機(jī)電專(zhuān)業(yè)畢業(yè)設(shè)計(jì)中英文翻譯資料--圓柱凸輪的設(shè)計(jì)和加工

1、英文資料翻譯英文原文：Design and machining of cylindrical cams with translating conical followers By DerMin Tsay and Hsien Min Wei A simple approach to the profile determination and machining of cylindrical cams with translating conical followers is presented .On the basis of the theory of envelopes for a 1-pa

2、rameter family of surfaces,a cam profile with a translating conical follower can be easily designed once the follower-motion program has been given .In the investigation of geometric characteristics ,it enables the contact line and the pressure angle to be analysed using the obtained analytical prof

3、ile expressions .In the process of machining ,the required cutter path is provided for a tapered endmill cutter ,whose size may be identical to or smaller than that of the conical follower .A numerical example is given to illustrate the application of the procedure . Keywords : cylindrical cams, env

4、elopes , CAD/CAMA cylindrical cam is a 3D cam which drives its follower in a groove cut on the periphery of a cylinder .The follower, which is either cylindrical or conical, may translate or oscillate. The cam rotates about its longitudinal axis, and transmits a transmits a translation or oscillatio

5、n displacement to the follower at the same time. Mechanisms of this type have long been used in many devices, such as elevators, knitting machines, packing machines, and indexing rotary tables. In deriving the profile of a 3Dcam, various methods have used. Dhande et al.1 and Chakraborty and dhande2

6、developed a method to find the profiles of planar and spatial cams. The method used is based on the concept that the common normal vector and the relative velocity vector are orthogonal to each other at the point of contact between the cam and the follower surfaces. Borisov3 proposed an approach to

7、the problem of designing cylindrical-cam mechanisms by a computer algorithm. By this method, the contour of a cylindrical cam can be considered as a developed linear surface, and therefore the design problem reduces to one of finding the centre and side profiles of the cam track on a development of

8、the effective cylinder. Instantaneous screw-motion theory4 has been applied to the design of cam mechanisms. Gonzalez-Palacios et al.4 used the theory to generate surfaces of planar, spherical, and spatial indexing cam mechanisms in a unified framework. Gonzalez-Palacios and Angeles5 again used the

9、theory to determine the surface geometry of spherical cam-oscillating roller-follower mechanisms. Considering machining for cylindrical cams by cylindrical cutters whose sizes are identical to those of the followers, Papaioannou and Kiritsis6 proposed a procedure for selecting the cutter step by sol

10、ving a constrained optimization problem. The research presented in this paper shows q new, easy procedure for determining the cylindrical-cam profile equations and providing the cutter path required in the machining process. This is accomplished by the sue of the theory of envelopes for a 1-paramete

11、r family of surfaces described in parametric form7 to define the cam profiles. Hanson and Churchill8 introduced the theory of envelopes for a 1-parameter family of plane curves in implicit form to determine the equations of plate-cam profiles Chan and Pisano9 extended the envelope theory for the geo

12、metry of plate cams to irregular-surface follower systems. They derived an analytical description of cam profiles for general cam-follower systems, and gave an example to demonstrate the method in numerical form. Using the theory of envelopes for a 2-parameter family of surfaces in implicit form, Ts

13、ay and Hwang10 obtained the profile equations of camoids. According to the method, the profile of a cam is regarded as an envelope for the family of the follower shapes in different cam-follower positions when the cam rotates for a complete cycle.THEORY OF ENVELPOES FOR 1-PARAMETER FAMILY OF SURFACE

14、S IN PARAMETRIC FORMIn 3D xyz Cartesian space , a 1-parameter family of surfaces can be given in parametric form as (1)where is the parameter of the family, and u1, u 2, are the parameters for a particular surface of the family. Then, the envelope for the family described in Equation 1 satisfies equ

15、ation 1 and the following Equation: (2)where the right-hand side is a constant zero7. Litvin showed the proving process of the theorem in detail. If we can solve Equation2 and substitute into equation1to eliminate one of the three parameters u1, u 2, and , we may obtain the envelope in parametric fo

16、rm. However, one important thing should be pointed out here. Equations 1 and 2 can also be satisfied by the singular points of surfaces described below I the family, even if they do not belong to the envelope. Points which are regular points of surfaces of the family and satisfy Equation 2 lie on th

17、e envelope. The condition for the singular points of a surface is discussed here. a parametric representation of a surface is (3)where u1 and u 2 are the parameters of the surface. A point of the surface that corresponds to in a given parameterization is called a singular point of the parameterizati

18、on. A point of a surface is called singular if it is singular for every parameterization of the surface7. A point that is singular in one parameterization of a surface may not be singular in other parameterizations. For a fixed value of , equations 1 and 2 represent, in general, a curve on the surfa

19、ce which corresponds to this value of the parameter. If this is not a line of singular points, the curve slso lies on the envelope. The surface and the envelope are tangent to each other along this curve. Such curves are called characteristic lines of the family7. they can be used to find the contac

20、t lines between the surfaces of the cylindrical cam and the follower.THEORY OF ENVELOPES FOR DETERMINATION OF CYLINDRICAL-CAM PROFILESOn the basis of the theory of envelopes, the profile of a cylindrical cam can be regarded as the envelope of the family of follower surfaces in relative positions bet

21、ween the cylindrical cam and the follower while the motion of cam proceeds. In such a condition, the input parameters of the cylindrical cam serve as the family parameters. Because the cylindrical or conical follower surface can be expressed in parametric form without difficulty, the theory of envel

22、opes for a 1-parameter of surfaces represented in parametric form (see equations 1 and 2) is used in determining the analytical equations of cylindrical-cam profiles. As stated in the last section, a check for singular points on the follower surface is always needed. Figure 1a shows a cylindrical-ca

23、m mechanism with a translating conical follower. The axis which the follower translates along is parallel to the axis of rotation of the cylindrical cam. a is the offset, that is, the normal distance between the longitudinal axis of the cam and that of the follower. R and L are the radius and the ax

24、ial length of the cam, respectively.The rotation angle of the cylindrical cam is 2 about its axis. The distance traveled by the follower is s1 , which is a function of parameter 2 ,as follows: (4)The displacement relationship (see equation 4 ) for the translating follower is assumed to be given.In f

25、igure 1b, the relative position of the follower when the follower moves is shown. The follower is in the form of a frustum of a cone. The semicone angle is , and the smallest radius is r. 1 is the height, and is the normal distance from the xz plane to the base of the cone. The fixed coordinate syst

26、em Oxyz is located in such a way that the z axis is along the rotation axis of the cam, and the y axis is parallel to the longitudinal axis of the conical follower. the unit vectors of the x axis, y axis and z axis are i , j and k, respectively. By the use of the envelope technique to generate the c

27、ylindrical-cam profile, the cam is assumed to be stationary. The follower rotates about the dam axis in the opposite direction. It is assumed that the follower rotates through an angle 2 about the axis. At the same time, the follower is transmitted a linear displacement s1 by the cam, as shown in Fi

28、gure 1b. Consequently using the technique, if we introduce and as two parameters for the follower surface, the family of the follower surfaces can be described as (5)where 02piAnd 2 is the independent parameter of the cam motion. Referring to theory of envelopes for surfaces represented in parametri

29、c form (see equations 1and 2), we proceed with the solving process by finding (6) There are no singular points on the family of surfaces, since(r +tan) 0 in actual applications. The profile equation satisfies equation 5 and the following equation:(7)Where or (8)Where Substituting equation 8 into equ

30、ation 5, and eliminating , we obtain the profile equation of the cylindrical cam with a translating conical follower, and denote it as (9)As shown in equation 8, is a function of the selected follower-motion program and the dimensional parameters. As a consequence, the cylindrical-com profile can be

31、 controlled by the chosen follower-motion curves and the dimensional parameters. Two values of correspond to the two groove walls of the cylindrical cam. Now the profile of the cylindrical cam with a translating conical follower is derived by the new proposed method. As stated above, Dhande et al.1

32、and Chakraborty and Dhande2 have derived the profile equation of the same type of cam by the method of contact points. A comparison of the result is carried out here. Since the same fixed coordinate system and symbols are used, one can easily see that the profile equation is identical although the m

33、ethods used are different. Moreover, we find that the process of finding the cam profile is significantly reduced by this method.CONTACT LINEAt every moment, the cylindrical cam touches the follower along space lines. The contact lines between the cylindrical cam and its follower are discussed in th

34、is section. The concept of characteristic lines in the theory of envelopes for a 1-parameter family of surfaces mentioned above could be applied to finding the contact lines in a cylindrical com. The profile of a cylindrical cam with a translating conical follower is given by Equation9. Then, the co

35、ntact line at a specific value of 2, say 20, is (10)Where, in Equation 10, the value of is a function of defined by Equation 8. The contact lines between the surfaces of the cam and the follower at each moment is determined by Equation 10. we see that the relationship between the two parameters and

36、of the follower surface is given by Equation 8, a nonlinear function. Thus, one can easily find that the contact line is not always a straight line on the conical follower surface.PRESSURE ANGLEThe angle that the common normal vector of the cam and the follower makes with the path of the follower is

37、 called the pressure angle12. the pressure angle must be considered when designing a cam, and it is a measure of the instantaneous force-transmission properties of the mechanism13. The magnitude of the pressure angle in such a cam-follower system affects the efficiency of the cam. The smaller the pr

38、essure angle is, the higher its efficiency because14. In figure2, the unit normal vector which passes through the point of contact between the cylindrical cam and the translating conical follower in the inversion position, i.e. point C, is denoted by n. The path of the follower labeled as the unit v

39、ector p is parallel to the axis of the follower. from the definition, the pressure angle is the angle between the unit vectors n and p. Since, at the point of contact, the envelope and the surface of the family possesses the same tangent plane, the unit normal of the cylindrical-cam surface is the s

40、ame as that of the follower surface. Referring to the family equation Equation5 and Figure2, we can obtain the unit vector as (11)where the value of is given by equation 8, and the unit vector of the follower path is (12)By the use of their inner product, the pressure angle can be obtained by the fo

41、llowing equation: (13) The pressure angle derived here is identical to that used in the early work carried out by Chakraborty and Dhande2.CUTTER PATH In this section, the cutter path required for machining the cylindrical cam with a translating conical follower is found by applying the procedure des

42、cribed below. Usually, with the considerations of dimensional accuracy and surface finish, the most convenient way to machine a cylindrical cam is to use a cutter whose size is identical to that of the conical roller. In the process of machining, the cylindrical blank is held on a rotary table of a

43、4-axis milling machine. As the table rotates, the cutter, simulating the given follower-motion program, moves parallel to the axis of the cylindrical blank. Thus the cutter moves along the ruled surface generated by the follower axis, and the cam surface is then machined along the contact lines step

44、 by step. If we have no cutter of the same shape, an available cutter of a smaller size could also be sued to generate the cam surface. Under the circumstances, the cutter path must be found for a general endmill cutter. Figure 3 shows a tapered endmill cutter machining a curved surface. The front p

45、ortion of the tool is in the form of a cone. The smallest radius is R, and the semicone angle is . If the cutter moves along a curve =0 on the surface X=X（，2），the angle between the unit vector of the cutter axis ax and the unit common normal vector n at contact point C is determined by (14)Thus the

46、path of the point on the cutter axis that the vector n passes through is (15)and the tip centre T follows the path (16)Figure 4 shows a tapered endmill cutter machining the groove wall of a cylindrical cam. The axis of the tapered endmill is parallel to the y axis. Note that the two conditions （17）

47、(18) for the geometric parameters of the cutter and the roller follower must hold, or otherwise the cutter would not fit the groove. The unit vector of the cutter axis is (19)For the profile of the cylindrical cam with a translating conical follower given by equation 9, the angle is determined by th

48、e inner product: (20)Thus, by using the results obtained earlier, the position of the tip centre of the cutter can be derived as (21)whereNUMERICAL EXAMPLEThe procedures developed are applied in this section to determine the cylindrical-cam profile, and to analyse its characteristics. The motion pro

49、gram of the follower for the cylindrical cam with a translating cylindrical cam is given as (22)where h and are two constants. And h=20 units and =60. The motion program is a dwell-rise-dwell-return-dwell curve, and the rise and return portions are cycloidal curves 15. Figure 5 shows the motion prog

50、ram. The dimensional parameters used for the cylindrical cam and the follower are as follows:semicone angle of follower = 0height of follower 1 =15 unitsdistance from bottom of follower to xz plane =55 unitssmallest radius of follower r =7.5 unitsoffset a = 20 unitsradius of cam R = 73 unitsaxial le

51、ngth of cam L = 100 unitsThe profile of the cylindrical cam obtained by applying Equation 9 is shown in Figure 6. In Figure 6, the groove wall with the smaller z coordinates is side , and the other is side . The variations of the pressure angles for the rise and return portions are shown in Figures

52、7 and 8 for side and , respectively. It can be seen that the pressure angles for both sides happen to be identical.CONCLUSIONSAs has been shown above , the application of the theory of envelopes affords a convenient and versatile tool for determining the cylinder-cam profiles with translating conica

53、l followers. By means of the analytical cam profile equations, it can be easily extended to accomplish the task for the analysis of the contact line and the pressure angle. Further , the cutter path required in the process of machining is generated for tapered endmill cutters. Since the same fixed c

54、oordinate system and symbols are used in this study, one can see that the results for cam profiles and pressure angles are identical to those obtained in previous research1,2. Only one coordinate system is used in this approach. As a result, the process of derivation is simple. Work is currently und

55、er way to facilitate the implementation of the tool path for the machining of the cylindrical cam on a numerically controlled milling machine. 翻譯： 圓柱凸輪的設(shè)計(jì)和加工有人提出了具有平移圓錐傳動(dòng)件的圓柱凸輪的輪廓確定及其機(jī)加工的簡(jiǎn)單方法.在單參數(shù)曲面族的包絡(luò)線理論的基礎(chǔ)上,給定從動(dòng)件運(yùn)動(dòng)規(guī)律的具有平移圓錐傳動(dòng)件的圓柱凸輪的輪廓的設(shè)計(jì)是很簡(jiǎn)單的.通過(guò)這種設(shè)計(jì)方法得到的輪廓曲線可以進(jìn)行凸輪切線和壓力角等幾何特征的分析研究.在機(jī)加工過(guò)程中,可以使用錐形端銑

56、刀,它的尺寸小于等于圓錐傳動(dòng)件的尺寸.很多實(shí)例證明該方法的實(shí)用性.關(guān)鍵詞:圓柱凸輪,包絡(luò)線,計(jì)算機(jī)輔助設(shè)計(jì)和計(jì)算機(jī)輔助制造.圓柱凸輪是利用其圓周上的溝槽來(lái)驅(qū)動(dòng)傳動(dòng)件的空間凸輪.傳動(dòng)件是圓柱或者圓錐形狀的,可以做平行移動(dòng)也可以做擺動(dòng).凸輪繞著它的縱向軸線旋轉(zhuǎn),同時(shí)將平移或擺動(dòng)運(yùn)動(dòng)傳遞給傳動(dòng)件.這種機(jī)械原理長(zhǎng)期廣泛應(yīng)用在各種設(shè)備中,比如,運(yùn)輸機(jī),紡織機(jī),包裝機(jī),旋轉(zhuǎn)分度盤(pán)等等.為獲得三維凸輪的輪廓曲線,曾用過(guò)各種方法.DHANDE 和CHAKRABORTY 和 DHANDE 發(fā)明了確定平面和立體凸輪輪廓的一種方法.這種方法是在一個(gè)前提下使用的,即認(rèn)為在主動(dòng)輪和從動(dòng)件交點(diǎn)處,凸輪的徑向矢量和速度矢量二者相互垂直.BROISOV提出了借助計(jì)算機(jī)輔助計(jì)算的方法來(lái)解決圓柱凸輪機(jī)構(gòu)設(shè)計(jì)上的問(wèn)題.通過(guò)這種方法,可以把圓柱凸輪的輪廓考慮成為展開(kāi)的線性曲面.這樣,設(shè)計(jì)時(shí)就只需在實(shí)際圓柱上找到凸輪軌跡的中心和輪廓邊緣.瞬間螺旋運(yùn)動(dòng)理論已經(jīng)應(yīng)用到凸輪機(jī)構(gòu)的設(shè)計(jì)中.GONZALEZ-PALACIOS在統(tǒng)一標(biāo)準(zhǔn)下應(yīng)用這種理論得到了平面,球面和柱面凸輪機(jī)構(gòu). GONZALEZ-PALACIOS和ANGLES又應(yīng)用這個(gè)理論確定了球面擺動(dòng)輥?zhàn)油馆啓C(jī)構(gòu)的幾何形狀.考慮到用與傳動(dòng)件同樣尺寸的圓柱刀具加工圓柱凸輪,PA