V.I. Babitsky

Theory of Vibro-Impact Systems and Applications

Many situations in the applied sciences are modeled by systems of nonlinear PDE. The questions of global existence, boundedness, exponential growth or blow-up, that is, the fact that the solution becomes unbounded in finite time, are central in the mathematical analysis of these PDE and have important physical interpretations. In particular, very rapid growth and blow-up phenomena describe explosions and other singular behavior in combustion theory and relate to the onset of turbulence in fluid dynamics. This new book of professor B. Straughan discusses several PDE and systems of PDE modeling a variety of phenomena including: vortex sheet breakdown, Rayleigh–Taylor instability, sonoluminescence, Benard–Marangoni convection, glacier physics, ferrohydrodynamics, chemotaxis, nonlinear elasticity, shear flow in granular materials. The emphasis is on the description of the rich variety of problems from the applied sciences where blow-up or rapid growth play a central role. The book also includes in Chapter 1 a useful review of some of the relevant methods that have been developed for establishing blowup and in Chapter 2 an analysis of systems of nonlinear parabolic equations with convective terms; decay, boundedness and blow-up of solutions are discussed. General blow-up results for certain classes of Volterra integral equations originating from problems in combustion theory and fluid dynamics are presented in Chapter 5. The bibliography is rich and up to date. The book is certainly an important addition to the existing literature on the subject even though, the limited number of pages and the variety of the problems discussed do not always allow for a selfcontained presentation: in certain cases the author is obliged to limit himself to just quote results from the literature and to address the reader to the original works for a proof and a discussion of the physical significance of the results.

Ultrasonically assisted turning of aviation materials

Abstract The results of the research in ultrasonically assisted machining are presented. Turning of some modern aviation materials was conducted with ultrasonic vibration applied in the feed direction using an autoresonant control system. Cutting conditions were typical of those used for manufacture. The roughness and roundness of the ultrasonically and conventionally machined workpieces were measured and compared. The results obtained show that the application of ultrasonic vibration can improve the surface quality considerably. Improvements of up to 25–50% have been achieved.

Ultrasonic cutting as a nonlinear (vibro-impact) process

The machining process with the superimposing of ultrasonics is considered. The accumulated experimental results are explained theoretically in the framework of rheological models. It is confirmed that under the influence of high frequency vibration, the phenomenological transformation of elasto-plasticity into visco-plasticity and fluidization of dry friction occurs. The dynamic characteristics of transformed machining processes are obtained. They include the dependence of reduced cutting forces on the material and vibration parameters. It is shown that excitation of the vibro-impact mode of tool-workpiece interaction is the most effective way of using ultrasonic influence on dynamical characteristics of machining. The dynamics of an ultrasonic cutting machine under technological load is investigated. The nonlinear amplitude response of the vibrating tool in the process of cutting is obtained. The theoretical results are confirmed by experiments. The method of stabilization of resonant ultrasonic excitation is described. The advantages of ultrasonic cutting and possible ways of using it are discussed.

Vibration control of linear split Stirling cryogenic cooler for airborne infrared application

Modern infrared imagers often rely on the split Stirling cryogenic coolers the linear compressors of which are the well-known sources of harmonic disturbance. The traditional method of their passive isolation fails to meet the restraints on the static and dynamic deflections which are originated by the combined action of the airborne g-loading and harsh random vibration.

Modelling of vibro-impact penetration of self-exciting percussive-rotary drill bit

Abstract The penetration of a drilling tool into a hard medium under periodic impact action is analyzed and the simulation model presented. This is further development of previously investigated model of a self-excited percussive-rotary drilling system. The system used the stick–slip phenomenon to generate an impact action superimposed on the drilling process. A phenomenological visco-elasto-plastic model of the media is used and the system response is studied numerically, first as a forced vibration and second as a result of a self-excited vibro-impact process. Relief of the main drive has been obtained and an increase in the rate of penetration is observed with increased impact intensity and hardening of the medium. Results of the preliminary drilling experiment with superimposed dynamic action have shown an improvement in the rate of penetration.

Energy-based analysis of ultrasonically assisted turning

The process of ultrasonically-assisted turning (UAT) is a superposition of vibration of a cutting tool on its standard movement in conventional turning (CT). The former technique has several advantages compared with the latter, one of the main being a significant decrease in the level of cutting forces. I n this paper the effects observed in UAT are analysed employing ideas of dynamic fracture mechanics. The active stage of loading duration depends heavily on ultrasonic frequency and the cutting speed; he application of the fracture criterion based on the notion of incubation time makes it possible to calculate a dependence of this duration on its threshold amplitude. An estimation of energy, necessary to create a threshold pulse in the materi al, is made by solving the contact Hertz problem. The obtained time dependence of energy has a marked minimum. Thus, the existence of energy-efficient loading duration is demonstrated. This ex plains the decrease in the cutting force resulting from supe rimposed ultrasonic vibration. The obtained results are in agreement with experiments on ultrasonic assisted machining of aluminium and Inconel 718 alloy.

Analysis of Machinability of Ti- and Ni-Based Alloys

Efficient machining of advanced Ti- and Ni-based alloys, which are typically difficult-to-machine, is a challenge that needs to be addressed by the industry. During a typical machining operation of such alloys, high cutting forces imposed by a tool on the work-piece material lead to severe deformations in the process zone, along with high stresses, strains and temperatures in the material, eventually affecting the quality of finished work-piece. Conventional machining (CT) of Ti- and Ni-based alloys is typically characterized by low depths of cuts and relatively low feed rates, thus adversely affecting the material removal rates (MRR) in the machining process. In the present work, a novel machining technique, known as Ultrasonically Assisted Turning (UAT) is shown to dramatically improve machining of these intractable alloys. The developed machining process is capable of high MRR with an improved surface quality of the turned work-piece. Average cutting forces are significantly lower in UAT when compared to those in traditional turning techniques at the same machining parameters, demonstrating the capability of vibration-assisted machining as a viable machining method for the future.

Vibration protection of sensitive components of infrared equipment in harsh environments

This article addresses the principles of optimal vibration protection of the internal sensitive components of infrared equipment from harsh environmental vibration. The authors have developed an approach to the design of external vibration isolators with properties to minimise the vibration-induced line-of-sight jitter which is caused by the relative deflection of the infrared sensor and the optic system, subject to strict constraints on the allowable sway space of the entire electro-optic package. In this approach, the package itself is used as the first-level vibration isolation stage relative to the internal highly responsive components.

Damage Assessment of a Cracked Bar: Effect of Material Nonlinearity on Vibro-Impact Response

Structural health monitoring is receiving much attention as a means to prevent catastrophic failure in structures in operating conditions. In most cases fracture is caused by the growth of crack, which cannot be precluded in many engineering structures. Moreover, to have an accurate quantitative estimate of crack tolerance of a structure to prevent fracture of load bearing components, an effective non-destructive evaluation procedure becomes necessary to monitor the structure under working conditions.

Stresses in Ultrasonically Assisted Turning

Ultrasonically assisted turning (UAT) is a novel material-processing technology, where high frequency vibration (frequency f ≈ 20kHz, amplitude a ≈15μm) is superimposed on the movement of the cutting tool. Advantages of UAT have been demonstrated for a broad spectrum of applications. Compared to conventional turning (CT), this technique allows significant improvements in processing intractable materials, such as high-strength aerospace alloys, composites and ceramics. Superimposed ultrasonic vibration yields a noticeable decrease in cutting forces, as well as a superior surface finish. A vibro-impact interaction between the tool and workpiece in UAT in the process of continuous chip formation leads to a dynamically changing stress distribution in the process zone as compared to the quasistatic one in CT. The paper presents a three-dimensional, fully thermomechanically coupled computational model of UAT incorporating a non-linear elasto-plastic material model with strain-rate sensitivity and contact interaction with friction at the chip–tool interface. 3D stress distributions in the cutting region are analysed for a representative cycle of ultrasonic vibration. The dependence of various process parameters, such as shear stresses and cutting forces on vibration frequency and amplitude is also studied.