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Article(id=1228046474227941985, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.02.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1653840000000, receivedDateStr=2022-05-30, revisedDate=1658073600000, revisedDateStr=2022-07-18, acceptedDate=null, acceptedDateStr=null, onlineDate=1770718695456, onlineDateStr=2026-02-10, pubDate=1709049600000, pubDateStr=2024-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770718695456, onlineIssueDateStr=2026-02-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770718695456, creator=13701087609, updateTime=1770718695456, updator=13701087609, issue=Issue{id=1228046469559681568, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='2', pageStart='191', pageEnd='364', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770718694343, creator=13701087609, updateTime=1770795432451, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228368332575928712, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228368332575928713, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=218, endPage=225, ext={EN=ArticleExt(id=1228046474534126185, articleId=1228046474227941985, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Modeling and experiment of ultrasonic resonant Braille display cell’s squeeze film, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

At present，traditional Braille books have had difficulty meeting the needs of the blind，this paper proposes a new type of ultrasonic resonant Braille display cell based on the squeeze film generated by ultrasonic vibration. The Reynolds equation which determines the aerodynamic characteristics of the squeeze film is derived theoretically，the mechanical model and approximate solution of the output buoyancy are obtained by using the “piston effect” of the squeeze film，the vibration characteristics and output performance test of Braille display cell were tested using the built experimental platform. The results show that the resonant frequency of the Braille display cell is 30.8 kHz，when the peak-to-peak value of the excitation voltage is 130 Vpp to 200 Vpp，a stable squeeze film with certain buoyancy can be formed. The theoretical calculation results are basically consistent with the experimental results. In the experiment，three kinds of samples can be lifted from 13.92 μm to 47.71 μm，Braille display cell has sufficient output performance.

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目前传统的盲文书籍已经难以满足盲人的阅读需求，本文基于超声振动产生的挤压膜提出了一种超声谐振式盲文点显胞元。理论推导了决定挤压膜气动力学特性的Reynolds方程，利用挤压膜的“活塞效应”得到了输出托浮力的力学模型及近似解，利用搭建的实验平台开展了盲文点显胞元的振动特性测试和输出性能测试。结果表明：该盲文点显胞元的谐振频率为30.8 kHz，激励电压峰峰值在130~200 Vpp时，可以形成稳定且具备一定托浮能力的挤压膜。理论计算值与实验实测数据基本吻合，实验中三种不同质量的试样可被托起13.92~47.71 μm的高度，盲文点显胞元具备足够的输出性能。

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李国平（1967―），男，博士，教授。E-mail： 。
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赵琪啸（1998—），男，硕士研究生。E-mail： 。

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赵琪啸（1998—），男，硕士研究生。E-mail： 。

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赵琪啸（1998—），男，硕士研究生。E-mail： 。

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Parameters of Braille display cell

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参数数值
压电陶瓷片半径/mm12.50
压电陶瓷片厚度/mm2.00
玻璃覆层半径/mm12.50
玻璃覆层厚度/mm2.00
压电背衬架支撑部外径/mm23.00
压电背衬架支撑部内径/mm25.00
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盲文点显胞元参数

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参数数值
压电陶瓷片半径/mm12.50
压电陶瓷片厚度/mm2.00
玻璃覆层半径/mm12.50
玻璃覆层厚度/mm2.00
压电背衬架支撑部外径/mm23.00
压电背衬架支撑部内径/mm25.00
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Parameters of squeeze film analysis model

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参数数值
挤压膜半径/mm12.5
空气动力黏度/（Pa∙s）1.79×10-5
环境压强/MPa0.101
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挤压膜分析模型参数

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参数数值
挤压膜半径/mm12.5
空气动力黏度/（Pa∙s）1.79×10-5
环境压强/MPa0.101
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超声谐振式盲文点显胞元的挤压膜建模及实验研究
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赵琪啸 1 , 李国平 1 , 韩凯 1 , 项四通 1 , 魏燕定 2 , 娄军强 1, 2
振动工程学报 | 2024,37(2): 218-225
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振动工程学报 | 2024, 37(2): 218-225
超声谐振式盲文点显胞元的挤压膜建模及实验研究
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赵琪啸1 , 李国平1 , 韩凯1, 项四通1, 魏燕定2, 娄军强1, 2
作者信息
  • 1宁波大学机械工程与力学学院, 浙江　宁波　315211
  • 2浙江大学浙江省先进制造技术重点研究实验室, 浙江　杭州　310027

    • 赵琪啸（1998—），男，硕士研究生。E-mail： 。

通讯作者:

李国平（1967―），男，博士，教授。E-mail： 。
Modeling and experiment of ultrasonic resonant Braille display cell’s squeeze film
Qi-xiao ZHAO1 , Guo-ping LI1 , Kai HAN1, Si-tong XIANG1, Yan-ding Wei2, Jun-qiang LOU1, 2
Affiliations
  • 1Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China
  • 2Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
出版时间: 2024-02-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.02.004
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摘要
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目前传统的盲文书籍已经难以满足盲人的阅读需求，本文基于超声振动产生的挤压膜提出了一种超声谐振式盲文点显胞元。理论推导了决定挤压膜气动力学特性的Reynolds方程，利用挤压膜的“活塞效应”得到了输出托浮力的力学模型及近似解，利用搭建的实验平台开展了盲文点显胞元的振动特性测试和输出性能测试。结果表明：该盲文点显胞元的谐振频率为30.8 kHz，激励电压峰峰值在130~200 Vpp时，可以形成稳定且具备一定托浮能力的挤压膜。理论计算值与实验实测数据基本吻合，实验中三种不同质量的试样可被托起13.92~47.71 μm的高度，盲文点显胞元具备足够的输出性能。

超声振动  /  盲文点显  /  压电作动器  /  挤压膜效应

At present，traditional Braille books have had difficulty meeting the needs of the blind，this paper proposes a new type of ultrasonic resonant Braille display cell based on the squeeze film generated by ultrasonic vibration. The Reynolds equation which determines the aerodynamic characteristics of the squeeze film is derived theoretically，the mechanical model and approximate solution of the output buoyancy are obtained by using the “piston effect” of the squeeze film，the vibration characteristics and output performance test of Braille display cell were tested using the built experimental platform. The results show that the resonant frequency of the Braille display cell is 30.8 kHz，when the peak-to-peak value of the excitation voltage is 130 Vpp to 200 Vpp，a stable squeeze film with certain buoyancy can be formed. The theoretical calculation results are basically consistent with the experimental results. In the experiment，three kinds of samples can be lifted from 13.92 μm to 47.71 μm，Braille display cell has sufficient output performance.

ultrasonic vibration  /  Braille display  /  piezoelectric actuator  /  squeeze film effect
赵琪啸, 李国平, 韩凯, 项四通, 魏燕定, 娄军强. 超声谐振式盲文点显胞元的挤压膜建模及实验研究. 振动工程学报, 2024 , 37 (2) : 218 -225 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.02.004
Qi-xiao ZHAO, Guo-ping LI, Kai HAN, Si-tong XIANG, Yan-ding Wei, Jun-qiang LOU. Modeling and experiment of ultrasonic resonant Braille display cell’s squeeze film[J]. Journal of Vibration Engineering, 2024 , 37 (2) : 218 -225 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.02.004
正文
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引言
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根据世界卫生组织最新发布的数据，全球约有超过2.951亿人存在视力障碍，其中4330万人失明［1］，他们只能依赖于触觉、听觉还有残存的视觉来获取相关文字信息。盲文作为一种为盲人开发的文本，是一种利用触觉向盲人传递信息的重要手段。盲文单元由三行两列六个触点构成，触点也被称为胞元，由不同的胞元凸起组合组成不同的字符。随着科学技术的不断发展，人类走进了互联网时代，海量的信息扑面而来。但是盲人获取信息的手段仍然匮乏，使用纸质的盲文书本相当麻烦，且无法更新。因此，关于动态刷新的盲文点显装置的研究具有重要的意义，已经引起了国内外学者的关注。Qu等［2］提出了一种由摩擦电纳米发电机驱动的介电弹性体盲文装置，通过两层薄膜间的摩擦产生超过3 kV的电压以及低于2 μA的电流，使介电弹性体形变，加压腔室内空气，薄膜受空气压力变形凸起，形成凸起的触点。Frediani等［3］使用智能材料介电弹性体减少了点显装置的轴向尺寸，提高了其便携性。Kim等［4］提出了一种电磁驱动式的盲文点显装置，利用特殊的闩锁结构实现了低功耗、高频响和触点的高保持力。Zhou等［5］引入电触觉技术，在保证较高识别率的情况下，使盲文点显装置在成本、寿命、能耗和便携性上提升显著。Xie等［6］开发了一种基于气动膜执行器的可刷新2D盲文显示面板，通过使用新型的可变刚度聚合物膜，实现单独控制每个点或同时控制多个点，而无需复杂的气道设计。上述盲文点显装置在响应速度、接触力、识别率上都拥有良好的表现，但是依然存在成本较高或是结构复杂等缺点，并且机械结构可能会产生噪音，干扰视障人士使用。
声波传递的过程是能量相互传递的过程，其中振动频率高于20 kHz的声波是超声波，超声波能引发很多效应：热效应、化学效应、空化效应、机械效应等，且可以通过声耦合其他介质［7］而应用于切削［8］、检测结构、灭菌、雾化等领域。超声波亦可作为一种实现动态刷新盲文的手段。并且压电材料的出现更进一步推进了超声波技术的发展。压电材料作为一种具有驱动功能且响应快速、动态性能好等优点［9-10］的材料，可制成贴片式压电作动器用作超声源，实现电能到机械能的转换。在空气中，当压电作动器高频振荡，且频率达到超声级并具有一定振幅时，其表面与另一近距离物体之间就会生成有承载能力的气膜，该现象被称为挤压膜效应。该效应最早被Watanabe等［11］应用于触觉，利用朗之万超声换能器施加了几个微米的振动波，产生挤压膜减小了接触力，引起摩擦力改变，从而实现了触觉再现。Winfield等［12］研制出一种新型的触觉再现装置T-PaD，得到了该装置激励电压与动态托浮能力之间的映射关系，通过调节T-PaD的激励电压控制手指与T-PaD之间的切向力，以创建纹理触感。Wiertlewski等［13］基于挤压膜效应研究了摩擦感减小的原因，得出了皮肤与振动表面间可以产生动态托浮的结论。Biet等［14］将PI91型压电陶瓷片和铍铜片粘在一起，提出以铜铍为基板的StimTac触觉反馈装置，在表征气体压膜效应大小的概念——“挤压数模型”的基础上，引入了手指表皮微观模型和高频振动板的粗糙度概念［15］，提出了基于气体压膜的触觉反馈挤压数模型。
上述研究都是利用超声波的挤压膜效应生成具有托浮能力的挤压膜，以抵消一部分接触力，通过大面积的触觉显示器向使用者传递连续变化的粗糙感，以显示触觉纹理。该种实现触觉再现的方式具有成本低廉、结构简单紧凑、响应速度极高、寿命长等优势。但关于理论模型的研究内容较少，或缺少量化的参数表征信息传递的性能。本文针对目前盲文点显装置存在的问题，参考基于挤压膜效应的触觉显示装置，提出一种盲文点显胞元，将基于挤压膜的触觉显示装置化整为零，制成单个盲文胞元，直接利用挤压膜轴向的托浮力将皮肤托起，向人体传递盲文凸起的信息，以供视障者使用。人体皮肤通过机械感受器接受机械刺激，其反应主要由机械刺激的压力和位移所决定，盲文点显胞元的刺激性能满足人类皮肤上机械感受器的感知阈值，其值分别为300 N/m和100 nm［16］。通过建立决定盲文点显胞元气动力学特性的Reynolds方程，并在特定条件下得到该方程的近似解，从而建立盲文点显胞元的输出力学模型。通过振动特性测试，得到盲文点显胞元的最佳激励条件。最后对盲文点显胞元进行性能测试，对理论模型和性能进行验证。
1　超声谐振式盲文点显胞元的基本结构及原理
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盲文点显胞元的基本结构如图1所示，主要由压电背衬架、压电陶瓷片和玻璃覆层三部分组成。由压电陶瓷片和玻璃片粘接成超声波振子，再把超声波振子的压电片面边缘粘接到等外径背衬架上进行波节固定。在工作过程中，压电陶瓷片受电信号激励产生逆压电效应发生形变。压电陶瓷d31工作模态具有良好的弯曲振动特性［17］，在压电片径向伸缩位移受限制时，转为上下起伏的弯曲受迫振动。当此受迫振动达到一定幅值，并且拥有超声级别的频率时，在其表面上将产生具有托浮能力的空气薄膜即挤压膜。其振动形式如图2所示。
盲文点显胞元的性能主要由挤压膜决定，挤压膜的刚度越大，则盲文点显胞元的动态范围越高，性能越好。同时挤压膜的刚度又与盲文点显胞元的超声振动相关，故为了在超声频率下拥有良好的输出性能，盲文点显胞元的振幅要尽可能大，需要使超声激励信号的频率与盲文点显胞元的谐振频率保持一致［18］。根据Wiesendanger等［19］的研究，此种结构盲文点显胞元的振幅由压电层应变量，以及覆层与压电层的杨氏模量之比和厚度比决定。其谐振频率由振动理论中圆形薄板的谐振频率得到［20］，其值与总厚度、半径等参数相关。经过计算，平衡振幅、功耗和谐振频率之间的关系，并参考前人的设计得到盲文点显胞元的尺寸参数，由表1给出。
2　挤压膜的理论模型
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工作过程中假设被托浮皮肤表面是平整的，且与盲文点显胞元始终平行，两者不存在旋转运动和横向相对运动，只有轴向相对运动。由于皮肤和盲文点显胞元之间的挤压膜厚度和盲文点显胞元的振幅都很小，可知该挤压膜的雷诺数极小，空气运动状态主要为层流黏性流动。根据Bao［21］的理论，此时空气的惯性效应可以被忽略，而主要由空气的黏性效应决定。同时进一步将空气视为理想气体，流动时的黏度恒定。综上所述，描述挤压膜压力分布的Reynolds方程可简化为：
式中　 p为皮肤与盲文点显胞元之间挤压膜的压强；μ为气体动力黏度；t为时间；ρ为挤压膜的密度；x和y为空间坐标分量；h为挤压膜的厚度。
根据理想气体多变状态下的物态方程，空气的密度与压强之间有以下关系：
式中　 pa为环境压强（此处为标准大气压强）；ρ0为环境空气密度（此处为20 ℃下的空气密度）；κ为多变系数。
根据式（2）可知，密度也可以被压强所代替。故式（1）进一步定义为：
式中　 P=p/pa。
将式（3）做无量纲化处理，挤压膜呈中心对称分布，可得到该式在柱坐标下的表达为：
式中　 R=r/r0，其中，r为径向坐标，r0为点显胞元的半径；H=h/h0为无量纲挤压膜厚度，其中h0为一个振动周期内挤压膜的平均厚度，即被托浮物的托浮高度；σ为挤压系数，，其中ω为盲文点显胞元激振频率；T=ωt。
3　超声谐振式盲文点显胞元的理论模型
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3.1　高挤压系数下的挤压膜工作过程分析
一般Reynolds方程很难得到解析解，而在一些前提条件下，可以获取描述柱坐标下挤压膜性质的Reynolds方程的近似解。且由式（4）可知，挤压膜的特性由挤压系数σ和无量纲挤压膜厚度H决定。
其中挤压系数σ因为挤压膜厚度相当地小，盲文点显胞元的工作频率又相当高，故其值较大。一般认为σ值超过10时，挤压膜中的空气因为黏性几乎不会逸出，挤压膜就会有足够的刚度和稳定性［15］。此时被托浮物就如同密封气缸内的活塞，该现象被称为挤压膜的“活塞效应”［22］。此时可以把σ视为∞，该情况称为高挤压系数状态，以此建立力学模型。利用表2中的参数，我们可以计算盲文点显胞元在不同工作条件中的挤压系数的数值，如图3所示。因为没有考虑气体稀薄效应和被托浮物及盲文点显胞元表面的粗糙度，故只讨论托浮高度为10 μm以上的情况。从图3中可知，在盲文点显胞元的工作频率附近，绝大多数工作情况都满足“活塞效应”的要求。
图4为盲文点显胞元工作时生成挤压膜的示意图，图中av0为盲文点显胞元的峰值振幅，为简化模型，上方物体为被托浮物，下方为盲文点显胞元。当盲文点显胞元静止时，被托浮物与其接触；当盲文点显胞元工作时，盲文点显胞元与被托浮物之间气隙的体积随着盲文点显胞元的振动而不断改变，一个振动周期包含了正向挤压与反向挤压两个过程。由于盲文点显胞元的振动属于超声频率，一个振动周期极短，于是气隙中的空气受到高频循环挤压，形成了挤压膜。根据挤压膜的“活塞效应”可知，挤压膜的压强和体积关系满足多变状态下的理想气体状态方程，其表达式为：
式中　 V为挤压膜的体积；C为常数。
挤压膜的体积随简谐振动而体现出相同的变化规律，而体积的变化导致了压强的非线性变化，如图5所示。盲文点显胞元刚开始工作时，托浮高度还较低，挤压膜的体积较小，在V1min~V1max之间变化，其体积的变化规律体现为图中深红色实线。该曲线经过理想气体状态方程的黄色曲线的映射，可以得到其对应的压强。压强变化规律体现为墨绿色实线，大小在P1min~P2max间变化，平均压强为。远高于大气压强Pa，而这种超压即是挤压膜具有托浮能力的原因，且此时托浮能力大于被浮物轴向力，被托浮物继续上升，挤压膜体积增大。当挤压膜体积上升至Vmin~Vmax之间变化时，变化规律如图中粉红色点划线所示，对应的压强变化规律体现为亮绿色点划线，大小在Pmin~Pmax间变化，平均压强为。此时气膜的平均压强略高于大气压强，挤压膜的托浮力与被托浮物向下的轴向力相当，被托浮物的高度不再变化达到平衡。此时挤压膜在一个振动周期内的平均体积为V0。
3.2　高挤压系数下的挤压膜力学模型
瞬态的挤压膜厚度主要是由托浮高度与盲文点显胞元工作时的振动决定的，故无量纲挤压膜厚度H也可以表示为：
式中　 εL=av（r）/h0，其中，av（r）为盲文点显胞元径向上的振幅方程，εL为无量纲化的盲文点显胞元振幅。
根据式（5）可以得到挤压膜的压强p为：
挤压膜对皮肤输出的托浮力是由挤压膜周期变换的压强导致的，产生的力是挤压膜压强在时间和位置上的积分［23］：
将式（8）利用泰勒级数展开，可以得到托浮力：
式中　 为无量纲化的等效振幅。
谐振时将av（r）进行拟合以后得到：
将将式（10）代入式（9），可以求得近似的托浮力为：
根据一维热转移方程可知，声波频率越高，热量传递越快。在气体中声波频率超过109 Hz时，热量的传播速度才高于声速。而该盲文点显胞元工作频率仅为104 Hz量级，故其热量传递远小于声波速度，工作过程可以视为绝热过程，此时κ=1.4。
依据所建立的力学模型，可以获得挤压膜输出的托浮力与托浮高度和峰值振幅之间的关系，如图6所示，该图显示托浮力与中心峰值振幅具有正相关性，而其与托浮高度呈负相关性。
4　超声谐振式盲文点显胞元的特性测试
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4.1　盲文点显胞元的振动特性测试
盲文点显胞元采用环氧树脂（3M-DP460）把压电陶瓷片（P-51）分别与玻璃覆层和压电背衬架粘接后，置于真空干燥箱内静压12个小时（设定箱内温度为80 ℃，压强为0.06 MPa）使胶层均匀且薄。使用螺栓将盲文点显胞元固定于隔振台上，将单点激光测振仪（SOPTOP，LV-S01，位移分辨率为15 pm）的高精密激光干涉仪安装于三角架上，使用水平仪和丁字尺确保高精密激光干涉仪发出的偏振光垂直入射盲文点显胞元的表面，并聚焦于表面的中心。搭建盲文点显胞元振动响应测试系统，其结构框图如图7所示。测试过程中，信号发生器（RIGOL DG1022U）发出初始简谐激励信号，该激励信号通过功率放大器（Trek PZD700A，增益倍数为200）放大后输出到压电陶瓷片，压电片因逆压电效应随激励信号振动。与此同时，单点激光测振仪的信号处理器以960 kHz的采样频率，实时获取盲文点显胞元中心的振动速度。测得的振动信号经过光纤通过网线接口传输到PC机［24］。此测试系统基于单点激光测振仪LV-S01系统自带的QUICK SA软件完成，测试系统实物如图8所示。
对压电陶瓷片施加电压为150 V的简谐扫频信号（频率范围为25~34 kHz），持续时间为20 s。测得盲文点显胞元的时域响应如图9（a）所示。并对采集的振动响应数据进行FFT分析处理后，可以获得其频域响应如图9（b）所示。根据图中信息可知，该盲文点显胞元的谐振频率为30.8 kHz。
输入频率为30.8 kHz的简谐激励信号，激励电压以5 V为增量从100 V增加到200 V，采集21组盲文点显胞元的振动幅值数据。在输入150 V的激励信号时，盲文点显胞元的谐振响应如图10所示，其振幅为1.3089 μm。盲文点显胞元的谐振响应中心峰值振幅与激励电压的关系如图11所示。
4.2　盲文点显胞元的输出性能测试
选取与盲文点显胞元相同直径不同重量的玻璃片作为被托浮的试样，在盲文点显胞元未工作时对齐置于胞元上。其中试样一的质量为0.8461 g，试样二的质量为2.6575 g，试样三的质量为3.0820 g。测试系统的结构不变，在盲文点显胞元工作时，以49.02 kHz的采样频率采集试样的托浮高度信息，以试样的托浮高度表征盲文点显胞元凸起的性能。
在前文中已得到盲文点显胞元振幅与谐振激励电压的关系。本次测试选取了间隔为5 V从130 V到200 V的15组谐振激励电压，并将简谐谐振激励信号经过0.3 Hz的方波调制，记录盲文点显胞元上玻璃试样的托浮高度，各进行3次测试并取平均值。得到每个试样在15组不同激励电压下托浮高度的数据。在激励电压分别为140 V与180 V时，试样一的起伏情况如图12所示。在所有托浮高度数据中，试样每次被托浮起的高度的差值较小，重复性能良好。在被托起时，托浮高度的波动也都不超过2 μm。且激励电压越大，波动就越小，稳定性与重复性越好。
将峰值振幅与激励电压的关系代入到不同激励电压下的托浮高度数据，得到实验实测数据与理论计算值的对比结果如图13所示。从图13中可知，实验实测数据与理论计算值基本吻合。由实验实测与理论计算所得的托浮高度可知，实验数据的拟合线总是低于理论值。这是由于理论值是在理想状态下得到的，而实际上即便满足了“活塞效应”的条件，仍会有少量气体泄漏，削弱挤压膜的托浮能力。并且在进行盲文点显胞元振动特性测试时，盲文点显胞元都是在空载状态下，加上有重量的被托浮物后，盲文点显胞元的谐振频率不可避免地随之发生变化，试样的重力也直接影响了盲文点显胞元的振动特性，导致振幅变小，影响了挤压膜刚度而使托浮高度下降。另外，从图中可以看出，实验数据拟合线的斜率要大于理论值的斜率。实验数据与理论值的差值随激励电压的上升表现出逐渐变小的趋势。特别是当输入激励电压较小时，实验数据与理论值相差较大，这是由于盲文点显胞元的振动减弱，使挤压膜刚度下降、厚度变薄。此时挤压膜受物体表面粗糙度的影响变大容易不稳定，气体稀薄效应显现，导致了更大的差值。但是随着振幅变大，被托浮试样的高度上升导致挤压系数σ减小，致使“活塞效应”减弱，使理论值与实验数据的差距再次变大。
5　结论
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基于挤压膜效应，提出了一种盲文点显胞元。利用Reynolds方程实现了对挤压膜的气动力学描述，建立了输出托浮力的力学模型，并开展了盲文点显胞元振动特性和性能实验。结果表明实验实测数据与理论计算值基本一致，验证了理论模型的正确性和该盲文点显胞元的可行性。该盲文点显胞元具有结构简单、安装方便、易于加工、结构紧凑等特点。之后将进一步优化结构，选取合适的驱动和控制方式以降低功耗，提高响应速度，并对多个盲文点显胞元进行排列组成六点盲文，形成可用的盲文点显器。
基金
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  • 国家自然科学基金资助项目(51975517)
  • 国家自然科学基金资助项目(52075273)
  • 国家自然科学基金资助项目(51805276)
  • 浙江省自然科学基金公益项目(LGF21E050002)
  • 浙江省省属高校基本科研业务费专项资金资助项目(SJLY2021014)
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文章信息
doi: 10.16385/j.cnki.issn.1004-4523.2024.02.004
  • 接收时间：2022-05-30
  • 首发时间：2026-02-10
  • 出版时间：2024-02-28
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  • 收稿日期：2022-05-30
  • 修回日期：2022-07-18
基金
国家自然科学基金资助项目(51975517)
国家自然科学基金资助项目(52075273)
国家自然科学基金资助项目(51805276)
浙江省自然科学基金公益项目(LGF21E050002)
浙江省省属高校基本科研业务费专项资金资助项目(SJLY2021014)
作者信息
    1宁波大学机械工程与力学学院, 浙江　宁波　315211
    2浙江大学浙江省先进制造技术重点研究实验室, 浙江　杭州　310027

通讯作者:

李国平（1967―），男，博士，教授。E-mail： 。
参考文献
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https://castjournals.cast.org.cn/joweb/zdgcxb/CN/10.16385/j.cnki.issn.1004-4523.2024.02.004
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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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