双向耦合仿真方法的合理性。等效热网络法建模过程相对复杂，电磁-热双向耦合仿真方法求解速度慢，所需时间较长。
在电机冷却方式的研究上，江从喜等[12]讨论了汽车来流速度对轮毂电机温升的影响，结果表明，在高速工况下，电机需要加装散热翅片或采用水冷散热方式才能满足使用要求。刘浩等[13]、姚弘义[14]研究了冷却水道类型及水道结构尺寸对水道散热和压降的影响，结果表明，水道类型及其结构尺寸参数对进出口压降和水道散热能力的影响较大。WANG Zheng等[15]针对永磁同步直线电机冷却问题，在铁芯和绕组间填充了高导热材料，并且采用绕组和铁芯直接冷却结构，显著提高了电机的冷却性能。KANG Ming等[16]考虑电机机壳水冷时，转子冷却困难，因此，提出了一种自通风冷却结构，改进电机通风结构能有效提高电机散热能力，但会使电机结构更加复杂或增加电机成本。WANG Yuncong等[17]提出了一种综合评价方法来描述结构对水道性能的影响，通过卷积神经网络和粒子群集成算法得到了水道最佳的结构尺寸。HYEON等[18]提出了一种带有导流板的冷却系统，同时对导流板进行了优化设计，将冷却效果提高了28%。
综上，针对轮毂电机散热问题，本文基于CFD仿真方法，采用机壳水冷的冷却方式，通过Fluent软件对某特种车辆用15 kW永磁同步轮毂电机温度场进行分析，研究水道结构参数对电机温度和水道压降的影响，进一步对冷却水道截面尺寸参数进行多目标优化研究，旨在保证轮毂电机温升合理，有效降低水道压降，提高冷却系统效率。
1 轮毂电机冷却结构设计
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本文以某特种车辆用15 kW永磁同步轮毂电机为研究对象，电机采用8极式内转子结构，外部配备减速机构，电机主要参数见表1。
为了使冷却系统能满足电机不同工况下的需求，以电机在最大爬坡度工况下的损耗为冷却系统散热需求。本文采用蛇形冷却水道，设计的冷却结构如图1所示，其中水道数目28条，水道宽度a为17 mm，水道高度b为8 mm。
2 轮毂电机温度场分析
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2.1 电机热源与边界条件确定
电机在运行过程中会产生各种损耗，这些损耗会导致电机产生温升。电机损耗主要包括定转子铁损、永磁体涡流损耗和绕组铜耗。
电机铁芯铁损计算式为：
P F e = k h f B 1 x + k e f 2 B 1 2 + k e x ( f B 1 ) 1.5 。
式中：kh为铁芯磁滞损耗系数：f为交变电流频率，单位Hz；B1为电机磁密幅值，单位T；ke为涡流损耗系数；kex为附加损耗系数。
本文所研究的电机采用的铁芯材料为DW315_50，其损耗系数参考值见表2。
永磁体涡流损耗计算式为：
P w = ∑ N ∫ J n 2 2 σ d V 。
式中：σ为永磁体电导率，单位S/m；Jn为永磁体涡流密度，单位A/m2。
在计算损耗时，定转子铁损及涡流损耗可通过有限元方法求解，结果如图2所示。
绕组铜损可通过式（3）直接计算。
P c u = m I 2 R 。
式中：m为电机相数；I为绕组相电流有效值，单位A；R为每相绕组电阻值，单位Ω。
通过计算单位体积损耗，得到轮毂电机各部件产热率，见表3。
对轮毂电机进行温度场仿真，需要确定各边界面上的对流换热系数。绕组端部和定转子端面的对流换热系数可根据文献［19］中的相关公式进行计算。
机壳外表面对流换热系数可计算为：
h s = 7.68 v a i r 0.78 。
式中：vair为轮毂电机机壳表面上空气运动速度，单位m/s；hs为电机机壳外表面对流换热系数。
转子铁芯端面对流换热系数可计算为：
h r h = N u r λ a i r R r 。
式中：Rr为转子外径，单位m；Nur为转子端部努塞尔特常数；hrh为转子端部对流换热系数，单位W/（m2·K）； λ air为空气导热系数，单位W/（m·K）。
定子铁心端面换热系数可计算为：
h s h = 15 + v r 0.7 。
式中：hsh为定子两端面处的对流换热系数，单位W/（m2·K）；vr为转子表面圆周速度，单位m/s。
定子绕组端部对流换热系数可计算为：
h c o = N u c λ a i r d e 。
式中：hco为绕组端部对流换热系数，单位W/（m2·K）；Nuc为绕组端部努塞尔特常数；de为绕组端部等效直径，单位m。
2.2 轮毂电机温升试验验证
为验证轮毂电机温升CFD模型的合理性，需要对轮毂电机进行温升试验，对额定功率和额定转速下轮毂电机温升进行试验，试验台架硬件连接逻辑框如图3所示。
轮毂电机温升最高处为绕组，因此，在绕组端部设置温度传感器，检测绕组温度变化。
由图4可知，在额定功率及额定转速下，轮毂电机温度在40 min达到热平衡状态，通过试验和仿真得到的最高温度分别为68.54 ℃和67.04 ℃，仿真值与试验值误差为1.50 ℃，在合理范围内，验证了轮毂电机温升模型的准确性。
2.3 轮毂电机温度场仿真分析
对轮毂电机温度场进行仿真，仿真条件为：冷却液为纯水，冷却液流量为4 L/min，冷却液入口温度为55 ℃。温升曲线如图5所示。
由图5可知，在水冷条件下，随着电机运行时间的增加，电机各部位的温度逐渐上升并趋于稳定。
电机达到热平衡状态时，绕组温度达到114.46 ℃，绝缘层温度达到114.05 ℃，定子铁芯温度达到89.92 ℃，转子铁芯温度达到70.87 ℃，永磁体温度达到70.64 ℃。电机采用F级绝缘，各部件最高温度均满足要求。
图6和图7分别为轮毂电机两个对称面上的温度分布云图，由图可知，电机绕组部位温度最高，这主要是绕组损耗最大，产热功率最大，同时绕组包裹绝缘层，导致绕组处热量容易积累，造成较大的温升；电机定子铁芯温度较高；机壳温度最低；转子和永磁体损耗较小。
图8为电机在对称面上径向温度监测点示意图。由图9可知，电机在径向的温差较大，最大温差达到47.56 ℃。气隙区域（点7～9）两侧温度出现突增，这主要是因为空气热阻较大，所以接近绕组一侧气隙温度较高，接近转子一侧气隙温度较低。绕组区域（点13～19），温度为电机径向最大，且在径向上温度变化很小，这主要是因为绕组区域损耗较高，周围又有绝缘层隔热作用。定子和机壳区域（分别为点21～28和点28～32），该区域温度变化较小，主要是因为定子铁芯与机壳导热系数较大。
由图10可知，水道进出水口压降为6 889.40 Pa，高压区域位于进水口附近几段水道，靠近出水口压力逐渐降低。
3 轮毂电机冷却结构优化
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本文采用的蛇形冷却水道，其结构参数中变化范围较大的主要包括水道数目和水道宽度，水道高度受到机壳尺寸限制，变化范围较小。通过调整这些尺寸参数，可以降低水道压降，提高冷却系统散热效率。
3.1 冷却水道数目确定
为了确定冷却水道数目选择多少条比较合适，需要研究水道数目对电机温度场和冷却液流场的影响，在前文设计的蛇形水道基础上，只改变水道数目，其他结构参数不变，材料属性和边界条件与之前保持一致，分别建立水道数目为12、16、20、24、28、32条的冷却水套进行仿真。
图11为不同水道数目时电机最高温度与压降变化趋势，由图可知，随着水道数目的增加，电机最高温度不断下降，水道压降不断增加。这主要是因为水道数目的增加会造成水道长度，水道弯折次数和水道与机壳接触面积的增加，导致机壳散热能力增强，沿程损失和局部损失增加。水道数目从12条增加到32条，电机最高温度从116.14 ℃下降到了114.461 ℃，水道压降从5 844 Pa增加到了9 821 Pa。
随着水道数目增加到24条，电机最高温度逐渐稳定，继续增加水道数目会增加水道压降，因此，结合冷却水道数目对轮毂电机温度和水道压降的影响，确定冷却水道数目为24条。
3.2 冷却水道宽度初步确定
在冷却液流量一定的前提下，改变水道宽度会影响水道横截面积，使水道流速发生改变，从而影响冷却液在水道内的流动。为了确定冷却水道宽度，需要研究水道宽度对电机温度场和流场的影响。根据前文的分析，水道数目为24条，只改变水道宽度，其他结构参数不变，材料属性和边界条件保持一致，水道截面宽度分别为13、17、21、25、29 mm。
表4给出了不同水道宽度时的电机最高温度，分析表中数据可知，改变水道宽度对电机最高温度有一定影响。
图12为不同水道宽度下水道平均流速和进出口压降的变化趋势。由图可知，随着水道宽度的增加，水道内平均流速不断降低，这主要是由水道横截面积变化引起的。压降变化同冷却液流速变化趋势类似，当水道宽度从21 mm增加到25 mm时，水道压降变化出现了波动，这主要是因为水道宽度的变化引起了水道内冷却液流动特性的改变。
图13为水道截面宽度分别为21 mm和27 mm时水道速度流线图。
由图13可知，水道截面尺寸变化时，会影响冷却液的流动状态，但同样不会影响水道内速度分布趋势。水道宽度为21 mm和27 mm时，两者最大流速分别为1.143 7 m/s和1.443 8 m/s。
一般来讲，增加水道宽度，水道截面面积增大，在入水口流量不变的情况下可以降低冷却液在水道内的流速，从而减小压降，但水道宽度增加过多后，会引起冷却液流动状态发生改变，产生较多涡流，如图13b所示。大量涡流的存在将会使流体平均速度增大，水道压降增加，因此，在设计水道宽度时需要避免大量涡流的出现。结合水道宽度对电机温度场和流场的影响分析，初步确定水道宽度取21 mm。
3.3 冷却水道结构多目标优化研究
根据前文的分析，水道数目选取24条，水道宽度初步选择21 mm，水道高度初步设计为8 mm，为了进一步减小水道进出口压降，提高冷却系统散热效率，对水道截面宽度a和高度b进行优化。其中，a的取值范围为19～23 mm，b的取值范围为7～9 mm。设计变量水平及取值范围见表5。
根据设计变量及水平数，采用全因子试验设计表，冷却系统优化的响应变量为电机最高温度Tmax和水道压降ΔP，通过仿真得到各方案结果，在优化软件Modefrontier中建立Kriging代理模型，并通过NSGA-Ⅱ遗传算法进行多目标优化，该多目标优化问题的数学模型为：
M i n i m i z e      T m a x ( a , b ) , Δ P ( a , b ) , S u b j e c t   t o   19   m m ≤ a ≤ 23   m m ,
7   m m ≤ b ≤ 9   m m   。
通过Kriging代理模型和NSGA-Ⅱ遗传算法，对水道宽度和高度进行多目标优化，得到该多目标优化问题的Pareto最优解集如图14所示。
从图14中选择一个最优解，并与优化前的结果进行比较，结果见表6。由表6可知，优化之后水道宽度为21.2 mm，水道高度为8.5 mm，电机最高温度只增加了0.19%，达到了115.46 ℃，仍能满足使用需求，但水道压降降低了16.03%。
4 结论
收起
本文以一台特种车辆用15 kW，2 000 r/min的永磁同步轮毂电机为研究对象，以最大爬坡度下电机损耗为散热要求，对电机冷却结构进行设计，同时对电机温度场进行分析，最后对冷却水道截面尺寸进行多目标优化，主要结论如下。
1）轮毂电机达到热平衡状态时，电机绕组部位温度最高，这主要是绕组损耗最大，产热功率最大，同时绕组包裹绝缘层，导热系数小，导致绕组处热量容易积累，同时绝缘层和气隙处导热系数小，温度梯度较大。
2）冷却水道数目和水道宽度需取合适的值，水道数目较少时电机最高温度较大，水道数目太多时会造成较大的水道压降。水道宽度较小时水道散热能力较强，但水道压降大，随着水道宽度的增加，可降低水道压降，但水道宽度过大时会产生大量涡流，使水道压降较大。
3）通过Kriging代理模型和NSGA-Ⅱ遗传算法，对水道宽度和高度进行多目标优化，优化之后水道宽度为21.2 mm，水道高度为8.5 mm，电机最高温度只增加了0.22 ℃，但水道压降降低了904.19 Pa，有效提高了冷却系统的散热效率。
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2025年第15卷第2期
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doi: 10.3969/j.issn.2095‒1469.2025.02.04
  • 接收时间：2024-02-03
  • 首发时间：2025-07-20
  • 出版时间：2025-03-20
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  • 收稿日期：2024-02-03
  • 修回日期：2024-04-22
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    1 南京理工大学，南京 210094
    2 南京依维柯汽车有限公司，南京 210037
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2种不同金属材料的力学参数
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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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