RU2117824C1 - Toothed gear for screw-rotor machine - Google Patents

Abstract

FIELD: compressor construction. SUBSTANCE: toothed gear end section has tooth profile asymmetrical with respect to straight line extending through tooth apex and center of revolution of rotor. Rotor with lesser number of passes at low pressure side from projection circle to initial circle is defined by joined portions disposed in succession from tooth apex to base: curve described by exponential function and arcs of circles of larger and lesser radii. Center of arc of larger radius is offset from straight line connecting center of screw with tooth apex to high pressure side. Portions of rotor with large number of passes make envelopes of related portions of rotor with small number of passes. EFFECT: increased efficiency and loading capacity of screw-rotor machine. 2 dwg

Description

 The invention relates to compressor technology, namely to screw expansion machines, and can be used in screw compressors.

 The working process in a screw machine takes place in paired cavities, which are formed by hollows of screws with a larger and smaller number of approaches. The better the paired cavities are isolated and the less leakage between them, the higher the volumetric and energy coefficients of the machine.

In general terms, the basic requirements that gearing of screw machines must satisfy can be formulated as follows [1, p. sixteen]
1. The engagement of the screws should ensure tightness in the transverse, that is, in the direction normal to the plane of the longitudinal axes. In other words, the engagement should ensure the tightness of the screws between the high and low pressure areas.

 2. The engagement of the screws must ensure axial tightness, i.e. tightness between paired cavities.

 The tightness of the screw machine between the high and low pressure areas is determined by the leakage rate from high-pressure paired cavities in the cavity, which are currently connected to the low-pressure chamber (compressor suction chamber and expander outlet chamber). The amount of leakage is affected by the relative length of the contact line and the resistance to gas leakage, determined by the length of the throttling path.

 The degree of tightness of the screw machine in the axial direction is determined by flows between the paired cavities through the axial hole in the area of the screw boring in the high-pressure region (triangular gap) and along the ridges of the teeth of the screws.

 Known gears of screw machines [1, p. 19] with screw teeth asymmetric in the end section, in which the tooth profile of the screw with a smaller number of visits from the high pressure side is made according to the cycloid, which allows to reduce axial leakage by reducing the triangular gap. Profiles of the teeth of the screws from the low pressure side are performed along curves, allowing to reduce the relative length of the contact line by reducing its absolute value and increasing the total area of the hollows of the screws.

Also known is the gearing of a screw machine, selected as a prototype, in which a part of the profile of a tooth of a screw with a smaller number of entries from the low pressure side is outlined by two arcs of circles of larger and smaller radii, successively located from the top of the tooth to its base, with the center of the arc of a smaller radius located on a straight line passing through the top of the tooth and the center of rotation of the rotor, and the center of the other is biased towards high pressure, which allows to reduce the relative length of the contact line and increase the total th area depressions screws, i.e. performance [2]. One of the disadvantages of this engagement is the small length of the gas throttling path along the top of the screw tooth with a smaller number of starts, which leads to an increase in the pressure difference in the plane of the screws with a larger and smaller number of starts, and, consequently, to a decrease in the efficiency of the machine [1, p. 214 - 215],
As you know, in the place of contact of the screws there are energy losses associated with the friction of surfaces against each other. These losses increase with decreasing pressure angle, i.e. the angle between the normal to the profile at the point of its intersection with the initial circle and the normal to this circle. With decreasing pressure angle, the load capacity decreases, since increasing energy losses lead to increased wear of the teeth.

 Another disadvantage of this engagement is the low pressure angle.

 An object of the invention is to increase the efficiency and load capacity by increasing the length of the throttling path along the top of the rotor tooth with a smaller number of strokes and increasing the pressure angle while decreasing with respect to the length of the contact line.

 This problem is achieved by the fact that in the gearing of a screw machine, containing two parallel-located with mutually bent screw surfaces of the rotor with a large and small number of approaches, each of which in the end section has a tooth profile asymmetric with respect to a straight line passing through the top of the tooth and the center of rotation rotor, part of the profile with a smaller number of approaches from the low pressure side from the circumference of the protrusions to the initial circumference are formed by two arcs of smaller and larger radius, the last of which executed equal to 1.35 tooth height, and its center is shifted towards high pressure by a distance equal to 0.2 tooth height.

A curve ρ = ρ ₀ -a ₁ φ ² -a ₂ φ ^{2n is} introduced into the profile, where the radius is the vector ρ drawn from a point lying on a straight line drawn from the center of rotation to the top of the tooth and lagging by ρ ₀ equal to 1 , 0 - 1.1 tooth height, φ is the polar angle, n is an integer. Moreover, this curve and the curves formed by arcs of circles of larger and smaller radius are located sequentially from the top of the tooth to its base and are conjugated. Moreover, the coefficients a ₁ and a _{2 are} determined from the condition that the functions and their first derivatives are equal at the conjugation point of the curve and the circular arc of a larger radius, circular arcs of larger and smaller radii are made up, respectively, of more than 1.35 to 1.45 and 0.7 - 0, 3 tooth heights, the center of the arc of a larger radius is offset by a distance of more than 0.2 to 0.27 of the height of the tooth, and the radii of the central circles passing through the points of intersection of the curves and the initial circle are respectively 0.94 - 0.97 and 0.25 - 0.35 tooth height.

, где f_1п, f_2п - соответственно площади впадин винтов с меньшим и большим числом заходов, R_1н - радиуса начальной окружности винта с меньшим числом заходов, h = R₁ - R_1н - высота зуба, R₁ - радиус внешней окружности винта с меньшим числом заходов.In FIG. 1 shows the gearing of a screw machine, and FIG. 2 - dependence of the relative total area of the depressions (f _1p + f _2p ) / R $\genfrac{}{}{0ex}{}{\text{2}}{\text{1n}}$ , The relative length of the line contact along section BE L _BE / R _1N, the relative length of the total contact line of the line for all sites profile ΣL / R _1N and relative contact line length ΣL • R _{1 N} / (f _H1 + f _2n) by the relative magnitude of radius greater circular arcs

, where f _1p , f _2p are, respectively, the area of the hollows of the screws with a smaller and larger number of entries, R _1n is the radius of the initial circumference of the screw with a smaller number of entries, h = R ₁ - R _1n is the height of the tooth, R ₁ is the radius of the outer circumference of the screw with fewer calls.

 The gearing of the screw machine (Fig. 1) contains the rotors 1 and 2 with a smaller and a larger number of approaches.

The profile of tooth 3 is asymmetric with respect to the straight line O ₁ B ₁ passing through the center of rotation of the rotor 1 and the top of the tooth B ₁ ; accordingly, the profile of the cavity 4 is asymmetric with respect to the straight line O ₂ B ₂ passing through the center of rotation of the rotor 2 and the lower point of the cavity B ₂ .

On the high-pressure side, the profile of the rotor tooth with a smaller number of starts A ₁ B _{1 is} made according to the cycloid formed by the point A _{2 of the} initial circle R _{2n of the} rotor with a large number of runs when the latter is rolling along the initial circle R _1n without sliding, and the tooth profile with a large number of runs A ₂ B ₂ - along the cycloid formed by the point B _{1 of} tooth 3 during rolling without sliding of the circle R _1n along R _2n .

On the low-pressure side, the profile of the rotor tooth with a smaller number of strokes is formed by the curves B ₁ C ₁ , C ₁ D ₁ , D ₁ E ₁ , E ₁ F ₁ sequentially located from the top of the tooth to its base. Section B ₁ C _{1 is} formed by the curve ρ = ρ ₀ -a ₁ φ ² -a ₂ φ ²ⁿ , section C ₁ D ₁ is an arc of a circle of a larger radius R, the center of which is offset from the straight line connecting the center of the rotor with the tooth tip O ₁ B ₁ by l in the direction of high pressure, and the section D ₁ E ₁ - by an arc of a circle of smaller radius.

The tooth leg (i.e., the part of the tooth lying between the circles R _1n and the circumference of the depressions is made around a circle of radius r ₀ .

The boundaries of the plots are the central circles of radii R _C1 , R _D1 , R _1n , and the differences (R _C1 - R _1n ) and (R _D1 - R _1n ) are respectively 0.94 - 0.97 and 0.25 - 0.35 from tooth height h.

The radius vector ρ is drawn from the point O _ρ lying on the line connecting the center of the rotor to the top of the tooth, at a distance ρ ₀ from the top of the tooth, equal to 1.0 - 1.1 from h. The value of n is an integer of four, and the value of the constants a ₁ and a ₂ is determined based on the equality of the functions and their first derivatives at the point C _{1 of} conjugation of the first and second sections. The coordinates of the center of the arc of a smaller radius are determined based on the equality of functions and their first derivatives at the point D _{1 of the} conjugation of the second and third sections, as well as the thickness of the rotor tooth with a large number of approaches E ₂ G ₂ , equal to 0.4 - 0.5 of h.

A circle of radius r ₀ touches the initial circle of the rotor 1, and the value of its radius and the coordinates of the center are determined from the equality of functions and their first derivatives at the point E ₁ .

On the low pressure side, the profile of the rotor tooth with a large number of strokes is formed by the curves B ₂ C ₂ , C ₂ D ₂ , D ₂ E ₂ , E ₂ F ₂ , which are the envelopes of the curves B ₁ C ₁ , C ₁ D ₁ , D ₁ E ₁ , E ₁ F ₁ .

The profile of screws with the following basic geometric characteristics was calculated:
a rotor with a smaller number of approaches: the radius of the outer circle R ₁ = 107.5 mm, the radius of the initial circle R _1n = 64 mm, the radius of the circumference of the depressions R _1vn = 62 mm, the number of teeth Z ₁ = 4;
a rotor with a large number of approaches: the radius of the outer circle R ₂ = 98 mm, the radius of the initial circle R _2n = 96 mm, the radius of the circumference of the depressions R _2vn = 52.5 mm, the number of teeth Z ₂ = 6;
the distance between the centers of the rotor A = 160 mm.

 With the geometric dimensions given above, the value of the depth of the gap on the nose of tooth 3 is B = 5.6 - 6.3 mm, while with the same basic geometric dimensions of the screws and nose made according to [2], the value B = 2 , 51 mm, i.e. less 2.2 - 2.5 times. The greater depth of the gap determines greater resistance to gas overflowing along the screw ridge with a large number of starts, a smaller pressure difference in the hollows of the screws, and, consequently, an increase in the economic efficiency of the screw machine.

в точке его пересечения E₁ с начальной окружностью и нормальною к этой окружности O₁E₁) до величины 60 - 65^o против 48,5^o для винтов таких же основных геометрических размеров, выполненных по [2].The magnitude and coordinates of the center of the arc of a smaller radius make it possible to increase the pressure angle α _p (i.e., the angle between the normal to the profile

at the point of its intersection E ₁ with the initial circle and normal to this circle O ₁ E ₁ ) to a value of 60 - 65 ^o versus 48.5 ^o for screws of the same basic geometric dimensions, made according to [2].

With an increase in the pressure angle α _p , the energy loss due to the friction of the surfaces of the screws decreases and, therefore, the load capacity of the screws increases due to a decrease in the wear of the teeth.

The main curve of tooth 1 is the portion C ₁ D ₁ described by a circle of a larger radius R. FIG. Figure 2 shows the dependences from which it follows that with an increase in the relative value of R / h, the total relative area of the troughs increases (f _1p + f _2p ) / R $\genfrac{}{}{0ex}{}{\text{2}}{\text{1n}}$ determining the performance of a screw machine. If the value R = (1,35 - 1,45) • h value is the relative length of the contact line section _BE L BE / R _1N relative value of the total length of the contact line on all sites of the screw engagement ΣL / R _1N and the value of the total length of the contact line, divided by the total area of the troughs ΣL • R _{1 N} / (f + f _{2n 1H),} have the lowest values. Moreover, the displacement of the center of the circle with a larger radius is 0.2 - 0.27 h.

 As you know, the moment of gas forces on the driven screw of the compressor with an asymmetric tooth profile, considered in SU, copyright certificate N 1135922, is directed towards its rotation and is 12 - 16% of the moment on the lead screw [1, p. 349].

 This value of the moment makes it difficult to use this profile in the expansion machine. The moment of resistance to rotation of the screw of the friction forces is always directed against rotation and, in the case of using screws with such a profile in the expander, the moment from gas forces will act in the same direction (the direction of rotation of the rotor 2 in Fig. 1 for the expander will be counterclockwise, and the moment friction and gas forces - clockwise). As a result, the profile surfaces will transmit a moment equal to the sum of these moments, which will lead to increased wear of the screw surfaces and friction losses of their surfaces.

 In the proposed screw profile, the moment on the screw with a large number of starts in FIG. 1 is also directed clockwise, but it is only 2 - 3% of the moment on the screw with fewer starts. As a result, the moment transmitted through the side surfaces of the profiles will be significantly reduced when using rotors in an expansion machine. This moment also allows you to use this profile in a compressor machine.

 Thus, the execution of part of the profile from the low pressure side according to the curves described above allows, with an increase in resistance along the top of the screw crest with a smaller number of starts and an increase in load capacity, at the same time reduce the relative length of the contact line by 1.5 - 2%, which increases the efficiency of the screw machine.

Sources of information
1. Sakun I.A. Screw compressors. - L .: Engineering, 1970.

 2. SU copyright certificate, 1135922, F 04 C 18/16, 1985

Claims (1)

Toothed gearing of a screw machine, containing two rotors with a large and small number of strokes parallel to the mutually bent helical surfaces of the rotor, each of which in the end section has a tooth profile asymmetric with respect to a straight line passing through the tooth apex and the center of rotation of the rotor, part of the profile with a smaller number of strokes from the low pressure side from the circumference of the protrusions to the initial circumference is formed by two arcs of smaller and larger radii, the last of which is made equal to 1.35 of the height of the tooth, and its price p is biased toward the high pressure at 0.2 tooth height, characterized in that the profile is introduced curve
ρ = ρ ₀ -a ₁ φ ² -a ₂ φ ²ⁿ ,
where the radius vector ρ is drawn from a point lying on a straight line drawn from the center of rotation to the top of the tooth and spaced ρ ₀ equal to 1.0 - 1.1 tooth height, φ is the polar angle, n is an integer, at the same time, this curve and the curves formed by arcs of circles of larger and smaller radii are located sequentially from the top of the tooth to its base and are conjugated, and the coefficients a ₁ and a _{2 are} determined from the condition that the functions and their first derivatives are equal at the junction of the curve and the arc of a circle of greater radius, circular arcs of a larger and of smaller radii are made by components, respectively, over 1.35 to 1.45 and 0.7 - 0.8 of the tooth height, the center of the arc of a larger radius is offset by a distance of more than 0.2 to 0.27 of the tooth height, and the difference of the radii of the central circles passing through the points of conjugation of the curves and the initial circumference are respectively 0.94 - 0.97 and 0.25 - 0.35 of the height of the tooth.

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