RU2150566C1 - Method for optimizing geometry of the profile of single-screw hydraulic machine working elements - Google Patents

Abstract

FIELD: oil and mining industries, general mechanical engineering. SUBSTANCE: method involves including factors of geometry in calculations and calculating contact stresses in working elements. Novelty is that tooth shape factor C_e = r_c/e is chosen depending on off-centroid factor C_o = r/e and on displacement of original contour of rack C_Δ = Δx/e by maximum of criterion of wear resistance П_w.r. which is, essentially, ratio of square root of relative reduced curvature radius

to relative rate of slip of rotor and stator profiles

where e is engagement eccentricity, M; D_cntr is contour diameter, m; r is equidistance radius, m; Δx is displacement of rack original contour, m; e is distance from point of contact to engagement pole, m, ρ is reduced radius of profile curvature. EFFECT: improved reliability and wear resistance of working elements. 2 cl, 10 dwg

Description

 The invention relates to petroleum engineering, in particular to single-screw multi-start pumps and hydraulic motors with cycloidal gearing, and can be used in various fields of mining and in general engineering, for example, when drilling wells using a downhole hydraulic motor.

A generally recognized method for optimizing the working bodies of multi-start single-screw hydraulic machines is known, based on the selection of rational values of the tooth shape coefficients C _e and eccentricity C _o providing a smooth profile and a minimum of contact pressures (Downhole screw motors for drilling wells / M.T.Gusman and others M. , Nedra, 1981). The disadvantage of this method is that when choosing a profile does not take into account the actual offset of the initial contour of the cycloidal rail, i.e. Optimization is done for perfect cycloidal engagement.

The traditional profile of the working bodies of downhole screw motors with constant (independent) coefficients of eccentricity (C _o = 1,175) and tooth shape (C _e = 2,175) is known, in which the displacement coefficient C _{Δ of the} original rail contour, based on the smoothness of the profiles, can vary in the range C _Δ = - 2 ... 2 (Industry standard OST 39-164-84 Transmission gear rotor-stator of a downhole screw motor). The disadvantage of the traditional profile is the independence of the adopted dimensionless coefficients from the qualitative indicators of engagement, which does not always allow to obtain the optimal shape of the profiles.

 Of the known profiles of the working bodies of multi-start single-screw hydraulic machines, the closest to the proposed one is the profile in which, in order to reduce contact stresses in the rotor-stator pair, the tooth shape coefficient is a variable parameter and is selected depending on the kinematic ratio and the shape factor of the helical surface (as USSR N 1778367). However, this invention also does not take into account the effect of the displacement of the original rail circuit on the level of contact stresses.

 The objective of the invention is to increase the reliability and durability of a single-screw hydraulic machine, taking into account all the geometric parameters of the engagement of the profiles of the working bodies, including the displacement of the original circuit.

и отношение

к безразмерной скорости скольжения профилей

.The problem is solved in that the profile of the working bodies, which is the envelope of the family of contours of the cycloidal rail, is selected according to the maximum criteria of wear resistance P _and , which are taken as the relative reduced radius of curvature of the profiles

and attitude

to dimensionless sliding velocity of profiles

.

 The invention is further explained in the description and is accompanied by drawings, where in FIG. 1 shows a diagram of the formation of a cycloidal profile by the method of rolling in a rack; in FIG. 2-6 - profiles of the working bodies with a kinematic ratio of i - 5: 6 of the same contour diameter and different displacement coefficients; in FIG. 7 - dependences of the relative reduced radius of curvature of the conjugate profiles (i = 5: 6) on the tooth shape coefficient at various displacement coefficients; in FIG. 8-10 - optimal profiles of the working bodies, providing maximum relative reduced radius of curvature.

The working body of a single-screw hydraulic machine is a screw gerotor mechanism (VGM) - a helical gear tooth pair of internal cycloidal gearing, consisting of Z ₁ - lead elastic stator and Z ₂ - lead (Z ₂ = Z ₁ - 1) metal rotor, between which helical surfaces work cameras.

The working bodies are profiled (Fig. 1) from the initial contour of the cycloidal rail 3 (equidistant of the shifted shortened cycloid 1) associated with the instrumental straight line 4, along which circle 6 is rolled to form a cycloid. The cycloidal bar profile is formed as the envelope of the family of contours of the rail when the instrumental straight line is stationary guide circle 5. In General, to ensure a given contour diameter of the working bodies D _{to the} rail is shifted relative to the instrumental line by the value Δ x (Fig . 1). If there is no displacement (Δ x = 0), the rack profile becomes the ideal cycloidal profile. Graphically, it can be obtained in the classical way by rolling the circle 6 along the guide circle 5.

- кинематическое отношение i = Z₂ : Z₁
- коэффициент внецентроидности C_o = r/e
- коэффициент эквидистанты (формы зуба) C_e = r_ц/e
- коэффициент смещения исходного контура рейки C_Δ = Δx/e
- коэффициент натяга в паре C_δ= δ/e
- коэффициент формы винтовой поверхности C_т = t/d_ср
- число шагов рабочих органов k
где r - радиус катящейся окружности; r_ц - радиус эквидистанты; e - эксцентриситет; δ - диаметральный натяг; d_ср - средний диаметр ротора; t - шаг ротора.The shape of the working bodies with a given contour diameter is fully characterized by eight dimensionless coefficients:
- gearing type coefficient

- kinematic ratio i = Z ₂ : Z ₁
- coefficient of eccentroidity C _o = r / e
- equidistant ratio (tooth shape) C _e = r _c / e
- the displacement coefficient of the original rail contour C _Δ = Δx / e
is the interference coefficient in the pair C _δ = δ / e
- the coefficient of the shape of the helical surface C _t = t / d _cf
- the number of steps of the working bodies k
where r is the radius of the rolling circle; r _c is the equidistant radius; e is the eccentricity; δ is the diametric interference; d _cf - the average diameter of the rotor; t is the pitch of the rotor.

The first six coefficients determine the profile of the working bodies in the end section. The parameter C _t characterizes the spatial geometry of the hydraulic machine.

The spatial geometry is optimized depending on the mode of operation of the VGM. The spatial geometry of the VGM engines is subject to the reliability requirements for their start-up (C _t = 5.5 ... 12.0). In pump mode, there is no danger of self-braking, and therefore the shape of the screw surfaces is selected for energy reasons based on the achievement of a minimum length of contact lines (C _t = 1.5 ... 3.5).

определяет тип циклоидального зацепления. В гидромашинах получило распространение гипоциклоидальное зацепление (

= -1).Coefficient sign

determines the type of cycloidal engagement. In hydraulic machines, hypocycloidal engagement (

= -1).

 The interference coefficient and the number of steps of the working bodies are selected depending on the required operational parameters (engine torque, pump pressure) in order to ensure the specified characteristics of the hydraulic machine.

 Since the MTBF to failure is mainly determined by the frictional wear of the rotor-stator pair, the minimum wear rate of the working bodies is taken as a criterion for the optimality of the flat geometry of the VGM.

In conjugations with variable contact conditions, like VGM, the wear rate W depends on the contact voltage K and the sliding speed U _c
W = CK ^m U _ck ⁿ , (1)
where C is the coefficient of wear resistance of materials and working conditions of the pair; m, n - indicators of influence.

,
где N - удельная нормальная нагрузка; E - приведенный модуль упругости материалов рабочих органов; ρ^* - приведенный радиус кривизны сопряженных поверхностей рабочих органов.In design calculations, the hypothesis of the equivalent influence of power and speed factors (m = n = 1) is accepted, in which case W is determined by the product of K and U _ck
W = CKU _SC (2)
If the contact stress exerts a dominant influence on the wear rate (n = 0)
W = CK (3)
Contact stresses in the general case depend on the acting hydraulic and inertial forces, geometric parameters and elastic properties of the materials of the working bodies. With sufficient accuracy, the contact voltage is determined by the Hertz formula

,
where N is the specific normal load; E is the reduced modulus of elasticity of the materials of the working bodies; ρ ^* is the reduced radius of curvature of the mating surfaces of the working bodies.

Для машин с фиксированными значениями геометрических параметров C_δ, С_т, k при прочих равных условиях (PE = const)

где

- относительный приведенный радиус кривизны сопряженных профилей (отношение приведенного радиуса кривизны профилей ρ к эксцентриситету):

;

зависит от фазы зацепления и является критерием уровня контактных напряжений рабочих органов гидромашины с заданным кинематическим отношением.An analysis of expression (4) shows that in the “hertz" formulation, the contact voltage does not depend on the contour diameter and is expressed by the functional dependence

For machines with fixed values of geometric parameters C _δ , С _t , k, all other things being equal (PE = const)

Where

- the relative reduced radius of curvature of the conjugate profiles (the ratio of the reduced radius of curvature of the profiles ρ to the eccentricity):

;

depends on the phase of engagement and is a criterion for the level of contact stresses of the working bodies of a hydraulic machine with a given kinematic ratio.

The slip velocity in the rotor-stator pair depends on the angular velocity ω and the distance l from the point of contact to the pole of engagement
v _ck = ωl (7)
l like ρ is a variable and depends on the phase of engagement.

где

- относительное расстояние от точки касания до полюса зацепления

выражает безразмерную скорость скольжения

и является критерием уровня скольжения рабочих органов.For hydraulic machines with constant contour diameter and angular velocity (D _k ) = const; ω = const)

Where

- relative distance from the point of contact to the pole of engagement

expresses dimensionless sliding speed

and is a criterion for the level of sliding of the working bodies.

 Since both the contact stress and the sliding speed reach the maximum value at the contact of the protrusion of the rotor tooth, the wear rate of the working bodies is determined by the contact conditions of the protrusion of the rotor tooth.

- для случая, соответствующего (2);

- для случая, когда закон изнашивания описывается выражением (3).As a criterion of wear resistance P _and , providing a minimum wear rate, you can take

- for the case corresponding to (2);

- for the case when the law of wear is described by expression (3).

Относительный приведенный радиус кривизны

где

- относительный радиус кривизны скелета профиля статора.Maximum relative sliding speed

Relative reduced radius of curvature

Where

- the relative radius of curvature of the skeleton of the stator profile.

Предложенный способ оптимизации геометрических параметров профиля рабочих органов одновинтовой гидромашины заключается в том, что при заданном кинематическом отношении i находится оптимальное сочетание между коэффициентами C_o, C_Δ , C_e, обеспечивающее максимум одного из критериев износостойкости. Исследование функций (9) и (10) показывает, что они имеют экстремальный характер (фиг. 7), т.е. при заданном кинематическом отношении ВГМ каждому коэффициенту внецентроидности C_o и смещения C_Δ соответствует определенная форма зуба, при которой скорость изнашивания рабочих органов становится минимальной.In the general case of rack and pinion gearing

The proposed method for optimizing the geometric parameters of the profile of the working parts of a single-rotor hydraulic machine is that for a given kinematic ratio i there is an optimal combination between the coefficients C _o , C _Δ , C _e , providing a maximum of one of the criteria for wear resistance. The study of functions (9) and (10) shows that they are of an extreme nature (Fig. 7), i.e. for a given kinematic relation of the HMG, each coefficient of eccentroticity C _o and displacement C _Δ corresponds to a certain tooth shape, at which the wear rate of the working organs becomes minimal.

 Other things being equal, the relative reduced radius of curvature increases with an increase in the displacement coefficient (Fig. 7), therefore, when designing a VGM, preference should be given to engagement with a positive displacement.

With an increase in the displacement coefficient, the optimal value of the tooth shape coefficient C _e increases (Fig. 7).

For the used in practice profiles of multi-start HMV with hypocycloidal engagement and an eccentricity coefficient close to unity (C _o = 1.175), the optimal range of variation of the tooth shape coefficient depending on the displacement (negative or positive) is within
C _e = 2.0 ... 3.5 at C _Δ <0
C _e = 3.0 ... 5.0 for C _Δ > 0,
where the upper boundaries of the intervals correspond to the VGM with a small number of teeth (Z ₂ <5).

Using the optimal shape profiles VGM practically does not affect the characteristics of the hydraulic machine, since C _e influence on the displacement volume when C _e the change from the standard value (C _e = 2,175) to the boundary of the proposed range of values and maintaining the shape of the screw surface coefficient C _m does not exceed 10%.

.As an example in FIG. Figures 8–10 show the optimal SHM profiles with a kinematic ratio of l = 5: 6 for three different displacements of the initial rail contour corresponding to displacement coefficients C _Δ = -1, C _Δ = 0, C _Δ = 1, calculated for the standard value of the coefficient of eccentricity (C _o = 1,175) by criterion

.

Claims (2)

1. A method for optimizing the geometric parameters of the profile of the working parts of a single-rotor hydraulic machine, including selecting a tooth shape in a rotor-stator pair, characterized in that the tooth shape coefficient C _e = r _{c / e is} chosen depending on the eccentricity coefficients C _e = r / e and displacement the initial contour of the rail C _Δ = Δx / l according to the maximum criterion of wear resistance P _and representing the ratio of the square root relative to the reduced radius of curvature

and relative sliding speed of the rotor and stator profiles

where l is the eccentricity of the mesh, m;
D _to - contour diameter, m;
r is the radius of the rolling circle, m;
r _c is the radius of the equidistant, m;
Δx is the displacement of the initial contour of the rail, m;
l is the distance from the point of contact to the pole of engagement, m;
ρ is the reduced radius of curvature of the profiles. 2. The method according to p. 1, characterized in that as a criterion of wear resistance take the relative reduced radius of curvature of the mating profiles

.

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