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英文翻译2A model of the working operatiors of a quarry excavator.pdf
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MECHANIZATION AND AUTOMATION OF MINING OPERATIONS A MODEL OF THE WORKING OPERATIONS OF A QUARRY EXCAVATOR E. V. Gaisler, A. P. Mattis, E. A. Mochalov, and S. V. Shishaev We develop a methematical model of the process of open-pit mining with a quarry ex- cavator using a bucket that has active blades driven by impact blocks installed in the front wall. The bucket operates as follows. When the bucket comes in contact with a rock area that can be broken by a force greater than the sum of the forces of friction of the tool on the sleeve and the force of activation of the starting device, the impact blocks are energized. The action of these blocks causes the bucket blades to enter the rock to a depth X, weakening the zone located directly under the blades and forming the so-called disrupted bonding zone i. This zone requires much less force to be broken than an in- tact mass. With such active buckets, strong rocks can be excavated without preloosening. The main parameters describing the movements of the bucket during excavation include the mechanical properties of the rock, the variation of these properties under the effect of the impact, the working characteristics of the drives of the actuator mechanisms, and the parameters of the equipment. Two types of destruction take place during the course of excavation: cutting and impact breaking. The geometric sum of forces acting on all the faces of a blade represents the resist- ance to intrusion. The projection of this sum onto the axis of the impact block is Pl; the projection onto the direction perpendicular to the axis is P2. The sum of forces act- ing perpendicularly to the bucket-traveling plane is equal to zero because block fracturing is mainly performed. The following assumptions are made for a mathematical model describing the motions of the bucket: ? - the center of mass of the rock in the bucket is stationary relative to the bucket; - chips are separated continuously; - the loads on the bucket blades are equal; - the blades penetrate the rock instantaneously upon impact; -the resistance to the bucket-filling is disregarded; - the moment of friction relative to the rotation axis of the arm is disregarded. With these assumptions, the motion of the bucket can be interpreted as the motion of a two-dimensional mechanism under the effect of external forces, which includes the force developed by the drives of the pressure mechanism and the lift mechanism, the gravity force, and the resistance force of the rock face. The position of the bucket at each point in time is defined by the coordinate r(t), the distance (OC), and (t) - the angle between the boom and the bucket stick. The kinetic energy of this mechanism is expressed as = ( + m) ,- + JT (1) where m 1 is the rock mass and the bucket; m 2 is the mass of the stick and the empty bucket; J is the moment of inertia of the bucket with rock and the stick relative to its rotation axis Institute of Mining, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Trans- lated from Fiziko-Tekhnicheskie Problemy Razrabotki Po!eznykh Iskopaemykh, No. 2, pp. 60-67, March-April, 1991. Original article .submitted September 25, 1990. 0038-5581/91/2702-0131512.50 ?9 1992 Plenum Publishing Corporation 131 Y = ml (r + lCBii)+ J + mi(r- rl) 2 + IGA), (2) where J1 is the moment of inertia of an empty bucket and the stick relative to the center of mass and r - rl is the coordinate of the center of mass of the empty bucket with the stick. The rock mass in the bucket m depends on the path traveled by the front edge of the bucket and the initial shape of the rock face. In order to write an expression for the rate of mass increment, we will consider the scheme in Fig. 2. Suppose that the path traveled by the bucket edge by the time t is described by the curve f2(r2, 2) The ini- tial shape of the face by the curve f3(r3, 3), where r2, , r3, 3 are polar coordinates with the origin at zero. During the time dt the bucket edge travels a distance ICDI; in that case, since d 2 = d 3 the mass increment within the time dt is specified by I dm = T ,B (I OC l I OD I -I OA . I OB I) sin da 2, where 0 is the rock density and B is the width of the bucket edge. We see from the diagram that loci = r, ION = r= dr, IOAI = r, IOBI = r dr3. Considering that sinda da 2 and disregarding the squares of the infinitesimal variables, we write 1 a, = r,z (, - d) a. The increment d 2 is equal to the product at the angular speed of the stick at the time t and the increment dt, i.e., d 2 = da 3 = &dt. The rate of increment of the mass is now ex- pressed as dNl o , = .-7- = _ ,i (d - ,.:,) =. (3) The mass falling into the bucket during the time t is defined by ! m, = J s ()dT 0 This mass m I is only a function of the time t. Making use of the fundamental equation of the dynamics of a variable-mass point (Mesh- cherskiis equation), we can demonstrate that Lagrangian equations are applicable to the mechanical system that consists of variable-mass material points if the absolute velocity of the associated mass is equal to zero. Consider a mechanical system comprised of n material points with masses ml, m 2 . m i, ., m n, that move with velocities v i. Lagrangian equations for m i = const have been derived in 2, p. 340. Consider the case of m i = mi(t). In following 2, we introduce generalized coordinates q, such that i = ri(ql, q2, , qs, t), where r i is the position vector of the ith mass. Now, i = )1 )j, Oli Oi j I uqj Uqj Oq) where j is generalized velocity. The kinetic energy of the mechanical system at any time point is defined as 1 - T ?niViU i . We find partial derivatives of kinetic energy with respect to the generalized coordinate qj and the generalized velocity j: or = - oi aqj miUi -r- , i=l aqi 132 _ ih, i - Or i OT mivl mivi Oqj = i=1 Oqj i= Oqj We differentiate this expression with respect to time . Consider now the first sum, taking into account the fundamental equation of the dynamics of variable-mass point for the case where the absolute velocity of the associated mass is equal to zero 2, p. 143 , am v =F, m.-7 + - where P is the resultant of the forces applied to the point. For a nonfree material point with variable mass, we have elT, i dm - m l -77 + -d-f vi = F., + 7 , where Ri is the resultant of the reactions of constraints applied to the ith point. Now, 7, + m, - . , + 7, + 7, - , = i=1 S - - . Or i = (F+n)=Q+&. i=l The second sum is, in fact, 8T/Sqj 2, p. 342. We obtain dt = Qj + o + OT Oq) For a system with stationary perfect constraints QjR = 0 d OT 07 It is the Lagrangian equation for a mechanical system consisting of variable-mass material points under the assumption that the absolute velocity of the associated mass is equal to zero. As we see, it is identical to a Lagrangian equation derived for a constant mass of material points belonging to the mechanical system. The Lagrangian motion equations for this mechanism are r - u-7- = QJ 7 , ,A , - = Q (5) where QI, Q2 are generalized forces acting on displacements 6r and 6, respectively, l Q, = - , o, ( - /- ,-o., / o - + :,- ,.o I + + (m + m).gcos(- ), O, = l).r.sin(-OCD) r + I CDI/ ) .P.sin cos (n - OCD) / (6) 133 Fig. 1 Fig. i. Fig. 2. C D Fig. 2 Design scheme for an excavator with an active bucket. Evaluation of the increment of rock weight in the bucket. 12(t). t + P3, (10) where U is the coefficient of friction of the tool in the bucket sleeve Pa as the force of activation of the automatic starting device. The stroke is made at the time l= 11+ Tl+ T2, where T l is the actuation time of the device and T 2 is the impact cycle time. Upon impact, blades penetrate the rock to a length which is a function of the rock properties, the blade geometry, and the impact energy. Studies in situ and laboratory experiments measuring the penetration of the blade upon impact, conducted by the Institute of Mining, the iInstitute of Construction Machines, the Skochinski Institute, and the Karaganda Polytechnic 4-6, suggest the existence of some characteristic of the bed being fractured which can be used to assess the fracturing efficacy. For such a characteristic the specific energ 7 capacity of fracturing can be used and measured per a unit of strength of the bed, e.g., the rocks ultimate uniaxial compressive strength, i.e., i A.K E, = .,./,.% 2.78t(I -, (11) where A is the single-impact energy, J; K 0 is the transfer coefficient of the impact energy to the bed; x is the penetration of the blade in one stroke, m; F is the transverse cross sectional area of the fracturing track m2; and o 0 is the ultimate uniaxial compressive strength of the rock, kN/m 2. The value of E 0 depends on the mechanical properties of the bed and its condition. The range of specific destructive energy capacity per stroke in certain permafrost grounds with a tool shaped as a symmetric wedge, measured by a single stroke of the density gauge devised by the Road Construction Research Institute, is indicated in Table i. The pene- tration of a blade can be defined by A.K.2.78.10-7 E,I ?9 I:. % :33.3 Besides, E 0 can be measured experimentally or estimated from the data reported in 7-9. After the impact, the movement of the bucket is described again by Eqs. (2) and (8), but with the condition P = 0, P2 = 0, until the front edge of the bucket travels the dis- tance x. 135 g, deg 4 5 , sec Fig. 3. Bucket stick rotation angle vs. time (i - digging without adjust- ment for C weakening after impact, 2, 3 - linear and quadratic weakening of C, respectively; 4 - experimental data; i-3 - rock (f = 5; C l = 30 x 106 H/m2; = 0.5), 4 - siltstone f = 5-6, C I = (32-36)106 N/m2; = 0.5. The condition for transition to mode 3 in time appears as 2 2 1 2 (t) + r2 (l) - 2 .r, (4).r (/:). cos ( (l) - (t) x . ( 12 ) After (12) is satisfied, cutting in mode 3 begins. The rock resistance to destruction is generally described by the familiar expression = o.tgp+ C, (13) where o is normal pressure, 0 is the internal friction angle, and C is the rock cohesion. The Mohr-Coulomb criterion can be formulated as a function of principal stresses under destructive load i0: o, = o0+ 03 ?9 tg2(5 + p/2), (14) where o I is the largest principal stress corresponding to the maximum of the stress-strain curve. Expressing o I and o 2 in terms of T and o and solving simultaneously Eqs. (13) and (14), we obtain an expression of the uniaxial compressive ultimate strength o 0 as a function of cohesion C: Oo= 2 .C .tg(45+ 0/2). Expression (15) shows that the main characteristic of the alteration of rock properties after impact is a drop in cohesion. The cohesion in the bed is defined as (15) C = C,l, (16) where C I is rock cohesion in a lump; 11 is the structural weakening coefficient of the bed, which is a function of the average lump size, the main crack network, and the direction of the mine advance 8. After the impact, the cohesion C(t3) = C.2, where 12 is a coefficient representing additional weakening of the bed by impact loads. At the load application point, the material is crushed. According to Popov 7, k2 after the impact is reduced to 0.0005. As the blade moves through the disrupted bonding zone, the value rises to its initial level according to a certain pattern (studying the behavior of C = f(x) is a separate subject). In a first approximation, the size of the zone and the cohesion value can be estimated from the results of 7-9. The movement of the bucket in the disrupted bonding zone is described by (2)-(10), plus additional con- straints imposed on C (the rock cohesion). With increasing C, the values of Pl and P2 grow. The further movement of the bucket follows mode 1 or 2, depending on whether con- dition (i0) is met. 136 Equations (2)-(8) hold for all the modes of bucket movement, with the respective con- straints imposed on P1, P2, and C. Transitions between the modes occur depending on whether conditions (9) and (i0) are satisfied. A mathematical model composed of (4), (6), and (8), which describes the working process of an excavator with an active bucket, consists of a set of nonlinear differential equations. A modified Merson algorithm with an automatic step selection and accuracy control was used to solve this sytem. The model has been programmed for a computer in an interactive mode. In the course of solution, the trajectory of the bucket can be adjusted by selecting load characteristics of the drives of lift and pressure mechanisms, i.e., by choosing the appropriate functions fl(), f2(, &), which correspond to the actual process of excavator control. Several alternatives were computed to evaluate this model. The results are illustrated by solid plots in Fig. 3. In the first situation, the fracturing is caused entirely by impact loads. The energy of a single stroke is insufficient to create a disrupted bonding zone (curve i). The other two cases are characterized by different forms of weakening of cohesion in the dis- rupted bonding zone (2, linear weakening; 3, quadratic weakening). The modeling results were compared with the data of in situ experiments on siltstone in the Krasnogorsk section of Kemerovougol Enterprises (dashed line in Fig. 3). A qualitative similarity was observed between the model and the actual process (the data discrepancy did not exceed 30%). The smallest discrepancy was observed with the linear cohesion weakening in the disrupted bond zone. With his mathematical model one can investigate the parameters of the working process in various !excavation conditions for design of these machines to meet specific technical and economic characteristics and mining objectives. LITERATURE CITED i. A. I. Fedulov and V. N. Labutin, Impact Coal Destruction in Russianl, Nauka, Novo- sibirsk (1
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