Stick-slip algorithm in a tangential contact force model for multi-body system dynamics

Contact force of Multi-body dynamics (MBD) system can be classified two parts. First is a normal force and the other is a tangential force called friction force. And the friction force can be represented by two states such as stick and slip. The stick-slip phenomenon is simply described as a simple contact model which is a rigid body contacted on a sloped surface. If the calculated friction coefficient between the body and sloped surface is less than the static friction coefficient, the body should be stuck. If the calculated friction coefficient is greater than the static friction coefficient, the body will be sliding along the surface. The phenomenon is called as stick and slip state of friction, respectively. Usually many researchers and commercial MBD software used a coulomb friction force model which is defined with an only function of relative velocity. This kind of friction force model will be called a conventional friction force model in this paper. A big problem of the conventional model can not describe a stick state of friction phenomenon. In the case of conventional friction force model, the body will be sliding even though friction state is stick. Because, the relative velocity must have a non-zero value in order to generate the friction force. To solve this kind of problem, we propose a stick-slip friction force model including a spring like force. In the case of stick-slip friction force model, the body can be stuck on the sloped surface because the friction force will be a non-zero value, even though the relative velocity approaches zero. We defined a relative displacement variable called stiction deformation. In this paper, the stick-slip friction model is proposed and applied in the contact algorithm of MBD system. And then two friction models are compared with numerical examples. With the proposed stick-slip friction model, more realistic results are achieved.     

一种三自由度电动仿真平台的设计

介绍一种由伺服电动缸驱动的三自由度运动平台。详细叙述了3RPS并联机构的运动学反解,设计了电气控制系统。采用经典PID双闭环控制,经试验验证表明,充分利用计算机的计算特性,设计合适的控制软件,采用低成本、易维护的电动缸也可以达到和液压缸一样良好的控制性能。     

Analysis of a planar 3 degree-of-freedom adjustable compliance mechanism

In this work, a planar three degree-of-freedom parallel mechanism as another type of assembly device which utilizes joint compliances is proposed. In order to generate the desired operational compliance characteristics at RCC point, these joint compliances can be adjusted either by properly replacing the joint compliances or by actively controlling stiffness at joints. The operational compliance matrix for this mechanism is obtained explicitly by symbolic manipulation, and its operational compliance characteristics are examined. It is found that the RCC point exists at the center of the workspace when the mechanism maintains symmetric configurations. Compliance characteristics and its sensitivity of this mechanism are analyzed with respect to the magnitude of the diagonal compliance components and two different matrix norms by measuring compliance sensitivity. It is expected that the analysis results provide the designer with a helpful information to determine a set of optimal parameters of this RCC mechanism.     

Thermo-mechanical model of frictional self-excited vibrations

A novel thermo-mechanical model of frictional self-excited stick-slip vibrations is proposed. Contrary to the tribo-mechanical models known in literature, the proposed model does not include any massless elastic parts. The applied friction force depends on a relative velocity of the sliding bodies. The period of vibrations depends on both heating expansion conditions and on conditions of heat taking up (giving up). Stability of the stationary solutions is studied. A computation of contact parameters during heating of the bodies is performed. Possibility of the existence of frictional auto-vibrations is shown.     

摆振引起叶片损坏的故障分析

通过对风力发电机组叶片的运行工况进行分析和模拟计算,验证了叶片损坏的主要原因是在风力发电机组失速工况下,摆振方向的振动出现发散,叶片承受的动态载荷过大造成损坏。     

一种压电式六维加速度传感器的校准方法研究

基于多只压电式单轴加速度传感器的压电式六维加速度传感器的传感误差主要由多只压电式单轴加速度传感器的安装误差和输出误差决定.为了对压电式六维加速度传感器的传感误差进行估计和补偿,提出并研究了一种压电式六维加速度传感器的校准方法,建立了压电式六维加速度传感器的校准模型.在此基础上,分析了校准过程中加速度激励误差对校准结果的影响和最佳角加速度激励频率的范围,建立了对校准误差进行估计的方法.研究结果表明,利用所建立的校准方法和校准误差估计方法不仅能够准确地实现压电式六维加速度传感器的校准,而且能够对校准结果的误差进行估计.该研究工作为压电式六维加速度传感器的误差补偿和精度提高奠定了基础.     

Stick-slip conditions in the general motion of a planar rigid body

In this paper we study combined translational and rotational (general) motion of planar rigid bodies in the presence of dry coulomb friction contact. Despite the cases where the body has pure translational/ rotational motion or can be assumed as a point mass, during the general motion, distinct points of the rigid body move in different directions which cause the friction force vector at each point to be different. Therefore, the direction and the magnitude of the overall friction force cannot be intuitively defined. Here the concept of instantaneous center of rotation is used as an effective method to determine the resultant friction force and moment. The main contribution of this paper is to propose novel stick-slip switching conditions for the general in-plane motion of rigid bodies. Simulation results for some combination of external forces are provided and some experimental tests are designed and conducted for practical verification of the proposed stick-slip conditions.     

Stick-slip vibration of a moving oscillator on an axially flexible beam

This study investigates the stick-slip vibration between an axially flexible beam fixed at both ends and an oscillator moving on the beam. After deriving the equations of motion for the stick and slip states, the stick-slip vibrations between the oscillator and the beam are analyzed. In addition, to obtain the irregularly changed contact position due to the axial deformation of the beam and oscillator movement, a mathematical expression for the contact position is derived. It is found that the long-period stick-slip vibration is influenced mainly by the oscillator and the short-period vibration is influenced mainly by axial deformation of the beam. Furthermore, the dynamic responses show that even if a high damping ratio is applied to the oscillator, stick-slip vibration due to axial deformation of the beam can occur. Finally, the analysis shows that a kind of the internal resonance occurs between the oscillator and the beam when the harmonics of the natural frequency of the oscillator match the natural frequencies of the beam.

     

Frequency response of non-linear single degree-of-freedom systems

Simple linear Kelvin or Maxwell models cannot predict adequately the response of many practical systems to vibration excitation. A more realistic model consisting of a mass between two preloaded non-linear (cubic elasticity springs) and restrained by a Coulomb and viscous damper is proposed. A harmonic motion solution, satisfying “on the average” the non-linear differential equation of motion of the model is developed whereby equations for frequency response curves are obtained. Expressions for relative and absolute transmissibility as well as their values at resonance are developed, these are shown to properly reduce to the respective exact expressions of a Kelvin model and friction damped linear spring. Although the model is intended mainly for quantitative design in packaging engineering problems, it is suitable for studying general vibration isolation problems as well.     

一种压电式六维加速度传感器的快速原型及其特性

介绍了一种压电式六维加速度传感器,研究了其敏感单元的布局原理,建立了相应的六维加速度传感方程以实现对6只压电式单轴加速度传感器的输出进行解耦得到刚体运动的六维加速度.在此基础上,采用基于实时仿真系统(dSPACEDS1103和MATLAB/Simulink)的快速控制原型(rapid control prototyping,RCP)技术建立了压电式六维加速度传感器的快速原型.在六维随机振动激励和固定轴旋转振动激励情况下对开发的压电式六维加速度传感器的快速原型的传感性能进行了实验测试.研究结果表明该压电式六维加速度传感器的快速原型能够实现六维加速度的传感,建立的传感方程能够准确地解算出刚体运动的六维加速度.     

Free vibrations of a snowboard

Because of the rapid increase in the number of snowboarders many kinds of snowboards have been developed recently. To design a snowboard or to improve its quality, the natural frequency of the snowboard seems to be one of the most important properties to be discussed. In this study whether or not one can accurately estimate the natural frequency of the snowboard by using the numerical approach proposed for a free vibration of an inhomogeneous plate is discussed. First, the convergency of the natural frequency is discussed from the numerical results. Next, this study investigates whether or not the natural frequency is accurate enough for practical usage by comparing the natural frequencies obtained numerically with those obtained experimentally. Finally, the effect of snow on the natural frequencies is discussed.     

Multi-axial creep rupture of a model structure using a two parameter material model

A simplified, two parameter creep curve model is developed, which represents primary-secondary-tertiary creep behaviour. The two parameters are related via the secondary strain respectively to: the sum of secondary and primary strains; and, the sum of secondary and tertiary strains. Techniques are described for fitting the model to laboratory data; and, for the determination of the parameters which characterize primary-secondary and secondary-tertiary creep. The single state variable theory used to describe tertiary creep is compared with mechanisms based models and shown to closely predict the effect of stress-state on rupture strain. A two bar plane strain model component subjected to steady load is studied and used to determine the effect on the component lifetime of primary creep; and, of the multi-axial creep rupture criterion. The representative rupture stress is found to be weakly dependent on primary creep and strongly dependent on the multi-axial rupture criterion of the material.     

气缸爬行现象的建模与仿真

气缸低速运动时会出现时走时停或时快时慢的“爬行”现象。文章阐述了气缸产生爬行的原因，分析了爬行现象的机理，建立了气缸爬行现象的数学模型。用MATLAB6．5对气缸爬行现象的数学模型进行了动态特性仿真，通过理论分析和仿真计算，分析了导致气缸产生爬行现象的影响因素。     

Analysis for a planar 3 degree-of-freedom parallel mechanism with actively adjustable stiffness characteristics

A planar three degree-of-freedom parallel manipulator has been extensively studied as the fundamental example of general parallel manipulators. It is proven from previous work (Kim, et. al., 1996) that when three identical joint compliances are attached to the three base joints of the mechanism in its symmetric configurations, this mechanism possesses a completely decoupled compliance characteristic at the object space, which is the important operational requirement for an RCC device. In this work, we are concerned with the adjustability of the output compliance matrix of this mechanism, by employing redundancy on either joint compliances or on actuators. Two approaches are suggested to achieve this purpose. In the first approach, the stiffness modulation is achieved through purely redundant passive springs or decoupled feedback stiffness gains. In the second approach, stiffness modulation is achieved through antagonistic actuation of the system actuators. General stiffness models are derived for both cases. Based on these stiffness models, stiffness modulation algorithms are formulated. The capability of actively adjustable stiffness will be very effective in several robotic applications.     

机器人操作臂振动的最优控制理论研究

本文就操作臂的末杆在其运动终点的振动控制问题进行了理论研究。首先建立了末杆的力学模型,并用有限元法建立了该模型的动力学方程;然后建立了振动控制问题的框图,并给出了有关的传递函数和脉冲响应函数的表达式;进而建立了振动抑制问题的最优控制的数学模型;最后就该数学模型提出了一种近似解析方法,并给出了一示例。     

新型扭转振动工具降粘特性分析及PID控制策略研究

在深井和超深井勘探开发过程中,广泛存在着粘滑振动现象,该现象不仅造成机械钻速降低,驱动能量大量浪费;而且还会加速钻具老化和失效,严重威胁钻井安全。为了有效地控制钻柱的粘滑振动,首先提出了一种新型扭转振动工具;其次建立了基于该工具的钻柱系统的理论模型;最后用PID控制方法对新型扭转振动工具的降粘特性进行了研究。结果表明:该工具能够有效地控制钻柱的粘滑振动,两种PID控制方程均能对期望稳态转速进行实时监控,对比两者,U2控制方程具有更快的调节能力和更好的控制性能,且前期无粘滑现象的发生。     

黏滑振动理论及其在铁路机车中的应用

为研究机车处于黏着极限态时轮对的动态行为,提出平均滑动率和动态滑动率的概念并对黏滑振动稳定性及其振动特点进行分析.黏滑振动是介于黏着和滑动的动态过程,其稳定性取决于轮轨黏着,减小平均滑动率和动态滑动率有利于黏滑振动稳定.当轮对在黏着及滑动状态的往复交替时,轮对旋转与轮对纵向振动通过轮轨纵向切向力耦合,轮对的纵向振动频率为轮对旋转固有振动频率的整数倍.建立机车机电、控制一体化系统动力学模型,再现轨面黏着条件降低时轮对黏滑振动现象,对理论分析结果进行验证.研究结果表明:增大机车一系纵向刚度,电动机吊挂刚度有利于黏滑振动稳定性,提高机车黏着性能,需要合理匹配轮对纵向定位刚度和电动机吊挂刚度,避免机车黏滑振动时引起结构共振.     

Optimal synthesis of a wrist-type 6 degree-of-freedom force/ torque sensor using Stewart Platform Structure

The F/T sensor investigated in this study utilizes the Stewart Platform Mechanism Structure. Normally-employed 6-prismatic joints are replaced by 6-prismatic bars, which are extensible and compressible only along the axial direction of the bars. The complete analyses for the design of this kind of F/T sensor are conducted: the position analysis, the first-order and second-order kinematic analyses, and the force-deformation analysis based on the first-order kinematic characteristics of the system. Lastly, a dimensional synthesis for the F/T sensor is performed based on the kinematic isotropic index.     

Robots with increased number of degree-of-freedom with single exciting force

This paper presents the results of the development and investigation of a new class of novel multi-degree-of-freedom robots based on a new concept – the application of kinematic pairs with alternating degree-of-freedom (DOF) controlled by a single force or moment, changing its direction in space. The number of DOF of the kinematic pairs is controlled periodically from 0 to 3, exploiting the dependence of frictional forces on the oscillation in the contact zone of links. The advantages of this new class of robots include significant weight reduction, simple design and control, and specific applications in space robotics and soft robotic spines. In more complicated cases of trunk robots, elastic kinematic pairs are used with a number of DOF controlled by electro- or magneto-rheological fluids with viscosities that change as a result of applied electric or magnetic fields. Expressions for the generalized inertia matrix of the robots with a large number of joints have been derived using the computer algebra technique with the subsequent automatic program code generation. As shown in this paper, such an application could drastically reduce the number of floating point product operations for an efficient numerical simulation of robots.     

球基微操作器黏滑摩擦过程建模与分析

球基微操作器通过压电陶瓷管端部与微操作球之间惯性摩擦形成的相对位移实现微操作球三自由度的运动,这种摩擦运动中存在黏滑现象。在简化球面高副连接的条件下,建立了球基微操作器双质量摩擦振子等效工程模型,对球基微操作器黏滑驱动过程进行了阶段细分,基于等效工程模型及动态LuGre摩擦模型建立了黏滑摩擦过程的动力学方程。运用数值仿真方法分析了球基微操作器的参数特性曲线,进行了运动测试实验,进一步验证了分析的正确性。