EP1340912A1 - Internal gear machine with teeth clearance - Google Patents

Abstract

The annular gear machine has an inner gearwheel (1) with external teeth (1a) meshing with internal teeth (2i) on a second gearwheel (2) with a pitch circle axis (D2) eccentric to the rotational axis of the inner gearwheel. The intermeshing teeth have a radial (PR) and a tangential gear running clearance, with the tangential clearance smaller than the radial clearance. The profile of the tooth points or tooth roots of the teeth is formed by or from the locus curve of a point on the circumference of a pitch circle, the radius of which steadily decreases or decreases from the flank regions to the apex region. An Independent claim is included for a gear set for an annular gear machine of the displacement type.

Description

The invention is with the backlash of gear sets of gerotor pumps and gerotor motors of the positive displacement type.

Toothed ring pumps compress a working fluid and thereby promote it from one Low pressure side to a high pressure side, while ring gear motors from a lower Pressurized working fluid to be driven, which is supplied to a high-pressure side and is discharged to a low pressure side of the gerotor motor. Both types of one Tooth ring machine have a gear set, which has an inner spur gear with a External teeth and an outer spur gear having an internal toothing. The Internal toothing generally has one more tooth than the outer toothing. The two gears are in meshing meshing. At a Relative rotation of the two gears arise between the teeth of the inner wheel and the teeth of the outer wheel encircling, increasing and decreasing Fluid cells, which the fluid in an operation as a pump from a low pressure side to a high-pressure side and in an operation as an engine from a high-pressure side to a Lead low pressure side of the gear ring machine.

For such gear sets, it has been proven, the tooth tips of the inner wheel and the Toothed feet of the outer wheel as epicycloids and the toothed feet of the inner wheel and the To form tooth tips of the outer wheel as Hypozykloiden. The epicycloids become by unrolling a small pitch circle, the inner wheel and the outer wheel can be the same, but not necessarily, on the pitch circle of the inner wheel or the Outer wheel formed. The hypocycloids are formed accordingly, again is true that the small pitch circles at the inner wheel and the outer wheel advantageously Although should be the same, but not equal.

Depending on the speed and the pressure level of the working fluid, the backlash of the Both gears may be different. At high relative speed of the gears is a large backlash desirable because of the frictional and the Temperature differences of the two gears. At low relative speed and mostly high working pressure on the high pressure side, small tooth games are desirable to to keep the volumetric losses (leakage) low. But there are also other influencing factors which are noteworthy for the dimensioning of the dental games are. Such other factors are in particular the unavoidable out-of-roundness the gearing due to a never perfect manufacturing, the accuracy of Rotary bearing of one of the gears or both gears and the deviation an actual eccentricity of the gears of one of the calculation of Gears based eccentricity. As eccentricity is in this As usual understood the distance of Wälzkreisachsen the gears.

DE 42 00 883 solves the problem of radial backlash in that the Epicycloids or the hypocycloids or both in combination to a certain extent Dimensionally flattened towards their Wälzkreisen. In order to get the flattening is for the respective cycloids a smaller rolling circle unrolled on a large fixed circle, wherein However, the profile of the gearing does not have a point on the circumference of the small Rollkreises, but is described by a point that depends on the scope of small pitch circle is shifted to its center point. The cycloids thus obtained the teeth are connected by straight pieces. That at the point the deepest meshing required tangential backlash, i. the backlash, is characterized by an equidistant withdrawal by the rolling of the rolling circles obtained contour of at least one of the teeth. In this known The type of interlocking, however, is the calculation of the point in the transition from the epicycloids to the hypocycloids consuming. Furthermore arise mechanical noises due to unsteady points.

EP 1 016 784 A recommends the cycloids of the inner rotor and of the outer rotor Rolling of four small rolling circles, each with different radii to produce. By this measure, while a radial backlash while avoiding discontinued jobs, but this is due to the Production instructions of epi- and hypocycloids with a tangential backlash bought, which is larger than the radial backlash. In the area of the deepest tooth intervention Thus, the gap formed between the teeth widens from the apex of the engaging tooth head to the flanks of the tooth in question. The gearing is problematic. Too large a backlash in the circumferential direction leads in the area of Wälzkreises to a hammering of the teeth in the circumferential direction, because hydraulic and dynamic forces cause a Flankenanlagewechsel. Is this tangential backlash too large, the liquid film between the sliding rolling tooth flanks is too thick and accordingly the attenuation of the caused by the edge system change Push too small. A hammering of the teeth on each other is inevitable, especially at high speeds, low viscosity of the working fluid and large Run, Full diameters. Furthermore, the enlargement of the backlash is towards the flanks the volumetric efficiency of the ring gear machine detrimental.

It is an object of the invention to intermesh teeth of a innenachsigen gear set of a ring gear machine to be designed so that the volumetric efficiency improves and the noise of the Gear set is reduced. At the same time, however, the gearing should be on based on a simple mathematical generation rule.

A ring gear machine, as the invention relates, has a housing with a Gear chamber into which an inflow and outflow for a working fluid open. The Working fluid is preferably a liquid, in particular a lubricating oil or a Hydraulic fluid. The ring gear machine further comprises a gear set at least one externally toothed inner gear and an inner toothed outer Gear wheel meshing with each other in a meshing engagement. If both gears rotate relative to the housing, the gear set is in the gear chamber added. If one of the gears is a stator, it forms the gear chamber preferably with. The at least two gears have eccentric to each other Rolling circle axes. The internal toothing of the outer gear has at least one Tooth more than the external toothing of the inner gear; preferably it has exactly one more tooth. In a rotary drive of one of the gears form the intermeshing gears expanding and compressing, i. yourself increasing and decreasing delivery cells, the working fluid from the inflow to lead to the drain.

The at least two gears of the gear set rotate in most Both applications are each about their own Wälzkreisachse, the housing Usually forms a pivot bearing for one of the two gears and the other is not rotatably connected to a rotary drive or driven member. In relation to However, the housing does not need to have both of the at least two gears around it Rotate rotary axes. An external gear that is stationary relative to the housing so-called external stator, is particularly known in so-called orbit machines, the derive their name from that the inner gear in the relative to the housing resting external stator performs two superimposed rotational movements, namely a Kreisorbitbewegung to a housing-fixed axis of rotation and a rotational movement the own rolling circle axis.

What the tooth shape of at least one of the intermeshing gears As far as their tooth heads or tooth roots or their tooth tips and tooth roots are concerned derived in combination of cycloids, i. the relevant tooth head contour or Tooth base contour can be generated by rolling a rolling circle on a fixed circuit become. The fixed circle is concentric with the rolling circle axis of the relevant Toothing. When we talk about derived cycloids in the following, they will Cycloids understood by rolling a rolling circle with variable radius can be generated on a fixed circuit. The intermeshing Gears have in the course of a radial and a tangential backlash. The radial backlash is called the distance of the top circle of a toothing to the Base circle of the other teeth understood, if the teeth the eccentricity to each other, which is based on their generation. The tangential Backlash is under the same condition the backlash backlash, i. the backlash in the circumferential direction, measured on the pitch circle of one of the gears the site of the deepest meshing.

The invention is related to the above definition of the toothed running games. The However, practical measurement is conveniently carried out in a measuring machine by the Gears of the gear set individually measured their head and Fußkreis after and out The data obtained from these are used to calculate the number of sprocket plays.

A particularly simple method of measurement which is also suitable for the practical measurement is that the radial backlash P _{R is} measured as the distance between the opposing tooth tips at the point of least tooth engagement, when the toothed wheels are removed and with their two teeth in place Deepest tooth engagement are pressed radially against each other. If the two teeth in this state pressed exactly only radially against each other, so remains at the point of the deepest meshing on both sides of the apex of the engaging tooth head in the circumferential direction ever a backlash between the two teeth. The sum of these two-sided flank plays on the pitch circle of one of the gears represents in a first approximation the tangential backlash. By actually pushing the teeth against each other, a radial backlash at the point of least tooth engagement can also be determined in a first approximation simply by inserting a filling gauge between the opposite tooth heads of the toothings.

However, the practical ways of measuring the backlash are only supplementary pointed out, since the two Zahnlaufspiele, as already noted above, on the Generation based conditions, such as in particular exact eccentricity, are related. The more exact the production of the gears and the measuring method for the Tooth games are, the more are the determined by practical measurement Tooth games, however, the mathematical Zahnlaufspielen in the context of the invention be approximate.

According to the invention, the intermeshing serrations are designed to the tangential tooth clearance is smaller than the radial tooth play. After inventive generation rule of at least one of the teeth the profile of the tooth heads or the tooth feet of this toothing from the locus or formed from the locus of a point on the circumference of a small pitch circle, its radius is from the two flank areas to the apex area for the Generation of the tooth head profile steadily reduced or for the generation of the Tooth profile steadily increased. Also advantageous is a Zahnfußprofil, of the Locus or from the locus of a point to the circumference of a small rolling circle is formed whose radius extends from the two flank regions to the apex region each tooth root steadily reduced. Such a Zahnfußprofil, to the pitch circle of the relevant gear is flattened in accordance with the invention is, on the one hand mathematically and therefore also practically in a simple manner and can produce serve in particular to improve the support of the gears to each other and also to a dead volume to an engaging, flattened tooth head reduce. In connection with the flattening of the tooth feet, such a flattened Tooth head in particular a tooth head according to the invention or else one according to a be another flattened tooth head. The applicant retains it before, a gear with a toothing according to the invention Generating rule of the rolling circle variation and a gear set with such a Gear, in particular a gear set for a ring gear machine, even without that Claiming feature of the inventively larger radial backlash.

Preferably, the radius of the respective rolling circle changes from both Base points of each tooth tip or tooth root on the pitch circle of the teeth steadily. The generated or generated according to this rule locus can directly form the relevant profile. However, the profile can only be on such based on a locus, for example, behind the corresponding locus equidistant withdrawn. The deviation of the profile from the to However, generation locus generated locus is at most so large that thereby the present invention small tangential gear play can be adjusted.

The rolling circle can be a small rolling circle that does not have the larger fixed circle encloses and rolls on the fixed circuit outside. However, the rolling circle can also be a be large rolling circle, which rolls on the outside of the fixed circuit, but in this case encloses a smaller fixed circle. Mathematically, it is a crank movement of two cranks, in the plane of the pitch circle of the teeth to be generated. The Both cranks are connected together in a swivel joint. The one of the two Cranking rotates about a fixed pivot point on the pitch axis, while that of the fixed pivot point outer of the two cranks around the fulcrum of the rotated joint joint. The angular velocities of the two cranks are different, but always constant. When unrolling a non-enclosing small rolling circle on a large fixed circle is rotating around the fixed pivot point inner crank longer than the one rotating around the pivot of the common pivot outer crank. In case of unrolling an enclosing large pitch circle a small fixed circle, the inner crank is smaller than the outer crank. That through both rolling movements, i. through both crank ratios, each the same Toothing can be generated, for example, has O. Baier in "rotary and Rotary piston engines as internal combustion engines ", VDI reports No. 45, 1960, explained. This is also the invention invoked by not defining whether it is the rolling circle is about the smaller or the larger of the two circles. In addition, the invention is defined by the definition of the tooth tip profile and / or Zahnfußprofils not as locus of a point on the circumference of a rolling circle limited to the fact that for the generation of the relevant profile actually the radius of the respective rolling circle is changed. If the same locus also by Rolling a rolling circle with a constant radius at one to the Wälzkreisachse concentric circle with constantly changing radius or by another rule can be generated, so also produced according to such a production rule Profile understood as being according to the invention.

A small tangential backlash provides for a small shock pulse path between the tooth flanks of the two gears and for another thinner fluid film between the tooth flanks, the higher squeezed bridge builds up and In this way, a touch of the tooth flanks better than in the known Gears prevented.

It is easy to see that the invention provides a simple possibility, in the Application case specific tooth play requirements to take into account. You get in the design of the tooth configuration a great deal of freedom. It just can not the tooth play can be predetermined at the most important tooth engagement points, but at the same time there may be specific requirements of production technology be taken into account, such as heat distortion, distortion during calibration of Sintering or deformation of the broaching or sintering tools when broaching or Pressing the gear blanks. If the ring gear machine according to the invention with very operated at high working pressures, which can be up to several 100 bar, must with elastic deformations of the gears are calculated, which also corrections makes the chosen tooth shape necessary. Such corrections are classic Cycloidal gears, which with the help of rolling circles and fixed circuits each with constant Radii were generated, not possible. The systematic modification of cycloids, which proposes the invention, combines the advantage of a simple production rule with the freedom gained with regard to the particular application adapted variation of the track clearance.

The invention is therefore also advantageous with regard to the production of the gears, because the manufacturing tolerances measured over the tooth thickness, i. in the circumferential direction, can be much smaller than the manufacturing tolerances measured over the Diameter of the gears, i. in the radial direction. This is due to concentricity errors and the oval distortion of the gears conditionally. Especially with gerotor pumps whose inner gear is mounted directly on a crankshaft of a reciprocating engine, the is known to perform a strong radial movement in their main camps is a increased radial backlash of the meshing gears advantageous. This Mounting case usually occurs in lubricating oil pumps for internal combustion engines of Vehicles, which is a preferred use of an inventive Represents toothed ring pump.

The calculation of the curve points of the locus of the invention is mathematical with a running parameter very easy. As a running parameter is preferably the Central angle χ between the X-axis and a driving beam, namely the inner Crank, chosen. The X-axis and this beam meet at the center of the Pitch circle of the respective gear, i. in the pitch circle axis. With the usual Incremental calculation is the incremental calculation in increments of the Running parameters very easy. There are also no discontinuities in the Transition from the tooth tips to the tooth feet. So is an inventively generated Tooth tip of the external toothing tangentially in an example hypocycloid Tooth base or a tooth root also generated according to the invention over. The same goes for Of course, for a tooth root of the external toothing produced according to the invention, the in this case tangentially in an example epicycloid tooth head or a also produced according to the invention tooth head of the external teeth merges. These it is in the teeth formed according to the invention to the internal teeth, so applies this analogously for example epicycloid or according to the invention of Epicycloid derived tooth feet and, for example, hypocycloid or according to the invention of hypocycloid derived tooth heads.

Accordingly, the variable radius of the rolling circle for the tooth tips and / or the tooth roots is not r = constant, but r = r (χ). If, in the case of the inventive generation of the tooth heads, the largest radius of the rolling circle is designated as r _0, and in the case of the generation of the tooth feet according to the invention with r ₀ the smallest radius of the rolling circle, then r (χ) = r ₀ ± Δ r (χ) , where r (χ) = r ₀ is continuous in the outermost point of the tooth tip or tooth root flank and Δ r (χ), preferably is continuously differentiable.

The function according to which the rolling circle radius changes according to the invention can after Specifications of convenience are selected. The rolling circle radius can be in particular after a linear function or a function at least second Order, preferably a conic function such as a Parabola function or a polynomial change. Particularly preferred are sine and Cosine functions, especially because of their simplicity. The change of the Rolling circle can also be based on empirical values given to support points and be approximated using an interpolation function on the nodes. A such obtained interpolation function is in the context of the invention as Experience function called.

Particularly preferably, the rolling circle radius is changed from a constant value r ₀ ≠ 0 after a function Δr (χ), the slope zero on both sides of the vertex of the inventively generated tooth tip or tooth root at the starting point at χ = 0 and at the end point at χ = 2χ _s where χ _s denotes the central angle of the vertex.

The change of the pitch circle radius is on each side of the vertex of each of the Tooth heads or each of the tooth feet preferably the same, so that the invention generated tooth heads and / or tooth feet on both sides of its apex have symmetrical profile.

For the production of the tooth head profile according to the invention and / or Zahnfußprofils can also have several different functions, preferably from the group of mentioned, are juxtaposed, as long as these functions are continuous, preferably continuously differentiable and therefore tangential, merge into each other. The change of the Radius should be monotone, i. for the generation of the tooth tip profile, for example, that the radius in rolling from the vertex of the tooth tip to both Flanks should grow monotonously. The change of the radius does not have to continuously during the entire rolling process, although a continuous change is beneficial. So the radius can piecewise quite be constant, especially in the area of the tooth flanks, to get to the vertex For example, to reduce a tooth head, the radius function per Toothed or dented, however, is steadily everywhere.

The counter-toothing to the toothing produced according to the invention is preferably also produced according to the invention, i. it preferably also has Tooth heads and / or tooth feet produced according to the invention. The counter teeth however, for example, it may also be pure epi- and hypocycloid gearing, i. Tooth heads and toothed feet, which preferably exact or extended or truncated epicycloids and preferably exact or extended or truncated Hypocycloids are. Thus, in particular the tooth heads of the external teeth and the tooth tips of the internal teeth are respectively produced according to the invention, while the Toothed feet of the external teeth Hypocycloids and the toothed feet of the internal teeth Epicycloids are. However, the counter-toothing does not necessarily have to be made up of epi- and Hypocycloids exist, for example, they can also according to the gearing law be formed. However, it is preferred if both gears only tooth heads and having tooth roots which are cycloidal or derived from cycloids in accordance with the invention are mixed forms as described and further possible according to the claims should be.

If at least one toothing produced according to the invention either only the Tooth heads or only the tooth roots in accordance with the invention of a cycloid are derived, the generation of the tooth heads according to the invention is preferred, although the generation according to the invention only of the tooth roots is already advantageous. Due to the flattening of the tooth heads according to the invention, the required radial Tooth play in the area of the least tooth engagement and at the same time room for Squeezing fluid can be obtained in the region of the deepest tooth engagement. If only the Toothed feet are generated by enlargement of the rolling circle according to the invention is at least still created room for squeezing fluid in the area of the deepest meshing, while the required radial backlash in the area of the lowest meshing can be achieved by other, possibly known measures.

For the generation of the radial toothed play it is usually sufficient that only one rolling circle radius of one of the two teeth when rolling on the respective fixed circle for the formation of the tooth tip profile is changed continuously. However, if to reduce harmful spaces and for optimum radial guidance of the gears against each other, the tooth heads and tooth roots of the counter teeth their shape as closely as possible to the toothing according to the invention, it is readily possible to produce the counter teeth according to the invention. Thus, it may be advantageous for a radial support of the rotors against each other to _" zoom" the tooth roots of the counter teeth radially closer to the inventively formed tooth heads by most advantageously also produced according to the invention, but like the tooth heads by reducing their rolling radius to the apex of each tooth root ,

The tangential track clearance should account for 20 to 60% of the radial backlash, this indication is again based on the mathematical rack games assuming a exact eccentricity is related. It is particularly preferred if the tangential Role play about half as large as the radial backlash is.

With very small toothed running games can with increasing relative speed between the meshing gears at the point of the deepest meshing so-called Extrusion crush pressures occur that lead to strong noise and also to increased noise Wear of the gears can result. To avoid this, can also be at the formed according to the invention in the tooth gaps of one or optionally two gears indentations, preferably in the form of narrow Axialnuten be provided, which are in particular associated with the drain, so that large crushing pressure peaks can be reduced without the intervention and Sprocket play conditions are disturbed.

To minimize fluctuations in the instantaneous delivery volume of To obtain the ring gear pump, it should be on the associated pitch circle or pitch circle measured circumferential extension of the tooth spaces and teeth of the gears either be designed according to claim 12 or according to claim 13.

The tangential toothed play can advantageously by an equidistant Withdrawal can be obtained from either of the two gears after the two Gears according to the mathematical generating the locus Production rule were made on a tangential backlash of zero. Also Advantageously, however, the radial and the tangential track clearance already alone by the variation of the rolling circle radius only for the tooth heads of one of the Gears are obtained. Is it in the counter-toothing to a cycloidal gearing, so the tangential backlash can also be obtained by that the rolling circle of the toothed feet of the counter toothing compared to a Roll circle radius with tangential zero play greater by half the tangential tooth play is selected while the radius of the rolling circle of the teeth heads of the counter-toothing around half the tangential tooth play smaller than a rolling circle radius with tangential Zero game is chosen. The extent of the tooth gaps measured on the pitch circle The counter toothing is then larger by the tangential tooth play and the on the Wälzkreis measured thickness of the tooth heads of the counter teeth is around the tangential Tooth clearance smaller than with a counter toothing, their tooth gaps and tooth tips on the pitch circle ever the same extent and thickness as the invention Have teeth. Likewise, it is of course possible in reverse, the cycloids Counter toothing on nominal size and the inventive toothing on setting of the desired tangential backlash. If necessary, that can Tangential backlash through a variation of a rolling circle radius in combination with a equidistant withdrawal of one of the gears or even, if necessary Both teeth are formed.

For completeness, it should be mentioned that the generation rule according to the invention Even with so-called gerotor gears can be used with advantage. There is in the outer gear a precisely circular tooth head shape provided with constant tooth flank radius. This constant tooth flank radius is historic conditioned, because a circular cylindrical shape manufacturing technology particularly easy to is mastering. Are the tooth tips of the outer gear through in the gear rotatably mounted rollers formed, so the constant radius is even mandatory. The with the circular tooth-teeth meshing counter-toothing, i. the external toothing of the inner gear, is formed according to the invention. However, these are not the variation of a rolling circle that rolls on a fixed circle. Rather, it will in the generator process, also referred to as an envelope process, the radius of the circular arc of the gerotor toothing varies. With the variation, however, that becomes The goal is to prevent interference between the two gears. It exists namely the problem that by flank touch laterally from the lowest and lowest meshing the distance between the opposing heads the two teeth at the point of least tooth engagement unfavorably large and as a result the volumetric efficiency drops.

The variation of the circular arcs of the gerotor toothing, namely the internal toothing of the outer gear is performed so that the tooth tips of the outer teeth of the inner gear are slimmer than it is in the envelope process usually the Case is. It has according to the invention, the radius of the arc of the tooth head of the Internal toothing its lowest value when the vertex of the tooth head of the External toothing is generated. Starting from the vertex to the two Flank areas of the teeth of the outer teeth becomes the radius of the circular arc the tooth tips of the internal toothing increases, so that as a result the tooth tip of the External toothing on the pitch circle is slimmer than he is after the Hüllfigur process would be with constant arc radius. This will increase the risk of Interference by lateral meshing, i. by flank contact, avoided or at least reduced. The formation according to the invention is advantageous especially when sealing problems between the conveyor cells and / or Deformations of the inner gear due to high working pressures are to be feared.

Insofar as further advantageous embodiments are described in the subclaims, so reference is made in this regard to the dependent claims.

Beyond the ring gear machine, the invention is also applicable to a gear set directed, the intermeshing gears with at least one According to the invention generated toothing comprises or of these two gears already being formed alone.

Figur 1

eine Ansicht auf eine Innenzahnringpumpe mit einem innenachsigen Zahnradlaufsatz,

Figur 2

den Zahnradlaufsatz der Figur 1,

Figur 3

die Erzeugung eines Zahnkopfes,

Figur 4

einen Bereich tiefsten Zahneingriffs eines Zahnradlaufsatzes nach einem ersten Ausführungsbeispiel,

Figur 5

einen Bereich tiefsten Zahneingriffs eines Zahnradlaufsatzes nach einem zweiten Ausführungsbeispiel,

Figur 6

einen Bereich tiefsten Zahneingriffs eines Zahnradlaufsatzes nach einem dritten Ausführungsbeispiel,

Figur 7

einen Zahnradlaufsatz mit Quetschfluidräumen,

Figur 8

einen Zahnradlaufsatz, dessen Zähne und Zahnlücken über dem jeweiligen Wälzkreis gemessen unterschiedlich dick sind,

Figur 9

eine Orbit-Maschine mit einem äußeren Zahnrad, das verdrehgesichert mit einem Gehäuse verbunden ist, und

Figur 10

einen Zahnradlaufsatz einer Orbit-Maschine mit einem äußeren Zahnrad, dessen Zähne von Rollen gebildet werden.

Preferred embodiments of the invention are explained below with reference to figures. The features disclosed in the exemplary embodiments each individually and in each disclosed combination advantageously further extend the subject matter of the claims. Even features that are only disclosed in one of the examples further form the other examples or show alternatives to individual features or combinations of features, unless otherwise stated or only the case can be. Show it:

FIG. 1

a view of an internal gear pump with an internal gear set,

FIG. 2

the gear wheel set of Figure 1,

FIG. 3

the generation of a tooth head,

FIG. 4

a region of deepest tooth engagement of a toothed wheel set according to a first embodiment,

FIG. 5

a region of deepest meshing of a gear set according to a second embodiment,

FIG. 6

a region of deepest meshing engagement of a toothed wheel set according to a third embodiment,

FIG. 7

a gear set with squish fluid spaces,

FIG. 8

a toothed wheel set whose teeth and tooth gaps are measured differently over the respective pitch circle,

FIG. 9

an orbit machine with an outer gear which is secured against rotation with a housing, and

FIG. 10

a gear set of an orbit machine with an outer gear whose teeth are formed by rollers.

1 shows a gerotor pump in a view perpendicular to a gear set, which is rotatably received in a gear chamber 4 of a pump housing 3. One Cover of the pump housing 3 is omitted, so that the gear chamber 4 with the Cog wheel set is recognizable. The toothed wheel set of the toothed ring pump is shown in FIG. 2 again shown alone.

The gerotor pump has an inner gear 1 with an outer toothing 1a and a outer gear 2 with an internal toothing 2i, which form the Zahnradlaufsatz. The external toothing 1a has one tooth less than the internal toothing 2i. To that innenachsigen Zahnradlaufsatz is basically noted that the number of teeth Internal toothing 2i preferably at least four and preferably at most 15 and even more preferably at least five. In the exemplary embodiment, the Internal teeth 2i twelve teeth.

A rotational axis D _{1 of} the inner gear 1 is parallel spaced, that is eccentric, to a rotational axis D _{2 of} the outer gear 2. The eccentricity, ie the distance between the two axes of rotation D ₁ and D ₂ , is denoted by "e". Further, the pitch circle of the inner gear 1 and the pitch circle of the outer gear 2 are indicated and designated by W ₁ and W ₂ . The axes of rotation D ₁ and D ₂ are consistent with the Wälzkreisachsen the gears 1 and 2 match.

The inner gear 1 and the outer gear 2 form a fluid conveying space between them. This fluid conveying space is subdivided into conveying cells 7 which are sealed off from each other in a pressure-tight manner. The individual conveyor cells 7 are each formed between two successive teeth of the external toothing 1a and the internal toothing 2i by having two consecutive teeth of the external toothing 1a head or flank contact with two consecutive radially opposite teeth of the internal teeth 2i. Between the tooth tips of the two teeth 1a and 2i there is a slight radial tooth clearance at the point of least tooth engagement. This game is in the event that the axes of rotation D ₁ and D ₂ to each other have the theoretical eccentricity e, which is based on the generation of the teeth _{1 a} and ₂ i, designated P _R. The gap corresponding to the radial clearance P _R should be designed so that the unavoidable losses are as small as possible.

From the diametrically opposite area of deepest meshing to the area the smallest tooth engagement, the conveyor cells 7 are increasing in the direction of rotation D. greater, then from the area of least meshing again to decrease. The increasing delivery cells 7 form a pump operation Low pressure side and the smaller conveyor cells 7 a high pressure side. The Low pressure side is with a pump inlet and the high pressure side with a Pump outlet connected. In the housing 1 are in the region of the conveyor cells 7 axially closely spaced, kidney-shaped groove openings 10 and 11 except that Webs are separated. The opening 10 covers conveyor cells 7 on the Low pressure side and accordingly forms an inflow, in pump operation a low-pressure opening, and the other opening 11 forms accordingly Outlet opening, in pump operation, a high-pressure opening. In a motor operation, the With such a ring gear machine is also possible, the conditions would of course vice versa. In the area of the deepest meshing and in the area of the the smallest tooth engagement forms the housing each have a sealing ridge between the adjacent inlet and outlet openings 10 and 11.

In a rotary driving of the one of the gears 1 and 2 is by the expanding delivery cells 7 on the low pressure side fluid through the opening 10th sucked, transported over the area of least gear mesh and on the High pressure side under higher pressure again through the opening 11 to the pump outlet conveyed away. In the exemplary embodiment, the pump receives its rotary drive from a Rotary drive member 5, which is formed by a drive shaft. The inner gear 1 is connected against rotation with the rotary drive member 5.

In a preferred use of the pump as a lubricating oil pump for a Internal combustion engine, i. as an engine oil pump, it is in the rotary drive member. 5 usually immediately around the crankshaft or the output shaft of a transmission, whose input shaft is the crankshaft of the engine. Likewise, that can Rotary drive member by a balance shaft for a force balance or Torque compensation of the motor are formed. Other rotary drive members are However, also conceivable, especially in other uses of the pump, for example, as a hydraulic pump for a servo drive of a motor vehicle. Instead of To drive the inner gear 1, the outer gear 2 could also rotate be and take the inner gear 1 with its rotary motion. in the Embodiment, however, is the outer gear 2, as in most Use cases usual, rotatably mounted in the housing 3 over its outer circumference.

The external toothing 1a and the internal toothing 2i are formed such that the radial toothed play P _{R is} greater than the tangential toothed play, in the region of deepest tooth engagement on the pitch circle of one of the gears 1 and 2 in the circumferential direction, ie in the tangential direction, as the distance between the trailing tooth flanks is measured when the leading tooth flank of the driving gear touches the counter flank of the driven gear. The profile of the external toothing 1a and the profile of the internal toothing 2i is in each case formed by cycloids or is derived from cycloids, ie the tooth heads and the toothed feet of the toothings 1a and 2i can be produced by rolling rolling circles on fixed circles. In order to obtain the greater radial tooth clearance P _R compared with the tangential tooth play, the profile of the tooth heads of at least one of the toothings 1a and 2i is in a special way opposite a cycloid which is produced by rolling a constant radius rolling circle on a constant radius fixed circle , radially flattened. The profile of the tooth heads of the counter teeth 1a or 2i may also be flattened, or it may for example also be formed by a cycloid obtained by rolling a constant radius pitch circle on a fixed circle of constant radius. In principle, although not preferred, the counter teeth 1a or 2i may even have a more acute tooth head profile than the cycloid, as long as it is ensured that the radial tooth clearance P _{R is} greater than the tangential tooth clearance.

In the exemplary embodiment, the profile of the tooth roots of the external toothing 1a is a hypocycloid and the profile of the tooth roots of the internal toothing 2i is an epicycloid. Both cycloids are produced by rolling their rolling circle, each with a constant radius on the pitch circle W ₁ or W _{2 of} the respective gear 1 and 2, wherein the pitch circle of the epicyclic is preferably not equal to the pitch circle of Hypozykloiden.

In Figure 3 is an example of the inner gear 1, the generation of a tooth head illustrated. However, the ratio of tooth thickness to gear diameter for the purpose of illustration greater than in the inner shown in Figure 1 Gear 1.

With R in Figure 3, the radius of the pitch circle W ₁ is designated. The rolling circle W ₁ forms the concentric to the rotation axis D ₁ large fixed circuit on which a smaller rolling circle B rolls to produce the tooth heads outside. The small rolling circle B has a radius b, which changes continuously during unrolling. As exemplified in Figure 3 on a single tooth head, each of the tooth tips of the inner gear 1 is formed identically. Due to the change of the radius r, the small rolling circle B is not actually a rolling circle. However, the term "rolling circle" is still used for illustrative purposes.

Mathematically, the rolling process can be treated W ₁ in particular by the movement of two cranks in the plane of the fixed circle and the rolling circle. One of these two cranks is the straight line F, which connects the center 0 of the fixed circuit W ₁ with the center M of the rolling circle B. The center 0 of the fixed circuit W ₁ lies on the pitch circle axis D ₁ . The other crank is a straight line with the length of the radius b of the rolling circle B. The straight line b connects a point on the circumference of the rolling circle B with the center M. The line F forms an inner crank seen from the pivot point 0 and the straight line b outer crank. The two cranks F and b are pivotally connected to each other at the center M.

A firmly connected to the gear 1, Cartesian X, Y coordinate system with the origin in the center 0 of the fixed circuit W ₁ is also shown in Figure 3. In an initial position in which the two cranks F and b are superimposed on the X-axis, the end point of the outer crank b is denoted by A. This point A on the circumference of the rolling circle B is in the starting position also on the fixed circuit W ₁ . The central angle χ between the above-defined X-axis and the inner crank F serves as a running parameter of the crank movement. In the starting position, the central angle χ is therefore equal to zero. A rolling of the rolling circle B corresponds to a rotational movement of the inner crank F to the center 0 of the fixed circuit W ₁ , which is superimposed on a rotational movement of the outer crank b about the center M of the rolling circle B. In Figure 3, the rolling circle B is located in the starting position, two intermediate positions and an end position. In the end position, the point A of the outer crank b has returned to the fixed circuit W ₁ . In one of the two intermediate positions, the point A on the circumference of the rolling circle B coincides with the vertex S of the tooth tip profile. In this position of the rolling circle B, the outer crank b forms the aligned extension of the inner crank F. The outer crank b has its smallest length in this position, which corresponds to the smallest radius b _{min of} the rolling circle B. The associated center angle is also entered and denoted by χ _s . Its largest radius b0 has the rolling circle B in the starting position at χ = 0 and the end position at χ = 2χ _s . Starting from the middle position χ = χ _s , in which the point A coincides with the vertex S of the tooth tip, the radius b of the rolling circle B increases monotonically and symmetrically on both sides of the vertex S until it reaches its maximum value b on the fixed circle W _{1 0 has} reached. The length of the inner crank F is constant during unrolling. For the length of the outer crank b applies: b (χ) = b 0 - Δb (χ) with χ ∈ (0, 2χ s ). Δb is preferably a sine or cosine function, for example: Δb (χ) = (C / 2) sin ((πχ) / (2χ s )), where the constant C / 2 is the amount of the length by which the pitch radius at the apex of the tooth tip or tooth root deviates from b ₀ . According to the above function .DELTA.b (.theta.), The length of the outer crank b changes according to the amount of the part of the sine function which is between two consecutive zeros. Even more advantageously, however, the length of the outer crank b changes according to the amount of the part of a sine or cosine function which is between a minimum of the function concerned and an adjacent maximum, since in this case the length of the outer crank b is in the flank regions of the tooth tip is closer to the epicycloid of the pitch circle with the constant radius r ₀ approximated. Thus Δb (χ) can satisfy in particular one of the following two equations: Δb (χ) = (C / 2) ∥ sin ((πχ) / 2χ s ) - π / 2) | - 1 | Δb (χ) = (C / 2) ∥ cos ((πχ) / (2χ s ) | - 1 |, where the vertical bars as usual denote the amount.

In FIG. 4 and the subsequent FIGS. 5 and 6, the toothings 1a and 2i are respectively drawn for the case in which the two axes of rotation D ₁ and D ₂ have the eccentricity e which is the basis of the generation of the teeth 1a and 2i and the vertex S ₁ of FIG Tooth tip of the external toothing 1a and the apex S _{2 of} the tooth root of the internal teeth 2i lie on the same radial. Of course, in the course of the gear set, the two gears 1a and 2i do not take this theoretical position because one of the gears 1 and 2 rotates the other one. However, FIGS. 4 to 6 serve to illustrate example tooth pairings.

FIG. 4 shows the point of the deepest tooth engagement for a toothed wheel set according to the exemplary embodiment of FIGS. 1 and 2, in which only the outer toothing 1a of the inner toothed wheel 1 is designed according to the invention. The profile of each of the teeth heads of the outer toothing 1a is derived from an epicycloid as described above with reference to FIG. 3 and is accordingly denoted by E1 _mod . The profile of the tooth roots of the outer toothing 1a, however, is a Hypozykloide H1, which is generated by rolling a small rolling circle with a constant radius inside the pitch circle W ₁ . On the pitch circle W _{1 of} the inner gear 1, the tooth tips and tooth roots of the outer gear 1a tangentially merge into each other. The internal teeth 2i of the external gear 2 has a conventional cycloid profile with hypocycloid tooth tips H2 and epicycloid tooth roots E2, which can be generated by rolling small pitch circles on the pitch circle W _{2 of} the external gear 2. The pitch circle for the generation of the hypocycloid tooth heads H2 has the same constant radius as the pitch circle for generating the hypocycloidal tooth tips H1 of the internal gear 1. The epicycloids E2 are measured over the pitch circle W _{2 of} the external gear 2 as thick as the epicycloid-derived tooth tips E1 _{mod of} the internal gear 1.

Starting from the constant pitch circle radius for generating the epicycloids E2, the change function .DELTA.b for the generation of the tooth tip profile of the external toothing 1a should be such that the length of the variable pitch circle B unrolled on the pitch circle W ₁ or pitch circle of the internal gear 1 equals the thickness of the epicycloid E2 the internal toothing is 2i. The generation instructions of the teeth 1a and 2i thus result in a tangential tooth clearance P _T of zero, which is not feasible in practice. To between the gears 1 and 2 a tangential backlash P _T as low as possible, but to obtain the relative movement of sufficient size, one of the two generated as described above teeth 1a and 2i over their entire profile equidistant, ie normal to the profile, withdrawn, for example by means of wire erosion of a gear sintered blank obtained according to the production instructions. The amount Ω the equidistant withdrawal is in the example with measured over the respective rolling circle of the same thickness of the epicycloid E2 and derived epicycloid E1 _mod accordingly equal to P _T / 2. Thus, in the region of the deepest tooth engagement, the two vertices S ₁ and S _{2 have} a radial spacing, which results as the sum of Ω = P _T / 2 and 2 (b ₂ -b _min ), where b _{2 is} the constant radius of the Roll circle of epicycloid E2 is. This radial distance corresponds to the radial clearance, ie for P _R P _R = 2 (b ₂ - b _min ) + Ω.

The same radial backlash P _R results in the example of Figure 4 at the point of least tooth engagement between the tooth tips of the two gears 1a and 2i.

By combining the generation according to the invention of, for example, the tooth head profile of the inner gear 1 and an equidistant withdrawal, also known as offset, the tangential tooth play P _{T can be} replaced by the equidistant withdrawal and the tooth head clearance P _R by the superposition of the equidistant withdrawal and the radius change Δb according to the invention (χ _s ) are formed. This results in even more variation possibilities than would already be possible on account of the inventive generation of the profile of at least one of the teeth 1a and 2i alone.

If, for example, a tangential tooth clearance P _T of 0.02 mm and a radial backlash P _R of 0.06 mm are to be used in the exemplary embodiment of FIG. 4, then the equidistant retraction would be Ω = 0.01 mm and the abovementioned radius difference (b ₂ -b _min ) = b ₂ - (b ₀ - Δb (χ _s )) = 0.05 mm.

FIG. 5 shows the point of deepest tooth engagement for a toothed wheel set, in which both the external toothing 1a and the internal toothing 2i are produced according to the invention. Both the tooth head profile of the external toothing 1a and the tooth head profile of the internal toothing 2i are flattened in the manner according to the invention as described with reference to FIG. 3 to the respective pitch circle W ₁ and W ₂ . The cycloid derived tooth head profiles are designated E1 _mod and H2 _mod . Since the flattening of the tooth head profiles brought about by rolling circle variation may be identical in the external toothing 1a on the one hand and the internal toothing 2i on the other hand, but need not be identical, the radial distance between the vertices of the tooth heads and the tooth roots is designated differently by P _R and P ' _R , where you have to turn the curves H1 _mod and H2 mentally in the position of deepest meshing. The tangential tooth clearance P _T is obtained by offset production, ie by equidistant withdrawal by the amount Ω of at least one, preferably only one, of the two toothings 1a and 2i, as in the case of the toothed wheel set of FIG. At the point of least tooth engagement, however, in the toothings 1a and 2i of FIG. 5, the distance between the opposing tooth heads is not P _R , but P _R + P ' _R + Ω.

FIG. 6 shows the point of deepest tooth engagement for a toothed wheel set according to a third exemplary embodiment. The tooth head profiles E1 _mod and H2 _mod are formed according to the invention. The two Zahnfußprofile H1 _mod and E2 _mod are each generated by rolling a rolling circle with a variable radius on the pitch circle W _{1 of} a rolling circle with variable radius and the pitch circle W _{2 of} the outer gear 2. In the generation of the Zahnfußprofile, however, reduces the radius of the respective rolling circle from the apex of the tooth root to both tooth flanks to reduce the dead spaces between the tooth roots and engaging tooth heads to a sufficient for the absorption and discharge of the squeezing fluid Quetschfluidraum. It is assumed that the radial tooth clearance corresponds overall to that of the embodiment of FIG.

Figure 7 shows two meshing gears 1 and 2 with teeth 1a and 2i, at least one of which is produced according to the invention. To be deepest in the area To create meshing spaces for crushing fluid or already existing ones in the reason of each of the roots of the inner gear 1 is one each Axialnut 8 incorporated. Form the gears 1 and 2, the gear set one Toothed ring pump, so is each of the axial grooves 8 with the outflow of the ring gear pump in Connection. The teeth 1a and 2i correspond to the teaching of claim 13, after which the teeth of the inner gear 1 on the pitch circle or pitch circle of the Gear 1 measured thinner than the tooth spaces are. If the ratio of on the Rolling or pitch circle measured circumferential extension of the tooth gaps to the teeth chosen from the range between 1.5 and 3 will be the inevitable minimizes instantaneous flow pulsations of the pump.

FIG. 8 serves to illustrate the teaching of claim 12, according to which Flow pulsations also by the reverse choice of the ratio of Extending the circumference can be achieved. In the embodiment of Figure 8 are Accordingly, the teeth of the external toothing 1a thinner than their tooth gaps.

The ring gear machine of Figure 9 is operated as a motor. The outer gear 2 is distributed over a plurality of evenly over the circumference of the gear 2 arranged bolt 9 rotatably connected to the housing 3 and forms thus a stator with the internal teeth 2i. The ring gear machine is called Orbit machine trained. The inner gear 1 has over its outer toothing 1a In addition, an internal toothing, which in a meshing tooth engagement with a Drive pinion 6 is rotatably mounted on a drive shaft 5. At least one of the teeth 1a and 2i is formed according to the invention. She can in particular as explained with reference to FIG. 3.

Figure 10 shows another example of a gear set, which is also an outer Gear 2 includes, which forms a stator of an orbital machine in the installed state. In the embodiment of Figure 10, the outer gear 2 has a Gerotor internal toothing 2i 'up. The teeth, especially the tooth heads, the internal teeth 2i 'of the outer gear 2 are formed by rollers 12 which are at their for Wälzkreisachse of the outer gear 2 parallel central longitudinal axes individually rotatable with the rest of the outer gear 2 are connected. All roles 12 have the same constant radius.

The counter-toothing, namely the outer toothing 1a 'of the inner gear 1, is also generated by a radius variation, but not by rolling one Rolling circle on a fixed circuit, but by a variation of the radius of the rollers 12th in the generator or envelope process, by which the external toothing 1a 'generates becomes. However, in the envelope process, the radius of the rollers 12 does not become constant but is steadily increased from a lowest value. The The smallest value is the radius of the rollers 12 for the extraction of the vertex each of the teeth heads of the external teeth 1a 'on. From the vertices to the two flank areas, preferably into the two bases of Zahnkopfflanken on the pitch circle, of each of the teeth heads of the external teeth 1a 'becomes the radius the rollers 12 increases to the value that the rollers 12 actually executed internal teeth 2i 'have. It thus becomes the tangential backlash opposite the tangential backlash from the constant radius working Envelope process enlarged.

Claims (18)

Positive displacement ring gear pump or motor comprising: a) a housing (3) containing a gear chamber (4) having at least one inflow opening (10) and at least one outflow opening (11) for a working fluid, b) an inner gear (1) accommodated in the gear chamber (4), which gear is rotatable about an axis of rotation (D ₁ ) and has an external toothing (1a), c) a gear (2) having an axis of rotation (D ₁ ) of the inner gear (1) eccentric Wälzkreisachse (D ₂ ) and the Wälzkreisachse (D ₂ ) an internal toothing (2i), the at least one tooth more than the external toothing (1a) is in meshing engagement with the external toothing (1a) to form expanding and compressing delivery cells (7) during a rotational movement which one of the toothed wheels (1, 2) makes relative to the other; carrying the working fluid from the at least one inflow port (10) to the at least one outflow port (11), d) wherein the tooth heads or the tooth roots of at least one of the two toothings (1a, 2i) have a profile derived from a cycloid, which can be generated by rolling a rolling circle on a fixed circle, e) and wherein the intermeshing toothings (1a, 2i) have a radial and a tangential toothed play (P _R , P _T ),
characterized in that f) the tangential tooth clearance (P _T ) is smaller than the radial tooth play (P _R ) g) and the profile of the tooth tips or feet is formed by the at least one of the teeth (1a, 2i) from or out of the locus of a point on the circumference of a pitch circle whose radius is from the two flank areas to the apex area in the case of the tooth tips steadily reduced in size or, in the case of the tooth feet, either steadily increased or continuously reduced in size. Tooth ring machine according to claim 1, characterized in that the profile of the tooth heads is formed by or from the locus of a point on the circumference of a first pitch circle, the radius of which continuously decreases from the two flank areas to the apex area of the tooth tips, and that the profile of the tooth roots is formed by or from the locus of a point on the circumference of a second pitch circle whose radius increases steadily from the two flank areas to the apex area of the tooth roots. Toothed ring machine according to one of the preceding claims, characterized in that the profile of the tooth heads of the other of the two gears (1a, 2i) is formed by or from the locus of a point on the circumference of a third pitch circle whose radius extends from the two flank areas to the Crown area of the tooth heads steadily reduced. Toothed ring machine according to one of the preceding claims, characterized in that the profile of the tooth roots of the other of the two gears (1a, 2i) is formed by or from the locus of a point on the circumference of a fourth rolling circle whose radius extends from the two flank areas to the Vertex area of the feet steadily increased. Toothed ring machine according to one of claims 1 to 3, characterized in that the profile of the tooth heads of the at least one of the toothings (1a, 2i) is formed by or from the locus of a point on the circumference of a rolling circle whose radius is different from the two flank areas to the peak area of the tooth tips is continuously reduced, and that the profile of the tooth roots of the other of the two gears (1a, 2i) is formed by or from the locus of a point on the circumference of a fourth pitch circle whose radius is from the two flank areas to the apex area the tooth feet steadily reduced. Toothed ring machine according to one of the preceding claims, characterized in that the radius of the rolling circle is at the unwinding that according to a linear function or a sine or cosine function or a function of at least second order, preferably a conic section function or a polynomial changes. Gear ring machine according to one of the preceding claims, characterized in that the radius of the rolling circle changes during the rolling according to an experience function. Toothed ring machine according to one of the preceding claims, characterized in that the tangential toothed play (P _T ) amounts to 20 to 60% of the radial toothed play (P _R ). Toothed ring machine according to one of the preceding claims, characterized in that the profile of at least one of the two gears (3a, 4i) is withdrawn equidistantly in comparison to the generating profile of the profile forming the locus to a part of the tangential Zahnlaufspiels (P ₁ ) or preferably to measure the total tangential tooth clearance (P _T ) measured on the pitch circle (W ₁ , W ₂ ). Toothed ring machine according to one of the preceding claims, characterized in that the tooth head profiles and Zahnfußprofile of both gears (1a, 2i) derived cycloid or cycloids and the generating wheels of the profiles are coordinated with each other so that from the loci of the points at the peripheries of the rolling circles a part of the tangential tooth clearance (P _T ) measured on the pitch circle (W ₁ , W ₂ ) or, preferably, the entire tangential track clearance (P _T ) is obtained. Gear ring machine according to one of the preceding claims, characterized in that the profiles of the tooth heads and the tooth roots of the toothings (1a, 2i) at transitions point tangentially toward one another. Toothed ring machine according to one of the preceding claims, characterized in that only one of the two gears (1a, 2i) has a profile for the generation of which the rolling circle of the tooth tips and / or the rolling circle of the tooth tips changes. Toothed ring machine according to one of claims 1 to 11, characterized in that the profiles of the tooth tips and / or feet of both teeth (1a, 2i) are formed by or from the loci of points on the circumference of rolling circles whose radii are different from the one Gradually change the vertex area to the two flank areas of the tooth tips and / or feet. Toothed ring machine according to one of the preceding claims, characterized in that measured on the associated pitch circle circumferential extent of the tooth gaps of the external toothing (1a) and teeth of the internal toothing (2i) 1.5 to 3 times the measured on the associated rolling circle circumferential extent of the teeth of the external toothing ( 1a) and tooth gaps of the internal toothing (2i) is. Tooth ring machine according to one of claims 1 to 13, characterized in that measured on the associated pitch circle circumferential extent of the teeth of the external toothing (1a) and tooth gaps of the internal toothing (2i) 1.5 to 3 times the measured on the associated pitch circle circumferential extent of the tooth gaps External teeth (1a) and teeth of the internal teeth (2i) is. Gear ring machine according to at least one of the preceding claims, characterized in that in the tooth roots of at least one of the toothings (1a, 2i) indentations (8) are provided for crushing fluid. Gear ring machine according to one of the preceding claims, characterized in that one of the gear wheels (1, 2), preferably the outer gear (2), for a motor operation forms a relative to the housing (3) non-rotatable stator. Gear set for a positive displacement ring gear machine, preferably a ring gear machine according to any one of the preceding claims, comprising a) an inner gear (1) with an outer toothing (1a), b) an outer gear (2) with an internal toothing (2i) having at least one tooth more than the external toothing (1a) and with the external toothing (1a) in a meshing tooth engagement of the toothings (1a, 2i), in which an axis of rotation (D ₁ ) of one of the gears (1, 2) to a pitch circle axis (D ₂ ) of the other of the gears (1, 2) is eccentric, forming expanding and compressing cells, c) wherein the tooth tips or the tooth roots of at least one of the teeth (1a, 2i) have a profile derived from a cycloid, which can be generated by rolling a rolling circle on a fixed circle, d) and wherein the intermeshing toothings (1a, 2i) have a radial and a tangential toothed play (P _R , P _T ),
characterized in that e) the tangential toothed play (P _T ) is smaller than the radial toothed play (P _R ) f) and the profile of the tooth tips or feet is formed by the at least one of the teeth (1a, 2i) from or out of the locus of a point on the circumference of a rolling circle whose radius is from the two flank areas to the apex area in the case of the tooth heads steadily reduced in size or, in the case of the tooth feet, either steadily increased or continuously reduced in size.

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