直动滚子从动件凸轮机构效率研究
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摘要
本文作者通过详细地分析直动滚子从动件凸轮机构的两种受力状态，
推导出了直动滚子从动件凸轮机构在推程阶段以及回程阶段的瞬时效率公
式以及在推程阶段、回程阶段以及整个运动循环内的总效率公式。第一次
给出了完善的效率公式，为正确进行效率计算和理论分析奠定了基础。研
究了在给定的各种不同基本设计参数情况下所决定的凸轮的轴心许用区
内，对于不同大小、不同的轴心位置的凸轮，直动滚子从动件凸轮机构的
瞬时效率在推程阶段和回程阶段的变化规律以及总效率分别在推程阶段、
回程阶段以及整个运动循环周期内的变化规律。探讨了凸轮机构的效率和
一些设计参数之间的关系，特别是凸轮机构的效率和压力角之间的关系，
给出了效率的真实变化规律。这对于澄清效率和压力角在理论上的争议，
有着十分重要的理论参考价值。
同时，作者编写了追求效率最高的单目标优化程序以及既追求效率
高、又追求加工性能好的双目标优化设计的通用程序。双目标优化设计程
序同时还具有对所设计出的凸轮机构的运动过程进行仿真模拟显示的功
能。通过比较余弦加速度和正弦加速度这两种从动件运动规律的优化结果，
得出了一些具有参考价值的结论。这是一个全新的双目标优化设计。该程
序通用性强，并可扩充为多种从动件运动规律的凸轮的优化设计，在凸轮
的设计和加工方面有着很大的实用价值。
以上所推导的公式、结论以及程序同样适用于尖底直动从动件凸轮机
构。以上研究工作丰富了凸轮机构的理论，有着十分重要的理论和实用价
值。
In this paper, the author has inferred the instantaneous efficiency equation during rise and return and the general efficiency equation during rise, return and the whole motion cycle respectively by analyzing two kinds of force states of in-line roller follower cam mechanisms in detail. The complete efficiency equations are presented for the first time, so foundation is settled for correct efficiency calculation and theory analysis. In the axes permitted area determined by different given basic design parameters, for different size and different axes position ,the instantaneous efficiency variation rule during rise and return and the whole efficiency variation nile during rise, return and the motion cycle of in-line follower cam mechanisms has been studied respectively. The relationship between cam mechanisms?efficiency and some design parameters, especially the relationship between efficiency and pressure angle of cam mechanisms, has been discussed and the real variation rule of efficiency has been given.
These mentioned above have very important theory抯 reference value for clarifying dispute about the theory of the relationship between efficiency and pressure angle.
At the same time, the author has written the single-target optimization design抯 program that is used to design cams which have the highest efficiency and the double-target optimization design抯 program which is used to design cams which have higher efficiency and better machine characteristic. There is the function of the double-target optimization design抯 program displaying the designed cam mechanism抯 simulated whole motion procedure as well. By comparing optimum cams of simple harmonic follower-motion basic curve with optimum cams of cycloidal follower-motion basic curve, some conclusion of reference values are drawn. It is a completely new double-target optimization design. There is good general use of this program .The program can be enlarged so that it can be used to design cams for many kinds of follower-motion basic curve. There is great practical value of it for cam design and cam machining.
All these equations, conclusion and programs can also be applied to in-line knife-edge follower cam mechanisms. The above-mentioned study has enlarged the theory of cam mechanisms and has very important theory抯 value and practical value.
推导出了直动滚子从动件凸轮机构在推程阶段以及回程阶段的瞬时效率公
式以及在推程阶段、回程阶段以及整个运动循环内的总效率公式。第一次
给出了完善的效率公式，为正确进行效率计算和理论分析奠定了基础。研
究了在给定的各种不同基本设计参数情况下所决定的凸轮的轴心许用区
内，对于不同大小、不同的轴心位置的凸轮，直动滚子从动件凸轮机构的
瞬时效率在推程阶段和回程阶段的变化规律以及总效率分别在推程阶段、
回程阶段以及整个运动循环周期内的变化规律。探讨了凸轮机构的效率和
一些设计参数之间的关系，特别是凸轮机构的效率和压力角之间的关系，
给出了效率的真实变化规律。这对于澄清效率和压力角在理论上的争议，
有着十分重要的理论参考价值。
同时，作者编写了追求效率最高的单目标优化程序以及既追求效率
高、又追求加工性能好的双目标优化设计的通用程序。双目标优化设计程
序同时还具有对所设计出的凸轮机构的运动过程进行仿真模拟显示的功
能。通过比较余弦加速度和正弦加速度这两种从动件运动规律的优化结果，
得出了一些具有参考价值的结论。这是一个全新的双目标优化设计。该程
序通用性强，并可扩充为多种从动件运动规律的凸轮的优化设计，在凸轮
的设计和加工方面有着很大的实用价值。
以上所推导的公式、结论以及程序同样适用于尖底直动从动件凸轮机
构。以上研究工作丰富了凸轮机构的理论，有着十分重要的理论和实用价
值。
In this paper, the author has inferred the instantaneous efficiency equation during rise and return and the general efficiency equation during rise, return and the whole motion cycle respectively by analyzing two kinds of force states of in-line roller follower cam mechanisms in detail. The complete efficiency equations are presented for the first time, so foundation is settled for correct efficiency calculation and theory analysis. In the axes permitted area determined by different given basic design parameters, for different size and different axes position ,the instantaneous efficiency variation rule during rise and return and the whole efficiency variation nile during rise, return and the motion cycle of in-line follower cam mechanisms has been studied respectively. The relationship between cam mechanisms?efficiency and some design parameters, especially the relationship between efficiency and pressure angle of cam mechanisms, has been discussed and the real variation rule of efficiency has been given.
These mentioned above have very important theory抯 reference value for clarifying dispute about the theory of the relationship between efficiency and pressure angle.
At the same time, the author has written the single-target optimization design抯 program that is used to design cams which have the highest efficiency and the double-target optimization design抯 program which is used to design cams which have higher efficiency and better machine characteristic. There is the function of the double-target optimization design抯 program displaying the designed cam mechanism抯 simulated whole motion procedure as well. By comparing optimum cams of simple harmonic follower-motion basic curve with optimum cams of cycloidal follower-motion basic curve, some conclusion of reference values are drawn. It is a completely new double-target optimization design. There is good general use of this program .The program can be enlarged so that it can be used to design cams for many kinds of follower-motion basic curve. There is great practical value of it for cam design and cam machining.
All these equations, conclusion and programs can also be applied to in-line knife-edge follower cam mechanisms. The above-mentioned study has enlarged the theory of cam mechanisms and has very important theory抯 value and practical value.
引文
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2 FAN.Y. CHEN.Mechanics and Design of Cam Mechanisms. Pergamon Press Inc., Newyork, 1982:1～11, 15～124, 34～52
3 孙恒．机械原理．第五版．高等教育出版社，1996：196～238
4 Makino, H., Ohde, T..Motion Control of the Direct Actuator. Annals of the CIRP. 1991,Vol.40 No. 1:375～378
5 Kanzaki, K., Kobayashi, Nobuaki. Output of Cam Motion Curve by DC Servo Motor and High Speed Positioning .Proc. of the Fifth World Congress on Theory of Machines and Mechanisms, 1995:739～743
6 Yamada, I., Nakagawa, M..Reduction of Residual Vibrations in Positioning Control Mechanism. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design. 1995,Vol. 107,47～52
7 于强，孔午光．高速机构运动规律的主动设计．机械传动．1993，(4)：25～29
8 蔡惠普．抛物余弦型凸轮从动件运动规律研究．机械设计．1993，(4)：13～15
9 徐辛伯．用Bezier函数表达凸轮机构运动方程．机械设计．1994，(3)：25～29
10 牧野洋．自动机械机构学．胡茂松 译．科学出版社，1980：4～47
11 Neklutin,C.N..Mechanisms and Cams for Automatic Machines.New York, American Elsevier, 1969:1～235
12 Kwakernaak,H., Smith,J..Minimum Vibration Cam Profile.ASME Journal of Mechanical Engineer for Science. 1968,Vol. 10:219～227
13 Kanzaki,K., Itao,K..Polydyne Cam Mechanism for Typehead Positioning. Transactions of the ASME Journal of Engineering for Industry. 1972,Vol. 94:250～254
14 Berzak,N..Optimazation of Cam-Follower Systems With Kinematic and Dynamic Constraints. ASME Journal of Mechanicl Design. 1982,Vol.104: 29～33
15 Chew, M., Chuang,C.H.. Designing For Lower Residual Vibrations in High-Speed Cam-Follower Systems Over a Range of Speeds. ASME Design Engineering Division. Publication DE..1990,Vol.26:23～31
16 姚燕安和张策．凸轮曲线连续性与残余振动关系的理论解释．机械科学与技术．1998，No．6：872～874
17 Xie Chun. The New Determination and Method of the Axle Center Region About the Oscilating Follower. Proceedings of International Conference on Mechanical Transmissions andMechanisms,Tianjin,China 1997:466～467
18 田政典．按许用压力角确定直动动从动件凸轮轴心的最新方法．机械设计．1995，(10)：32～36
计．1995，(10)：32～36
19 吴玉光．摆动滚子从动件盘状凸轮机构基本尺寸的精确求解方法．机械设计．1996，(5)：14～16
20 张一同．确定凸轮轴心许用区的一种新的解析法．机械设计．1999，Vol．16(4)：35～36
21 贺贤贵．滚子从动件盘形凸轮按效率最高和体积最小的优化设计．机械工程学报．1988，Vol．24：91～95
22 张一同．直动从动件凸轮曲率半径和压力角随导路偏距的变化关系．燕山大学学报．1999，(3)：216～218
23 D.M.Tsay, B.J.Lin. Profile determination of planar and spatial cams with cylindrical roller-followers. Journal of Mechanical Engineering Science. 1996:565～574
24 G.S.Hwang, D.M.Tsay, M.H.Huang. Profile determination of plate cams with oscillating convex arbitrary-shaped followers. Journal of Mechanical. Engineering Science. 1996:333～349
25 Dai Zhong Su. AN INTEGRATED SYSTEM FOR TOTAL DESIGN OF DISC CAMS WITH ROLLER FOLLOWERS.MTM.97:389～401
26 Emeritus.Exact Response Analysis and Dynamic Design of Cam-Follower System Using Laplace Transforms. Transactions of the ASME, 1997,Vol. 119:360～368
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