机械设计外文翻译-凸轮机构的优化方法【中文2029字】【PDF+中文WORD】
机械设计外文翻译-凸轮机构的优化方法【中文2029字】【PDF+中文WORD】,中文2029字,PDF+中文WORD,机械设计,外文,翻译,凸轮,机构,优化,方法,中文,2029,PDF,WORD
【中文2029字】
凸轮机构的优化方法
摘要：在本文中,我们介绍了优化凸轮机构基础的标准，我们也进行了几种类型的机构的计算。我们研究在简单的机械结构参数对于旋转凸轮和从动件（平面或曲线）平移的曲率半径的影响和对传动角的影响。之后，我们提出了凸轮和平面旋转从动件机构的优化计算，以及有圆形槽帮助的从动件凸轮机构的优化计算。为了更容易解释结果，我们根据AutoCAD中所产生的计算程序的脚本文件得到了凸轮的可视化。
关键字：凸轮，曲率半径，结构参数，压力角，圆形小树林
1. 优化标准
长期优化这个词来自于拉丁语——擎天柱，这是最高级的，这意味着最好的，非常好，正确的表示，合适等。据罗马尼亚语言词典解释，通过对优化的了解——技术——总体的科学研究（论文），这是最好的寻找一个解决问题办法的选择，或者根据另一个定义，在过程中不断改进，直到找到最好的解决方案。
在数学上，通过优化已知的理解，微积分允许找到一个或多个参数的值所相对应的最大的一个函数。
对于一个凸轮机构，优化准则之一是曲率半径的标准，根据这个标准，该从动件是平的或者有正曲率半径的凸轮的曲率半径一定是正的甚至高于规定值。
另一个必须被考虑到的标准是压力角（用α表示），压力角必须满足的条件是当是压力角在加大，的时候，压力角在减小。
2. 简单的平移从动件的凸轮机构优化
这样一个平底从动件（图1），凸轮的参数坐标如下：
图1：一个旋转凸轮和平底从动件的机构
从1式得
也推演得到了曲率半径的表达式：
例如，如果位移定律是：
然后曲率半径是：
最小，由下式给出：
在这种情况下，对于，最小的曲率半径变成无效的，凸轮的形状如图2a，当，曲率半径取消的地方为（图2b）对于有负值，凸轮变成非功能性的。
如果我们用平底从动件在这些条件下，可以得到技术功能的凸轮。
图2：带有无效或者负的曲率半径的非功能性凸轮
让我们考虑在一般情况下，平的从动件在顶部处曲率半径是负的确定半径为r的圆形从动件，从而是凸轮变得实用。
这个从动件的槽的方程（图3）：
从等式中得到：
推导曲率族的方程为：
取决于参数
图3.凸轮旋转和平面旋转从动件的机构
方程的包络检测方程：
转化为：
由式子（10）得到凸轮的方程，检验方程（12），在顶部满足条件
得到曲率半径为：
已知
得到：
接下来，因为已知
从方程（16）和给予的条件得到：
3. 转动从动件机构的优化
对于初学者，认为一个具有长度扁平的从动件的机构如图3，位移的规律为：
从方程：
可以得到凸轮的方程：
这里：
图4：旋转凸轮和平面旋转从动件机构
用参数表示切点到点之间的距离，压力角的关系作为结果由下式得出：
曲率半径为：
压力角a取决于从尺寸和d的角的振幅。
数值分析是由表格与步骤通过计算有限的差异衍生物组值R + b和d得到Dj =。
位移规律是：
根据方程(19)÷(24)得到一个计算程序在帕斯卡。这适用于不同的值。
首先解释更容易得到的结果，在凸轮可视化方面非常有用，从而得到不同的参数。
这种可视化是在AutoCAD中，计算程序使用一个脚本文件所产生的。
在图5中表示的情况下所获得的凸轮。
在d=40和d=60这个情况时，可以看到，所获得的凸轮不起作用，有些地方有负曲率半径。
在d=20这个情况下，凸轮技术上是无用的，尽管它有连续的形态，在j=60°和j=240°被注意到有凹陷，扁平的从动件不能连续的在凸轮槽的外部轮廓上运动。
从压力角的角度来看，它是确定的，在升降过程中，对于来讲
图5：在b=5的情况下所得到的凸轮
在R0=10，b=5，d=20时，虽然它得到的凸轮技术上讲是无功能的，但是，通过保持相同的尺寸，通过使用一个圆形槽从动件可以获得一种解决方案使得在技术上有功能（图6）。
图6：旋转凸轮和圆形旋转机构
所以得出：
——从动件的方程：
——一般方程：
推导得到方程：
——抓的条件是：
——凸轮的方程：
其中是从方程中推导得到的
——压力角等于：
在给出了前面的值的情况下在数值上凸轮在技术上不起作用，有着更多的考虑
接着表示在不同情况下的凸轮取得的机构和不同曲率半径的曲线的从动件。
图7表示的是在R0=10，b=5，d=20的情况下，光灰色的凸轮是平扁的从动件所得到的，黑色的凸轮是曲率半径为r=100，50，30，10的曲面从动件所得到的。
图7：b=5，d=20情况下所得到的凸轮
对于有着平的从动件的机构（浅灰色凸轮），凸轮是没有功能性的。在所有的4例曲线从动件所得到的凸轮是功能的，在压力角满足条件，在速度的提升和速度的降低中。可以观察到，通过降低从动件的曲率半径是为了得到一个有着更大的最小曲率半径的凸轮。
4. 结论
在本文中介绍了两种优化准则：标准的最小施加的曲率半径和压力角的标准。
本文是研究结构参数对于曲率半径的影响和在计算程序帮助下的压力角。
为了更加容易的解释结果，所得的凸轮是考虑到不同的参数的可视化。这个可视化是在AutoCAD中，计算程序使用一个脚本文件所产生的。
对于优化的凸轮机构与一个圆形沟槽从动件，在保持相同的机构上的措施，得到了在技术上具有功能性的凸轮。
它研究了第三个参数的影响：圆形从动件的半径。
它被认为是有用的在叠加所得到的凸轮带有平的从动件和带有不同曲率半径的圆形从动件。
作者：Claudia–Mari Popa , Dinel Popa
国籍：美国
出处：ANALELE UNIVERSITĂłII“EFTIMIE MURGU” RESIłA 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_
收藏