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.     

Recursive newton-euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems

The main objective of this paper is to develop a recursive formulation for the flexible dynamic manufacturing analysis of open-loop robotic systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields. These time invariant quantities represent the dynamic manufacturing couplings between the rigid body motion and elastic deformation. This formulation applies recursive procedures with the generalized Newton-Euler equations for flexible bodies to obtain a large, loosely coupled system equation describing motion in flexible manufacturing systems. The techniques used to solve the system equations can be implemented in any computer system. The algorithms presented in this investigation are illustrated using cylindrical joints for open-loop robotic systems, which can be easily extended to revolute, slider and rigid joints. The recursive Newton-Euler formulation developed in this paper is demonstrated with a robotic system using cylindrical mechanical joints.     

Elimination of Stick-Slip Motion in Sliding of Split or Rough Surface

Here, we present a mass-less quasi-static model of stick-slip phenomenon built exclusively on the difference between higher static and lower kinetic friction force. The model allows explaining the disappearance of stick-slip motion when elastic surface slid in contact with rigid counter-face bears large amount of small outgrowths. Adjusting the model parameters, it is also possible simulating systems with different transient responses. The results obtained may also be helpful in understanding the variety of sliding behavior of different materials.     

Recursive Newton–Euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems

The main objective of this paper is to develop a recursive formulation for the flexible dynamic manufacturing analysis of open-loop robotic systems. The nonlinear generalized Newton–Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields. These time invariant quantities represent the dynamic manufacturing couplings between the rigid body motion and elastic deformation. This formulation applies recursive procedures with the generalized Newton–Euler equations for flexible bodies to obtain a large, loosely coupled system equation describing motion in flexible manufacturing systems. The techniques used to solve the system equations can be implemented in any computer system. The algorithms presented in this investigation are illustrated using cylindrical joints for open-loop robotic systems, which can be easily extended to revolute, slider and rigid joints. The recursive Newton–Euler formulation developed in this paper is demonstrated with a robotic system using cylindrical mechanical joints.     

Stick-Slip Motion in Boundary Lubrication

Using dynamical analysis for a pin-on-disk sliding system and the consideration of meniscus formation at the sliding interface, a wide range of experimental observations on stick-slip motion can be explained. It is shown that when the initial growth rate of the static friction force is larger than about half the product of the substrate speed and the spring constant, slick-slip motion occurs in that sliding system. The critical substrate speed or the critical spring constant, above which stick-slip motion ceases, can thus be determined. It is also shown that the saturation substrate speed, below which stick-slip motion retains its maximum stick-slip amplitude, is inversely proportional to the total growth time of the static friction force. The maximum stick-slip amplitude is proportional to the final difference between the static and kinetic friction force. For a thicker surface liquid-film, the initial growth rate and the final static friction force are larger but the total growth time is shorter, resulting in a larger critical speed, a larger stick-slip amplitude, and a larger saturation speed. For rougher contact surfaces, the initial growth rate is larger but the final static friction force and the total growth lime are smaller, resulting in a larger critical speed, a smaller stick-slip amplitude, and a larger saturation speed.     

Theoretical study of thermofrictional oscillations due to negative friction-temperature characteristic

Analytical study on oscillations of a body on a moving counterbody has been done by assuming imperfect frictional thermal contact and friction that decreases with contact temperature. It has been shown that stick-slip oscillation occurs due to decrease of friction coefficient when the body moves in the opposite direction to the counterbody. Dynamical characteristics, such as conditions for stable sliding and limit cycles, have been studied. Normal force between the bodies has significant effect on sliding stability.     

On the motion of the structure varying multibody systems with two-dimensional dry friction

In the present paper the dynamics of the structure varying multibody systems caused by stick-slip motion with two-dimensional dry friction are analyzed. The methods to determine friction force both in stick and slip states are described. The direct method of considering the wagon bogie system as a structure varying system was used to consider two dimensional friction at the wheelset-side frame connection. The concept of friction direction angle used to determine the friction force components of two-dimensional dry friction both in the stick and slip motion states was used. A speed depended friction coefficient was used and described approximately by hyperbolic secant function. All switch conditions were derived and friction forces both for stick and slip states. Some simulation results are provided.     

纳观纹理表面相关参数对滑动摩擦过程的影响

采用分子动力学方法研究了半球形刚性压头在单晶铜纹理表面上的纳观黏着滑动摩擦过程。对不同纹理密度下纹理形状和纹理深度对黏滑摩擦性能的影响进行了全面研究,通过对比分析不同纹理参数下的滑动摩擦力和基体变形,揭示了上述参数对纹理表面黏滑摩擦的影响规律。模拟结果表明:在相同的纹理密度下,柱状纹理表面的滑动摩擦力小于矩形纹理表面。相比矩形纹理,柱状纹理表面的结构稳定性较差,但纹理表面的结构稳定性随着纹理密度的增加而加强。在相同的纹理密度下,矩形纹理表面的滑动摩擦力随着纹理深度的增加而减小。     

Pre-sliding friction control using the sliding mode controller with hysteresis friction compensator

Friction phenomenon can be described as two parts, which are the pre-sliding and sliding regions. In the motion of the sliding region, the friction force depends on the velocity of the system and consists of the Coulomb, stick-slip, Streibeck effect and viscous frictions. The friction force in the pre-sliding region, which occurs before the breakaway, depends on the position of the system. In the case of the motion of the friction in the sliding region, the LuGre model describes well the friction phenomenon and is used widely to identify the friction model, but the motion of the friction in the pre-sliding such as hysteresis phenomenon cannot be expressed well. In this paper, a modified friction model for the motion of the friction in the pre-sliding region is suggested which can consider the hysteresis phenomenon as the Preisach model. In order to show the effectiveness of the proposed friction model, the sliding mode controller (SMC) with hysteresis friction compensator is synthesized for a ball-screw servo system.     

Dynamic modelling of planar mechanisms using point coordinates

In the present study, the dynamic modelling of planar mechanisms that consist of a system of rigid bodies is carried out using point coordiantes. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then for the resulting equivalent system of particles, the concepts of linear and angular momentums are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.     

Motion of a solid body supported on a narrow rectangular area on a horizontal plane with orthotropic friction. Part 1. Inertia motion

The problem of motion of a solid body which rests on a narrow rectangular area carried on a horizontal plane is discussed, assuming that the force of friction is orthotropic. A relationship is formulated between the velocity of the point of intersection of the diagonals of this area and the angular velocity of the body at the moment of stopping. The findings can be applied to simulation of the motion of a system of bodies and to solution of contact problems.     

Numerical analysis of stick-slip instability by a rate-dependent elastoplastic formulation for friction

In various fields of engineering, it is important to clarify friction-induced vibration, such as stick-slip motion, for a wide range of scales from microscopic elements to continental plates. In the present study, we apply a rate- and state-dependent friction model [30] (Hashiguchi and Ozaki, 2008), which can rationally describe the reciprocal transition between the static friction and the kinetic friction by a unified formulation, to the simulation of stick-slip instability for a one-degree-of-freedom spring-mass system under various conditions. It is verified that the various basic experimental findings on stick-slip motion can be pertinently described by the present approach. Moreover, the effect of the dynamic characteristics of the system, such as the mass, stiffness and driving velocity, is discussed, and parameters prescribing the rate of reciprocal transition of static-kinetic frictions and the preliminary microscopic sliding on the instability of the stick-slip motion are also discussed.     

On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints

The uniqueness of simulated motion of an overconstrained rigid body mechanism with joint friction is studied. The investigated issue originates in the problem of joint reactions solvability. It is known that in case of redundant constraints existence the constraint reaction forces cannot be — in general — uniquely determined. It can be proved, however, that — under certain conditions — selected reactions can be specified uniquely. Analytical and numerical methods for reactions solvability analysis are available. It is shown in this paper that indeterminacy of normal reactions results in indeterminacy of friction forces, and moreover, non-uniqueness of friction forces results in non-uniqueness of simulated motion. A method of finding these joints, for which friction forces are unique, is presented. It is also proved that if only uniquely solvable friction effects are introduced, then simulated motion of the mechanism is unique, otherwise it is not. Finally, examples of dynamic analysis of overconstrained mechanisms with joint friction are presented; unique and non-unique results are obtained.     

NONLINER VIBRATION ANALYSIS OF THE PLATE WITH DRY FRICTION SUPPORT CONDITION

The rigid-interface friction model is usually used in the nonlinear vibration of the rectangular plate with dry friction support edges. The present study provides an extension by using a hysteretic spring friction model and taking account of the stick-slip motion of the plate. Results for a range of problem parameters have been obtained. The results show that the nonlinear frequency response behavior of the system can be quite different from the rigid-interface friction model. The effects of the stiffness at friction interfaces and the stick-slip motion on the nonlinear vibration of the plate are significant and hence cannot be neglected.     

Measurement of the rotational inertia of bodies by using mechanical spectroscopy

In this paper, mechanical spectroscopy was used to study the rotational inertia of bodies. In order to verify and show its importance in relation to other techniques, measurements of the internal friction and rotational inertia of a body with liquid or sand inside were carried out. For a solid without axes and planes of symmetry, properties such as the matrix, directions and principal moments of inertia, variation of the rotational inertia for each of the coordinate planes, and the ellipsoid of inertia were determined. Force sensors and rotational motion were used in the measurements taken in an arrangement that was specifically designed for this type of measure.     

Tribological behavior of reciprocating friction drive system under lubricated contact

The dynamic friction and wear behaviors are investigated in reciprocating friction drive system using a 0.45% carbon steel pair. The effects of various operating parameters on the traction force, stick and slip time, and friction modes are examined under the lubricated contacts. Moreover, the critical operating conditions in classifying three friction modes are also established. Results show that the fluid friction induced by the shearing of lubricant dominates the variation of traction force and produces the positive slope γ at the first period of slip in the traction force–relative sliding velocity curve. The γ value decreases at higher driver speed during stick-slip motion due to the thicker fluid film and shear thinning effect. The γ value increases due to the asperity interactions as the friction region is transferred from stick-slip to sticking with normal load from 196 to 980 N. Furthermore, it is also found that the static friction force is independent of stick time for the tangential loading rate ranged from 1.12 to 16.8 s⁻¹. The transition region produces the severest wear under the different driver speeds, but the wear is insensitive to the friction regions and the severe wear only occurs at higher normal load due to the action of Hertzian contact.     

A computer method for the dynamic analysis of a system of rigid bodies in plane motion

This paper presents a computer method for the dynamic analysis of a system of rigid bodies in plane motion. The formulation rests upon the idea of replacing a rigid body by a dynamically equivalent constrained system of particles. Newton’s second law is applied to study the motion of the resulting system of particles without introducing any rotational coordinates. A velocity transformation is used to transform the equations of motion to a reduced set. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and few cut-joints constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.     

Acoustic output from stick-slip friction

An investigation into the correlation between the friction characteristics produced during stick-slip motion and the noise and vibration of a loading system caused by the frictional contact is presented. Various material combinations at the contact have produced distinctly different friction characteristics.Results show the presence of acoustic signals in some contact combinations and not in others. At this stage the reasons for this are not fully understood, but some common underlying trends are discussed.     

界面摩擦过程黏滑行为特征研究

通过建立界面摩擦系统动力学模型,并利用原子力显微镜测试云母、石英以及单晶硅片界面摩擦条件下的黏滑行为特征,探讨摩擦系统内外因素对黏滑频率、幅值的影响。结果表明:同一实验条件下,不同材料的黏滑频率与黏滑波动幅值不同;缓慢滑动时,黏滑的频率主要取决于表面势场的频率,波动幅值取决于表面势场强度,随着滑动速度逐渐增大,黏滑频率同时取决于表面势场频率和探针系统的固有频率,波动幅值取决于表面势场强度和探针系统结构;滑动速度较大时,黏滑频率及波动幅值主要取决于探针系统,且随着滑动速度增大,波动幅值逐渐减小。     

黏滑驱动式小型精密运动平台

为满足微纳操作系统对精密驱动技术的需求,本文提出了一种基于黏滑原理的小型精密运动平台。该平台将柔性铰链、惯性质量块以及弹性元件结合为独立的定子基座,并与压电叠堆、陶瓷球固连为定子,安装在平台基座底部,通过螺钉调节弹性元件端部垂直方向的位置,就可以改变定子与移动台间的预压力,进而获得最佳的驱动力。为研究黏滑驱动的运动机理,分析各参数对平台运动的影响,进行了力学建模;而摩擦力作为黏滑驱动的关键因素,为了能准确地表达黏滑驱动的摩擦机理,在力学建模中引入了LuGre摩擦模型,并利用Matlab/Simulink软件进行了仿真分析。设计加工的黏滑驱动平台的整体尺寸为40mm×40mm×18mm,质量为32g。试验表明:该平台最小可实现10nm的运动步长,速度最高可达2.5mm/s,行程为22mm。