Article(id=1322907594486067262, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322907425740825534, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1725206400000, receivedDateStr=2024-09-02, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793335348960, onlineDateStr=2026-10-30, pubDate=1750780800000, pubDateStr=2025-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793335348960, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793335348960, creator=13701087609, updateTime=1793335348960, updator=13701087609, issue=Issue{id=1322907425740825534, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='6', pageStart='1', pageEnd='300', issueExtLink='null', onlineDate='null', pubDate='1750780800000', pubDateStr='2025-06-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793335308726, creator='13701087609', updateTime=1793335308726, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=229, endPage=236, ext={EN=ArticleExt(id=1322907594658033727, articleId=1322907594486067262, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Grinding Performance of Vertical Spiral Stirred Mill Based on DEM-CFD Coupling, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to explore the influence mechanism of structural parameters of vertical spiral stirred mill on grinding performance, the coupling method of discrete element method (DEM) and computational fluid dynamics (CFD) was used to systematically analyze the effects of mill bottom gap, side gap and helical lift angle on grinding performance. Firstly, the numerical model of the vertical spiral stirred mill was constructed, and the dynamic characteristics of the medium in the grinding process were revealed by simulation. Secondly, the grinding test was carried out based on the test bench, and the accuracy of the simulation model was verified by the driving torque of the spiral agitator. The results show that the maximum error is only 3.85%. Finally, through multi-parameter simulation and orthogonal test, the influence degree of each structural parameter on grinding performance was quantified, and a comprehensive evaluation method based on energy utilization rate, torque, average normal force and tangential force was proposed. The results show that the side gap of the mill has the most significant effect on the grinding performance, followed by the bottom gap and the helical lift angle. The optimal parameter combination is the ratio of the bottom gap to the medium sphere diameter A=4.0, the ratio of the side gap to the sphere diameter B=3.0 and the helical lift angle C=0.61. The research can provide a reference for the structural optimization and performance improvement of vertical spiral stirred mill.

, authors=Defang ZOU1, Zihan HE1, Wenda YU1, Di QU2, Shebin LU2, authorsList=Defang ZOU, Zihan HE, Wenda YU, Di QU, Shebin LU, authorCompany=null, correspAuthors=null, 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, fund=null), CN=ArticleExt(id=1322907601901596802, articleId=1322907594486067262, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于DEM-CFD耦合的立式螺旋搅拌磨粉磨性能研究, columnId=1226462295946085268, journalTitle=矿业研究与开发, columnName=矿山机电与矿业智能化, runingTitle=null, highlight=null, articleAbstract=

为探究立式螺旋搅拌磨机结构参数对粉磨性能的影响机制,采用离散元(DEM)与计算流体动力学(CFD)耦合方法,系统分析了磨机底隙、侧隙及搅拌器螺旋升角对粉磨性能的作用规律。首先,构建了立式螺旋搅拌磨机的数值模型,通过仿真揭示了粉磨过程中介质的动力学特性;其次,基于试验台开展了粉磨试验,以螺旋搅拌器驱动转矩为指标验证了仿真模型的准确性,结果显示最大误差仅为3.85%;最后,通过多参数仿真与正交试验,量化了各结构参数对粉磨性能的影响程度,并提出了以能量利用率、转矩、平均法向力和切向力为指标的综合评价方法。研究表明,磨机侧隙对粉磨性能的影响最为显著,其次是底隙和螺旋升角;最优参数组合为底隙与介质球径之比A=4.0、侧隙与球径之比B=3.0、螺旋升角C=0.61。研究可为立式螺旋搅拌磨机的结构优化与性能提升提供参考。

, authors=邹德芳1, 贺子涵1, 于文达1, 曲迪2, 路社斌2, authorsList=邹德芳, 贺子涵, 于文达, 曲迪, 路社斌, authorCompany=null, correspAuthors=null, authorNote=

邹德芳(1978—),女,黑龙江绥化人,硕士,正高级实验师,主要研究方向为矿山机械数字化技术。E-mail:

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邹德芳(1978—),女,黑龙江绥化人,硕士,正高级实验师,主要研究方向为矿山机械数字化技术。E-mail:

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邹德芳(1978—),女,黑龙江绥化人,硕士,正高级实验师,主要研究方向为矿山机械数字化技术。E-mail:

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Analysis on the factors affecting the grinding efficiency of wet ball mill by orthogonal experiment method [J]. Mining Research and Development, 2020, 40(5):149-153., articleTitle=Analysis on the factors affecting the grinding efficiency of wet ball mill by orthogonal experiment method, refAbstract=null)], funds=[Fund(id=1322907608314687694, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, awardId=JYTMS20231604, language=CN, fundingSource=辽宁省教育厅高校基本科研项目面上项目(JYTMS20231604), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1322907602191003779, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, xref=1., ext=[AuthorCompanyExt(id=1322907602195198084, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, companyId=1322907602191003779, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang, Liaoning 110168, China), 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Structural parameters of the model

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筒体内径/mm筒体外径/mm筒体高度/mm搅拌器外径/mm导程/mm底隙/mm螺旋个数螺旋圈数
2502705501801206023
), ArticleFig(id=1322907606913790149, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=CN, label=表1, caption=

模型结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
筒体内径/mm筒体外径/mm筒体高度/mm搅拌器外径/mm导程/mm底隙/mm螺旋个数螺旋圈数
2502705501801206023
), ArticleFig(id=1322907606989287622, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=EN, label=Table 2, caption=

Simulation parameters setting[14]

, figureFileSmall=null, figureFileBig=null, tableContent=
介质泊松比介质球密度/(kg/m3)恢复系数滚动摩擦因数
0.327 8500.80.5
静摩擦因数筒体密度/(kg/m3)仿真时长/s搅拌器转速/(r/min)
0.257 850580
), ArticleFig(id=1322907607081562311, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=CN, label=表2, caption=

仿真参数设置[14]

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介质泊松比介质球密度/(kg/m3)恢复系数滚动摩擦因数
0.327 8500.80.5
静摩擦因数筒体密度/(kg/m3)仿真时长/s搅拌器转速/(r/min)
0.257 850580
), ArticleFig(id=1322907607157059784, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=EN, label=Table 3, caption=

Test factors and levels

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水平因素
A(LD/DR)B(LC/DR)C螺旋升角(S′/D)
13.02.00.56
24.02.50.61
35.03.00.67
46.03.50.72
), ArticleFig(id=1322907607261917385, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=CN, label=表3, caption=

试验因素及水平

, figureFileSmall=null, figureFileBig=null, tableContent=
水平因素
A(LD/DR)B(LC/DR)C螺旋升角(S′/D)
13.02.00.56
24.02.50.61
35.03.00.67
46.03.50.72
), ArticleFig(id=1322907607337414858, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=EN, label=Table 4, caption=

Simulation test programmes and results

, figureFileSmall=null, figureFileBig=null, tableContent=
编号AB螺旋升角C Qi
13.02.00.561.2360.7011.1941.0261.038
23.02.50.610.9700.9700.9460.9830.965
33.03.00.670.9170.8050.9620.9940.902
43.03.50.720.7530.8660.9130.9730.844
54.02.00.610.9691.1921.0131.1001.062
64.02.50.560.6561.4010.9831.1100.997
74.03.00.721.2421.0301.1781.0361.138
84.03.50.670.8631.5041.0761.1321.128
95.02.00.670.9091.0230.9751.0260.971
105.02.50.721.2010.6510.8910.8670.939
115.03.00.561.3690.7271.1290.9831.083
125.03.50.611.0060.7330.8340.8570.876
136.02.00.720.9241.3041.0121.0471.069
146.02.50.670.9700.9660.8850.9310.950
156.03.00.611.2441.0451.0820.9831.121
166.03.50.560.7711.1070.8890.9620.918
), ArticleFig(id=1322907607538741451, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=CN, label=表4, caption=

仿真试验方案及结果

, figureFileSmall=null, figureFileBig=null, tableContent=
编号AB螺旋升角C Qi
13.02.00.561.2360.7011.1941.0261.038
23.02.50.610.9700.9700.9460.9830.965
33.03.00.670.9170.8050.9620.9940.902
43.03.50.720.7530.8660.9130.9730.844
54.02.00.610.9691.1921.0131.1001.062
64.02.50.560.6561.4010.9831.1100.997
74.03.00.721.2421.0301.1781.0361.138
84.03.50.670.8631.5041.0761.1321.128
95.02.00.670.9091.0230.9751.0260.971
105.02.50.721.2010.6510.8910.8670.939
115.03.00.561.3690.7271.1290.9831.083
125.03.50.611.0060.7330.8340.8570.876
136.02.00.720.9241.3041.0121.0471.069
146.02.50.670.9700.9660.8850.9310.950
156.03.00.611.2441.0451.0820.9831.121
166.03.50.560.7711.1070.8890.9620.918
), ArticleFig(id=1322907607870091468, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=EN, label=Table 5, caption=

Analysis results of influence degrees

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因素
ABC
0.9371.0351.009
1.0810.9631.012
0.9671.1010.988
1.0150.9420.992
), ArticleFig(id=1322907608004309197, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907594486067262, language=CN, label=表5, caption=

影响程度结果分析

, figureFileSmall=null, figureFileBig=null, tableContent=
因素
ABC
0.9371.0351.009
1.0810.9631.012
0.9671.1010.988
1.0150.9420.992
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基于DEM-CFD耦合的立式螺旋搅拌磨粉磨性能研究
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邹德芳 1 , 贺子涵 1 , 于文达 1 , 曲迪 2 , 路社斌 2
矿业研究与开发 | 矿山机电与矿业智能化 2025,45(6): 229-236
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矿业研究与开发 |矿山机电与矿业智能化 2025 , 45 (6) : 229 -236
基于DEM-CFD耦合的立式螺旋搅拌磨粉磨性能研究
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邹德芳1 , 贺子涵1, 于文达1, 曲迪2, 路社斌2
作者信息
  • 1.沈阳建筑大学 机械工程学院,辽宁 沈阳 110168
  • 2.北方重工富勒(沈阳)矿业有限公司,辽宁 沈阳 110027
作者简介:

邹德芳(1978—),女,黑龙江绥化人,硕士,正高级实验师,主要研究方向为矿山机械数字化技术。E-mail:

Grinding Performance of Vertical Spiral Stirred Mill Based on DEM-CFD Coupling
Defang ZOU1 , Zihan HE1, Wenda YU1, Di QU2, Shebin LU2
Affiliations
  • 1.School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang, Liaoning 110168, China
  • 2.Northern Heavy Industry Fuller (Shenyang) Mining Co., Ltd., Shenyang, Liaoning 110027, China
出版时间: 2025-06-25
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为探究立式螺旋搅拌磨机结构参数对粉磨性能的影响机制,采用离散元(DEM)与计算流体动力学(CFD)耦合方法,系统分析了磨机底隙、侧隙及搅拌器螺旋升角对粉磨性能的作用规律。首先,构建了立式螺旋搅拌磨机的数值模型,通过仿真揭示了粉磨过程中介质的动力学特性;其次,基于试验台开展了粉磨试验,以螺旋搅拌器驱动转矩为指标验证了仿真模型的准确性,结果显示最大误差仅为3.85%;最后,通过多参数仿真与正交试验,量化了各结构参数对粉磨性能的影响程度,并提出了以能量利用率、转矩、平均法向力和切向力为指标的综合评价方法。研究表明,磨机侧隙对粉磨性能的影响最为显著,其次是底隙和螺旋升角;最优参数组合为底隙与介质球径之比A=4.0、侧隙与球径之比B=3.0、螺旋升角C=0.61。研究可为立式螺旋搅拌磨机的结构优化与性能提升提供参考。

立式螺旋搅拌磨机  /  结构参数  /  粉磨性能  /  DEM-CFD耦合  /  正交试验

In order to explore the influence mechanism of structural parameters of vertical spiral stirred mill on grinding performance, the coupling method of discrete element method (DEM) and computational fluid dynamics (CFD) was used to systematically analyze the effects of mill bottom gap, side gap and helical lift angle on grinding performance. Firstly, the numerical model of the vertical spiral stirred mill was constructed, and the dynamic characteristics of the medium in the grinding process were revealed by simulation. Secondly, the grinding test was carried out based on the test bench, and the accuracy of the simulation model was verified by the driving torque of the spiral agitator. The results show that the maximum error is only 3.85%. Finally, through multi-parameter simulation and orthogonal test, the influence degree of each structural parameter on grinding performance was quantified, and a comprehensive evaluation method based on energy utilization rate, torque, average normal force and tangential force was proposed. The results show that the side gap of the mill has the most significant effect on the grinding performance, followed by the bottom gap and the helical lift angle. The optimal parameter combination is the ratio of the bottom gap to the medium sphere diameter A=4.0, the ratio of the side gap to the sphere diameter B=3.0 and the helical lift angle C=0.61. The research can provide a reference for the structural optimization and performance improvement of vertical spiral stirred mill.

Vertical spiral stirred mill  /  Structural parameter  /  Grinding performance  /  DEM-CFD coupling  /  Orthogonal test
邹德芳, 贺子涵, 于文达, 曲迪, 路社斌. 基于DEM-CFD耦合的立式螺旋搅拌磨粉磨性能研究. 矿业研究与开发, 2025 , 45 (6) : 229 -236 .
Defang ZOU, Zihan HE, Wenda YU, Di QU, Shebin LU. Grinding Performance of Vertical Spiral Stirred Mill Based on DEM-CFD Coupling[J]. Mining Research and Development, 2025 , 45 (6) : 229 -236 .
立式螺旋搅拌磨机是一种节能环保、生产效率高的粉磨设备[1],磨矿介质一般为钢球或陶瓷球[2]。与球磨机相比,立式螺旋搅拌磨机细磨能力更强,正逐渐替代球磨机进行细磨、再磨以及超细磨作业。因此,基于螺旋粉磨机理提升粉磨性能成为国内外学者的主要研究方向[3]。
离散单元法(DEM)是用于分析磨机粉磨机理的常用方法之一。王珊[4]基于DEM法系统分析了搅拌盘结构对搅拌磨机粉磨效率的影响;刘长远[5]通过DEM法探究了不同结构和工艺参数对磨机粉磨性能的影响;RHYMER等[6]采用离散元法研究了研磨介质颗粒的恢复系统和滑动摩擦因数对粉磨性能的影响;OLIVEIRA等[7]利用离散元法模拟了立式螺旋搅拌磨机中的破碎过程,并实现了驱动功率的准确预测;HOU[8]利用离散元法研究了磨机的操作参数对粉磨性能的影响规律。尽管上述文献从固相研磨介质的动力学特性角度探讨了影响磨机性能的因素,但均未考虑粉磨过程中矿浆流动对磨机粉磨性能的影响,这种单一固相的研究视角使结论存在一定的局限性。
随着数值模拟技术的不断发展,DEM-CFD耦合法因其能够有效模拟固液两相介质的相互作用,已成为探索磨机的粉磨机理的重要手段[9]。如刘正彬[10]通过建立立式螺旋搅拌磨机的耦合动力学模型与DEM-CFD耦合模型,系统分析了磨机的力学特性,并在此基础上构建了异步电机的数学模型;高旭东[11]利用立式螺旋搅拌磨机的DEM-CFD耦合模型,分析了搅拌器转速等关键参数对粉磨性能的影响机制。尽管国内外学者已对立式螺旋搅拌磨机的粉磨机理开展了大量研究,但现有研究在搅拌轴螺旋叶片螺旋升角、叶片外缘到筒体内壁的间隙(侧隙)、叶片底部到筒体底部的间隙(底隙)等结构参数对粉磨性能的综合影响仍显不足。
本研究采用基于DEM-CFD耦合法,系统模拟了立式螺旋搅拌磨机的工作过程,并结合试验台的数据验证了仿真模型的准确性;在此基础上通过多参数仿真分析,探究了不同结构参数对粉磨性能的影响规律,并提出了一种综合评价粉磨性能指标,采用多元变量相关性分析,评估了磨机底隙、侧隙、螺旋叶片螺旋升角等关键参数对粉磨性能的影响程度。研究成果以期为立式螺旋搅拌磨机的设计与结构优化提供参考。
立式螺旋搅拌磨机主要由螺旋搅拌器、驱动装置、筒体、介质及回收装置等组成。为了简化计算,本研究对磨机进行简化处理[12-13]。简化后的模型只包括搅拌器和筒体,其结构参数与试验台一致,简化模型如图1所示,具体结构参数见表1。
在利用网格处理软件对模型进行网格划分后,将其导入仿真软件,利用耦合插件,将模型的流场信息与颗粒信息进行传递,搭建DEM-CFD耦合模型,其耦合流程如图2 所示。
本研究中选用的筒体和介质球材质均为碳钢,介质填充率为60%,介质球尺寸为10 mm,其他材料参数设置见表2。
为了验证仿真参数设置及结果的准确性,采用试验台进行粉磨试验。分别选取转速为40 r/min、60 r/min、80 r/min进行3组试验与仿真,得到不同转速下的螺旋搅拌器转矩随时间变化曲线,并计算了试验和仿真结果之间的误差,结果如图3所示。
通过对比图3可知,3种转速下仿真结果预测的最大误差为转速80 r/min条件下的3.85%。由此可知,本文建立的立式螺旋搅拌磨机DEM-CFD耦合模型能够准确描述介质和矿浆多相流运动规律。为接下来讨论结构参数与粉磨性能的映射关系提供方法。
在立式螺旋搅拌磨机的作业过程中,磨机侧隙、底隙和搅拌器螺旋升角的设计直接影响到物料在磨机中的运动状态。合理的结构设计可以改善粉磨性能,降低能耗和设备磨损,提高生产效率。
设置30 mm、40 mm、50 mm、60 mm四种底隙变量,分析底隙对立式螺旋搅拌磨机粉磨性能的影响,为方便表示,将磨机底隙的大小LD改写为与介质球径倍数关系,即底隙与介质球径之比A=LD/DR,其中DR为介质球球径。
图4为磨机搅拌器转矩随底隙变化曲线。因为介质球球径不变,从图4中可以看出,转矩随底隙的增加而减小。这是由于随着底隙的增加,大量介质球被留在底隙的空间内,从而参与磨料循环的介质球数量减少,搅拌器所受负载减少,进而转矩减小。底隙过小将导致介质球卡顿,增加了摩擦力,当搅拌器旋转时,摩擦力使得搅拌器需要更大的力才能旋转,这就增加了搅拌器的转矩。
在立式螺旋搅拌磨机工作时,物料的粉磨主要依靠搅拌器旋转带动介质球运动碰撞获得能量,但实际工作中能量在传递过程中有损耗[15]。真正有效传递给介质球的能量,可以通过介质球的总碰撞能与搅拌器提供能量之比来评估,即能量利用率。能量利用率越高,表明转化给介质球的有用功越多[16],介质球在运动过程中获得的动能就越大,用于粉磨物料的能量也就越多,从而提升粉磨性能。
磨机能量转化率可以通过式(1)求得:
式中:P为搅拌器的功率,W;T为搅拌器所受的扭矩,N·m;n为搅拌器的转速,r/min。
能量利用率ψ可由式(2)得出:
式中:EZ为单位时间内介质球总碰撞能,J;t为单位时间,取1 s。
图5为介质球碰撞能和能量利用率随底隙变化的曲线。从图5中可以看出,随着磨机底隙的增加,介质球的碰撞能逐渐减小,能量利用率先增大后减小,在底隙与介质球径之比A=4.0时达到最大。
在立式螺旋搅拌磨机进行粉磨作业时,当粉磨的物料颗粒之间的平均法向力达到最小抗压力时,物料颗粒可以实现有效粉磨。同时,物料之间的平均切向力大于受到的最小剪切力时,也会实现有效粉磨[17]。
根据岩石破碎理论,计算物料的最小抗压力值Fn和最小剪切力Fτ:
式中:σn为矿料的抗压强度,Pa;S为矿料的受力面积,m2。
图6为介质平均切向力和平均法向力随底隙变化的曲线。由图6可知,在A由3.0增加到6.0的过程中,介质球的平均法向力和平均切向力均不断减小。当底隙减小时,介质球与磨机底部的接触增加,介质球受到的压力变大,介质球间的压力传递增强。根据岩石破碎理论,较大的法向力和切向力可以增加物料之间的碰撞频率和强度,有助于提高破碎效率。但过大的法向力和切向力可能导致介质球和设备磨损加剧[18]。因此,在实际应用中,需要根据具体情况来调整和控制平均法向力和平均切向力,以达到最佳的粉磨性能和设备运行状态。
图7为磨机搅拌器转矩随侧隙变化曲线,图8为介质球碰撞能和能量利用率随侧隙变化曲线。为方便表示,将磨机侧隙的大小LC同样改写为与介质球径倍数关系,即侧隙与介质球径之比B=LC/DR,其中DR为介质球球径。
从图7可以看出,随着侧隙的增加,搅拌器所受转矩逐渐减小。这是因为当侧隙减小时,介质球在搅拌器和磨机筒壁之间的空间变得狭窄,介质球的分布更加密集,与搅拌器之间的接触面积变大,搅拌器在旋转过程中要克服更大的阻力。
从图8可以看出,介质球的总碰撞能随着磨机侧隙的增加而减小,这是因为磨机侧隙越小,介质球分布变得更密集,它们之间以及搅拌器和磨机内壁之间的碰撞频率增加,总碰撞能增大。随着侧隙的增加,能量利用率先增大后减小,在侧隙与介质球径之比B为3.0时达到最大。
介质球所受的平均法向力和平均切向力随侧隙变化曲线如图9所示。随着侧隙的增加,搅拌器所能带动的介质球数量减少,这使介质球之间的碰撞强度降低。介质球之间的有效接触面积减小,相对滑动和剪切作用也随之减小,从而介质球所受的平均法向力和平均切向力逐渐变小。
图10为搅拌器转矩随搅拌器螺旋升角变化的曲线。为方便表示,用C=S′/D来表示不同搅拌器螺旋升角,S′为搅拌器导程,D为搅拌器直径。从图10可以看出,随着搅拌器螺旋升角的增加,搅拌器所受转矩先增加后减小。图11为介质球总碰撞能和能量利用率随螺旋升角变化曲线。从图11可以看出,介质球的总碰撞能及其能量利用率随着螺旋升角增加逐渐增大,在螺旋升角C为0.67时最大。介质球所受的平均法向力和平均切向力随搅拌器螺旋升角变化趋势如图12所示。由图12可知,介质球所受的平均法向力和平均切向力的大小随着搅拌器螺旋升角的增加而增大。
随着搅拌器螺旋升角的增加,介质球在底部堆积,增加了局部压力和摩擦,转矩随之增加;处在同一空间的介质球数量增多,碰撞频率增加,从而使总碰撞能增加;介质球受到水平方向的阻力也逐渐增大,从而使所受平均法向力和平均切向力增大。
为了研究磨机底隙、侧隙和搅拌器螺旋升角对立式螺旋搅拌磨机粉磨性能的综合影响,对这3个因素进行正交试验,每个因素选取4个水平,具体数值见表3。试验为三因素四水平试验,选择L16(43)的正交表。
为了综合评价立式螺旋搅拌磨机的粉磨性能,选择能量利用率x1、转矩x2、平均法向力x3、平均切向力x4等多个参考指标开展仿真和计算。设定权重系数分别为0.4, 0.3, 0.15, 0.15,详细的理论依据参考文献[16]。对于参考指标的计算,由式(5)、式(6)和式(7)所得。
效率指标平均值为:
则试验效率指标值为:
式中:n=1, 2,3, 4;i=1, 2,⋯,16。
则粉磨性能综合指标Qi为:
通过仿真及计算,试验方案及结果见表4。
为减少计算量,采用直观分析法对各因素影响程度进行分析[19]。对因素A分析如下,其中表示平均影响程度。
因为,所以因素A的最优水平是A2。
同理可对因素B、C进行影响程度分析,结果见表5。
由表5可知,因为,所以因素B的最优水平是B3。
对于因素C有:,所以因素C的最优水平是C2。
选用每个因素影响程度的最大和最小值计算综合平均值的极差R以区分因素的重要程度:
极差的大小反映了各因素对试验指标的影响程度,极差越大,影响程度越大。因此对于本次试验来说,3个因素影响程度B>A>C,即侧隙>底隙>螺旋升角。
通过上述计算分析可知最优水平组合为A2B3C2。在设计的16组试验中,由表4可知,第7组的粉磨性能指标最佳,其对应的因素组合为A2B3C4。由于因素A、B的影响程度远大于因素C,因此确定最优组合方案为A2B3C2,即底隙与介质球径之比A=4.0、侧隙与球径之比B=3.0、螺旋升角C=0.61。
本文建立了立式螺旋搅拌磨机DEM-CFD耦合模型,对磨机的粉磨过程进行了仿真分析与试验验证,得出以下结论。
(1)随着立式螺旋搅拌磨机的侧隙、底隙增加,磨机搅拌器转矩、介质球所受的平均法向力和切向力逐渐减小,粉磨性能逐渐降低;介质球能量利用率先增大后减小,在底隙与介质球径之比A=4.0时,侧隙与介质球径之比B=3.0时均能达到最大。
(2)随着立式螺旋搅拌磨机搅拌器的螺旋升角增加,磨机搅拌器转矩和介质球能量利用率先增加再减小。在螺旋升角C为0.67时最大,物料粉磨性能最好。
(3)结合能量利用率、搅拌器转矩、平均法向力和平均切向力,提出一种粉磨性能综合评价方法。采用正交试验,分析了磨机侧隙、底隙和搅拌器螺旋升角的综合影响,影响度排序为磨机侧隙>底隙>搅拌器螺旋升角。最优参数组合为底隙与介质球径之比A=4.0,侧隙与介质球径之比B=3.0,螺旋升角C=0.61。本文的研究方法为立式螺旋搅拌磨机的结构优化与性能提升提供了参考。
  • 辽宁省教育厅高校基本科研项目面上项目(JYTMS20231604)
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2025年第45卷第6期
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  • 接收时间:2024-09-02
  • 首发时间:2026-10-30
  • 出版时间:2025-06-25
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  • 收稿日期:2024-09-02
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辽宁省教育厅高校基本科研项目面上项目(JYTMS20231604)
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    1.沈阳建筑大学 机械工程学院,辽宁 沈阳 110168
    2.北方重工富勒(沈阳)矿业有限公司,辽宁 沈阳 110027
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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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