四柱萬能液壓機系統(tǒng)設計【YA32-1000KN型四柱萬能液壓機】
四柱萬能液壓機系統(tǒng)設計【YA32-1000KN型四柱萬能液壓機】,YA32-1000KN型四柱萬能液壓機,四柱萬能液壓機系統(tǒng)設計【YA32-1000KN型四柱萬能液壓機】,萬能,液壓機,系統(tǒng),設計,ya32,kn,型四柱
英文文獻
HYDRAULIC EQUIPMENT OF PLIABLE FORCE FOR MAINTENANCE AND MECHANICAL WORKING
Abstract.The collaboration between the Hydraulic and Pneumatic Acting Systems Engineering Department and the SC HYDRAMOLD SRL firm led to the realization of some performances products on the hydraulics and pneumatics segment.The paper proposes to offer the most representative hydraulic pliable equipments force for mechanical working and maintenance.A big part from the hydraulic equipments is patented or claim of patent,the technology and technological originality being totally part of those.
Because the paper has a prevalent technical character,in the presentation will be got off especially the performance characteristics of the areas used and the hydraulic equipments advantages of the pliable force.
Key words:hydraulic equipment,maintenance,mecanical working.
1. Introduction
The multi-functional modular equipments,pliable,for mechanical working, that are based on the hydraulic drive are destined to the manufacturing plant IMM also to the manufacturing plant of maintenance of the big company framework from energetic,petrochemistry,transport.All the equipments what are adduced in work are submitted in the framework of DISAHP research and make the study of other papers.Taking account the finite space of a work,there will be proposed from the large palette of hydraulic pliable equipments force a new or modernized equipments series from each segment developed by the SC HYDRAMOLD SRL firm(pressure sources,hydraulic presses,hydraulic tools, hydraulic equipment of 3000 bar,hydraulic lift equipment),following as in the next works it will be published other modern hydraulic equipments.
2.Hydraulic Equipments Analysis Force
2.1 Pressure Sources
The pressure sources of the force hydraulic equipments yielded by the SC HYDRAMOLD SRL are:the hydraulic acting units that have electric or thermal engine and the hydraulic manual or pedal pumps.
·Hydraulic drive unit description with electric engine
The electro-hydraulic drive units HUEH are high pressure sources for the hydraulic cylinder supplying with simple or double action from some equipments structure,hydraulic installations or appliances,and they work with relative small rate flow and pressures of until 700 bars,(Fig.1).The working developed pressure can be adjusted depending on task:30-700 bar.
Fig.1–The electro-hydraulic drive unit[1]
1- electric engine;2-multiplier;3-oil receiver;4-operator’s desk.
Table 1
·Advantages
The electro-hydraulic drive unit advantages(HUEH)are:they offer the possibility to maintain into the pressure,respectively the hydraulic obstruct of the task and dispose of a precise setting of the pressure depending on the task until 700 bar;it allows the permanent control of the cylinder stroke and also the automatic commutation from the first step to the second pressure step respectively from the fast start to the technological breakthrough;it allows electric remote command,while the charging voltage is of 24 Vcc,having the oil temperature monitoring possibility and the automatic disconnect to the value of 55°C;it has the hydraulic components of the hydraulic panel(pump,valve, slide valve)and it functions in optimal behavior to maximum from the half nominal pressure,providing for advanced reliability;it has a low level noise (under 70 db);it confers the simultaneous supplying possibility of 2,3 or 4 cylinders-through to an attached branch[2,3].
·The hydraulic drive unit description with heat engine
The hydraulic drive units with heat engine(HUMUTH)proceed from the new products scale with a distinguished resilience into the field,and they function with small flow rate and pressures of until 700 bar,(fig.2).
Fig.2–The hydraulic drive unit with heat engine[4]
1- heat engine;2-multiplier;3-operator’s desk;4-oil receiver.
Table 2
The hydraulic drive unit characteristics with heat engine[1].
The hydraulic drive unit with heat engine has a manual command for thestart and the changing of the pressure steps from the 1st step to the 2nd step itmakes manual too[4].
·Advantages
The hydraulic drive unit offers similar advantages with those presented at the hydraulic drive unit with electric engine.The additional advantage consists of the mobility into the field as the result of a low weight and it doesn’t depend of a fixed power source(for example the connected of the unit to the line system).
2.2.Hydraulic Presses
The hydraulic press workshop HPH-075 is composed from a stand shut framework(fixed top traverse columns,adjustable bottom traverse,basic plate) removable,a hydraulic cylinder with double action HCHD-075.150 installed on a transversal carriage,a plates set,pressing bolts and nuts,(Fig.3).
Fig.3.–The hydraulic press 75[tf]
1- Basic plate;2-Columns;3-Bottom traverse;4-Hydraulic cylinder HCHD-075.125;
5-Top traverse;6-Pressing bolts;7-Pressing plates.
Table 3
The hydraulic press characteristics[1].
Among the direct applications of this hydraulic presses deserve reminded: pressing and gear puller off of the transmission shafts from the gear boxes; pressing and puller ball bearings from the attack pinions from the tapering groups;pressing and extraction from jammed subsets;cold deformation for various proof sample.
·Advantages
The hydraulic press has a modular construction,removable,having an indexed settlement system of the inferior traverse,at the various determinate heights of range of 75[mm].
The transverse carriage of press represents an easy settlement system of the hydraulic cylinder position allowing thus the pressing axle regulation;
The hydraulic press has plates set,bolts and pressing nuts for the realization of all technological operations;
From the press project result an optimal report between its weight and achieved force owing to the acting to maximum pressures 700 bar,as effect of a reduced weight it is easy of carried.
2.3.Hydraulic tools
The hydraulic tool scale used in the mechanical processing and maintenance is various,with many applications in the mechanical engineering.There are reminded among these hydraulic tools:the device of the bending pipes and the hydraulic device of cutting.
·The Device Description of Bending Pipes
The bending template,fixed on acting rod of the hydraulic cylinder and having the suitable skewers profile so pipe dimension as well as inflexion beam,it will act over pipe that follows to be distorted;the pipe guides on the two ferries of the rest,fixed between the device plates.The superior plate of the appliance it can bate to allow the introduction of the template and of the ferries of the rest(Fig.5).
The device of bending pipes type HDIT.M-020.300 is an equipment, hydraulic driven and it is destined to the bending at cold of the installations pipes in the maintenance and repairs sectors.
Table 4
The device characteristics of bending pipes[1]
Fig.5.–The device of bending pipes[1]
1- Tripod;2-Fixed plate;3-Turnover plate;4-Bolt;
5-Hydraulic cylinder HCHD-020.300,6-Form.
Table 5
The working characteristics of device of bending pipes HDIT.M-020.300[1]
·The Hydraulic Device Description of Cutting 20[tf]
The device is formed from a metallic body,realized through welded construction,a hydraulic cylinder with simple action HCHS-020.028,a movable knife jointly mounted with the cylinder rod and a fixed knife body, (Fig.6).
The hydraulic cylinder acting it realizes through the connection to a highpressure source(manual pump HPHM-700 or hydraulic pedal pump HPHP-700),through a fast coupling and hydraulic flexible pipe.
The semi-finished product it installs between the two knives,while the cutting knife and the counter-knife establish the debiting of the semi-finished product from the steel.The retirement of the cutting knife it realizes by a spring incorporated into a cylinder.The hydraulic device of cutting HFMO-020.028 is a hydraulic drive device,used in the producing processes and maintenance with the view of cuttings at cold of the circular,square,hexagonal and flat bars steel.The movable knife run is of 28[mm]and the maximum pressure 700[bar],[1].
Fig.6.–The hydraulic device of cutting 20[tf]
1--2-Movable knife;3-Fixed knife;4-Feed nipple with oil under pressure.
Table 6
The working characteristics of hydraulic device of cutting type HFMO-020.028,[1].
·Advantages
There are important to notice,among the hydraulic device advantages of cutting:the compact structure and modern design;the easy drivability and the reduced weight;it eliminates the useless physicals work of the operator;it lowers the appropriated time procedure.
Scaling Behaviour of Pressure-Driven Micro-Hydraulic Systems
ABSTRACT
This paper presents a lumped network approach for the modelling and design of micro-hydraulic systems.A hydraulic oscillator has been built consisting of hydraulic resistors,capacitors and transistors(pressure controlled valves).The scaling of micro-hydraulic networks consisting of linear resistors,capacitors and inertances has been studied.An important result is that to make smaller networks faster,driving pressures should increase with reducing size.
1 INTRODUCTION
Micro-hydraulic systems can be modeled and designed using a generalized physical system description[1,2].This approach is based on the assumption that it is possible to
separate and concentrate properties of a system into interconnected subsystems.It has proven its great value in the design of electronic circuits.The lumped network approach also offers a powerful design tool for microfluidic systems[3-5].To illustrate the far-reaching analogy between different physical domains,we have rebuilt an electronic astable multivibrator network in the hydraulic domain[4].The system consists of hydraulic capacitors, resistors,transistors and(parasitic)coils.Based on this micro-hydraulic system the scaling behaviour of low Re (Reynolds number)hydraulic systems has been analyzed.
2 HYDRAULIC FUNDAMENTALS
In every physical domain a conserved quantity q can be distinguished[1].The flow is the rate of exchange of this conserved quantity between subsystems.In the hydraulic domain the flow variable is the volume flow. The effort is the tension that governs the exchange of the conserved quantity between subsystems.In the hydraulic
domain the effort variable is the pressure p[Pa].
2.1 Hydraulic Resistors
The hydraulic resistor physically is a liquid flow restriction,symbolically represented as in fig.1a.For a linear flow resistor,the resistance R is defined by:
Where p12=p1–p2 is the pressure drop across the resistor, and the volume flow through the resistor.At sufficient low Re the flow in a duct is laminar and fully developed (Poisseuille flow),and the pressure drop p across the duct is proportional to the volume flow rate.For a duct of arbitrary cross section the resistance is given by[6]:
Where f is the Fanning friction factor,L is the length of the channel,μis the viscosity of the liquid,Dh the hydrodynamic diameter,and A the cross sectional area.For a laminar fully developed flow the product f*Re=k,a dimensionless constant only depending on the shape of the cross section.The hydraulic resistors we have tested,were realized by anisotropic KOH-etching into a<100>silicon wafer and closing of the channel by anodic bonding of a glass wafer onto the silicon.Fig.1b-d show a side view,a cross section and a top view of the implemented restrictionsrespectively.
Figure 1:Hydraulic resistor.a)Symbolic representation
b)Side-view of realized restrictions c)Cross section of
ealized restrictions d)Top view of a realized restriction.
For these triangular channels with a top width of 2w the resistance is given by:
The limits of the linear regime have been determined analytically and verified experimentally for liquids[7]. Entrance and exit effects result in a non-linear relation
between p12 and.They can be neglected if the channel is long compared to the hydrodynamic entrance length.At low Re the entrance length Lhy increases linearly with Re.For circular channels with a diameter d this is expressed by [6]:
2.2 Hydraulic Capacitors
The hydraulic capacitor physically is an elastic membrane across which a pressure difference can be maintained.It is symbolically represented in fig.2a.The capacitor establishes a relation between the pressure drop across the membrane and the displaced volume.For a linear capacitor the capacitance C is defined by:
Where V is the volume of the displaced liquid by bending of the membrane.Because the volume V is created by accumulation of the volume flow,(5)can be rewritten to
find a relation between effort and flow:
Figure 2:Hydraulic capacitor a)Symbolic representation b)Cross section of a capacitor realized in glass-silicon-glass technology,showing the deflection of the membrane under influence of a pressure difference.
Fig.2b shows a cross section of a capacitor realized in a glass-silicon-glass sandwich.For deflections smaller than the thickness of the membrane there is a linear relation between the applied pressure difference and the membrane deflection.In this case a simple expression for the capacitance can be derived:
Where a is the radius of the membrane,and D is the flexural rigidity of the membrane,defined by ,in which E [Pa] is the Young's modulus,ν[-] the Poission's ratio,and h[m] the thickness of the membrane.
中文翻譯
柔韌力液壓設備維修和機械加工
摘要:液壓和氣動代理系統(tǒng)工程部門和SC HYDRAMOLD SRL公司的合作實現(xiàn)了一些表演上的液壓與氣動領域的產(chǎn)品. 文章提出了提供最具代表性的為機械加工和維護液壓圓滑設備力量。液壓設備的大部分組成部分是有專利的或是專利的要求,技術或技術創(chuàng)新即這些專利的整個部分
因為文章有一個普遍的技術特征,在演示文稿將完成特別是使用地區(qū)和液壓設備的柔韌力優(yōu)勢的性能特點。
關鍵詞:液壓裝置、維修、力學性能工作。
1.介紹
使機械工作具有柔韌性的多功能模塊化設備,這在液壓傳動基礎上,實現(xiàn)了IMM的生產(chǎn)廠從有力的石化,交通方面的公司向維護大公司的框架生產(chǎn)公司的轉(zhuǎn)化。所有的同時考慮到有限的工作空間,將有提出從大型液壓設備的調(diào)色板柔韌力由公司的SC HYDRAMOLD?。樱遥蹋▔毫υ?,液壓機,液壓工具,液壓設備而開發(fā)的每一段新的或現(xiàn)代化的設備系列3000酒吧,液壓升降設備),在它下面將公布下一液壓設備等現(xiàn)代作品。在工作中用到的設備呈現(xiàn)在DISAHP框架研究報告中并對其他文件作了研究。
2. 液壓設備分析力
2.1壓力源
力量水力設備的壓力來源由SC HYDRAMOLD SRL產(chǎn)生了是:有電或熱量引擎和水力指南或腳蹬泵浦的水力代理單位
·與電引擎的水力驅(qū)動裝置描述
電動液壓的驅(qū)動裝置HUEH是供應以簡單或雙重行動的液壓缸的高壓來源從一些設備結構、水力設施或者裝置,并且他們與直到700個酒吧一起使用相對小率流程和壓力, (Fig.1)。工作被發(fā)展的壓力可以根據(jù)任務被調(diào)整:30-700吧。
Fig.1–電動液壓的驅(qū)動裝置[1]
1- 電引擎; 2乘算器; 3油接收器; 4-工作臺。
表 1
電動液壓驅(qū)動驅(qū)動裝置特點[1]
油接收器[l]
10;20;30;40
電引擎[kw]
1.5-4
高壓流速[l/min]
0.5-1.5
低壓流速[l/min]
6-16
最大壓力[吧]
700
重量[kg]
84-176
· 優(yōu)勢
電動液壓的驅(qū)動裝置好處(HUEH)是:他們提供可能性維護入壓力,各自水力阻礙任務并且根據(jù)直到700吧的任務處理壓力的一個精確設置; 它允許圓筒沖程的永久控制并且從第一步的自動換向到第二壓力步分別從快速的開始到技術突破; 它允許電遙遠的命令,而電荷電勢是24 Vcc,有油溫監(jiān)視可能性和自動斷開對55°C的價值; 它有水力盤區(qū)(泵浦、閥門,滑閥)的液壓元件,并且它在優(yōu)選的行為起作用對從半公稱壓力的最大值,提供先進的可靠性; 它有低級噪聲(在70 db以下); 它同時供應的可能性的2,3或4圓筒通過對一個附上分支[2,3]。
·用熱引擎的液壓驅(qū)動裝置描述
用熱引擎(HUMUTH)的液壓驅(qū)動裝置從與卓越的韌性的新產(chǎn)品標度入領域和他們進行起作用與直到700吧小流速和壓力, (fig.2)。
圖2-熱發(fā)電機的液壓驅(qū)動裝置[4]
1 - 熱機,2加速器; 3操作臺,4油接收器
表 2
用熱引擎[1]的水力驅(qū)動裝置特征
油接收器[L]
10
電動發(fā)動機功率[kw]
1.2
高壓流速[L/min]
0.35
低壓流速[L/min]
3.3
最大壓力[巴]
700
重量[Kg]
40
用熱機的液壓驅(qū)動裝置有一個開始的命令,壓力的變化從第一步到第二步同樣使人工操作化[4].
·優(yōu)點
水力驅(qū)動裝置提供與那些的相似的好處被提出在與電引擎的水力驅(qū)動裝置的優(yōu)點。另外的好處包括流動性到由于低重量的領域里和它不依靠一個固定的電源(例如被連接對于系統(tǒng)的單元)。
2.2液壓機
液壓機是用于各種各樣的應用的設備例如:冷的變形、切割,固化,煞車皮和推力板, 壓力軸承拉出器。這些水壓機可以為其他適合他們是需要的機械的應用按提取強迫要求作用。
液壓機描述
水壓機車間HPH-075從被關閉的立場組成框架(固定的上面橫斷專欄、可調(diào)整的底部橫斷,基本的板材) 可移動的,在具有雙重作用的HCHD-075.150的液壓缸上安裝的一橫截支架,被設置的板材,按螺栓和螺母, (Fig.3)。
Fig.3.–液壓機75[tf]
1基本盤; 2專欄;3底部橫斷;4液壓缸HCHD-075.125;
5上部橫斷; 6壓力螺栓; 7壓力板材。
表3
液壓機特點
力[tf]
70
沖程[mm]
150
壓力[bar]
700
在直接應用這之中水壓機該當提醒:脫套和齒輪制帽工人從工具箱的傳動軸; 從攻擊小齒輪末端的緊迫和制帽滾珠軸承從逐漸變細的小組; 從被阻塞的子集的按和提取; 各種各樣的證明樣品的冷的變形。
優(yōu)點
液壓機具有?;瘶嬙?,可移動,并且有下等橫斷的一個被標注的解決系統(tǒng),在各種各樣的75 [mm]的范圍的確定高度。鍛壓橫向支架代表液壓缸位置的一個容易的解決系統(tǒng)因而允許緊迫的軌章程; 液壓機有實現(xiàn)所有技術操作的板材設置,螺栓和緊迫螺母;
從這個項目結果,因為減少的重量的作用它是容易運載,在它的重量和達到的力量之間的一個優(yōu)選的報告由于行動對最大值達到700吧。
2.3 液壓工具
在機械加工和維修的過程中使用的工具是多種多樣的,許過應用在機械工程里。那些在液壓工具之中被提到的:彎曲管道的設備和切割的液壓設備。
·彎曲的管子的設備描述
彎曲的模板,固定在液壓缸的代理標尺和有適當?shù)拇璩?,因此用管道輸送維度并且變化射線,它將行動在跟隨被變形的管子; 在休息的二條輪渡的管子指南,固定在設備板材之間。它可能降低允許模板介紹和剩余裝置的優(yōu)越板材(Fig.5)的渡輪。
彎曲管子類型設備HDIT.M 020.300是液壓驅(qū)動的設備,并且它注定在維護的并且修理區(qū)段的設施管子寒冷時彎曲。
表 4
彎管的設備特點描述[1]
過載[tf]
200
沖程[mm]
60
管直徑
2”-4”
壓力[bar]
700
圖5 –彎管設備[1]
1三腳架; 2固定板材; 3轉(zhuǎn)板; 4螺栓;
5 HCHD-020.300,6型液壓缸
表 5
HDIT.M-020.300型彎管設備的工作特點[1]
管的彎曲
外徑
[toli/mm]
3/8’
[17]
1/2’’
[21,25]
3/4’’
3/4’’
[26,4]
1’’
[33,5]
1’’1/4
[42,25]
1’’1/2
[48,25]
2’’
[60]
壁厚
[mm]
2,75
3,25
3,5
4
4
4,25
4,5
形式
曲率半徑
[mm]
50
64
90
120
150
200
235
最大彎曲角度
[grad]
120
指導數(shù)
2支 , 普遍的
·切割20[tf]的力的液壓設備的描述
設備有一個金屬體,通過被焊接的構造實現(xiàn),這個構造就是簡型HCHS-020.028液壓缸。一個可以一個可以移動的刀具和液壓桿和一個固定的刀體裝在一起,(如圖6).
實行操作的液壓缸通過與一個高壓源(HPHP-700的人工泵或液壓腳蹬泵),通過一個快速的聯(lián)結和液壓的靈活的管子。
半成品位于兩把刀具之間,而切割刀和柜臺刀建立從鋼的半成品中除去,它安裝在二把刀子之間的半成品,而切刀和柜臺刀子建立扣除從鋼的半成品。它在春天之前體會被合并到圓筒里切刀的退休。切開HFMO-020.028水力設備是一個水力推進設備,用于生產(chǎn)的過程和維護有切口看法在鋼圓,方形,六角和的扁桿的寒冷??梢苿拥牡蹲颖寂苁?8 [mm]和最大壓力700 [吧], [1]。
圖6-切割20[tf]的力的液壓設備
1-金屬體;2-移動刀;3-固定刀;4-用壓力油的油口。
表 6
HFMO-020.028型切割型號的液壓設備的工作特點。[1]
·優(yōu)點
在這些液壓設備的優(yōu)點中有一些重要的值得去注意:緊密的結構;簡單的操作和減少的重量;它可以除去工人無用的勞作;降低了時間過程。
壓力驅(qū)動的微型液壓系統(tǒng)的縮放行為
摘要
本文提出了一種對微型液壓系統(tǒng)的成型與設計的一種混合網(wǎng)狀方法。被修造了的包括水力電阻器、容積和交換器(壓力控制閥)的一臺液壓振蕩器。包括線性電阻器、容積和的微水力網(wǎng)絡結垢被學習了。一個重要結果是使更小的網(wǎng)絡更加快速的那,推進壓力應該增加與減少大小。
1介紹
微型液壓系統(tǒng)建模這種假設和設計,可以使用一個廣義的物理系統(tǒng)的描述[1,2]。這種方法是基于一種假設,這種假設就是它可能分開和集中系統(tǒng)的部分進入相互聯(lián)系的子系統(tǒng),它已證明了其在電路設計中的電路設計中的大的價值。泵的網(wǎng)狀方法的液壓系統(tǒng)[3-5]給微流體系統(tǒng)的功能強大的設計工具。為了說明不同
物理領域的深遠的比喻,我們已在液壓領域建立了一個電子無穩(wěn)態(tài)多諧網(wǎng)絡[4].
液壓系統(tǒng)由容器,阻抗器,(寄生)卷組成?;谖⑿鸵簤合到y(tǒng)的低重(雷諾數(shù))的液壓系統(tǒng)進行分析。
2液壓原理
在每個物理領域被保存的數(shù)量q可以被區(qū)分的[1]。流速在子系統(tǒng)之間保存的數(shù)量交換率。在液壓領域流程可變物是容量流。 作用是處理被保存的數(shù)量交換在子系統(tǒng)之間的緊張。在液壓領域作用可變物是壓力p [Pa]。
2.1液壓阻抗器
液壓阻抗是對液體流動的限制,象征性地在表示在fig.1a中,因為線性流阻,阻力R定義為:
那里p12=p1–p2是橫跨阻抗器的降壓,和 容量流經(jīng)阻抗器。在充足低關于在輸送管的流程是層流和充分發(fā)展的(流程),并且橫跨輸送管的降壓p與體積流率成比例。對于任意橫剖面輸送管給抵抗[6] :
這里f是扇面摩擦因子, L是渠道的長度、μ是液體的黏度, Dh水力直徑和A是橫截面面積。為層流充分發(fā)展的流程產(chǎn)品f*Re=k,一個無維的僅常數(shù)根據(jù)橫剖面的形狀。我們對非均質(zhì)性的酸值蝕刻測試了,體會入渠道和結束由玻璃簿塊正極接合的在硅上的水力阻抗器。Fig.1b-d展示一張側視圖、被使用的一個橫剖面和一張頂視圖。
圖1 :水力阻抗器.a)象征性的代表b)受制約的邊角度c)橫剖面d)頂視圖。
對于與2w的頂面寬度的這些三角渠道的阻抗:
分析確定了線性體的極限并且為液體[7]實驗性地被核實了。 入口和出口作用導致了在 p12和之間的非線性聯(lián)系。如果渠道是長的與水力入口長度比較,它們可以被忽略。由于低雷諾數(shù),入口長度Lhy隨著雷諾數(shù)線性地增加。帶有直徑d的圓形渠道可以被[6]表達:
2.2液壓容器
液壓容器完全是壓力區(qū)別可以被維護的一個彈性膜。在fig.2a中容器象征性地代表建立在降壓橫跨面和被偏移的容量之間的聯(lián)系。對于一臺線性電容器電容C可以被定義:
這里V是被偏移的液體的容量通過的彎曲膜。由于容量v由容量流的儲積造成, (5)是被重寫并發(fā)現(xiàn)在作用和流程之間的聯(lián)系:
圖2 :在玻璃硅玻璃技術下的電容器的水力電容器a)象征b)橫剖面,顯示膜的偏折在壓力區(qū)別的影響之下。
Fig.2b顯示了在玻璃硅玻璃夾心中的電容器的一個橫剖面。對于偏折小于膜的厚度有在應用的壓力區(qū)別和膜偏折之間的一個線性關系。在這種情況下電容的一個簡單表達式可以獲得:
那里a膜的半徑和D是膜的彎曲堅硬,定義由, E [Pa]是典型、ν 的比率和h [m]膜的厚度。
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