Contact with friction of a rigid cylinder with an elastic half-space

An exact solution to the problem of indentation with friction of a rigid cylinder into an elastic half-space is presented. The corresponding boundary-value problem is formulated in planar bipolar coordinates, and reduced to a singular integral equation with respect to the unknown normal stress in the slip zones. An exact analytical solution of this equation is constructed using the Wiener-Hopf technique, which allowed for a detailed analysis of the contact stresses, strain, displacement, and relative slip zone sizes. Also, a simple analytical solution is furnished in the limiting case of full stick between the cylinder and half-space.     

Multiple impacts with friction in rigid multibody systems

An impact model for two-dimensional contact situations is developed which contains the main physical effects of a compliance element in the normal direction and a series of a compliance and Coulomb friction elements in the tangential direction. For systems with multiple impacts a unilateral formulation based on Poisson's hypothesis is used to describe the impulses which are transferred in the normal direction. The event of an impact is divided into two phases. The phase of compression ends with vanishing approaching velocity if normal impulses are transferred and is equivalent to a completely inelastic collision. The phase of expansion allows the bodies to separate under the action of the normal impulses whenever they are large enough. The absolute values of the tangential impulses are bounded by the magnitudes of the normal impulses, due to the Coulomb friction relationship on the impulse level. One part of the transferred tangential impulse during compression is assumed to be partly reversible which may be regarded as an application of Poisson's law. The remaining part is completely irreversible and considered friction. This formulation contains the special case of completely elastic tangential impacts as well as the situation when only Coulomb friction acts. It is proven that the presented impact model is always dissipative or energy preserving. The evaluation of the problem is done by solving one set of complementarity conditions during compression and a nearly identical set of equations during expansion. The theory is applied to some basic examples which demonstrate the difference between Newton's and Poisson's hypotheses.     

A complementarity-based rolling friction model for rigid contacts

In this work (also, preprint ANL/MCS-P3020-0812, Argonne National Laboratory) we introduce a complementarity-based rolling friction model to characterize dissipative phenomena at the interface between moving parts. Since the formulation is based on differential inclusions, the model fits well in the context of nonsmooth dynamics, and it does not require short integration timesteps. The method encompasses a rolling resistance limit for static cases, similar to what happens for sliding friction; this is a simple yet efficient approach to problems involving transitions from rolling to resting, and vice-versa. We propose a convex relaxation of the formulation in order to achieve algorithmic robustness and stability; moreover, we show the side effects of the convexification. A natural application of the model is the dynamics of granular materials, because of the high computational efficiency and the need for only a small set of parameters. In particular, when used as a micromechanical model for rolling resistance between granular particles, the model can provide an alternative way to capture the effect of irregular shapes. Other applications can be related to real-time simulations of rolling parts in bearing and guideways, as shown in examples.     

The supersonic motion of a rigid body in an elastic medium with friction

The plane problem of supersonic steady motion of a body in an elastic medium is solved. Two possible cases of body motion are considered depending on its velocity. In the first case, the body moves at a velocity greater than the velocity of transverse waves but smaller than the velocity of longitudinal waves. In the second case, the body moves at a velocity greater than the velocity of longitudinal waves. An analytic solution of the problem under study is obtained and analyzed. It is shown that friction substantially influences the penetration process.     

捷联惯导系统罗经法自对准

研究了摇摆状态下捷联惯导系统罗经法自对准技术,设计了水平、方位精对准参数以及基于MATLAB／SIMULINK的参数分析系统,最后进行了基于VC＋＋6．0的捷联惯导系统罗经法自对准的软件设计、仿真分析与精度评估。仿真结果表明,罗经法自对准在不同海情、不同初始姿态误差角、全方位、带量化误差的条件下均具有较高的对准精度、较好的快速性和动态品质,能够满足捷联惯导系统在摇摆基座下实现自对准的要求,同时为下一步的工程应用提供了依据。     

Global controllability of certain systems of rigid bodies under friction

We consider Lagrangian systems with bounded potential energy, with control constraints known in advance, and with friction. We present several sufficient conditions for the global controllability in the case of a cyclic coordinate assuming that the dry friction forces acting in the system satisfy the Amonton-Coulomb law. In particular, we prove the global controllability of a system of three equal masses successively connected by linear springs on a common rough line when the only controlling action is a bounded force applied to the first load. A majority of well-known results concerning controllability (in the traditional sense [1]) of dynamical systems were obtained only for the cases in which the continuity of the right-hand side of the differential equation is either assumed in advance or is ensured by part of the controlling resources. In the present paper, we give several sufficient conditions for the global controllability of systems of rigid bodies under the action of dry friction forces; the number of controls can be less than the number of degrees of freedom. The main idea of our approach consists in searching and using auxiliary “attainable” curves in the phase space such that these curves lie outside the domains of “nonsmoothness” of the system.     

Localized interaction models with non-constant friction for rigid penetrating impactors

We suggest approximate penetration models for rigid body penetration that take into account sliding velocity (SV) and pressure dependence of the friction coefficient (FC). It is showed that introducing variable FC in a localized interaction model (LIM) yields a model that belongs to the class of LIM. We developed a general method for determining the depth of penetration (DOP) using the piecewise linear approximation of the impactor’s generatrix. For some classes of SV dependent friction models we obtained analytical formulas for calculating the DOP. Using the experimental data available in the literature, we determined the dependencies of FC vs. pressure and SV. We conducted numerical modeling of penetration of a metal striker into metal and concrete shields employing models with variable and constant FC. Numerical simulations showed that taking into account variable FC strongly effects the DOP when FC changes appreciably for large velocities that are characteristic for the high-speed penetration.     

Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface

The paper deals with the estimation of the pressure distribution, the shape of contact and the friction force at the interface of a flat soft elastic solid moving on a rigid half-space with a slightly wavy surface. In this case an unsymmetrical contact is considered and justified with the adhesion hysteresis. For soft solids as rubber and polymers the friction originates mainly from two different contributions: the internal friction due to the viscoelastic properties of the bulk and the adhesive processes at the interface of the two solids. In the paper the authors focus on the latter contribution to friction. It is known, indeed, that for soft solids, as rubber, the adhesion hysteresis is, at least qualitatively, related to friction: the larger the adhesion hysteresis the larger the friction. Several mechanisms may govern the adhesion hysteresis, such as the interdigitation process between the polymer chains, the local small-scale viscoelasticity or the local elastic instabilities. In the paper the authors propose a model to link, from the continuum mechanics point of view, the friction to the adhesion hysteresis. A simple one-length scale roughness model is considered having a sinusoidal profile. For partial contact conditions the detached zone is taken to be a mode I propagating crack. Due to the adhesion hysteresis, the crack is affected by two different values of the strain energy release rate at the advancing and receding edges respectively. As a result, an unsymmetrical contact and a friction force arise. Additionally, the stability of the equilibrium configurations is discussed and the adherence force for jumping out of contact and the critical load for snapping into full contact are estimated.     

The sliding interface crack with friction between elastic and rigid bodies

The paper analyzes the frictional sliding crack at the interface between a semi-infinite elastic body and a rigid one. It gives solutions in complex form for non-homogeneous loading at infinity and explicit solutions for polynomial loading at the interface. It is found that the singularities at the crack tips are different and that they are related to distinct kinematics at the crack tips. Firstly, we postulate that the geometry of the equilibrium crack with crack-tip positions b and a is determined by the conditions of square integrable stresses and continuous displacement at both crack tips. The crack geometry solution is not unique and is defined by any compatible pair (b,a) belonging to a quasi-elliptical curve. Then we prove that, for an equilibrium crack under given applied load, the “energy release rate” G_tip, defined at each crack tip by the J_ε-integral along a semi-circular path, centered at the crack tip, with vanishing radius ε, vanishes. For arbitrarily shaped paths embracing the whole crack, with end points on the unbroken zone, the J-integral is path-independent and has the significance of the rate, with respect to the crack length, of energy dissipated by friction on the crack.     

Discontinuous dynamics for a class of 3-DOF friction and collision system with symmetric bilateral rigid constraints

Nonlinear Dynamics - This paper deals with the discontinuous dynamic behaviors of a class of three-degree-of-freedom friction and collision system with symmetric bilateral rigid constraints by...     

Spinning rigid bodies driven by orbital forcing: the role of dry friction

Nonlinear Dynamics - A “circular orbital forcing” makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this...     

捷联罗经的动基座自对准技术

在分析捷联罗经对准原理的基础上,改进了一种在航向和水平姿态完全未知条件下的捷联罗经对准方法,将对准方法划分为四个步骤:水平粗对准、航向估算、水平再对准和罗经航向对准,并给出了航向估算的公式.载体存在速度时会对罗经对准产生影响,因此提出了一种适用于捷联罗经的惯性传感器校正方法,推导了陀螺和加速度计信号校正的公式,将由于载体运动产生的陀螺和加速度计信号滤除,在此基础上结合上述的对准方法完成罗经自对准.对"匀速+晃动"、"加速+晃动"和"拐弯+晃动"三种情况下的罗经自对准进行了仿真,仿真结果证明该方法可以有效地实现运动基座下的罗经对准.     

Bi-potential method applied for dynamics problems of rigid bodies involving friction and multiple impacts

Nonlinear Dynamics - This study aims to extend the application of the bi-potential method to solve the dynamics problems of rigid bodies involving friction and multiple impacts. The key issue is...     

A hybrid scheme for simulation of planar rigid bodies with impacts and friction using impact mappings

This paper introduces numerical techniques necessary for the implementation of impact maps derived from an energetic impact law for rigid-body impacts with friction at isolated contact points. In particular the work focuses on methodologies for long-term simulation with behaviours such as dynamic transitions and chatter. The methods are based on hybrid event-driven numerical solvers for ordinary differential equations together with system states to deal with the transitions. A slender rod impacting a periodically oscillating surface is used as an example to illustrate implementation and methods. The numerical scheme for the rod system is used to show how symmetry can play an important role in the presence of friction for long-term dynamics. This will show that surface oscillations with low frequencies tend to lead to periodic motions of the rod that are independent of friction. For higher frequencies however the periodic solutions are not that common and irregular motion ensues.     

A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

Contact of a rigid cylinder indenting an elastic layer sliding over a rigid substrate

Details of the integral transform solution of the state of stress in a layer resting on but sliding over a rigid substrate, in the presence of interfacial friction, is studied. The free surface of the layer is subject to a localised contact, which is represented as a piecewise linear distribution of tractions, using the Bentall–Johnson procedure. The influence functions needed are derived and their properties discussed and compared with those already available for other interface conditions. Lastly, the procedure is applied to the problem of a shrink fit tyre which, under severe tyre/road tangential loading, can be ‘torn’ around the wheel (here, the substrate).     

Vibrational Dynamics of a Centrifuged Fluid Layer

The dynamics of a low-viscosity fluid layer inside a rotating cylinder under transverse translational vibration relative to the rotation axis is investigated experimentally. A novel vibrational effect, the generation of intense azimuthal fluid flows with velocities comparable with the cavity rotation velocity, is revealed. The structure and intensity of the vibrational flows and the flow transformation with variation of the determining dimensionless parameters (frequency and vibrational acceleration) are studied.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 147–156.Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Polezhaev.