MT Chap6 Design of Cam Mechanisms

2020-02-27 165浏览

  • 1.
  • 2.6.1 Introduction 1. Composition and Characteristics of Cam Mechanisms A cam mechanism consists of cam, follower and frame, and it belongs to the category of higher pair mechanism. Fig 6-1 shows two kinds of cam mechanisms，in which Fig 6- 1a shows a disk cam with a translating follower, and Fig 6-1b shows a disk cam with an oscillating Fig.6-1 Cam mechanisms(盘形凸轮机构) follower. Cam mechanism is widely used in automatic machines, internal combustion engines, machine tools, printing machines, and so on. Compared to linkages, cams are easier designed to give a specific output motion. Cams also have a simple structure and reliable performance.
  • 3.2. Types of Cam Mechanisms (1) Types of cams Disc cam（ Fig6-1） Translating cam（ Fig6-2） Spatial cam（ Fig6-3） (2) Types of follower shapes （Fig6-4） Knife edge follower Roller follower Flat faced follower Spherical faced follower (3) Types of follower motion （Fig6-4、Fig6-5） Reciprocating follower Oscillating follower (4) Types of motion constraints Force closure（Fig6-6） Form closure（Fig6-7）
  • 4.Fig.6-2 Translating cam mechanisms(移动凸轮机构) Fig.6-3 Spatial cam mechanisms(空间凸轮机构)
  • 5.Fig.6-4 Follower types(从动件的分类) Fig.6-5 Disc cam with radial follower (直动从动件盘形凸轮机构)
  • 6.Fig.6-6 Force-closed cam mechanism (力封闭凸轮机构) Fig.6-7 Form-closed cam mechanism(形封闭式凸轮机构)
  • 7.3. Cams Terminology 1) Cam profile 2) Basic circle 3) Trace point 9) Stroke 10) Angle of ascent 4) Pitch curve of the 11) Angle of descent cam 12) Angle dwelt at the 5) Prime circle 6) Pressure angle 7) Rise travel 8) Return travel highest position 13) Angle dwelt at the lowest position 14) Cam angle 15) Follower displacement
  • 8.Fig.6-8 Nomenclatures of cam mechanism (凸轮机构名 词术语) 1—follower(从动件)2—pressure angle(压力角)3—trace p oint(轨迹点) 4—pitch curve(理论廓线)5—cam profile(凸轮实际廓线) 6—prime circle(理论廓线基圆)7—base circle(实际廓线 基圆) Fig.6-9 Cam angle and follo wer displacement(凸轮转角 与从动件的位移)
  • 9.Fig.6-10 Motion of the follower(凸轮机构运动循环图)
  • 10.6.2 Basic Types of Follower Motion and Design 1. Basic Types of Follower Motions (1) Polynomial motions 1) Constant velocity motion Fig.6-11 Constant-velocity curve (等速运动规律)
  • 11.2) Constant acceleration and deceleration motion Fig.6-12 Constant acceleration and deceleration curve(等加速等减速运动规律)
  • 12.3）The 3-4-5 polynomial motion Fig.6-13 3-4-5polynomial curve (五次多项式运动规律)
  • 13.(2) Trigonometric motions The motions of trigonometric form a re simple harmonic motion which has a cosine acceleration curv e and cycloid motion which has a sine acceleration curve. 1) Simple harmonic motion Fig.6-14 Simple harmonic motion(简谐运动) Fig.6-15 Cosine acceleration curve(余弦运动规律)
  • 14.2) Cycloid motion Fig.6-16 Cycloid motion(摆线运动) Fig.6-17 Sine acceleration curve(正弦运动规律)
  • 15.2. Combination of Basic Follower Motions (1)The criteria of combination of the follower motion 1) According to the desired function of the follower, a basic curve has been de termined first, and then another basic curve which would like to minimize the in ertia force and kinetic energy of the follower has been selected. 2) The combined curve must have excellent boundary conditions at the beginn ing point and the end point of the travel. 3) The displacement curve, velocity curve, acceleration curve or jerk curve m ust be continuous at the connecting points between the two curves to satisfy a s mooth surface of the cam. This can reduce or eliminate the vibration and noise. 4) It is useful to improve the dynamic features.
  • 16.(2) Examples of combined motion curve As we know in Fig 6-11, the accelerations at the beginning point and the end point of the follower motion are infinite. A modified curve, such as cycloid curve, polynomial curve, can be evolved，in which the accelerations are reduced to a finite values. This can be done by rounding the sharp corners of the displacement curve so that the velocity changes are gradual at the beginning point and the end point of the follower motion. When we use half cycloid match constant velocity curve at the beginning and the end of the displacement curve, the modified constant velocity curve can be obtained shown in Fig 6-18. Fig.6-18 Modified constant velocity curve(改进的等速运动规律)
  • 17.3. Selection of the Basic Motion of the Follower Therefore, the criteria selecting the follower motion curves are asfollows:1) It must satisfy the desired follower motion. 2) Dynamic force is proportional to acceleration, so the maximu m acceleration of the follower must be as small as possible. 3)Kinetic energy is proportional to velocity, so the maximum ve locity of the follower must be as small as possible. 4)The derivation of acceleration, that is jerk, is as continuous as possible.
  • 18.6.3 Cam Profile Synthesis 1. The Principle of Inversion The principle of inversion is convenient to design the cam profile, in which the cam is imagined to be stationary, while the follower rotates about the cam center at the cams angular velocity in the opposite direction. The locus formed by the follower trace point which has the absolute angular motion about the cam center and the relative translating motion along the follower guide is the cam profile. The fundamental basis for all cam synthesis is that the cam profile is developed by fixing the cam and moving the follower around the cam to its respective relative positions. This tenet must be remembered and the synthesis procedures will be easily understood and retained.
  • 19.Fig 6-19a shows inverse procedures of a cam with the knife edge follower. We can obtain the cam profile. In Fig 6-19b, the trace point is the roller center. We can only obtain the cam s pitch curve. The envelope curve of the roller is the actual profile of the cam. Fig.6-19 Principle of inversion 1(反转原理1)
  • 20.If we design a cam with a flat faced follower, the intersection of the follower guide and the flat face is the trace point B0. Through these points, such as B1, B 2, draw the flat faces; the curve tangential to the flat faces is the cam actual profile. This is shown in Fig 620a. Fig 6-20b shows a disc cam mechanism with an oscillating roller follower. Fig.6-20 Principle of inversion 2(反转原理2)
  • 21.2. Synthesis of Cam Profiles (1) Disc cam with translating roller follower Fig 6-21a shows the disc cam wit h an offset translating roller follower, and the following data relative to the cam synthesis are known. They are radius of prime circle r0, offset of the follower a xis e, radius of the roller rr, and follower motion s=s(φ). Fig.6-21 Cam synthesis with translating roller follower(直动滚子从动件盘形凸轮的 轮廓曲线设计)
  • 22.(2) Disc cam with translating flat faced follower Fig 6-22 shows a cam mechanism with translating flat aced follower in which the origin of the Cartesian Oxy coordinate system is located at the cams rotating center and the y axis followeris defined parallel to the follower guide. Fig.6-22 Cam synthesis with translating flat-faced follower(直动平底从动件盘形凸轮的廓线设计)
  • 23.(3) Disc cam with oscillating roller follower Fig 6-23 shows a cam mechanism having an oscillating roller follower, in which the origin of the Cartesian Oxy coordinate system is located at the cam rotating center O and the y axis passes through the oscillating pivot of the follower. Fig.6-23 Cam synthesis with oscillating roller follower (摆动滚子从动件盘形凸轮的廓线设计)
  • 24.6.4 Sizes of Cam Mechanisms 1. Pressure Angle of Cam Mechanism (1) The pressure angle of cam mechanism with translating follower Fig 6-24a s hows a cam mechanism with translating roller follower. Fig.6-24 Pressure angle of radial cam with translating follower(直动从动件盘形凸 轮机构的压力角)
  • 25.(2) The pressure angle of cam mechanism with oscillating follower Fig 625a shows a cam mechanism with oscillating roller follower. The pressure angle is described in this figure also, and the pressure angle of cam mechanism with oscillating flat faced follower is described in Fig6-25b. (3) Allowable pressure angle The allowable pressure angles are shown in Tab 6-1. Fig.6-25 Pressure angle of radial cam with oscillating follower(摆动从动件盘形凸 轮机构压力角)
  • 26.2. Sizes of Cam Mechanism (1) Radius of prime circle The shape of the cam in general is controlled by pressure angle. As the cam becomes smaller, the pressure angle becomes lar ger. This can be shown in the following formula. The radius of curvature is a mathematical property of a function, and its valueis:we can solve the minimum radius of curvature of the cam profile ρmin, then simultaneously solve equations (6-23) of the cam profile having flat faced follower. Weget:
  • 27.(2) Radius of roller The cam s curvature is important in selecting the proper size of roller or length of the flat face of the follower.  to have a minimum radius of curvature of the cam profile, the radius of the roller must be less than that of the minimum radius of curvature of the cam pitch curve. Thatis:rr ≤0.8 ρmin From the viewpoint of strength, the radius of roller must satisfy the followingcondition:rr ≥(0.1~0.5) r0 Fig.6-26 Relationship between the roller and the ca m pitch curve(凸轮滚子尺寸与廓线的关系)
  • 28.(3) The length of the flat face of the follower When the cam rotates about its center, the flat faced follower must maintain contact with the cam surface at all times so that the flat face has sufficient length. The length of the flat face of the follower can be determined in Fig 6-27. Fig.6-27 Length of the flat-faced follower(平底从动件的长度)
  • 29.(4) Offset The direction and magnitude of the offset can influence the pressure angle of cam mechanisms. To reduce the pressure angle, the location of the offset can be determined by observing. The maximum offset eis:
  • 30.6.5 Computer aided Design of Cam Mechanisms Fig.6-28 Cam profile design procedure (凸轮廓线设计过程)
  • 31.Example 6-1 Design a disc cam mechanism with translating offset roller f ollower shown in Fig 6-29. The follower motionsare:Rise the follower w ith the cycloid motion for 135°; Lower the follower with the simple harmo nic motion for 100°; Dwell for 45° at the high position of the follower; D well for 80° at the high position of the follower; The radius of the cam pri me circle is r0=65mm; the radius of the roller is rr=12mm, and the offset i s e=12mm. The cam rotates about its center with an angular velocity ω=12 rad/s counterclockwise. Fig.6-29 Cam profile design (凸轮轮廓曲线的设计) Fig.6-30 Cam pitch curve and profile(凸轮 的理论廓线和实际廓线)
  • 32.Tab.6-2 Cam angle φ凸轮 Pitch curve理论廓线坐标 转角 x y 140° 49．869 -78．1 150° 35．549 -85．573 160° 20．149 -90．446 170° 4．138 -92．571 180° -12．000 -91．883 190° -27．588 -87．354 200° -41．300 -78．384 210° -52．012 -66．088 220° -59．255 -51．948 230° -63．271 -37．426 240° -64．875 -23．599 250° -65．136 -10．937 Cam profile实际廓线坐标 43．41 30．945 17．54 3．602 -10．446 -22．548 -33．375 -42．031 -48．038 -51．47 -52．894 -53．136 -67．986 -74．491 -78．733 -80．583 -79．984 -76．463 -69．373 -59．426 -47．684 -35．247 -22．92 -11．005
  • 33.260° -64．996 0．725 -52．997 0．591 270° -63．883 12 -52．089 9．785 280° -60．828 22．911 -49．599 18．681 290° -55．926 33．125 -45．601 27．01 300° -49．324 42．334 -40．218 34．518 310° -41．224 50．256 -33．613 40．978 320° -31．870 56．65 -25．987 46．192 330° -21．549 61．324 -17．571 50．003 340° -10．573 64．134 -8．621 52．294 350° 0．725 64．996 0．591 52．997 360° 12．000 63．883 9．785 52．089