外文翻译--液压支架的最优化设计

外文翻译--液压支架的最优化设计内容摘要：

tion of above problem will give us response of hydraulic support for the ideal system. Real response will be different because of tolerances of various parameters of the system.， which is why the maximal allowed tolerances of parameters a1， a2， a4 will be calculated， with help of methods of mathematical programming. deterministic model of the hydraulic support At first it is necessary to develop an appropriate mechanical model of the hydraulic support. It could be based on the following assumptions: the links are rigid bodies. the motion of individual links is relatively slow. The hydraulic support is a mechanism with one degree of freedom. Its kinematics can be modeled with synchronous motion of two fourbar mechanisms FEDG and AEDB (Oblak et ). The leading fourbar mechanism AEDB has a decisive influence on the motion of the hydraulic support. Mechanism 2 is used to drive the support by a hydraulic actuator. The motion of the support is well described by the trajectory L of the coupler point C. Therefore， the task is to find the optimal values of link lengths of mechanism 1 by requiring the trajectory of the point C is as near as possible to the desired trajectory K. The synthesis of the fourbar mechanism 1 has been performed with help of kinematics equations of motion given by Rao and Dukkipati (1989). The general situation is depicted in . Equations trajectory L of the point C will be written in the coordinate frame considered. Coordinates x and y of the point C will be written with the typical parameters of a fourbar mechanism a1， a2， a6 . The coordinates of points B and D are cos5axxB  (1) sin5ayyB  (2)    c o s6axx D (3)    sin6ayy D (4) The parameters a1， a2， a6 are related to each other by 2222 ayx BB  (5)   24221 ayax DD  (6) By substituting (1)－ (4) into (5)－ (6) the response equations of the support are obtained as     0s i nc o s 222525  aayax  (7)       0s i nc os 2426216  aayaax  (8) This equation represents the base of the mathematical model for calculating the optimal values of parameters a1， a2， a4. Mathematical model The mathematical model of the system will be formulated in the form proposed by Haug and Arora (1979) : min f(u， v)， (9) subject to constraints   0vugi ， i=1， 2，„， l (10) and response equations   0vuhj ， j=l， 2，„， m (11) The vector u=[u1„ un]T is called the vector of design variables， v=[v1„ vm]T is the vector of response variables and f in (9) is the objective function. To perform the optimal design of the leading fourbar mechanism AEDB， the vector of design variables is defined as u=[ a1 a2 a4]T， (12) and the vector of response variables as v=[x y]T． (13) The dimensions a3， a5， a6 of the corresponding links are kept fixed. The objective function is defined as some “measure of difference” between the trajectory L and the desired trajectory K as f(u， v) =max[g0(y) － f0(y)]2 (14) where x= g0(y) is the equation of the curve K and x= f0(y) is the equation of the curve L. Suitable limitations for our system will be chosen. The system must satisfy the wellknown Grasshoff conditions     02143  aaaa (15)     04132  aaaa (16) Inequalities (15) and (16) express the property of a fourbar mechanism， where the links a2， a4 may only oscillate. The condition uuu  (17) prescribes the lower and upper bounds of the design variables. The problems (9)(11) is not be directly solvable with the usual gradientbased optimizations methods. This could be circumvented by introducing an artificial design variable un+1 as proposed by Hsieh and Arora (1984). The new formulation exhibiting a more convenient form may be written as min un+1 (18) subject to   0v ，ugi ， i=1， 2„， 1 (19)   0v 1  nuuf ， ， (20) and response equations   0v ，uhj j=l， 2，„ m (21) where u=[u1… un un+1]T and v=[v1… vm]T . A nonlinear programming problem of the leading fourbar mechanism AEDB can therefore be defined as min 7a ， (22) subject to constraints     02143  aaaa (23)     04132  aaaa (24) 111 aaa ，222 aaa ，444 aaa 。