RU2232317C1 - Gyrator mechanism of helical hydraulic machine - Google Patents

Abstract

FIELD: gear-type gyrator mechanisms; drilling oil and gas wells.

SUBSTANCE: proposed gyrator mechanism has gear pair rotor-stator of internal cycloidal engagement whose teeth are in constant contact. Addendum modification shift is set taking into number of teeth according by the following relationships:

and maximum permissible magnitude of stator contour diameter are equal to

where

are maximum permissible positive and negative addendum modification shifts; a is engagement eccentricity;

is number of teeth of stator and rotor;

is root circle diameter at absence of shift.

EFFECT: enhanced adaptability.

9 dwg

Description

The invention relates to gear gerotor mechanisms of internal gearing (GM) with a difference in the number of teeth of its parts (stator and rotor) equal to one. The rotor axis is offset from the stator axis by the amount of engagement eccentricity. The end profiles of their teeth are made conjugated with a common initial gearing contour, which is a rail profile outlined by the equidistant of a shortened cycloid, while the initial rail contour (RBI) and stator and rotor profiles have an offset perpendicular to the axis of the mechanism. The tooth profiles of the stator and rotor are smooth and are in continuous contact with interference.

Similar mechanisms can be used in hydraulic machines as working bodies, for example, hydraulic motors (and pumps) in the helical shape of the teeth of organs and the execution of the teeth of the stator from an elastic material.

Known GM with internal gearing, containing two gear links: a stator and a rotor with a difference in the number of their teeth equal to one. The end profiles of the teeth of the stator and rotor are made in the form of curves enveloped by a common initial contour of the rack, the profile of which is outlined by the equidistant of a shortened cycloid. The general initial contour of the rail has an offset Δh ₁ during the formation of the stator profile and Δh _{2 of the} rotor. To reduce the errors of engagement, symmetrical displacements of the initial contour of the rail relative to the instrumental centroids r _{w1 of the} stator and r _{w2 of the} rotor, the values of which are equal

where: a is the eccentricity of the meshing mechanism,

r is the radius of the rolling circle forming a cycloid of the general initial contour of the rail.

The r / e ratio is usually set to 1.1..1.3, so the offset is small. For example, for a = 5 and r = 1.2a, the displacements are equal

The most important parameter of the gerotor mechanisms is the stator contour diameter D _k associated with the nominal diameter D _{fl of the} circumference of its depressions by the ratio:

where D _f1 = 2 (rZ ₁ –r + a + r _c ) is the nominal diameter of the circumference of the stator troughs;

Z ₁ is the number of stator teeth;

r _c - the distance from the shortened cycloid to the points of the original contour of the rail, assigned within (1.5 ... 2.5) a.

A change in D _k affects the technical characteristic of the hydraulic motor, since the area of the passage section S, the torque M _cr and the rotation speed n at the output end of the hydraulic motor depend on D _k .

The disadvantage of this mechanism is that with the standardization of the shape of the initial engagement contour (rack), the contour diameter can only be changed by replacing the number of teeth Z ₁ or eccentricity a. This imposes restrictions on the design of the mechanism and the optimization of the technical characteristics of the hydraulic motor.

Closer in technical solution to the proposed invention is the gerotor mechanism described in OST 39-164-84 [1]. It adopted the following parameters of the initial meshing contour: r = 1,175a, r _c = 2,175a, and the initial circuit may have an offset Δh _1,2 , which can be changed over a fairly wide range:

where a is a positive offset; -2a is negative.

Due to relation (1), the value of the contour diameter of the stator can be assigned quite freely and steplessly. Therefore, the design of the mechanism has great structural flexibility in comparison with the analogue.

The drawback of the OCT-designed mechanism is that when assigning the displacement limits of the initial engagement contour, the standard does not take into account the number of stator and rotor teeth. Therefore, positive mixing with the number of teeth Z = 2 ... 10 and negative displacement at Z ≥ 5 (Fig. 5) turn out to be underestimated, which does not allow full use of the maximum allowable displacements according to the smoothness conditions of the stator or rotor profiles. At the same time, the negative displacement (-2a) at Z <5 is overestimated, which leads to undercutting of the tooth profile and disruption of the continuity of their contact.

The task of the invention is to increase the structural flexibility of the gearing and increase the efficiency of the hydraulic motor. An increase in the design flexibility of engagement is provided by changing and optimizing the shape of the profiles by varying the magnitude of the displacement of the profiles. Improving the efficiency of the hydraulic motor is provided by improving its technical characteristics.

The solution to this problem is achieved by the fact that in the well-known gerotor mechanism containing a stator and an enclosed rotor eccentrically located in it, the teeth of which are in continuous contact and have a difference of their numbers equal to unity, the end profiles of the stator and rotor are formed by a common initial contour of the rail (mesh) with an offset, and the profile of this contour is outlined by the equidistant of a shortened cycloid, according to the invention, the largest allowable positive and largest allowable negative bias of the original rail contour for ayut conditions of absence of shear rotor teeth profile and condition profile to lack undercut cavities of the stator with the performance ratios:

and the permissible value of the contour diameter is limited by:

Where

Δh _P , Δh _OT - positive and negative, respectively, the offset of the initial contour of the rail (or the offset of the stator and rotor profiles);

D _kmax , D _Kmin - the largest and smallest value of the contour diameter;

a - eccentricity of the meshing mechanism;

Z _1,2 - the number of teeth of the stator and rotor, respectively;

D _fl is the nominal diameter of the stator troughs with a displacement of the initial rail contour equal to zero, which, given the fact that Z ₁ = Z ₂ +1, is determined by the formula:

where r is the radius of the rolling circle forming a normal cycloid of the original rail contour, equal to 1,175a;

r _c is the distance from the shortened cycloid to the profile points of the original rail contour, equal to 2.175a.

The invention is illustrated by drawings.

On figa shows the profile of the rotor with a slice at the head of the tooth with a positive offset of the original contour of the staff (RBI), Z ₂ = 5, D _a = 69,125, Δh _P = 7, a = 3,5, r = 4,1125, r _c = 7.6125, and Fig. 1b shows a stator profile with an undercut of the cavity at the tooth leg with a negative displacement of the initial rail contour (RBI), Z ₁ = 5, D _a = 37.125, Δh _OT = 7, a = 3.5 , r = 4.1125, r _c = 7.6125. Point K indicates a kink in the profile.

Figure 2 shows the RBI determined by the coordinates X _p , Y _{p the} angle of the profile α _p and the radius of curvature ρ _p at the current point M The bottom vertex of the profile of the RBI touches the base straight cycloid. Point П denotes the inflection of the RBI profile, determined by the parameter Ψ _П = arccos (а / r).

Figure 3 fixes the moment of engagement of the RBI with the profile of the tooth of the rotor or the profile of the cavity of the stator when you rotate their coordinate axes X _d Y _d at an angle φ. The initial circle of radius r _w1,2 = r _z1,2 is tangent to the initial line of RBI at the point of link R.

Figure 4 shows the permissible displacement of the RBI corresponding to each point of its profile, depending on the parameter Ψ for a specific number of teeth Z = 6, with a = 1, r = 1.75, r _c = 2.175. Curve A refers to a positive bias, B to a negative bias.

The values of ψ _ex correspond to the extrema of curves A and B.

Figure 5 shows the maximum permissible displacement of the RBI, determined by the parameter ψ _ex depending on the number of teeth of the stator or rotor. Curve A refers to a positive bias. B - to negative, lines C and D - correspond to the recommended displacements according to OST 39-164-84 according to relation (1).

In Fig.6 a, b, c shows the engagement of the GM and their errors in the form of lateral interference (or clearances, for example, in Fig.6c - at the head of the tooth) for all the teeth of the stator and rotor, and - in the absence of displacement of the stator profile: D _k = 63.35, Δh _1P = 0, Δh _2P = + 0.6125, the outer diameter of the rotor D _a2 = 66.3, b - with its maximum permissible negative offset Δh _lOT : D _K = 48.173, Δh _{loot =} -7 , 58828, Δh _{2 from} = -6.9825, D _a2 = 41.173, c - at the maximum permissible positive offset Δh _1P : D _k = 75.995, Δh _1P = + 5.1275, Δh _2P = + 5.7100, D _a2 = 68,995, where Δh ₁ is the stator profile offset, Δh ₂ is the rotor profile offset. The index S denotes the element of the flow area for the liquid, and S ₂ <S ₁ <S ₃ . Index "p" refers to a positive offset, and the minus sign and index "from" to negative, index 1 refers to the stator profile, and index 2 refers to the profile of the rotor.

6 also shows the offset Δh _{2 of} the rotor profile. It is associated with a displacement of the stator profile by the ratio:

where j is the diametrical interference in the engagement of the GM, specified on the top and in the cavity of the rotor profile.

The present invention provides increased structural flexibility of the engagement of the GM and increase the efficiency of the hydraulic motor. An increase in the constructive flexibility of the engagement of the GM occurs due to the optimization of the shape of the tooth profiles of the mechanism with ensuring the smoothness of the tooth profiles of the mechanism for any number of stator and rotor teeth by taking into account the specific number of their teeth. The shape of the profiles depends on the offset values. The amount of displacement depends on the specific number of teeth. Accounting for a specific number of GM teeth is provided by analytically sound calculation. The smoothness of the profiles leads to the continuity of the contact of the teeth of the stator and rotor. The optimization of the shape of the profiles improves the contact between the teeth of the hydraulic motor. The efficiency of the hydraulic motor is increased by optimizing its technical characteristics, since a rational choice of the contour diameter increases either the torque or the frequency of rotation of the hydraulic motor, depending on the required characteristics and the contour diameter of the stator.

In the prototype, with a change in the number of teeth, the ratio (1) should change, which is not taken into account in the prototype and with the above numbers of teeth leads to disruption in the continuity of contact between the teeth of the stator and rotor.

The proposed gerotor mechanism is a gear pair with an internal cycloid gearing containing two parts - a male metal rotor and a female stator with elastic teeth formed in the mold core. The difference between the numbers of teeth of the stator and rotor is equal to one. The end profiles of the stator and rotor are made conjugated to a common initial gearing contour of the mechanism, which is a rail with a profile defined by the equidistant of a shortened cycloid, the initial contour having a positive or negative bias perpendicular to the axis of the mechanism, and the profiles of the teeth of the rotor and stator have a smooth shape and are in continuous contact.

The smoothness of the profiles eliminates the cutting of the tops of the teeth of the rotor or core of the stator mold (figa) and the cutting of their troughs (figb). A profile slice occurs at an unacceptably large positive offset of the RBI, and a cut occurs at an unacceptably large negative offset. When cutting and undercutting the teeth of the rotor or stator (core), break points A appear on their profiles (Fig. 1 a, b), which in mathematics are called singular points. At the break point, the radius of curvature ρ _{d of} the part profile (stator or rotor) is zero:

Where

When substituting (4) in (3), the maximum permissible displacement of the RBI. corresponding to the appearance of the break point on the part profile, is determined by the analytical dependence:

Δh P. _OT - positive and negative displacement of the RBI, respectively, relative to the initial circumference of the part (or from the axis of its rotation),

α _p - angle profile of RBI (figure 2, 3) at the current point

r _W is the radius of the initial circumference of the part (figure 3),

Z is the number of teeth of the stator or rotor,

r is the radius of the rolling circle forming a normal RBI cycloid,

L is the distance from the point M of the contact of the RBI (figure 3) with the point of the profile of the part to the pole P of the mesh;

X _p - ordinate profile of RBI (figure 3):

a is the radius of the circle forming a shortened cycloid RBI equal to the eccentricity of the mesh,

r _c - the distance from the shortened cycloid to each point of RBI,

Ψ - the angular parameter of the cycloid, variable within 0 ... Ψ _P ;

Ψп - the boundary value Ψ corresponding to the inflection point P (Fig.2, 3)

ρ _p is the radius of curvature of the RBI profile at the current point

The plus sign and index "p" in dependence (5) refer to a positive offset, the minus sign and the index "from" to negative. With a slight decrease in the values of the positive displacement by 0.1 .... 0.3 mm and an increase in the negative displacement by the same value, the break point disappears.

For example, the values of positive and negative bias calculated by dependence (5) for the number of teeth Z = 6 (for one of ten values of the number of teeth with RBI parameters according to OST 39-164-84, а = 1, r = 1,175а, r _c = 2,175a and a change in the parameter Ψ within 0 ... Ψ _p ) are shown in the graph (Fig. 4).

Curve A in the graph corresponds to a positive displacement _P Δh, which has a minimum Δh _p = 1.80125 when Ψ = Ψ _ex = 0.28934, and the curve B corresponds to a negative displacement, which has a peak _RT = -2.17891 Δh at Ψ = Ψ _ex = 0.42482. The offset is considered positive when the base straight line of the RBI (Fig. 2) is offset from the axis of rotation O _{d of the} stator or rotor and negative when when to the axis.

These extremes correspond to the largest permissible RBI displacements, excluding cutting or trimming the part profile with the number of teeth Z = 6. The maximum permissible displacements of the RBI for other numbers of teeth for a = 1 are represented by curves A and B in figure 5. At values a> 1, the maximum permissible displacements increase by a factor of one.

The study of the engagement of the stator and rotor showed that the largest (maximum) permissible positive offset of the RBI is limited by cutting the tops of the teeth of the rotor (figa), and negative - by cutting the profile of the stator troughs (fig.1b).

To simplify the calculation of the values of the largest permissible displacements of the RBI, curves A and B (Fig. 5) are replaced by exponential functions. Then the largest allowable positive and negative bias of the RBI is calculated by the relations:

Thus, bypassing the time-consuming studies to determine the maximum displacements from the dependence (5) and their graphical representation in Figs. 4, 5, the studies are reduced to the calculation of simple exponential functions from the dependences (2).

When designing a GM, the so-called stator contour diameter D _k is usually specified. Its value should be limited to:

Where

D _k is the adopted stator contour diameter specified by the designer.

D _f1 is the nominal diameter of the circumference of the stator cavities, which is determined by the formula:

The outer diameter of the rotor D _a2 is determined by the dependence:

where j is the diametrical interference in the engagement of the GM, j = (-0.02 ... 0.08) a.

In the case of an arbitrary specification of the diameter D _k , the RBI displacement for the stator is determined by the ratio:

and for the rotor

while the values of Δh _1,2 should be within:

When designing a GM from a general RBI, errors in the engagement of the stator and rotor arise in most cases in the form of interference on the lateral sides of the tooth profile at any RBI offset (Fig. 6). Engagement errors are limited to a tolerance of 0.1 mm. If they exceed the specified tolerance, then the offset values Δh _{P, OT} should be reduced or the corresponding value of the diametrical interference fit j, which redistributes or reduces the errors of engagement _, should be set.

These relationships (2) are illustrated in FIG. 5:

1. If

that smoothness is ensured, undercuts and slices disappear, and the fracture point K disappears in Figs. la, 1b, thereby ensuring continuity of the contact of the teeth, and changes in the contour diameter D _k in accordance with relation (2) are limited by limits.

2. If

then the profiles are smooth, on the verge of the appearance of slices and undercuts.

3. If

then the smoothness is violated, and slices and undercuts occur (figa, b) with break points K, the continuity of the contact of the teeth of the stator and rotor is violated.

In one case, the rotor limits, and in the other, the stator.

We give an example 1 of the calculation of D _k with a positive shift of RBI from the condition that there is no cut in the profile of the teeth of the rotor (Fig.6c).

Given: a = 3.5, r = 1.175; a = 4.1125, h = 2a,

r _c = 2.175 · a = 7.6125, D _f2nom = 63.75, D _a2nom = 56.35.

For the invention:

=5,71;Δh _2P = 0.73 $\genfrac{}{}{0ex}{}{\text{0.5}}{\text{2}}$ = 0.73 · 3.5 ·

= 5.71;

D _a2 = D _a2nom +2 (Δh _2P + re) = 56.35 + 2 · (5.71 + 4.1125-3.5) = 68.995;

D _Kmax = D _a2 + 2 · a = 68.995 + 2 · 3.5 = 75.995.

For prototype:

Δh _2P = a = 3.5;

D _a2 = D _a2nom +2 (Δh _2P + re) = 56.35 + 2 · (3.5 + 4.1125-3.5) = 64.57;

D _Kmax = D _a2 + 2 · a = 64.575 + 2 · 3.5 = 71.575;

that is, the shortage of the prototype diameter by 4.42 mm compared to the proposed one.

The reduction in diameter is extremely possible by

With increasing Z, this percentage will increase, for example, at Z = 9, the increase is 100%, which is illustrated in Fig. 5.

We give an example 2 of the calculation of D _K with a negative bias of the RBI from the condition that there is no undercut of the stator profile (Fig.6b).

For the invention:

Δh _1OT = 1.04 $\genfrac{}{}{0ex}{}{\text{0.41}}{\text{1}}$ = 1.04 · 3.5 · 6 ^0.41 = -7.58828;

D _Kmin = D _f1 -2Δh _1OT = 63.35-2 · 7.58828 = 48.173;

D _a2 = D _Kmin -2a = 48.173-2.3.5 = 41.173.

For prototype:

Δh _1OT = -2a = -7;

D _Kmin = D _f1 -2Δh _1OT = 63.35-2 · | -2 · a | = 49.35;

D _a2 = D _Kmin -2a = 49.35-2.3.5 = 42.35.

When comparing with the results of the present invention, D _Kmin and D _a2 are obtained more, but this is unacceptable, as it will result in a slice of the profile of the troughs and stator, limited by the ratio:

Thus, these calculations substantiate the limits of the RBI displacement.

The advantage of the inventive gerotor mechanism is to improve the quality of its engagement, excluding trimming or cutting profiles of the stator and rotor by reasonably calculating the maximum permissible displacement boundaries of the RBI, taking into account the number of teeth and the accuracy of engagement of the mechanism. However, with the number of teeth Z _1.2 > 5, these boundaries expand by 1.2 ... 2 times, which increases the designability of the designed GM.

Sources of information

1. OST 39-164-84. Transmission gear rotor-stator of a downhole screw motor.

Claims (1)

The gerotor mechanism of a screw hydraulic machine containing a stator and an enclosed rotor eccentrically located in it, the teeth of which are in continuous contact and have a difference of their numbers equal to unity, the end profiles of the stator and rotor are formed by a common initial contour of the rack (mesh) with an offset, and the profile of this contour outlined by the equidistant of a shortened cycloid, characterized in that the largest permissible positive and largest permissible negative bias of the original rail contour are given with the fulfillment of the relations

and the permissible value of the contour diameter is limited by:

Where

Δh _P , Δh _OT - the largest allowable positive and largest allowable negative bias, respectively, of the original contour of the rail; D _kmax , D _kmin - the largest and smallest values of the contour diameter; a - eccentricity of the meshing mechanism; Z _1,2 - the number of teeth of the stator and rotor, respectively; D _fl is the nominal diameter of the stator troughs in the absence of mixing of the initial circuit, which is set by the formula

where Z ₂ is the number of teeth of the rotor; r is the radius of the rolling circle forming a normal cycloid of the original rail contour; r _c is the distance from the shortened cycloid to the profile points of the original rail contour.

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