RU2411496C2 - Method of experimental-theoretical determination of friction performance of friction pair for torque transfer and device for implementation of this method - Google Patents

Abstract

FIELD: machine building.

SUBSTANCE: tested friction pair is loaded by means of calibrated loads with torque facilitating its successive rotation in forward and reverse directions, then torques M₁ and M₂ occurring at gear rotation correspondingly in direct and reverse directions are recorded with instrument; by value of theses measurements there are evaluated friction losses in gear. Load (net) moment M_net is recorded when friction pair is idle. Moment M_r of resistance is calculated as half of difference of values between M₁ and M₂. Calculated functional dependence M_r=f(M_net) in form of two massifs of experimental values is approximated by the least-squares method with linear dependence M_r=f_fr M_net+M_i, where f_fr - is friction coefficient, M_i is moment of idle run of friction pair; M_i=F_eng·r, where F_eng is force of engagement, r is radius of friction pair. On base of obtained constants of the approximating function there is determined required functional characteristics f_fr and F_eng. The device consists of a unit-cable system with loading means in form of calibrated loads connected to it on one side, and with a drive mechanism and the recording instrument - a dynamo-metre or dynamo-graph - on another side. Further, the device consists of a frame whereon there is hinged a drive lever with a sector so, that movement of the lever is restricted with stops within boundaries of the sector. On a lower part of the sector there is secured one end of the cable going vertically to a drive pulley, enveloping it and going vertically down, when it touches a deviating unit connected to the recording instrument. On another end of the cable there are arranged the calibrating loads. The drive pulley is coupled with a shaft, on journals of which there are mounted the tested friction pairs of rotary motion; the latter are rigidly fixed on two supports secured on the frame by means of two split cases.

EFFECT: determination of friction characteristics in friction pairs for torque transfer.

4 cl, 6 dwg

Description

The invention relates to experimental-theoretical determination of the frictional characteristics of a friction pair.

There are known [1, 2, 3] methods for determining frictional losses in a pair of sliding friction, which confirm that the frictional forces in a pair of sliding friction obey the Amonton-Coulomb law [4], which seems to be a linear functional dependence

where F _FR - total frictional force, N; F _TP - friction force, N; F _sc - the strength of molecular cohesion, N; f _TP is the coefficient of friction; F _H - normal force in a pair of friction.

Dependence (1) is established for the conditions of contact of bodies on the plane. However, when creating (designing) machines, the need most often arises to evaluate frictional losses during transmission of rotational motion, which is not ensured on the basis of this dependence.

Closest to the technical nature of the present invention is a method for determining the technical condition of mechanical gears, in which the test mechanical gear is loaded with a known torque, then it is scrolled evenly during forward and reverse travel and by the difference in recorded torque values in the first and second tests and the value of the actual torque torque determine the amount of mechanical loss in the transmission [5]. However, the known method does not allow to determine the coefficient f _{TP of} friction and the force F _sc molecular cohesion in the friction pair to transmit rotational motion.

The aim of the invention is to determine the frictional characteristics (coefficient f _TP friction and force F _sc molecular cohesion) in the friction pairs to transmit rotational motion.

This goal is achieved by the fact that the tested friction pair for transmitting rotational motion is loaded with torque using calibration weights, it is rotated sequentially in the forward direction (the loads go up) and the opposite direction (the loads go down), the torques M ₁ are fixed with a recording device M _2, resulting in the transfer while rotating it respectively in forward and reverse directions, fixed load (useful) M _field in the absence of rotation of the friction pair, calculating moment M _C const otivleniya as a half value of the difference M ₁ and M _2, the resulting functional relationship M _C = f (M _floor) as two sets of experimental values is approximated by a linear dependence of the method of least squares _MS = f _TP · M _floor + M _X (2), where f _TP is the coefficient of friction; M _X is the idle time of the friction pair, M _X = F _sc · r, where r is the radius of the friction pair; and based on the obtained constants of the approximating function, the desired frictional characteristics f _TP and F _sc are determined.

The principal novelty of the proposed method is that to determine the desired characteristics using the functional dependence (2)

where M _With - the moment of resistance to rolling a pair of friction, N · m;

M _floor = F _H · r is the useful torque transmitted by the friction pair, N · m;

M _X - the idle time of the friction pair, N · m

The functional dependence (2) is derived on the basis of the Amonton-Coulomb law.

For clarity, we use figure 1, which graphically presents the interaction of forces in a pair of sliding friction to transmit rotational motion:

F _H is the normal force acting in a friction pair (the force transmitted from one element of the friction pair to transmit rotational motion to another is always normal with respect to the surface of the contacting bodies regardless of its (force) directivity in the vertical plane);

F _TP - friction force, part of the frictional forces, determined in proportion to the value of the normal force in the friction pair;

F _sc - the adhesion force, part of the frictional forces, determined by the magnitude of the molecular adhesion forces in the friction pair.

Figure 1 shows that when performing a rotational motion, the frictional forces arising in the pair are balanced by the circumferential force F _C :

Taking into account the rotational motion, it is necessary to present the parameters included in formula (3) in a new quality.

F _C = -F _FR - the circumferential force in the kinematic pair spent on overcoming the total frictional forces.

As a load indicator when transmitting rotational motion, the magnitude of the torque is used. For this purpose, we multiply the right and left sides of equation (3) by the shoulder r, on which frictional forces arise, and as a result we obtain the equation of moments

We rewrite equation (4) in a more convenient form

where M _With - the moment of resistance to rolling a pair of friction, N · m;

M _floor = F _H · r is the useful torque transmitted by the friction pair, N · m;

M _sc - the moment due to the forces of molecular cohesion, i.e. the moment that occurs when the friction pair scrolls even in the absence of useful torque. In other words, this indicator is the idle time of the friction pair, M _sc = M _X, H · m

So, we will finalize

M _C = f _TP · M _floor + M _X.

A graphical representation of the dependence (2) is presented in figure 2.

New in the proposed technical solution is that to obtain the desired parameters, a friction pair is used not of translational, but of rotational motion.

The novelty in comparison with the prototype is that the experimental values of the functional dependence M _C = f (M _floor ) are approximated by a linear function of the form (2) using the known least squares method [7]. As a result of approximating the experimental values, the constants of the approximating function are determined - f _TP and M _X , on the basis of which the magnitude of the desired frictional characteristics is then determined.

Also new is the use of the following dependencies to determine the values of M _gender and M _C. Figure 3 shows the relationship between these parameters and the values of M ₁ and M ₂ , which are fixed using a measuring device.

Figure 4 shows a device for implementing this method, General view; figure 5 is the same plan.

As a prototype for this device, a stand was adopted for implementing the method for determining the technical condition of mechanical gears [6]. The bench includes a test transmission with input and output shafts on which drive pulleys are mounted, while one pulley is connected to the calibration weights with a cable, and the second pulley is also connected to a load device (winch) using a cable. The last cable is thrown through a deflecting unit connected to a dynamometer (or dynamograph), which records the tension of the cable. Based on the registration of the tension forces of the cables on the input and output pulleys and the radii of these pulleys, the torques on the input and output shafts are determined for the forward and reverse runs of the test gear.

The main disadvantage of the prototype is that both the input and output shafts of the test gear are loaded in addition to bending torque, which creates an additional load on the supports and, therefore, excludes the possibility of using the dependence (2), which establishes the dependence of the frictional losses in the test support only under the influence of the normal force acting in it, without taking into account the additional effect of the bending moment on the drive shaft.

In the proposed device, the disadvantage of the prototype is eliminated by the fact that a pulley is installed on the drive shaft between the two test supports or, as an option, directly above the support (suspension support). Due to the absence of cantilever parts on the shaft, the possibility of bending moments on its bearings is excluded.

A drive cable is thrown over the pulley, calibration weights are installed at one end of the cable, and the other end of the cable, also directed vertically downward, is connected to the load lever. In view of this, both ends of the cable tension the system in one direction, which provides a double value of the normal force on the test supports and, accordingly, reduces the need for calibration weights.

The device consists of a frame 1, on which the drive lever 2 with sector 3 is pivotally mounted, the movement of the lever 2 within the sector 3 is limited by stops 4. On the lower part of sector 3, one end of the inextensible thread (cable) 5 is fixed, which, in contact with the deflecting unit 6 passes vertically to the drive pulley 7, wraps around the latter and descends vertically down. At the other end of the thread 5, removable calibration weights 8 are fixed.

The pulley 7 is rigidly connected to the shaft 9, on the trunnions of which the test pairs of friction of the rotational movement 10 are mounted. The latter, with the help of two detachable cases 11, are rigidly attached to two bearings 12, which are mounted on the frame 1.

The deflecting unit 6 is connected to the recording device (dynamometer or dynamograph) 13. The second eye of the recording device 13 is attached to the screw tension device 14, with which, after fixing the calibration weights 8 on the thread 5, the necessary initial tension of the measuring mechanism of the recording device 13 is established.

Figure 3 shows a chart of readings of the recording device 13: I - zero value, i.e. instrument readings in the absence of calibration weights; II - indications during the installation of calibration weights, but in the absence of movement of the tested friction pair 10 (the drive lever is fixed by the stop), in this case “a” of the scale divisions of the device is fixed; III - the readings of the device with the direct rotation of the friction pair 10 (the loads rise), in this case “b” of the scale divisions of the device 13 is fixed; IV - the readings of the device 13 during the reverse rotation of the friction pair 10 (the loads are lowered), it is fixed “in” the scale divisions of the device 13.

The operation of the device, the sequence of determining the desired parameters

The recording sequence of the recording instrument is presented in figure 3.

Position I - (there is no movement of the friction pair, calibration weights are not fixed on the cable) the zero value of the torque in the friction pair is recorded by the recording device.

In position II (calibration weights are fixed on the cable, but there is no movement of the friction pair), the value of the useful torque equal to

where m is the mass of cargo calibration cargo 8, kg; g is the value of the acceleration of gravity, m / s ² ; R is the radius of the drive pulley 7, m; ΔM is the division value of the scale of the recording device 13, N · m; and - the number of divisions on the scale of the device 13 when registering the value of M _floor . Where should

State III (goods rise)

M ₁ is the torque recorded in the friction pair 10 during the forward stroke, M ₁ = ΔM · b, where b is the number of divisions on the scale of the device when registering the moment M ₁ .

State IV (goods are lowered)

M ₂ is the torque recorded in the friction pair 10 during the reverse stroke, M ₂ = ΔM · in, where in is the number of divisions on the scale of the device when registering the moment M ₂ .

The moment M _{C of the} resistance of a pair of friction of rotation at a given useful torque M _floor

Step by step changing the mass m of calibration weights and using the sequence of actions I ... IV and dependences (6), (7), (8), we obtain the functional dependence M _C = f (M _sex ) in the form of separate experimental points. Then, approximating the array of the obtained experimental values by the least squares method by linear dependence (5), we find the constants of the approximating function f _TP , M _X , which determine the desired values of the friction characteristics of the friction pair f _TP and F _sc .

The described method and device for determining frictional losses in friction pairs allow us to find the desired parameters also for rolling friction pairs - ball and roller bearings. All dependencies and the sequence of measurements are saved. The only condition that needs to be considered is as follows.

Since there are two surfaces of contacting bodies in rolling bearings (a rolling body and an inner bearing race, a rolling body and an outer bearing race), the radius of a circle passing through the conditionally accept the action of the total circumferential resistance force in the kinematic pair centers of rolling bodies (see Fig.6).

BIBLIOGRAPHY

1. Kostetsky B.I. Friction, lubrication and wear in machines. - Kiev: Technique, 1970.

2. Kragelsky IV, Dobychin MN, Combalov B.C. Basics of friction and wear calculations. - M.: Mechanical Engineering, 1977.

3. Soloviev A.I. The efficiency of mechanisms and machines. - M.: Mechanical Engineering, 1966.

4. Colomb C.A. Theorie des mashines simples. Memoires de mathematigue de physigue l 'Akademie des sciences. 1785.V.10. P.161-331.

5. Patent No. 2037800 C1 of the Russian Federation. A method for determining the technical condition of mechanical gears / I.K.Alexandrov. - Publ. in B.I. No. 17, 1995.

6. Alexandrov I.K. A stand for determining mechanical losses in a transmission / Automotive industry. - 1996. - No. 8.

7. Korn G., Korn T. Handbook of mathematics (for scientists and engineers). - M .: Nauka, 1973, 831 s.

Claims (4)

1. The method of experimental-theoretical determination of the frictional characteristics of a friction pair of a rotational motion transmission, namely, that the tested friction pair for transmitting rotational motion is loaded with torque using calibration weights, it is rotated sequentially in the forward direction (the loads rise) and in the opposite direction ( the loads are lowered), fix with the help of a recording device the torques M ₁ and M ₂ arising in the transmission when it rotates in the forward and reverse directions, respectively directions and the magnitude of these indications evaluate frictional transmission loss, characterized in that the load (useful) moment M _{floor is} fixed in the absence of rotation of the friction pair, the moment M _{C of} resistance is calculated as half the difference between the values of M ₁ and M ₂ , the obtained functional dependence M _C = f (M _floor ) in the form of two arrays of experimental values are approximated by the least squares method with a linear dependence M _C = f _TP · M _floor + M _X , where f _TP is the coefficient of friction; M _X is the idle time of the friction pair, M _X = F _sc · r, where F _sc is the adhesion force, r is the radius of the friction pair; and based on the obtained constants of the approximating function, the desired frictional characteristics f _TP and F _sc are determined. 2. The method according to claim 1, characterized in that when using ball or roller bearings as the test pair of rolling friction pairs, the radius r is taken as the radius of the circle passing through the centers of the rolling bodies. 3. A device for determining the frictional characteristics of a friction pair, containing a block-cable system, to which, on the one hand, a load device is connected in the form of calibration weights, and on the other hand, the drive mechanism and the recording device are a dynamometer or dynamograph, characterized in that it consists of frame, on which the drive lever with the sector is pivotally mounted so that the movement of the lever within the sector is limited by stops, one end of the cable is fixed on the lower part of the sector, which is in contact with the pivotally connected with a recording device, the deflecting unit passes vertically to the drive pulley, wraps it around and descends vertically downwards, calibration weights are fixed on the other end of the cable, the drive pulley is rigidly connected to the shaft, on the trunnions of which are tested rotational friction pairs, the latter are rigidly connected with two detachable cases attached to two supports that are mounted on the frame. 4. The device according to claim 3, characterized in that the recording device with a second eye is connected to a screw tensioner.

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