Lecture 1. Dynamic characteristics of structural elements,

reducible to systems with one degree of freedom

Lecture outline

Damping and its characteristics.

Experimental methods for determining damping characteristics.

Factors influencing the damping properties of materials.

Forced oscillations of a single-mass system.

Behavior of the system in the private region, frequency response and phase response.

1. Damping and its characteristics

The study of structural dynamics is of great importance for understanding and assessing the performance characteristics of any product. Good dynamic performance is the basis for continuous and satisfactory operation. Analysis of the dynamic properties of a structure is necessary to assess its performance characteristics and material fatigue. The most important characteristic of the system is damping. Under resonance conditions, the behavior of the system and the quality factor are determined only by its damping properties. At resonance, the system behaves like a “pure” damper. Damping is any effect that dissipates the energy of the system.

Oscillations of a real system caused by a single disturbance gradually fade. The reason for attenuation, in addition to gas-dynamic resistance, is the forces of inelastic resistance caused by internal friction in the material of the oscillating structure, friction in kinematic pairs and supports, and friction with the external environment. These forces cause dissipation (dissipation) of mechanical energy. The ability of a system to absorb the energy of cyclic deformation is called damping capacity.

The damping capacity determines the attenuation of free vibrations and the limitation of the amplitude of resonant vibrations of the system and its elements, which is one of the main factors in the dynamic strength of vibrating elements and the stable operation of microsystem devices and microdevices.

Inelastic resistance forces are related to velocities v points of the system, and to describe them they use a power law

Where k 1 ,n- experienced regulars.

At n = 1 expression (1) describes the linear resistance.

Due to internal friction during cyclic deformation of materials, a deviation from Hooke’s law is observed, i.e. the relationship between stress and strain is described not by a linear relationship, but by two curves forming a hysteresis loop. This also applies to the connection between the load P onto the system and corresponding movement x (Fig. 1).

Fig.1 . Hysteresis loop

A measure of energy dissipation during oscillations per cycle is the area of ​​the hysteresis loop  W, which is determined only by the displacement amplitude and is described by the dependence

Where - amplitude of movement; k 2 ,n- constant, depending on the material and type of construction.

During longitudinal and bending vibrations, normal stresses  in viscoelastic materials are associated with relative deformation  by the equality

during torsional vibrations, tangential stresses  are represented in the form

Where , G - elasticity and shear moduli; ,  - linear and angular deformations; b- damping coefficient.

Let us consider free vibrations of a single-mass system with linear resistance using the example of the viscoelastic model shown in Fig. 2. Taking into account elastic forces kx and linear viscous resistance, the differential equation of mass motion has the form

Where m- weight; b- damping coefficient in the system; k - rigidity of elastic mass suspension; x- movement.

Fig.2. Model of a viscoelastic body

Let us denote and b/ 2m = n. Here the coefficient n characterizes the reduced damping in the system, it should not be confused with the exponent in equations (1) and (2).

Let us write differential equation (4) in the form

where is the natural circular frequency of the system ( ) ;  - relative damping coefficient ().

The general solution to equation (5), subject to the inequality, can be represented in the form

Where X  - initial amplitude and phase angle, respectively; - circular frequency of damped oscillations; n- reduced damping; t- time.

The oscillation curve is presented in Fig. 3, where the damped nature of the process with a circular frequency is visible.

Fig.3 . Damped oscillation curve

Let us consider successive deviations corresponding to those moments in time when:

Where t 1 - time corresponding to the first largest deviation; T- duration of one oscillatory cycle,

The ratio of two successive peak amplitude values ​​remains constant at all times:

Therefore, for any value i equality is true

Magnitude nT = is called the logarithmic oscillation damping decrement and is used as a characteristic of the damping properties of the oscillatory system.

Regardless of the nature of energy losses for the main characteristic of the damping properties of mechanical systems at a given amplitude a steady oscillations are considered to be relative energy dissipation

where is the irreversibly dissipated energy per oscillation cycle; - amplitude energy of elastic deformation.

From (6) it is clear that the relative energy dissipation is twice the logarithmic decrement.

System quality factor Q is expressed as the ratio of the maximum resonant amplitude of oscillations of the system to its deformation from the action of a static driving force. Magnitude Q–1, its inverse, is called internal friction.

During vibrations in viscoelastic materials, a phase shift is observed between stress and strain by a certain angle  . Voltage can be represented as the sum of two components (Fig. 4), where j- imaginary unit. The component coincides in direction with the deformation and is associated with the elastic energy of the body. The component leads the deformation by 90 and is associated with loss energy. Therefore, the phase shift tangent tg, also called the loss tangent, is often used to characterize the damping properties of a material.

Fig.4. Vector voltage diagram

The indicated damping characteristics are related to each other by the following relationships:

Example. Determine the logarithmic decrement and the change in the natural circular frequency due to damping, if during one oscillatory cycle the amplitude of oscillations of the elastic system is halved.

Using formula (6) we find the logarithmic decrement of oscillations

from where we determine the reduced damping

From this equation we find that the reduced damping is very small in comparison with the natural circular frequency of the system: .

Let us determine the natural circular frequency of damped oscillations

which differs by 0.6% from the frequency of undamped oscillations.

2. Experimental methods for determining damping characteristics

Solving practical problems about vibrations requires reliable information about the characteristics of structural damping, which can only be accurately obtained experimentally.

Free Damped Oscillation Method most often used due to the simplicity of the experiment. The method involves obtaining oscillograms of free damped oscillations of a mechanical system. According to the rate of decrease in amplitude A vibrations determine the relative dissipation of energy

Where X i and - two subsequent amplitudes at the beginning and end, respectively i- th period of oscillation.

When constructing the envelope of damped oscillations X(N) (Fig. 5) the value of the logarithmic decrement strictly corresponds to 0.5 X. For any level of attenuation and any amplitude dependence, the logarithmic decrement is determined by the formula

where is the number of cycles in the area under the tangent drawn to the envelope at the point with the amplitude under consideration.

Fig.5. Determination of decrement from the envelope of damped oscillations

Resonance curve method is based on obtaining an experimental amplitude-frequency characteristic - the amplitude dependence A displacement (deformation) of steady-state oscillations from the frequency  of harmonic excitation (Fig. 6). The damping properties of the system are assessed by the width of the peak or valley.

Fig.6. Amplitude-frequency characteristic of the oscillatory system

For linear systems and the levels of resonant peak  used in practice = 0,5 and  = 0.707 (see Fig. 6), the following expressions are used for the logarithmic oscillation decrement corresponding to the resonant oscillation frequency of the system:

where is the resonant frequency;   is the width of the resonant peak at level  of its height.

3. Factors affecting the damping properties of materials

Technical materials, to a greater or lesser extent, absorb the energy of cyclic deformation, converting it into heat, which is then dissipated. The damping capacity of structural materials is considered as an independent characteristic, determined experimentally taking into account real technological and operational factors. Known structural materials differ in damping capacity quite significantly (by three orders of magnitude). The following are approximate maximum values ​​of the logarithmic vibration decrement for various materials at a stress amplitude equal to one tenth of the yield strength of a given material, at room temperature:

Metal materials

Magnesium alloys 0.13…0.3

Manganese-copper alloys 0.10…0.25

Nickel-titanium alloys 0.10…0.15

Cobalt-nickel alloys 0.06…0.12

Copper-aluminum alloys 0.04…0.1

Chromium steel 0.01…0.04

Carbon steel 0.002…0.01

Aluminum alloys 0.001…0.01

Brass and bronze 0.001…0.003

Titanium alloys 0.005…0.0015

Non-metallic materials

Filled rubber 0.1…0.5

Nylon 0.25…0.45

Fluoroplastic 0.17…0.45

Polypropylene 0.36…0.40

Polyethylene 0.26…0.39

Plexiglas 0.14…0.28

Foam plastic 0.06…0.24

Epoxy resins 0.06…0.18

Textolite 0.04…0.12

Fiberglass 0.02…0.10

Research results indicate that the damping properties of materials depend on many factors: the chemical composition and structure of the material; amplitudes of cyclic deformation (stress) and inhomogeneity of the stress state; temperature and heat treatment; static tension and external magnetic field; preliminary plastic deformation, etc.

A general pattern for most materials is an increase in damping properties with increasing temperature, the amplitude of cyclic stresses and the size of the high-stress zone.

4. Forced oscillations of a single-mass system

We will construct a mathematical model of a single-mass system under kinematic excitation using Newton’s second law. Forced oscillations of mass are described by the equation of motion obtained by summing the forces of inertia, damping, elasticity and excitation (Fig. 2):

Where x- movement of mass relative to the base; - movement of the base.

After the transformation, the equation of motion has the form

where is the reduced damping, ; - natural circular frequency of the SE, - rigidity of the elastic element.

When solving equation (7) it has the form

,

where is the amplitude of damped and forced oscillations; - initial phase of natural damped oscillations and phase angle; - circular frequency of forced oscillations.

Displacements after the damping of natural oscillations of the inertial mass are described by the equation

where  1 is the frequency mismatch coefficient, ; - relative damping coefficient, ; K d - dynamic coefficient; - static displacement of the inertial mass under the influence of inertial force.

Phase angle  is determined by the formula

The last two equations are the amplitude-frequency (AFC) and phase-frequency (PFC) characteristics of the system.

5. Behavior of the system in the private region, frequency response and phase response

The case when the frequency of external influences coincides with the frequency of free oscillations (natural frequency) is called resonance. The most unfavorable for the operation of products are resonant mechanical vibrations. In resonant modes, the amplitude of vibrations of system elements and their overloads increase sharply and dangerous alternating stresses arise in structural parts. In the absence of viscous resistance forces in the case of resonance, the amplitude of forced oscillations, increasing over time, tends to infinity. This is explained by the fact that if vibrations occur with their own frequency, then the inertial forces are balanced by quasi-elastic forces at any vibration amplitudes. Disturbing factors become unbalanced and increase the amplitude of oscillations.

The graphical solution of equation (7) is presented in Fig. 7 in the form of frequency characteristics. The static displacement of the system (at ) is determined only by the rigidity of the elastic element k. At low frequencies the response, determined primarily by stiffness, is in phase with the external excitation.

Fig.7. Amplitude-frequency (a) and phase-frequency (b) characteristics

As the frequency increases, the inherent inertial force of the mass has an increasing influence. At resonance (the frequencies of forced and natural oscillations coincide), the response of the SE is determined by damping, since the components corresponding to the mass and stiffness of the spring are mutually balanced. The compliance of the system increases, and the response of the SE lags behind the excitation by 90 o. At frequencies exceeding the main one, the inherent component of the mass has an effect and the system begins to behave like a pure mass. The compliance of the system decreases and the reaction lags behind the excitation by 180 o.

The invention can be used in the field of mechanical engineering to absorb and reduce shock loads. The damper contains a rod 2 with a cutting device mounted on it, consisting of a support sleeve 5, a cutter head 7 and a sleeve 10 made of plastic material installed between them. At the end 8 of the cutter head 7, in contact with the sleeve 10, there are wedge-shaped teeth 9, and the sleeve 10 is equipped with an annular collar 11. When the damper operates, the teeth 9 of the cutter head 7 cut off the shoulder 11 of the sleeve 10, reducing impact loads acting on the damped object. The technical result consists in increasing the energy intensity of the damper, eliminating its jamming when the damped object is subject to loads directed at an angle, and maintaining the damping capacity of the device under repeated shock loads. 2 salary f-ly, 3 ill.

The invention relates to the field of mechanical engineering and can be used in the design of devices for absorbing and reducing shock loads. A damper is known, containing a cylindrical body and a rod placed in it with friction pads, which are connected to the rod and interact with the inner surface of the body (see a.c. . No. 297518, class F 16 F 11/00, 1969). The disadvantage of this device is the instability of the damping characteristics due to large fluctuations in the friction coefficient depending on the state of the rubbing surfaces (ambient temperature, presence of contamination on surfaces, coating, lubricants, etc.). As a result of the analysis of scientific, technical and patent literature, a well-known device for absorbing the impact energy of a car, containing a cylindrical body and a rod and a cutting device located in it, consisting of a cutter head fixedly fixed, was adopted as a prototype of the claimed device on the rod, and a set of cutting elements interacting with the inner surface of the body (see. French patent No. 2137258, cl. F 16 F 7/00, 1972 - prototype). The disadvantages of this device are also the instability of the damping properties, possible jamming of the cutting elements in the body of the cylindrical body due to the unevenness and uncertainty of the depth of cutting of the cutting elements into the side surface of the body, especially under shock loads acting at an angle on the damped structure, because the knife head of the cutting device is fixedly mounted on the rod. Jamming can lead to loss of damping properties of the device and even breakage of the cutting elements when they cut into the body. This damper has a relatively low energy intensity due to the limited stroke of the cutting elements along the axis of the body and the significant resistance of the body metal (albeit plastic) to the penetration of cutting elements into it. In addition, the known damper reduces loads only during a single impact and cannot reduce repeated loads oscillatory damping nature, which usually occur after the first impact, maximum in amplitude value. The purpose of the proposed device is to obtain more stable damping properties compared to the prototype, increase the energy intensity of the damper and expand the scope of its application (the ability to reduce oscillatory loads and loads acting under angle to the damper axis). To achieve this goal in the proposed device, the process of introducing (plunging) cutting elements into the body material is replaced by cutting a thin-walled collar of a bushing made of a plastic material, for example, an aluminum alloy such as AMts or AD. To do this, a cutting device consisting of a cutter head, a support sleeve and a sleeve made of plastic material installed between them is installed on a rod mounted on the body of the damped structure. At the end of the cutter head, in contact with the bushing made of plastic material, there are wedge-shaped teeth, and on the bushing made of plastic material there is an annular belt or collar. Moreover, the cutter head is installed on the rod coaxially with a sleeve made of plastic material, covering it due to its larger diameter, i.e. is centered along its outer diameter, and, in addition, has the ability to move relative to it in the axial direction. In the initial position, the wedge-shaped teeth of the cutter head rest with their apexes (contact) on the annular collar of the bushing and when the damper operates, i.e. under the action of shock loads, interact with it, namely, they cut grooves in the collar of the bushing and cut it off with their lateral surfaces. Replacing the uncertain process of introducing the cutting elements of the cutter head into the body of the body (prototype) by cutting the collar of the bushing with the teeth of the cutter head (the proposed device) makes it possible to obtain more stable and defined damping properties of the device. The proposed device does not have the possibility of jamming, because even under the action of loads directed at an angle to the damper axis, the cylindrical body of the cutter head will move along the side surface of the bushing under the action of the axial component of the load. The choice of a bushing material with certain mechanical (plastic) properties and the thickness of its bead (and therefore the area of ​​cut of the bead) make it possible to unambiguously determine the impact force leading to complete or partial cutting of the annular bead, and by varying the height and angle at the apex of the wedge-shaped teeth cutting the bead, it is possible to ensure the necessary stroke of the damper to absorb impact energy, thereby ensuring its necessary energy intensity. Making grooves in the collar of the bushing and pre-installing the tops of the wedge-shaped teeth in these grooves improves the characteristics of the damper, because in this case, the tops of the teeth do not cut through the original grooves (in this case, unwanted bending and creasing of the collar may occur), but immediately begin to cut off the bushing collar with their side surfaces (a “clean” cut occurs). The presence of a compression spring in the proposed device, installed on the rod between the body damped structure and a washer for the rod fastening nut, ensures the installation (return) of the rod with the support to its original position after the first impact on the support. This makes it possible to reduce not only single shock loads, but also possible repeated loads. Figure 1 shows a general view of the damper in its original state. A variant of the device is shown with pre-made grooves in the bushing shoulder and with the tops of the cutter head teeth installed in them. Figure 2 shows a general view of the damper after activation when the bushing shoulder is partially cut (such a cut of the shoulder is possible after the first impact). Figure 3 shows a general view damper after activation when the bushing shoulder is completely cut off (after subsequent repeated impacts). The damper is installed on the body 1 of the shock-absorbing structure and secured to it through the rod 2 with a nut 3 and washer 4. One end of the rod 2 is fixed to the body 1, a support is installed at the other end of the rod 6, which absorbs shock loads acting on the structure. The cutting device of the damper consists of a support sleeve 5, a cutter head 7, at the end 8 of which wedge-shaped teeth 9 are made, and a sleeve 10 made of plastic material, equipped with an annular collar 11. Support sleeve 5, cutter head 7 and the sleeve 10 are installed on the rod 2, and the sleeve 10 is placed between the cutter head 7 and the support sleeve 5. In this case, the inner diameter of the cutter head 7 is made larger than the outer diameter of the sleeve 10, the body of the cutter head 7 covers the body of the sleeve 10, thereby being centered along the outer diameter of the sleeve 10 to ensure uniform cutting of the bead 11 and to ensure free movement of the cutter head 7 relative to (along) the sleeve 10 when the damper is activated. The contact of the cutter head 7 and the sleeve 10 is carried out in such a way that the wedge-shaped teeth 9, made at the end 8 of the cutter head 7, with their vertices 12 are installed on the shoulder 11 and come into contact with it. The support sleeve 5 serves as a support for the sleeve 10, the diameter of the sleeve 5 must be made no larger than the diameter of the sleeve 10 to ensure that its flange 11 is cut by the teeth 9 of the cutter head 7 and the free movement of the teeth 9 of the cutter head 7 along the sleeve 10 when the damper is activated. To improve the characteristics of the damper in On the shoulder 11 of the bushing 10, grooves 13 are pre-made into which the tops 12 of the teeth 9 of the cutter head 7 are installed. In this case, the number of teeth on the end 8 of the cutter head 7 is equal to the number of grooves 13 of the shoulder 11 of the bushing 10. In this case, when the damper is activated, the cut of the shoulder 11 of the bushing 10 occurs directly on the side surfaces 14 of teeth 9. The compression spring 15, covering the support sleeve 5, the cutter head 7 and the sleeve 10 made of plastic material (cutting device) and installed on the rod 2 between the body 1 of the shock-absorbing structure and the washer 4 of the nut 5, ensures the installation of the rod 2 , washers 4, nuts 3 and supports 6 to their original position after the initial impact for subsequent damping of possible repeated impacts. The damper works as follows. When the support 6 hits an obstacle, the shock loads on the body 1 of the shock-absorbing structure are transmitted through the damper, namely through the support 6, nut 3, washer 4, rod 2. Under the action of the axial component of the shock load, the cutter head 7 with rod 2 moves along the sleeve 10. At the same time, its teeth 9 with their vertices 12 cut grooves in the shoulder 11 of the sleeve 10 and with their lateral surfaces 14, upon subsequent movement along the sleeve 10, cut off its shoulder 11 (see figures 2 and 3) due to their wedge-shaped shape (width of the teeth increases with the change in the height of the teeth from their top to the base). The cutting of the sections of the shoulder between the teeth can be partial or complete, depending on the impact force and the geometric parameters of the shoulder 11 and the mechanical properties of the material of the sleeve 10. In the case of preliminary making of grooves 13 in the shoulder 11 of the sleeve 10 and installation of the peaks 12 of the teeth 9 of the cutter head 7 in them ( see figure 1), when the damper is activated, the cut of the collar 11 will occur directly by the side surfaces 14 of the teeth 9. The cut of the bushing collar by the teeth of the cutter head will occur not only after the first impact of the maximum value, but also with subsequent impacts of a smaller value due to installation (return) rod 2, washer 4, nut 3 and support 6 into the initial position by spring 15, which is compressed under the action of shock loads (movement of the cutter head 7 relative to the sleeve 10); after the end of the impact loads, spring 15 is decompressed. In this case, the cutter head 7 partially cuts off the collar 11 of the bushing 10 after the first impact (see figure 2) and with subsequent impacts continues to further cut off the collar (see figure 3). Thus, the shock load acting on the body 1 of the structure is reduced due to forces of plastic cutting of sections of the bushing flange by the teeth of the cutter head. The claimed device, in comparison with the technical solution adopted as a prototype, makes it possible to effectively reduce both axial loads and loads directed at an angle to the damper axis, as well as shock loads of a repeated nature, eliminating the possibility jamming of the cutting elements (there is no cutting of the teeth into the material of the bushing body, there is only a cut of its shoulder). At the same time, the energy intensity of the damper increases and the stability of its damping properties improves. Calculations carried out by the authors, as well as full-scale tests of the device as part of standard products and bench tests as part of development products showed the significant effectiveness of the proposed technical solution for damping shock loads.

Claim

1. A damper containing a housing, a rod and a cutting device placed on it, interacting with the inner surface of the housing, characterized in that the cutting device is made in the form of a knife head with wedge-shaped teeth, a support sleeve and a sleeve made of plastic material installed between them, equipped with an annular collar , wherein the cutter head is centered along the outer diameter of the sleeve with the collar with the ability to move relative to it, and the wedge-shaped teeth of the cutter head interact with the collar of the sleeve with their vertices.2. The damper according to claim 1, characterized in that the annular collar of the bushing has grooves in which the tops of the wedge-shaped teeth of the cutter head are installed, while the teeth interact with the collar of the bushing with their lateral surfaces.3. Damper according to claims 1 and 2, characterized in that a spring is installed on the rod, covering the cutting device.

In mechanics, an impact is a mechanical action of material bodies, leading to a finite change in the velocities of their points in an infinitesimal period of time. Impact motion is a motion that occurs as a result of a single interaction of a body (medium) with the system under consideration, provided that the shortest period of natural oscillations of the system or its time constant is commensurate with or greater than the interaction time.

During impact interaction, shock accelerations, speed or displacement are determined at the points under consideration. Collectively, such impacts and reactions are called impact processes. Mechanical shocks can be single, multiple or complex. Single and multiple impact processes can affect the apparatus in the longitudinal, transverse and any intermediate directions. Complex shock loads impact an object in two or three mutually perpendicular planes simultaneously. Shock loads on an aircraft can be either non-periodic or periodic. The occurrence of shock loads is associated with a sharp change in the acceleration, speed or direction of movement of the aircraft. Most often, in real conditions, a complex single shock process occurs, which is a combination of a simple shock pulse with superimposed oscillations.

Main characteristics of the impact process:

• laws of change in time of impact acceleration a(t), speed V(t) and displacement X(t) \ duration of impact acceleration t - time interval from the moment of appearance to the moment of disappearance of shock acceleration, satisfying the condition a> an, where an - peak impact acceleration;
• duration of the front of shock acceleration Tf - the time interval from the moment of appearance of shock acceleration to the moment corresponding to its peak value;
• coefficient of superimposed oscillations of shock acceleration - the ratio of the total sum of the absolute values ​​of the increments between adjacent and extreme values ​​of shock acceleration to its double peak value;
• impact acceleration impulse - the integral of impact acceleration over a time equal to the duration of its action.

According to the shape of the curve of the functional dependence of movement parameters, shock processes are divided into simple and complex. Simple processes do not contain high-frequency components, and their characteristics are approximated by simple analytical functions. The name of the function is determined by the shape of the curve that approximates the dependence of acceleration on time (half-sine, cosaneusoidal, rectangular, triangular, sawtooth, trapezoidal, etc.).

A mechanical shock is characterized by a rapid release of energy, resulting in local elastic or plastic deformations, excitation of stress waves and other effects, sometimes leading to malfunction and destruction of the aircraft structure. The shock load applied to the aircraft excites rapidly damping natural vibrations in it. The value of overload during impact, the nature and speed of stress distribution throughout the aircraft structure are determined by the force and duration of the impact, and the nature of the change in acceleration. An impact affecting an aircraft can cause its mechanical destruction. Depending on the duration, complexity of the impact process and its maximum acceleration during testing, the degree of rigidity of the aircraft’s structural elements is determined. A simple blow can cause destruction due to the occurrence of strong, albeit short-term, overstresses in the material. A complex impact can lead to the accumulation of fatigue microstrains. Since the aircraft structure has resonant properties, even a simple blow can cause an oscillatory reaction in its elements, also accompanied by fatigue phenomena.

Mechanical overloads cause deformation and breakage of parts, loosening of connections (welded, threaded and rivet), unscrewing of screws and nuts, movement of mechanisms and controls, as a result of which the adjustment and configuration of devices changes and other malfunctions appear.

The fight against the harmful effects of mechanical overloads is carried out in various ways: increasing the strength of the structure, using parts and elements with increased mechanical strength, using shock absorbers and special packaging, and rational placement of devices. Measures to protect against the harmful effects of mechanical overloads are divided into two groups:

1. measures aimed at ensuring the required mechanical strength and rigidity of the structure;
2. measures aimed at isolating structural elements from mechanical influences.

In the latter case, various shock-absorbing agents, insulating gaskets, compensators and dampers are used.

The general objective of testing an aircraft for impact loads is to check the ability of the aircraft and all its elements to perform their functions during and after impact, i.e. maintain its technical parameters during impact and after it within the limits specified in the regulatory and technical documents.

The main requirements for impact tests in laboratory conditions are the maximum proximity of the result of a test impact on an object to the effect of a real impact under natural operating conditions and the reproducibility of the impact.

When reproducing shock loading modes in laboratory conditions, restrictions are imposed on the shape of the instantaneous acceleration pulse as a function of time (Fig. 2.50), as well as on the permissible limits of deviations of the pulse shape. Almost every shock pulse on a laboratory bench is accompanied by pulsation, which is a consequence of resonance phenomena in shock installations and auxiliary equipment. Since the spectrum of the shock pulse is mainly a characteristic of the destructive effect of the impact, even a small pulsation superimposed can make the measurement results unreliable.

Test facilities that simulate individual impacts followed by vibrations constitute a special class of mechanical testing equipment. Impact stands can be classified according to various criteria (Fig. 2.5!):

I - based on the principle of shock pulse formation;

II - by the nature of the tests;

III - according to the type of reproducible shock loading;

IV - according to the principle of action;

V - by energy source.

In general, the shock test bench diagram consists of the following elements (Fig. 2.52): the test object mounted on a platform or container together with a shock overload sensor; acceleration means for communicating the required speed to the object; braking device; control systems; recording equipment for recording the studied parameters of the object and the law of change in shock overload; primary converters; auxiliary devices for adjusting the operating modes of the tested object; power sources necessary for the operation of the test object and recording equipment.

The simplest stand for impact testing in laboratory conditions is a stand that operates on the principle of dropping the test object attached to a carriage from a certain height, i.e. using gravity to accelerate. In this case, the shape of the shock pulse is determined by the material and shape of the colliding surfaces. At such stands it is possible to provide acceleration up to 80,000 m/s2. In Fig. 2.53, a and b show fundamentally possible diagrams of such stands.

In the first option (Fig. 2.53, a) a special cam 3 with a ratcheting tooth is driven by a motor. When the cam reaches the maximum height H, the table 1 with the test object 2 falls onto the braking devices 4, which give it a blow. The impact overload depends on the height of the fall H, the rigidity of the braking elements k, the total mass of the table and the test object M and is determined by the following relationship:

By varying this value, you can get different overloads. In the second option (Fig. 2.53, b) the stand operates using the drop method.

Test stands that use a hydraulic or pneumatic drive to accelerate the carriage are practically independent of gravity. In Fig. Figure 2.54 shows two options for pneumatic impact stands.

The principle of operation of the stand with an air gun (Fig. 2.54, a) is as follows. Compressed gas is supplied to the working chamber /. When a given pressure is reached, which is controlled by a pressure gauge, the automatic release device 2 of the container 3, where the test object is located, is activated. When leaving the barrel 4 of the air gun, the container contacts the device 5, which allows you to measure the speed of movement of the container. The air gun is attached to the support posts through shock absorbers b. The specified braking law on the shock absorber 7 is implemented by changing the hydraulic resistance of the flowing fluid 9 in the gap between the specially profiled needle 8 and the hole in the shock absorber 7.

The design diagram of another pneumatic shock test bench (Fig. 2.54, b) consists of a test object 1, a carriage 2 on which the test object is installed, a gasket 3 and a brake device 4, valves 5 that allow the creation of specified gas pressure differences on piston b, and gas supply system 7. The braking device is activated immediately after the collision of the carriage and the spacer to prevent the carriage from reversing and distorting the shape of the shock pulse. The management of such stands can be automated. They can reproduce a wide range of shock loads.

Rubber shock absorbers, springs, and, in some cases, linear asynchronous motors can be used as an accelerating device.

The capabilities of almost all impact stands are determined by the design of the braking devices:

1. The impact of the test object with a rigid plate is characterized by braking due to the occurrence of elastic forces in the contact zone. This method of braking the test object allows one to obtain large values ​​of overloads with a small front of their increase (Fig. 2.55, a).

2. To obtain overloads in a wide range, from tens to tens of thousands of units, with a rise time from tens of microseconds to several milliseconds, deformable elements in the form of a plate or spacer lying on a rigid base are used. The materials of these gaskets can be steel, brass, copper, lead, rubber, etc. (Fig. 2.55, b).

3. To ensure any specific (specified) law of change in n and m in a small range, deformable elements are used in the form of a tip (crasher), which is installed between the impact bench plate and the test object (Fig. 2.55, c).

4. To reproduce an impact with a relatively long braking distance, a braking device is used, consisting of a lead, plastically deformable plate located on a rigid base of the stand, and a rigid tip of the corresponding profile embedded into it (Fig. 2.55, d), fixed to an object or platform of the stand . Such braking devices make it possible to obtain overloads in a wide range of n(t) with a short rise time, reaching tens of milliseconds.

5. An elastic element in the form of a spring (Fig. 2.55, d) installed on the moving part of the impact stand can be used as a braking device. This type of braking provides relatively small overloads of a half-sinusoidal shape with a duration measured in milliseconds.

6. A punchable metal plate, fixed along the contour at the base of the installation, in combination with the rigid tip of the platform or container, ensures relatively low overloads (Fig. 2.55, e).

7. Deformable elements installed on the movable platform of the stand (Fig. 2.55, g), in combination with a rigid conical catcher, provide long-acting overloads with a rise time of up to tens of milliseconds.

8. A braking device with a deformable washer (Fig. 2.55, h) allows you to obtain large braking distances for an object (up to 200 - 300 mm) with small deformations of the washer.

9. Creating intense shock pulses with large fronts in laboratory conditions is possible using a pneumatic braking device (Fig. 2.55, s). The advantages of a pneumatic damper include its reusable action, as well as the ability to reproduce shock pulses of various shapes, including those with a significant specified front.

10. In the practice of conducting impact tests, a braking device in the form of a hydraulic shock absorber has been widely used (see Fig. 2.54, a). When the test object hits the shock absorber, its rod is immersed in liquid. The liquid is pushed out through the rod point according to the law determined by the profile of the control needle. By changing the needle profile, it is possible to implement different types of braking laws. The needle profile can be obtained by calculation, but it is too difficult to take into account, for example, the presence of air in the piston cavity, frictional forces in sealing devices, etc. Therefore, the calculated profile must be experimentally corrected. Thus, using the computational and experimental method, it is possible to obtain the profile necessary for the implementation of any braking law.

Carrying out impact tests in laboratory conditions also puts forward a number of special requirements for the installation of the facility. For example, the maximum permissible movement in the transverse direction should not exceed 30% of the nominal value; both when testing for impact resistance and when testing for impact strength, the product must be able to be installed in three mutually perpendicular positions with the reproduction of the required number of shock pulses. The one-time characteristics of the measuring and recording equipment must be identical over a wide range of frequencies, which guarantees the correct registration of the ratios of the various frequency components of the measured pulse.

Due to the diversity of transfer functions of different mechanical systems, the same shock spectrum can be produced by a different shock pulse shape. This means that there is no one-to-one correspondence between a certain time function of acceleration and the shock spectrum. Therefore, from a technical point of view, it is more correct to set specifications for impact tests that contain requirements for the shock spectrum, rather than for the time characteristic of acceleration. This primarily relates to the mechanism of fatigue failure of materials due to the accumulation of loading cycles, which may vary from test to test, although the peak values ​​of acceleration and stress will remain constant.

When modeling impact processes, it is advisable to compile systems of defining parameters based on the identified factors necessary for a fairly complete determination of the desired value, which sometimes can only be found experimentally.

Considering the impact of a massive, freely moving rigid body on a deformable element of a relatively small size (for example, on a braking device of a stand) fixed on a rigid base, it is necessary to determine the parameters of the impact process and establish the conditions under which such processes will be similar to each other. In the general case of spatial motion of a body, six equations can be compiled, three of which are given by the law of conservation of momentum, two by the laws of conservation of mass and energy, and the sixth is the equation of state. These equations include the following quantities: three components of velocity Vx Vy\Vz> density p, Pressure p and entropy. Neglecting dissipative forces and considering the state of the deformed volume to be isentropic, we can exclude entropy from the number of determining parameters. Since only the movement of the center of mass of the body is considered, it is possible not to include the velocity components Vx, Vy among the determining parameters; Vz and coordinates of points L", Y, Z inside the deformable object. The state of the deformable volume will be characterized by the following defining parameters:

• material density p;
• pressure p, which is more expedient to take into account through the value of the maximum local deformation and Otmax, considering it as a generalized parameter of the force characteristic in the contact zone;
• initial impact velocity V0, which is directed normal to the surface on which the deformable element is installed;
• current time t;
• body weight t;
• acceleration of free fall g;
• modulus of elasticity of materials E, since the stressed state of the body upon impact (except for the contact zone) is considered elastic;
• characteristic geometric parameter of the body (or deformable element) D.

In accordance with the TS-theorem, from eight parameters, among which three have independent dimensions, it is possible to compose five independent dimensionless complexes:

Dimensionless complexes, composed of the determined parameters of the impact process, will be some independent functions of the dimensionless complexes P1 - P5.

The parameters to be determined include:

• current local deformation a;
• body speed V;
• contact force P;
• tension inside the body a.

Therefore, we can write the functional relationships:

The type of functions /1, /2, /e, /4 can be established experimentally, taking into account a large number of defining parameters.

If, during an impact, residual deformations do not appear in sections of the body outside the contact zone, then the deformation will have a local character, and, therefore, the complex R5 = pY^/E can be excluded.

The complex Jl2 = Pttjjjax) ~ Cm is called the coefficient of relative body mass.

The coefficient of resistance to plastic deformation Cp is directly related to the strength characteristic indicator N (the compliance coefficient of the material, depending on the shape of the colliding bodies) by the following dependence:

where p is the reduced density of materials in the contact zone; Cm = m/(ra?) is the reduced relative mass of colliding bodies, characterizing the ratio of their reduced mass M to the reduced mass of the deformed volume in the contact zone; xV is a dimensionless parameter characterizing the relative work of deformation.

The function Cp - /3(R1(R1, R3, R4) can be used to determine overloads:

If we ensure equality of the numerical values ​​of the dimensionless complexes IJlt R2, R3, R4 for two impact processes, then these conditions, i.e.

will represent criteria for the similarity of these processes.

If the specified conditions are met, the numerical values ​​of the functions /b/g./z» L» te- at similar moments of time will be the same -V CtZoimax- const; ^r= const; Cp = const, which allows us to determine the parameters of one impact process by simply recalculating the parameters of another process. Necessary and sufficient requirements for physical modeling of impact processes can be formulated as follows:

1. The working parts of the model and the full-scale object must be geometrically similar.
2. Dimensionless complexes composed of defining parametres must satisfy condition (2.68). Introducing scale factors.

It must be borne in mind that when modeling only the parameters of the impact process, the stressed states of bodies (natural and model) will necessarily be different.

The invention relates to the field of shock absorber testing and can be used in the design of impact-protective devices made of composite materials. The purpose of the invention is to obtain characteristics of shock absorbers showing the efficiency of their operation under shock impacts (impact damping efficiency coefficients of shock absorbers associated with structural damping, damping in materials, as well as due to different acoustic stiffness of various shock absorber elements, etc.) Tests are carried out on an installation , the quality factor of which is no less than an order of magnitude higher than the quality factor of the shock absorber. The required coefficient is equal to the product of coefficients associated with various physical properties of the shock absorber. In this case, replacing damping liners with liners made of various materials with pre-known damping properties makes it possible to determine each of the coefficients as a result of analyzing the shock spectra obtained during impact tests. Technical effect - improving the quality of research into the process of operation of shock absorbers under shock impacts. 6 ill.

The proposed technical solution relates to the field of testing shock absorbers made of composite materials to determine their damping properties under impact. The recent use of new materials (metal rubber, carbon fiber plastic, etc.) in protection systems against vibration-impact loads on ships, airplanes, and spacecraft requires a fairly accurate determination of the effectiveness of each shock absorber element. Currently, various methods are known for determining the damping properties of shock absorbers. For example, when studying shock absorbers operating under fairly slowly changing external influences, the method of estimating the absorption coefficient by analyzing the hysteresis loop is used (I.M. Babakov “Theory of Oscillations”, pp. 153-154, M.: Nauka, 1968). However, such tests consider the energy dissipation over a complete vibration cycle. To protect equipment from shock impacts (often explosive in nature), shock absorbers are used, which should primarily reduce the amplitude of the leading edge of the shock wave of deformation. Reducing secondary vibration is usually not a big problem. The most suitable in this case is to analyze the amplitude-frequency characteristics or the total values ​​of the impact before and after the shock absorber. For example (A. Nashif et al. Damping of vibrations, p. 190, M.: Mir, 1988, prototype), the method for constructing the amplitude-frequency characteristic consists of exciting vibrations in the test sample, measuring the exciting force applied at a given point, determining the dynamic response using accelerometers and strain sensors, and then comparing the amplitude-frequency response before and after the shock absorber. The use of a harmonic Fourier analyzer, as well as similar computational techniques, as a rule, is only valid for the case of “aftereffect” (when the impact has already ended and secondary vibration is being studied). In addition, the use of testing installations with a fairly low quality factor (for example, vibration stands) leads to an overestimation of the damping properties of shock absorbers. The method described above also does not allow separating the dispersion of external influences due to various physical properties of shock absorbers (structural damping, reflection from boundaries, etc.). The purpose of this technical solution is to partially eliminate the above-mentioned shortcomings, which will make it possible to more qualitatively study the process of shock absorbers operating under shock impacts. The proposed technical solution differs in that the shock absorber is loaded in an installation whose quality factor is at least an order of magnitude greater than the quality factor of the shock absorber, and tests are carried out sequentially, first obtaining the relationship between forces and deformations in the shock absorber under impact, then determining the acoustic stiffness of the shock absorber at various levels loading, after which tests are carried out with liners of the same design made of different materials with predetermined damping properties, and the impact damping efficiency is assessed by comparing shock acceleration spectra at control points, and the impact damping efficiency coefficient is presented as a product of the coefficients , each of which is determined by analyzing the shock acceleration spectra of tests of the previously mentioned liners. The essence of the proposed technical solution is illustrated by drawings, where in Fig. 1 shows a shock absorber made of metal rubber 7VSh60/15, Fig. Figure 2 shows the relationship between forces and deformations p- (hysteresis loop), Young's modulus (as the tangent of the angle) and the speed of sound in the material, Fig. 3 shows a diagram of the experimental setup; FIG. 4-6 show the total impact damping efficiency coefficient, the coefficient obtained due to structural damping, and the coefficient obtained due to dissipation in metal rubber. Let us consider, as an example, a shock absorber made of metal rubber (Fig. 1) and try to evaluate the damping properties of the shock absorber using the proposed algorithm. When a deformation wave approaches a shock absorber, it is both reflected due to various impact stiffnesses and dissipated in the material (metal rubber of the shock absorber) and due to the structural damping of the shock absorber itself (tightening ratio, clearances, etc.). Let be the total impact damping efficiency factor. i = 1i 2i 3i ,

Where 1i is the coefficient associated with structural damping;

2i - coefficient associated with the values ​​of acoustic rigidity;

3i is a coefficient related to scattering in the material. It is obvious that for the materials used 3i = 1 (except for metal rubber, since the dimensions of the liners are small, and scattering in the material begins to affect only at L>1 m, and even then amounting to 1-2% per 1 m. O.D. Alimov and etc. Impact, propagation of deformation waves in shock systems. M.: Nauka, 1982). The damping efficiency coefficient itself for the shock spectrum is understood as the amplitude-frequency characteristic of the ratio of the shock spectra of accelerations of the VIP before and after the shock absorber:

1 = A B1i /A B2i . Coefficient

Shows the effectiveness of different liners, since 1i = const (the same shock absorber), and for all liners, except metal rubber, 3i = 1, then

Ij = ( 1i 2i 3i)/( 1j 2j 3j) = 2i 3i / 2j . Let us consider a material whose acoustic rigidity is equal to the acoustic rigidity of metal rubber, then

That is, we obtain the shock wave damping coefficient, which characterizes the properties of metal rubber. As is known (L.G. Shaimordanov. Statistical mechanics of deformable fibrous non-woven porous bodies. Krasnoyarsk, 1989), metal rubber is a material with pronounced nonlinear characteristics. In addition, the damping properties of a material may depend on the speed (under impact and explosive influences) and the type of loading. At the same time, the hysteresis loop (its limiting right branch) for a metal rubber shock absorber in the region of limiting deformations does not depend on the loading speed. Thus, knowing the dependence P- (hysteresis loop) and the magnitude of the impact action (in the form of a force impulse), it is possible to obtain the Young’s modulus and, consequently, the speed of sound for any moment in time (Fig. 2). By selecting different magnitudes of impacts and values ​​of acoustic stiffness, it is possible to obtain impact damping efficiency coefficients depending on the strength of the external impact. Obviously, during such tests, the dissipation of external influences should be minimal. There is a well-known formula connecting the quality factor Q and the logarithmic decrement of oscillations: Q = 3.141.../, a = lnA1/A2, where A1 and A2 are the amplitudes of two adjacent oscillations. This shows that even with an increase in the quality factor by an order of magnitude (80-100, for conventional designs approximately 8-10), energy dissipation in the experimental setup can be neglected. Using the concept of the shock spectrum of accelerations to assess the efficiency of shock absorbers under shock impacts allows us to correctly analyze the operation of shock absorbers both at the moment of application of the load and after the end of its action (O.P. Doyar “Algorithm for calculating the shock spectrum” in the collection Dynamics of Systems. Numerical methods for studying dynamic systems. Nistru: Kishenev, 1982, pp. 124-128). An example of the practical implementation of the proposed method. Using the proposed method, damping coefficients were determined for the 7VSh60/15 shock absorber used in the vibration-impact protection belt of one of the spacecraft developed by NPO PM (Fig. 1). The test setup diagram is shown in Fig. 3, where 1 - waveguides, 2 - shock absorber, 3 - ABC-052 accelerometers. 15 bolt explosions were carried out. The force impulse for the bolt was obtained earlier. Dynamic deformations of the shock absorber were recorded using the high-speed photo recording method. The dependence of the density of the material (metal rubber) on the force was taken according to the shock absorber’s passport data. For replacement, liners made of steel, bronze, aluminum, textolite, and fluoroplastic were used. An 8x54 explosive bolt was used as a source of impact. When replacing a metal-rubber liner with a steel liner (material of the body and fastening elements), you can immediately obtain the coefficient associated with structural damping, because other scattering effects are excluded. In fig. 4, 5 show graphs of the total impact damping coefficient and the damping coefficient associated with structural damping, and FIG. Figure 6 shows the coefficient obtained due to shock dissipation in metal rubber. The impact level was 6 kN. The measurement range for amplitude is up to 6000 g, and for frequency up to 10,000 Hz. The total error of measurements and processing did not exceed 9-11%.

CLAIM