機械設計制造及其自動化外文翻譯 ---液壓支架的最優(yōu)化設計（英文）

1、Struct Multidisc Optim 20, 76–82 ? Springer-Verlag 2000Optimal design of hydraulic supportM. Oblak, B. Harl and B. ButinarAbstract This paper describes a procedure for optimal determination of two groups of parameters of

2、 a hydraulic support employed in the mining industry. The procedure is based on mathematical programming methods. In the first step, the optimal values of some parameters of the leading four-bar mechanism are found in or

3、der to ensure the desired motion of the support with minimal transver- sal displacements. In the second step, maximal tolerances of the optimal values of the leading four-bar mechanism are calculated, so the response of

4、hydraulic support will be satisfying.Key words four-bar mechanism, optimal design, math- ematical programming, approximation method, tolerance1 IntroductionThe designer aims to find the best design for the mechan- ical s

5、ystem considered. Part of this effort is the optimal choice of some selected parameters of a system. Methods of mathematical programming can be used, if a suitable mathematical model of the system is made. Of course, it

6、depends on the type of the system. With this formulation, good computer support is assured to look for optimal pa- rameters of the system. The hydraulic support (Fig. 1) described by Harl (1998) is a part of the mining i

7、ndustry equipment in the mine Velenje-Slovenia, used for protection of work- ing environment in the gallery. It consists of two four-barReceived April 13, 1999M. Oblak1, B. Harl2 and B. Butinar31 Faculty of Mechanical En

8、gineering, Smetanova 17, 2000 Maribor, Slovenia e-mail: maks.oblak@uni-mb.si 2 M.P.P. Razvoj d.o.o., Ptujska 184, 2000 Maribor, Slovenia e-mail: bostjan.harl@uni-mb.si 3 Faculty of Chemistry and Chemical Engineering, Sme

9、tanova 17, 2000 Maribor, Slovenia e-mail: branko.butinar@uni-mb.simechanisms FEDG and AEDB as shown in Fig. 2. The mechanism AEDB defines the path of coupler point C and the mechanism FEDG is used to drive the support by

10、 a hydraulic actuator.Fig. 1 Hydraulic supportIt is required that the motion of the support, more precisely, the motion of point C in Fig. 2, is vertical with minimal transversal displacements. If this is not the case, t

11、he hydraulic support will not work properly because it is stranded on removal of the earth machine. A prototype of the hydraulic support was tested in a laboratory (Grm 1992). The support exhibited large transversal disp

12、lacements, which would reduce its em- ployability. Therefore, a redesign was necessary. The project should be improved with minimal cost if pos-782.1 Mathematical modelThe mathematical model of the system will be formula

13、ted in the form proposed by Haug and Arora (1979):min f(u, v) , (9)subject to constraintsgi(u, v) ≤ 0 , i = 1, 2, . . . , ? , (10)and response equationshj(u, v) = 0 , j = 1, 2, . . . , m . (11)The vector u = [u1 . . . un

14、]T is called the vector of design variables, v = [v1 . . . vm]T is the vector of response vari- ables and f in (9) is the objective function. To perform the optimal design of the leading four-bar mechanism AEDB, the vect

15、or of design variables is de- fined asu = [a1 a2 a4]T , (12)and the vector of response variables asv = [x y]T . (13)The dimensions a3, a5, a6 of the corresponding links are kept fixed. The objective function is defined a

16、s some “measure of difference” between the trajectory L and the desired tra- jectory K asf(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. Sui

17、table limitations for our system will be chosen. The system must satisfy the well-known Grasshoff conditions(a3 +a4)?(a1 +a2) ≤ 0 , (15)(a2 +a3)?(a1 +a4) ≤ 0 . (16)Inequalities (15) and (16) express the property of a fou

18、r- bar mechanism, where the links a2, a4 may only oscillate. The conditionu ≤ u ≤ u (17)prescribes the lower and upper bounds of the design vari- ables. The problem (9)–(11) is not directly solvable with the usual gradie

19、nt-based optimization methods. This couldbe circumvented by introducing an artificial design vari- able un+1 as proposed by Hsieh and Arora (1984). The new formulation exhibiting a more convenient form may be written asm

20、in un+1 , (18)subject togi(u, v) ≤ 0 , i = 1, 2, . . . , ? , (19)f(u, v)?un+1 ≤ 0 , (20)and response equationshj(u, v) = 0 , j = 1, 2, . . . , m , (21)where u = [u1 . . . un un+1]T and v = [v1 . . . vm]T . A nonlinear pr

21、ogramming problem of the leading four- bar mechanism AEDB can therefore be defined asmin a7 , (22)subject to constraints(a3 +a4)?(a1 +a2) ≤ 0 , (23)(a2 +a3)?(a1 +a4) ≤ 0 , (24)a1 ≤ a1 ≤ a1 , a2 ≤ a2 ≤ a2 ,a4 ≤ a4 ≤ a4 ,

22、(25)[g0(y)?f0(y)]2 ?a7 ≤ 0 , (y ∈ ? ?y, y ? ?) , (26)and response equations(x?a5 cos Θ)2 +(y ?a5 sin Θ)2 ?a2 2 = 0 , (27)[x?a6 cos(Θ +γ)?a1]2+[y ?a6 sin(Θ +γ)]2 ?a2 4 = 0 . (28)This formulation enables the minimization o