機(jī)械設(shè)計(jì)外文翻譯-凸輪機(jī)構(gòu)的優(yōu)化方法【中文2029字】【PDF+中文WORD】
機(jī)械設(shè)計(jì)外文翻譯-凸輪機(jī)構(gòu)的優(yōu)化方法【中文2029字】【PDF+中文WORD】,中文2029字,PDF+中文WORD,機(jī)械設(shè)計(jì),外文,翻譯,凸輪,機(jī)構(gòu),優(yōu)化,方法,中文,2029,PDF,WORD
【中文2029字】
凸輪機(jī)構(gòu)的優(yōu)化方法
摘要：在本文中,我們介紹了優(yōu)化凸輪機(jī)構(gòu)基礎(chǔ)的標(biāo)準(zhǔn)，我們也進(jìn)行了幾種類型的機(jī)構(gòu)的計(jì)算。我們研究在簡(jiǎn)單的機(jī)械結(jié)構(gòu)參數(shù)對(duì)于旋轉(zhuǎn)凸輪和從動(dòng)件（平面或曲線）平移的曲率半徑的影響和對(duì)傳動(dòng)角的影響。之后，我們提出了凸輪和平面旋轉(zhuǎn)從動(dòng)件機(jī)構(gòu)的優(yōu)化計(jì)算，以及有圓形槽幫助的從動(dòng)件凸輪機(jī)構(gòu)的優(yōu)化計(jì)算。為了更容易解釋結(jié)果，我們根據(jù)AutoCAD中所產(chǎn)生的計(jì)算程序的腳本文件得到了凸輪的可視化。
關(guān)鍵字：凸輪，曲率半徑，結(jié)構(gòu)參數(shù)，壓力角，圓形小樹林
1. 優(yōu)化標(biāo)準(zhǔn)
長(zhǎng)期優(yōu)化這個(gè)詞來自于拉丁語(yǔ)——擎天柱，這是最高級(jí)的，這意味著最好的，非常好，正確的表示，合適等。據(jù)羅馬尼亞語(yǔ)言詞典解釋，通過對(duì)優(yōu)化的了解——技術(shù)——總體的科學(xué)研究（論文），這是最好的尋找一個(gè)解決問題辦法的選擇，或者根據(jù)另一個(gè)定義，在過程中不斷改進(jìn)，直到找到最好的解決方案。
在數(shù)學(xué)上，通過優(yōu)化已知的理解，微積分允許找到一個(gè)或多個(gè)參數(shù)的值所相對(duì)應(yīng)的最大的一個(gè)函數(shù)。
對(duì)于一個(gè)凸輪機(jī)構(gòu)，優(yōu)化準(zhǔn)則之一是曲率半徑的標(biāo)準(zhǔn)，根據(jù)這個(gè)標(biāo)準(zhǔn)，該從動(dòng)件是平的或者有正曲率半徑的凸輪的曲率半徑一定是正的甚至高于規(guī)定值。
另一個(gè)必須被考慮到的標(biāo)準(zhǔn)是壓力角（用α表示），壓力角必須滿足的條件是當(dāng)是壓力角在加大，的時(shí)候，壓力角在減小。
2. 簡(jiǎn)單的平移從動(dòng)件的凸輪機(jī)構(gòu)優(yōu)化
這樣一個(gè)平底從動(dòng)件（圖1），凸輪的參數(shù)坐標(biāo)如下：
圖1：一個(gè)旋轉(zhuǎn)凸輪和平底從動(dòng)件的機(jī)構(gòu)
從1式得
也推演得到了曲率半徑的表達(dá)式：
例如，如果位移定律是：
然后曲率半徑是：
最小，由下式給出：
在這種情況下，對(duì)于，最小的曲率半徑變成無效的，凸輪的形狀如圖2a，當(dāng)，曲率半徑取消的地方為（圖2b）對(duì)于有負(fù)值，凸輪變成非功能性的。
如果我們用平底從動(dòng)件在這些條件下，可以得到技術(shù)功能的凸輪。
圖2：帶有無效或者負(fù)的曲率半徑的非功能性凸輪
讓我們考慮在一般情況下，平的從動(dòng)件在頂部處曲率半徑是負(fù)的確定半徑為r的圓形從動(dòng)件，從而是凸輪變得實(shí)用。
這個(gè)從動(dòng)件的槽的方程（圖3）：
從等式中得到：
推導(dǎo)曲率族的方程為：
取決于參數(shù)
圖3.凸輪旋轉(zhuǎn)和平面旋轉(zhuǎn)從動(dòng)件的機(jī)構(gòu)
方程的包絡(luò)檢測(cè)方程：
轉(zhuǎn)化為：
由式子（10）得到凸輪的方程，檢驗(yàn)方程（12），在頂部滿足條件
得到曲率半徑為：
已知
得到：
接下來，因?yàn)橐阎?
從方程（16）和給予的條件得到：
3. 轉(zhuǎn)動(dòng)從動(dòng)件機(jī)構(gòu)的優(yōu)化
對(duì)于初學(xué)者，認(rèn)為一個(gè)具有長(zhǎng)度扁平的從動(dòng)件的機(jī)構(gòu)如圖3，位移的規(guī)律為：
從方程：
可以得到凸輪的方程：
這里：
圖4：旋轉(zhuǎn)凸輪和平面旋轉(zhuǎn)從動(dòng)件機(jī)構(gòu)
用參數(shù)表示切點(diǎn)到點(diǎn)之間的距離，壓力角的關(guān)系作為結(jié)果由下式得出：
曲率半徑為：
壓力角a取決于從尺寸和d的角的振幅。
數(shù)值分析是由表格與步驟通過計(jì)算有限的差異衍生物組值R + b和d得到Dj =。
位移規(guī)律是：
根據(jù)方程(19)÷(24)得到一個(gè)計(jì)算程序在帕斯卡。這適用于不同的值。
首先解釋更容易得到的結(jié)果，在凸輪可視化方面非常有用，從而得到不同的參數(shù)。
這種可視化是在AutoCAD中，計(jì)算程序使用一個(gè)腳本文件所產(chǎn)生的。
在圖5中表示的情況下所獲得的凸輪。
在d=40和d=60這個(gè)情況時(shí)，可以看到，所獲得的凸輪不起作用，有些地方有負(fù)曲率半徑。
在d=20這個(gè)情況下，凸輪技術(shù)上是無用的，盡管它有連續(xù)的形態(tài)，在j=60°和j=240°被注意到有凹陷，扁平的從動(dòng)件不能連續(xù)的在凸輪槽的外部輪廓上運(yùn)動(dòng)。
從壓力角的角度來看，它是確定的，在升降過程中，對(duì)于來講
圖5：在b=5的情況下所得到的凸輪
在R0=10，b=5，d=20時(shí)，雖然它得到的凸輪技術(shù)上講是無功能的，但是，通過保持相同的尺寸，通過使用一個(gè)圓形槽從動(dòng)件可以獲得一種解決方案使得在技術(shù)上有功能（圖6）。
圖6：旋轉(zhuǎn)凸輪和圓形旋轉(zhuǎn)機(jī)構(gòu)
所以得出：
——從動(dòng)件的方程：
——一般方程：
推導(dǎo)得到方程：
——抓的條件是：
——凸輪的方程：
其中是從方程中推導(dǎo)得到的
——壓力角等于：
在給出了前面的值的情況下在數(shù)值上凸輪在技術(shù)上不起作用，有著更多的考慮
接著表示在不同情況下的凸輪取得的機(jī)構(gòu)和不同曲率半徑的曲線的從動(dòng)件。
圖7表示的是在R0=10，b=5，d=20的情況下，光灰色的凸輪是平扁的從動(dòng)件所得到的，黑色的凸輪是曲率半徑為r=100，50，30，10的曲面從動(dòng)件所得到的。
圖7：b=5，d=20情況下所得到的凸輪
對(duì)于有著平的從動(dòng)件的機(jī)構(gòu)（淺灰色凸輪），凸輪是沒有功能性的。在所有的4例曲線從動(dòng)件所得到的凸輪是功能的，在壓力角滿足條件，在速度的提升和速度的降低中。可以觀察到，通過降低從動(dòng)件的曲率半徑是為了得到一個(gè)有著更大的最小曲率半徑的凸輪。
4. 結(jié)論
在本文中介紹了兩種優(yōu)化準(zhǔn)則：標(biāo)準(zhǔn)的最小施加的曲率半徑和壓力角的標(biāo)準(zhǔn)。
本文是研究結(jié)構(gòu)參數(shù)對(duì)于曲率半徑的影響和在計(jì)算程序幫助下的壓力角。
為了更加容易的解釋結(jié)果，所得的凸輪是考慮到不同的參數(shù)的可視化。這個(gè)可視化是在AutoCAD中，計(jì)算程序使用一個(gè)腳本文件所產(chǎn)生的。
對(duì)于優(yōu)化的凸輪機(jī)構(gòu)與一個(gè)圓形溝槽從動(dòng)件，在保持相同的機(jī)構(gòu)上的措施，得到了在技術(shù)上具有功能性的凸輪。
它研究了第三個(gè)參數(shù)的影響：圓形從動(dòng)件的半徑。
它被認(rèn)為是有用的在疊加所得到的凸輪帶有平的從動(dòng)件和帶有不同曲率半徑的圓形從動(dòng)件。
作者：Claudia–Mari Popa , Dinel Popa
國(guó)籍：美國(guó)
出處：ANALELE UNIVERSIT??II“EFTIMIE MURGU” RESI?A Fascicula de Inginerie
65 Claudia Mari Popa,Dinel Popa Optimisation Methods for Cam Mechanisms Abstract.In this paper we present the criteria which represent the base of optimizing the cam mechanisms and also we perform the calculations for several types of mechanisms.We study the influence of the constructive parameters in case of the simple machines with rotation cam and follower(flat or curve)of translation on the curvature radius and that of the transmission angle.As it follows,we present the optimization calculations of the cam and flat rotation follower mechanisms,as well as the calculations for optimizing the cam mechanisms by circular groove followers help.For an easier interpretation of the results,we have visualized the obtained cam in AutoCAD according to the script files generated by a calculation program.Keywords:cam,curvature radius,constructive parameters,pressure angle,circular grove.1.Optimisation criteria The term of optimization comes from the Latin word optimus,which is the su-perlative of good,which means the best,very good,properly indicated,suited etc.According to Explaining Dictionary of Romanian Language,by optimization is under-stood technically the ensemble of scientific research(papers)that is looking for the best option in finding a solution for a problem or,according to another definition,the process of constant improving until the best solution it is reached.Mathematically,by optimization is understood the reasoning,the calculus permits in finding values of one or more parameters which correspond to the maximum of a function.In the case of a cam mechanism,one of the optimization criteria is the criteria of the curvature radius,according to that,the curvature radius of the cam in the case of a follower which is flat or has a positive curvature radius must be positive and even higher then an imposed value.ANALELE UNIVERSITII “EFTIMIE MURGU”REIA ANUL XVII,NR.1,2010,ISSN 1453-7397 66 Another criteria that must be taken into account is that of the pressure angle(noted with)which must fulfill the condition cr,where 030=cr at in-creasing and 060 at decreasing.On the basis of this two criteria will be obtained better condition for the com-plex cam mechanisms to function.Next we will define as a technically functional cam the cam that is obtained by classic procedures of processing of a tool machine,having the curvature radius positive and that respects the condition of the critical pressure angle(cr).2.The optimisation of simple cam mechanisms with transla-tion follower There is considered the case of a flat follower(fig.1),case where the para-metrical coordinates of the cam are:,sincos)(;cossin)(00ssRyssRx+=+=(1)and .2sAO=(2)xOA2OYysRX0 Figure 1.Mechanism with rotation cam and flat translation follower.From(1)are deducted:;sin)(;cos)(00ssRyssRx+=+=(3),cos)(sin)(;sin)(cos)(00ssRssyssRssx+=+=(4)and its also deducted the expression of the curvature radius:67|)()(2/322yxyxyxRc+=;0ssRRc+=.(5)If,for example,the displacement law is:)2cos1(0=hs.(6)Then the curvature radius is 2cos3000hhRRc+=(7)and becomes minimum for 2=when is given by:00min2hRRc=.(8)In this case,for hR20=the minimum curvature radius becomes null and the cam has the shape from figure 2,a,and if 002hR the curvature radius is canceled in the points where 2;2(fig.2,b)and have negative value for 2 and the cam becomes nonfunctional.If we use flat follower in these conditions we can obtain cams technically functional.yxyx Figure 2.Nonfunctional cams with null or negative curvature radius.Let us consider the general case where the curvature radius at the top in the case of a flat follower becomes negative 0)(max0+ssR and to determine the radius r of the circular follower so that the cam will be functionally.The equations of the followers groove(fig.3)are ,cos;sin22ryrx=(8)and from the equalities:68 ,coscossin;sinsincos0rsrRyxyryxxAA+=(9)are deducted the equations of the curvature family ),()cos(cos)();,()sin(sin)(210frsrRyfrsrRx=+=+=;(10)that depends on the parameters,.OxAr220vA2R +r+syXyxY Figure 3.Mechanism with rotation cam and flat rotation follower.The equation of the envelope checks the equation:02211=ffff,(11)that becomes srRs+=0 tg.(12)The cam equations are given by the relations(10)where checks the equa-tion(12).In the top(2=)are fulfilled the conditions ;0;0;0;max=ssss 69 ;0;Rsmax0=+=sr(13)(1();(;0max0max0rsRxrsRyx+=+=and the curvature radius is|1|)(|)()(max232/322+=+=rsRxyyxyyxyxyxRc.(14)Knowing that 0max0+=srRs,(15)is deducted )1)()()(max0max02max0+=srRssRrsRRc.(16)And next,by knowing that 01;0maxcR is obtained:)(max02max0ssRsRr+.(18)3.The optimisation of mechanisms with rotation follower For the starters,is considered the mechanism with a flat follower from figure 3 that has the lengths bRd,0 and the displacement rule:)(22=.(19)From the equations:,sincossin;cossincos202+=+=+=bRyxydyxx(20)are obtained the equations of the cam:),cos()sin(cos)(sin);sin()cos(sin)(cos220220+=+=bbRdybbRdx(21)where 1sin)(cos2202+=bRd.(22)70 bxO22Oy1O2xR01X22yY Figure 4.Mechanism with rotation cam and flat rotation follower.The parameter represents the distance from the tangent point until the point 2O and as a result the pressure angle is given by the relation:=b arctg.(23)The curvature radius|)()(2322yxyxyxRc+=(24)and the pressure angle depends of the amplitude 02 of angle 2 as from the dimensions bR+0 and d.The numerical analyze is made tabular with the step 01=calculation the derivates by limited differences with sets of values for bR+and d.Is considered the displacement rule:)2cos1(202=;2sin102=.(25)On the basis of the relations(19)(24)is made a calculation program in Pascal.This works for different sets of values.To begin interpreting much easier the obtained results it is useful in visualizing the cam that is obtained with the varying parameters.This visualization is made in AutoCAD,based on a script file generated by the calculation program.In figure 5 is represented the cam obtained in the case 100=R,5=b.It is observed that in the cases where 60=d and 40=d that the obtained cams are nonfunctional and have negative curvature radius on some parts.71 In the case where 20=d the cam is technically nonfunctional although it has a continuous aspect,at=60 and=240 are noticed holes,the flat follower cannot continuing the external contour of the cams groove.From the point of view of the pressure angle it is ok,at the lifting maneuver=21.746max for=120.R0=10;b=5;d=20yxR0=10;b=5;d=60yxR0=10;b=5;d=10yxR0=10;b=5;d=40yx Figure 5.The cams obtained in the case b=5.In the case where 100=R,5=b and 20=d though it was obtained a cam technically nonfunctional,but by keeping the same dimensions can be obtained a solution technically functional by using the follower with a circular groove(fig.6).72 rb1xR02OO1y2xXdy22Y Figure 6.Mechanism with rotation cam and circularly rotation.So are obtained:-the equations of the follower sin2rdx+=;cos22ryyo=;(26)-the general equations ,cossincossin;sincossincos2222202222yxyrRyxyyxdyxxo+=+=+=(27)which are deducted the equations:);cos()sin(cos)(sin);sin()cos(sin)(cos2222020222220+=+=yxyrRdyyxyrRdxo(28)-the grabbing condition is:)1(cos)(sin)1(sin)(cos202202222022+=yyrRddyrRdtg,(29)-the equation of the cam ),cos()cos()sin(cos)(sin);sin()sin()cos(sin)(cos2202202022022020+=+=rydyrRdyrydyrRdx(30)where is deducted from the equation(29)-the pressure angle is:73 +=sincosarctg02rdry.(31)In the numerical case are given the values considered in the previous case of cam technically nonfunctional and there more is considered bry02.Next is represented for different cases the cam obtained in the case of a mechanism with curve follower and different curvature radius.In figure 7 it was represented for the case100=R,5=b,20=d,with light grey the cam obtained in the case of a mechanism with flat follower and with black the cab obtained in the case of a curve follower with the curvature radius of the follower of:10,30,50,100=r.R0=10;b=5;d=20r=30yxr=100yxr=10yxr=50yx Figure 7.The cams obtained in the case b=5 and d=20.In the case of the mechanism with a flat follower(the light grey cam)there is no functional cam.In all the four cases of curve follower the obtained cam is func-tional,the pressure angle fulfilling the condition cr as both for the lifting race and for the descend race.There is observed that by lowering the curvature radius of the follower is obtained a cam with a bigger minimum curvature radius 74 4.Conclusions In this paper are presented two major optimization criteria:the criteria of the minimum imposed curvature radius and the criteria of the pressure angle.It is studied the influence of constructive parameters over the curvature radius and the pressure angle with the help of a calculation program.For an easier interpretation of the results,the obtained cam was visualized considering the parameters that vary.This visualization is made in AutoCAD,using a script file generated by a calculation program.In the case of optimizing the cam mechanism with a circular grooved follower,keeping the same constructive measures,were obtained technically functional cams.It was studied the influence of a third parameter:the radius of the circular follower.It was considered useful in overlaying the obtained cams with flat follower with the cams with a circular follower with different curvature radius of the follower.References 1 Dudi,Fl.and Diaconescu,D.,Optimizarea structural a mecanis-melor,Technical Publishing House,Bucharest,1987.2 Notash,L.,Fenton,R.G.,Mills,IK.,Optimal design of flexible cam mechanisms,Eighth world congress on the theory of machines and mechanisms,pg.695-698,Prague,Czechoslovakia,1991.3 Pandrea,N.,Popa,D.,Mecanisme.Teorie i aplicaii CAD,Technical Publishing House,Bucharest,2000.Addresses:Prof.Dr.Eng.Claudia Mari Popa,Grup colar“Armand Clinescu”,Pitesti,Str.I.C.Brtianu,nr.44,Piteti,claudia_mari_ Prof.Dr.Eng.Dinel Popa,University of Piteti,Str.Trgul din Vale,nr.1,Piteti,dinel_
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