Force Pulse Research Articles

Discrete Cutaneous Feedback for Reducing Dimensions of Wearable Haptic Devices

In this article, we explore alternative cutaneous haptic feedback for rendering modulation of the grasping force. The aim of the study was to reduce power requirements and in turn dimensions of the actuators, in wearable devices applied to virtual or teleoperated manipulation. This is critical in certain rehabilitation or training scenarios where haptics should not interfere with dexterity of the user. In the study, we experimented discrete, pulsed cutaneous force feedback and compared it with conventional continuous proportional feedback, in a virtual pick and place task. We made use of wearable thimbles based on voice coil actuators in order to provide high-quality, low-noise haptic feedback to the participants. The evaluation was performed on the basis of both objective measurements of task performance (measured virtual forces and correct ratio) and a questionnaire evaluating participants’ preferences for the different feedback conditions. On the basis of the obtained results, in the article, we discuss the possibility of providing high-frequency, discretized cutaneous feedback only, driven by modulation of the grasping force. The opportunity is to reduce volume and mass of the actuators and also to consider alternative design solutions, due to the different requirements in terms of static and high-frequency components of the output force.

Ret kinase-mediated mechanical induction of colon stem cells by tumor growth pressure stimulates cancer progression in vivo

How mechanical stress actively impacts the physiology and pathophysiology of cells and tissues is little investigated in vivo. The colon is constantly submitted to multi-frequency spontaneous pulsatile mechanical waves, which highest frequency functions, of 2 s period, remain poorly understood. Here we find in vivo that high frequency pulsatile mechanical stresses maintain the physiological level of mice colon stem cells (SC) through the mechanosensitive Ret kinase. When permanently stimulated by a magnetic mimicking-tumor growth analogue pressure, we find that SC levels pathologically increase and undergo mechanically induced hyperproliferation and tumorigenic transformation. To mimic the high frequency pulsatile mechanical waves, we used a generator of pulsed magnetic force stimulation in colonic tissues pre-magnetized with ultra-magnetic liposomes. We observed the pulsatile stresses using last generation ultra-wave dynamical high-resolution imaging. Finally, we find that the specific pharmacological inhibition of Ret mechanical activation induces the regression of spontaneous formation of SC, of CSC markers, and of spontaneous sporadic tumorigenesis in Apc mutated mice colons. Consistently, in human colon cancer tissues, Ret activation in epithelial cells increases with tumor grade, and partially decreases in leaking invasive carcinoma. High frequency pulsatile physiological mechanical stresses thus constitute a new niche that Ret-dependently fuels mice colon physiological SC level. This process is pathologically over-activated in the presence of permanent pressure due to the growth of tumors initiated by pre-existing genetic alteration, leading to mechanotransductive self-enhanced tumor progression in vivo, and repressed by pharmacological inhibition of Ret.

Technological Capabilities of Impulse Rotators

In the article “Technological capabilities of impulse rotators” the results of use of impulse rotators in some technological processes, differential adjustment of their motion with kinematic and dynamic vibration exciter are considered. Equation of kinetic energy of impulse rotator allows to determine mutual influence of design elements on rational use of supplied pulse energy for useful work. Positive qualities of kinematic torsional vibration exciters are noted, the main of which is organization of force pulse regularity and its considerable force possibilities of pulse creation. A generalized graph of the change of productivity and wear of the working element of the pulse converter compared to the static one is given.Features of impulse rotators with kinematic excitation of torsional oscillations make it possible to change the mode of work performance, to apply low-energy processes of individual operations. Transportation way of destruction products by the screw with use of an impulse rotator on breeds above average fortress excludes use of the compressor. Machines with rolling and spring impact tools do not correspond to the screw method of destruction products discharge and require compressor use. In this case, the energy intensity of production unit increases more than twice.

The Influence of Altered-Gravity on Bimanual Coordination: Retention and Transfer.

Many of the activities associated with spaceflight require individuals to coordinate actions between the limbs (e.g., controlling a rover, landing a spacecraft). However, research investigating the influence of gravity on bimanual coordination has been limited. The current experiment was designed to determine an individual’s ability to adapt to altered-gravity when performing a complex bimanual force coordination task, and to identify constraints that influence coordination dynamics in altered-gravity. A tilt table was used to simulate gravity on Earth [90° head-up tilt (HUT)] and microgravity [6° head-down tilt (HDT)]. Right limb dominant participants (N = 12) were required to produce 1:1 in-phase and 1:2 multi-frequency force patterns. Lissajous information was provided to guide performance. Participants performed 14, 20 s trials at 90° HUT (Earth). Following a 30-min rest period, participants performed, for each coordination pattern, two retention trials (Earth) followed by two transfer trials in simulated microgravity (6° HDT). Results indicated that participants were able to transfer their training performance during the Earth condition to the microgravity condition with no additional training. No differences between gravity conditions for measures associated with timing (interpeak interval ratio, phase angle slope ratio) were observed. However, despite the effective timing of the force pulses, there were differences in measures associated with force production (peak force, STD of peak force mean force). The results of this study suggest that Lissajous displays may help counteract manual control decrements observed during microgravity. Future work should continue to explore constraints that can facilitate or interfere with bimanual control performance in altered-gravity environments.

Toward better metal flow control in electrohydraulic sheet forming by combining with electromagnetic approach

Electrohydraulic sheet forming is a high-velocity manufacturing process, which utilizes a pressure pulse induced by underwater electrical discharge to plastically shape metals. It has attracted wide interest for its potential to shape metal materials with poor formability. Such advantages can be exploited by combining this process with the conventional stamping process or by using it solely. In both cases, the dominant deformation mode is stretching, implying substantial thinning of sheet metal. The goal of this paper is to improve the material flow control in electrohydraulic sheet forming. A controllable drawing deformation mode is introduced into the electrohydraulic sheet forming process by using a radial inward pulsed Lorentz force at sheet edge induced by an electromagnetic coil, which can substantially enhance the draw-in of the sheet flange. The flexible combination of the stretching deformation and the introduced drawing deformation allows active control of the high-velocity material flow behavior, thus enabling much better control of the final forming quality. About 20 % improvement of the forming height limit is observed from the experimental results. Furthermore, a numerical model is established to better understand the process mechanism, and the critical roles of the amplitude and the action timing of the radial inward Lorentz force are identified.

МОДЕЛИРОВАНИЕ ПРОЦЕССОВ И МЕТРОЛОГИЯ В ЭЛЕКТРОИМПУЛЬСНЫХ СИСТЕМАХ

Electromagnetic force pulses are forces of mutual repulsion between the inductor and the anchor. Under their action, the anchor is shifted towards the cleaned surface of the affected object and elastic vibrations are transmitted to it. In electro-pulse interaction systems, the duration of the energy accumulation process, and then its release in extremely small time intervals, allows to obtain the maximum possible values of mechanical impulse action on the surface of the affected object. The maximum operating voltage on a capacitive energy storage device can reach 5 kV or higher. Electro-pulse interaction systems are shock-type devices. Compared with other devices of similar purpose (vibrators, electromagnetic or pneumatic shock mechanisms), they have no competition in terms of cleaning efficiency.

ERFWHG CHANGE IN THE PULSE-POWER CHARACTERISTICS OF THE ENGINE WORKING WITH THE CYLINDER DISCONNECTING IN IDLE MODE

The parameters of gas-dynamic processes in the engine cylinders affect the forces on the supports. By evaluating the impulse actions and peak values of the forces on the supports, it is possible to evaluate the efficiency of each cylinder. (Research purpose) The research purpose is studying the process of changing the external impulse-power characteristics of an internal combustion engine operating in idle mode with some disconnected cylinders. (Materials and methods) The article presents a methodology for quantifying the impulse effect of the engine on the supports during the combustion cycle and expansion of each cylinder and experimental studies on a diesel four-cylinder four-stroke engine D-243. During the research, the fuel supply to one, two and three cylinders was gradually turned off and the forces arising in the supports were recorded using strain sensors and a set of measuring equipment. (Results and discussion) With uniform engine operation with a minimum crankshaft rotation speed in idle mode, the peak values of the forces on the supports during the combustion and expansion cycles reached an average value of 200 newtons, the magnitude of their impulse action takes an average value of 8.2 kilonewtons-seconds equal for all cylinders. With the gradual shutdown of the cylinders, the peak values of the forces on the supports at the combustion and expansion stroke increase to 910 newtons when working with only one cylinder, and the average value of the force pulse is 50 kilonewtons-seconds. The depressurization of non-working cylinders increases the peak force effect of the working engine cylinder on the supports to 1200 newtons, and the pulsed force effect up to 85 kilonewtons-seconds. (Conclusions) The proposed methodology for evaluating the parameters of the gas-dynamic processes of the engine based on the external pulse-power characteristics will allow to quickly assess the technical condition and efficiency of each cylinder and the engine as a whole.

Means of Air Bleed in the Working Process of a Pneumatic Percussion Mechanism for Construction, Installation and Reconstruction of Structures

The features of synthesized mechanisms with changes in the striker design elements represented as bypass channels made by straight broken lines and curved lines of at least second order of curvature on the side surface along the rod forming part of the stepped striker are considered in the paper. A physical and mathematical description and qualitative assessment of changes in air distribution processes during air bleed between working chambers are presented. Differences in description restrictions for the air bleed process when changing the shape of bypass channels made in the form of channel flats on the rod part of the stepped striker are shown. Differences in bypassing systems imply realization of different processes of force pulse formation in working chambers in pneumatic percussion mechanisms. A list of the constructive solutions’ considered variants directions in pneumatic machines of impact action on the machined medium with any acceptable values of energy parameters in the presence of appropriate equipment for compressed air supply by pressure and productivity is offered. The recommendations on the use of design solutions of the specified channels implementing shock and vibration working processes in the mechanisms of pneumatic shock machines of a particular purpose have been developed.

Reduction of the auto seismic component of error of a ballistic laser gravimeter by excitation of an induction-dynamic catapult from an AC voltage source

The purpose of the study is to analyse the influence of the excitation of an induction-dynamic catapult of a ballistic laser gravimeter from an AC voltage source at different frequencies on electromechanical indicators that provide a reduced value of the auto seismic component of error in measuring the gravitational acceleration g due to a decrease in the recoil force. A mathematical model of the gravimeter catapult when excited from an AC voltage source is proposed, taking into account the interrelated electrical, magnetic and mechanical processes. The nature of the electromechanical processes in the catapult of the gravimeter with such excitation has been established. It is shown that a phase shift occurs between the currents in active elements, as a result of which positive (repulsive) pulses of the electrodynamic force alternate with negative (attractive) pulses of force. A criterion for the efficiency of the gravimeter catapult has been introduced, taking into account the maximum value of push of the test body at the smallest values of the electrodynamic force and current of the inductor winding. It was found that the highest efficiency of the gravimeter catapult is provided at a frequency of 250 Hz, at which the catapult efficiency is 3.5 times higher than at a frequency of 50 Hz. It is shown that the transition from the method of excitation of an induction-dynamic catapult with one short pulse to excitation from an AC voltage source makes it possible to reduce the uncertainty in measuring the gravitational acceleration.

Dynamic Response of Rock-like Materials Based on SHPB Pulse Waveform Characteristics.

Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in the split-Hopkinson pressure bar (SHPB) numerical simulation research. In response to this problem, this paper discusses the effects of different pulse types and pulse waveforms on the incident waveform and dynamic response characteristics of specimens based on particle flow code (PFC). The research identifies a critical interval of rock dynamic strength, where the dynamic strength of the specimen is independent of the strain rate but increases with the amplitude of the incident stress wave. When the critical interval is exceeded, the dynamic strength is determined by the strain rate and strain rate gradient. The strain rate of the specimen is only related to the slope of the incident stress wave and is independent of its amplitude. It is also determined that the inertia effect cannot be eliminated in the SHPB. The slope of the velocity pulse waveform determines the strain rate of the specimen, the slope of the force pulse waveform determines the strain rate gradient of the specimen, and the upper bottom time determines the strain rate of the specimen. It provides a reference for SHPB numerical simulation. A dynamic strength prediction model of rock-like materials is then proposed, which considers the effects of strain rate and strain rate gradient.

A Comparative Study on the Temperature Effect of Solid Birch Wood and Solid Beech Wood under Impact Loading.

In order to use wood for structural and load-bearing purposes in mechanical engineering, basic information on the impact behaviour of the material over a wide temperature range is needed. Diffuse porous hardwoods such as solid birch wood (Betula pendula) and solid beech wood (Fagus sylvatica) are particularly suited for the production of engineered wood products (EWPs) such as laminated veneer lumber (LVL) or plywood due to their processability in a veneer peeling process. In the frame of this study, solid birch wood and solid beech wood samples (300 × 20 × 20 mm3) were characterised by means of an impact pendulum test setup (working capacity of 150 J) at five temperature levels, ranging from −30 °C to +90 °C. The pendulum hammer (mass = 15 kg) was equipped with an acceleration sensor in order to obtain the acceleration pulse and deceleration force besides the impact bending energy. In both solid birch wood and solid beech wood, the deceleration forces were highest at temperatures at and below zero. While the average impact bending energy for solid birch wood remained almost constant over the whole considered temperature range, it was far less stable and prone to higher scattering for solid beech wood.

DISSIPATIVE OSCILLATORS’ POWER CHARACTERISTIC NON-SYMMETRY DYNAMIC EFFECT

The features of motion of a non-linear oscillator under the instantaneous force pulse loading are studied. The elastic characteristic of the oscillator is given by a polygonal chain consisting of two linear segments. The focus of the paper is on the influence of the dissipative forces on the possibility of occurrence of the elastic characteristic non-symmetry dynamic effect, studied previously without taking into account the influence of these forces. Four types of drag forces are considered, namely linear viscous friction, Coulomb dry friction, position friction, and quadratic viscous resistance. For the cases of linear viscous friction and Coulomb dry friction the analytical solutions of the differential equation of oscillations are found by the fitting method and the formulae for computing the swings are derived. The conditions on the parameters of the problem are determined for which the elastic characteristic non-symmetry dynamic effect occurs in the system. The conditions for the effect to occur in the system with the position friction are derived from the energy relations without solving the differential equation of motion. In the case of quadratic viscous friction the first integral of the differential equation of motion is given by the Lambert function of either positive or negative argument depending on the value of the initial velocity. The elastic characteristic non-symmetry dynamic effect is shown to occur for small initial velocities, whereas it is absent from the system when the initial velocities are sufficiently large. The values of the Lambert function are proposed to be computed by either linear interpolation of the known data or approximation of the Lambert function by elementary functions using asymptotic formulae which approximation error is less than 1%. The theoretical study presented in the paper is followed up by computational examples. The results of the computations by the formulae proposed in the paper are shown to be in perfect agreement with the results of numerical integration of the differential equation of motion of the oscillator using a computer.

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state.

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

Numerical investigation on rock‐breaking mechanism and cutting temperature of compound percussive drilling with a single PDC cutter

AbstractCompound percussive drilling technology is a new method to improve the rock‐breaking efficiency in deep hard formation. In order to study the rock‐breaking mechanism of compound impact drilling, the thermal‐structure coupling simulation of the dynamic rock‐breaking process with a single PDC cutter was investigated by using ABAQUS software. The influence of impact parameters on the rock‐breaking performance and cutting temperature was analyzed. The results proved that the compound impact load changes the rock failure mode and improves the rock‐breaking efficiency. Compared with steady load cutting, the rock broken volume under compound impact increased by 7.5%, and the mechanical specific energy (MSE) decreased by 12.3%. As the axial impact load amplitude increases, the MSE increases gradually. With an increase in torsional impact load amplitude and impact frequency, the MSE decreases first and then increases, and the optimal torsional static load ratio is 0.3, and the optimal impact frequency is 30 Hz. In addition, the cutting temperature of the compound percussive drilling is higher than that of the steady load cutting, and it increases with the impact load amplitude and decreases with the frequency. For the three impact load waveforms—sine, triangle, and square in this paper, the rock‐breaking efficiency under the condition of sine waveform is the largest when the dynamic amplitude of the pulse force is fixed, and the cutting temperature under the condition of square waveform is the highest. Finally, based on the analysis of the rock‐breaking mechanism, a novel compound percussive drilling tool was designed and tested in the field.

Predictive design of impact absorbers for mitigating resonances of flexible structures using a semi-analytical approach

Analytical conditions are available for the optimum design of impact absorbers (or Vibro-Impact Nonlinear Energy Sinks) for the special case where the host structure is well described as a rigid body. Accordingly, the analysis relies on the assumption that the impacts cause immediate dissipation in the contact region, which is modeled in terms of a coefficient of restitution (Newton’s impact law) that is assumed to be known and fixed. When a flexible host structure is considered instead, the impact absorber not only dissipates energy at the time instances of impact, but, and perhaps more importantly, it inflicts nonlinear energy scattering between structural modes. Hence, it is crucial to account for such nonlinear energy transfers yielding energy redistribution within the modal space of the structure. In the present work, we develop a design approach for flexible host structures. We consider the case of a forced excitation near primary resonance with a well-separated mode. We demonstrate that the time scales of the impact and the resonant vibration can be decoupled. On the long time scale, the dynamics of the host structure can be properly reduced to the fundamental harmonic of the resonant mode. A light impact absorber responds to this enforced motion, and we show that the conventional Slow Invariant Manifold of the dynamics is recovered for the commonly considered regime of two symmetric impacts per period. On the short time scale of the impact dynamics, the contact mechanics and elasto-dynamics must be finely resolved. We show that it is sufficient to run a numerical simulation of a single impact event with representative pre-impact velocity. From this short-time simulation, we derive an effective modal coefficient of restitution and the properties of the contact force pulse, needed to approximate the behavior on the long time scale. We derive a closed-form expression of the periodic resonant response and establish that the design problem can be reduced to four dimensionless parameters. We demonstrate the approach for the numerical example of a cantilevered beam with a spherical impact absorber. We conclude that the proposed semi-analytical procedure enables deep qualitative understanding of the problem and, at the same time, yields a quantitatively accurate prediction of the optimum design.

Use of the toolholder with the oriented stiffness for ultrasonic turning

An effective way of processing difficult-to-machine materials is ultrasonic cutting, which is carried out by applying ultrasonic vibrations to the movement of the cutter and contributes to a significant reduction in cutting force and increase processing productivity. The article presents the results of research on the efficiency of using a new device for ultrasonic cutting with an electrostrictive vibrating drive. The source of ultrasonic vibrations is an electrostrictive vibratory drive, which provides oscillations in the range of 10 - 20 kHz with amplitude of 10 - 15 microns. Experimental studies have confirmed the effectiveness of the proposed design of the toolholder to transmit the wave of ultrasonic vibrations almost perpendicular to the axis of the vibratory drive, which allows you to unload the vibrating drive from the cutting force and use vibration pulses only to deform elastic elements by the amplitude of ultrasonic vibrations. The device provides conditions for processing of difficult-to-process materials, allows increasing accuracy of processing of details, to reduce roughness of the processed surfaces and to increase productivity of processing.

Multiperiodic magnetoplasmonic gratings fabricated by the pulse force nanolithography

We propose a novel, to the best of our knowledge, technique for magnetoplasmonic nanostructures fabrication based on the pulse force nanolithography method. It allows one to create the high-quality magnetoplasmonic nanostructures that have lower total losses than the gratings made by the electron-beam lithography. The method provides control of the surface plasmon polaritons excitation efficiency by varying the grating parameters such as the scratching depth or the number of scratches in a single period. The quality of the plasmonic gratings was estimated by means of the transverse magneto-optical Kerr effect that is extremely sensitive to the finesse of a plasmonic structure.

Rate-related study on mechanical properties and fracture characteristics in aluminium alloy via electromagnetic ring expansion test

The uniform one-dimensional tension can be easily realized by the electromagnetic ring expansion (EMRE) test at high strain rates of 103-104 s−1, which utilizes strong pulsed electromagnetic force to deform materials. However, the accurate and rapid acquisition of the time-dependent stress, strain and strain rate in EMRE test has been a bottleneck that hinders its wide application. Based on the electromagnetism and the principle of virtual velocity in plastic dynamics, a stress analytical model considering both the electromagnetic and inertial components is established. The whole EMRE process of deformation, strain localization and fracture for 5052 aluminium alloy (AA5052) which is widely used in the automotive and aerospace industries is collected by a measurement system with microsecond time-resolved imaging, and then the true stress-strain-strain rate relationship is calculated based on the above analytical model. In addition, the dynamic mechanical properties of AA5052 under EMRE test are contrastively analyzed with those under the split Hopkinson tension bar (SHTB) and quasi-static tests. The ductility and formability of AA5052 under EMRE are improved due to the inertial and eddy current effects which is demonstrated by fracture characteristics observed using Scanning Electron Microscopy (SEM).

Noise Reduction Design of Steam Control Valve

The internal steam fluid pressure pulse force is the excitation source of control valve. Based on the Lighthill equation and the orifice injection shunt noise reduction theory, the flow noise and air noise calculations of throttling devices are carried out for the eccentric rotary control valve and the cage sleeve control valve, and the design improvements are presented for noise control of the valves. When there is no noise reduction internals, the air noise caused by the steam control valve with a pressure of 4.5MPa in front of the valve is greater than 95dB. The preset orifice plate reduces the pressure in the control valve to 50% of that before the valve, then the small hole Shunt method for noise reduction can be employed. When the two-stage orifice plate is installed and the number of second-stage holes is greater than 100, the air noise of the eccentric rotary steam control valve is lower than 80dB, and the first-stage orifice plate is installed. The air noise of the bored sleeve type steam control valve with preset orifice plate is also lower than 80dB, but it is easier to meet the low noise design requirements of the steam control valve than the improving method used in above sleeve type steam control valve.

КОЛИВАННЯ ІМПУЛЬСНО НАВАНТАЖЕНОГО ОСЦИЛЯТОРА ЗІ СТЕПЕНЕВИМ ПОЗИЦІЙНИМ ТЕРТЯМ

Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the amplitude of oscillations, but also an increase in the durations of half-cycles, which is characteristic of nonlinear systems with a rigid force characteristic. Approximate displacement calculations use Pade-type approximations for periodic Ateb-functions. The error of these approximations is less than one percent. From the obtained analytical relations, as separate cases, the known dependences covered in the theory of oscillations for linear positional friction follow. It is shown that even in the case of nonlinear positional friction the process of oscillations caused by an instantaneous momentum has many oscillations and is not limited in time. In the case of power positional friction, the oscillation ranges of the pulse-loaded oscillator can be calculated by elementary formulas. The calculation of displacements in time is associated with the use of periodic Ateb-functions, the values of which are not difficult to determine by known asymptotic formulas. Calculations confirm that the obtained approximate formula does not give large errors. In order to verify the adequacy of the obtained analytical solutions, numerical computer integration of the original nonlinear differential equation of motion was performed. The results of the calculation, which lead to analytical and numerical solutions of the Cauchy problem, are well matched.