機(jī)制畢業(yè)設(shè)計(jì)---偏心旋轉(zhuǎn)- 擺動式凸輪機(jī)構(gòu)設(shè)計(jì)

1、<p>　　附錄二 外文資料翻譯</p><p><b>　　外文原文：</b></p><p>　　Design of Eccentric Rotating-swinging Cam Mechanism</p><p>　　Abstract： The cam profile curve of an eccentric rotati

2、ng-swinging cam mechanism is designed by using polar coordinate vector method. Firstly, the components of the mechanism are represented by polar coordinate vectors, then, the motion law of the slave roller of the cam is

3、deduced from the motion law of the follower step by step according to the vector graph of the cam mechanism; lastly, the actual cam profile curve is figured out by the motion law of the slave roller. This method has the

4、proper</p><p>　　Key words: Cam mechanism; Polar coordinate vector ； Motion analysis ; Profile curve</p><p>　　0 Introduction</p><p>　　In practice, many of the automated mechanical sy

5、stems, often using the convex wheel and connecting rod body composed of a combination of actions to achieve specific motion components requirements. In the combination mechanism, by design a specific cam profile curve to

6、 control the movement of the body machine, which are driven by the follower to get motion laws. During the design of cam profile curve, the first need is that according to the actual movement of follower requirements in

7、order to kno</p><p><b>　　Fig.1</b></p><p>　　Among them, the exact cam profile, high-efficiency analysis and solution of a cam machine is the core task of the design structure. We use

8、 polar coordinate vectors of a typical eccentric rotation - swinging cam mechanism into the contour curve design calculations. Figure 1 is an eccentric rotation - swing cam. Under the drive of the original motivation ca

9、m 1, cam2 and crank 8 has the constant speed rotation, they speed the same in the opposite direction. Rotation of cam 1, cam 4 push the pendul</p><p>　　1 　 Cam Mechanism Motion Analysis</p><p>　

10、　The analysis of planar linkage movement is usually based on the known components of the movement rule to deduce the other components on the motion law of a point, vector-dimensional kinematic analysis of the common meth

11、od. Motion vector analysis theory is based on vector polygons of mechanism set up, using the known vector and support vector to establish a closed triangle, according to the establishment of vector equation and solve for

12、 the unknown vector, so in turn the vector from the known to </p><p>　　Altogether has 6 parameters in this equation set (a, b, c, ), if has 4 parameters for known, then may extract other 2 parameters. Menstr

13、uation carries on when the movement analysis using arrow the must first establish the organization the vector chart, establishes this organization according to the chart 1 in organization diagram vector chart as shown in

14、 Figure 2. Because was vector already extracted from the moving parts law of motion, therefore, the movement analyzed is by starts from the movi</p><p><b>　　Fig.2</b></p><p>　　As a r

15、esult of crank by constant angular speed uniform speed rotation, therefore known. Had determined from the moving parts law of motion, is also known

16、 </p><p>　　Obtain and the solid company in the same place, therefore may obtain </p><p>　　by in the form

17、ula, is between and thefixed included angle. may obtain ，and the adding together is</p><p><b>　　That is </b></p><p>　　In the formula, is the known quantity, may calculate results in

18、. may obtain, and together is </p><p><b>　　That is</b></p><p>　　Because and fix on the rack, therefore, , are known; as a result of , known, may calculate obtains ,. Then obtain

19、and the adding together is</p><p>　　In the formula, is the known quantity, obtain, .Because and tied together, therefore may obtain by </p><p>　　by in the formula, is the angle between and fix

20、ed included angle.</p><p>　　The solution of cam profile</p><p>　　Adding and together to diameter may obtain the cam theoretical profile</p><p><b>　　That is</b></p&g

21、t;<p>　　In the formula, is the known quantity, may obtain, </p><p>　　The above computation obtains θ11 is opposite in fixed motionless coordinate system , when consideration cam rotation, if in the c

22、am rotates in one round-long process to take 360 equal time-gaps, namely 0, 1, 2…359, and supposes the 0th position to the diameter for the cam zero curve, then the angle of the position-i to the diameter relative zero c

23、urve is </p><p>　　In order to calculate the real profile of the cam, needs to establish the cam first actual between the outline and roller center relations as shown in Figure 3, according to Figure 3 vector

24、's geometry relations, the cam real profile diameter may obtain by the theoretical profile to diameter and roller's radius vector computation </p><p><b>　　Fig.3</b></p><p>　

25、　In the formula,,，is the known quantity, because the direction is vertical to the roller and cam real profile contact point position real profile tangent the direction, therefore, may extract the contact point cam real p

26、rofile the first tangent bearing.</p><p>　　According to the reverse principle of design, is presently fixed the cam, but other parts of organization0 circle the axis anti-clockwise rotation θ0 angle by the

27、angular speed, the rotation later may obtain</p><p><b>　　That is </b></p><p>　　may obtain the above equation left side to the time derivation L11θ0 along tangential increase vector δ

28、L11θ0 </p><p>　　In type (19), δLθ011 the yaw namely for the contact point cam real profile's tangent bearing, may obtain the equality right side imaginary component dividing real part </p><p&g

29、t;　　this time, the tangent yaw is</p><p>　　Then, the cam real profile's normal direction also will be</p><p>　　θ12 substitution type (16) might calculate to the angle obtains l13, θ13, will

30、thus obtain the cam real profile.</p><p><b>　　Fig.4</b></p><p>　　Extracts θ13 is opposite in the fixed motionless coordinate system, when tests ponders the cam the rotation, then the

31、 ith position cam to the diameter relative zero curve's position angle is</p><p>　　According to type (16) and type (23), the use assigns the organization design parameter, may calculate through the MATLA

32、B programming obtains master cam's real profile curve as shown in Figure 4. Uses between the auxiliary cam and master cam's conjugate relations may calculate obtains the auxiliary cam profile curve .</p>&

33、lt;p>　　conclusion</p><p>　　We used the polar coordinate vector method to realize one kind of biased revolving - to suspend to move the type cam gear the cam contour curve design calculation. Was opposite

34、in the graphic method, the polar coordinate vector method carried on the cam contour curve through the analysis method the solution, this method computation was precise, could complete has the compound movement from the

35、moving parts cam gear design. Along with the automatic device to the cam gear movement precision's enha</p><p><b>　　譯文：</b></p><p>　　偏心旋轉(zhuǎn)- 擺動式凸輪機(jī)構(gòu)設(shè)計(jì)</p><p>　　摘要 運(yùn)用極

36、坐標(biāo)矢量法對一種偏心旋轉(zhuǎn)—擺動式凸輪機(jī)構(gòu)的凸輪輪廓曲線進(jìn)行了設(shè)計(jì)計(jì)算。首先,將機(jī)構(gòu)中的構(gòu)件用極坐標(biāo)矢量來表示;然后,根據(jù)凸輪機(jī)構(gòu)的矢量圖,由從動件的運(yùn)動規(guī)律逐步推導(dǎo)出凸輪從動滾子的運(yùn)動規(guī)律;最后,由從動滾子的運(yùn)動規(guī)律求解出凸輪的實(shí)際輪廓。這種方法具有計(jì)算精確的特點(diǎn),能夠完成具有復(fù)雜運(yùn)動從動件的凸輪機(jī)構(gòu)的設(shè)計(jì)。</p><p>　　關(guān)鍵詞 凸輪機(jī)構(gòu) 極坐標(biāo)矢量 運(yùn)動分析 輪廓曲線</p><p&

37、gt;<b>　　0 引言</b></p><p>　　在實(shí)際應(yīng)用的許多自動機(jī)械系統(tǒng)中, 常常使用凸輪與連桿組成的組合機(jī)構(gòu)來實(shí)現(xiàn)動作部件的特定運(yùn)動要求。在組合機(jī)構(gòu)中, 通過設(shè)計(jì)出特定的凸輪輪廓曲線來對機(jī)構(gòu)的運(yùn)動進(jìn)行控制, 從而得到所需要的從動件運(yùn)動規(guī)律。在進(jìn)行凸輪輪廓曲線設(shè)計(jì)時, 首先需要根據(jù)從動件的實(shí)際運(yùn)動要求, 設(shè)計(jì)出從動件運(yùn)動規(guī)律的數(shù)學(xué)表達(dá)式;然后, 根據(jù)機(jī)構(gòu)的結(jié)構(gòu)參數(shù), 由從動件的運(yùn)

38、動規(guī)律推導(dǎo)出從動滾子的運(yùn)動規(guī)律;最后,根據(jù)凸輪從動滾子的運(yùn)動規(guī)律確定凸輪的實(shí)際輪廓 。其中,凸輪輪廓曲線的精確、高效率分析和求解是凸輪機(jī)構(gòu)設(shè)計(jì)中的核心任務(wù)。我們運(yùn)用極坐標(biāo)矢量法對一種典型的偏心旋轉(zhuǎn)—擺動式凸輪機(jī)構(gòu)的凸輪輪廓曲線進(jìn)行了設(shè)計(jì)計(jì)算。如圖1 所示是一個偏心旋轉(zhuǎn)—擺動式凸輪機(jī)構(gòu)。</p><p>　　在原動機(jī)的驅(qū)動下,凸輪1、2 與曲柄8的進(jìn)行恒速轉(zhuǎn)動, 他們轉(zhuǎn)速相同, 方向相反。凸輪1 的轉(zhuǎn)動推動擺桿4

39、的擺動,擺桿4 再通過連桿6帶動從動件擺臂7 的擺動。曲柄8 的旋轉(zhuǎn)帶動從動件擺臂7 的偏心旋轉(zhuǎn)。從而實(shí)現(xiàn)從動件擺臂在平面內(nèi)的復(fù)合運(yùn)動。擺臂的運(yùn)動過程由推程段、交接段、緩沖段、遠(yuǎn)休止段、回程段和近休止段組成。在推程段、緩沖段和回程段,從動件有加減速運(yùn)動,所以為這些階段選擇5 次多項(xiàng)式運(yùn)動規(guī)律;在交接段,從動件進(jìn)行恒速旋轉(zhuǎn), 這一階段的運(yùn)動方程為1 次多項(xiàng)式;在遠(yuǎn)休止段和近休止段,從動件保持靜止。將各個運(yùn)動階段的邊界條件代入運(yùn)動方程可計(jì)算

40、得到從動件運(yùn)動規(guī)律的數(shù)學(xué)表達(dá)式 。</p><p>　　1 凸輪機(jī)構(gòu)的運(yùn)動分析</p><p>　　平面連桿機(jī)構(gòu)的運(yùn)動分析通常是根據(jù)已知構(gòu)件的運(yùn)動規(guī)律來推導(dǎo)出其他構(gòu)件上某一點(diǎn)的運(yùn)動規(guī)律, 矢量法是平面機(jī)構(gòu)運(yùn)動分析的常用方法 。矢量法運(yùn)動分析的原理是根據(jù)機(jī)構(gòu)簡圖建立矢量多邊形, 利用已知的矢量和輔助矢量建立封閉的矢量三角形, 依其建立矢量方程并求解未知矢量, 這樣依次從已知的矢量到達(dá)最終的目

41、標(biāo)矢量, 從而實(shí)現(xiàn)機(jī)構(gòu)的運(yùn)動分析。矢量的復(fù)數(shù)極坐標(biāo)表示使得矢量的大小和方向能夠方便地表示成代數(shù)形式或指數(shù)形式, 這樣進(jìn)行矢量的各種運(yùn)算時非常方便。我們根據(jù)計(jì)算出的從動件運(yùn)動規(guī)律,利用矢量法推導(dǎo)出凸輪從動滾子中心的運(yùn)動規(guī)律,并進(jìn)一步計(jì)算得到凸輪的實(shí)際輪廓曲線。</p><p>　　在矢量的極坐標(biāo)表示法中, 極徑和極角用來表示復(fù)數(shù)矢量的模和方向角,矢量加法的一般形式為</p><p><

42、b>　　即</b></p><p>　　式中, a , b , c 為矢量的模,α,β,γ 為矢量的方向角。將上式用三角函數(shù)展開,可以得到下面的方程組</p><p>　　在該方程組中共有6 個參數(shù)( a , b , c ,α,β,γ) ,如果有4 個參數(shù)為已知,則可以求出另外2 個參數(shù)。運(yùn)用矢量法進(jìn)行運(yùn)動分析時首先要建立機(jī)構(gòu)的矢量圖,根據(jù)圖1 中的機(jī)構(gòu)簡圖建立該機(jī)構(gòu)的矢

43、量圖如圖2 所示。</p><p>　　由于從動件的運(yùn)動規(guī)律即矢量L2 已經(jīng)求出,因此,運(yùn)動分析是由從動件開始,逐步推導(dǎo)出凸輪的從動滾子中心的運(yùn)動軌跡,也就是凸輪的理論輪廓曲線,然后根據(jù)從動滾子中心的運(yùn)動規(guī)律確定凸輪的實(shí)際輪廓曲線。</p><p>　　由于曲柄以恒定的角速度勻速轉(zhuǎn)動, 所以L1 已知。從動件的運(yùn)動規(guī)律已確定,也就是L2 已知</p><p>　　并

44、且L3 與L2 固連在一起,所以就可以由L2得到L3</p><p>　　式中,φ 為L2 與L3之間的固定夾角。將L1與L3 相加可以得到</p><p><b>　　即</b></p><p>　　式中, l1 , l3 ,θ1 ,θ3 為已知量,可以計(jì)算得到l4 ,θ4 。將L4 與L5 相加可以得到</p><p&g

45、t;<b>　　即</b></p><p>　　由于O2 和O3 均固定在機(jī)架上,所以l5 ,θ5 已知;又由于l4 ,θ4 已知,可以計(jì)算得到l6 ,θ6 。將L6與L7相加可以得到</p><p><b>　　即</b></p><p>　　式中, l6 , l7 , l8 ,θ6 為已知量,可以計(jì)算得到θ7 ,θ8

46、。由于L9 與L8 固連在一起,所以就可以由L8 得到L9</p><p>　　式中,η為L8 與L9 之間的固定夾角。</p><p><b>　　2 凸輪輪廓的求解</b></p><p>　　將L9 與L10相加可以得到凸輪的理論輪廓向徑</p><p><b>　　即</b></p&g

47、t;<p>　　式中, l9 , l10 ,θ9 ,θ10為已知量,可以計(jì)算得到l11 ,θ11 。</p><p>　　為了計(jì)算凸輪的實(shí)際輪廓,需要先建立凸輪的實(shí)際輪廓與滾子中心之間的關(guān)系如圖3 所示,</p><p>　　根據(jù)圖3 中矢量之間的幾何關(guān)系,凸輪的實(shí)際輪廓向徑L13可以由理論輪廓向徑L11與滾子的半徑矢量L12計(jì)算得到</p><p>

48、　　式中, l11 , l12 ,θ11 為已知量, 由于L12的方向垂直于滾子與凸輪實(shí)際輪廓接觸點(diǎn)位置實(shí)際輪廓的切線方向,所以, 可以先求出接觸點(diǎn)凸輪實(shí)際輪廓的切線方向。</p><p>　　按照反轉(zhuǎn)法設(shè)計(jì)原理,現(xiàn)將凸輪固定,而機(jī)構(gòu)的其他部分以角速度¢0 繞O1 軸逆時針轉(zhuǎn)動θ0角轉(zhuǎn)動以后可以得到</p><p><b>　　即</b></p>

49、<p>　　將上式的左邊對時間求導(dǎo)可以得到L11θ0沿切向的增量矢量ΔL11θ0</p><p>　　在式(19) 中,ΔLθ的方向角即為接觸點(diǎn)凸輪實(shí)際輪廓的切線方向,將等式右邊的虛部除以實(shí)部可以得到</p><p>　　此時,切線的方向角為</p><p>　　那么, 凸輪實(shí)際輪廓的法線方向也就是L12的方向角為</p><p&g

50、t;　　將θ12代入式(16) 可以計(jì)算得到l13 、θ13 , 從而得到凸輪的實(shí)際輪廓。</p><p>　　所求出的θ13是相對于固定不動的坐標(biāo)系的, 當(dāng)考慮凸輪的轉(zhuǎn)動時, 則第 個位置凸輪向徑相對零線的位置角為</p><p>　　根據(jù)式(16) 和式(23) ,利用給定的機(jī)構(gòu)結(jié)構(gòu)參數(shù),通過MATLAB 編程可以計(jì)算得到主凸輪的實(shí)際輪廓曲線如圖4 所示。利用輔凸輪與主凸輪之間的共軛關(guān)

51、系可以計(jì)算得到輔凸輪的輪廓線。</p><p><b>　　3 結(jié)論</b></p><p>　　我們利用極坐標(biāo)矢量法實(shí)現(xiàn)了一種偏心旋轉(zhuǎn)—擺動式凸輪機(jī)構(gòu)的凸輪輪廓曲線的設(shè)計(jì)計(jì)算。相對于圖解法來說,極坐標(biāo)矢量法通過解析的方法進(jìn)行凸輪輪廓曲線的求解,這種方法計(jì)算精確,能夠完成具有復(fù)雜運(yùn)動從動件的凸輪機(jī)構(gòu)的設(shè)計(jì)。隨著自動機(jī)械對凸輪機(jī)構(gòu)運(yùn)動精度的提高以及凸輪CAD/ CAM