Impact tests. Impact phenomenon Displacement of points upon impact

An attempt to analyze the injury risk of blows to the head with a bare fist, compared with blows in a boxing glove.

Impact theory.

A blow in mechanics is a short-term interaction of bodies, as a result of which their speeds change. The impact force depends, according to Newton's law, on the effective mass of the impacting body and its acceleration:

Rice. 1 Curve of impact force development in time

F = m*a (1),

where
F - strength,
m is the mass,
a - acceleration.

If we consider the impact in time, then the interaction lasts a very short time - from ten thousandths (instantaneous quasi-elastic impacts) to tenths of a second (inelastic impacts). The impact force at the beginning of the impact quickly increases to its maximum value, and then drops to zero (Fig. 1). Its maximum value can be very large. However, the main measure of shock interaction is not the force, but the shock impulse numerically equal to the area under the F(t) curve. It can be calculated as an integral:

(2)

where
S - shock impulse,
t1 and t2 are the start and end times of the impact,
F(t) is the dependence of impact force F on time t.

Since the collision process lasts a very short time, in our case it can be considered as an instantaneous change in the velocities of the colliding bodies.

In the process of impact, as in any natural phenomena, the law of conservation of energy must be observed. Therefore, it is natural to write the following equation:

E1 + E2 = E'1 + E'2 + E1p + E2p (3)

where
E1 and E2 are the kinetic energies of the first and second body before the impact,
E'1 and E'2 - kinetic energies after impact,
E1p and E2p are the energies of losses during impact in the first and second bodies e.

The relation between the kinetic energy after the impact and the energy of losses is one of the main problems in the theory of impact.

The sequence of mechanical phenomena upon impact is such that first the deformation of the bodies occurs, during which the kinetic energy of motion is converted into the potential energy of elastic deformation. Potential energy is then converted back into kinetic energy. Depending on what part of the potential energy goes into kinetic energy, and what part is lost, being dissipated by heating and deformation, three types of impact are distinguished:

Absolutely elastic impact All mechanical energy is conserved. This is an idealized collision model, however, in some cases, for example, in the case of billiard ball impacts, the impact pattern is close to a perfectly elastic impact.
Absolutely inelastic impact– the deformation energy is completely converted into heat. Example: landing in jumps and dismounts, hitting a plasticine ball against a wall, etc. With an absolutely inelastic impact, the velocities of the interacting bodies after the impact are equal (the bodies stick together).
Partially inelastic impact- part of the elastic deformation energy is converted into the kinetic energy of motion.

In reality, all impacts are either absolutely or partially inelastic. Newton proposed to characterize an inelastic impact by the so-called recovery factor. It is equal to the ratio of the velocities of the interacting bodies after and before the impact. The smaller this coefficient, the more energy is spent on non-kinetic components E1p and E2p (heating, deformation). Theoretically, this coefficient cannot be obtained, it is determined empirically and can be calculated using the following formula:

where
v1 , v2 are the velocities of the bodies before the impact,
v'1, v'2 - after the impact.

At k = 0, the impact will be absolutely inelastic, and at k = 1, it will be absolutely elastic. The recovery factor depends on the elastic properties of the colliding bodies. For example, it will be different when a tennis ball hits different grounds and rackets of different types and qualities. The recovery coefficient is not just a characteristic of the material, since it also depends on the speed of impact interaction - it decreases with increasing speed. The handbooks give values for the recovery factor for some materials for impact velocities of less than 3 m/s.

Biomechanics of impact actions

Percussion in biomechanics are called actions, the result of which is achieved by mechanical impact. In percussion actions, there are:

backswing- a movement that precedes the impact movement and leads to an increase in the distance between the impact link of the body and the object on which the impact is applied. This phase is the most variable.
shock movement- from the end of the swing to the start of the strike.
Impact interaction (or actual impact)- collision of colliding bodies.
Post-impact movement- the movement of the impact link of the body after the termination of contact with the object on which the impact is applied.

With a mechanical impact, the speed of a body (for example, a ball) after the impact is the higher, the greater the speed of the striking link immediately before the impact. With strikes in sports, such a dependence is not necessary. For example, when serving in tennis, an increase in the speed of the racket can lead to a decrease in the speed of the ball, since the impact mass during strokes performed by the athlete is not constant: it depends on the coordination of his movements. If, for example, a strike is performed by bending the wrist or with a relaxed hand, then only the mass of the racket and hand will interact with the ball. If, at the moment of impact, the striking link is fixed by the activity of the antagonist muscles and represents, as it were, a single solid body, then the mass of this entire link will take part in the impact interaction.

Sometimes an athlete throws two shots at the same speed, but the speed of the ball or the force of the blow is different. This is due to the fact that the impact mass is not the same. The value of the impact mass can be used as a criterion for the effectiveness of the impact technique. Since it is quite difficult to calculate the impact mass, the effectiveness of the impact interaction is estimated as the ratio of the projectile speed after impact and the speed of the impact element before impact. This indicator is different in different types of strikes. For example, in football it varies from 1.20 to 1.65. It also depends on the weight of the athlete.

Some athletes who have a very strong blow (in boxing, volleyball, football, etc.) do not differ in great muscle strength. But they are able to communicate a high speed to the striking segment and, at the moment of impact, interact with the struck body with a large impact mass.

Many striking sports actions cannot be considered as a "pure" strike, the basis of the theory of which is outlined above. In the theory of impact in mechanics, it is assumed that the impact occurs so quickly and the impact forces are so large that all other forces can be neglected. In many striking actions in sports, these assumptions are not justified. The impact time in them, although short, still cannot be neglected; the path of impact interaction, along which the colliding bodies move together during the impact, can reach 20-30 cm.

Therefore, in sports impact actions, in principle, it is possible to change the amount of movement during the impact due to the action of forces not related to the impact itself. If the impact link during impact is additionally accelerated due to muscle activity, the impact impulse and, accordingly, the projectile's departure speed increase; if it is arbitrarily slowed down, the shock impulse and take-off speed are reduced (this is sometimes necessary for accurate shortened shots, for example, when passing the ball to a partner). Some hitting moves, in which the additional momentum gain during the hitting is very large, are generally something between throwing and hitting (this is sometimes done in second pass in volleyball).

Coordination of movements with the most powerful blows is subject to two requirements:

communication of the highest speed to the striking link by the moment of contact with the struck body. In this phase of movement, the same methods of increasing speed are used as in other moving actions;
increase in impact mass at the moment of impact. This is achieved by "fixing" the individual links of the striking segment by simultaneously turning on the antagonist muscles and increasing the radius of rotation. For example, in boxing and karate, the force of a blow with the right hand is approximately doubled if the axis of rotation passes near the left shoulder joint, compared with blows in which the axis of rotation coincides with the central longitudinal axis of the body.

The impact time is so short that it is already impossible to correct the mistakes made. Therefore, the accuracy of the strike is decisively ensured by the correct actions during the swing and the striking movement. For example, in football, the position of the supporting leg determines the target accuracy for beginners by about 60-80%.

The tactics of sports competitions often require strikes that are unexpected for the enemy (“hidden”). This is achieved by performing strikes without preparation (sometimes even without a swing), after deceptive movements (feints), etc. The biomechanical characteristics of the strikes change, since they are usually performed in such cases due to the action of only distal segments (wrist strikes).

Distal - [ex. end, phalanx] (distalis) - the end of the muscle or bone of the limb or the whole structure (phalanx, muscle) most distant from the body.

Punch with and without a boxing glove.

Recently, in some sports circles, serious debate has flared up about the greater trauma to the brain of punches with a boxing glove than punches with a bare hand. Let's try to get an answer to this question using the available research data and the elementary laws of physics.

Where could such thoughts come from? I dare to suggest that mainly from observations of the process of hitting a boxing bag. Studies have been conducted in which Smith and Hemil, in their work published in 1986, measured the speed of an athlete's fist and the speed of a punching bag. Strictly speaking, the danger of a concussion is determined by the amount of acceleration of the head, and not by speed. However, according to the reported speed of the bag, one can only indirectly judge the magnitude of the acceleration, since it is assumed that this speed was developed in a short period of impact time.

The bag was hit in three different ways: with a bare fist, with a karate glove, and with a boxing glove. Indeed, the speed of the bag when hit with a glove was about 15% higher than when hit with a fist. Consider the physical background of the study. As mentioned above, all impacts are partially inelastic and part of the energy of the impact link is spent on the residual deformation of the projectile, the rest of the energy is spent on imparting kinetic energy to the projectile. The share of this energy is characterized by the recovery factor.

Let us make a reservation right away for greater clarity that when considering the strain energy and the energy of translational motion, a large strain energy plays a positive role, because less energy is left for forward movement. In this case, we are talking about elastic deformations that do not pose a health hazard, while the energy of translational motion is directly related to acceleration and is dangerous for the brain.

Calculate the recovery factor of the boxing bag according to the data obtained by Smith and Hemil. The mass of the bag was 33 kg. The experimental results showed insignificant differences in fist speed for different types of gloves (bare fist: 11.03±1.96 m/s, in karate glove: 11.89±2.10 m/s, in boxing glove: 11.57±3.43 m/s). The average fist velocity was 11.5 m/s. Differences in bag momentum were found for different types of gloves. A punch with a boxing glove caused more bag momentum (53.73±15.35 Ns) than a punch with a bare fist (46.4±17.40 Ns) or with a karate glove (42.0±18.7 Ns), which had almost equal values. To determine the speed of the bag from its momentum, you need to divide the momentum of the bag by its mass:

v = p/m (5)

where
v is the speed of the bag,
p is the momentum of the bag,
m is the mass of the bag.

Using the formula for calculating the recovery factor (4) and assuming that the speed of the fist after the impact is zero, we obtain a value for a bare fist strike of about 0.12, i.e. k = 12%. For the case of a punch with a boxing glove, k = 14%. This confirms our life experience - a blow to a boxing bag is almost completely inelastic and almost all the impact energy is spent on its deformation.

It should be noted separately that the fist in a karate glove had the highest speed. The momentum of the bag when hit with a karate glove was the smallest. Bare fist strikes in this study were in the middle. This can be explained by the fact that the athletes were afraid to hurt their hand and reflexively reduced the speed and force of the blow. When hit in a karate glove, such fear did not arise.

What happens if you get hit in the head? Let us turn to another 2005 study by Valilko, Viano and Beer, which investigated boxing punches with gloves on a specially designed dummy (Fig. 2). In this work, all impact parameters and impact on the head and neck of the dummy were studied in detail. The neck of the dummy was an elastic metal spring, so this model can be considered as a model of a boxer ready to hit with tense neck muscles. Let's use the forward motion data of the dummy's head and calculate the recovery factor (k) for a direct blow to the head.

Rice. 2 Study of Valilko, Viano and Bira - a boxer strikes a dummy.

The average hand speed before impact was 9.14 m/s, and the average head speed after impact was 2.97 m/s. Thus, according to the same formula (4), the recovery factor k = 32%. This means that 32% of the energy went into the kinetic movement of the head, and 68% went into the deformation of the neck and glove. Speaking about the neck deformation energy, we are not talking about the geometric deformation (curvature) of the cervical region, but about the energy that the neck muscles (in this case, the spring) expended to keep the head stationary. In fact, this is the energy of resistance to impact. The deformation of the mannequin's face, as well as the human facial skull, is out of the question. Human bones are very strong material. In table. 1 shows the coefficient of elasticity (Young's modulus) of several materials. The larger this coefficient, the stiffer the material. The table shows that in terms of rigidity, bone is slightly inferior to concrete.

Table 1. Coefficients of elasticity (Young's moduli) of different materials.

What will be the recovery factor for a blow to the head with a bare fist? There are no studies on this. But let's try to figure out the possible consequences. When punching, as well as when hitting with a glove, most of the energy will be taken by the muscles of the neck, provided, of course, that they are tense. In the work of Valilko, Viano and Beer, it is impossible to separate the deformation energy of the glove from the deformation energy of the dummy's neck, but it can be assumed that the lion's share of the total deformation energy has gone into neck deformation. Therefore, it can be assumed that when hitting with a bare fist, the difference in the recovery coefficient will not exceed 2-5% compared to hitting with a glove, as was the case in the work of Smith and Hemil, where the difference was 2%. Obviously, a difference of 2% is not significant.

The above calculations were made on the basis of data on the rectilinear acceleration of the head after the impact. But for all their relative complexity, they are very far from predicting the traumatism of a blow. The English physicist Holborn, who worked with gel models of the brain in 1943, was one of the first to put forward rotational acceleration of the head as the main parameter of brain injury. Ommai et al. reported that a rotational acceleration of 4500 rad/s2 results in concussion and severe axonal injury. Earlier work by the same author states that rotational acceleration above 1800 rad/s2 creates a 50% chance of concussion. The article by Valilko, Viano and Bira gives the parameters of 18 different strikes. If we take the same boxer and his punch with a hand speed of 9.5 m / s and a punch with a speed of 6.7 m / s, then in the first case the recovery coefficient is 32%, and in the second it is already 49%. According to all our calculations, it turns out that the second impact is more traumatic: a higher recovery factor (more energy was spent in the forward movement of the head), a large effective mass (2.1 kg and 4.4 kg), a slightly higher acceleration of the head (67 g and 68 g ). However, if we compare the rotational acceleration of the head produced by these two impacts, we will see that the first impact is more traumatic (7723 rad/s2 and 5209 rad/s2, respectively). Moreover, the difference in numbers is quite significant. This fact indicates that the traumatism of a blow depends on a large number of variables and one cannot be guided only by the impulse p = mv when assessing the effectiveness of a blow. Of great importance here is the place of impact, so as to cause the greatest rotation of the head. In connection with the above data, it turns out that the boxing glove factor in injuries and concussions does not play the main role.

Summing up our article, we note the following. Factors influencing brain injury when hitting with and without a boxing glove do not differ significantly and can change either in one direction or the other, depending on the boxer and the type of punch. Much more significant factors influencing the concussion lie outside the considered plane, such as the type and location of the blow to the head, which determine its rotational moment.

At the same time, we should not forget that boxing gloves are designed primarily to protect the soft tissues of the face. Strikes without gloves lead to damage to bones, joints and soft tissues in both the attacker and the attacked athlete. The most common and painful of these is an injury called the "boxer's knuckle".

Boxer's knuckle is a well-known term in sports medicine used to describe a hand injury - damage to the articular capsule of the metacarpophalangeal joint (usually II or III), namely the fibers that hold the tendon of the extensor muscle of the fingers.

The danger of contracting various infections, including hepatitis C or HIV viruses, and a host of other unpleasant consequences, including an unattractive appearance, strongly dismiss the thesis that fighting with bare hands is safer for health.

References:

1. Lamash B.E. Lectures on biomechanics. https://www.dvgu.ru/meteo/book/BioMechan.htm
2. Smith PK, Hamill J. The effect of punching glove type and skill level on momentum transfer. 1986, J. Hum. mov. Stud. vol.12, pp. 153-161.
3. Walilko T.J., Viano D.C. and Bir C.A. Biomechanics of the head for Olympic boxer punches to the face. 2005, Br J Sports Med. vol.39, pp.710-719
4 Holbourn A.H.S. Mechanics of head injury. 1943, Lancet. vol.2, pp.438-441.
5. Ommaya A.K., Goldsmith W., Thibault L. Biomechanics and neuropathology of adult and pediatric head injury. 2002, Br J Neurosurg. vol.16, no.3, pp.220–242.

6. sportmedicine.ru

In mechanics, impact is the mechanical action of material bodies, leading to a finite change in the velocities of their points in an infinitely small 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 smallest period of natural oscillations of the system or its time constant are commensurate or greater than the interaction time.

During impact interaction at the points under consideration, impact accelerations, speed or displacement are determined. Together, such impacts and reactions are called shock processes. Mechanical shocks can be single, multiple and complex. Single and multiple impact processes can affect the apparatus in the longitudinal, transverse and any intermediate directions. Complex impact loads act on an object in two or three mutually perpendicular planes simultaneously. Impact loads on an aircraft can be both non-periodic and 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 there is a complex single shock process, which is a combination of a simple shock pulse with superimposed oscillations.

The main characteristics of the shock process:

laws of change in time of impact acceleration a(t), velocity V(t) and displacement X(t) peak shock acceleration;
duration of shock acceleration front Tf - time interval from the moment of occurrence of shock acceleration to the moment corresponding to its peak value;
the coefficient of superimposed fluctuations of shock acceleration - the ratio of the total sum of the absolute values of increments between adjacent and extreme values of shock acceleration to its doubled 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 motion 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 approximating the dependence of acceleration on time (half-sinusoidal, cosanusoidal, 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 damped natural oscillations in it. The value of overload upon impact, the nature and rate of stress distribution over the structure of the aircraft are determined by the force and duration of the impact, and the nature of the change in acceleration. Impact, acting on the 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 structural elements is determined. A simple impact 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 microdeformations. Since the aircraft design has resonant properties, even a simple impact can cause an oscillatory reaction in its elements, also accompanied by fatigue phenomena.

Mechanical overloads cause deformation and breakage of parts, loosening of joints (welded, threaded and riveted), unscrewing screws and nuts, movement of mechanisms and controls, as a result of which the adjustment and adjustment 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:

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

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

The general task of testing an aircraft for impact loads is to check the ability of an aircraft and all its elements to perform their functions during and after impact, i.e. maintain their 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 approximation of the result of a test impact on an object to the effect of a real impact in natural operating conditions and reproducibility of the impact.

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

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

I - according to the principle of shock impulse 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 - according to the energy source.

In general, the scheme of the shock stand 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 investigated parameters of the object and the law of change of shock overload; primary converters; auxiliary devices for adjusting the modes of operation of the tested object; power supplies necessary for the operation of the tested object and recording equipment.

The simplest stand for impact testing in laboratory conditions is a stand that operates on the principle of dropping a test object fixed on a carriage from a certain height, i.e. using the earth's gravity to disperse. In this case, the shape of the shock pulse is determined by the material and shape of the colliding surfaces. On such stands it is possible to provide acceleration up to 80000 m/s2. On fig. 2.53, a and b shows the fundamentally possible schemes of such stands.

In the first version (Fig. 2.53, a) a special cam 3 with a ratchet tooth is driven by a motor. When the cam reaches the maximum height H, the table 1 with the test object 2 falls on the braking devices 4, which give it a blow. Impact overload depends on the height of the fall H, the stiffness of the braking elements h, 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 variant (Fig. 2.53, b), the stand works according to the drop method.

Test benches using a hydraulic or pneumatic drive to accelerate the carriage are practically independent of the action of gravity. On fig. 2.54 shows two options for impact pneumatic 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 the predetermined pressure is reached, which is controlled by the manometer, the automat 2 releases the container 3, where the test object is placed. When exiting the barrel 4 of the air gun, the container comes into contact with the device 5, which allows you to measure the speed of the container. The air gun is attached to the support posts through shock absorbers b. The given 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 structural diagram of another pneumatic shock stand, (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 you to create the specified gas pressure drops on the piston b, and gas supply systems 7. The brake device is activated immediately after the collision of the carriage and the pad to prevent the carriage from reversing and distorting the shock waveforms. The management of such stands can be automated. They can reproduce a wide range of shock loads.

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

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

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

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

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

4. To reproduce an impact with a relatively large deceleration path, a braking device is used, consisting of a lead, plastically deformable plate located on the rigid base of the stand, and a hard tip of the corresponding profile that is introduced into it (Fig. 2.55, d), fixed on the 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, up to tens of milliseconds.

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

6. A punchable metal plate, fixed along the contour at the base of the installation, in combination with a rigid tip of the platform or container, provides relatively small 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-term overloads with a rise time of up to tens of milliseconds.

8. A braking device with a deformable washer (Fig. 2.55, h) makes it possible to obtain large deceleration paths for an object (up to 200 - 300 mm) with small deformations of the washer.

9. The creation in laboratory conditions of intense shock pulses with large fronts is possible when using a pneumatic brake device (Fig. 2.55, s). The advantages of the pneumatic damper include its reusable action, as well as the possibility of reproducing shock pulses of various shapes, including those with a significant predetermined front.

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

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

Due to the variety of transfer functions of different mechanical systems, the same shock spectrum can be caused by a shock pulse of different shapes. This means that there is no one-to-one correspondence between some acceleration time function and the shock spectrum. Therefore, from a technical point of view, it is more correct to specify specifications for shock tests that contain requirements for the shock spectrum, and not for the time characteristic of acceleration. First of all, this refers to the mechanism of fatigue failure of materials due to the accumulation of loading cycles, which may be different from test to test, although the peak values of acceleration and stress will remain constant.

When modeling shock processes, it is expedient to compose a system of determining parameters according to the identified factors necessary for a fairly complete determination of the desired value, which can sometimes be found only experimentally.

Considering the impact of a massive, freely moving rigid body on a deformable element of a relatively small size (for example, on a brake device of a bench) fixed on a rigid base, it is required 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 the spatial motion of a body, six equations can be compiled, three of which give the law of conservation of momentum, two - the laws of conservation of mass and energy, the sixth is the equation of state. These equations include the following quantities: three velocity components Vx Vy \ Vz> density p, pressure p and entropy. Neglecting dissipative forces and assuming the state of the deformable volume to be isentropic, one can exclude entropy from the number of determining parameters. Since only the motion 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;
the initial impact velocity V0, which is directed along the normal to the surface on which the deformable element is installed;
current time t;
body weight t;
free fall acceleration g;
the modulus of elasticity of materials E, since the stress state of the body upon impact (with the exception of the contact zone) is considered elastic;
characteristic geometric parameter of the body (or deformable element) D.

In accordance with the TS-theorem, eight parameters, three of which have independent dimensions, can be used to compose five independent dimensionless complexes:

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

The parameters to be determined include:

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

Therefore, we can write functional relations:

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

If, upon impact, no residual deformations appear in the sections of the body outside the contact zone, then the deformation will have a local character, and, consequently, the complex R5 = pY^/E can be excluded.

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

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

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

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

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

will be criteria for the similarity of these processes.

When these conditions are met, the numerical values of the functions /b/g./z» L» me- will also be the same at similar moments of time -V CtZoimax-const; ^r= const; Cp = const, which makes it possible 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:

The working parts of the model and the natural object must be geometrically similar.
Dimensionless complexes, composed of defining para meters, must satisfy condition (2.68). Introducing scaling factors.

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

Impact mechanism. In the mechanics of an absolutely rigid body, impact is considered as a jump-like process, the duration of which is infinitely small. During the impact, at the point of contact of the colliding bodies, large, but instantly acting forces arise, leading to a finite change in the momentum. In real systems, finite forces always act during a finite time interval, and the collision of two moving bodies is associated with their deformation near the point of contact and the propagation of a compression wave inside these bodies. The duration of the impact depends on many physical factors: the elastic characteristics of the materials of the colliding bodies, their shape and size, the relative speed of approach, etc.

The change in acceleration with time is commonly called a shock acceleration impulse or a shock impulse, and the law of change in acceleration with time is called the form of a shock impulse. The main parameters of the shock pulse include peak shock acceleration (overload), the duration of the shock acceleration and the shape of the pulse.

There are three main types of product response to shock loads:

* ballistic (quasi-damping) mode of excitation (the period of EI natural oscillations is greater than the duration of the excitation pulse);

* quasi-resonant mode of excitation (the period of EI natural oscillations is approximately equal to the duration of the excitation pulse);

* static mode of excitation (the period of EI natural oscillations is less than the duration of the excitation pulse).

In the ballistic mode, the maximum value of the EM acceleration is always less than the peak acceleration of the impact pulse. Quasi-resonant The quasi-resonant excitation mode is the most rigid in terms of the magnitude of the excited accelerations (m is more than 1). In the static mode of excitation, the response of the ED completely repeats the acting pulse (m=1), the test results do not depend on the shape and duration of the pulse. Tests in the static region are equivalent to tests for the effects of linear acceleration, since it can be seen as a stroke of infinite duration.

Drop tests are carried out in a quasi-resonant mode of excitation. Impact strength is evaluated by the integrity of the design of the power plant (no cracks, chips).

Impact tests are carried out after impact tests under electrical load to verify the ability of the ED to perform its functions under mechanical shock conditions.

In addition to mechanical shock stands, electrodynamic and pneumatic shock stands are used. In electrodynamic stands, a current pulse is passed through the excitation coil of the moving system, the amplitude and duration of which are determined by the parameters of the shock pulse. On pneumatic stands, impact acceleration is obtained when the table collides with a projectile fired from an air gun.

The characteristics of shock stands vary widely: load capacity, load capacity - from 1 to 500 kg, number of beats per minute (adjustable) - from 5 to 120, maximum acceleration - from 200 to 6000 g, duration of blows - from 0.4 to 40 ms.