带铰弹性开环多体臂架变位姿固有频率算法

.作者:任武 吴运新 张赵威 曾谊晖
.来源期刊:中南大学学报(自然科学版)2015年第2期
.中文关键字:多体;臂架;铰弹性;传递矩阵法;振动;固有频率
.英文关键字:multibody; boom; joint elasticity; transfer matrix method; vibration; natural frequency
.中文摘要:针对多体泵车臂架作业中频繁位姿变换固有频率不易求解的问题,采用多体传递矩阵法建立四节臂架动力学模型,模型分为A和B 2个子系统,子系统A为第1节臂、支座油缸连接,子系统B为后3节臂、油缸连接。加入液压驱动油缸两端铰弹性的影响,进行整体模型封装分析4种常用位姿的固有频率,并在已有臂架实验台上进行实验验证。研究结果表明:采用多体传递矩阵法求解变位姿多体系统臂架固有频率避免了传统方法中重新设定计算的步骤,4种位姿加入铰弹性的固有频率均比理想铰降低且更接近实测值,为此类机械的变位姿频率计算和整车实时振动控制提供参考。
.英文摘要:In order to calculate the different postures natural frequencies of multibody mobile concrete pump truck boom, the transfer matrix method was adopted. Then a four-boom equivalent mechanical model was established. The model was divided into sub-system A and B. The sub-system A was linked to the first boom, standoffs and its hydraulic cylinder. The sub-system B was linked to the other three booms and cylinders. The revolute joint elasticity of the boom cylinder connection was also considered. After packaging the two sub-systems, the frequencies of four common postures were solved, and an experiment was carried out on a test rig. The results show that it is not necessary to reset the parameters and resolve in different posture frequency calculations by transfer matrix method. At the same time, the frequencies considering joints elasticity are smaller than those of ideal joints and are closer to the test ones. All of these provide reference for natural frequency calculation and real-time monitoring for mobile truck booms.
详细信息展示

DOI: 10.11817/j.issn.1672-7207.2015.02.016

带铰弹性开环多体臂架变位姿固有频率算法

任武1, 2,吴运新1, 2,张赵威1, 2,曾谊晖1, 2

(1. 中南大学 高性能复杂制造国家重点实验室,湖南 长沙,410083;

2. 中南大学 机电工程学院,湖南 长沙,410083)

摘要:针对多体泵车臂架作业中频繁位姿变换固有频率不易求解的问题,采用多体传递矩阵法建立四节臂架动力学模型,模型分为A和B 2个子系统,子系统A为第1节臂、支座油缸连接,子系统B为后3节臂、油缸连接。加入液压驱动油缸两端铰弹性的影响,进行整体模型封装分析4种常用位姿的固有频率,并在已有臂架实验台上进行实验验证。研究结果表明:采用多体传递矩阵法求解变位姿多体系统臂架固有频率避免了传统方法中重新设定计算的步骤,4种位姿加入铰弹性的固有频率均比理想铰降低且更接近实测值,为此类机械的变位姿频率计算和整车实时振动控制提供参考。

关键词:多体;臂架;铰弹性;传递矩阵法;振动;固有频率

中图分类号:TU646             文献标志码:A         文章编号:1672-7207(2015)02-0485-06

Multibody open-loop mobile concrete pump boom with joint elasticity multi posture natural frequency algorithm

REN Wu1, 2, WU Yunxin1, 2, ZHANG Zhaowei1, 2, ZENG Yihui1, 2

(1. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China;

2. School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China)

Abstract: In order to calculate the different postures natural frequencies of multibody mobile concrete pump truck boom, the transfer matrix method was adopted. Then a four-boom equivalent mechanical model was established. The model was divided into sub-system A and B. The sub-system A was linked to the first boom, standoffs and its hydraulic cylinder. The sub-system B was linked to the other three booms and cylinders. The revolute joint elasticity of the boom cylinder connection was also considered. After packaging the two sub-systems, the frequencies of four common postures were solved, and an experiment was carried out on a test rig. The results show that it is not necessary to reset the parameters and resolve in different posture frequency calculations by transfer matrix method. At the same time, the frequencies considering joints elasticity are smaller than those of ideal joints and are closer to the test ones. All of these provide reference for natural frequency calculation and real-time monitoring for mobile truck booms.

Key words: multibody; boom; joint elasticity; transfer matrix method; vibration; natural frequency

泵车臂架是典型的多体开环机械臂,目前最长的臂架已经到达101 m。大范围运动高柔度特征使其在低频工作时受到较大的振动,同时,臂架位姿的频繁变换导致固有频率不断变化,给设计分析带来不便。现有研究中,Cazzulani等[1]研究了泵车臂架加末端质量块的臂架振动固有频率变化。Liu等[2]建立了大范围运动刚柔双臂理想铰非线性运动方程,分析了臂的振动特性。刘杰等[3]分析了某泵车臂架多刚体模型并对多柔体臂架末端位移进行了探讨。王斌华等[4]研究了脉动和常速流混凝土对臂架振动频率的影响。贺尚红等[5-7]建立适用于机电液耦合系统频域的通用传递矩阵,提供一种更方便的仿真方法。Li等[8-9]建立了液压缸驱动柔性臂动力学模型并进行末端位移控制仿真。芮筱亭等[10]提出离散传递矩阵法并应用于自行火炮等多体武器系统动力学工程实例分析和频率求解。Flores[11]分析了旋转铰碰撞摩擦原理,建立了曲柄滑块运动仿真模型。白争锋等[12-14]研究了连杆机构运动副碰撞动力学特性,并进行了实验研究。Dupac等[15]分析了平面柔体连杆机构的弹性影响,指出弹性影响在此类机构动力学研究中不应忽视。大范围变姿态机械臂如混凝土泵车臂架的研究,通常将铰当成理想铰来分析,忽略了铰弹性碰撞的影响。本文作者以多体开环臂架为研究对象,利用传递矩阵法建立其多体模型和铰弹性模型,快速计算出其位姿变换时的固有频率,并通过臂架实验台验证模型的正确性和计算方法的合理性。

1  铰弹性碰撞理论和参数选取

Lankarani-Nikravesh模型是改进的Hertz接触模型[11],如式(1)所示:

            (1)

其中:

       (2)

          (3)

           (4)

Fn为接触碰撞力;K为接触物体的刚度系数,可根据Goldsmith碰撞实验得出;δ为穿透深度;C为接触碰撞阻尼系数;为接触碰撞相对速度;σn为销轴铰接系数;υ和E分别为材料泊松比和弹性模量,根据文献[13],n取1.5;Ri为销轴半径,Rj(j=1,2,3,4)分别为四节臂销的半径;ce为恢复系数,取0.9;为撞击点的初始相对速度。υ,E,Ri和Rj取值见表1。

表1  销轴套筒材料与结构参数

Table 1  Pin and bushing material structure property

2  带铰弹性臂架动力学模型

2.1  数学模型

多体开环臂架从根部算起主要由臂、连杆以及液压驱动油缸组成,几节臂架由多个六连杆串联而成,根据连接类型将臂架系统划分成2种子结构以提高建模效率如图1所示。

臂架的2种子结构分别是体元件和铰元件,这些元件传递矩阵依照连接关系进行初步组装得到各自子结构传递方程和传递矩阵,然后将2种子结构再封装成总传递方程和总传递矩阵,最后利用边界条件得到该系统的动力学特性。模型中臂架等效为弹性梁元件,连杆、油缸及活塞杆等效为刚体元件,旋转铰等效为弹簧阻尼系统,其刚度系数按式(2)计算,液压油等效为一定刚度的弹簧元件。忽略臂架左右扭转的影响,四节臂简化为欧拉-伯努利梁,假定臂架低速运动以忽略离心加速度和科氏加速度的影响,定义各连接点状态矢量为

       (5)

在模态坐标系下,式(5)中X, Y为线位移;Qz为角位移;Mz为内力矩;Qx和Qy为内力。

图1  臂架系统子结构划分

Fig. 1  Sub-structure diagram of mobile concrete truck boom

2.2  子结构的传递矩阵

臂架结构划分成子结构A和子结构B,其中结构A包括第1节臂、支座、驱动油缸以及液压油缸两端连接旋转铰;结构B又分为3个亚结构,包括后3节臂结构和相应液压缸两端旋转铰,如图2和图3所示。

图2  子结构A连接

Fig. 2  Connection of sub-structure A

子结构A中定义0为其输入端,8为其输出端,1,3和5为刚体元件,2,4和6为平面弹簧连接弹性单元,其中6为弹性铰,7为等截面欧拉-伯努利梁元件,根据传递矩阵法得到各元件的传递矩阵Ui, 将0~8元件结合可得到子结构A的传递方程:

           (6)

1,7和6连接处的位移和受力关系如下:

   (7)

由式(6)和式(7)可得:

                   (8)

转化矩阵E1~E3分别为:

         (9)

子结构A的传递方程如下:

                       (10)

子结构A的传递矩阵UA以及状态矢量ZA为:

         (11)

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