Generalization of the Prandtl problem for a creep model

An approximate solution to the problem of compression of an infinite layer of material between rough parallel plates is constructed with the creep equations being fulfilled. Constitutive relations in accordance with which the equivalent stress tends to a finite value as the equivalent strain rate tends to infinity are used. The behavior of the solution in the neighborhood of the maximum friction surface is studied. It is shown that the existence of the solution depends on one of the parameters included in the constitutive equations. If the solution exists, the equivalent strain rate tends to infinity in the neighborhood of the maximum friction surface, and the asymptotic behavior of the solution depends on the same parameter. It is established that there is a range of this parameter in which the nature of the change in the equivalent strain rate near the maximum friction surface is the same as in the solutions for rigid plastic materials.     

Compression of an axisymmetric layer on a rigid mandrel in creep

An approximate solution describing the compression of an axisymmetric layer ofmaterial on a rigid mandrel under the equations of the creep theory is constructed. The constitutive equation is introduced so that the equivalent stress tends to a finite value as the equivalent strain rate tends to infinity. Such a constitutive equation leads to a qualitatively different asymptotic behavior of the solution near the mandrel surface, on which the maximum friction law is satisfied, compared with the well-known solution for the creep model based on the power-law relationship between the equivalent stress and the equivalent strain rate. It is shown that the solution existence depends on the value of one of the parameters contained in the constitutive equations. If the solution exists, then the equivalent strain rate tends to infinity as the maximum friction surface is approached, and the qualitative asymptotic behavior of the solution depends on the value of the same parameter. There is a range of variation of this parameter for which the qualitative behavior of the equivalent strain rate near the maximum friction surface coincides with the behavior of the same variable in ideally rigid-plastic solutions.     

Influence of spring dynamics and friction on a spring-actuated cam system

Summary  The paper investigates two important aspects, friction and spring motion, of the dynamics of a spring-actuated cam system. The characteristics of the friction on the camshaft are analyzed using the nonlinear pendulum experiment, while the parameters of the friction model are estimated using the optimization technique. The analysis reveals that the friction of the camshaft depends on stick–slip, Stribeck effect and viscous damping. Spring elements are found to have much influence on the dynamic characteristics. Hence, they are modeled as four-degrees-of-freedom lumped masses with equivalent springs. The lumped masses and equivalent springs are obtained to match the static stiffness and natural frequency of the actual spring. The appropriateness of the derived friction and spring model are verified by its application to a vacuum circuit-breaker mechanism of the cam-follower type. Received 23 March 2000; accepted for publication 21 November 2000     

Strain rate intensity factors for a plastic material layer compressed between cylindrical surfaces

For some models of rigid-plastic bodies, the strain rate fields turn out to be singular near the maximum friction surfaces. In particular, the equivalent strain rate (the second invariant of the strain rate tensor) tends to infinity when approaching such frictions surfaces. The coefficient multiplying the leading singular term in the series expansion of the equivalent strain rate near the maximum friction surfaces is called the strain rate intensity factor. This coefficient occurs in several models predicting the development of intensive plastic deformation layers near friction surfaces and in equations describing the change in the material structure in such layers. In the present paper, the solution is constructed for the compression of a layer of a plastic material obeying the double shear model between cylindrical surfaces on each of which the maximum friction law holds. The dependence of two strain rate intensity factors on the material and process parameters is calculated and analyzed.     

等径通道挤压过程三维有限元模拟

利用三维有限元模型对等径通道挤压过程中变形分布的不均匀性进行了模拟,通过对不同摩擦系数下截面等效塑性应变分布比较发现:沿三个方向截面上的变形分布都不是均匀的,这说明二维有限元模型不能真实模拟等径通道挤压过程中试样中的变形分布。此外,摩擦对等效塑性应变分布及挤压力的影响较大,截面变形不均匀参数和最大等效塑性应变出现的位置随摩擦系数的增大而变化。压力-位移曲线的变化可以结合试样的变形过程来解释。     

Experimental and numerical investigation of a vertical vibration isolator for seismic applications

In near-fault seismic zones, the vertical acceleration experienced during a strong event can be greater than horizontal acceleration. Methods to reduce horizontal acceleration are applied in various forms and are in common use. However, methods to reduce vertical acceleration, and practical protection systems for these applications, remain elusive. One strategy to protect structures, which has been demonstrated to be effective in situations where the excitation is horizontal, is to isolate the structure. For vertical excitations, this is difficult due to the need to maintain sufficient stiffness and strength in the direction of gravitational loads. The need to maintain high stiffness for gravity loading while allowing flexibility for isolation during earthquakes has led to research on the use of High-Static-Low-Dynamic Stiffness Systems (HSLDSS) and in particular Quasi-Zero Stiffness Systems (QZSS), which have zero equivalent stiffness in the equilibrium position. Although effective, the QZSS is sensitive to mistuning and prone to large deformations for relatively small increments in static load for building applications. This paper presents the results of an analytical and experimental study in which a HSLDSS isolation system carrying a payload is subject to vertical base excitation using sinusoidal as well as actual, scaled earthquake signals. Static loading tests are also presented. This isolation system consists of rigid rotating arms, horizontal and vertical springs and a vertical damper. By a suitable selection of parameters this could also serve as a QZSS. Results show that both the QZSS and HSLDSS can significantly reduce the magnification of the force as well as the transmission of the acceleration and that the HSLDSS retains stiffness at the equilibrium position. The numerical model includes friction and is solved using direct integration of the equation of motion. Experimental results from a scale model agree well theoretical predictions.

     

Strain rate intensity factors for a plastic mass flow between two conical surfaces

The concept of strain rate intensity factor was introduced in [1], where the asymptotic expansion of the velocity field in a perfectly rigid-plastic material was obtained near the maximum friction surface, which is determined by the condition that the specific friction forces on this surface are equal to the simple shear yield strength. In particular, it was shown in this paper that near the maximum friction surface the equivalent strain rate (the second invariant of the strain rate tensor) tends to infinity inversely proportional to the square root of the distance to this surface. We note that the same result was obtained in the case of plane flow in [2]. The strain rate intensity factor is defined to be the coefficient of the leading singular number in the series expansion of the equivalent strain rate near the maximum friction surface. It was shown in [3] that there is a sufficiently complete formal analogy between the strain rate intensity factor and the stress intensity factor in mechanics of cracks [4]. In [5], it was suggested to use the concept of strain rate intensity factor to estimate the thickness of the layer near the friction surface where one should take into account viscosity effects. (Thus, this is an intensive strain layer formed as a result of a very large equivalent strain rate.) Therefore, the problem of calculating the strain rate intensity factor in specific processes is topical in the development of the general concept based on the use of the strain rate intensity factor and its applications in the theory of metal forming processes. These factors have already been calculated for several processes such as plane upsetting and drawing [3]. In the present paper, we calculate the distribution of the strain rate intensity factor in a plastic mass flow through an infinite converging channel formed by two conical surfaces on which the law of maximum friction acts (Fig. 1). A specific characteristic of this problem is the existence of two maximum friction surfaces and, accordingly, two distributions of the strain rate intensity factor. Since, according to the theory [5], the strain rate intensity factor is related to the thickness of the intensive strain layer near the friction surface, the solution of this problem may serve as a starting point for experimental confirmations of the theory. Note that the intensive strain layer thickness can be determined experimentally without any difficulties [6, 7] and the flow in an infinite channel of the shape under study can successfully model the tube drawing process [8].     

Design and test of a friction damper to reduce engine vibrations on a space launcher

Space launchers are submitted to complex vibration environments and this can impact the payload it is carrying. Ensuring the protection of the payload therefore requires the addition of a secondary system. In this paper, a rapid design method for the dimensioning of a friction damper is developed, based on the equivalent energy dissipation with that of a viscous damper. A friction damper is designed and a prototype is built. The friction damper is first characterised alone and it is then mounted inside a scale model of a launcher last stage. The friction damper is adequately modelled by a spring in series with a friction element. The damper prototype proves to efficiently damp the rocket engine vibrations, and the design method used for dimensioning the friction damper gives a good approximation for the optimal sliding force of the damper.     

金属往复滑动摩擦噪声源的识别

对金属往复滑动摩擦噪声进行了声学和动力学测量 ,通过对声压级和加速度进行时间历程波形分析、功率谱分析 ,确认摩擦噪声是由参加相对滑动的摩擦副的 1个或 2个部件的振动辐射所产生 ,摩擦噪声的声源体为参加摩擦运动的振动部件     

Vibrations of a rigid body with a controlled frictional electromagnetic seismic damper: nonlinear model

A nonlinear mathematical model of a gravitational vibratory system with a controlled electromagnetic seismic damper is developed. The dependence of the force of attraction of ferromagnetic bodies by the solenoid of the frictional device on the solenoid current is established for a specific solenoid design. The analytic expression for this force is derived by the least-squares method using a system of continuous piecewise-linear functions. It is used to describe the pressure of the solenoid on the friction surface. For multifrequency inertial excitation, the acceleration amplification factor is evaluated depending on the time constant and gain for two cases of control. The possibility of damping vibrations by controlling the absolute velocity and acceleration is established     

THE ERROR ANALYSIS IN MEASUREMENT OF RIGID BODY INERTIA BY THE FALLING BODY METHOD1)

为了分析刚体转动惯量实验测定中摩擦力矩变化对测量结果的影响,本文对采用落体法测角加速度方法进行了实测检验。结果表明,摩擦力矩随载物系统转速增大而显著增加,系统空载测量时,减速过程角加速度对应平均转速远大于加速过程平均转速,如果不进行修正,则导致计算结果偏低。而相同质量砝码拉动系统负载测量时,加速过程和减速过程对应平均转速相对接近,测量值主要受测量随机误差影响。上述结果有利于进一步开展转轴摩擦力矩随转速变化系统性的研究。     

Singular rigid/plastic solutions in anisotropic plasticity under plane strain conditions

Assuming a rigid plastic material model with arbitrary smooth yield criterion, it is shown that the plane strain solutions are singular in the vicinity of maximum friction surfaces. In particular, some components of the strain rate tensor and thus the equivalent strain rate approach infinity. It is also shown that the exact asymptotic representation of the solution near maximum friction surfaces depends on the shape of the yield contour in the Mohr stress plane.     

Equivalent linearizations for practical hysteretic systems

Experimental testing of a friction damped base isolation system has indicated a need for a new model of friction damping and for an appropriate equivalent linearization technique. The model for the damping adopted is a combination of viscous damping, constant Coulomb friction and linear Coulomb friction.This model is incorporated into the equation of motion for a single-degree-of-freedom system and the exact solutions are given for free vibrations and for steady-state vibrations excited by a harmonic force. The exact solution is taken as a basis for an equivalent linearization technique that can be used in conjunction with conventional design spectra for a practical design of such a system.     

Singular Solutions in an Axisymmetric Flow of a Medium Obeying the Double Shear Model

An asymptotic analysis of equations of an axisymmetric flow of a rigid-plastic material obeying the double shear model in the vicinity of surfaces with the maximum friction is performed. It is shown that the solution is singular if the friction surface coincides with the envelope of the family of characteristics. A possible character of the behavior of singular solutions in the vicinity of surfaces with the maximum friction is determined. In particular, the equivalent strain rate in the vicinity of the friction surface tends to infinity in an inverse proportion to the square root from the distance to this surface. Such a behavior of the equivalent strain rate is also observed in the classical theory of plasticity of materials whose yield condition is independent of the mean stress.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 180–186, September–October, 2005.     

Vibrational self-alignment of a rigid object exploiting friction

In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low friction to high friction coefficient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions.     

Dynamics of spatial structure-varying rigid multibody systems

Summary Couplings in machines and mechanisms exhibiting backlash and friction phenomena can be modeled as multibody systems with unilateral constraints and Coulomb friction. The structure of the differential-algebraic equations describing the system depends on the state of the constraints. The contact forces occurring at active constraints are taken into account in the equations of motion as Lagrange multipliers. Additionally, the kinematic conditions of all active constraints are formulated on the acceleration level. Contact and friction laws are sufficient conditions for state transitions of active constraints, and are represented by nonsmooth characteristics. Several formulations, like the linear complementarity problem, and two different nonlinear systems of equations are presented together with their solution method. The theory is applied to a mechanical system containing three-dimensional and coupled unilateral constraints with friction. Received 14 May 1998; accepted for publication 5 January 1999     

Analytical parametric study of bi-linear hysteretic model of dry friction under harmonic,impulse and random excitations

Hysteretic behavior due to some nonlinear sources is a common phenomenon in many dynamical systems. One of the sources of this behavior in mechanical systems is dry friction. Dry friction in bolted or riveted joints of mechanical structures makes their dynamic behavior hysteretic. Bi-linear hysteresis is one of the models that can be used to study these systems which is used in this paper. A SDOF system containing a bi-linear hysteretic element called Jenkins element under harmonic, impulse and random excitations is considered. For all three types of excitations, the effects of system and excitation parameters on the defined equivalent system parameters and the response specifications are studied. Harmonic balance method is employed for harmonic excitation studies, and optimum friction threshold for minimizing response amplitude is obtained versus other system parameters and response amplitude. Energy balance method is used for impulse excitation through which the desired decaying ratio can be achieved by tuning the friction threshold, depending on stiffness ratio. System under random excitation is investigated by equivalent linearization technique in two steps. At the first step, equivalent properties are obtained versus instantaneous amplitude of response. In this step, the paper contains the parametric study of system in which the variations of equivalent parameters are described when physical parameters of system or input intensity vary. Overall variance of system response is determined in the second step, and optimum sliding threshold is obtained to have minimum overall variance of system response.     

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

Summary The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.     

边坡岩体结构的三维失稳形式及稳定性分析研究

由两组结构面控制的四面体块体是岩体中最基本的结构体, 其稳定性取决于块体所受荷载及结构面上的摩阻力。正确判定边界面上摩阻力分布是评价块体稳定性的关键。本文提出的块体稳定性分析适用于岩体所受荷载为三维非共点力系。在不同外力作用下块体可产生平动、转动、翘扭及倾倒等各种三维失稳组合形式, 从而得到更为合理的块体稳定性评价。