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Article(id=1263881613939753109, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, articleNumber=null, orderNo=null, doi=10.16578/j.issn.1004.2539.2026.01.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1732464000000, receivedDateStr=2024-11-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1779262458547, onlineDateStr=2026-05-20, pubDate=1768406400000, pubDateStr=2026-01-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1779262458547, onlineIssueDateStr=2026-05-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1779262458547, creator=13041195026, updateTime=1779262458547, updator=13041195026, issue=Issue{id=1263881604263437054, tenantId=1146029695717560320, journalId=1263187878914834467, year='2026', volume='50', issue='1', pageStart='1', pageEnd='191', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1779262456241, creator=13041195026, updateTime=1779263107607, updator=13041195026, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1263884336399528882, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1263884336403723187, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=32, endPage=39, ext={EN=ArticleExt(id=1263881617840455835, articleId=1263881613939753109, tenantId=1146029695717560320, journalId=1263187878914834467, language=EN, title=Research on brake pedal feeling simulator based on magnetorheological dampers, columnId=1263881611804795649, journalTitle=Journal of Mechanical Transmission, columnName=Special Topic of Magnetic Transmission, runingTitle=null, highlight=null, articleAbstract=
Objective

To solve the problem of no direct mechanical or hydraulic connection between the brake actuator and the brake pedal in an electronic mechanical braking system, leading to no feedback of road feel, a brake pedal feeling simulator was proposed based on magnetorheological dampers.

Methods

Ansys/Maxwell and Matlab/Simulink were used as the platform. The structural design of the sinking brake pedal feeling simulator, the structural design of magnetorheological damper, magnetic circuit analysis and electromagnetic simulation were carried out respectively, and the simulation analysis of traditional proportional-integral-derivative (PID) and fuzzy adaptive PID control under different working conditions of the whole system was compared.

Results

The simulation results show that the brake pedal feeling simulator can track the characteristic curve of the traditional pedal well under different working conditions and has wide applicability. Compared with the traditional PID control effect, the fuzzy adaptive PID control has higher control precision and smaller control error, and has good application prospects.

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目的

针对电动汽车用磁流变液制动器结构参数优化需求，明确关键结构参数对制动性能的影响规律，获取最优参数组合，为其设计与工程应用提供支撑。

方法

首先，基于制动性能影响因素分析，选取制动间隙宽度h、制动盘数量n、制动盘外圆半径R2这3个关键因素；其次，以黏性制动力矩、常规制动力矩、最大制动力矩为评估指标，设计L₁₆（4³）正交试验；然后，通过Matlab/Simulink软件开展数值仿真与极差分析；最后，制作样机并完成试验验证。

结果

试验结果表明，零场下黏性制动力矩主要受制动间隙宽度影响，施磁后制动盘数量为首要影响因素，制动盘外圆半径次之；最优参数组合（h=1.5 mm、n=4、R₂=75 mm）下，常规制动力矩约为黏性制动力矩的68倍；输入电流为2.1 A时，最大输出制动力矩达240.3 N·m，通过调节磁场强度可实现制动力矩的无级调控。

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王道明（通信作者），男，1987年生，江苏盐城人，博士，教授；主要研究方向为车辆线控制动技术、智能结构与系统；。
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杨广鑫，男，1997年生，安徽合肥人，博士研究生；主要研究方向为磁流变液传动技术；。

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杨广鑫，男，1997年生，安徽合肥人，博士研究生；主要研究方向为磁流变液传动技术；。

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杨广鑫，男，1997年生，安徽合肥人，博士研究生；主要研究方向为磁流变液传动技术；。

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Journal of Mechanical Transmission，2022，46（8）：172-176., articleTitle=Optimization study of gear oil-air lubrication parameters based on orthogonal test method, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1263881636429611251, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881613939753109, xref=null, ext=[AuthorCompanyExt(id=1263881636668686581, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881613939753109, companyId=1263881636429611251, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Mechanical Engineering, Hefei University of Technology, Hefei230009, China), AuthorCompanyExt(id=1263881637004230904, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881613939753109, companyId=1263881636429611251, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=合肥工业大学 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ArticleFig(id=1263881679966487105, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881613939753109, language=EN, label=Tab. 1, caption=

Main parameters of an A00-class vehicle

, figureFileSmall=null, figureFileBig=null, tableContent=
车身参数值
车辆满载总质量Ga/kg1 150
轴距L/m2.34
重心至前轴距离l/m1.15
满载时重心高度hg/m0.55
轮胎滚动半径rm/m0.24
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A00级微型车主要参数

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车身参数值
车辆满载总质量Ga/kg1 150
轴距L/m2.34
重心至前轴距离l/m1.15
满载时重心高度hg/m0.55
轮胎滚动半径rm/m0.24
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Main performance parameters of the magnetorheological fluid

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性能参数值
密度/（g/mL）3.09
使用温度/℃-40~180
闪点/℃250
剪切屈服应力/kPa55（1.0 T）
表观黏度/（mPa·s）240（30 ℃）
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磁流变液主要性能参数

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性能参数值
密度/（g/mL）3.09
使用温度/℃-40~180
闪点/℃250
剪切屈服应力/kPa55（1.0 T）
表观黏度/（mPa·s）240（30 ℃）
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Factors and levels

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水平编号因素
h/mmnR2/mm
10.5170
21.0275
31.5380
42.0485
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因素水平

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水平编号因素
h/mmnR2/mm
10.5170
21.0275
31.5380
42.0485
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Orthogonal test schemes and simulation results

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试验

序号

因素水平计算结果（评估指标）
h/mmnR2/mmMη/（N·m）Mn/（N·m）Mmax/（N·m）
10.51702.00349.35265.03
20.52755.386125.634165.45
30.538010.609234.771308.995
40.548518.214383.258504.131
51.01751.34761.47181.379
61.02803.537152.978202.461
71.03856.830280.613371.268
81.04704.006193.403256.115
91.51801.17975.900100.641
101.52853.036185.558245.995
111.53702.003144.05191.085
121.54753.591244.087323.719
132.01851.13892.399122.617
142.02701.00195.699127.056
152.03752.020182.392242.116
162.04803.536302.419401.385
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正交试验方案与仿真结果

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试验

序号

因素水平计算结果（评估指标）
h/mmnR2/mmMη/（N·m）Mn/（N·m）Mmax/（N·m）
10.51702.00349.35265.03
20.52755.386125.634165.45
30.538010.609234.771308.995
40.548518.214383.258504.131
51.01751.34761.47181.379
61.02803.537152.978202.461
71.03856.830280.613371.268
81.04704.006193.403256.115
91.51801.17975.900100.641
101.52853.036185.558245.995
111.53702.003144.05191.085
121.54753.591244.087323.719
132.01851.13892.399122.617
142.02701.00195.699127.056
152.03752.020182.392242.116
162.04803.536302.419401.385
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Statistical analysis of average values

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平均值影响因素
hnR2
K1K1（Mη）9.0531.4172.253
K1（Mn）198.25469.781120.626
K1（Mmax）260.90292.417159.822
K2K2（Mη）3.9303.2403.086
K2（Mn）172.116139.967153.396
K2（Mmax）227.806185.241203.166
K3K3（Mη）2.4245.3664.715
K3（Mn）162.399210.457191.517
K3（Mmax）215.360278.366253.371
K4K4（Mη）1.9247.3377.305
K4（Mn）168.227280.792235.457
K4（Mmax）223.294371.338311.003
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平均值分析

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平均值影响因素
hnR2
K1K1（Mη）9.0531.4172.253
K1（Mn）198.25469.781120.626
K1（Mmax）260.90292.417159.822
K2K2（Mη）3.9303.2403.086
K2（Mn）172.116139.967153.396
K2（Mmax）227.806185.241203.166
K3K3（Mη）2.4245.3664.715
K3（Mn）162.399210.457191.517
K3（Mmax）215.360278.366253.371
K4K4（Mη）1.9247.3377.305
K4（Mn）168.227280.792235.457
K4（Mmax）223.294371.338311.003
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Analysis of the range R

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影响因素参数
R（Mη）R（Mn）R（Mmax）
h7.12935.85545.542
n5.920211.011278.921
R25.052114.831151.181
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极差R分析

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影响因素参数
R（Mη）R（Mn）R（Mmax）
h7.12935.85545.542
n5.920211.011278.921
R25.052114.831151.181
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Maximum output braking torque of the MRB

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序号线圈电流I/AMmax/（N·m）
10.346.5
20.9132.1
31.5206.7
42.1240.3
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磁流变液制动器的最大输出制动力矩

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序号线圈电流I/AMmax/（N·m）
10.346.5
20.9132.1
31.5206.7
42.1240.3
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基于正交试验法的磁流变液制动器设计和分析
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杨广鑫 , 王飞 , 周龙 , 王道明
机械传动 | 磁传动专题 2026,50(1): 32-39
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机械传动 | 磁传动专题 2026, 50(1): 32-39
基于正交试验法的磁流变液制动器设计和分析
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杨广鑫 , 王飞, 周龙, 王道明
作者信息
  • 合肥工业大学 机械工程学院，合肥230009

    • 杨广鑫，男，1997年生，安徽合肥人，博士研究生；主要研究方向为磁流变液传动技术；。

通讯作者:

王道明（通信作者），男，1987年生，江苏盐城人，博士，教授；主要研究方向为车辆线控制动技术、智能结构与系统；。
Research on brake pedal feeling simulator based on magnetorheological dampers
Yi ZHU , Hui SONG, Qi CHEN, Liangjian WANG
Affiliations
  • School of Mechanical Engineering, Hefei University of Technology, Hefei230009, China
出版时间: 2026-01-15 doi: 10.16578/j.issn.1004.2539.2026.01.005
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摘要
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目的

针对电动汽车用磁流变液制动器结构参数优化需求，明确关键结构参数对制动性能的影响规律，获取最优参数组合，为其设计与工程应用提供支撑。

方法

首先，基于制动性能影响因素分析，选取制动间隙宽度h、制动盘数量n、制动盘外圆半径R2这3个关键因素；其次，以黏性制动力矩、常规制动力矩、最大制动力矩为评估指标，设计L₁₆（4³）正交试验；然后，通过Matlab/Simulink软件开展数值仿真与极差分析；最后，制作样机并完成试验验证。

结果

试验结果表明，零场下黏性制动力矩主要受制动间隙宽度影响，施磁后制动盘数量为首要影响因素，制动盘外圆半径次之；最优参数组合（h=1.5 mm、n=4、R₂=75 mm）下，常规制动力矩约为黏性制动力矩的68倍；输入电流为2.1 A时，最大输出制动力矩达240.3 N·m，通过调节磁场强度可实现制动力矩的无级调控。

磁流变液  /  制动器  /  制动性能  /  正交试验  /  数值模拟
Objective

To solve the problem of no direct mechanical or hydraulic connection between the brake actuator and the brake pedal in an electronic mechanical braking system, leading to no feedback of road feel, a brake pedal feeling simulator was proposed based on magnetorheological dampers.

Methods

Ansys/Maxwell and Matlab/Simulink were used as the platform. The structural design of the sinking brake pedal feeling simulator, the structural design of magnetorheological damper, magnetic circuit analysis and electromagnetic simulation were carried out respectively, and the simulation analysis of traditional proportional-integral-derivative (PID) and fuzzy adaptive PID control under different working conditions of the whole system was compared.

Results

The simulation results show that the brake pedal feeling simulator can track the characteristic curve of the traditional pedal well under different working conditions and has wide applicability. Compared with the traditional PID control effect, the fuzzy adaptive PID control has higher control precision and smaller control error, and has good application prospects.

Brake-by-wire  /  Magnetorheological damper  /  Fuzzy adaptive PID  /  Pedal feeling simulator
杨广鑫, 王飞, 周龙, 王道明. 基于正交试验法的磁流变液制动器设计和分析. 机械传动, 2026 , 50 (1) : 32 -39 . DOI: 10.16578/j.issn.1004.2539.2026.01.005
Yi ZHU, Hui SONG, Qi CHEN, Liangjian WANG. Research on brake pedal feeling simulator based on magnetorheological dampers[J]. Journal of Mechanical Transmission, 2026 , 50 (1) : 32 -39 . DOI: 10.16578/j.issn.1004.2539.2026.01.005
正文
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0　引言
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制动系统是车辆不可或缺的组成部分，其性能直接影响车辆的行驶安全。目前，液压制动系统应用广泛，但其机械摩擦式的结构易产生零部件磨损、发热严重、制动效率较低、制动稳定性较差等问题[1]。磁流变液制动器是一种新型非接触式制动器，通过磁流变液在磁场作用下产生阻碍制动盘运动的制动力矩，并且可以通过改变磁场强度来调节制动力矩大小。
随着电动汽车的不断发展，智能电动汽车要求制动系统能够实现主动制动等功能[2]。磁流变液制动器具有响应迅速、控制简单和能耗低等优势，并且磁流变液制动器能够与电动汽车中的电子控制系统协同工作，适用于线控制动系统[3-4]。磁流变液制动器有潜力成为新型可靠的制动执行器，在车辆制动领域具有广泛的应用前景，也为未来智能电动汽车的制动执行器提供了一种选择方案。磁流变液制动器的制动性能、外形尺寸及质量都是需要关注的重点。
磁流变液制动器所展现出的优异性能吸引了国内外众多专家学者的关注。WANG等[5]研制了一种水冷散热的大转矩挤压式磁流变液制动器，通过试验研究了温度对大转矩磁流变液制动器传动特性的影响，结果表明，高温会使磁流变液传动性能下降。巩杭等[6]提出一种形状记忆合金与磁流变液交替的传动方法。CHEN等[7]设计了一种工作间隙尺寸可调的磁流变液制动器，研究表明，改变磁流变液工作间隙宽度能够控制输出制动力矩的大小。陈松等[8]设计了偏心式磁流变液制动器，用以提高制动性能。CAO等[9]提出一种用于电动汽车的梳齿盘式磁流变液制动器，通过电磁场仿真，研究了不同结构尺寸对其制动性能的影响。KARAKOC等[10]采用多目标优化设计方法，获得了磁流变液制动器的最优设计参数。ACHARYA等[11]利用多目标遗传算法计算了磁流变液制动器的最佳尺寸参数和磁流变液组成成分。
综上所述，现有研究对磁流变液制动器的制动性能展开了较为全面的分析，但综合考虑工作间隙尺寸、制动盘数量及其尺寸的研究较少。本文基于正交试验法进行相关研究，分析讨论了上述因素对磁流变液制动器制动性能影响的主次顺序。
1　磁流变液制动器
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磁流变液制动器采用非接触式制动形式，以磁流变液为工作介质，在保障制动性能的同时可避免摩擦磨损和振动等问题。图1为多盘式磁流变液制动器（Multi-disk Magnetorheological fluid Brake, Multi-disk MRB）结构示意图[12]。该制动器具有多个由固定盘和制动盘构成的工作间隙，用以填充磁流变液；此外，还包括轴、励磁线圈、壳体、导磁板、轴承、密封圈、螺栓等零部件。
磁流变液是一类典型的场响应型智能材料，在零场工况下具有优异的流动性。当外施磁场时，其内部磁性颗粒会沿磁场方向有序排列并形成磁链结构，流动性显著降低；随磁场强度持续增大，磁流变液的表观黏度呈非线性递增趋势，进而表现出可控的剪切屈服强度。在制动器中，磁流变液作为核心工作介质，通过制动工作间隙内磁流变液在外磁场作用下的剪切效应传递制动力矩；通过调控磁场强度，能够连续、快速且可逆地改变磁致剪切应力，从而实现对制动力矩与转速的无级调控。磁流变液所具备的可控性与流变特性，赋予了磁流变液制动器宽范围的制动力矩调节能力，使其在软制动领域展现出广阔的应用前景。
2　仿真分析模型
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2.1　目标制动力矩
车用磁流变液制动器作为制动系统中的制动执行器，其制动性能一直是研究的重点。输出制动力矩则是直观评价制动器性能优劣的关键指标之一。本文以某款A00级微型车为研究对象，其主要参数如表1所示。
根据《乘用车行车制动器性能要求及台架试验方法》[13]，当目标车辆满载时，若以4.41 m/s2（0.45g，g为重力加速度）的制动减速度进行制动，则后制动器所需提供的制动力矩Mc的计算式为
Mc=Jarm
式中，Mc为制动器的目标制动力矩；J为对应车轮的转动惯量；a为制动减速度。
转动惯量J的计算式为
J=Ga(l-0.45hg)   rm22L
将表1所示参数代入式（1）和式（2）可得，目标车辆满载时，以4.41 m/s2的制动减速度进行制动，磁流变液制动器的理论输出目标制动力矩为234.72 N·m。
2.2　制动力矩数学模型
实际工程应用中，常用Bingham模型来描述磁流变液所展现出的流变特性。磁流变液在磁场作用下提供的剪切应力τ为
τ=τB+ηγ
式中，τB为磁流变液的磁致剪切屈服应力；η为磁流变液的塑性黏度；γ为剪切应变率。
图2为磁流变液制动器简化示意图。
当制动盘以角速度ω旋转时，制动盘上任意半径r处某点的剪切应变率可表示为
γ=ω rh
式中，h为工作间隙（磁流变液工作区域）宽度。
采用微元法计算磁场作用下制动盘产生的制动力矩。随机选择盘上一微型环形区域dA，该环形区域产生的制动力矩dM可表示为
dM=rτdA=2πτ r2d r
磁流变液制动器的输出制动力矩主要由两部分组成，一部分是零场条件下由磁流变液本身黏性产生的黏性制动力矩；另一部分是磁场存在时磁流变液产生的制动力矩。结合式（3）、式（4）和式（5），在磁场作用下，磁流变液制动器中单个制动盘单面所能提供的输出制动力矩M1的计算式为
M1=∫R1R2dM=Mη+MB
式中，R1为制动盘的内圆半径；R2为制动盘的外圆半径；Mη为黏性制动力矩；MB为磁致制动力矩。
无磁场作用时，磁流变液表现为牛顿流体，单个工作间隙产生的黏性制动力矩Mη为
Mη=∫R1R22π r2ηγ dr=πη ω2hR24-R14
当励磁线圈通电产生磁场后，磁流变液表现为Bingham流体，单个工作间隙产生的磁致制动力矩MB为
MB=∫R1R22π r2τBdr=23πτBR23-R13
2.3　制动力矩数值计算
本文选用SG-MRF2035磁流变液，其主要性能参数如表2所示，其剪切屈服应力和磁场强度的关系曲线如图3所示。
本文通过Matlab/Simulink软件对磁流变液制动器的输出制动力矩进行仿真分析。为了便于计算，利用Matlab软件对磁流变液剪切屈服应力的测试值进行多项式拟合，得到磁流变液剪切屈服应力和磁感应强度的数值关系。根据拟合结果，磁流变液的剪切屈服应力τB可表示为
τB=127.133 9B4-318.087 5B3+                       202.014 3B2+40.861 4B-0.453 6
3　制动性能影响因素分析
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磁流变液制动器制动过程的本质为多物理场（电、磁、流、热、结构等）与磁流变液材料性能之间的相互作用。磁流变液具有显著的黏温特性，并存在诸如颗粒沉降等问题[14-15]。在制动器机械结构设计阶段，应优先考虑制动器中磁流变液工作区域宽度（工作间隙）、制动盘数量及其尺寸对制动性能的影响。
3.1　工作间隙宽度
磁流变液中的磁性颗粒主要沿磁感线方向形成磁链，对与剪切方向平行的磁场影响较小，因此，主要研究垂直剪切方向的磁场[16]。由图3可知，磁场强度直接影响磁流变液的剪切屈服应力。对于磁流变液制动器而言，在结构设计阶段应合理规划磁路并保证工作区域的磁场强度。
磁流变液制动器采用励磁线圈作为磁源，励磁线圈通电后，制动器内部会产生磁场，磁感线最先由一侧穿过制动器的外壳，然后依次穿过磁流变液、制动盘、固定盘等，最后穿过制动器另一侧的外壳，在制动器内部形成一个封闭的磁感线回路。依据安培环路定理和磁路欧姆定律可得
ϕ=NIZtotal
式中，ϕ为制动器内部的磁通量；N为线圈匝数；I为电流；Ztotal为磁流变液制动器总磁阻。
磁流变液制动器初始设计阶段，工作间隙处的磁场强度为预设期望值。由高斯定理可知，磁流变液工作区域的期望磁通量ϕE的计算式为
ϕE=B0S
式中，B0为预设磁场强度；S为制动盘有效工作面积。
磁阻Z的计算式为
Z=xuS
式中，x为磁路长度；u为材料的磁导率。
磁流变液工作区域磁阻ZMRF的计算式为
ZMRF=hπ uMRF(R22-R12)
式中，uMRF为磁流变液的磁导率。
结合式（7）可知，磁流变液制动器工作间隙宽度的变化直接影响该部分的磁阻大小以及磁流变液在工作中的黏性制动力矩Mη。由式（10）、式（11）和式（13）可知，不同的工作间隙h需要的励磁线圈匝数是不同的。
由此可见，磁流变液工作间隙的宽度越宽，制动器内部磁路的总磁阻Ztotal越大，表明需要更多匝数的线圈来提供更高的磁场强度。不仅如此，线圈匝数的增加会使线圈发热量增加。反之，工作间隙过小易使磁流变液温升过快，并且增大了加工和装配难度[17]。因此，宽度合适的工作间隙尺寸对于磁流变液制动器具有重要意义。
在实际应用中，工作间隙选取范围通常为0.5~2 mm[18]。对于多盘式磁流变液制动器，通过调整制动工作间隙尺寸，得到0.5、1.0、1.5、2.0 mm这4种不同尺寸的制动工作间隙，在同一制动盘数量和制动盘尺寸下对制动力矩进行数值模拟。
3.2　制动盘数量
结合式（7）、式（8）可知，本文研究的多盘式磁流变液制动器在磁场作用下的总输出制动力矩M可表示为
M=2nM1=2n(Mη+MB)=π nηωh(R24-R14)+43πnτB(R23-R13)
式中，n为制动盘的数量。
根据式（14），对于同样尺寸的工作间隙和制动盘，制动盘数量的增加能够显著提高磁流变液制动器的制动性能。然而，制动盘数量的增加必然会增大制动器的轴向尺寸。目前，传统汽车制动系统的总质量大约为60 kg[19]，磁流变液制动器的总质量应小于传统汽车制动系统总质量，并且在满足制动需求的同时实现轻量化设计。本文设计的磁流变液制动器中，制动盘、固定盘和壳体等构件的材质均为20钢，密度为7.85 g/cm3。以外圆半径R2=75 mm、内圆半径R1=37 mm和厚度为8 mm的制动盘为例，每增加一块制动盘，制动器的总质量大约增加0.84 kg（仅计算单个制动盘）。此外，制动盘数量增加，磁流变液工作间隙数量也会同比增加。
针对多盘式磁流变液制动器，通过调整制动盘数量，得到1、2、3、4这4种不同制动盘数量，在相同制动间隙和制动盘尺寸下对制动力矩进行数值模拟。
3.3　制动盘尺寸
本文所提出的多盘式磁流变液制动器的工作模式为剪切工作模式。在剪切模式下，根据牛顿内摩擦定律，制动力F为
F=τS
制动盘有效工作面积S的计算式为
S=π(R22-R12)
最初选定的传动轴半径为37 mm，所对应的制动盘内圆半径R1也为37 mm，所以，制动盘尺寸的变化主要体现在其外圆半径R2上。由式（16）可知，内圆半径R1不变时，制动盘有效工作面积随外圆半径R2的增大而增大。由式（7）~式（15）可知，外圆半径R2是磁流变液制动器设计过程中的重要指标之一，直接影响其制动性能。
针对多盘式磁流变液制动器，调整制动盘外圆半径，得到70、75、80、85 mm这4种不同尺寸的制动盘外圆半径，在相同制动间隙和制动盘数量下对制动力矩进行数值模拟。
综上所述，工作间隙尺寸、制动盘数量和制动盘尺寸是影响制动器制动性能的主要因素。因此，在磁流变液制动器设计过程中需要对其进行综合考虑。由图3可知，磁流变液剪切屈服应力随磁场强度的变化是非线性的，随磁场强度增加而增加，最后趋于稳定（达到饱和磁场强度）。因此，在后文进行的正交试验中，将磁流变液的黏性制动力矩Mη（ω=60 rad/s）、制动器的常规制动力矩Mn（B=0.5 T）和最大制动力矩Mmax（B=1 T）作为评估指标并进行分析。
4　正交试验设计分析
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4.1　正交试验设计
参数优化设计是机械系统设计过程中的重要步骤。对于磁流变液制动器而言，影响其制动性能的因素较多并且制作样机成本较高，正交试验法可以通过科学地安排试验，以较少的试验次数获得可靠结果[20-21]。
本文以磁流变液制动器制动性能为研究对象，通过改变制动间隙尺寸h、制动盘数量n以及制动盘外圆半径R2，获得具有不同结构参数的磁流变液制动器仿真模型；以磁流变液的黏性制动力矩Mη、制动器的常规制动力矩Mn和最大制动力矩Mmax为评价指标，探究上述3个因素中影响制动性能最大的因素并获取最佳组合方式。采用正交试验法，取3因素4水平进行制动性能探究，所以，选用L16（43）正交表。参数取值和试验结果分别如表3、表4所示。
4.2　正交统计分析
针对表4所示的正交试验数值结果，对每个评估指标按3个因素的4个水平分别开展统计并取平均值，可得到表5所示的平均值。然后，依据每个因素4个水平的平均值进行极差分析，得到表6所示的平均值极差R。图4~图6分别为3个评估指标随因素水平变化的折线图，图4~图6的横坐标分别为各因素对应的水平编号。
黏性制动力矩Mη由磁流变液自身黏性所产生。由式（7）可知，磁流变液的黏性制动力矩数值大小取决于磁流变液的黏度、转速以及制动器的结构参数（制动盘内外圆半径和工作间隙宽度）。因此，在制动过程中无法通过改变磁场对这部分进行主动调节。由表6可知，黏性制动力矩关于h、n、R2的极差大小分别为7.129、5.920、5.052 N∙m；相较来说，工作间隙宽度h对黏性制动力矩的影响较大。
由图4可知，磁流变液的黏性制动力矩随着工作间隙宽度h的增大而减小；而制动盘数量n和制动盘外圆半径R2的影响正好相反，磁流变液的黏性制动力矩与制动盘数量和制动盘外圆半径成正相关。
图5和图6分别为常规制动力矩Mn（B=0.5 T）和最大制动力矩Mmax（B=1 T）随各因素水平的变化趋势。显然，这两项评估指标变化趋势是相似的，两者的主要区别在于磁场强度不同，所以，相同条件下在数值上存在差异。
由表4可知，在同一磁流变液制动器结构尺寸下，磁流变液的黏性制动力矩Mη在数值上只占总输出制动力矩M中很小一部分。对于磁场作用下磁流变液制动器产生的制动力矩，各因素的主次顺序为n第1，R2次之，h最后。由此可知，增加制动盘数量对于提高磁流变液制动器制动性能是最有效的手段，其次是增加制动盘外圆半径及增大制动盘的有效工作面积。此外，制动盘数量对制动力矩的影响约是制动盘外圆半径的2倍，约是工作间隙宽度的6倍。结合图6可知，随着n因素水平的提高，最大制动力矩的增加尤为明显，n=4时的最大制动力矩约是n=1时的4倍。
综上所述，n因素水平的提高能够使磁流变液制动器的输出制动力矩大幅度上升，有利于提高其制动性能，并使其获得更大的可控制动力矩范围。相同条件下，磁致最大制动力矩是黏性制动力矩的数十倍。因此，在制动过程中，仅通过改变磁场大小便可实现对输出制动力矩的无级调控。对于本文所研究的磁流变液制动器，采用表4中第12组试验中的h3n4R22组合便可满足理论输出制动力矩为234.72 N·m的要求，其常规制动力矩为244.087 N·m，约为黏性制动力矩的68倍。该组合下磁流变液制动器输出制动力矩随磁场强度的变化如图7所示。
由图7可知，当磁流变液工作区域磁场强度达到0.48 T时，制动器的输出制动力矩就已经达到理论输出制动力矩，满足设计需求。另外，磁场强度为1 T时，该制动器的最大制动力矩约为320.09 N·m，在满足设计需求的同时可使其具有较大的制动力矩调节范围。
5　验证试验
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第4节中已经得出磁流变液制动器最优结构参数，即制动间隙尺寸h为1.5 mm，制动盘内外圆半径R1、R2分别为37、75 mm，制动盘数量n为4。利用关键结构参数，建立磁流变液制动器电磁场仿真模型，图8所示为输入电流为3 A时的电磁场仿真结果。
由图8可知，制动间隙处磁感应强度保持在0.56 T。根据式（8）、式（9）得出，该条件下制动器的理论输出制动力矩为263.86 N·m，达到设计需求。
以此为基础，搭建磁流变液制动器实物样机并对其输出特性展开试验研究。出于安全考虑，设定制动初速度为60 km/h，线圈输入电流分别为0.3、0.9、1.5、2.1 A。表7所示为试验过程中磁流变液制动器的最大输出制动力矩。线圈输入电流为2.1 A时，制动器的最大输出制动力矩已经达到240.3 N·m，大于第2.1节中的目标制动力矩。对于本文中的磁流变液制动器关键结构参数，采用表4中h3n4R22组合即可满足制动需求。
6　结论
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采用Matlab/Simulink软件，针对磁流变液制动器，就磁流变液作为工作介质的制动过程进行了仿真分析；就工作间隙、制动盘数量和制动盘尺寸对制动性能的影响进行了分析和讨论，得到以下结论：
1）零场条件下，磁流变液的黏性制动力矩主要受制动间隙尺寸影响；施加磁场后，制动盘数量是影响磁流变液制动器制动性能的主要因素，制动盘外圆半径次之。
2）磁流变液制动器制动性能受多重因素影响。本文中目标制动力矩为234.72 N·m，采用h3n4R22结构参数组合即可满足要求。基于该组参数搭建了制动器实物样机；输入电流为2.1 A时，其最大输出制动力矩可达240.3 N·m。
3）相同条件下，黏性制动力矩影响较小。因此，输出制动力矩在可控范围内的无级调节仅通过磁场强度的改变即可实现。
文献
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2026年第50卷第1期
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doi: 10.16578/j.issn.1004.2539.2026.01.005
  • 接收时间：2024-11-25
  • 首发时间：2026-05-20
  • 出版时间：2026-01-15
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  • 收稿日期：2024-11-25
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    合肥工业大学 机械工程学院，合肥230009

通讯作者:

王道明（通信作者），男，1987年生，江苏盐城人，博士，教授；主要研究方向为车辆线控制动技术、智能结构与系统；。
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2种不同金属材料的力学参数
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