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注： 1 英文翻译 Abstract. The vibration characteristics of inertial vibration feeders were analyzed. Combining active with passive vibration isolation, the hybrid vibration isolation of inertial vibration feeders was researched. Adopting the passive vibration isolation, the vibration transmissibility can be reduced efectively, but the work efficiency of the inertial vibration feeder is reduced too. By choosing right feedback variables and appropriate feedback gain, the vibration transmissibility and the work eficiency of the inertial vibration feeder can be improved markedly by the hybrid vibration isolation. When the velocity feedback gain is equal to the upper damping coeficient and the displacement feedback gain is equal to the upper spring stifness, the inertial vibration feeder has the best work eficiency and the vibration transmissibility approximates zero. The fuzzy PID control approach was used to design the active vibration control system. The simulation results show that the developed active vibration control system has good control performance. Keywords:inertial vibration feeder, hybrid vibration isolation, vibration transmissibility, fuzzy PID. Introduction The vibration feeder is an auto feeder that has been used in some high-speed machining processes.It is a typical device working with vibration. The most disadvantage of the vibration feeder is able to arouse the vibration of other parts of the machine or other instruments, and that arouses noise.When the parameters are designed or adjusted improperly, the noise is very large. This is the mostly problem of the vibration feeder 1. The usual solving way is to adopt vibration isolation and to choice the appropriate parameters of the vibration system. Consequently, the amplitude nts 注： 2 transferring to the groundwork and the infection of vibration on other machines are reduced, but the work efficiency of inertial vibration feeders is reduced too. In this paper, the vibration characteristics of inertial vibration feeders were analyzed, and the hybrid vibration isolation of inertial vibration feeders was researched. The hybrid vibration isolation system consists of the passive vibration isolation system and the active vibration isolation system 2,3. The active vibration isolation system adopts an electromagnetic actuator controlled by a fuzzy PID controller. The simulation results confirm that the vibration transmissibility and the work efficiency of the inertial vibration feeder can be improved markedly by the hybrid vibration isolation system. When the velocity feedback gain is equal to the upper damping coefficient and the displacement feedback gain is equal to the upper spring stifness, the inertial vibration feeder has the best work efficiency and the vibration transmissibility approximates zero . Model of an Inertial Vibration Feeder The inertial vibration feeder can be presented in a single-degree-of-freedom model as shown in Fig. l .Where m, k, c, and x1(t) are the mass, the spring stifness, the damper coefficient and the vibration displacement of the inertial vibration feeder; m is the eccentric mass; e is the eccentricity; F(t) is the exciting force acting in the inertial vibration feeder The equation of motion for the inertial vibration feeder is as follows: nts 注： 3 where M =m+m, The inertial vibration feeder is a device working with the vibration excited by inertial force.Therefore, the ratio of the vibration displacement x1(t) to the exciting force F(t) can be used as the work efficiency of the inertial vibration feeder. The frequency characteristic of the work efficiency can be obtained: where Fig.2 shows the frequency characteristic of the inertial vibration feeder(the work efficiency),where f 1 =0.05. In order to raise the work efficiency, the inertial vibration feeder works in the resonance area (Al =0.85-0.95). The force transferring to the groundwork is given by: .1 1 11( ) ( )()P t c k x txt (4) From equations (2) and (4), the vibration transmissibility can be obtained nts 注： 4 Fig.3 shows the vibration transmissibility of the inertial vibration feeder. It is shows that the vibration transmissibility nearby the resonance area is very large. In order to reduce the vibration transmissibility of the inertial vibration feeder, the vibration isolation technology should be adopted. Hybrid Vibration Isolation of an Inertial Vibration Feeder Fig.4 shows the dynamics model of the hybrid vibration isolation system of the inertial vibrating feeder. It is a two-degree-of-freedom vibration system consisting of the inertial vibrating feeder, the nts 注： 5 active vibration isolation system and the passive vibration isolation system. Where and x2(t) are the mass, the spring stiffiiess, the damper coefficient and the vibration displacement of the passive vibration isolation system. f (t) is the active control force produced by the electromagnetic actuator. The equation of motion for the hybrid vibration isolation system is as follows where K_ is the velocity feedback gain, Kd is the displacement feedback gain. From equations (6) and (7), the transfer function between the vibration displacement x1(t) and the exciting force F(t), that is the work efficiency of the inertial vibrating feeder, can be obtained: Where, The frequency characteristic of the work efficiency is as follows: nts 注： 6 In the hybrid vibration isolation system, the force transferring to the groundwork is given by: Therefore, the vibration transmissibility is given by: wher Changing the velocity feedback gain K_ and the displacement feedback gain Kd, the frequency characteristic (the work eficiency) and the vibration transmissibility of the inertial vibration feeder are shown in Fig.5 and Fig.6. Where f , =0.05, 2=0.3_u =0.2 and a=4. Fig.5 and Fig.6 show that the vibration transmissibility and the work eficiency of the inertial vibration feeder can be improved markedly by choosing right feedback variables and appropriate feedback gain for the hybrid vibration isolation system. When the velocity feedback gain K, is equal to zero and the displacement feedback gain Kd is equal to zero, that is in the state of passive vibration isolation, the vibration nts 注： 7 transmissibility can be reduced efectively, but the work efficiency of the inertial vibration feeder is reduced too (comparing with Fig.2 and Fig.3). When the velocity feedback gain is equal to the upper damping coeficient and the displacement feedback gain is equal to the upper spring stiffness (Kdik,=1、 K,Icl=1), the inertial vibration feeder has the best work efficiency and the vibration transmissibility approximates zero. Design of fuzzy PID control system A fuzzy PID controller is designed. The block diagram of the control system is shown in Fig.7. This system places the fuzzy inference engine above a conventional PID controller within the control hierarchy, continuously updating the coefficients based on the behavior of the system 4. We select the displacement error, its time derivative and its integral as inputs, and the coefficients of the PID controller (denoted by K1, K2, andK3)as outputs for the fuzzy inference system. The fuzzy controller adopts linguistic variables to describe the characteristics of the system.Therefore, to design a fuzzy controller, we must consider the measurement of input and output variables and the range of operation, the characteristics of the system to nts 注： 8 decide the universe of discourse of each linguistic variable, the fuzzy partition of the input and output spaces, and the choice of membership functions for the primary sets, in order to re-define each input, output variables in terms of linguistic variables. The database is used to store these linguistic variables and their definitions. Usually, within a linguistic universe the number of a partition of linguistic variables should be odd number. Its number will decide the status of a partition of the space. The more the linguistic variables, the more sophisticated the partition of spaces will be. In this system,the domain of each input is divided into three fuzzy sets: Negative (N), Zero (Z), Positive (P), and the domain of each output is divided into three fuzzy sets: Small (S), Medium (M) and Large (L).The membership functions associated with fuzzy sets are constructed using the method of defining uniform distribution. The overlap ratio of membership functions is 0.5, and they are distributed evenly among the entire universe of discourse. nts 注： 9 A fuzzy controller uses linguistically conditioned control rules to express the strategy of operating system. A set of multi-control rules constitutes a control rule base. Usually, the control rule base of the fuzzy controller is formed from operator experience and expert knowledge. The more the control rules, the more the eficiency of control will be 5,6. In order to design the rule base, we utilized our knowledge about the system under control, as well as the existing relationship between the coeficients of the PID and the performance of the hybrid vibration isolation system for the inertial vibration feeder. Table I reflects the developed rule base for the simulatio Simulation of Control System Simulation tests were carried out to assess the performance of the developed hybrid vibration isolation system for the inertial vibration feeder. In these simulations, the parameters of the vibration isolation system are shown as follows: Fig.8 shows the time history of vibration displacement in the state of passive vibration isolation.Fig.9 shows the time history of vibration displacement in the state of hybrid vibration isolation.Where x,is the vibration displacement of the inertial vibration feeder nts 注： 10 (m1),x2 is the vibration displacement of the middle body (m2). As shown in these figures, the inertial vibration feeder (ml) in the state of hybrid vibration isolation is more than two times as that in the state of passive vibration isolation, and the work eficiency isis improved markedly.The vibration displacement ofthe middle body (m2) in the state of hybrid to approximately 10% of that in the state of passive vibration isolation,and the vibration transmissibility is reduced markedly. The simulation results show that the vibration transmissibility and the work eficiency of inertial vibration feeder can be improved markedly by the developed hybrid vibration isolation system. Conclusions The vibration feeder is an auto feed device working with vibration. In order to raise the work eficiency, the inertial vibration feeder must work in the resonance area. The most disadvantage of the vibration feeder is able to arouse the vibration of other parts of the machine or other instruments,and that arouses noise. Adopting the passive vibration nts 注： 11 isolation, the vibration transmissibility can be reduced efectively, but the work eficiency of the inertial vibration feeder is reduced too. By choosing right feedback variables and appropriate feedback gain, the vibration transmissibility and the work eficiency of the inertial vibration feeder can be improved markedly by the hybrid vibration isolation. When the velocity feedback gain is equal to the upper damping coeficient and the displacement feedback gain is equal to the upper spring stifness (Kd/k,=1、 Kv/c1=l), the inertial vibration feeder has the best work efficiency and the vibration transmissibility approximates zero. The simulation results show that the developed fuzzy PID control system has good control performance. References I C.L. Zhang, L.P. Chen: Proceedings of the 3rd International Conference on Material Handling& International Conference on Freight Pipeline, Shanghai, China (1999), p. 514-528 2 K. Mizutani, Y. Fujita and H. Ohmori: 1996 IEEE, AMC96-MIE (1996), p. 577-582 3 T. Mizuno, K. Araki: Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy (1998), p. 609-613 4 A. Homaifar, Y.X. Shen and B.V. Stack: Proceedings of the American Control Conference, Arlington, VA (2001), p.1575-1580 5 YX. Shen, A. Homaifar and M. Bikdash: Proceedings of the 37th IEEE Conference on Decision &control, Tampa, Florida (1998), p. 2930-2933 nts 注： 12 6 T.L. Teng, C.P. Peng and C. Chuang: Computer Methods in Applied Mechanics And Engineering. 189 (2000), p. 439-448 nts 注： 13 振动隔离的惯性振动加料器 摘要 ：惯性振动加料器的振动特性分析 .结合现行的被动隔振来研究混合振动隔离的惯性振动加料器 .采用被动的隔振 ,振动传递率可以减少效率 ,但是惯性振动加料器的工作效率也减少经选择权利反馈变量和适当的反馈增益 ,振动传递率和惯性振动加料器的工作效率可以通过混合振动隔离来明显好转 .通过速度回授和位置回授获得阻尼系数和胜任上面的弹簧强度工作时就越明显好转 ,惯性振动加料器就有最好的工作效率和大约为的零振动传递率。模糊的比例 -积分 -微分控制的渐近弧过去常设计活性振动控制系统 .模拟结果表明发展活性振动 控制系统有好的控制性能。 关键字 惯性振动加料器混合振动隔离振动传递率模糊的个人识别数据。 介绍 振动加料器是一种已经被用于一些高速的机械加工的自动送料器 ,它是一种行得通典型振动装置 .振动加料器的大多数缺点能引起其他的机械装置或其他的装置振动，并且还引起噪声 .当参数设计或校准不正确时 ,噪音会很大 .这是振动加料器主要的问题 .通常的解决方法将采用隔振和选择振动系统的适当参数 .因此 ,幅度转入到基本工作和作用在其他的机械装置的振动影响是减少的 ,但是惯性振动加料器的工作效率也减少了 .在这个论文里 ,分析惯 性振动加料器的振动特性和研究惯性振动加料器的混合振动隔离 .混合振动隔离系统由被动的振动隔离系统和活性振动隔离系统组成 .活性振动隔离系统采用一个依据模糊的 PID控制器的电磁调节器控制 .模拟结果证实振动传递率和惯性振动加料器的工作效nts 注： 14 率是可以通过混合振动隔离系统明显好转 .当速度反馈获得胜任那上面的阻尼系数和位移回授获得胜任那上面的弹簧刚度 ,惯性振动加料器有最好的工作效率和传递率大约为零的振动传递率。 惯性振动加料器的模型 惯性振动加料器可以存在于单一程度的自由模型如图 1 所示 . m, k, c, and 1()xt是 弹簧刚度 ,阻尼系数和振动位移的惯性振动加料器 的计算量 ； m 是偏心质量 ;e 是偏心率； F(t)是在惯性振动加料器上的激振力 . 21() s i n s i nF t F t m e t （ 1） 惯性振动加料器的运动方程如下 : .1 1 1 1( ) ( ) ( ) ( )1M t c x t k x t F tx （ 2） 其中 M=m+m 惯性振动加料 器是通过惯性力对振动刺激行得通的一装置 .因此 ,振动位移1()xt和 激振力 F(t)的比率能被用做惯性振动加料器的工作效率 .工作效率的频率特性是可以获得的： 12 1 1 1( ) 1 1( ) 1 2XjF j k j g(3) 其中 1 1 1 1 1 1 1/ , / ( 2 ) , /nnc k M k M Fig.2表明惯性振动加料器的频率特性（工作效率）1 0.05 .为了nts 注： 15 提高工作效率 ,惯性振动加料器引进共振带1( 0 .8 5 0 .9 5 ) .这个力转化到给出的基本原理 : .1 1 11( ) ( )()P t c k x txt (4) 从等式 (2)和 (4)可以获得振动传递率 1211( ) 1 2( ) 1 2P j jF j j (5) Fig.3 表明惯性振动加料器的振动传递率 .它可以表明振动传递率附近的共振带是很大的 .为了减少惯性振动加料器的振动传递率 ,隔振技术将采用 . 惯性振动加料器的混合振动隔离 Fig.4表明惯性振动给料器的混合振动隔离系统的动态模型 .它是一个由二自由度振动体系组成的惯性振动给料器， nts 注： 16 活性振动隔离系统和被动的振动隔离系统 . 2 2 2,m kc 和 2()xt计算变量 .弹性刚度 ,阻尼系数和被动的振动隔离系统的振动位移 . ()aft是通过电磁调节器产生的主动控制力 .混合振动隔离系统节器运动方程如下 : 主动控制力 f(t)定义如下 : Kv是速度反馈获得， Kd是位移回授获得 .等式 (6)和 (7).传递函数在振动位移 x1 和激振力和那激振力之间 .也就是说惯性振动给料器的工作效率是可以获得的 : 其中 频率特性的工作效率如下： 其中 nts 注： 17 在混合振动隔离系统中 ,这种力转化的基本原理是给定的 : 所以，振动传递率给的是： 其中 Fig.5 和 Fig6.F(t)=0.05,.Fig.5 和 Fig.6 表明惯性振动加料器的振动传 送率和工作效率动是可以通过混合振动隔离系统选择权利反馈变量和适当的反馈增益明显好转 .当速度反馈获得 K 等于零和位移回授获得 Kd 等于零，也就是说在被动的隔振的状况 ,振动传递率可以有效的减少 ,但是惯性振动加料器的工作效率也减少了（与 Fig.2和 Fig.3相比 ).当速度反馈获得胜任上面的阻尼系数和位移回授获得胜任上面的弹簧刚度（ Kd/k=1,Kv/c=1),惯性振动加料器有最好的工作效率和大约为零的振动传递率 . nts 注： 18 模糊比例 -积分 -微分控制系统的设计 糊 PID 控制器是设计 .控制系统的方框图 Fig.7 所示 .这个系 统放置在模糊推理机传统的 PID 控制器内部控制层次之上 ,根据系统的性能连续地更新系统的系数 .我们选择偏移误差 ,它的时间导数和积分汇编程序输入 , PID控制器的系数（ K1， K2,和 K3）通过模糊的推理系统汇编程序输出 .模糊控制器采用语言变量来描述系统的特征 .因此