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jx0242-弧面凸轮数控转台的设计—3d建模与装配（带cad和文档）,jx0242-弧面凸轮数控转台的设计—3d建模与装配带cad和文档

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MATHEMATICAL COMPUTER MODELLING PERGAMON Mathematical and Computer Modelling 29 (1999) 69-87 Curvature Analysis of Roller-Follower Cam Mechanisms HONG-SEN YAN Departmentof Mechanical Engineering, National Cheng Kung University Tainan 70101, Taiwan, R.O.C. WEN-TENG CHENG Department of Mechanical Engineering, I-Shou University Ta-Shu, Kaohsiung Hsien 840, Taiwan, R.O.C. (Received January 1996; accepted January 1998) Abstract-The equations related to the curvature analysis of the roller-follower cam mechanisms are presented for roller surfaces being revolution surface, hyperboloidal surface, and globoidal surface. These equations give the expressions of the meshing function, the limit function of the first kind, and the limit function of the second kind. Once these functions are known, the principal curvatures of the cam surface, the relative normal curvatures of contacting surfaces, and the condition of undercutting can be derived. Three particular cam mechanisms with hyperboloidal roller are illustrated and the numerical comparison between 2-D and 3-D cam is given. 1999 Elsevier Science Ltd. All rights reserved. Keywords-” F ; 8”, , (3) I 0 0 01 1 0 cp -sp 0 T23 = (4 where we designate sine and cosine of the corresponding angle as symbols C and S, and the subscript ij in the designation Tij is the transformation matrix from coordinate systems Sj to s+ Transformation matrix Trs can be obtained by the successive matrix multiplication P13l = Pii GoI To21P231. (5) Transformation matrix Trs is expressed in partition matrix as follows: P131 P13l fT131= O l 1 where Rrs is a rotation matrix and drs is a translation column vector. Taking the derivatives of transformation matrix Tls, relative velocity matrix Wrs, and rela- tive angular velocity matrix firs are given by w131 = T131T i;3 = ;l3 $1 , (7) p131 = R131T , $1 , (11) v3 1 1 where wT31 = 1Pl31 71311. (12) Expanding equation (1 l), we have where w, wy, and w, are the components of the relative angular velocity between the roller and the cam, and TV, rr, and rz are the components of the relative translational velocity between the roller and the cam at the origin of coordinate system S3. All the components of the relative velocities are expressed in coordinate system S3. For the roller-follower cam mechanism, the meshing function Cpis defined as qe,u,q E n(3).vl)= nfW, q . (14) For the cam surface being conjugate to the roller surface at the point of contact, the equation of meshing is given by (e, 21,t = 0. (15) Simultaneous solution of equations (9) and (15) determines the contact line on the roller sur- face for any given time t, and simultaneous solution of equations (10) and (15) determines the corresponding contact line on the roller surface in the meantime. The limit function of the second kind at for mutually contacting surfaces Cr and C3 is expressed as (a,(e,u,t) = npTw;?-a)* (16) Let KY and $) be the principal curvatures of the roller surface C3, and in and bn be the corresponding principal directions in coordinate system S3. Then, the limit function of the first kind E is defined as 7,12 Q=Jvnz+Iry+, E = K$nz + wn Y, (17) C=$)VnY-IIZ, where wnz, WQ, ynxr and vnV are the components of the relative angular and sliding velocities in the tangent plane of mutually contact surfaces C3 and Cr as follows: wnIs = wp Tin (31) T bn, 1 9 my = w3 (18) 1 v = g. Using equations (A2) and (A4), the components of the relative velocity matrix Wis becomes w, = WY= 0, W%= (4; - l)Wl, rz = -aSf - 1) Se) wi, vu = (-aC - 1) + c (46 - 1) CO) WI, u* = 0. From equation (41), the meshing function is given by = (-aS(0+2)+b(fC (e+42)+b+;se)f. From equations (48) to (50), the coefficients 5 and C, and the limit function of the first kind are given by =(ac(e+2)-b(:-1)Ce), c= 0, E= -a2 - b2 (4: - 1)2 + 2ab (4; - 1) Cf& - acC (e+$2)+bc(&se -($a- i)ce)2. Example 2. Conical Cam with a Translating Conical Follower Figure 6 shows a conical cam with a translating conical follower. The conical cam rotates about the input axis while the follower translates along the output axis. The angle of rotation 41 is the parameter of motion of the cam, and the translational displacement s2 is that of the follower. In the meantime, let si = 0 and $9 = 0. The twisted angle from the input axis to the output axis is Q! and a = 0 for the two axes being intersected. Due to the rotation axis of the roller intersected with and perpendicular to the output axis, the distance b = 0 and the twisted angle p = 12. The distance from the origin of the coordinate system Ss to the apex of the conical roller is d and the angle between the rotation axis and the generating line of conical surface is y. And, the specified displacement relation is s2 = ss($i). Figure 6. Conical cam with a translating roller-follower. Curvature Analysis 81 For a conical roller, the value of the parameter c of equations (37) and (38) is zero. Therefore, the coordinates of the conical roller surface and its unit normal in coordinate system Ss are given = us8 tany -uC0tany d+u llT, (3) r3 1 7-p = SBC -cec+y -SylT, I where u 0, d 542) - ya(d + 4h + 5542) . I I r 1 I I Dwell .L_ 150 MS 2 (deg) _ 1 Dwell ji 120 Figure 8. Motion function. Example 4. Numerical Comparison Between 2-D and 3-D Cams The cam mechanisms of Example 1 and Example 3 are applied to offer the quantifiable com- parison between the 2-D and 3-D cams. They use the same roller radius, follower displacement, motion function, and distance between the input and output axes. The motion function cPs(&) shown in Figure 8 is divided into five intervals and that the second and the fourth intervals use modified sine motion. Table 1 shows the parameters and the functions which are used for the disk cam and the globoidal cam. Table 1. Parameters of disk cam and globoidal cam. a4 H.-S. YAN AND W.-T. CHENG Figure 9. Cam profile for disk cam. Figure 10. Cam profile for globoidal cam. 50 I I f I I I, I I I I I I I I I I 0 0 h (de Figure 11. Pressure angle for disk cam. Curvature Analysis 85 For the roller surface being a cylindrical surface, the pressure angles q&k and qs10 for the disk cam and the globoidal cam are derived as IbSfJ WV Cvdisk = (b2 + c2 + 2bcC6)“2 cqdO = (c2ce2 + u2)1/2. Figures 9-14 shows the cam profiles, the pressure angles, and the principal curvatures for the disk cam and the globoidal cam. As shown in Figure 10, the pressure angles for the Profiles 1 and 2 of the globoidal cam have the same value for the same 41 and u. CONCLUSION The rollers with cylindrical surface, conical surface, and globoidal surface are usually used in roller-follower cam mechanisms. The cylindrical surface and the conical surface are special cases of the hyperboloidal surface. For the rollers of revolution surface, hyperboloidal surface, and globoidal surface, the curvature analysis of the roller-follower cam mechanisms are presented in this paper. For the mutually contacting surfaces between the cam and the follower, the principal curvatures of the cam surface, the relative normal curvature, and the condition of undercutting are expressed in terms of the meshing function and the limit functions. And, these functions for the cam mechanisms with the three-roller surfaces are derived. The hyperboloidal surface and the globoidal surface are the particular cases of the axis-symmetric quadric surface while the later one is a particular case of the revolution surface. For the simplicity of programming, we just focus on the roller of revolution surface. Here, all the surface normals of the roller surfaces are directed outward the roller. Therefore, the limit function of the first kind must be minus in order to avoid the undercutting. APPENDIX The transformation matrix Trs is given by a1 CdJz + CaS41S42 a3(44lS42 + CaS41C4J2) - Sj3SaS1 -+%c42 + CaCd1S42 Pwiw42 + CffC41C2) - spsaclpl Z3 = SffSdJ2 SPCa + C&9aC42 I 0 0 (AlI -SP(-ChS4Q + CaS&C95,) - cpsasq+l a% - szSc&h + b(C$IC& + Ca&s#) -ww1w2 + CaC41wJ2) - CphYCc#q -a%h - szSaC& + b(-ShW2 + c0rc4s4) -SPSaC& + CPCa -61 + s2Ca + bSaS& 0 1 I. The relative velocity matrix Wrs is given by 0 -wz wy rz WZ 0 -% rrl w131 = I (4 -wy WI 0 72 0 0 0 0 I with the components w, = -&s&pz, wy = -&(SPCa + CPSaC42) + &sp, (A3) w, = -&(CPCa - Spsacqh) + 42cp, 86 H.-S. YAN AND W.-T. CHENG t I- u=S8 360 Figure 12. Pressure angle for globoidal cam. _._- 0 360 Figure 13. First principal curvature for disk cam. 0.04 , , , , ua58 / Figure 14. Principal curvatures for globoidal cam. Curvature Analysis 87 Tz = -&(aCoS+z + s2SaC&) - BlSdq2, Ty = $1(-Ccc/3 (b + aCq52)+ sosp(a + bC42)+ s2SaC/w2) + cj2bCP - 81 (Cc&P + SaC/3C42) + B2SP, (A3)(cont.) T= = $1 (CcxS (b + aC&) + SaCP (u + bCq&) - s2SaSPS42) - rj2bSP - B1 (Cc&p - S&3/%39) + B&p. The derivative of relative velocity matrix Wls is given by 0 -Ljz Lj, iz 0 -Ljz iv WZ w13 = (A4) 1 -&Jar iJz 0 i, 1. 0 0 0 0 I with the components . . l& = -4142SaC42 - lSwJ2, Ljy = &2cpsasq52 - $1 (SPCa + C/wap2) + J,sp, Lj* = 4142spsas42 + $1 (-cpccu + S/mYCq52) + $2cp, i, = -sac42 &s2 + &Sl + &(-aCaCq52 + s2SaS42) ( - $1 (aCaSq52 + s2SaC42) - IlScYS42, iv = CSaS42 (qi 1S2 + 42Bl + &$2 (aCCcxS, - bSaS/W+2 + sCSCYC) (A5) + $1 a (SaSP - CPYC) + b (-CaCp + Sk164) + s2CPSaSqi2 + &bC/3 - 51 (CCYSP+ SCYCPG#J)+ i2Sp, iz = -S/3SaSqs2 (” 182 + $2.41 + $142 (-aSpCcuS& - bSaCPS& - s2S&SaC&) + $1 a (SaCP + SPCaC&) + b (CdV3 + CPSaC42) - sSM+ - &bS/3 + lil (-C&j3 + SCYS/C)+ s2Cp. REFERENCES 1. M.L. Baxter, Curvature-acceleration relations for plane cams, ASME Z?unsactions, 483-469, (1948). 2. M. Kloomok and R.V. Muffley, Determination of radius of curvature for radial and swinging-follower cam systems, ASME Transactions, 795-802, (1956). 3. F.H. Raven, Analytical design of disk cams and three-dimensional cams by independent position equations, ASME IPransactions, Journal of Applied Mechanics, 18-24, (1959). 4. S. Yonggang, Curvature radius of disk cam pitch curve and profile, In Proceedings of the ph World Congress on Theory of Machines and Mechanisms, pp. 1665-1668, (1987). 5. F.L. Litvin, Theory of Gearing, (in Russian), Nauka, Moscow, (1968). 6. F.L. Litvin, P. Rahman and R.N. Goldrich, Mathematical models for synthesis and optimization of spiral bevel gear tooth surfaces, NASA Contractor Report 3553, (1982). 7. F.L. Litvin, Gear Geometry and Applied Theory, Prentice Hall, NJ, (1994). 8. S.G. Dhande and J. Chakraborty, Curvature analysis of surfaces in higher pair, Part 1: An analytical investigation, ASME 2%ansactions, Journal of Engineering for Industry 98, 397-402, (1976). 9. S.G. Dhande and J. Chakraborty, Curvature analysis of surfaces in higher pair, Part 2: Application to spatial cam mechanisms, ASME Transactions, Journal of Engineering for Industry 98, 403-409, (1976). 10. J. Chakraborty and S.G. Dhande, Kinematics and Geometry of Planar and Spatial Mechanisms, Wiley, New York, (1977). 11. C.H. Chen, Formula of reduced curvature of two conjugate surfaces with conjugate motions of two degrees of freedom, In Proceedings of the flh World Congress on Theory of Machines and Mechanisms, pp. 842-845, (1983). 12. D.R. Wu and J.S. Luo, A Geometric Theory of Conjugate Tooth Surfaces, World Scientific, (1992). 湘潭大学机械工程学院毕业设计工作中期检查表系 机电系 专业 机械设计制造及其自动化 班级 机械二班 姓 名杨杰学 号2006183924指导教师胡自化指导教师职称教授题目名称弧面凸轮数控转台设计3D建模与装配题目来源 科研 企业 其它课题名称题目性质 工程设计 理论研究 科学实验 软件开发 综合应用 其它资料情况1、选题是否有变化 有 否2、设计任务书 有 否3、文献综述是否完成 完成 未完成4、外文翻译 完成 未完成由学生填写目前研究设计到何阶段、进度状况：了解了弧面凸轮国外及国内的发展现状，弧面凸轮分度机构的主要优缺点及其应用情况。在现有的研究基础上深入了解了弧面凸轮的廓面方程、啮合方程的推导过程，进行了弧面凸轮的造型设计。学习了三维制图软件UG的基本造型功能和模拟仿真功能，并开始了解基于UG的二次开发模块，查阅了对其进行优化设计的理论方面的知识。由老师填写工作进度预测（按照任务书中时间计划） 提前完成按计划完成 拖后完成 无法完成工作态度（学生对毕业论文的认真程度、纪律及出勤情况）： 认真 较认真 一般 不认真质量评价（学生前期已完成的工作的质量情况） 优 良 中 差存在的问题与建议：周佳同学在这一阶段的毕业设计过程中，态度认真，工作刻苦，按计划完成了预定的设计工作，而且取得了较好的结果。 指导教师（签名）： 年 月 日建议检查结果： 通过 限期整改 缓答辩系意见： 签名： 年 月 日注：1、该表由指导教师和学生填写。2、此表作为附件装入毕业设计（论文）资料袋存档。 20061839243D 1仯 2 3 4 淽UG湦UG飬 飺 棬 1 2浵 湘潭大学兴湘学院毕业设计任务书设计题目： 弧面凸轮数控转台的设计3D建模与装配 学号： 2006183924 姓名： 杨杰 专业： 机械设计制造及其自动化 指导教师： 胡自化教授 系主任： 一、主要内容及基本要求 1、 熟悉和掌握弧面凸轮传动的工作原理； 2、 熟悉和理解弧面凸轮传动的结构参数； 3、 利用UG进行3D建模与装配 4、 总结和撰写毕业设计说明书一份； 5、 翻译相关外文资料一份。 二、重点研究的问题1、 熟悉弧面凸轮传动数控转台相关性能方面的知识； 2、 学习和使用UG三维建图软件和AUTO CAD软件； 3、 熟悉和理解弧面凸轮传动机构的结构参数。 三、进度安排序号各阶段完成的内容完成时间1文献检索第1周2消化资料第2周3和小组成员讨论，进行总体方案设计第3周4小组讨论，进行设计计算第4-5周5UG软件的学习第6-8周6用UG进行三维造型第9-11周7撰写毕业设计说明书第12周8进行毕业论文答辩第13周四、应收集的资料及主要参考文献 1 杨冬香 阳大志 基于不同滚子从动件类型的弧面凸轮CAD集成系统开发A 五邑大学机电工程系 广东江门2 张高峰 冯建军 .谭援强 基于圆锥滚子的弧面凸轮三维CAD J 现代机械 2004年第5期 湘潭大学机械工程学院 湖南湘潭3 董正卫 田立中 付宜利 .UG/Open API实用编程基础.M北京:清华大学出版社.2002.4 付本国 林晶 任晓云.UG NX5三维设计基础与工程范例.M北京:清华大学出版社.2007 5 刘昌祺 曹西京 凸轮机构设计M机械工业出版社 3D 2006183924 1 2 3 UG3D 4 5 1 2 UGAUTO CAD 3 11223巽344-55UG6-86UG9-11712813 1 CADA 繤 2 . CAD J 20045 3 .UG/Open API.M:廪.2002. 4 .UG NX5.M:廪.2007 5 M 湘潭大学兴湘学院毕业设计说明书题目：弧面凸轮数控转台的设计3D建模与装配专 业： 机械设计制造及其自动化 学 号： 2006183924 姓 名： 杨杰 指导教师： 胡自化 教授 完成日期： 2010.06.07 3D 2006183924 2010.06.07 湘 潭 大 学 兴湘学院 本科毕业设计开题报告题 目弧面凸轮数控转台设计3D建模与装配姓 名杨杰学号2006183924专 业机械设计制造及其自动化班级机械二班指导教师胡自化职称教授填写时间2010年4月23 日 2010年4月说 明1根据湘潭大学毕业设计(论文)工作管理规定，学生必须撰写毕业设计（论文）开题报告，由指导教师签署意见，系主任批准后实施。2开题报告是毕业设计（论文）答辩委员会对学生答辩资格审查的依据材料之一。学生应当在毕业设计（论文）工作前期内完成，开题报告不合格者不得参加答辩。3毕业设计(论文)开题报告各项内容要实事求是，逐条认真填写。其中的文字表达要明确、严谨，语言通顺，外来语要同时用原文和中文表达。第一次出现缩写词，须注出全称。4本报告中，由学生本人撰写的对课题和研究工作的分析及描述，应不少于2000字。5开题报告检查原则上在第24周完成，各系完成毕业设计开题检查后，应写一份开题情况总结报告。6. 填写说明：(1) 课题性质：可填写A工程设计；B论文；C. 工程技术研究；E.其它。(2) 课题来源：可填写A自然科学基金与部、省、市级以上科研课题；B企、事业单位委托课题；C校级基金课题；D自拟课题。(3) 除自拟课题外，其它课题必须要填写课题的名称。(4) 参考文献不能少于10篇。(5) 填写内容的字体大小为小四，表格所留空不够可增页。本科毕业设计(论文)开题报告学生姓名杨杰学 号2006183924专 业机械设计制造及其自动化指导教师胡自化职 称教授所在系机电系课题来源企、事业单位委托课题课题性质工程技术研究课题名称弧面凸轮数控转台设计一、选题的依据、课题的意义及国内外基本研究情况本设计是以新型传动数控转台的的设计为研究平台，针对弧面凸轮机构的设计仿真分析是整个弧面凸轮数控转台项目中的一个子项。在当代机械制造业飞速发展过程中，现代机床制造业正在向“高速、精密、复合、智能和环保”的方向前进，而高速、高效加工在其中扮演着重要角色。在发达国家，围绕高速、高效的新型的机构，不仅在技术开发方面投入了大量精力，而且在应用推广方面取得了前所未有的进展。弧面凸轮分度机构是由输入轴上的弧面凸轮与输出轴分度轮上的滚动轴承无间隙垂直啮合，从而实现间歇输出的新型传动机构。采用弧面凸轮分度机构的弧面凸轮分度箱，它已成为当今世界上精密驱动的主流装置。它具有高速性能好，运转平稳，传递扭矩大，定位时自锁，结构紧凑、体积小，噪音低、寿命长等显著优点，是代替槽轮机构、棘轮机构、不完全齿轮机构等