EP1875076B1 - Volumetric rotary machine with rotors having asymmetric profiles - Google Patents

Abstract

Rotary displacement machine having a housing and at least two twinned rotors of asymmetrical profile, the twinned rotors each made of a core on which projects a helicoidal thread which extends above the core like a tooth. The helicoidal thread having a first predetermined dimension in a direction radial to the longitudinal axis of the twinned rotors and above the surface of a rotor. The machine having a first flank with a position and length of arc predetermined such that the shape of the first flank and the shape of the second flank each connect to one of the opposite ends of a connecting segment which constitutes a helicoidal surface. The connecting segment having a second predetermined dimension in a direction radial to the longitudinal axis of the twinned rotors such that the ratio of the second dimension over the first dimension ranges between 0.005 and 0.1.

Description

The invention relates to an improvement to volumetric rotary machines.

The invention is concerned with volumetric rotating machines intended to receive compressible fluids and which can be used as a pumping machine or even as a prime mover.

The invention relates more particularly but not exclusively to machines which comprise a housing and at least two twin rotors, including a first rotor and a second rotor, said rotors being rotatably mounted in said housing and driven in opposite directions to one another. compared to each other.

The rotors are conventionally constituted by pieces in the form of screws, that is to say parts comprising a core which carries one or more threads whose pitch may be constant or variable along the longitudinal dimension of said rotor.

In the housing, the screws form a series of "linkless locks" for which the leakage due to the operating clearances as well as the architecture and geometry of the machine affect volumetric efficiency, energy efficiency and pressure. final obtained.

Because the rotors mesh in the manner of toothed wheels, it is considered that the thread or nets each constitute a tooth projecting from the central core.

The rotors can be represented in section along a transverse plane approximately orthogonal to the longitudinal axes of their core.

• le noyau du rotor considéré, et
• une partie de la dent qui est située à une distance prédéterminée dudit noyau et au niveau de laquelle lesdits premier flanc et second flanc sont reliés.

On these cuts, we can observe the shape of each tooth and, precisely, note that the outer contour of this tooth is defined by two opposite flanks, a first flank and a second flank which each extend between,

• the rotor core considered, and
• a portion of the tooth which is located at a predetermined distance from said core and at which said first and second flanks are connected.

In general, there are three categories of rotors depending on the transverse profile of the tooth or teeth of these rotors and, precisely, rotors with so-called conjugate transverse profiles, so-called symmetrical profile rotors and so-called asymmetrical profile rotors.

• un premier flanc concave et un deuxième flanc concave, ou
• un premier flanc sur lequel on peut distinguer deux portions consécutives dont une première portion concave et une deuxième portion convexe et un deuxième flanc sur lequel on peut également distinguer deux portions consécutives dont une troisième portion convexe et une quatrième portion concave.

As regards the expression "rotors with conjugate profiles", it characterizes the use of rotors with different tooth profiles and, in particular, on the one hand, a first rotor equipped with at least one tooth which presents a first convex flank and a second convex flank and secondly a second rotor equipped with at least one tooth which can present,

• a first concave sidewall and a second concave sidewall, or
• a first flank on which can be distinguished two consecutive portions including a first concave portion and a second convex portion and a second flank on which can also be distinguished two consecutive portions including a third convex portion and a fourth concave portion.

The manufacturing by machining of this type of rotors with conjugated profiles is relatively easy and the essential difficulty lies in the calculation of the profiles.

As regards the expression "rotors with so-called symmetrical profiles", it characterizes the use of rotors, on the one hand, including the first flank and the second flank of each tooth are symmetrical with respect to a radial axis passing through the middle of the tooth and, on the other hand, whose profile geometry is symmetrical and similar for both rotors.

The calculation of the profiles and the manufacturing by machining of this type of symmetrical profile rotors are easy, but the sealing resulting from the cooperation of the rotors in the areas of tooth heads (upper areas of the teeth) of the rotors is imperfect which affects negatively the volumetric efficiency of the machines that understand them.

As for the expression "asymmetric profile rotors", it characterizes the use of a first rotor and a second rotor which have similar profiles and of which at least one tooth has a first convex flank and a second concave flank DE-A-686 298 , GB-A-112104 the concavity and the convexity being accentuated to the point that the tooth affects a curved form. (See also documents US-A-4,445,831 and US-A-3,640,649 ).

Machines that include rotors of this type are characterized by their excellent performance in terms of volumetric efficiency and final pressure obtained.

It is criticized that this type of rotor that their manufacture by machining is made difficult because of the presence of a singularity in the form of acute angle which is located at the head of the concave side of the tooth.

The performances of the machines which implement rotors with asymmetrical profiles are strongly linked, on the one hand, to the fineness with which the aforementioned geometrical singularity is machined and, on the other hand, to the manner in which the rotors are assembled and adjusted. in order to obtain a predetermined operating clearance.

Machines using rotors with asymmetric profiles and variable pitch WO-A-02/08609 , also allow to obtain very good performance, but manufacturing and assembly tolerances are very restrictive.

It is easy to conceive that it is not possible to guarantee that the sharp edge located at the head of the concave side is uniformly machined along the edge, so that in practice a sharp edge located at the head of the concave side therefore presents regularity defects.

These machining defects result in irregularities in the operating clearance present between two concave sides when they cooperate along the screw and leaks, although localized deteriorate the performance of the machine.

In addition, the leading edge of the concave side is very sensitive to abrasion and the fluid passing through the machine can cause abrasive wear which rapidly deteriorates the performance of the machine.

The invention specifically relates to volumetric rotary machines whose rotors are said to asymmetrical profiles and a result that the invention aims to obtain is a machine which while being a less constraining manufacture does not meanwhile reduced performance.

Another result that the invention aims to obtain is a machine whose performance is maintained over time.

For this purpose, the invention relates to a machine of the aforementioned type, according to claim 1.

• figure 1 : en vue de dessus, deux rotors jumelés, chacun avec un filet à pas constant,
• figure 2 : une vue en coupe du jeu de rotors jumelés de la figure 1, selon un plan radial aux deux rotors,
• figure 3 : à plus grande échelle, l'un quelconque des rotors jumelés de la figure 1, vu en coupe selon un plan radial,
• figure 4 : à plus grande échelle, un détail de la figure 3,
• figure 5 : une section de l'engrènement des rotor de la figure 1 dans le plan V-V indiqué sur ladite figure 1,
• figure 6 : une section de l'engrènement des rotors de la figure 1 dans le plan VI-VI indiqué sur ladite figure 1,
• figure 7 : une section de l'engrènement des rotors de la figure 1 dans le plan VII-VII indiqué sur ladite figure 1,
• figure 8 : une section de l'engrènement des rotors de la figure 1 dans le plan légèrement décalé par rapport au plan V-V indiqué sur ladite figure 1,
• figure 9 : à grande échelle, un détail d'un des rotors de la figure 1 dans le plan IX-IX indiqué sur ladite figure 1,
• figure 10 : en vue de dessus, deux rotors jumelés, chacun avec un filet à pas variable,
• figure 11 : une vue en coupe du jeu de rotors jumelés de la figure 10, selon un plan radial aux deux rotors,
• figure 12 : en vue de dessus, deux rotors jumelés, chacun avec deux filets à pas variable,
• figure 13 : une vue en coupe du jeu de rotors jumelés de la figure 12, selon un plan radial aux deux rotors.

The invention will be better understood on reading the following description given by way of non-limiting example with reference to the attached drawing which shows schematically:

• figure 1 in top view, two twin rotors, each with a constant pitch thread,
• figure 2 : a sectional view of the twin rotor set of the figure 1 in a radial plane to both rotors,
• figure 3 : on a larger scale, any of the twin rotors of the figure 1 , seen in section along a radial plane,
• figure 4 : on a larger scale, a detail of the figure 3 ,
• figure 5 : a section of the rotor meshing of the figure 1 in the VV plane indicated on the figure 1 ,
• figure 6 : a section of the meshing of the rotors of the figure 1 in plan VI-VI indicated on the said figure 1 ,
• figure 7 : a section of the meshing of the rotors of the figure 1 in plan VII-VII indicated on the said figure 1 ,
• figure 8 : a section of the meshing of the rotors of the figure 1 in the plane slightly offset from the VV plane indicated on the figure 1 ,
• figure 9 : on a large scale, a detail of one of the rotors of the figure 1 in the IX-IX plan indicated on the said figure 1 ,
• figure 10 : in top view, two twin rotors, each with a variable pitch thread,
• figure 11 : a sectional view of the twin rotor set of the figure 10 in a radial plane to both rotors,
• figure 12 : in plan view, two twin rotors, each with two threads with variable pitch,
• figure 13 : a sectional view of the twin rotor set of the figure 12 , in a radial plane to the two rotors.

Referring to the drawing, there is shown a rotary machine volumetric 1 comprising a housing 2 and at least two twin rotors 3, 4 said profiles asymmetrical, including a first rotor 3 and a second rotor 4, said twin rotors 3, 4 being rotatably mounted in the housing 2 and driven in rotation about their longitudinal axis 6.

Preferably, but not limited to, the longitudinal axes 6 of the twin rotors 3, 4 are parallel.

• a dans une direction radiale à l'axe longitudinal 6 de celui des rotors jumelés 3, 4 considéré et au dessus de la surface 51 de ce rotor une première dimension prédéterminée "h",
• comprend un premier flanc 9 de forme concave et un deuxième flanc 10 de forme convexe qui se raccordent au niveau d'une partie supérieure 11 de la dent 8, ledit premier flanc 9 ayant une forme d'arc d'épicycloïde.

The twin rotors 3, 4 each consist of a core 5 on which protrudes at least one helical thread 7 which, observed in a cross-sectional view of that of the twin rotors 3, 4 considered, extends above said core 5 in the manner of a tooth 8, which tooth 8,

• in a direction radial to the longitudinal axis 6 of that of the twin rotors 3, 4 considered and above the surface 51 of this rotor a predetermined first dimension "h",
• comprises a first concave-shaped flank 9 and a second convex-shaped flank 10 which are connected at an upper portion 11 of the tooth 8, said first flank 9 having an epicycloid arc shape.

The twin rotors 3, 4 may be of constant pitch type or variable pitch type.

• d'une part, ledit premier flanc 9 a un tracé 92, dit tracé modifié 92, dont la position et la longueur d'arc sont prédéterminées de manière telle que ledit tracé modifié 92 de ce premier flanc 9 et le tracé conventionnel 101 du deuxième flanc 10 se raccordent chacun à l'une des extrémités opposées "B" et "C" d'un court segment, dit segment de raccordement 12, qui par sa présence tout au long du filet hélicoïdal 7 constitue une surface hélicoïdale 13, dite méplat, supprimant la présence d'une arête vive,
• d'autre part, ledit segment de raccordement 12 a, dans une direction radiale à l'axe longitudinal 6 de celui des rotors jumelés 3, 4 considéré, une deuxième dimension "L" prédéterminée, telle que le rapport de la deuxième dimension "L" sur la première dimension "h" est compris entre 0,005 et 0,1 (cinq millièmes et un dixième).

Remarkably, instead of including a first sidewall 9 and a second sidewall 10 whose conventional lines 91 and 101 are connected at a first point "W" so as to form a sharp edge along the helical thread 7:

• on the one hand, said first flank 9 has a path 92, said modified path 92, whose position and arc length are predetermined so that said modified path 92 of this first side 9 and the conventional path 101 of the second side 9 10 flank each connect to one of the opposite ends "B" and "C" of a short segment, said connecting segment 12, which by its presence along the helical thread 7 constitutes a helical surface 13, called flat , eliminating the presence of a sharp edge,
• on the other hand, said connecting segment 12 has, in a direction radial to the longitudinal axis 6 of that of the twin rotors 3, 4 considered, a second dimension "L" predetermined, such as the ratio of the second dimension "L""on the first dimension" h "is between 0.005 and 0.1 (five thousandths and one tenth).

When each tooth of the twin rotors 3, 4 is defined by a first sidewall 9 and a second sidewall 10 which are connected to an outer surface 14 of substantially cylindrical profile of half outer diameter "Ra", instead of this outer surface 14 is connected in drawing the first flank 9 at a first point "W" so as to form a sharp edge along the helical thread 7, the outer surface 14 is connected to the path of said first flank 9 by the connecting segment 12.

Preferably, the ratio of the second dimension "L" on the first dimension "h" is between 0.005 and 0.1 (five thousandths and one tenth), when the paired rotors 3, 4 have a diameter of between fifty millimeters ( 50 mm) and three hundred and fifty millimeters (350 mm).

• le tracé conventionnel 91 du premier flanc 9 et le cercle, dit cercle d'enveloppe "F" qui circonscrit celui des rotors jumelés 3, 4 considéré, ont un point d'intersection "W", dit premier point "W", situé sur une première droite "D1" qui passe par un deuxième point "O" situé sur l'axe longitudinal 6 de celui des rotors jumelés 3, 4 considéré,
• le tracé modifié 92 du premier flanc 9 et le cercle "F" ont un point d'intersection "Z", dit troisième point "Z", situé sur une deuxième droite "D2" qui passe par le deuxième point "O" et forme avec la première droite "D1" un premier angle Alfa dont la valeur peut être approchée par calcul selon la première équation, $$\mathit{ArcCos}\left[\frac{-{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">L</figure-callout>}}^2{\left(L-2<figure-callout\; id="2"\; label="\; Ra"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}"></figure-callout>\mathit{Ra}\mathit{}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">H</figure-callout>}}^2\left(L^2-2\mathit{LRa}+2{\mathit{<figure-callout\; id="2"\; label="Ra"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Ra</figure-callout>}}^2\right)}{2{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">H</figure-callout>}}^2\mathit{Ra}\left(-L+\mathit{Ra}\right)}\right]$$
  
  avec les valeurs des paramètres,
  • "Ra" qui représente le demi-diamètre extérieur de celui des rotors jumelés 3, 4 qui est considéré,
  • "L" qui représente l'amplitude du segment de raccordement 12 dans une direction radiale à celui des rotors jumelés considéré, la valeur de l'amplitude correspondant à la différence entre le demi diamètre extérieur "Ra" et la valeur d'un rayon "Rp" qui sépare l'axe longitudinal 6 du noyau 5 d'un point du segment de raccordement 12 qui est le plus proche de cet axe longitudinal 6,
  • "H" qui représente l'entraxe entre les rotors jumelés 3, 4.

In a remarkable way:

• the conventional path 91 of the first sidewall 9 and the circle, said envelope circle "F" which circumscribes that of the twin rotors 3, 4 considered, have a point of intersection "W", said first point "W", located on a first line "D1" which passes through a second point "O" located on the longitudinal axis 6 of that of the twin rotors 3, 4 considered,
• the modified path 92 of the first sidewall 9 and the circle "F" have a point of intersection "Z", said third point "Z", located on a second line "D2" which passes through the second point "O" and forms with the first line "D1" a first angle Alfa whose value can be approximated by calculation according to the first equation, $$\mathit{ArcCos}\left[\frac{-{\mathrm{The}}^2{\left(\mathrm{The}-2<figure-callout\; id="2"\; label="\; Ra"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\; </figure-callout>\mathit{Ra}\mathit{}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">H</figure-callout>}}^2\left({\mathrm{The}}^2-2\mathit{LRa}+2{\mathit{<figure-callout\; id="2"\; label="Ra"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Ra</figure-callout>}}^2\right)}{2{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">H</figure-callout>}}^2\mathit{Ra}\left(-\mathrm{The}+\mathit{Ra}\right)}\right]$$
  
  with the values of the parameters,
  • "Ra" which represents the outer half-diameter of that of twin rotors 3, 4 which is considered,
  • "L" which represents the amplitude of the connecting segment 12 in a direction radial to that of the paired rotors considered, the value of the amplitude corresponding to the difference between the outer half-diameter "Ra" and the value of a radius " Rp "which separates the longitudinal axis 6 of the core 5 from a point of the connecting segment 12 which is closest to this longitudinal axis 6,
  • "H" which represents the spacing between the twin rotors 3, 4.

The modified path 92 of the first sidewall 9 and the outer surface 51 of the core 5 are connected to a point "A".

avec:

• "H" qui représente l'entraxe entre les rotors jumelés 3, 4, et
• "Ra" qui représente le demi diamètre extérieur de celui des rotors jumelés 3, 4 qui est considéré.

In a still remarkable manner, the connecting segment 12 is inclined with respect to the first straight line "D1" of a second angle Beta whose value can be approximated by calculation according to the second equation, $$\mathrm{Arc\; Cosinus}\left(\mathrm{H}\mathrm{/}\left(\mathrm{2}\mathrm{Ra}\right)\right)$$

with:

• "H" which represents the spacing between the twin rotors 3, 4, and
• "Ra" which represents the half outer diameter of that of the twin rotors 3, 4 which is considered.

Practically, the position of the modified path 92 of the first sidewall 9 can be adjusted by oscillating the support of the conventional path 91 of said first sidewall 9, a first angle Alfa around the point O.

The connecting segment 12 is inclined with respect to the first straight line "D1" of a second angle Beta, this second angle being adjusted so that throughout the helical threads 7 of the twin rotors 3, 4, each helical surface 13 which is connected to a first sidewall 9 of one of the twin rotors 3, 4 can extend substantially parallel to at least one zone of the first sidewall 9 of the other of the twin rotors 3, 4, which adjoins the connecting segment 12 of this other rotor.

A machine according to the invention has, in place of the conventional sharp edge, a helical surface 13 formed by a flat.

Such a flat part can be, in particular by means of conventional tools, easily and precisely machined which guarantees less leakage than with a sharp edge.

The dispersion of performance with respect to machining and mounting tolerances will therefore be much lower, while providing a simplification of the machining of twin rotors and the possibility of increasing the machine operating clearances without degrading performance.

Advantageously, the helical surface 13 obtained by virtue of the presence of the flat remains a controlled surface, and this, that the pitch of the rotors is constant or variable.

As regards the flat, it is also desirable that its length remains small with respect to the height of the tooth, to avoid the appearance of a localized leak (an expression better known by the German term "Blasloch") which would be likely to degrade system performance ( Figures 7 and 8 ).

• un rayon "Ra" de 65 mm (soixante cinq millimètres) et une hauteur de dent "h" de 30 mm (trente millimètres), on a une largeur "L" de méplat 12 de 1 mm (un millimètre),
• un rayon "Ra" de 105 mm (cent cinq millimètres) et une hauteur de dent "h" de 60 mm (soixante millimètres), on a une largeur "L" de méplat 12 de 1,5 mm (un virgule cinq millimètre),
• un rayon "Ra" de 130 mm (cent trente millimètres) et une hauteur de dent "h" de 75 mm (soixante quinze millimètres), on a une largeur "L" de méplat 12 de 2 mm (deux millimètres).

As illustrative examples, for:

• a radius "Ra" of 65 mm (sixty five millimeters) and a tooth height "h" of 30 mm (thirty millimeters), we have a width "L" of flat surface 12 of 1 mm (one millimeter),
• a radius "Ra" of 105 mm (one hundred and five millimeters) and a tooth height "h" of 60 mm (sixty millimeters), one has a width "L" of flat 12 of 1.5 mm (one point five millimeters) ,
• a radius "Ra" of 130 mm (one hundred and thirty millimeters) and a height of tooth "h" of 75 mm (seventy-five millimeters), one has a width "L" of flat 12 of 2 mm (two millimeters).

On the drawings, in Figures 7 and 8 the localized leak was symbolized by a simple, unnoticed arrow.

It should be noted that the aforementioned dimensions, angles and profiles are defined at the operating clearance.

It should also be noted that the advertised characteristics are applicable to machines that include more than two rotors.

The fact that the rotors are of the same diameter, of different diameters, or even have different diameters according to their longitudinal dimension remains compatible with the present invention.

Claims (6)

1. Rotary displacement machine (1) comprising a housing (2) and at least two twinned rotors (3, 4) referred to as being of asymmetrical profile, of which a first rotor (3) and a second rotor (4), said twinned rotors (3, 4), being mounted rotating in the housing (2) and driven in rotation about their longitudinal axis (6)

   • these twinned rotors (3, 4) each being made up of a core (5) on which projects at least one helicoidal thread (7) which, seen in a cross-sectional view of that of the twinned rotors (3, 4) being considered, extends above said core (5) in the manner of a tooth (8), which tooth (8)

   • has a first predetermined dimension ("h") in a direction radial to the longitudinal axis (6) of that of the twinned rotors (3, 4) being considered and above the surface (51) of this rotor,

   • comprises a first flank (9) of concave shape and a second flank (10) of convex shape which connect at the level of an upper portion (11) of the tooth (8), said first flank (9) having the shape of an epicycloidal arc,

   this machine being characterized in that instead of comprising a first flank (9) and a second flank (10) whose conventional shapes (91) and (101) connect at a first point ("W') in such a way as to form a sharp edge along the helicoidal thread (7):

   - on the one hand, said first flank (9) has a shape (92), referred to as modified shape (92), whose position and length of arc are predetermined such that said modified shape (92) of this first flank (9) and the conventional shape (101) of the second flank (10) each connect to one of the opposite ends ("B") and ("C") of a short segment, referred to as connecting segment (12), which by its presence along the entire helicoidal thread (7) constitutes a helicoidal surface (13), referred to as flattened, eliminating the presence of a sharp edge,

   - on the other hand, said connecting segment (12) has, in a direction radial to the longitudinal axis (6) of that of the twinned rotors (3, 4) being considered, a second predetermined dimension ("L") such that the ratio of the second dimension ("L") over the first dimension ("h") ranges between 0.005 and 0.1 (five thousandths and one tenth).
2. Machine according to claim 1 characterized in that when each tooth (8) of the twinned rotors (3, 4) is defined by a first flank (9) and a second flank (10) which are connected to an outer surface (14) of substantially cylindrical profile of outer radius ("Ra"), instead of this outer surface (14) being connected to the shape of the first flank (9) at a first point ("W") in such a way as to form a sharp edge along the helicoidal thread (7), the outer surface (14) is connected to the shape of said first flank (9) by the connecting segment (12).
3. Machine according to claim 1 or 2, characterized in that the ratio of the second dimension ("L") over the first dimension ("h") ranges between 0.005 and 0.1 (five thousandths and one tenth), when the twinned rotors (3, 4) have a diameter ranging between fifty millimeters (50 mm) and three hundred fifty millimeters (350 mm).
4. Machine according to one of the claims 1 to 3, characterized in that the connecting segment (12) is inclined with respect to the first straight line ("D1") of a second angle beta, this second angle being adjusted such that along the entire helicoidal threads (7) of the twinned rotors (3, 4), each helicoidal surface (13) which connects to a first flank (9) of one of the twinned rotors (3, 4) is able to extend substantially parallel at least to a zone of the first flank (9) of the other of the twinned rotors (3, 4) which is contiguous to the connecting segment (12) of this other rotor.
5. Machine according to one of the claims 1 to 4 characterized in that the connecting segment (12) is inclined with respect to the first straight line ("D1 ") of a second angle beta the value of which is able to be approximated by calculation according to the second equation $$\mathrm{Arc\; Cosine}\left(\mathrm{H}\mathrm{/}\left(\mathrm{2}\mathrm{Ra}\right)\right)$$

   

   with :

   - ("H") which represents the center distance of axes between the twinned rotors (3, 4), and

   - ("Ra") which represents the outer radius of that of the twinned rotors (3, 4) being considered.
6. Machine according to any one of the claims 1 to 5, characterized in that :

   - the conventional shape (91) of the first flank (9) and the circle, referred to as addendum circle ("F") which circumscribes the one of the twinned rotors (3, 4) under consideration, have a point of intersection ("W"), referred to as first point ("W'), situated on a straight line ("D1") which passes through a second point ("O") situated on the longitudinal axis (6) of that of the twinned rotors (3, 4) under consideration,

   - the modified shape (92) of the first flank (9) and the circle ("F") have a point of intersection ("Z"), referred to as third point ("Z"), situated on a second straight line ("D2") which passes through the second point ("O") and forms with the first straight line ("D1") a first angle alpha, the value of which is able to be approximated by calculation according to the first equation $$\mathit{ArcCos}\left[\frac{-L^2{\left(L-2\mathit{Ra}\right)}^2+H^2\left(L^2-2\mathit{LRa}+2{\mathit{Ra}}^2\right)}{2H^2\mathit{Ra}\left(-L+\mathit{Ra}\right)}\right]$$

   

   with the values of the parameters

   • ("Ra") which represents the outer radius of that of the twinned rotors (3, 4) being considered,

   • ("L") which represents the relative value of the connecting segment (12) in one direction radial to that of the twinned rotors being considered, the magnitude of the relative value corresponding to the difference between the outer radius ("Ra") and the value of a radius ("Rp") which separates the longitudinal axis (6) of the core (5) from a point of the connecting segment (12) which is closest to this longitudinal axis (6),

   • ("H") which represents the center distance of axes between the twinned rotors (3, 4).

Images