RU2706243C1 - Method of selecting sports equipment with due allowance for rheological characteristics of snow road - Google Patents

Abstract

FIELD: sports.

SUBSTANCE: invention relates to the field of sports equipment and can be used for selection of the optimal inventory in such sports as skiing and biathlon. Method for selection of sports equipment, taking into account rheological characteristics of snow route provides for measurement of rheological characteristics of snow route, measurement of tensogeometric and amplitude-frequency characteristics of sports equipment and measurement of amplitude-frequency characteristics of "sports equipment – snow line" system, processing of obtained data and subsequent selection of optimal version, wherein when processing the obtained data, determining the snow trajectory damping coefficient, the ratio of the imposed vibration frequency of the "sports equipment – snow track" system to the natural frequency of the free snow road variations, and if snow drift damping coefficient is less than one, sports equipment is selected with such ratio of imposed oscillation frequency to natural frequency of free oscillations of snow route, which outputs system "sport inventory – snow track" from resonance zone (when ratio is close to one), wherein when the ratio of the imposed oscillation frequency to the natural frequency of the free vibrations of the snow route is less than one, then selecting the sports equipment with a natural frequency higher than the imposed frequency, and if the ratio of the imposed oscillation frequency to natural frequency of free oscillations of the snow route is greater than one, then sports equipment with frequency of natural oscillations is selected less than the imposed frequency.

EFFECT: disclosed is a method of selecting sports equipment based on rheological characteristics of the snow road.

1 cl, 26 dwg

Description

The invention relates to the field of sports equipment and can be used in the selection of equipment in sports such as cross-country skiing, biathlon, ski biathlon.

In all these sports, an important role is played by the forces of interaction of sports equipment with the surface of the track (with the external environment).

The most time-consuming and in many cases difficult to predict is the selection of equipment in skiing, biathlon and other cross-country skiing. This is due to a very large number of factors affecting the slip and a large number of their combinations in real conditions.

Until now, when selecting skis, only friction forces of the sliding surface (ski ointment, paraffin, material of the sliding surface, form of knurling, steelslift, etc.) and sliding resistance due to the shape of the arc of the deflection of the skis under the action of repulsive forces are taken into account.

Static and dynamic coefficients of friction are determined, for example, by Uktus-type instruments (AS USSR 1454488 from 1989 MKI A63C 11/04). Choose the option with the lowest dynamic coefficient for the ridge course or the best combination of static and dynamic coefficients for the classic course of movement. Another option for determining the coefficient of friction is the “mouse” rollback (a tetrahedral block with a pointed end, on each face of which a lubrication option is superimposed). Then measure the length of the roll "mouse" from the slope on each of the faces. The best ski preparation options are determined, and these options are tested by athletes on different terrain terrain. But the obtained results of such measurements are often contradictory and subjective, since a model is subjected to tests, which does not take into account all factors that influence the sliding of sports equipment. On the other hand, the science of tribology has made great strides in the fight against friction. Technologies for preparing the contact surface with the lowest friction coefficients have been developed. The struggle is to reduce the coefficient of friction by hundredths and thousandths of a percent. At the same time, the difference in the slip of two copies of equally prepared sports equipment from even one manufacturer is very significant and reaches several tens of percent. This suggests that in addition to the coefficients of friction, there are other factors affecting the resistance forces to the movement of sports equipment along the track.

Known electronic tracking system and the transmission of several heterogeneous data on the characteristics of the ski sliding in real time (AT502890 2007-06-15 MKI A63C 11/00). With the help of such a system, several indicators of the work of sports equipment and the current state of the athlete can be transmitted in parallel. For example, depending on the purpose of the measurements performed and the sensors used for this, the travel time of the path, the heart rate, repulsive power, or any other necessary parameters are measured. Such equipment makes it possible to use any known sensors to measure the motion parameters.

There is a known (RF Patent No. 2361638, IPC А63С 11/00,) method for selecting sports equipment, which consists in measuring the amplitude-frequency characteristics of the interaction of sports equipment with a track in the range of possible competitive movement speeds, subsequent processing of the data and determining the degree of turbulence of the phenomena that occur when moving equipment along the track, and then selecting sports equipment according to the criterion of the minimum degree of turbulence at competitive speed.

This method of selecting sports equipment allows you to take into account an important factor - the amplitude-frequency characteristic of sports equipment and laminar and turbulent phenomena that occur as a response to movement along a real track.

However, sports equipment when moving along a real track is exposed to many random processes, for example, such as overcoming bumps in the track, various inclusions of high density or vice versa looser sections, etc.

These random processes are not related to the turbulent phenomena themselves, but they affect the instantaneous values of the speed of movement. Therefore, the selection of sports equipment according to the criterion of the degree of turbulence as a ratio of instantaneous and average ripple speeds may not be sufficiently correct in the presence of noise - random processes occurring during the movement of a sports equipment along a real track.

A well-known method of selecting sports equipment (RF patent No. 2422184 IPC А63С 11/00), including measuring its amplitude-frequency characteristics directly while moving along a real route, processing the data and then choosing the best option, and, when processing the data, determine the spectral the ripple power density, and random pulsation and noise sources are identified and suppressed or filtered, and then sports equipment is selected according to the criterion of minimum energy competitive-scale fluctuations in speed.

However, this method does not allow to take into account all the rheological characteristics of the snow track, which can have a significant impact on the amplitude-frequency characteristics of sports equipment. In a real snow track, not only laminar and turbulent phenomena can occur, but also other dissipative phenomena. For example, this can be said about dry friction. In some conditions, dry friction can be a source of vibration. But in other conditions, dry friction leads to the disruption of vibrational energy. This can significantly affect the objectivity of the choice of sports equipment according to the criterion of minimum power density. Thus, experimental studies have proved that rheological phenomena at the contact play a significant role in the occurrence of frictional self-oscillations. (Yu. N. Kosterin. Mechanical self-oscillations during dry friction. M: Publishing House of the USSR Academy of Sciences, 1960. 212 p.))

Most scientists studying the physicomechanical properties of snow note that snow belongs to the category of elastic-viscous-plastic materials (Anfilofiev B.A. Study of the rheological properties of snow cover. / B.A. Anfilofiev, V.K. Lokhin // Proceedings of the Novosibirsk Institute of Railway Engineering (Novosibirsk, 1972. - Issue 141)

So, snow is characterized by its elastic properties when light loads are applied for a fairly short time. Under such conditions, the deformations are small and reversible when the applied stresses are eliminated; the snow structure is not disturbed. Plastic flow requires that a certain threshold voltage value is reached, after which it begins.

The difference between liquids and solids is not sharp and is kinetic (relaxation) in nature. With an increase in the strain rate, elastic stresses do not have time to relax, so the total resistance increases. The strains are additionally characterized by a new parameter equal to the relaxation time to the characteristic process time.

If, for example, the relaxation time is much longer than the voltage, then the body is called solid. If the relaxation time is short compared with the time of the stress, then the body behaves like a liquid.

We show this in the following example. If the time the load exerts on a typical fluid — water — is less than its stress relaxation period, then the flow does not have time to occur, and it behaves like an elastic body. For clarity, we can give an example of a jump from a tower into the water. The force of impact on water can be very large. Water behaves almost like a solid elastic body. But if you enter the water from the shore - the relaxation time is short compared with the time of the stress. Water manifests itself as a liquid.

From these positions, we will consider the interaction of a sports apparatus (ski) and a snow track.

Under the influence of peak pressures of the sliding surface of the ski, the snow track is deformed. Moreover, the deformation occurs cyclically. The sliding surface of the ski in the area with peak pressure overcomes the tensile strength of the snow track, deforms it until the pressure forces and the track reaction are equal. Then, due to the inertia of the longitudinal movement, the ski leaves the formed hole in the snowy track - it floats to the surface of the track until the next moment of overcoming the track's strength and again fails.

This happens, starting from a certain critical speed, at which the track relaxation time is comparable to the duration of the force impulse from the peak pressure of the ski in this section of the snow track.

At slow sliding speeds, when the path relaxation time is much shorter than the time of the force impulse from the ski pressure peaks, the snow track is constantly deformed (crushed) by the leading front of the peak pressures. The cyclic strain is negligible.

At high gliding speeds of the skis, and under conditions when the relaxation time of the track is long in comparison with the time of the action of the force impulse from the peaks of the pressure of the ski - the deformation of the track is small. But these deformations occur with small amplitudes and a high frequency.

This also applies to vertical deformations of the snow track and to horizontal ones. (With shear and volumetric deformation).

In the theory of oscillations, such a reaction of the system is called forced oscillations. (S.P. Timoshenko, D.H. Young, W. Weaver, “Fluctuations in Engineering,” p. 52, ed. Engineering, Moscow, 1985)

For a more complete understanding of the processes that occur when a ski glides along a snowy track, we can use ready-made solutions from the theory of vibrations.

Of interest to us is the so-called gain β for steady-state forced oscillations. The gain β takes into account the dynamic nature of the disturbing force.

The gain β depends on the frequency ratio ω / ρ, which is obtained by dividing the frequency of the disturbing force ω (the frequency of the force pulses from the pressure peaks of the skis) imposed on the system by the natural frequency of the system ρ free vibrations (relaxation time of the snow track).

In order to conduct a discussion of oscillations with better compliance with actual real conditions, it is necessary to take into account the influence of damping forces.

These forces can have various origins: dry friction between sliding surfaces, friction between surfaces separated by a lubricant, internal friction, etc. Resistance forces having a complex nature are usually replaced by equivalent viscous damping.

Equivalent damping is determined from the condition that in one cycle as much energy is dissipated during it as under the action of real resistance forces. The damping force always has a direction opposite to speed. The amplitude of the steady-state forced oscillation can be determined by multiplying the magnitude of the displacement under static load by the gain β.

. Где:

The gain β in this case depends not only on the frequency ratio ω / ρ, but also on the damping coefficient γ, which has the dimension of force per unit velocity. Damping coefficient

. Where:

- параметр демпфирования, δ - логарифмический декремент затухания, τ_д - период колебаний с демпфированием, с.Here:

is the damping parameter, δ is the logarithmic damping decrement, τ _d is the oscillation period with damping, s.

можно определить экспериментально. Для этого необходимо только определить из эксперимента отношение двух соседних амплитуд колебаний или вычислить другим способом логарифмический декремент затухания.Damping parameter

can be determined experimentally. For this, it is only necessary to determine from the experiment the ratio of two adjacent oscillation amplitudes or to calculate the logarithmic attenuation decrement in another way.

то система совершает периодические колебательные движения.If a

then the system makes periodic oscillatory movements.

то система не совершает колебательных движений, а постепенно движется обратно в положение равновесия. В подобном случае система называется передемпфированной, а ее движение апериодическим.If a

then the system does not oscillate, but gradually moves back to the equilibrium position. In this case, the system is called overdamped, and its movement is aperiodic.

то система впервые начинает терять свой колебательный характер. Это система с критическим коэффициентом вязкого демпфирования.If a

then the system for the first time begins to lose its oscillatory character. This is a critical viscous damping system.

имеет положительную величину, и демпфирование представляет собой силу сопротивления. При этом происходит рассеивание энергии, амплитуда колебаний постепенно уменьшается и движение затухает.Usually

is positive, and damping is a drag force. In this case, energy is dissipated, the amplitude of the oscillations gradually decreases and the motion damps.

However, there may be cases when, when moving, external energy is introduced into the system. There is an increase in the amplitude of the oscillations. In such cases, the term negative damping is used.

In the conditions of cross-country skiing, external energy is precisely introduced into the system “ski - snow track” when, for example, on a downhill, the potential energy of a skier is converted into kinetic. As a result, the sliding speed of the skis increases and the frequency ratio ω / ρ changes. As was discovered experimentally (not with skis), if the oscillating system is such that the steady state lies below the resonance zone, then it is very difficult to increase the frequency of the driving force ω (in skiing, the speed) in order to force the setup to pass through the resonance zone. The additional power spent for this purpose is spent on increasing the oscillation amplitudes, and the operational frequency of the moving parts of the installation (ski speed) changes little. The transition through resonance is not very difficult, provided that this transition is extremely fast.

(когда колебания затухают) относится к устойчивому движению, тогда как случай отрицательной величины

- к неустойчивому движению. Это объясняет имеющие место значительные разбросы времени прохождения контрольного участка спуска на одной паре лыж при повторных откатках.Positive case

(when the oscillations die out) refers to steady motion, while the case of a negative quantity

- to unstable movement. This explains the significant variations in the travel time of the control section of the descent on one pair of skis during repeated hauls.

In FIG. Figure 1 shows the change in the gain β depending on the frequency ratio ω / ρ for various values of the damping coefficient γ. It can be seen from these curves that when the imposed frequency ω is small compared to the natural frequency ρ, the gain β slightly differs from unity. Thus, during the oscillation, the displacement χ of the concentrated mass approximately coincides with the displacement caused by the action of the perturbing force.

For our case with skis, this happens, for example, at slow sliding speeds or on tracks, when the relaxation time of the track is much less than the time of the action of the force impulse from the peaks of the ski pressure. There is a constant deformation (crushing) of the snow track by the leading front of the peak pressures of the ski sliding surface. Ski pressure diagrams are practically the same as under stationary load in laboratory conditions. Ski gliding under these conditions, as is commonly believed, mainly depends on the shape of the ski plot and to a lesser extent on the coefficient of friction of the sliding surface.

When the imposed frequency ω is much larger than the natural frequency ρ, the gain β is close to zero regardless of the degree of damping. This means that the high-frequency disturbing force practically does not cause forced oscillations of the system with a low value of the natural frequency.

In our case with skis, this happens at high sliding speeds, or under conditions when the relaxation time of the route is long compared to the time of the action of the force impulse from the peaks of the pressure of the ski - the deformation of the route is small. Ski gliding under these conditions is less dependent on the ski plot, but more on the coefficient of friction.

When the imposed frequency ω becomes close to the natural frequency ρ, i.e. the ratio ω / ρ is close to unity; the gain β sharply increases. Its value at resonance or in the near-resonance region becomes very sensitive to changes in the damping coefficient.

В этом случае достигается наиболее быстрое затухание резонансных колебаний. Это можно достичь путем подбора соответствующих лыж, например, с меньшей длиной пиков давления лыж (увеличивающих навязанную частоту ω) или лыж с большей собственной частотой вибраций или установкой на лыжи демпфера для низких частот.For our case with skiing in these conditions. The struggle of trainers and servicemen to reduce the coefficient of friction and select the diagrams of skis that minimally deform the track provides a decrease in the damping coefficient and a decrease in energy loss. But under conditions when the ratio ω / ρ is close to unity (see Fig. 1), and the damping coefficient is small, this leads to resonance and large amplitudes of oscillations in the ski-snow-track system, beats and, ultimately, to an increase in damping energy loss and a decrease in ski sliding speed. The best conditions for reducing the amplitudes of the resonant vibrations of skis will be at a critical coefficient of viscous damping, when the damping parameter is equal to the natural frequency of the snow track

In this case, the fastest attenuation of resonant oscillations is achieved. This can be achieved by selecting the appropriate skis, for example, with a shorter length of the pressure peaks of the skis (increasing the imposed frequency ω) or skis with a higher natural vibration frequency or by installing a damper on the skis for low frequencies.

At present, when choosing and preparing sports equipment in top-level sports, the influence on the energy dissipation of the ratio of the imposed vibration frequency of the sports equipment – snow track system (frequency of impulses from pressure peaks of sports equipment) to the natural frequency of free vibrations of the snow track is not taken into account (time snow track relaxation).

However, these phenomena have a significant impact on the resistance forces to the movement of sports equipment and on the sliding speed on a snowy track.

To verify these theoretical conclusions, experimental studies were carried out in real ski conditions. To do this, in the seasons 2017-18 and 2018-19, in different weather conditions (a total of 46 days), measurements of tensogeometric and intrinsic amplitude-frequency characteristics of skis were carried out, rheological characteristics of the snow track were measured, measurements were made of the ski sliding speed on the slopes and the amplitude-frequency characteristics of the ski-snow-track system. The measurements were carried out on three pairs of skis from different manufacturers, with different tensogeometric characteristics and different amplitude-frequency characteristics.

To exclude the influence of the design features of skis, materials of a sliding surface, lubrication, etc. on the sliding speed, we first measured the speeds of each pair of skis on the slope without a damper (with their own amplitude-frequency characteristics), and then installed a low-frequency vibration damper on the skis (they changed their own amplitude -frequency characteristics of skis to a higher frequency region), and again measured the speed of the skis on the slope. The sliding speeds of skis were compared with a damper and without a damper, and the ratios of the imposed vibration frequency of the sports equipment – snow track system (frequency of force pulses from pressure peaks of the sports equipment) to the natural frequency of free vibrations of the snow track (relaxation time of the snow track) were determined.

Experimental studies of the sliding speed of skis on a snowy track confirmed a significant effect on the dissipation of ski energy of the ratio of the imposed oscillation frequency of the "sports equipment - snowy track" system (frequency of impulses from pressure peaks of sports equipment) to the natural frequency of free vibrations of the snowy track (relaxation time of the snowy track ), especially significant near the resonance zone, when the ratios of these frequencies are close to unity at low coefficients of damping of the snow path.

The aim of the invention is to increase the reliability of the selection of sports equipment by determining the ratio of the imposed oscillation frequency of the system "sports equipment - snow track" (frequency of impulses from pressure peaks of sports equipment) to the natural frequency of free vibrations of the snow track (relaxation time of the snow track) and the subsequent selection of sports equipment , with the length of the pressure peaks providing the lowest energy losses of the "sports equipment - snow track" system during the movement of a sports inv tarya in actual track over the entire range of competitive rates.

This goal is achieved by the fact that in the known method of selecting sports equipment taking into account the rheological characteristics of the snowy track, including measuring the rheological characteristics of the snowy track, measuring the strain-geometric and amplitude-frequency characteristics of the sports equipment and measuring the amplitude-frequency characteristics of the system "sports equipment - snow track", processing the obtained data and the subsequent selection of the best option, while processing the received data, determine the damping coefficient snow track, the ratio of the imposed vibration frequency of the system “sports equipment - snow track” (frequency of impulses from pressure peaks of sports equipment) to the natural frequency of free vibrations of the snow track (relaxation time of the snow track) and if the damping coefficient of the snow track is less than unity, then select sports equipment with such a ratio of the imposed vibration frequency to the natural frequency of free vibrations of the snow track, which derives the system "sports equipment - snow track" from p the resonance zone (when the ratio is close to unity), and when the ratio of the imposed vibration frequency to the natural frequency of free vibrations of the snow track is less than unity, then sports equipment with a natural vibration frequency exceeding the imposed frequency is chosen, and if the ratio of the imposed vibration frequency to the free natural frequency If there are more than one unit of snow path, then choose sports equipment with a frequency of natural vibrations less than the imposed frequency.

This method of selecting sports equipment, taking into account the rheological characteristics of the snowy track, in the conditions of maximum reduction of energy losses due to dry friction, viscous friction, deformation of the track, etc., which coaches and servicemen aspire to when preparing sports equipment for competitions, takes into account an important factor - the ratio of the imposed oscillation frequency of the system "sports equipment - snow track" (frequency of impulses of forces from the pressure peaks of sports equipment) to the natural frequency of free vibrations snowy track (relaxation time of the snow track), and thus increases the reliability of the selection of the optimal characteristics of sports equipment for real competition conditions.

This indicates the presence of novelty in the claimed method.

Comparison of the claimed method with other technical solutions of the same direction shows that a preliminary measurement of the tensogeometric and amplitude-frequency characteristics of the skis and the measurement of the damping coefficient of the snow track before the competition allows us to determine the ratio of the imposed vibration frequency of the "sports equipment - snow track" system (frequency of force pulses from peaks pressure of sports equipment) to the natural frequency of free oscillations of the snowy track (relaxation time of the snowy track). If the value of the damping coefficient is less than unity, then the ratio of the imposed and natural frequencies of the snow path must be taken into account. In this case, the maximum possible ski sliding speeds on the slopes are predicted and the allowable length of the ski pressure peaks is calculated, which provide the ratio of the imposed and natural frequencies of the snow path outside the resonance zone. This allows more accurate selection of sports equipment for real conditions of the snowy track.

Thus, we can conclude that the claimed method exceeds the existing level of technology.

In FIG. Figure 1 shows the change in the gain β depending on the frequency ratio ω / ρ for various values of the damping coefficient γ.

In FIG. 2 shows a sonogram of the Atomic ski natural frequency.

In FIG. Figure 3 shows a sonogram of the natural frequency of the Madshus ski.

In FIG. 4 shows a sonogram of the natural frequency of Fisher skis.

In FIG. 5 shows the length of the Atomic ski pressure peaks

In FIG. 6 shows the length of the pressure peaks of the Mudshus ski

In FIG. Figure 7 shows the lengths of the Fisher ski pressure peaks.

In FIG. Figure 8 shows the waveform of the accelerations of the ski-snow-track system.

In FIG. Figure 9 shows the snow track deformation in time 2019.03.13

In FIG. 10 shows snow track deformations over time. March 3, 2019

In FIG. Figure 11 shows a graph of the change in the sliding speed of skis along the slope of 2019.03.13.

In FIG. Figure 12 shows a sonogram of the amplitude-frequency characteristics of the Atomic-Snow Track ski system when sliding along the slope of March 03, 2013.

In FIG. Figure 13 shows a sonogram of the amplitude-frequency characteristics of the “Mudshuz-snow track” system when sliding along the slope of March 03, 2013.

In FIG. Figure 14 shows a sonogram of the amplitude-frequency characteristics of the Fisher-Snow Track ski system when skiing along the slope on March 03, 2013.

In FIG. 15 shows a comparison of the lengths of the pressure peaks of a Fisher ski pair on a snow track of different stiffness.

In FIG. Figure 16 shows a graph of the ski sliding speed along the slope 2019.03.17.

In FIG. Figure 17 shows a sonogram of the amplitude-frequency characteristics of the Atomic-Snow Track ski system when skis slip along the slope of March 03, 2017.

In FIG. Figure 18 shows a sonogram of the amplitude-frequency characteristics of the Madshouz-Snow Track ski system when skiing along the slope of March 03, 2017.

In FIG. Figure 19 shows a sonogram of the amplitude-frequency characteristics of the Fisher-Snow Track ski system when skiing along the slope of March 03, 2017.

In FIG. 20 shows the dependence of the damping coefficient of the oscillations on the frequency during inertial and structural damping.

In FIG. 21 shows skis with a damper.

In FIG. 22 shows a sonogram of the Atomic ski's own resonant frequency with a damper.

In FIG. 23 shows a sonogram of the natural resonant frequency of the Madshoes ski with a damper.

In FIG. 24 shows a sonogram of the natural resonant frequency of the Fisher ski with a damper.

In FIG. 25 shows a graph of ski speeds on the slopes with a damper and without a damper 2019.03.13

In FIG. Figure 26 shows a graph of the ski speed on the slopes with a damper and without a damper on 03/03/2017.

The method of selection of sports equipment is illustrated by the example of its implementation.

We have three pairs of skis with the following strain-geometric and amplitude-frequency characteristics. The initial data for the calculation.

Frequency response of skis.

The measurements were performed using the device according to the patent for utility model of the Russian Federation No. 111446. Sensors were installed on the ski.

In FIG. 2 shows a sonogram of the Atomic ski natural frequency.

R _a = 75 Hz. Quality factor - 130.92 On the abscissa axis on the sonogram - time, s. The ordinate is the frequency, Hz. The color shows the vibration amplitudes, dB.

In FIG. Figure 3 shows a sonogram of the natural frequency of the Madshus ski.

R _m = 90 Hz. Quality factor - 71.35

In FIG. 4 shows a sonogram of the natural frequency of Fisher skis.

R _f = 90 Hz. Quality factor - 75.73

Strain-geometric characteristics of skis. The measurements were performed on a bench according to the patent for a utility model of the Russian Federation No. 108616.

In FIG. 5. shows the length of the pressure peaks of the Atomic ski pair - L _a = 35/45 cm (Length of the back / front pressure peaks)

In FIG. 6. shows the length of the pressure peaks of the pair of skis Madshus - L _m = 28/32 cm

In FIG. 7. shows the length of the pressure peaks of the Fisher ski pair - L _f = 40/40 cm

The actual length of the pressure peaks in a snowy track may vary slightly and depends on the stiffness of the track. Appropriate adjustment of laboratory data is required.

To measure the actual length of pressure peaks on a snowy track at competitive speed, we used the device according to the utility model patent of the Russian Federation No. 111446. Sensors were buried in a snowy track. Example of measurement results.

In FIG. Figure 8 shows the waveform of the accelerations of the ski-snow-track system. On the abscissa axis on the waveform, we determine the transit time of the peak pressure of the ski along the sensor in the snow. From the time of exposure of the pressure peaks to the snow track and the known ski sliding speed, we determine the actual length of the pressure peaks. The sliding speed of the ski was measured with the device according to the patent for the invention of RF2600082.

Rheological characteristics of the snow track.

Examples for calculations are taken for two days, with different rheological characteristics of the snow track.

The measurements were made by a device similar to RF patent No. 2365915.

In FIG. Figure 9 shows the deformation of the snow track in time on the first day of March 03, 2013.

In FIG. 10 shows the deformation of the snow track in time on the second day of March 03, 2017

We calculate the damping coefficient of the snow track.

For 2019.03.13. The strain amplitude of the snow track decreased by 90% in 3 cycles and in 0.07 s. Stamp immersion depth in snow - 7.5 mm. See FIG. nine.

The oscillation period τ _d = 0,055 s.

The frequency ρ = 2π / τ _d = 2x3.14 / 0,055 = 114.2 Hz.

Logarithmic attenuation decrement δ = 1/3 × ln (1 / 0.1) = 0.767

=0,767/0,055=13.95Damping parameter

= 0.767 / 0.055 = 13.95

=13.95/114,2=0,122Damping coefficient

= 13.95 / 114.2 = 0.122

The damping coefficient is much less than unity. Consequently, the ratio of the imposed frequency and the natural frequency of the snow track will have a significant effect on the ski glide. It is necessary to calculate the frequency ratio.

For 2019.03.17. The strain amplitude of the snow track decreased by 99% for 1 cycle and for 0.06 s. The depth of immersion of the stamp in the snow is 18 mm. See FIG. 10.

The oscillation period is τ _d = 0.06 s.

Frequency ρ = 2π / τ _d = 2x3.14 / 0.06 = 104.67 Hz.

Logarithmic attenuation decrement δ = 1/1 × ln (1 / 0.01) = 4.605

=4.605/0,06=76,75Damping parameter

= 4.605 / 0.06 = 76.75

=76,75/104,67=0,73Damping coefficient

= 76.75 / 104.67 = 0.73

The damping coefficient is slightly less than unity. Therefore, for the second day, the ratio of the imposed frequency and the natural frequency of the snow track will have a lesser effect on the sliding of the skis, since the resonant vibrations are substantially damped. But this effect persists and can increase with an increase in the sliding speed of skis in individual sections of the distance and an increase in the imposed frequency. Since the damping coefficient is less than unity, it is also necessary to calculate the frequency ratio under these conditions.

We make the calculation of the ratio of the imposed frequency and the natural frequency of the snow track for the ski-snow track system.

We calculate the ratio of the imposed frequency and the natural frequency of the snow track for a speed of V = 5 m / s and the period of imposed oscillations τ _dl = L / V for three pairs of skis.

1 day 2019.03.13.

Atomic

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _a / V) = 2 × 3.14 / (0.35 / 5) = 89.7 Hz

Frequency ratio ω / ρ = 89.7 / 114.2 = 0.785

Madshouse

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _m / V) = 2 × 3.14 / (0.28 / 5) = 112.14 Hz

Frequency ratio ω / ρ = 112.14 / 114.2 = 0.982

Fisher

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _f / V) = 2 × 3.14 / (0.4 / 5) = 78.5 Hz

Frequency ratio ω / ρ = 78.5 / 114.2 = 0.687

Calculations show that the greatest influence on the sliding speed under 1 day conditions will be exerted by dissipative phenomena on the Madshus ski. They have the ratio of frequencies closest to one.

In the conditions of the first day, experimental rolling of all three pairs of skis was performed. To measure the speed of skis, the device according to the patent for the invention of the Russian Federation No. 2600082 was used.

Rollback was carried out on a slope 90 meters long six times on each pair. The maximum and minimum results were excluded, and the remaining 4 were averaged.

In FIG. 11. A graph of the ski sliding speed along the slope 2019.03.13 is presented.

Here, the abscissa axis is the distance, m. The ordinate axis is the ski sliding speed, m / s.

The results of the rollback completely coincides with the results of the above calculations. The best skis for these conditions are selected according to the criterion of the highest sliding speed.

At the same time as measuring the speed, the amplitude-frequency characteristics of the ski-snow-track system were recorded. For this, the device was used according to the patent for utility model of the Russian Federation No. 111446. The sensors were mounted on a ski.

In FIG. Figure 12 shows a sonogram of the amplitude-frequency characteristics of the Atomic-Snow Track ski system when sliding along the slope of March 03, 2013. The abscissa on the sonogram is time, s. The ordinate is the frequency, Hz. The color shows the vibration amplitudes, dB. The upper sonogram is horizontal vibrations. Lower sonogram - vertical vibrations.

In FIG. Figure 13 shows a sonogram of the amplitude-frequency characteristics of the “Madsuz-snow track” system when sliding along the slope of March 03, 2013.

In FIG. Figure 14 shows a sonogram of the amplitude-frequency characteristics of the Fisher-Snow Track ski system when skiing along the slope of March 03, 2013.

Sonograms make it possible to visually confirm the presence of resonance phenomena under conditions when the ratio ω / ρ is close to unity.

The presented sonograms show the presence of significant resonance oscillations in Madshouz skis (frequency ratio ω / ρ = 0.982) under conditions of 1 day of experiment.

2 day 2019.03.17.

The depth of immersion of the stamp in the snow is 10 mm more than 1 day. See Fig 10. This indicates a softer track. On a soft track, the length of the pressure peaks decreases. But this decrease is significantly dependent on the design of the skis. Example:

In FIG. 15 shows a comparison of the lengths of the pressure peaks of a Fisher ski pair on a track of different stiffness. Here, a purple graph of pressure peaks is obtained on a softer supporting surface of the bench.

We calculate the frequency ratio ω / ρ for 2019.03.17.

Atomic

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _a / V) = 2 × 3.14 / (0.30 / 5) = 104.7 Hz

Frequency ratio ω / ρ = 89.7 / 114.2 = 0.916

Madshouse

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _m / V) = 2 × 3.14 / (0.25 / 5) = 125.6 Hz

Frequency ratio ω / ρ = 112.14 / 114.2 = 0.981

Fisher

The frequency of impulses of forces from the pressure peaks of sports equipment:

ω = 2π / τ _dl = 2π / (L _f / V) = 2 × 3.14 / (0.39 / 5) = 83.73 Hz

Frequency ratio ω / ρ = 83.73 / 114.2 = 0.733

Calculations show that dissipative effects on Atomic skis will have the greatest impact on gliding speed under 2 days. Since the gain β has a maximum value when the values of the ratio ω / ρ are somewhat less than unity. See FIG. However, a high damping coefficient of the snowy path γ = 0.73 will dissipate the increasing amplitude of the resonant oscillations. A significant increase in resonant oscillations will not occur.

On the second day, experimental rolling of all three pairs of skis was also performed to verify the conclusions drawn from the calculation results.

In FIG. 16. A graph of the ski sliding speed along the slope 2019.03.17 is presented.

The results of the rollback also completely coincide with the results of the above calculations.

For the second day, sonograms of the amplitude-frequency characteristics of the ski-snow track system are also shown.

In FIG. 17. A sonogram of the amplitude-frequency characteristics of the Atomic-Snow Track ski system is presented when skis slip along the slope on 03/03/17.

In FIG. 18. A sonogram of the amplitude-frequency characteristics of the “Madshuz-snow track” system is presented when skis slip along the slope on 03/03/17.

In FIG. 19. A sonogram of the amplitude-frequency characteristics of the “Fisher-Snow Track” ski system is presented when skis slip along the slope of March 03, 17.17.

Sonograms show a significant effect of the high damping coefficient of the snowy track γ = 0.73 on the dissipation of the slip energy and vibration of the skis. An increase in resonance oscillations does not occur.

Now it is necessary to find out how the natural amplitude-frequency characteristics (and not the length of the pressure peaks) of the skis affect the damping of the oscillations of the ski-snow-track system and how this is related to the imposed frequency ω.

In the scientific literature it is customary to approximate damping by a combination of the contributions of resistances associated with two system matrices - the mass matrix and the stiffness matrix (Solving contact problems in ANSYS 6.1, CADFEM Representative Office. M., 2003.).

[C] = α [M] + β [K]

Where: [C] - resistance matrix

Coefficients α and β are known as Rayleigh damping constants. α - inertial damping, β - structural damping.

It was found that during inertial damping, low frequencies are damped more, and higher ones are weaker.

Structural damping is associated with energy losses due to the action of dry friction forces. In this type of damping, low frequencies attenuate less, higher ones more.

In FIG. 20. The dependence of the damping coefficient of the oscillations on the frequency during inertial and structural damping is shown. There is a minimum of energy loss in the frequency range f ₁ - f ₂ .

Returning to FIG. 1, then it can be seen that if the frequency ratios ω / ρ are small, when the relaxation time of the snow path is much shorter than the time of the force impulse from the pressure peaks of the skis, then inertial damping prevails. Skis with low natural frequencies (R <ω) will damp more energy under these conditions. It is preferable to use under these conditions skis with higher natural frequencies (R> ω).

If the ratio of frequencies ω / ρ is greater than unity, when the relaxation time of the snow path is longer than the duration of the force impulse from the pressure peaks of the skis, structural damping prevails. Skis with high natural frequencies (R> ω) will damp more energy under these conditions. It is preferable to use under these conditions skis with low natural frequencies (R <ω).

To experimentally verify these statements and exclude the influence on the results of the design features of the skis, the properties of the sliding surface, etc., we change the natural frequencies of the skis by installing low-frequency dampers on the skis.

In FIG. 21. presents photos of skis with a damper.

Got the old skis with new natural frequencies.

In FIG. 22. A sonogram of the natural frequency of Atomic skis with a damper is presented. The natural frequency of Atomic skis increased from 75 Hz to 180 Hz.

In FIG. 23. A sonogram of the natural frequency of the Mudshus ski with a damper is presented. The natural frequency of Madshoes skis increased from 90 Hz to 180 Hz.

In FIG. 24. A sonogram of the Fisher ski's own resonant frequency with a damper is presented. The natural frequency of Fisher skis increased from 90 Hz to 210 Hz.

Now we experimentally compare the speed of skis with a damper and without a damper on the first day - 2019.03.13

In FIG. 25. The ski speed is shown on the slopes with a damper and without a damper 2019.03.13.

All three pairs of skis have increased sliding speed. This confirms that if the frequency ratios ω / ρ are small, when the relaxation time of the snow path is much shorter than the time of the force impulse from the pressure peaks of the skis, then skiing with higher natural vibration frequencies (R> ω) is preferable.

For the second day 2019.03.17

In FIG. 26 The ski speed on the slope with a damper and without a damper is shown on 2019.03.17.

All three pairs of skis have increased sliding speed. This also confirms that if the frequency ratios ω / ρ are small, when the relaxation time of the snow path is less than the time of the force impulse from the pressure peaks of the skis, then skiing with higher natural vibration frequencies (R> ω) is preferable. But at the same time, we note that for Fisher skis (ω / ρ = 0.733), the increase in speed is noticeably less. This indicates the proximity of the border of the minimum energy loss in the frequency range f ₁ - f ₂ (See Fig. 20).

The results of the experimental studies showed high efficiency and increased reliability of the selection of sports equipment according to a new criterion - the ratio of the imposed vibration frequency of the "sports equipment - snow track" system (frequency of impulses from pressure peaks of sports equipment) to the natural frequency of free vibrations of the snow track (snow relaxation time tracks).

Claims (1)

A method for selecting sports equipment taking into account the rheological characteristics of the snowy track, including measuring the rheological characteristics of the snowy track, measuring the strain-geometrical and amplitude-frequency characteristics of the sports equipment and measuring the amplitude-frequency characteristics of the "sports equipment - snowy track" system, processing the data and then selecting the best option , characterized in that when processing the data obtained, the damping coefficient of the snow track is determined, the ratio on the specified oscillation frequency of the "sports equipment - snow track" system (the frequency of force pulses from the pressure peaks of the sports equipment) to the natural frequency of free vibrations of the snow track (relaxation time of the snow track), and if the damping coefficient of the snow track is less than unity, then sports equipment with such the ratio of the imposed oscillation frequency to the natural frequency of free oscillations of the snow track, which brings the "sports equipment - snow track" system out of the resonance zone (when the ratio narrow to unity), and when the ratio of the imposed vibration frequency to the natural frequency of free vibrations of the snow track is less than one, then sports equipment with a natural vibration frequency exceeding the imposed frequency is chosen, and if the ratio of the imposed vibration frequency to the natural frequency of free vibrations of the snow path is more than one, then choose sports equipment with a frequency of natural oscillations less than the imposed frequency.

Images