RU2672809C1 - Method for determining the coefficients of static and slipping friction - Google Patents

Abstract

FIELD: testing equipment.SUBSTANCE: invention relates to the field of mechanical testing of materials, in particular to the determination of the friction coefficient between specimens. One of the specimens, fixed immovably, is made with a working surface having a rectilinear or concave circular shape. Rectilinear guide element is placed at a certain distance from the fixed specimen. Movable specimen is made with two working edges, oppositely located on its diagonal having the length of d. Possibility of moving the movable specimen along the working surface of the fixed specimen is provided. Movable specimen is set so that one of its working edges is in contact with the fixed specimen, and the second, when touching the guide element, is located with such lagging from the first edge in the direction of travel, that a certain angle ϕ is formed between the diagonal of the movable specimen and the perpendicular to the working surface of the fixed specimen or to the line tangential to the circular working surface at the point of contact of the specimens. Load is placed in the middle part of the movable specimen to prevent its movement, and a shifting external force is applied in the immediate vicinity of the edge in contact with the guide element. Experimentally, the position of the movable specimen is found in which, at a minimum distance l from the edge of the movable specimen, in contact with the guide member, to the working surface of the fixed specimen in a direction perpendicular to it or to a line tangential to the circular working surface at the point of contact of the specimens, jamming of the movable specimen occurs and its movement is absent regardless of the magnitude of the shearing force. Distance l is measured and angle ϕ is calculated according to formula ϕ=arccos(l/d). Coefficient of friction between the fixed and movable specimens is determined by formula ƒ=tgϕ.EFFECT: possibility of determining the coefficients of static and slipping friction by measuring only linear dimensions, without measuring angles and frictional force, at any contact pressures created by a limited external load, to the nature of application of which no stringent requirements are imposed.4 cl, 3 dwg

Description

The present invention relates to the field of mechanical testing of materials, in particular, to the determination of the coefficient of friction between samples.

There is a method of determining the static coefficient of external friction between two samples located one on top of the other, which consists in measuring only one geometric parameter - the angle of inclination ϕ of the samples relative to the horizon at the time of sliding of the sample located on top [US patent No. 3020744, class. 73-9, cl. G01N 19/02, 1962]. After that, the rest friction coefficient ƒ _{pok is} calculated by the formula ƒ _pok = tgϕ.

This method avoids the time-consuming measurement of friction forces during experiments. The disadvantage of this method is to conduct tests at low specific pressure between the samples, which is determined by the low weight of the upper sample.

A known method for determining the static and dynamic coefficients of friction, also based on measuring angles characterizing the spatial position of the samples at the beginning and end of sliding on a concave curved surface [RF patent No. 2537745, class. G01N 19/02, publ. 01/10/2015]. To calculate the friction coefficients, the trigonometric functions of these angles are used, and the measurement of friction forces to determine the friction coefficients in this way is not required. The method can provide data at elevated contact pressures, for which an additional external force is applied to the upper sample, however, the realization of this possibility is difficult. This is due to the fact that the additional load must be applied strictly vertically, which can be realized only with the help of cargo. For this, the use of the envelope of prefix samples is provided, which complicates the device, increases its dimensions and mass, and complicates the conduct of the experiment. In addition, the accuracy of determining the friction coefficients in this way is reduced due to the relatively large errors in the measurement of small angles. This method is adopted as a prototype of the alleged invention.

The technical result of the proposed method is the ability to determine the coefficients of friction of rest and sliding without measuring the friction force and angles, at any contact pressure created by a limited external load, the nature of the application of which is not imposed stringent requirements, with the measurement and use in calculations only linear dimensions.

The technical result is achieved by the fact that to determine the coefficients of friction between two samples, one of them, fixed fixed, is made with a working surface having a rectilinear or concave circular shape. A rectilinear guide element is placed at a distance from the fixed sample. The second movable sample is made with two working edges oppositely located on the diagonal of the sample having length d. The movable sample is allowed to move along the stationary sample and the guide element and is set so that one of its working edges is in contact with the stationary sample, and the second, touching the guide element, is located behind the first edge in the direction of movement, in which between the diagonal and the perpendicular to a rectilinear working surface of a fixed sample, a certain angle ϕ is formed. If the working surface of the stationary sample has a circular shape, the angle ϕ of the diagonal of the diagonal is determined "relative to the line tangent to the circular working surface at the contact point of the samples. In the middle part of the movable sample, a load is applied that impedes its movement, and in the immediate vicinity of the edge in contact with the guide element, a shear external force is applied to the sample. Empirically determine the minimum distance l from this edge to the rectilinear working surface of a stationary sample in the direction perpendicular to it, at which the moving sample is jammed, preventing its movement regardless of the magnitude of the shear external force. If the working surface of the fixed sample has a circular shape, the minimum distance l from the edge in contact with the guide element is determined in the direction perpendicular to the line tangent to the circular working surface at the contact point of the samples. Using the found value of l, the diagonal angle ϕ is calculated by the formula ϕ = arcccos (l / d), after which the coefficient of friction between the stationary and moving samples is determined by the formula ƒ = tgϕ.

If the fixed sample has a rectilinear working surface, the guide element is set at a certain angle α relative to the line of the working surface of the fixed sample and provide a value of this angle that is less than the angle of friction ϕ between the test samples. If the stationary sample has a circular work surface, this condition is satisfied automatically.

The sliding friction coefficient is determined as follows. The movable specimen is set in a position in which the initial angle ϕ between the diagonal of the movable specimen and the perpendicular to the working surface of the fixed specimen or to the line tangent to the circular working surface at the contact point of the specimens is greater than the angle of friction between the specimens, and move along fixed sample in the direction of increasing distance l between the fixed sample and the guide element and reduce the angle ϕ until it stops due to jamming. For this position of the movable sample are tilt angle φ _ck its diagonals, which is determined by the value of friction coefficient ƒ = tgφ _{ck ck.}

To determine the static friction coefficients, the movable sample is successively installed at various points on the working surface of the fixed sample and empirically find the minimum distance l between the fixed sample and the guide element, at which the movement of the stationary moving sample is initially impossible due to jamming. For this position of the movable sample are _dormancy angle φ of inclination of its diagonal, the value of which is determined by the coefficient of static friction ƒ = tgφ _{dormancy dormancy.}

In FIG. 1 shows a diagram of the relative position of the samples and forces. applied to a movable sample and affecting the results of the experiment in the case of a rectilinear shape of the working surface of a stationary sample; in FIG. 2 shows a diagram of an experiment using a movable sample having a rod shape; in FIG. 3 shows a diagram of the experiment in the case when the working surface of a stationary sample has a circular concave shape, where:

1 - fixed sample;

2 - a directing element;

3 - moving sample;

4 - shifting device.

от этой кромки до прямолинейной рабочей поверхности неподвижного образца 1 или до линии, касательной к круговой рабочей поверхности, проведенной через точку контакта между образцами.The friction coefficients are determined as follows. The fixed sample 1 is made with a working surface having a rectilinear or concave circular shape. A rectilinear guide element 2 is placed at a distance from the fixed sample 1. Another movable sample 3 is made with two working edges oppositely located on the diagonal of the sample having length d. The movable sample 3 is allowed to move along the stationary sample 1 and the guide element 2. Then, the movable sample 3 is installed so that one of its working edges is in contact with the stationary sample 1, and the second edge, touching the guide element 2, is located behind the first edge in the direction of movement of the movable sample 3. In this case, between the diagonal and the perpendicular to the rectilinear working surface of the stationary sample 1, an acute angle ϕ is formed. If the working surface of the stationary sample 1 has a circular shape, the angle ϕ is counted from the line tangent to the circular working surface at the contact point of the samples. A load is applied to the middle part of the movable sample 3, which impedes its movement. As this load, the gravity force G of the moving sample 3 can be used when moving it vertically upward, it can be created by the friction force when the moving sample 3 is horizontally moved along the auxiliary surface, applied by an elastic element, etc. A shear external force R is applied near the edge of the movable sample 3 in contact with the guide element 2. By experimentally changing the positions of the movable sample 3 relative to the stationary sample 1, one can find one of these positions at which the jamming of the movable sample 3 prevents it from moving regardless of the magnitude applied force P occurs at a minimum distance

from this edge to the rectilinear working surface of the stationary sample 1 or to the line tangent to the circular working surface drawn through the point of contact between the samples.

The relationship of the friction coefficients with the geometric parameters of the system is determined by one of the conditions for the balance of forces acting on the moving sample 3. It consists in the fact that the total moment of these forces, calculated relative to the point O, at which the moving sample 3 contacts the guiding element 2, is equal to zero and is described by the equation :

where N is the reaction force from a stationary sample 1, normal to its working surface;

F _Tr - the friction force that prevents the movement of the movable sample 3 relative to the stationary 1.

The friction force F _{Tr is} proportional to the normal force N and the coefficient of friction between the samples ƒ, which allows you to convert equation (1):

From the expression (2) find the normal force N:

The resulting expression (3) allows us to formulate the mathematical condition for jamming the movable sample 3, It consists in the equality of the infinity of the normal force N and the proportional friction force F _Tr . This is achieved if the denominator is equal to zero in expression (3), i.e.

tgϕ-ƒ = 0,

Thus, the angle ϕ of the diagonal of the movable sample 3 in the jamming position is equal to the angle of friction between the samples, which allows us to determine the coefficient of friction

, достигнутого при заклинивании, используя для расчетов формулу,During the experiment, the diagonal angle ϕ of length d of the moving sample is found after measuring the distance

achieved by jamming using the formula for calculations,

Formulas (4) and (5) resulting from the equilibrium condition of the movable sample 2 remain valid even in the case when a shear external force P is applied not strictly at the edge of the movable sample 3, but at a certain distance from it. Calculations show that these formulas are also valid when the load is located that impedes the movement of the movable sample 3, with an offset from its geometric center. In the general case, the scope of formulas (4) and (5) extends to all cases when the external shear force P is closer to the edge touching the guide element 2, and the force preventing the movement G is closer to the edge touching the stationary sample 1. Change the position of external forces affects only the magnitude of the contact pressures between the samples, without changing the condition for jamming the movable sample 3. This feature allows you to determine the friction coefficients using long samples (Fig. 2), on which it is possible there is no external force applied directly to the working edge.

The considered equilibrium condition for the movable sample 3 is not the only one. An analysis of the remaining conditions shows that in practice an infinitely large value of the normal force N is unattainable, since this would require an infinitely large external force P. Accordingly, the angle of inclination of the diagonal ϕ achieved in real experiment is not exactly equal to the angle of friction, but only tends to it. However, the calculations show that even with small values of the force P, the achieved diagonal angle ϕ from the angle of friction differs insignificantly, by a few hundredths of a degree, which is many times less than other experimental errors, for example, with the inevitable error in measuring the angle. The error of the experimental results for the reason considered in the most adverse cases does not exceed 1%, which is negligible in the study of friction coefficients in comparison with other experimental errors. By changing the force P, it is possible not only to reduce the error in determining the coefficient of friction, but it is also quite easy to control the specific pressures on the contact surface of the samples.

в том случае, если рабочая поверхность неподвижного образца 1 прямолинейна, плоская поверхность направляющего элемента устанавливают под некоторым углом α относительно прямолинейной рабочей поверхности неподвижного образца 1. Это позволяет проводить опыты по определению коэффициента трения скольжения, а при определении коэффициента трения покоя дает возможность изменять расстояние

простым способом, выбирая исходное положение подвижного образца 3 в разных местах по длине рабочей поверхности неподвижного образца 1. При круговой вогнутой форме рабочей поверхности неподвижного образца 1 (фиг. 3) это условие выполняется автоматически.To simplify distance control

in the event that the working surface of the fixed sample 1 is straight, the flat surface of the guide element is set at an angle α relative to the rectilinear working surface of the fixed sample 1. This allows experiments to determine the coefficient of sliding friction, and when determining the coefficient of static friction makes it possible to change the distance

in a simple way, choosing the initial position of the movable sample 3 in different places along the length of the working surface of the stationary sample 1. With a circular concave shape of the working surface of the stationary sample 1 (Fig. 3), this condition is satisfied automatically.

минимально, а образующийся в этом положении подвижного образца 3 угол ϕ между его диагональю и перпендикуляром к рабочей поверхности неподвижного образца 1 больше угла трения покоя между образцами. Приложением внешней силы Р приводят подвижный образец 3 в движение с необходимой скоростью в направлении увеличения расстояния между неподвижным образцом 1 и направляющим элементом 2. В процессе перемещения подвижного образца 3, вследствие автоматического увеличения расстояния

, угол наклона диагонали ϕ постепенно уменьшается, приближаясь к углу трения скольжения и. в конечном счете, достигает его, что сопровождается заклиниванием подвижного образца 3. В положении, достигнутом в конце процесса скольжения подвижного образца 3, находят угол ϕ_ск наклона его диагонали, по значению которого определяют величину коэффициента трения скольжения ƒ_ск=tgϕ_ск.In the experiment to determine the coefficient of sliding friction, the movable sample 3 is installed where the distance

minimum, and the angle ϕ formed in this position of the movable sample 3 between its diagonal and the perpendicular to the working surface of the stationary sample 1 is greater than the angle of rest friction between the samples. By applying an external force P, the movable sample 3 is set in motion with the necessary speed in the direction of increasing the distance between the stationary sample 1 and the guide element 2. In the process of moving the movable sample 3, due to the automatic increase in distance

, the angle of inclination of the diagonal ϕ gradually decreases, approaching the angle of sliding friction and. ultimately, it reaches it, which is accompanied by jamming of the movable sample 3. In the position reached at the end of the sliding process of the movable sample 3, the angle ϕ _{cc of the} slope of its diagonal is found, the value of which determines the value of the sliding friction coefficient ƒ _ck = tgϕ _ck .

между неподвижным образцом 1 и направляющим элементом 2, при котором перемещение находящегося в покое подвижного образца 2 изначально невозможно вследствие заклинивания. Для этого положения подвижного образца 3 находят угол ϕ_пок наклона его диагонали, и по значению угла определяют коэффициент трения покоя ƒ_пок=tgϕ_пок.In the experiment to determine the coefficient of rest friction, the movable sample 3 is successively installed at various points on the working surface of the stationary sample 1 and the minimum distances are found experimentally

between the stationary sample 1 and the guide element 2, in which the movement of the resting movable sample 2 is initially impossible due to jamming. For this position of the movable sample 3, the angle ϕ of the _{pok of the} inclination of its diagonal is found, and the coefficient of friction of rest ƒ _pok = tgϕ _{pok is} determined by the value of the angle.

Claims (4)

1. The method of determining the coefficients of sliding friction and rest between two samples, in which one of the samples, fixed motionless, is made with a working surface having a rectilinear or concave circular shape, a rectilinear guide element is placed at a distance from the stationary sample, a movable sample is made with two workers edges oppositely located on its diagonal having a length d, and set the movable sample so that one of its working edge is in contact with the stationary sample m, the second - with a guiding element, while between the diagonal of the moving sample and the perpendicular to the working surface of the fixed sample or to the line tangent to the circular working surface at the contact point of the samples, an angle ϕ is formed, then a load is applied in the middle part of the moving sample to prevent it moving, and in close proximity to the edge in contact with the guide element, act on it with a shear external force, find the position of the movable sample in which it is jammed a moving sample with a minimum distance

from the edge of the movable sample in contact with the guide element to the working surface of the fixed sample in the direction perpendicular to it or to the line tangent to the circular working surface at the contact point of the samples, measure the distance

and calculate the angle ϕ by the formula

then determine the coefficient of friction between the stationary and moving samples by the formula ƒ = tgϕ. 2. The method of claim. 1, characterized in that in the case of rectilinear fixed specimen working surface a guide member relative thereto at an angle α, whose value is smaller than the angle φ _ck sliding friction between the test samples. 3. The method according to p. 1, characterized in that to determine the coefficient of sliding friction, the movable sample and the guide element are set so that the angle ϕ is greater than the angle of friction between the samples, move the movable sample along the stationary distance in the direction of increasing distance between the stationary sample and the guide element, and reducing the angle φ to the stopping of the movable wedge of the sample due to find the angle of inclination φ _ck diagonally movable specimen in this position and the value of this angle value is determined and s cient of friction ƒ = tgφ _{ck ck.} 4. The method according to p. 1, characterized in that to determine the coefficient of static friction, the movable sample is successively set at various points on the working surface of the stationary sample and empirically find the minimum distance

between the stationary sample and the guide member, wherein the movement in a state of rest of the movable sample originally impossible due to jamming, find the angle φ of inclination of the diagonal _dormancy specimen in this position, and its value is determined by the coefficient of static friction ƒ = tgφ _{dormancy dormancy.}

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