液压起重机俯仰运动的动态响应外文文献翻译、中英文翻译、外文翻译

1、外文文献Dynamic responses of hydraulic crane during luffing motionAbstractBased on the complete dynamic calculation method that was developed in our previous work, closed simulations for determining the dynamic responses of hydraulic crane during luffing motion with consideration of the cylinder drive s

2、ystem and luffing angle position control have been realized. Using Lagranges equation and the multi-body theory, the flexible model of crane luffing motion is established. The generalized cylinder driving forces are formulated with the virtual work principle. Coupling the boom structure, hydraulic a

3、ctuator and luffing angle position control system, the total system equations are established. The calculation results show that the dynamic responses of crane are more sensitive to the luffing acceleration, in comparison with the luffing velocity. It is seen that this method is very effective and c

4、onvenient for crane luffing simulation. It is also reasonably to see that the proposed complete dynamic method can be further used for optimal control of crane motion. Keywords: Dynamic response; Crane luffing motion; Multi-body theory; Hydraulic cylinder; Angle position control 1. IntroductionBoom

5、luffing is one of the fundamental motions of rotary cranes. Luffing motion is usually driven by hydraulic motors or cylinders in modern mobile cranes. During start-up or braking of the drive system, the dynamic forces can be produced, which are harmful not only to crane security, but also to health

6、of crane drivers. Because of the payload pendulum during boom motion, the dynamic forces can be very significant. For this reason, many studies on crane dynamics have been reported in the literature. Most of the published articles concentrated on dynamic responses of cranes during rotating and hoist

7、ing motion.Only a few works have payed attention to the luffing motion of crane. In our previous works, we have found that the method of “kinematic forcing” with the assumed profiles of the driving velocity and acceleration could not accurately describe the driving outputs during start-up and brakin

8、g of the system. It is seemed that these assumed start-up and braking velocity profiles are based on experience. Because of the large inertia forces of the crane structure, for start-up and braking of crane system, the driving force and torque generated by the motor or cylinder are time complicated

9、functions. These driving forces pay an important rule in exerting dynamic responses and control effects. To improve this situation, a new method for dynamic calculation of mobile cranes has been proposed in our previous work. In this method, the flexible model of the steel structure is coupled with

10、the model of the drive system. In that way the elastic deformation, the rigid body motion of the structure and the dynamic behavior of the drive system can be determined with one integrated model. We called as “complete dynamic calculation for mechanism”. Using the proposed method, we have presented

11、 complete dynamic models for rotating and hoisting motion of rotary crane. In this paper, the luffing dynamic behavior will be considered. The calculation will be realized for a hydraulic mobile rotary crane. Because the boom structure subjects not only elastic deformation, but also has large rigid

12、rotation, the flexible multi-body dynamic theory will be used to describe the boom luffing motion. The drive system is cylinder, which is described using hydraulic and control theory. The generalized cylinder driving forces will be derived using the virtual work principle. The total system will be d

13、escribed using the system state equations. The simulations of crane luffing motion will be carried out. 2. The method of complete dynamic calculationThe principle of complete dynamic calculation that is proposed in our previous work is based on the integrated model from flexible multi-body model of

14、the mechanism and the mathematical model of the drive system. The inputs are the desired state values of the mechanism, such as position or velocity. The outputs are the dynamic responses of the complete system, which consists of the mechanism system and the drive system with control. See Fig. 1. Fi

15、g. 1. The principle of complete dynamic calculation for mechanism.Using Lagranges equation, the mechanism motion is given by (1)where T is total kinetic energy, q is the vector of the generalized coordinates, Qin is the vector of the internal generalized forces, Qa is the vector of the applied

16、external forces, Qd is the vector of the generalized driving forces and are the Lagrange multiplies, which describe the constraint forces between the connecting bodies. The constrained conditions of the bodies can be written in the following vector equation:C(q,t)=0 (2)The drive system has a signifi

17、cant influence on the dynamic responses of the driven mechanism and should be included in the dynamic model. Electronic and hydraulic drive systems with control are usually used in mobile cranes. In general, the drive system with control can be described using the following first order explicit diff

18、erential equation: (3)where z is the state space vector of the drive system, q is the feedback vector from the driven mechanism. According to the corresponding physical law for the drive system, such as electronic or hydraulic, the driving forces, in general, can be expressed through following algeb

19、raic equation:Qd=fd(z,t) (4)The equations of motion for the complete system will be achieved through the combination of Eqs. (1), (2), (3) and (4). The fundamental problem of complete dynamic calculation for mechanism is, with consideration of the inputs and the boundary conditions, to solve all of

20、the time variables q, , z, Qd simultaneously. 3. Flexible multi-body formulations for the luffing mechanismThe luffing mechanism is often driven by hydraulic cylinders in modern cranes. The boom structure has not only large rigid moving, such as translational and rotational for different application

21、s during luffing, but also undergo elastic deformations that are generated by the applied heavy payloads. To describe these motions and their couplings, the multi-body dynamic theory should be used .3.1. Multi-body formulations of the luffing boomsIn the flexible multi-body theory, the large rigid b

22、ody motion is usually described in the global inertia reference system xyz, as shown in Fig. 2. On the other hand, the body reference system is selected to measure the body deformations in the luffing mechanism. Fig. 2. Flexible luffing booms driven by a hydraulic cylinder.Fig. 2 shows two flex

23、ible bodies m and n, which are driven by a hydraulic cylinder. The position vectors Rm and Rn, the rotation vectors m and n determinate the location and direction of the body references and , respectively. For body m, the deformable current position vector of the arbitrary point p respect to the ine

24、rtia reference can be described as (5)for body n, we have also (6)with and are the elastic position vectors of point p and q, measured in the body reference; Am and An are the transformation matrixes, which are matrix functions of m and n, respectively. The elastic position vectors can be approximat

25、ely interpolated by nodal parameters and for body m and n, using the well-known classical numerical methods, such as the finite element method or the RayleighRitz Method .3.2. Formulations of the generalized driving forces during luffing motionThe generalized driving forces Qd generated by the cylin

26、der can be formulated using the virtual work principle. Assuming that the cylinder is a rigid body system, thus the distance between link points p and q, showing in Fig. 2, is given by lc=lc1+lc2+x (7)where x is the cylinder piston moving, lc1 and lc2 are the piston stab lengths, which are assumed t

27、o be constant. The virtual work of the cylinder thrust force on the virtual displacement of the piston moving x is given by Wc=Fkx=Fklc (8)where Fk is the actuating force, generated by the cylinder pressures. In considering of , which is the relative position vector of the two connected points q and

28、 p in body n and m ,yields (9)By differentiating of lc with respect to time, we have (10)Therefore, (11)and (12)where , are the angle velocity matrixes, which can be formulated by m and n; , are the skew symmetric matrixes of the shape functions Hm and Hn; The values of Hm and Hn can be calculated u

29、sing the node coordinates of p and q in the body reference; , are the skew symmetric matrixes of the generalized coordinates qm and qn of body m and n, respectively. Thus, we have (13)Let (14) (15)By substituting into Eqs. (9) and (8), yields the virtual work (16)Thus, the generalized forces are giv

30、en by (17) (18)where , and are the generalized driving forces applied to the coordinates Rm, m and of the body m and , and are the generalized driving forces applied to the coordinates Rn, n and of the body n, respectively. 3.3. Formulations of the luffing hydraulic circuit with angle position contr

31、olThe cylinder actuating force Fk in Eqs. (17) and (18) can be determined using the well-known hydraulic theory 8. The luffing mechanism of modern cranes is usually driven by hydraulic circuit with control, showing in Fig. 3. The cylinder is controlled with a zero-lapped 4/3-spool valve, which is dr

32、iven by a feedback gain for different controlling, such as position or velocity control. Fig. 3. Luffing cylinder system.The flows through the spool valve are given by the turbulent equations as follows: (19) (20)where xv is moving of the control valve, ps is the system supply pressure and Bv i

33、s the flow coefficient of the valve. pa and pb are the pressures in chamber a and chamber b of the cylinder, respectively. Considering that the boom is usually driven to transfer to a desired luffing angle, the angle position control is used. In this case, the PI controller can be used for describin

34、g the feedback gain vy: (21)where xd is error between the desired luffing angle w and the output angular state value q, Kp is the proportional control parameter, Tp is time constant. Thus, Eq. (21) can be written in general form as follows: (22)Considering that the valve is driven by vy, the moving

35、xv of the valve can be described using the corresponding physic principle, such as Newtons Law with the following state equations: (23)where uv is the velocity of moving xv. The pressure rates in the both cylinder chambers a and b can be calculated by the continuity equations (24)in which Qa and Qb

36、are the flows given in (19) and (20); Aa and Ab are the piston areas of the cylinder chambers a and b; Ca is the hydraulic capacity for the side in chamber a and Cb is for the side in chamber b, respectively; Both sides consist of the total oil volumes for cylinder chambers. Qr1 and Qr2 are the flow

37、s of the relies valves s1 and s2, respectively; is the piston moving rate, which can be calculated by (25)Substituting (10), (11) and (12) into (25), it is clear that the piston moving rate can be formulated using the generalized coordinate q and the corresponding generalized velocity u. Therefore,

38、in general, we have (26)The cylinder actuating force Fk is given by (27)with c is the damping coefficient of the cylinder. Substituting (27) into (17) and (18), having the generalized driving forces, which can be, in general, given byQd=Qd(pa,pb,q,u) (28) 4. The total system equationsHaving determin

39、ed the equations of the flexible luffing boom structure, the hydraulic circuit with position control, one can write the total system equations as (29)withwhereand I is identity matrix. The system equations (29) are mixed system of differential and algebraic equations that have to be solved simultane

40、ously. By solving Eq. (29) not only the responses of the mechanism q, u and , but also the dynamic behavior of the luffing drive system, such as the valve moving xv, the moving velocity uv and the feedback gain vy, the system pressures pa, pb, the flows Qa, Qb and the output driving forces Qd can be

41、 simultaneously obtained. With arbitrary inputs of desired values and parameters of the controller, the corresponding dynamic responses of the total crane system can be obtained. This is very convenient for computer simulation of crane motions. 5. Numerical exampleUsing the method described in the p

42、revious sections, the numerical simulation of crane luffing motion that is driven by a hydraulic actuator with angle control will be carried out. The superstructure of this crane consists of a main luffing boom with a payload, which is driven by a cylinder from a initial angle position 0 to a desire

43、d angle position during the total luffing motion. Fig. 4 shows this crane with coordinate systems. The following assumptions will be used: (1) The motion is only on the luffing plane xoy, the payload is regarded as a point mass. The payload can have pendulum motion on the plane, but without twisting

44、. The load hoisting will not occur during the boom luffing motion.(2) The luffing boom is flexible, the payload rope is elastic, but the crane bases are regarded as rigid bodies. The damping forces of the luffing boom will be neglected.(3) The oil is compressible, oil leakage of the hydraulic system

45、 is not considered. Fig. 4. Crane luffing motion.中文翻译液压起重机俯仰运动的动态响应摘 要基于我们早期工作中形成的一套完整的动态计算方法，现在已实现了对于决定液压起重机在俯仰运动中，考虑液压缸传动系统和起重机臂转动角度位置控制的情况下的动态响应的闭式模拟。运用拉格朗日方程式和多体理论，建立起重机俯仰运动的挠性模型。广义液压缸驱动力用虚功原理公式表达。机臂结构、液压执行机构和机臂转动角度位置控制系统相互耦合，建立整个系统的平衡方程。计算结果表明较之俯仰运动速度，起重机的动态响应对俯仰运动的加速度更为敏感。由此可见，这种方法对于进行起重机

46、俯仰运动模拟是非常有效和方便的，并且我们可以明显看出提出的这种完全动态方法能够进一步用来对起重机动作进行理想控制。1. 前 言悬臂俯仰运动是回转式起重机的一种基本动作。在现代汽车起重机中，由液压马达或液压缸来驱动。在传动系统的启动或制动中，产生的力不仅对起重机的安全性不利而且对其操作人员的健康有害。由于在悬臂动作时的有效负荷振动，这种力是相当大的。基于此种情况，在文献中有许多关于起重机动力学特性的研究。大多数发表的文章都提到起重机在回转和起升动作时的动态响应问题。但是对起重机俯仰运动动作的研究很少。在我们早期研究中已经发现那种在假定驱动速度和加速度剖面下运动加压的方法不能准确的描述在系统启动和

47、制动过程中传动的输出量。这些假定的启动和制动加速度剖面依靠经验来确定，由于起重机结构的巨大惯性力，对于起重机系统的启动和制动过程，这种由马达或液压缸产生的驱动力和扭矩是时间的复杂函数。这种驱动力对系统的动态响应和操作有效性发挥了重要作用。 为了改善这种情形，在我们的早期工作中已经提出了一种新的针对汽车起重机的动力学计算方法。这种方法将钢结构的挠性模型与传动系统联系起来。通过这种方法就可以用一个完整的模型来描述钢结构的弹性变形、刚体动作以及传动系统的动态行为。我们称作“机构的完全动态计算”。运用这种方法，我们已经提出了基于回转起重机回转和起升动作的完全动态模型，在本文中我们将探讨俯仰动作的动态行

48、为，实现对液压汽车回转起重机的计算。因为悬臂结构问题不仅涉及弹性变形而且还要涉及巨大的刚性回转，我们将采用挠性多体动态理论来描述起重机悬臂的俯仰运动。传动系统是液压缸，它通过采用液压和控制理论来描述。广义液压缸驱动力将采用虚功原理导出。整个系统将采用系统状态平衡方程来描述，由此可以实现起重机俯仰动作的模拟。2. 完全动态计算方法在我们早期工作中提出的完全动态计算原理是基于机构挠性多体模型和传动系统的数学模型相结合的综合模型而提出的。输入是我们需要的机构的状态值，如位置或速度。输出是整个系统的动态响应，它包括机械和控制传动系统，见图1图1 机构完全动态计算原理运用拉格朗日方程式，机构动作表示为

49、(1)这里T总动能，q是广义坐标矢量，Qin是内部广义力矢量，Qa是外部作用力矢量，Qd是广义驱动力矢量，是拉格朗日因子，它用来描述个连接体间的约束力，机构踢得约束条件可以用下面矢量方程表示： C(q,t)=0 (2)传动系统对驱动机构的动态响应的影响很大，所以它也应包含在动态模型之中。在汽车起重机中一般采用电子和液压传动控制系统。通常传动控制系统可以采用下面一阶显示微分方程表示： (3)这里z 是传动系统的一个状态空间矢量，q 是来自驱动机构的反馈矢量。传动系统根据相应的物理定律，例如电子或液压的物理定律，这种驱动力通常用下面的代数方程来表示：Qd=fd(z,t) (4)整个系统的运动方程可

50、以通过联立方程（1）（2）（3）和（4）来得到。在考虑输入和边界条件的情况下，机构的完全动态计算的基本问题是将所有的时间变量q, , z, Q同时求解出来。3. 俯仰机构的挠性多体公式表述在现代起重机中，俯仰机构通常由液压缸来驱动。悬臂结构不仅由刚性运动，例如在俯仰动作时的不同场合下的平移和回转，并且还承受由于重负荷产生的弹性变形。为了描述这些动作和它们之间的关系，这里采用多体动态理论。3.1 悬臂俯仰运动的多体公式表述在挠性多体理论中，这种大的刚体运动，通常在整体惯性参考系xyz 中描述，见图2. 另外，在体参考系中是用来测量机构俯仰运动中的体变形的。图2. 液压缸驱动的挠性俯仰动作的悬臂

51、图2 给出了两种由液压缸驱动的挠性体m和n,位置矢量Rm 和 Rn，回转矢量m 和 n，分别确定了体参考系和的位置和方向。 对于体m，涉及到惯性参照的任意点p的可变当前位置矢量可以这样描述： (5)对于体n，我们同样有 (6)其中和 是点p和点q的弹性位置矢量，它们在体参照系中测量得到；Am 和An 是转换矩阵，它们分别是m 和 n的矩阵函数。这种弹性位置矢量近似以体m和n的节点参数内插值替换，采用我们熟知的经典数值算法，例如有限元或瑞利里茨方法。3.2 俯仰运动中的广义驱动力的公式表述这种由液压缸产生的广义驱动力Qd能够用虚功原理表达出来，假设液压缸是一个刚体系统，因而可以给出如图连接点p和点q间的距离： lc=lc1+lc2+x (7)其中x是液压缸活塞的位移，lc