RU2507423C2 - Method for determining operating parameters at quasi-linear law of their change in band-and-shoe brakes of boring winches - Google Patents

Abstract

FIELD: machine building.

SUBSTANCE: at quasi-linear law of change of rotation frequency of a brake pulley from the steady-state value to zero at startup of a loaded elevator the operating parameters of a band-and-shoe brake, which are included in the first group, are determined in the following sequence: the brake pulley rotation mode is evaluated; then, braking time, tension of a tight strand of a brake band, maximum and minimum specific loads in friction pairs, a brake moment developed by friction assemblies are determined; besides, brake moment reserve coefficient, power consumption of friction assemblies, forces applied by a drill man to a brake control lever, and efficiency coefficient of the brake are determined. Then, subsequent determination of operating parameters included in the second, the third and the fourth groups relative to a band-and-shoe brake of the boring winch takes place.

EFFECT: possible determination of operating parameters at quasi-linear law of their change in band-and-shoe brakes with interconnected power, thermal and wear-friction properties of their friction pairs and limiting allowable restrictions of speed, dynamic and thermal modes, which provide serviceable state of a boring winch brake system.

4 cl, 34 dwg

Description

The invention relates to mechanical engineering and can be used in tape-shoe brakes of drill hoists.

A known method for determining the operational parameters of serial tape-shoe brakes of drawworks, in which friction linings are attached to the brake band. The operational parameters are as follows: tension force of the running branch of the brake band; maximum and minimum specific loads arising in friction pairs; braking moment developed by friction pairs; energy intensity of friction pairs; general deformation of the elements of the brake system; forces exerted by the driller to the brake control lever; the duration of the braking cycle, etc. [1, 2, analogue]. However, these methods of determining operational parameters are not subject to the linear law of changing the speed of the brake pulley from a steady value to zero.

There is a method of heating, natural and forced cooling of brake pulleys of tape and shoe brakes of drawworks to determine the amount of heat that is generated, accumulated and dissipated into the environment from matte and polished surfaces of brake pulleys [2, prototype]. However, these methods do not indicate patterns according to which heat is accumulated in the body of the brake pulley and dissipated from its surfaces.

The objective of the invention is the development of a method for determining operational parameters with a quasilinear regularity of their change in band brakes with the interconnected power, thermal and wear-friction properties of their friction pairs and limiting permissible limitations of speed, dynamic and thermal conditions that ensure the working state of the winch brake system.

Compared with the analogue and prototype, the proposed methods for determining the operational parameters with a quasilinear regularity of their change in the band brake shoe winches have the following advantages:

- allows you to sequentially switch from the first to the fourth group of operational parameters of tape-shoe brakes taking into account their friction pairs, friction units and design features with a number of limitations;

- the presence of restrictions relating not only to the power and thermal load of the friction brake assemblies, but I have limitations with respect to the whole brake system;

- allows you to establish a relationship between the operational parameters of the tape-shoe brake, which evaluate the speed, dynamic and thermal conditions both for the main elements and for the whole brake system;

- allows you to track the influence of the previous operational parameter on the next, especially with regard to the wear-friction properties of brake friction pairs.

This goal is achieved by the fact that in a band brake with a quasilinear law of changing the speed of the brake pulley from a steady value to zero during the descent of a loaded elevator, the operational parameters are summarized in the first group as applied to the drawbar brake of a drawworks in the following sequence: brake pulley rotation mode; determine: braking time; tension of the running branch of the brake belt; maximum and minimum specific loads in friction pairs; braking torque developed by friction units; safety factor of braking torque; energy intensity of friction units; forces exerted by the driller to the brake control lever; brake efficiency. The definition of operational parameters, summarized in the second group as applied to the drawbar brake of a drawworks, is performed in the following sequence: safety factor for the cross section of the brake band; deformation of the brake belt when the friction lining is placed on an arc of its girth with variable and constant pitch; radial deformation of the friction lining; evaluate the total deformation of the elements of the brake system.

Determination of operational parameters, summarized in the third group as applied to the drawbar brake of a drawworks, is carried out in the following sequence: heat, temperatures and their distribution over the thickness of the pulley rim with a quasilinear pattern of specific loads in the friction brake assemblies; the intensity of heat from the surfaces of the brake pulley; heat flux distribution coefficient between the elements of the brake pulley and the friction lining. With quasilinear laws of change: rotational speed of the brake pulley from a steady value to zero; deformations of the brake belt and the amount of generated, accumulated and dissipated heat from the friction assemblies during the descent of the elevator, the pattern of wear of the working surfaces of the friction linings (fourth group) is likened to the patterns of changes in the specific loads in the friction pairs of the brake, and the thermal condition of the friction assemblies predominates the brakes.

от угла обхвата (α) накладками рабочей поверхности тормозного шкива (1 - 9,48°; 2 - 37,5°; 3 - 50°; 4 - 75°; 5 - 90°; 6 - 135°; 7 - 180°; 8 - 225°; 9 - 270°) и коэффициента трения между ними в серийных ленточно-колодочных тормозах буровых лебедок; на фиг.11 показаны закономерности изменения средних значений удельных нагрузок (р) при постоянном (1) и переменном (2) коэффициенте трения при взаимодействии поверхностей накладок с поверхностью шкива по длине тормозной ленты в ленточно-колодочном тормозе БУ-2500 ЭП; на фиг.12 и 13 проиллюстрированы динамика изменения удельных нагрузок (p) и их неравномерности (Δp) по ширине накладок (n) вдоль тормозной ленты в ленточно-колодочном тормозе БУ-2500 ЭП; на фиг.14 и 15 показаны закономерности распределения долевых тормозных моментов, создаваемых каждой фрикционной накладкой, при постоянном $$\left(M_{f_c}\right)$$

и переменном $$\left(M_{f_v}\right)$$

коэффициентах трения и динамика распределения их разности (ΔM) по длине ленты ленточно-колодочного тормоза БУ-2500 ЭП; на фиг.16 проиллюстрирована закономерность изменения работы трения (А), создаваемой фрикционными узлами тормоза, от скорости замедления (ε) его тормозного шкива (при условии построения кривых 1, 2 и 3, что ε₁>ε₂, а ε₂<ε₃); на фиг.17 представлена номограмма для выбора усилия (F_p), прикладываемого бурильщиком к рукоятке рычага управления тормозом, в зависимости от количества свечей (N), скорости спуска инструмента (ω) и энергоемкости $$\left(P_{r_{Ш}}\right)$$

, которая реализуется фрикционными узлами тормоза буровой лебедки У2-5-5; на фиг.18, 19, 20 показаны схемы сил, действующие: в узле «накладка-лента»; на участке ленты над i-ой накладкой; при определении деформаций участков ленты; на фиг.18, 19 и 20 использованы следующие буквенные и цифровые обозначения: dN, N_i - приращение нормального усилия и его i-oe значение; dF_i, F_i - приращение силы трения и ее i-ое значение; 2 - тормозная лента; 3 - фрикционная накладка; на фиг.21 представлены закономерности изменения относительных деформаций (ε₁) участков тормозной ленты при расположении по дуге ее обхвата фрикционных накладок с постоянным (1, 1') и переменным (2, 2') шагом: расчетные (1, 2) и экспериментальные (1', 2') данные: 1-8 и

- нумерация зазоров между накладками; на фиг.22, 23 и 24 показаны: уточненная схема ленточно-колодочного тормоза; расчетная схема тормоза и положение кривошипа в тормозе; на фиг.25 проиллюстрирована закономерность перемещения сбегающих концов тормозных лент в зависимости от угла поворота рычага управления тормоза; на фиг.26 приведена номограмма для определения угла поворота кривошипа (β) в зависимости от усилия натяжения сбегающей ветви тормозной ленты (прямые 7, 11; 8, 12; 9, 13 и 10, 14-40, 30, 20 и 10 кН), угла ее обхвата (α) и удельной нагрузки (кривые 1, 4; 2, 5 и 3, 6-1,0; 2,5 и 3,6 МПа) при постоянном (4-10) и переменном (1-3, 11-14) коэффициентах трения во взаимодействующих парах трения ленточно-колодочного тормоза БУ-2500 ЭП; на фиг.27 и 28 показаны закономерности изменения скорости скольжения (υ) на фрикционном контакте, поверхностной температуры (t) и температурного градиента (grad t) в металлическом фрикционном элементе при единичном торможении по времени (τ_Т) на четырех периодах процесса в случае, когда температура поверхности трения не превышает и превышает допустимую для материала фрикционной накладки; на фиг.29 представлена диаграмма роста поверхностной температуры правого (кривая 1) и левого (кривая 2) тормозного шкива при спуске колонны бурильных труб (5, 10, 20…70 - количество свечей, имеющих диаметр 141 мм и длину 25 м - обозначено ступенчатой волнистой кривой) до глубины 1800 м в зависимости от времени спуска и их остывания (кривая 3); на фиг.30 показан перепад температур по толщине обода тормозного шкива для случаев: 1 - внутренняя поверхность обода шкива покрыта теплоизоляцией; изготовления обода тормозного шкива из материалов: 2 - стали 35ХНМ; 3 - стали 35; 4 - меди; на фиг.31 представлена зависимость коэффициента линейного расширения стали от температуры; на фиг.32 проиллюстрирована закономерность увеличения диаметра шкива ленточно-колодочного тормоза буровой лебедки У2-5-5 в результате теплового расширения; на фиг.32 проиллюстрирована закономерность изменения коэффициента трения серийного углеродного фрикционного композиционного материала (УФКМ) типа «Тармар» в зависимости от удельных нагрузок и температуры на поверхности трения, полученные на машине трения 2168УМТ «Унитриб»; на фиг.34 проиллюстрирована закономерность изменения линейного износа серийных УФКМ типа «Тармар» в зависимости от удельных нагрузок и температуры на поверхности трения, полученные на машине трения 2168УМТ «Унитриб».Figure 1 shows the kinematic diagram of a drawworks; figure 2 shows a kinematic diagram of the tape-shoe brake of a drawworks; figure 3 section along AA figure 2 is a transverse section of the friction unit of the brake; 4 and 5 show the arrangement of friction linings on the brake belt with constant and variable pitch; figure 6 illustrates the pattern of change in the angular velocity of the brake pulley (ω) when it is braking from time (τ); Figures 7 and 8 show the pattern of change in the average value of the coefficient of friction (f) and its uneven distribution (Δf) along the width of the friction linings (n) along the tape in the tape-block brake BU-2500 EP; figure 9 shows the pattern of change in the efforts of the tension of the tape (5) along the length of the tape at a constant (1) and variable (2) coefficient of friction in the friction brake assemblies BU-2500 EP; figure 10 presents the patterns of change in the ratio $$\raisebox{1ex}{$S_H$}\!\left/ \!\raisebox{-1ex}{$S_C$}\right.=e^{f\alpha }$$

from the angle of coverage (α) by the lining of the working surface of the brake pulley (1 - 9.48 °; 2 - 37.5 °; 3 - 50 °; 4 - 75 °; 5 - 90 °; 6 - 135 °; 7 - 180 ° ; 8 - 225 °; 9 - 270 °) and the coefficient of friction between them in serial tape-shoe brakes of drill winches; figure 11 shows the patterns of change in the average values of specific loads (p) at a constant (1) and variable (2) coefficient of friction during the interaction of the surfaces of the linings with the surface of the pulley along the length of the brake band in the tape-shoe brake BU-2500 EP; on Fig and 13 illustrates the dynamics of changes in specific loads (p) and their unevenness (Δp) along the width of the linings (n) along the brake band in the tape-shoe brake BU-2500 EP; on Fig and 15 shows the patterns of distribution of the shared braking moments created by each friction lining, with a constant $$\left(M_{f_c}\right)$$

and variable $$\left(M_{f_v}\right)$$

friction coefficients and dynamics of the distribution of their difference (ΔM) along the length of the tape of the tape-block brake BU-2500 EP; Fig. 16 illustrates the pattern of change in the work of friction (A) created by the friction brake assemblies on the deceleration rate (ε) of its brake pulley (provided that curves 1, 2 and 3 are constructed that ε ₁ > ε ₂ and ε ₂ <ε ₃ ); on Fig presents nomogram for selecting the force (F _p ) applied by the driller to the handle of the brake control lever, depending on the number of candles (N), the speed of the tool (ω) and energy consumption $$\left(P_{r_W}\right)$$

, which is implemented by friction brake assemblies of the U2-5-5 winch; on Fig, 19, 20 shows a diagram of the forces acting: in the node "pad-tape"; on the tape section above the i-th pad; when determining the deformation of the tape sections; in FIGS. 18, 19 and 20, the following alphanumeric designations are used: dN, N _i — increment of the normal force and its i-oe value; dF _i , F _i - increment of the friction force and its i-th value; 2 - a brake tape; 3 - friction lining; on Fig presents the patterns of change in the relative deformations (ε ₁ ) of the sections of the brake belt when the friction linings are arranged along the arc of its girth with a constant (1, 1 ') and a variable (2, 2') step: calculated (1, 2) and experimental (1 ', 2') data: 1-8 and

- numbering of gaps between overlays; on Fig, 23 and 24 shows: an updated diagram of the tape-shoe brake; design calculation of the brake and the position of the crank in the brake; on Fig illustrates the pattern of movement of the runaway ends of the brake bands, depending on the angle of rotation of the brake control lever; Fig.26 shows a nomogram for determining the angle of rotation of the crank (β) depending on the tension force of the runaway branch of the brake band (straight lines 7, 11; 8, 12; 9, 13 and 10, 14-40, 30, 20 and 10 kN) , its girth angle (α) and specific load (curves 1, 4; 2, 5 and 3, 6-1.0; 2.5 and 3.6 MPa) with constant (4-10) and variable (1-3 11-14) the friction coefficients in the interacting friction pairs of the tape-shoe brake BU-2500 EP; on Fig and 28 shows the patterns of change of sliding speed (υ) at the frictional contact, surface temperature (t) and temperature gradient (grad t) in the metal friction element with a single time braking (τ _T ) for four periods of the process, when the temperature of the friction surface does not exceed and exceeds the allowable for the material of the friction lining; on Fig presents a growth chart of the surface temperature of the right (curve 1) and left (curve 2) brake pulley when lowering the drill pipe string (5, 10, 20 ... 70 - the number of candles having a diameter of 141 mm and a length of 25 m is indicated by a step wavy curve) to a depth of 1800 m depending on the time of descent and their cooling (curve 3); on Fig shows the temperature difference across the thickness of the rim of the brake pulley for cases: 1 - the inner surface of the rim of the pulley is covered with thermal insulation; manufacturing the brake pulley rim from materials: 2 - 35XHM steel; 3 - steel 35; 4 - copper; on Fig presents the dependence of the coefficient of linear expansion of steel on temperature; on Fig illustrates the pattern of increasing the diameter of the pulley of the band brake shoe winch U2-5-5 as a result of thermal expansion; on Fig illustrates the pattern of change in the coefficient of friction of a serial carbon friction composite material (UFKM) type "Tarmar" depending on the specific loads and temperature on the friction surface obtained on a friction machine 2168UMT "Unitrib"; on Fig illustrates the pattern of linear wear of serial UFKM type "Tarmar" depending on the specific loads and temperature on the friction surface obtained on a friction machine 2168UMT "Unitrib".

According to figures 1, 2, 3 and 22, the tape-shoe brake contains brake bands 2 on which friction linings 3 can be mounted with a variable (figure 4) and constant (figure 5) step. The brake bands 2 have a running (I) and a running (II) branch, which are subject to tension S _H and S _C. On the side of the runaway branch (II), the brake bands 2 are attached to the balancer 11 through the rods 13 and 14, and on the side of the branches (I) running on them, to the connecting rod journals 6 of the crankshaft 10. The latter also has cranks 9 and 12 with a radius r. A brake control lever 1 is connected to the crankshaft 10, to which a driver F _p is applied to one of the connecting rod necks 6 of the crankshaft 10, the rod of the pneumatic cylinder 8 is connected, which is connected to the compressed air network through a valve 7. The brake bands 2 with the linings 3 during operation of the brake interact with the pulleys 4 that are installed on the brakes interact with the pulleys 4 that are mounted on the drum 5. The last rope is wound (not shown in figure 1), included in the hoist system of the hoisting complex drilling rig.

Serial tape-shoe brakes of a drawworks operate as follows. By moving the handle 1, the crankshaft 10 is rotated, as a result of which the driller tightens the brake belts 2 with friction linings 3 and they sit on the brake pulleys 4. The tape-block brake is characterized by the following stages: initial (first), intermediate (second) and final (third). Let us dwell on each of the stages separately.

At the initial stage of braking, the friction linings 3 located in the middle part of the brake belt 2 interact with the working surface of the brake pulley 4. The front of interaction extends towards the friction linings 3 of the running branch (I) of the brake belt 2.

The intermediate stage of braking is characterized by the further spread of the interaction front towards the friction linings 3 of the runaway branch (II) of the brake belt 2.

The final stage of braking is characterized by the fact that almost all the fixed pads 3 of the brake belt 2 interact with the working surface of the rotating pulley 4. During braking, the sequence of friction surfaces coming into contact is repeated. The complete braking cycle is completed by stopping the brake pulleys 4 with the drum 5. The control of the winch brake is also carried out by supplying compressed air through the driller's valve 7 to the pneumatic cylinder 8, the rod of which is connected to one of the connecting rod journals of the crankshaft 10 of the brake. The pressure value of the compressed air in the pneumatic cylinder 8 is regulated by turning the crane 7 of the driller.

When uneven wear of the friction linings 3 mounted on the belts 2, the balancer 11 at the time of braking slightly deviates from the horizontal position and evens the load on the runaway branch (II) of the brake belts 2, while ensuring uniform and simultaneous girth of the brake pulleys 4. Thanks to ball joints the transfer of loads from the brake bands 2 to the balancer 11 is not changed.

It is known that the friction nodes of the brake and the rope of the hoist system of the hoisting complex of the drilling rig are experiencing the greatest loads when the drill string is lowered into the well.

By changing the weight of the drill pipe string that is lowered into the well in the drilling rig, and with it the high-speed, dynamic and thermal conditions of the friction units and mechanical drive units, and as a result, the wear-friction properties of their friction pairs.

We show that there is a significant relationship between the friction processes during the interaction of the working surfaces of the linings with the working surface of the brake pulley with the parameters of the mechanical system of the drawbar brake of the drawworks ensuring their operability.

The equation of dynamic equilibrium during the descent of a loaded elevator has the form

$$M_{\mathrm{from}t}-M_T-M=I_{b.\mathrm{at}.}\frac{d\omega }{dt},\left(\mathrm{one}\right)$$

- угловое ускорение (замедление) барабанного вала лебедки.where M _article - static moment on the drum shaft of the winch from the weight of the drill string; M _T , M - braking moments developed by hydrodynamic and tape-shoe brakes; I _b.v. - the moment of inertia of the drum shaft of the winch and the masses brought to it; $$\frac{d\omega }{dt}$$

- angular acceleration (deceleration) of the drum shaft of the winch.

An analysis of equation (1) shows that in the process of operational control, a driller can affect the nature of the process only by changing M _T and M. However, if drilling is carried out up to 1500-1700 m, then the drill string is run by the driller without using a hydrodynamic brake. The shape of the process tachogram changes only due to a change in M, i.e. there is a law of reducing the speed of the system from a steady value to zero.

The variety of descent modes of the loaded elevator showed that the use of the tape-shoe brake can be reduced to three types of modes: quasilinear, quasicosinusoidal and quasiparabolic laws of speed reduction in the deceleration section.

The shape of the tachogram in the deceleration section is ultimately determined by the effective value of the braking torque developed by the band brake, which, in accordance with equation (1), has the form

$$M=M_{\mathrm{from}t}-I_{b.\mathrm{at}.}\frac{d\omega }{dt}.\left(2\right)$$

Let us dwell on the quasilinear law of reducing the speed of the brake pulley in the deceleration section during the descent of the loaded elevator and establish its effect on the operational parameters of the winch belt brake shoe (without taking into account the braking torque developed by the hydrodynamic brake). In this case, the operating parameters of the brake system are grouped as follows:

first group:

- rotation mode of the brake pulley;

- braking time;

- the tension of the branches of the brake tape;

- patterns of changes in specific loads in friction pairs;

- patterns of change in braking moments in friction pairs;

- safety factor of braking torque;

- patterns of change in the friction friction units;

- energy intensity of friction units;

- the force exerted on the brake control lever;

- coefficient of performance;

second group:

- safety factor of the cross section of the brake tape;

- deformation of the brake tape;

- deformation of the friction lining;

- general deformation of the elements of the brake system;

third group:

- heat, temperature and their distribution over the thickness of the rim of the brake pulley;

- heat transfer rate;

- distribution coefficient of heat flux in the friction brake assemblies;

- thermal deformation of the rim of the brake pulley and friction lining;

fourth group:

- wear of the working surfaces of the friction linings from the mechanical and thermal factors.

Consider the first group of operational parameters of the tape-shoe brake, provided that when the loaded elevator is lowered, a quasilinear law of pulley speed reduction in the deceleration section takes place.

FIRST GROUP OF OPERATIONAL PARAMETERS

Brake pulley rotation mode

The change in the coefficient of friction, friction forces, specific loads and braking torque depends on the shape of the tachogram, i.e. from patterns of change in the angular speed of the brake pulley (from steady-state ω ₀ at the beginning of the braking process to zero). Of the existing variety of loading modes of the friction units of the tape-shoe brake, the most frequently encountered under operating conditions is the quasilinear law, the tachogram of which is described by the dependence of the form

$${\omega }_{\mathrm{one}}={\omega }_0\left(\mathrm{one}-\frac{t}{t_{\mathrm{TO}}}\right),\left(3\right)$$

where ω ₁ , ω ₀ and t are the current and initial value of the angular velocity of the brake pulley and the implementation time of the first; ω ₀ = ε _m t _k , ε _m - deceleration of the brake pulley; t _to - the duration of the braking process.

Figure 6 illustrates the pattern of change in the angular velocity of the pulley during its braking in time.

Braking time

The braking time of the tape-block brake depends on the current weight of the drill string being lowered (G), the type of winch (I _b.v. - moment of inertia of the drum shaft of the winch and the masses brought to it; R - design radius of the drum shaft of the winch) and wear-friction properties of brake friction pairs, brake efficiency (η _L.Т. ), multiplicity of the tackle system (i) and its coefficient of efficiency (η _T.S. ), type of well. The braking time of the tape-shoe brake is determined mainly experimentally. Approximately, analytically, the braking time is determined by the dependence of the form

$$t_{\mathrm{to}}=\frac{2l}{{\upsilon }_c},\left(\mathrm{four}\right)$$

where l is the length of one candle; υ _c is the linear velocity of the descent of the candle.

Tension of branches of a brake tape

One of the main operational parameters of tape brake shoes is the tension of the running (S _H ) and running (S _C ) branches of the brake belt, the difference of which is the friction force (F _T ). The latter is determined in a similar way for sections of the brake belt above each lining that represents a separate brake device assembly. In this case, one of the tension of the brake tape is specified by a certain value, and the second is determined. Basically, the tension of the running branch of the brake belt is determined by the well-known Euler dependence

$$S_H=S_C{e}^{f\alpha },\left(5\right)$$

where e is the base of the natural logarithm; α is the angle of coverage of the pulley plates; f is the coefficient of sliding friction in a pair of "friction lining-brake pulley".

It is known that when calculating the operational parameters of tape and shoe brakes of drawworks, average values of the friction coefficient from a certain interval for a given pair of friction are used. For example, for materials FK-24A - 35KHNL steel it is 0.3-0.4. The performed calculations with the values of the coefficient of friction of 0.3; 0.35 and 0.4 (the difference between the upper and lower values of the coefficient of friction is 25%), do not give reliable information about the dynamic loading of friction pairs of the brake. Therefore, to compare the calculation results for estimating the braking moment developed by each friction lining located on the arc of the brake belt, when interacting with the working surface of the brake pulley, it is necessary to have values of a certain average coefficient of friction for all pairs of “pulley-lining”, as well as a variable coefficient friction, which is the functional dependence of the coefficient of friction on the specific load, surface temperature, sliding speed and other destabilizing factors and intercepts a certain range of variation of the friction coefficient. The coefficient of friction is determined by the known methods of Kragelsky I.V., Chichinadze A.V., Mirzadzhanova DB, Dzhanakhmetova A.Kh. and other scientists.

Figure 7 shows the change in the average value of the coefficient of friction and its uneven distribution (Fig. 8) along the width of the friction linings along the brake band in the tape-shoe brake BU-2500 EP. Hereafter, from the first to the tenth number - the friction lining of the runaway branch of the brake band, and from the 11th to the 20th - on the run. From Fig.7 it follows that the coefficient of friction is 0.345 under the first plate in a pair of friction and smoothly drops to 0.25 on the twentieth plate. As for the uneven change in the coefficient of friction along the width of the linings along the brake band (Fig. 8), the following picture took place here. On the runaway branch of the tape, bursts of unevenness of the change in the coefficient of friction were as follows; maximum - on the 2nd and 3rd overlays; the middle ones on the 4th, 5th, 9th and 10th overlays and the minimum ones on the 1st, 6th, 7th and 8th overlays. The following was observed on the runaway branch of the belt: maximum deviations of the friction coefficient on the 12th, 13th, 14th and 18th linings, average ones on the 16th and 19th linings; minimal - on the 11th, 15th, 17th and 20th overlays.

Figure 9 presents the results of the tension of the brake band over each brake lining at constant (1) and variable (2) values of the coefficient of friction. From these curves it follows that curve 2 passes slightly higher and more than curves 1, i.e. with a variable coefficient of friction in pairs of "pad-pulley" is realized large tension of the brake belt. Here you can see that the change in tension along the length of the tape over the 5th and up to the 16th lining is almost constant and equal to the maximum value, and to the ends of the branches of the tape over the 1st to 4th and over the 16th to the 20th minimum values.

We show the influence of the girth angle of the plate (α) of the working surface of the pulley and the friction coefficient between them on the value of the ratio S _H / S _C. Figure 10 shows the dependence of the ratio S _H / S _C = e ^fα on the angle of ^coverage of the friction linings of the working surface of the brake pulley and the friction coefficient. From this graphical dependence it follows that with an increase in α and f, the ratio increases sharply, which leads to a significant difference in the specific loads between the friction pairs of the running and running branches of the brake belt, despite the fact that with an increase in the angle of circumference of each pulley plate, the difference in specific loads between the running and running surfaces of the friction linings is reduced.

Specific loads in friction pairs

In a tape-shoe brake with friction linings located on the brake belt, the maximum specific loads occur in the friction pairs “slip-pulley” are determined by the dependence of the type

$$p_{\max }=\frac{2S_H}{R_w{b}_{\mathrm{one}}}\le \left[p\right],\left(6\right)$$

where R _W - the radius of the working surface of the brake pulley; b ₁ - the width of the friction lining; [p] - permissible value of the specific load for the material of the pad.

The minimum specific loads arising in the friction pairs of the brake are determined by the dependence of the type

$$p_{mix}=\frac{2S_C}{R_w{b}_{\mathrm{one}}}.\left(7\right)$$

The patterns of change in the average values of specific loads at a constant (1) and variable (2) coefficient of friction during the interaction of the surfaces of the linings with the surface of the pulley along the length of the brake belt are shown in Fig. 11. From the graphical dependencies it follows that the difference between the specific loads under the linings located at the ends of the brake band (1-5th and 19-20th) is insignificant, and under the other linings it changes by almost a constant value.

On Fig illustrates the dynamics of changes in specific loads under each friction lining, divided into five zones along the length of the brake belt, and the unevenness of their changes is shown in Fig. 13. The maximum specific loads, varying from 1.65 to 1.75 MPa, act on the 20th plate, and the minimum - from 0.4 to 0.435 MPa - on the first. As for the non-uniformity of changes in specific loads along the length of the tape, the greatest non-uniformity is observed under the oncoming branch of the tape: the maximum values are on the 13th, 16th, 18th and 19th overlays; the average values are on the 12th, 14th, 15th and 20th linings and the minimum are on the 11th and 17th linings. The overlays of the runaway branch of the tape do not have such large bursts of unevenness in the change in specific loads, except for the 10th lining. Comparisons of the values of the non-uniformity of changes in specific loads are observed on the 2nd, 3rd, 4th, 5th, 6th, 7th, and 9th overlays, and the minimum - only on the 1st and 8th overlays.

Braking moment

An assessment of the loading of the brake tape branches with the linings, as well as a review of each lining with a portion of the brake belt above it, allows us to state that the latter is a separate brake device, which, depending on its geometric position, develops different braking torque.

и переменном $$\left(M_{f_v}\right)$$

коэффициентах трения по длине тормозной ленты. Если изобразить в виде графических зависимостей М=f(α) при постоянном и переменном коэффициенте трения, то с математической точки зрения построенные кривые будут представлять собой продифференцированную по углу обхвата шкива лентой с накладками зависимость тормозного момента, а площадь под соответствующей кривой будет равна суммарному тормозному моменту, создаваемого ленточно-колодочным тормозом.On Fig illustrates the distribution of the shared braking moments created by each friction lining, with a constant $$\left(M_{f_c}\right)$$

and variable $$\left(M_{f_v}\right)$$

coefficients of friction along the length of the brake belt. If we depict M = f (α) in the form of graphical dependences at a constant and variable coefficient of friction, then from the mathematical point of view, the curves constructed will be the dependence of the braking moment, differentiated by the angle of the pulley’s circumference with a strip with overlays, and the area under the corresponding curve will be equal to the total braking the moment created by the tape-shoe brake.

From the analysis of the distribution of shared braking moments, it is seen that each lining located on the runaway branch of the brake belt has a greater braking torque with a variable coefficient of friction than with a constant one. This is due to the fact that on the runaway branch of the belt, the specific loads in the friction pairs are minimal, therefore the friction coefficient f = 0.345-0.31 (Fig. 7) is larger in terms of the average value f = 0.308. As the specific loads in the friction pairs increase from the ribbon running towards the runaway branch, the friction coefficient decreases and becomes lower than the average value (f = 0.307-0.253), however, the braking moment to the 14th lining with a constant coefficient of friction remains large braking moment with its variable value . On the 14th pad, the braking moments are equal, and then there is an increase in braking torque with a variable coefficient of friction. From the diagram of the distribution of braking moments on the strip of the tape it follows that the total braking torque with variable f is 67.55 kNm, and with a constant coefficient of friction - 67.672 kNm, i.e. their difference is 0.122 kNm.

при переменном и постоянном коэффициентах трения, создаваемых каждой парой трения тормоза.On Fig shows the dynamics of the distribution of the difference in braking moments $$\left(\Delta M=M_{f_v}-M_{f_c}\right)$$

with variable and constant friction coefficients created by each brake friction pair.

Let us analyze the difference ΔM, which takes place on the overlays of the runaway branch of the tape. The difference in braking torque is positive and reaches its maximum value on the 10th pad. On the running branch of the tape, the difference between the braking moments decreases and on the 14th lining it is zero and then until the 20th lining it is negative, since, as noted above, the braking moment developed by the overlays of the running branch of the tape is less with a variable than with a constant coefficient of friction .

The braking torque developed by the friction units of the band brake shoe is determined by the type

$${\displaystyle \sum _n^{i=\mathrm{one}}{M}_T=}{\displaystyle \sum _n^{i=\mathrm{one}}{F}_T\cdot R_w},\left(8\right)$$

where F _T is the friction force arising on the interaction surfaces of the friction brake assemblies.

Developed braking torque by friction pairs, must be compared with the greatest braking torque, determined from the condition of applying breaking strength to the hoist rope

$$M_{T_{\max }}=\frac{F_{T_{\mathrm{to}}}}{\left[k_{\mathrm{to}}\right]}\left[r_b+a_{\mathrm{one}}\left(z_{\mathrm{one}}-\mathrm{one}\right)\right];\left(9\right)$$

$$M_{T_{\max }}>>M,\left(10\right)$$

- разрывная нагрузка талевого каната; [k_к] - коэффициент запаса прочности каната; r_b - радиус навивки каната на барабан лебедки; a ₁ - расстояние между центрами сечений канатов в смежных слоях их навивки; z₁ - количество слоев навивки каната на барабан лебедки.Where $$F_{T_{\mathrm{to}}}$$

- breaking load of the hoist rope; [k _to ] is the safety factor of the rope; r _b is the radius of the winding of the rope on the winch drum; a ₁ - the distance between the centers of the cross sections of the ropes in adjacent layers of their winding; z ₁ - the number of layers of winding the rope on the winch drum.

Safety factor

The safety factor of the braking torque (β _m ) is determined using the dependence of the form

$${\beta }_m=\frac{M_T}{M_{\mathrm{from}t}}\le \left[{\beta }_m\right],\left(\mathrm{eleven}\right)$$

where M _article - static moment on the drum shaft of the winch from the weight of the drill string; [β _m ] - the allowable value of the safety factor of the braking torque.

The magnitude of the possible dynamic loads in the elements of the hoisting mechanism largely depends on the safety factor of the braking torque, which is taken into account when designing the brake systems. The larger this coefficient, the slower the braking to be carried out with greater deceleration, and therefore, large specific loads in the friction pairs and a greater amount of heat will be generated on their surfaces, as well as large dynamic loads can occur in the rope. The safety factor of the braking torque is taken equal to k = 1.5-2.0. However, a rigorous justification of the value of this coefficient in the literature is not given, therefore, its value is chosen for reasons of safety of hoisting operations.

The safety factor of the braking torque of the tape-shoe brake mainly depends on the mass of the winch drum brought to the hook. A significant part of the excess braking torque is spent on damping the kinetic energy of the rotating winch drum, and not the descent drill pipe string. When determining the safety factor of the braking torque, one should proceed from the optimal value of deceleration provided by the band brake, both from the point of view of the emerging dynamic loads and the time required for the braking operation.

If we reduce the reduced mass of the winch drum by 35-45%, then the safety factor of the braking torque will be k = 2.0-2.1, and tape-shoe brakes in this case will provide maximum deceleration of the loaded hook ε = 1.5 m / from ² .

Friction work

The friction during braking of the brake pulley is described by the equation

$$A={\displaystyle \underset{0}{\overset{t_{\mathrm{to}}}{\int }}M\omega dt},\left(12\right)$$

where M and ω are the current values of the braking torque and the angular speed of the pulley.

The dependence of the friction during braking of the brake pulley from its deceleration is presented in Fig.16.

Energy intensity of brake friction assemblies

The energy intensity of the friction units of the band brake shoe is determined after the completion of the braking process

$$P_{r_w}=\frac{R_{m}n{R}_w^2{b}_{\mathrm{one}}\alpha f_{\mathrm{one}}{V}_{r_{\mathrm{to}}}{i}_{\mathrm{one}}\cdot {10}^3}{r_{H_{\max }}}\le \left[P_{r_w}\right],\left(13\right)$$

- средние удельные нагрузки на поверхностях пар трения; А₁=nb₁R_шα - теоретическая площадь взаимодействия внутренних поверхностей фрикционных накладок и рабочей поверхности тормозного шкива; $$V_{r_{к}}$$

- средняя скорость спуска нагруженного элеватора, которая зависит от длины свечи, спускаемой в скважину; i₁ - передаточное отношение механического привода тормоза; $$r_{H_{\max }}$$

- максимальный радиус навивки каната на барабан.Where $$p_m=\frac{p_{\max }+p_{\min }}{2}$$

- average specific loads on the surfaces of friction pairs; And ₁ = nb ₁ R _w α - the theoretical area of interaction of the inner surfaces of the friction linings and the working surface of the brake pulley; $$V_{r_{\mathrm{to}}}$$

- the average speed of the descent of the loaded elevator, which depends on the length of the candle, lowered into the well; i ₁ - gear ratio of the mechanical brake drive; $$r_{H_{\max }}$$

- the maximum radius of the winding of the rope on the drum.

.Permissible power consumption of friction units of the tape-shoe brake $$\left[P_{r_w}\right]=800\frac{\mathrm{to}\mathrm{<figure-callout\; id="2"\; label="AT\; t\; m"\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">AT\; </figure-callout>}t}{m^{}}$$

.

The force exerted on the brake control lever

The efforts exerted by the driller to the control lever of the tape-block brake is determined by the dependence of the type

$$F_p=S_C\frac{k_{\mathrm{to}}\left[r_b+{\alpha }_{\mathrm{one}}\left(z-\mathrm{one}\right)\right]}{\left(e^{n\alpha f\frac{R_w}{R_0}}-\mathrm{one}\right)R_w\cdot i_{\mathrm{one}}\cdot \eta }\le \left[F_p\right],\left(\mathrm{fourteen}\right)$$

where R ₀ is the radius of the inner surface of the brake tape; η is the efficiency of the mechanical brake drive.

In this case, the allowable force exerted by the driller to the brake control lever is [F _p ] = (300-400) N.

буровой лебедки У2-5-5. Порядок определения F_p на фиг.17 показано пунктирными линиями (N=30 свечей; ω=10 с^-1; F_p=300 Н и $$P_{r_{ш}}=3225$$

кВт/м²).Fig. 17 shows a nomogram for selecting the force F _p , which is applied to the brake control lever and allows controlling the descent of the drill string, consisting of the N-th number of candles due to changes in the angular velocity of the brake pulley using the energy consumption of the friction brake assemblies $$\left(P_{r_w}\right)$$

U2-5-5 winch. The determination procedure for F _p in Fig. 17 is shown by dashed lines (N = 30 candles; ω = 10 s ⁻¹ ; F _p = 300 N and $$P_{r_w}=3225$$

kW / m ² ).

Brake performance

The efficiency of the band brake shoe winches is determined by the ratio of the mass of the drill pipe string to the total amount of braked reduced masses

$${\eta }_{L.T.}=\frac{m_{b.t.}}{{\displaystyle \sum m_{P.M.}}}.\left(\mathrm{fifteen}\right)$$

Analysis of the operation of drilling rigs of various classes shows that this ratio varies within the range of 0.12-0.25, i.e. is very low.

An increase in the ratio of these masses is possible by reducing the moment of inertia of the winch drum and, in particular, by reducing the diameter and thickness of the rim of its brake pulleys.

The thickness of the rim (δ) of the brake pulley is determined through its regulated moment of inertia (I _W )

, $$\delta =\frac{2I_w\cdot g}{\pi \left(R_w^{\mathrm{four}}-R_{\mathrm{at}}^{\mathrm{four}}\right)\gamma }$$

,

where g is the acceleration of gravity; R _in - the radius of the inner surface of the brake pulley; γ is the specific gravity of the pulley rim material.

The diameter of the brake pulley is determined from the condition that the tape-shoe brake reaches the moment that allows the drill string to run at maximum weight, as well as keeping them on weight.

SECOND GROUP OF OPERATIONAL PARAMETERS

Safety factor of the brake belt cross section

The safety factor (n _T ) of the cross section of the brake tape is determined by the dependence of the type

$$n_T=\frac{{\sigma }_{-\mathrm{one}}}{\frac{{\sigma }_a{k}_{\delta }}{\epsilon {\beta }_l}+{\psi }_{\sigma }{\sigma }_{\max }}\le \left[n_T\right],\left(16\right)$$

where σ _-1 is the endurance limit for a symmetric loading cycle; σ _a , σ _max - amplitude and maximum stress of the cycle; k _δ is the effective stress concentration coefficient; ψ _σ is the coefficient depending on the material of the tape; ε and β _l are coefficients that take into account the dimensions of the cross section of the tape and the cleanliness class of its working surface.

The maximum voltage in the cross section of the brake tape is determined by the type

$${\sigma }_{\max }=\frac{S_i}{{\delta }_l\left({\mathrm{at}}_l-m_P{\mathrm{at}}_P\right)},\left(17\right)$$

where S _i is the tensile force acting in the cross section of the brake band; δ _l , in _l - thickness and width of the brake tape; m _P , in _P - the number of grooves in the cross section of the tape and the width of one groove.

Moreover, the allowable value of the safety factor of the brake tape [n _T ] = 2.

Brake belt deformation

The expression for determining the complete elongation of the brake band when the friction lining with a variable pitch is located on the arc of its girth has the following form

$$\Delta l=\frac{S_{\mathrm{FROM}}{R}_0}{E{A}_l}\cdot \left[\begin{array}{c}\frac{\mathrm{one}}{f}\left(e^{f\alpha }-\mathrm{one}\right)\cdot \left(\mathrm{one}+e^{f\alpha }+e^{2f\alpha }+...+e^{f\alpha \left(n-\mathrm{one}\right)}\right)+\\ +e^{f\alpha }\left({\beta }_{\mathrm{one}}+e^{\mathrm{<figure-callout\; id="2"\; label="f\; \alpha \; \beta "\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">f\; </figure-callout>}\alpha }{\beta }_{}{}_2+...+e^{\left(n-2\right)f\alpha }{\beta }_{n-\mathrm{one}}\right)+\frac{\mathrm{one}}{2R_0}\left(l_C+l_H{e}^{nf\alpha }\right)\end{array}\right];\left(\mathrm{eighteen}\right)$$

where A _L is the cross-sectional area of the brake tape; β _i is the angle between the ends of adjacent friction linings; l _C and l _H - the length of the runaway and oncoming branches of the tape.

For a brake tape with a uniform spacing of the pads, when β ₁ = β ₂ = ... = β _n-1 = β, equation (18) takes the following form

$$\Delta l=\frac{S_{\mathrm{FROM}}{R}_0}{E{A}_l}\cdot \left[\begin{array}{c}\frac{\mathrm{one}}{f}\left(e^{f\alpha }-\mathrm{one}\right)\cdot \left(\mathrm{one}+e^{f\alpha }+e^{2f\alpha }+...+e^{f\alpha \left(n-\mathrm{one}\right)}\right)+\\ +\beta e^{f\alpha }\left(\mathrm{one}+e^{f\alpha }+...+e^{\left(n-2\right)f\alpha }\right)+\frac{\mathrm{one}}{2R_0}\left(l_C+l_H{e}^{nf\alpha }\right)\end{array}\right].\left(19\right)$$

On Fig, 19, and 20 shows a diagram of the forces acting: in the site of the patch-tape on the tape over the i-th patch; when determining the deformation of sections of the tape; 1 - a brake tape; 2 - friction lining.

- нумерация зазоров между накладками; представлены на фиг.21.Regularities of changes in the relative deformations of sections of the brake belt when the friction linings are placed along the arc of its girth with a constant (1, 1 ') and a variable (2, 2') step: calculated (1, 2) and experimental (1 ', 2') data: 1-8 and

- numbering of gaps between overlays; presented in Fig.21.

Friction pad deformations

Each friction lining in the tape-brake brake experiences compression stresses in the radial direction arising from the reaction forces of the brake belt and pulley, as well as bending stresses in the circumferential direction, arising from the frictional force of the working and non-working surfaces of the lining on the pulley and belt.

The radial deformations of the friction lining are described by a dependence of the form

$$\Delta \delta =\frac{{\delta }_H{\displaystyle \sum _{i=\mathrm{one}}^n{S}_{C_i}{\alpha }_i}}{E_H{B}_{\mathrm{one}}},\left(\mathrm{twenty}\right)$$

where δ _H is the thickness of the friction lining; E _H is the modulus of elasticity of the lining material.

General deformation of the brake system elements

The total deformation of the elements of the brake system, compensated by the angles β ₁ and β ₂ rotation of the crank shaft of the tape-shoe brake is determined by the dependencies of the form

$${\beta }_{\mathrm{one}}=\frac{{\Delta }_L+{\Delta }_T}{r}+\frac{64M_{\mathrm{at}R}l}{G\pi d^{\mathrm{four}}};\left(21\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_2=\frac{{\Delta }_L+{\Delta }_T}{r}-\frac{64M_{\mathrm{at}R}l}{G\pi d^{\mathrm{four}}},\left(22\right)$$

where Δ _L , Δ _T - deformation of brake bands and their rods; r is the radius of the crank of the crankshaft; M _BP = M is the torque equal to the braking torque at the end of braking for various types of friction brake assemblies; l is the distance between the cranks; G is the shear modulus; d is the diameter of the brake shaft.

From the graphical dependence presented in Fig. 26, it follows that when the angle of rotation ψ> 30 ° of the control lever of the driller, the displacement of the runaway ends of the brake bands (ΔS _PS ) remains almost constant with a slight fluctuation in the position height (Δδ) of the balancer.

Calculations to assess the total deformation of the elements of the brake system were performed in relation to the tape-shoe brake BU-2500 EP with the following initial data: l ₁ = 0.22 m; l ₂ = 3.1 m; l ₃ = 0.31 m; r = 0.08 m; R = 0.59 m; α = 70 °; A _L = 1.1 · 10 ^-2 m ² ; f = 0.3; E _L = 2 · 10 ⁵ N / mm ² ; E _N = 0.1 · 10 ⁵ N / mm ² ; C _T = 690 MN / m; C _l = 0.13 MN / m.

The nomogram consists of two interconnected families, the left side of which (Fig. 27) shows a family of graphical dependencies of the total braking torque of the tape brake shoe БУ-2500 ЭП from the maximum angle of the pulley grip tape with overlays at specific loads of 1.5 MPa (curves 1, 4), 1.0 MPa (curves 2, 5) and 0.5 MPa (curves 12), 40 kN (straight lines 7, 11), while straight lines 1, 8, 9 and 10 correspond to a constant coefficient of friction, and straight lines 11 , 12, 13, and 14 to the variable.

For example, let us determine from the nomogram the angle of rotation of the crank caused by deformations of the brake elements, for the case φ ₀ = 4.0 rad, p = 1.5 MPa, S _C = 30 kN, the friction coefficient is constant. From the point on the abscissa axis corresponding to φ ₀ = 4.0 rad, draw a vertical line until it intersects curve 4. From the obtained point, lower the perpendicular to the ordinate axis (braking moments) and obtain the value M = 72 kNm. Extending the perpendicular to the right side of the nomogram to the intersection with straight line 8 and lowering the perpendicular from the obtained point to the abscissa axis, we obtain the value of the crank angle β = 5.3 · 10 ^-5 rad caused by deformations of the band brake shoe elements.

THIRD OPERATING PARAMETERS GROUP

Heat, temperature and their distribution over the thickness of the rim of the brake pulley

The energy balance of the tribosystem is described by an equation of the form (dependence established by A.V. Chichinadze)

$$W_T=Q+\Delta E,\left(23\right)$$

where Q is the heat transfer energy of the friction units with the environment; ΔЕ is the change in internal energy, which is the sum of the energy used to change the structure of the material and the heating energy of the friction units.

Based on the dependence (23), it is necessary to know the amount of heat used for heating and cooling the brake pulley. According to the developed method of heating and cooling the brake pulleys of the drawbar brake of a drawworks when evaluating their heat balance, the amount of heat is determined in four stages [3]. At the first stage, heating is carried out, for example, by electric means, heat-insulated from the environment and non-heat-insulated pulleys. The difference in the quantities of heat will be its loss due to radiation and natural convective heat transfer to the environment. At the second stage, heat losses from an already heated pulley to the environment are determined by radiation and natural convective heat transfer. At the third stage, the thermally insulated protrusion of the pulley from the drum flange and the non-thermally insulated pulley is heated, which makes it possible to determine the heat loss by conductive heat transfer. At the fourth stage, the pulley is forcedly cooled from its predetermined thermal state at a constant pulley rotation frequency, thus determining the intensity of radiation and forced convective cooling of the matte and polished (working) surfaces of the brake pulleys.

Thus, methods for heating and cooling brake pulleys are implemented in laboratory and industrial conditions, i.e. when they are in statics and dynamics.

Friction units of tape and shoe brakes of drawworks operate in aperiodic, cyclic braking mode. With this mode of operation (t _y = t _T + t _oxl ), the heat generated on the friction surface is partially spent on heating, mainly metal friction elements, partially removed to the environment (by convection and radiation) and to parts in contact with the friction elements (conductive heat transfer). The temperature of the friction elements in this case increases from cycle to cycle until a steady-state value is reached when during the braking cycle the amount of heat generated on the friction surface during time t _T will be equal to the amount of heat removed to the environment and to the parts in contact with the friction elements.

A further increase in the thermal load of the working parts of the brake to a level exceeding the permissible temperature for the material of the friction linings can cause a critical steady-state temperature of the friction pairs. In this case, the temperature head between the inner and working surfaces of the rim of the brake pulley will be minimal (heat exchange with the environment is minimal), and the steady state thermal friction pairs will be maintained for a long time due to burnout of the binder components in the material of the friction linings.

According to Fig.27, we will analyze the single braking implemented on the model brake stand taking into account changes in the sliding speed at the friction contact, temperatures (below the permissible temperature for each friction material and temperature gradient, dividing the entire braking process in time into four periods.

The first period, 0≤τ≤τ ₁ , is characterized by high sliding speeds (the temperature flash on microcontact is already quite high, and the volumetric temperature has not changed yet), low temperatures of the working and non-working surfaces of the rim of the brake pulley, and low normal micro-gradients. The duration of the period is determined by the increase in the specific load on the friction contact. The duration of this period is short, and according to experimental studies, does not exceed 3% of the total duration of braking.

The second period, τ ₁ ≤τ _T <τ ₂ , is characterized by high sliding speeds, increasing specific loads, high temperatures of the working and non-working surfaces of the rim of the brake pulley, and temperature gradients (the rim of the pulley was heated); in this case, the temperature flash passes through a maximum, and the volumetric temperature increases.

The third period is τ ₂ ≤τ _T <τ ₃ . During this period of time, when braking, the sliding velocities at the frictional contact are quite high, the specific loads are steady-state, the highest temperature of the friction surface (almost quasistable), the temperature gradient drops rapidly, as the volumetric temperature increases rapidly, and the temperature flash decreases sharply.

The fourth period is τ ₃ ≤τ _T. During this period of the braking process, the sliding speeds at the friction contact are very low (close to zero, the specific load is constant, the temperature of the friction surface of the rim of the brake pulley smoothly decreases and approaches the volumetric temperature, the temperature gradient is very small, the temperature flash is practically zero. The duration of this period is zero. 5-8% of the total time limit.

Let us proceed with the analysis of unit braking implemented in the model bench taking into account changes in the sliding speed at the friction contact, temperatures (higher than the permissible value for the friction material) and the temperature gradient, based on the initial breakdown of the entire braking process in time for four periods (see Fig. 7b ) In this case, the regularity of the change in the sliding velocity at the frictional contact remained the same, i.e. linear. In this case, the breakdown of the entire braking process in time for four periods is leveled for the surface temperatures of the working and non-working surfaces of the rim of the brake pulley, as well as temperature gradients (with a “+” sign the temperature gradient is shown in the direction of increasing temperatures, ie for a partially open working the surface of the rim of the brake pulley, when the pads are on the brake belt, with the sign “-” shows the temperature gradient in the direction of decreasing temperatures, ie for an almost closed working surface of the rim of the brake w kiva friction linings). From the foregoing, it follows that even with an increase in the specific loads on the friction contact, stabilization of surface temperatures is observed with a slight change in the temperature gradient of the rim of the brake pulley.

Experimental data on heating and cooling of brake pulleys obtained by B.A. Zlobin presented in Fig.29. It follows from the latter that the increase in the surface temperature of the right (curve 1) and left (curve 2) brake pulley when the drill string is lowered into the borehole is quasilinear in nature and likened to patterns of change in specific loads in the friction brake assemblies. Curve 3 also has the same pattern when cooling brake pulleys.

Calculation of the surface temperatures of friction pairs of friction tape-shoe brakes of drill hoists is carried out according to well-known methods Chichinadze A.V., Mirzadzhanova DB, Dzhanakhmetova A.Kh., Volchenko A.I. and other scientists.

The temperature distribution (differential) over the thickness of the rim of the brake pulley (see Fig. 30) depends on the material from which it is made and its thermophysical properties (heat capacity, thermal diffusivity and thermal conductivity), rim thickness and the amount of heat supplied to the polished (working) surface pulley. It should be noted that with an increase in the thickness of the rim of the brake pulley, an increase in the temperature difference between its surfaces and, consequently, the intensity of heat transfer from matte surfaces are observed.

Heat transfer rate

The heat transfer rate from the surfaces of the brake pulley is determined by the dependencies of the form when:

natural and forced convective heat transfer

$${\alpha }_{\mathrm{to}}=\frac{Q_{\mathrm{one}}-Q_2}{A_w\cdot {\tau }_0\left(t_{\mathrm{one}}-t_2\right)};\left(24\right)$$

radiation heat transfer

$${\alpha }_l=\frac{{\mathrm{from}}_{l_i}\left[{\left(\frac{T_{\mathrm{one}}}{\mathrm{one\; hundred}}\right)}^{\mathrm{four}}-{\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{\mathrm{one\; hundred}}\right)}^{\mathrm{four}}\right]}{T_{\mathrm{one}}-{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">T</figure-callout>}}_2},\left(25\right)$$

- коэффициент излучения материала тормозного шкива, $$\raisebox{1ex}{$Вт$}\!\left/ \!\raisebox{-1ex}{$\left({м}^2\cdot {К}^4\right)$}\right.$$

.where Q ₁ , Q ₂ and t ₁ (T ₁ ), t ₂ (T ₂ ) - the amount of heat and the corresponding surface temperature of the brake pulley that it has before cooling and at the end of its completion; And _w is the total surface area (matte and polished) of heat transfer of the brake pulley; τ ₀ is the cooling time; $${\mathrm{from}}_{l_i}$$

- emissivity of the material of the brake pulley, $$\raisebox{1ex}{$\mathrm{AT}t$}\!\left/ \!\raisebox{-1ex}{$\left({\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="00000091.png,00000094.png"\; state="\{\{state\}\}">m</figure-callout>}}^2\cdot {\mathrm{TO}}^{\mathrm{four}}\right)$}\right.$$

.

The coefficient of emission of heat from a polished surface, which is the working surface of the rim of the brake pulley, is 3.31 times less than the same coefficient for the matte surfaces of the pulley. At the same time, the ratio of the areas of the polished surface to the matte, for example, in the brake pulleys of the U2-5-5 winch is 2.64.

As follows from dependences (24) and (25), the components of complex heat transfer directly depend on the temperature of the cooled surfaces of the brake pulley.

The distribution coefficient of heat flux between the friction surfaces of the friction units

The distribution coefficient of heat fluxes between the rubbing surfaces of friction units with large contact sizes in the tape-shoe brakes of the drawworks is determined by the dependence of the form

$$k_{T.P.}=\frac{{\displaystyle \sum {\alpha }_{\mathrm{from}R}}}{{\displaystyle \sum {\alpha }_{\mathrm{from}R}}+{{\displaystyle \sum {\alpha }_{\mathrm{from}R}}}^{\text{'}\text{'}}},\left(26\right)$$

where ∑α _cp is the average reduced heat transfer of the metal friction elements of the band brake; Срα _sr '- the average reduced heat transfer of the friction linings located on the arc of the brake band.

An analysis of the heat flux distribution between two rubbing bodies shows that when working with friction material based on asbestos (rolled tape, asbestos woven tape), only a small part of the heat flux (3-4%) is spent on heating the friction lining, while the bulk of it (96 -97%) passes through the brake pulley (according to M.P. Aleksandrov).

When using friction materials of a ceramic-metal type (on a copper or iron base), a much larger part of the heat flux passes through the friction pad, and part of it passing through the brake pulley decreases, respectively, to 62.0% (with a steel pulley) and to 79.0 % (with cast iron pulley) [according to M.P. Alexandrova].

Thermal deformation of the rim of the brake pulley and friction lining

The thermal radial deformation of the pulley rim is determined by the dependence of the type

$$W_t={\delta }_w{\alpha }_{t_w}\Delta t\left[\begin{array}{l}\mathrm{one}-\frac{x}{l}+\frac{V_0\left({\beta }_{\mathrm{to}}l\right)}{{\beta }_{\mathrm{to}}l\left[{\mathrm{<figure-callout\; id="0"\; label="V"\; filenames="00000102.png,00000104.png"\; state="\{\{state\}\}">V</figure-callout>}}_0^2\left({\beta }_{\mathrm{to}}l\right)+\mathrm{four}{V}_{\mathrm{one}}\left({\beta }_{\mathrm{to}}l\right)V_3\left({\beta }_{\mathrm{to}}l\right)\right]}{V}_{\mathrm{one}}\left({\beta }_{\mathrm{to}}l\right)-\\ \frac{V_{\mathrm{one}}\left({\beta }_{\mathrm{to}}l\right)}{{\beta }_{\mathrm{to}}l\left[{\mathrm{<figure-callout\; id="0"\; label="V"\; filenames="00000102.png,00000104.png"\; state="\{\{state\}\}">V</figure-callout>}}_0^2\left({\beta }_{\mathrm{to}}l\right)+\mathrm{four}{V}_{\mathrm{one}}\left({\beta }_{\mathrm{to}}l\right)V_3\left({\beta }_{\mathrm{to}}l\right)\right]}{V}_0\left({\beta }_{\mathrm{to}}l\right)\end{array}\right],\left(27\right)$$

- коэффициент линейного расширения материала обода тормозного шкива; Δt - повышение поверхностной температуры обода тормозного шкива; V₀(β_кl), V₁(β_кl), V₃(β_кl) - функции А.И.Крылова; x - текущее значение ширины обода шкива; l - ширина обода шкива; $${\beta }_{к}=\sqrt[4]{\raisebox{1ex}{${\delta }^2{k}^4\left(k^2-1\right)$}\!\left/ \!\raisebox{-1ex}{$48R_{ш}{}^6$}\right.}$$

- вспомогательный коэффициент; k-oe - уравнение системы.where δ _W - the thickness of the rim of the brake pulley; $${\alpha }_{t_w}$$

- coefficient of linear expansion of the material of the rim of the brake pulley; Δt is the increase in the surface temperature of the rim of the brake pulley; V ₀ (β _to l), V ₁ (β _to l), V ₃ (β _to l) - functions of A.I. Krylov; x is the current pulley rim width; l is the width of the rim of the pulley; $${\beta }_{\mathrm{to}}=\sqrt[\mathrm{four}]{\raisebox{1ex}{${\delta }^2{k}^{\mathrm{four}}\left(k^2-\mathrm{one}\right)$}\!\left/ \!\raisebox{-1ex}{$48{\mathrm{<figure-callout\; id="6"\; label="R\; w"\; filenames="00000094.png,00000095.png"\; state="\{\{state\}\}">R\; </figure-callout>}}_w{}^6$}\right.}$$

- auxiliary factor; k-oe is the equation of the system.

From dependence (27) it follows that the main influence on the thermal radial deformation of the rim of the brake pulley is exerted by the temperature difference between its surfaces and the coefficient of linear expansion of the material of the rim of the brake pulley.

Dependence (27) in a simplified form has the following form

$$W_t={\delta }_w{\alpha }_{t_w}\Delta t.\left(28\right)$$

A comparison of the calculated data obtained according to dependences (27) and (28) showed that their deviation does not exceed 3-4%, therefore, it is recommended to use dependence (28) to estimate the thermal radial deformations of the rim of the brake pulley.

и поверхности трения фрикционных накладок $$\left(R_{r_{н}}\right)$$

в результате термического расширения будут равныDue to thermal expansion, the diameter of the friction surface of the brake pulley increases, and the friction linings are reduced, which provides an even more complete fit of the contacting surfaces. Pulley Working Radii $$\left(R_{r_w}\right)$$

and friction surfaces of friction linings $$\left(R_{r_n}\right)$$

as a result of thermal expansion will be equal

$$R_{r_w}=R_w+\Delta {\delta }_{r_w}=R_w+{\delta }_w{\alpha }_{t_w}\Delta t;\left(\mathrm{29th}\right)$$

$$R_{r_n}=R_n+\Delta {\delta }_{r_n}=R_n-{\delta }_n{\alpha }_{t_n}\Delta t,\left(\mathrm{thirty}\right)$$

- коэффициент линейного расширения материала накладки.where R _n is the radius of the working surface of the lining; $${\alpha }_{t_n}$$

- coefficient of linear expansion of the lining material.

It can be assumed that the surface temperature under the pads during braking along the perimeter of the treadmill of the pulley is evenly distributed, and the higher the frequency of rotation of the pulley, the more uniform the temperature field. Therefore, the cross-sectional shape of the pulley as a result of thermal expansion will not change. The temperature field of the friction linings, which are stationary in the tangential direction, is likened to a specific load diagram: the maximum temperatures of the friction surface of the linings are observed on the oncoming branch of the brake band, the minimum on the oncoming branch, i.e. Δt for the overlays of both branches of the tape is different. And this difference is all the more tangible, the more loaded the brake mechanism. Consequently, the negative component of expression (30) will be larger in magnitude for the overlays of the incident branch of the tape. In this regard, full contact of the mating surfaces will be achieved earlier on the oncoming branch of the brake belt than on the runaway.

On Fig shows the dependence of the coefficient of linear expansion of steel from the surface temperature of the product, taking into account the temperature correction. The dynamics of changes in the diameters of the friction surfaces of the pulley and linings depending on their temperature is presented in Fig. 32. From the latter it follows that in the absence of running-in, the equality of the diameters of the rubbing surfaces can be achieved at a temperature of 660 ° C, which is higher than acceptable for the material of the friction linings. The linear expansion coefficients of the pulley materials and linings differ by an order of magnitude, therefore, the expansion (when heated) and the narrowing (when cooling) of the brake pulley is much more intense than the linings. The diameter of the friction surface (d _P ) of the overlays of the running branch of the tape (D _H ) having a higher temperature decreases by a larger amount than the diameter of the surface of friction of the overlays of the running branch (D _C ). As a result of running-in, we have D _C ≈d _П ≈d _ш . When cooling, the largest change in the diameter of the friction surface will occur again on the lining of the running branch, and when the working parts of the brake are completely cooled, the diameter of the friction surface of the lining of the running branch will be more than D _C and both of these parameters will be greater than d _w . Thus, the reloading of the brake will occur with a larger difference in the diameters of the friction surface of the pulley and the linings, and the maximum difference of the indicated parameters will be on the incident branch of the belt. Therefore, the contact zone of the pads with a pulley on the oncoming branch will be narrower than the contact zone of the running branch. This causes the redistribution of specific loads across the width of the pads.

A significant effect on the values of the friction coefficients and specific loads in the friction pairs of the brake is exerted by their thermal state. On Fig presents the regularity of the change in the coefficient of friction of the Tarmar type UFKM material at specific loads p from 0.5 to 1.2 MPa on the friction surface obtained on the friction machine 2168 UMT “Unitrib” from the surface temperature (according to A.V. Chichinadze).

As can be seen from Fig. 33 at t = 50-70 ° C, the friction coefficient f = 0.18-0.2, and when heated to t = 200-400 ° C, its growth is observed to f = 0.26-0.32 . With a further increase in t to 1000 ° C, the friction coefficient smoothly decreases to f = 0.2-0.22.

FOURTH GROUP OF OPERATIONAL PARAMETERS

Quasilinear wear of friction linings

In the fatigue wear of the material of the friction linings, thermal and mechanical factors have a significant effect. Thermal fatigue is caused by repeated heating and cooling, which create cyclic stresses in the material of the surface of the lining and cutting temperature gradients. In addition, exposure to thermal energy contributes to the decomposition of the constituent components of the patch material. Mechanical fatigue is caused by repeated stresses under conditions of sharp braking by the tape-block brake, a micro cut occurs, which is a relatively sudden destruction of the friction material of the lining, previously weakened by thermal exposure. It is established that the thermal condition of the brake friction assemblies exerts a predominant influence on the wear of the linings.

On Fig presents the pattern of linear wear of UFKM type "Tarmar" at specific loads p from 0.5 to 1.2 MPa on the friction surface obtained on a friction machine 2168 UMT "Unitrib" from the surface temperature (according to A.V. Chichinadze).

The greatest wear occurs at low temperatures t = 100-200 ° C and is I _h = (4.0-6.5) · 10 ^-8 m / m. At temperatures t = 450-1000 ° C, the linear wear rate is very small and varies within I _h = (0.05-2.0) · 10 ^-8 m / m. In this case, the pattern of wear of the working surfaces of the friction linings is likened to the pattern of change in specific loads in the friction pairs of the brake (see Fig. 11).

Thus, the computational and experimental methods for determining the operational parameters with a quasilinear pattern of their change in the band brake shoe winches are illustrated.

Sources of information taken into account during the examination:

1. Ilsky A.L., Mironov Yu.V., Chernobyl A.G. Calculation and design of drilling equipment. - M .: Nedra, 1985 .-- 452 p. [analog].

2. Alexandrov M.P., Lysyakov A.G., Fedoseyev V.N., Novozhilov N.V. Braking Devices: Reference. - M.: Mechanical Engineering, 1986. - 311 p. [analog].

3. Pat. 2279579 C2 RF IPC ⁷ F16D 65/813 dated 02/10/2006 [prototype].

Claims (4)

1. A method for determining operational parameters with a quasilinear regularity of their change in band-brake brakes of drill hoists containing a winch drum resting on a lifting shaft, and on which a rope of the hoist system is wound, and from the ends of which brake pulleys are installed, the working surfaces of which envelope brake bands with friction linings with constant and variable pitch mounted on their circumference arc, and the ends of the runaway branches of the brake bands through the rods attached to the balancer, and their ends of descending branches - to the crank crankshaft necks, which is connected through the transmission device to the brake control lever, characterized in that, with a quasilinear law, the speed of the brake pulley changes from the established value to zero when the loaded elevator is lowered, the operational parameters are reduced to the first group -block brake perform in the following sequence:
- the rotation mode of the brake pulley is described by the dependence of the form:
$${\omega }_{\mathrm{one}}={\omega }_0\left(\mathrm{one}-\frac{t}{t_{\mathrm{TO}}}\right),\left(\mathrm{one}\right)$$

where ω ₁ , ω ₀ and t are the current and initial value of the angular velocity of the brake pulley and the implementation time of the first; ω ₀ = ε _m t _k ; ε _m - deceleration of the brake pulley; t _to - the duration of the braking process;
- the braking time is determined by the dependence of the form:
$$t_{\mathrm{to}}=\frac{2l}{{\upsilon }_c},\left(2\right)$$

where l is the length of one candle; υ _c is the linear velocity of the descent of the candle;
- the tension of the oncoming branch (S _H ) of the brake tape is determined by the dependence of the form:
$$S_H=S_C{e}^{f\alpha },\left(3\right)$$

where S _C is the tension of the runaway branch of the brake tape; e is the base of the natural logarithm; α is the angle of coverage of the pulley plates; f is the coefficient of sliding friction in a pair of "slip-pulley";
- maximum (p _max ) and minimum (p _min ) specific loads acting on the incoming and outgoing branches of the brake belt in friction pairs are determined by the dependencies of the form:
$$p_{\max }=\frac{2S_H}{R_w{b}_{\mathrm{one}}}\le \left[p\right];\left(\mathrm{four}\right)$$

$$p_{\min }=\frac{2S_C}{R_w{b}_{\mathrm{one}}},\left(5\right)$$

where R _W - the radius of the working surface of the brake pulley; b ₁ - the width of the friction lining; [p] is the allowable value of the specific load for the lining material;
- the braking torque developed by the friction units of the tape-shoe brake is determined by the dependence of the form:
$${\displaystyle \sum _n^{i=\mathrm{one}}{M}_T=}{\displaystyle \sum _n^{i=\mathrm{one}}{F}_T\cdot R_w<<M_{T_{\max }}},\left(6\right)$$

where F _T is the friction force arising on the interaction surfaces of the friction brake assemblies; $$M_{T_{\max }}$$

- the greatest braking moment,
determined from the condition of applying breaking strength to the hoist rope;
$$M_{T_{\max }}=\frac{F_{T_{\mathrm{to}}}}{\left[k_{\mathrm{to}}\right]}\left[r_b+{\alpha }_{\mathrm{one}}\left(z_{\mathrm{one}}-\mathrm{one}\right)\right];\left(7\right)$$

Where $$F_{T_{\mathrm{to}}}$$

- breaking load of the hoist rope; [k _to ] is the safety factor of the rope; r _b is the radius of the winding of the rope on the winch drum; α ₁ - the distance between the centers of the cross sections of the ropes in adjacent layers of their winding; z ₁ - the number of layers of winding the rope on the winch drum;
- safety factor of braking torque (β _m ), determined using the dependence of the form:
$${\beta }_m=\frac{M_T}{M_{\mathrm{from}t}}\le \left[{\beta }_m\right],\left(8\right)$$

where M _article - static moment on the drum shaft of the winch from the weight of the drill string; [β _m ] is the allowable value of the safety factor of the braking torque;
- the friction work performed by the friction brake assemblies is determined by the dependence of the form:
$$A={\displaystyle \underset{0}{\overset{t_{\mathrm{to}}}{\int }}M\omega dt},\left(9\right)$$

where M and ω are the current values of the braking torque and the angular velocity of the pulley;
- energy consumption of friction brake assemblies $$\left(P_{r_w}\right)$$

determined by the dependence of the form:
$$P_{r_w}=\frac{R_{m}n{R}_w^2{b}_{\mathrm{one}}\alpha f_{\mathrm{one}}{V}_{r_{\mathrm{to}}}{i}_{\mathrm{one}}\cdot {10}^3}{r_{H_{\max }}}\le \left[P_{r_w}\right],\left(10\right)$$

Where $$p_m=\frac{p_{\max }+p_{\min }}{2}$$

- average specific loads on the surfaces of friction pairs; And ₁ = nb ₁ R _w α - the theoretical area of interaction of the inner surfaces of the friction linings and the working surface of the brake pulley; $$V_{r_{\mathrm{to}}}$$

- the average speed of the descent of the loaded elevator, which depends on the length of the candle, lowered into the well; i _l - gear ratio of the mechanical brake drive; $$r_{H_{\max }}$$

- the maximum radius of the winding of the rope on the drum,
while the allowable energy consumption of the friction units of the tape-shoe brake $$\left[P_{r_w}\right]=8000\frac{\mathrm{to}\mathrm{AT}t}{m^2}$$

;
- efforts (F _p ) applied by the driller to the control lever of the tape-block brake is determined by the dependence of the form:
$$F_p=S_C\frac{k_{\mathrm{to}}\left[r_b+{\alpha }_{\mathrm{one}}\left(z-\mathrm{one}\right)\right]}{\left(e^{n\alpha f\frac{R_w}{R_0}}-\mathrm{one}\right)R_w\cdot i_{\mathrm{one}}\cdot \eta }\le \left[F_p\right],\left(\mathrm{eleven}\right)$$

where R ₀ is the radius of the inner surface of the brake tape; η is the efficiency of the mechanical brake drive, while the allowable force applied by the driller to the brake control lever is [F _p ] = (300-400) H;
- the efficiency of the tape-shoe brake, determined by the dependence of the form:
$${\eta }_{L.T.}=\frac{m_{b.t.}}{{\displaystyle \sum m_{P.M.}}},\left(12\right)$$

where m _b.t. - mass of the drill pipe string; ∑m _P.M. - the total amount of braked reduced masses to the drum shaft of the winch;
while operating parameters S _H and S _C p _max and p _min , and $${\displaystyle \sum _n^{i=\mathrm{one}}{M}_T}$$

are determined both for the nth number of individual braking devices, and for the whole tape-shoe brake with constant and variable friction coefficients in its friction units. 2. The method for determining operational parameters in case of a quasilinear pattern of their change in the band brake of the drawworks according to claim 1, characterized in that when the quasilinear law changes the deformation of the brake belt (when installing on its arc the girth of the friction linings with constant and variable pitch) at the descent of the elevator, the definition of operational parameters, summarized in the second group, tape-shoe brake is performed in the following sequence:
- safety factor (n _T ) for the cross section of the brake tape is determined by the dependence of
$$n_T=\frac{{\sigma }_{-\mathrm{one}}}{\frac{{\sigma }_a{k}_{\delta }}{\epsilon {\beta }_l}+{\psi }_{\sigma }{\sigma }_{\max }}\le \left[n_T\right],\left(13\right)$$

where σ _-1 is the endurance limit for a symmetric loading cycle; σ _a , σ _max - amplitude and maximum stress of the cycle; k _δ is the effective stress concentration coefficient; ψ _σ is the coefficient depending on the material of the tape; ε and β _l are coefficients that take into account the dimensions of the cross section of the tape and the cleanliness class of its working surface; [n _T ] is the permissible value of the safety factor of the brake tape, [n _T ] = 2.0;
- deformations of the brake tape are described by dependencies (14) and (15) when located on the arc of its girth of the linings with a step:
variables
$$\Delta l=\frac{S_{\mathrm{FROM}}{R}_0}{E{A}_l}\cdot \left[\begin{array}{c}\frac{\mathrm{one}}{f}\left(e^{f\alpha }-\mathrm{one}\right)\cdot \left(\mathrm{one}+e^{f\alpha }+e^{2f\alpha }+...+e^{f\alpha \left(n-\mathrm{one}\right)}\right)+\\ +e^{f\alpha }\left({\beta }_{\mathrm{one}}+e^{f\alpha }{\beta }_2+...+e^{\left(n-2\right)f\alpha }{\beta }_{n-\mathrm{one}}\right)+\frac{\mathrm{one}}{2R_0}\left(l_C+l_H{e}^{nf\alpha }\right)\end{array}\right];\left(\mathrm{fourteen}\right)$$

constant (provided that β ₁ = β ₂ = ... = β _n-1 = β)
$$\Delta l=\frac{S_{\mathrm{FROM}}{R}_0}{E{A}_l}\cdot \left[\begin{array}{c}\frac{\mathrm{one}}{f}\left(e^{f\alpha }-\mathrm{one}\right)\cdot \left(\mathrm{one}+e^{f\alpha }+e^{2f\alpha }+...+e^{f\alpha \left(n-\mathrm{one}\right)}\right)+\\ +\beta e^{f\alpha }\left(\mathrm{one}+e^{f\alpha }+...+e^{\left(n-2\right)f\alpha }\right)+\frac{\mathrm{one}}{2R_0}\left(l_C+l_H{e}^{nf\alpha }\right)\end{array}\right],\left(\mathrm{fifteen}\right)$$

where A _l - the cross-sectional area of the brake tape; β _i is the angle between the ends of adjacent friction linings; l _C and l _H - the length of the runaway and oncoming branches of the tape;
- the radial deformation of the friction lining is determined using the dependence of the form:
$$\Delta \delta =\frac{{\delta }_H{\displaystyle \sum _{i=\mathrm{one}}^n{S}_{C_i}{\alpha }_i}}{E_H{B}_{\mathrm{one}}},\left(16\right)$$

where δ _H is the thickness of the friction lining: E _H is the elastic modulus of the lining material;
- the total deformation of the elements of the brake system is determined by the dependence of the form:
$${\beta }_{\mathrm{one}}=\frac{{\Delta }_L+{\Delta }_T}{r}+\frac{64M_{\mathrm{at}R}l}{G\pi d^{\mathrm{four}}};\left(17\right)$$

$${\beta }_2=\frac{{\Delta }_L+{\Delta }_T}{r}-\frac{64M_{\mathrm{at}R}l}{G\pi d^{\mathrm{four}}},\left(\mathrm{eighteen}\right)$$

where Δ _L , Δ _T - deformation of brake bands and their rods; r is the radius of the crank of the crankshaft; M _BP = M is the torque equal to the braking torque at the end of braking for various types of friction brake assemblies; l is the distance between the cranks; G is the shear modulus; d is the diameter of the brake shaft. 3. The method for determining operational parameters with a quasilinear pattern of change in the band brake of the drawworks according to claim 2, characterized in that, with the quasilinear law, changes in the amount of heat that is generated on the surface of the friction units, and then accumulated in them and later dissipated from them into the environment when the elevator is lowered, the temperature field of the friction linings, which are stationary in the tangential direction, is likened to the specific load diagram, the definition of operational pa ametrov tabulated third group belt drum brake operate in the following sequence:
- the intensity of heat from the surfaces of the brake pulley is determined by the dependence of the type for: natural and forced convective heat transfer
$${\alpha }_{\mathrm{to}}=\frac{Q_{\mathrm{one}}-Q_2}{A_w\cdot {\tau }_0\left(t_{\mathrm{one}}-t_2\right)};\left(19\right)$$

radiation heat transfer
$${\alpha }_l=\frac{{\mathrm{from}}_{l_i}\left[{\left(\frac{T_{\mathrm{one}}}{\mathrm{one\; hundred}}\right)}^{\mathrm{four}}-{\left(\frac{T_2}{\mathrm{one\; hundred}}\right)}^{\mathrm{four}}\right]}{T_{\mathrm{one}}-T_2},\left(\mathrm{twenty}\right)$$

where Q ₁ , Q ₂ and t ₁ (T ₁ ), t ₂ (T ₂ ) - the amount of heat and the corresponding surface temperature of the brake pulley that it has before cooling and at the end of its completion; And _w is the total surface area (matte and polished) of heat transfer of the brake pulley; τ ₀ is the cooling time; $${\mathrm{from}}_{l_i}$$

- emissivity of the material of the brake pulley, $$\raisebox{1ex}{$\mathrm{AT}t$}\!\left/ \!\raisebox{-1ex}{$\left(m^2\cdot {\mathrm{TO}}^{\mathrm{four}}\right)$}\right.;$$

- the distribution coefficient of heat flows between the friction surfaces of the friction units having large contact sizes are determined by the dependence of the form:
$$k_{T.P.}=\frac{{\displaystyle \sum {\alpha }_{\mathrm{from}R}}}{{\displaystyle \sum {\alpha }_{\mathrm{from}R}}+{\displaystyle \sum {\alpha }_{\mathrm{from}R}\text{'}\text{'}}},\left(21\right)$$

where ср α _sr is the average reduced heat transfer of metal friction elements of the tape-shoe brake; ∑α _cp 'is the average reduced heat transfer of the friction linings located on the arc of the brake belt;
- thermal radial deformation of the pulley rim is determined by the type
$$W_t={\delta }_w{\alpha }_{t_w}\Delta t,\left(22\right)$$

where δ _W - the thickness of the rim of the brake pulley; $${\alpha }_{t_w}$$

- coefficient of linear expansion of the material of the rim of the brake pulley; Δt is the temperature difference between the surfaces of the pulley rim. 4. A method for determining operational parameters in the case of a quasilinear pattern of change in the band brake of the drawworks according to claim 2 or 3, characterized in that in the case of a quasilinear law changes in the speed of rotation of the brake pulley from a steady value to zero, deformations of the brake belt and the amount of generated , accumulated and dissipated heat from the friction units during the descent of the elevator, the pattern of change in wear of the working surfaces of the friction pads (fourth group) is likened to a pattern and changes in specific loads in the friction pairs of the brake, and the prevailing effect on the amount of wear on the linings is exerted by the thermal state of the friction brake assemblies.

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