弧面凸轮数控转台的设计-机械部分【含CAD图纸】
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MATHEMATICAL COMPUTER PERGAMON Mathematical and Computer Modelling 29 (1999) 69-87 MODELLING Curvature Analysis of Roller-Follower Cam Mechanisms HONG-SEN YAN Department of 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”, , I 1 (3) 0 0 01 T23 = 0 cp -sp 0 (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 To21 P231. (5) Transformation matrix Trs is expressed in partition matrix as follows: P131 P13l fT131 = O 1 l 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 , 1 (11) where wT31 = 1 Pl31 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 Cp is defined as qe,u,q E n(3) .vl) = nf W, 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) = np T w; ?-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 T in 1 9 my = w3 1 (31) T bn, (18) 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) CfSO) u tan y (Sa + tan ycace) +c2as2e(u set y tan r)2 - u tan y (s;sase + siC8) (u /Tsec y). Example 3. Concave Globoidal Cam with an Oscillating Hyperboloidal Follower The settings of the coordinate systems for the concave globoidal cam with a hyperboloidal follower is shown in Figure 7. The globoidal cam rotates about the input axis with rotation angle 41, while the follower oscillates about the output axis with rotation angle $2. Thus, let sr = 0 and 52 = 0. The shortest d is t ante between the input and output axes is a and the twisted 82 H.-S.YAN AND W.-T. CHENG Figure 7. Concave globoidal cam with an oscillating hyperboloidal follower. angle a is r/Z. For the relative location of the rotation axis of the roller and the output axis, the distance b = 0 and the twisted angle S = 7r/2. The roller has a distance d from the origin of the coordinate system Ss to its base circle. And, the relation between the input and the output displacements is given by 42 = ) , B = w1 (cdq5 - 21 (tan 7 (a + dS42) - c sec2 7959 - U2 tan 7 sec2 7S42) , c = 0. From equation (42), the equation of meshing is given by ysC2 + (234; + y32) (d + 215X” 7) = 0. Furthermore, the limit function of the second kind is given by !Bt = II II Nt3) -1(AtsinB+Btcosf3+Ct), a3 where Curvature Analysis At = W: (cdC) , Bt = wf (cd l(N(3)11-1 ( (z3$i + y3c42&) (d + ?JSeC2 7) . nom equations (48) to (SO), the coefficients c and C, and the limit function of the first kind are given by 542) - ya(d + 4h + 5542) . 150 2 (deg) I I r .L_ MS i _ 1 Dwell j 1 I I Dwell 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. 50 0 Figure 10. Cam profile for globoidal cam. I I f I I I, I I I I I I I I I I 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 Cvdisk = IbSfJ WV (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 Z3 = I -+%c42 + CaCd1S42 Pwiw42 + CffC41C2) - spsaclpl SffSdJ2 SPCa + C&9aC42 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& 1 I. 0 The relative velocity matrix Wrs is given by w131 = 0 -wz wy rz WZ 0 -% rrl -wy WI 0 72 0 0 0 0 with the components w, = -&s&pz, I I (4 wy = -&(SPCa + CPSaC42) + &sp, w, = -&(CPCa - Spsacqh) + 42cp, (A3) 86 H.-S. YAN AND W.-T. CHENG t I- u=S8 360 Figure 12. Pressure angle for globoidal cam. _._- 0 Figure 13. First principal curvature for disk cam. 360 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, 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 1 w13 = WZ 0 -Ljz iv 1. I -&Jar iJz 0 i, 0 0 0 0 (A3)(cont.) (A4) 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). 湘潭大学兴湘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 名余启良学 号2006183928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的设计机械部分题目来源 科研 企业 其它课题名称8吨绞磨变速器设计题目性质 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:了解了弧面凸轮在国内外的发展现状,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基本结构类型,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。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: 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。 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的设计机械部分姓 名余启良学号2006183928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22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)开题报告学生姓名余启良学 号2006183928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导师发布课题性质工程技术研究课题名称弧面凸轮数控转台的设计机械部分一、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。由于生产工艺的要求,广泛使用的各种自动机械中往往需要机构来实现周期性的转位、分度动作,实现这种运动的机构称为间歇机构。随着自动机械向高速化、精密化、轻量化的方向发展,对间歇机构提出越来越高的要求。常用的间歇机构主要包括棘轮机构、槽轮机构、针轮机构、不完全齿轮机构及各种凸轮型间歇机构,其中前四种间歇机构由于分度定位精度低,运动不够稳定,高速时有较大冲击,只适用于低速、轻载的场合。凸轮型间歇机构结构简单,能自动定位,动静比可任意选择,与传统的几种间歇机构相比,更适用于要求高速、高分度精度的场合,因而成为现代间歇机构发展的主要方向。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、不完全齿轮机构等传统间歇机构的理想产品。从参数化和可视化的虚拟设计技术出发,基于UG软件, 建立了弧面分度凸轮机构的参数化设计、造型和运动仿真, 得出分度盘的转速以及滚子与凸轮的啮合力并进行分析,获得比较直观的结果.为弧面分度凸轮机构的运动性能研究和企业的产品优化设计提供研究参考。研究现状:弧面分度凸轮机构是二十世纪20年代美国工程师C.N.Neklutin发明的,当时Neklutin称此机构为滚子齿形凸轮分度机构。二十世纪50年代该机构由C.N.Neklutin所创办的Ferguson公司首先进行了标准化系列化生产。我国从二十世纪七十年代末对该机构也开始了研制工作,在弧面分度凸轮机构的理论研究、设计制造等方面做了大量的工作。弧面分度凸轮机构从50年代开始投产以来,经过不断改进,已成为应用最广泛、产量最大的凸轮分度机构产品。二、研究内容、预计达到的目标、关键理论和技术、技术指标、完成课题的方案和主要措施本设计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重要环节。课题组在详细了解国内外在此方面的发展情况,并通过结合现在已开发的同类产品,在此基础上进行优化设计,使产品性能更加优越,体积进一步减小。在项目研制过程中,我利用互联网和学校图书馆详细的了解了弧面凸轮的基本结构类型,廓面方程,啮合规律等方面的知识,对现有的弧面凸轮进行了了解,查阅了有关资料。本课题在设计造型和动态的模拟仿真方面采用计算机辅助设计的技术,利用UG软件及基于UG二次开发模块建模,UG的动态仿真,进一步缩短了设计周期,降低了设计成本,有助于促进了设计工作的规范化、系列化和标准化,从而提高该产品设计开发能力。主要的工作内容有以下几个方面:1)设计计算部分:在结合指导老师所给的数据的情况下,分析确定凸轮分度机构传动方案;在了解了弧面凸轮的廓面方程、啮合方程的基础上通过计算分析,确定弧面凸轮的参数,校核弧面凸轮强度;完成弧面凸轮的啮合齿轮的设计计算;在传动部分设计完成后,进行转台的联接设计及转台自锁问题的解决。2)工程仿真分析部分:本论文利用三维软件UG及基于UG二次开发模块对弧面凸轮机构进行三维建模,画出零件三维图形;利用UG软件对弧面凸轮机构模型进行模拟仿真;对内啮合齿轮传动进行动力学分析。三、主要特色及工作进度主要特色: 利用计算机辅助设计技术,基于UG及其二次开发模块等软件对理论设计的进行参数化建模,动态仿真和结构的优化设计。工作进度: 收集查阅了有关弧面凸轮的发展现状、主要参数方程的推导等方面的资料,制定了设计提纲和计划,完成了软件的应用学习。四、主要参考文献(按作者、文章名、刊物名、刊期及页码列出)1濮良贵,纪名刚. 机械设计M. 北京:高等教育出版社,2002.2胡宗武等. 非标准机械设备设计手册M. 北京:机械工业出版社,2005.3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J. 机电工程技术,2009.4葛正浩,蔡小霞,王月华. 应用包络面理论建立弧面凸轮廓面方程J,2004.6张高峰,杨世平,陈华章,周玉衡,谭援强.弧面分度凸轮的三维CADJ.机械传动,20037王其超,我国弧面分度凸轮机构研究的综述及进展,机械设计,19978胡自化,张平. 连续分度空间弧面凸轮的多轴数控加工工艺研究J . 中国机程,2006 9张高峰,杨世平,陈华章,等. D-H 方法在弧面分度凸轮机构设计中的应用J . 机械传动,2003 10张高峰杨世平,陈华章,周玉衡,谭援强. 弧面分度凸轮机构的研究与展望J.机械传动,2003指导教师意 见指导教师签名: 年 月 日系意见 系主任签名: 年 月 日院意见 教学院长签名: 年 月 日湘潭大学兴湘学院毕业设计任务书论文(设计)题目: 弧面凸轮数控转台的设计机械部分 学号: 2006183928 姓名: 余启良 专业:机械设计制造及其自动化 指导教师: 胡自化 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.进行弧面凸轮传动数控转台的设计。 3.熟悉和理解弧面凸轮的结构参数。 4.使用AUTO CAD绘图。 5.总结和撰写毕业设计说明书一份。 6.翻译相关外文资料一份。 二、重点研究的问题 1.熟悉和掌握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 查阅资料、调研 第1-2周2 进行总体方案设计 第3周3 学习和使用Auto CAD软件 第4-5周4 计算结构尺寸和数据 第6-10周5 使用Auto CAD软件作图 第11周6 撰写毕业设计计算说明书 第12-13周7 答辩 第13周四、应收集的资料及主要参考文献1濮良贵,纪名刚. 机械设计M. 北京:高等教育出版社,2002.2胡宗武等. 非标准机械设备设计手册M. 北京:机械工业出版社,2005.3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J. 机电工程技术,2009.4葛正浩,蔡小霞,王月华. 应用包络面理论建立弧面凸轮廓面方程J,2004.6张高峰,杨世平,陈华章,周玉衡,谭援强.弧面分度凸轮的三维CADJ.机械传动,20037王其超,我国弧面分度凸轮机构研究的综述及进展,机械设计,19978胡自化,张平. 连续分度空间弧面凸轮的多轴数控加工工艺研究J . 中国机程,2006 9张高峰,杨世平,陈华章,等. D-H 方法在弧面分度凸轮机构设计中的应用J . 机械传动,2003 10张高峰杨世平,陈华章,周玉衡,谭援强. 弧面分度凸轮机构的研究与展望J.机械传动,2003
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