EP1340913A2 - Gear pump - Google Patents

Abstract

The gear teeth of the annular gear machine are formed from gear points (4k,3k) and gear roots (4f,3f) formed from curves of the second or higher order, whereby the curves on their ends point tangentially to one another, and at least the curves which form the tooth points, or at least the curves which form the tooth roots, are cycloids. One of the tooth profile contours formed by the curves is gradually differentiable, and preferably twice differentiable by piece. An Independent claim is included for a gear set for an annular gear machine such as a pump or motor.

Description

The invention relates to a toothing of a gear, further one with the gear formed gear set and finally one formed with the gear set Gear machine. In the gear machine, which is preferably an internal axis Gear machine, it can be a motor or preferably a Act positive displacement pump.

Gerotor pumps with a gear wheel set consisting of a are known externally toothed inner rotor and an internally toothed outer rotor, which together in a meshing tooth mesh. Form the toothing of the two rotors rotating, expanding and compressing delivery cells for a working fluid. The for Formation of the intermeshing toothing cells have epi and / or Hypocycloids or trochoids formed tooth tips and tooth feet. If alternating, for example, one of the two toothed teeth is formed by epicycloids and hypocycloids, one results from kinematic Derivation according to the gearing law also produces counter gearing as Interlocking of alternating epicycloids and hypocycloids. The In practice, however, both theoretical tooth profiles thus obtained cannot roll on each other and would due to the deepest meshing in the area complete coverage of the base of the tooth base and the top of the tooth head cannot be controlled Cause noise problems due to pinch oil effects.

To solve the noise problem, EP 1 016 784 A1 proposes that together intermeshing toothings of the inner rotor and the outer rotor each as To form cycloid interlocking with complete epi- and hypocycloids, but the Epicycloids of internal rotor teeth with smaller pitch circles than that Epicycloids of the outer rotor and the hypocycloids of the teeth of the outer rotor with smaller rolling circles than the hypocycloids of the teeth of the inner rotor produce. As a result, however, the backlash is increased in the same way as space for squeeze oil. Noises are at the expense of the volumetric Efficiency reduced.

A gerotor pump that has been tried and tested in practice is described, for example, in EP 0 552 443 B1 described. To the basically unavoidable backlash between the The tooth tips of the inner rotor and the tooth tips of the External rotor and, if applicable, the tooth bases interacting with the tooth heads of the other rotor is flattened towards the pitch circle of the rotor in question. The intermeshing gears are designed as cycloid gears, however, for the purpose of flattening, they are shortened epicycloids and Hypocycloids formed. Because the epicycloids and hypocycloids on the pitch circle because of the Shortening no longer meet seamlessly, the transitions are through Line pieces bridged. However, discontinuities occur at the transition points in turn cause noise problems. Furthermore, the squeeze rooms are still not ideal.

It is an object of the invention to provide a gear that is preferred in one Use as a feed wheel of a gear pump or driven gear of a gear motor Reduction of noise in the operation of the pump or motor contributes.

According to a first aspect of the invention, a gear has a toothing, the abutting tooth heads and tooth bases of curves of second or higher order are formed that point tangentially towards each other at their ends. This means that the tooth profile at the transition points between the curves forming the tooth heads and the curves forming the tooth bases are not only continuous, but also differentiable. The profile contour of the toothing can preferably be continuously differentiated everywhere. Furthermore are at least the curves that form the tooth tips, or at least the curves that form the Form tooth bases, no cycloids, whereby the term cycloid in the sense of Invention can also be understood as a shortened or elongated cycloid (trochoid) should. That the profile contour of the tooth tips and / or the tooth feet is not cycloid, means that the curves in question are not on a non-slip rolling of Rolling circles are based on a fixed circle, for example by initially acting as a cycloid shaped and then processed with an offset to a required Get tooth play.

The toothing preferably comprises at least four teeth. It extends preferentially over the entire inner or outer circumference of the gear.

Although less preferred, it is basically conceivable to use the one according to the invention Form toothing in such a way that the tooth tips of cycloids and the tooth feet of each are formed by a curve of at least second order, preferably one Curve of a conic section, in particular an arc of a circle or an ellipse or an arc of an ellipse-like curve that is tangent to the ends of the curve neighboring cycloid arches point so that there are no kinks at the transitions arise. The tooth heads of the counter toothing can be made of cycloids and the tooth feet are preferably also each formed by a curve of at least second order. Between the curves and the engaging cycloids of the two gears would advantageous pinch oil spaces are formed. As an example in this version are described with a toothing formed from cycloids and non-cycloids preferably the tooth bases from the non-cycloid curves of the second or higher order educated. In principle, however, the tooth tips of non-cycloid curves can also second or higher order and the tooth feet are formed cycloid.

In preferred embodiments, both the tooth heads and the tooth feet are not from Cycloids formed, neither by epi- and hypcycloids nor by shortened or elongated epi- or hypocycloids. The tooth tips and are particularly preferred Nodules are also not formed by other curves that are created with the help of rolling circles that roll smoothly on the pitch or pitch circle of the gear. In preferred designs, the profile contour of the tooth heads is a conical arc. Even more preferred is the profile contour of the tooth feet, one curve curve each Conic section, i.e. a circular arc, elliptical arch, hyperbolic arch or a parabolic arch. Another preferred example is higher order ellipse-like curves, for example, a Cassini curve in its elliptical shape, which is also the Profile contour of the tooth tips and / or the tooth feet can form. Forms an ellipse or elliptical curve the profile contour, the ratio of the length of the large Major axis to the length of the minor major axis preferably at least 1.1 and preferably at most 2. An aspect ratio ranging from 1.25 to 1.6 particularly preferred.

It is advantageous to form the profile contour of the tooth heads each by means of a curved curve a first shape and the formation of the profile contour of the tooth feet each by one Curve of a different, second form. So can the tooth heads and the tooth feet for example, are each formed by elliptical arcs, but the curved arcs of Tooth tips of a different ellipse than the curve arcs of the tooth feet are taken. Even more preferably, an arc of a curve of a first type forms the tooth heads, preferably each an ellipse arc or an arc of an ellipse-like curve, and each an arc of a curve of a different type, the tooth feet, preferably an arc each. Of course, the same curve arcs for the tooth tips and each same curve curves are used for the tooth feet of the toothing.

According to a second aspect of the invention, a gear has a toothing, the abutting tooth heads and tooth bases of curves of second or higher order are formed, the curves pointing tangentially to one another at their ends and the curves that form the flanks of the tooth tips, arcs of an ellipse with uneven ones Main axes or arcs of an ellipse-like curve, preferably a Cassini curve in their elliptical shape. Although the crowns of the tooth heads are quite flattened and / or the tooth flanks with the tooth feet through short straight sections connected, it is preferred if the elliptical or ellipse-like Arches not only the flanks of the tooth tips, but also their apices in one single continuous curve up to the two connection points with the form adjacent tooth feet. As far as in the above and below as well as in the Claims a feature specific to the first aspect of the invention is described, such a feature also forms the gear according to the second aspect the invention further advantageous, unless it is contrary to the second aspect of Invention stands. It is therefore particularly preferred if the gear wheel follows a gear wheel is both aspects of the invention.

In particular, the tooth heads and tooth gaps on the pitch circle or pitch circle of the Gear measured have different thicknesses, with flow pulsations with in comparison to the tooth bases of wider tooth heads of the gear according to the invention, but can also be reduced with tooth heads that are narrower than the tooth feet can, as in EP 0 552 443 B1 and EP 1 016 784 A1 for other profiles has already been described. On the other hand, the flow pulsations are already caused by the Training the toothing according to the invention compared to the known solutions diminished, so that a toothing of tooth heads and tooth feet that are the same thickness are already advantageous.

The curves that form the tooth tips or tooth tip flanks preferably meet directly to the curves that form the tooth bases, so that the tooth profile is everywhere has finite curvature. Basically possible, although less preferred, however, the two curves could also be connected by straight lines. Indeed in such an embodiment of the toothing, every connecting straight line that is connected to the Extend the curves following the ends of the straight line tangentially or into these two Enter curves tangentially. There is one everywhere for the sliding movement of the tooth flanks curved course, however, cheaper.

The curved curves of the tooth tips and the curved curves of the tooth feet preferably meet on the pitch circle of the gear wheel and are nestled there. It is but also possible, the joints between the tooth tip curves and the tooth root curves to move a little bit from the pitch circle outwards or inwards and not only in the less preferred version, in which the curve ends are over straight sections are interconnected, but also in the preferred embodiment of the immediate clash.

The invention further relates to a gear wheel set consisting of at least two gear wheels exists, which are in mesh or can be brought to roll against each other. At least one of the gears has teeth of the type according to the invention.

The counter toothing of the other gear of the at least two gears is above it entire profile or it will be preferred only your tooth base profile after the Gearing law kinematically derived from the gearing according to the invention. forms the gear wheel set conveyor wheels of a gerotor pump or driven wheels of a Toothed ring motor, so between the toothing according to the invention and that counter toothing formed due to the difference in the number of teeth of the two in Interlocking gears a constant rolling and sliding of the tooth flanks and get enough pinch spaces for the working fluid. The noise of the Gear wheel set is therefore combined with high volumetric efficiency reduced.

In a particularly preferred embodiment, only the profile of the tooth feet Counter toothing according to the toothing law kinematically from the invention Gearing derived, while the profile of the tooth heads of the counter gearing Envelope cuts of the tooth profile of the toothing according to the invention is obtained. The The curve of the tooth heads of the counter-toothing is the connecting line of points Tooth curve of the toothing according to the invention. The tooth tip curve of the Counter toothing envelops the tooth tooth of the counter toothing concerned turned tooth tip curves of the toothing according to the invention. The the Tooth profile of the counter toothing connecting line of these points can especially a spline function.

Because of the so between the tooth bases of the toothing according to the invention and the Cavities of the counter-toothing cavities formed on the one hand more advantageous Space for squeezing fluid was created, but on the other hand a dead volume of working fluid is transported around the circumference, it can be quite advantageous, the profile of the tooth feet flatten the gearing according to the invention, i.e. the tooth feet in their respective Bring the vertex area closer to the pitch circle of the gear. The result of this resulting deviation from, for example, the exact circular arc shape or the otherwise selected tooth root curve is preferably such that the tooth root curve nevertheless continuous, particularly preferably at least piecewise twice continuously, differentiable is.

The at least two, preferably exactly two, meshing Gear teeth of the gear wheel set preferably each have such a tooth profile contour, that the rolling tooth flanks of the gears sealed against each other Form cells. If the gear wheel set is an internal axis set and all fluid cells only be formed by the toothing, as is preferably the case when the Difference in the number of teeth of the gears is one, so the tooth heads are the Gears shaped in such a way that at the point of minimal tooth engagement a radially narrow one Gap remains. Basically, this also applies when using a sickle internal-axis gear sets where the difference in the number of teeth is greater than one is. There is preferably a minimal running game, so that on the one hand Manufacturing tolerances compensated, but on the other hand, losses caused by the gap in the area of the slightest tooth engagement or between the tooth heads and a sickle be minimized. In the area of deepest tooth engagement, in which one tooth head of the one Gearing with a deepest engagement in a tooth base of the other gearing engages, according to the invention, a cavity serving as a squeeze space for the Working fluid of the gear machine is formed.

The above-mentioned criteria are preferably met in that the Gearing of a gear according to the invention is specified as a master gearing and the counter-toothing is designed based on this specification so that the tight Fluid cells and the rolling flanks are formed. In particular the rolling flanks of the Counter teeth, as far as the rolling flanks belong to the tooth root curve, are by Kinematic derivation based on the gearing law. In a preferred one Forming the tooth bases of the toothing according to the invention as circular arcs results the cavity or squeeze space at the point of the deepest meshing of the Gearing by itself.

The cavity can also be made with an indentation of the tooth feet of the gearwheel gearing according to the invention are formed. Instead, or in combination with such indentations in the toothing according to the invention, the gear with Counter-toothing in his tooth feet each has an indentation to form the Have cavity. The toothing according to the invention can be used for the indentations each have a discontinuity in the derivation or also at the transitions of the curve curves according to the invention in and out of the indentation be continuously differentiable. However, the toothing according to the invention preferably does not have such indentations so that their tooth profile contour not only on the tooth heads, but also in the Tooth feet each by a smooth, continuous curve of an inventive Curve is formed.

The counter toothing can advantageously be based on interpolating spline functions Support points can be obtained. The support points of the tooth root curve are preferred by kinematic derivation of the gearing according to the invention Gearing law and that of the tooth tip curve preferably from envelope cuts Tooth curve of the master toothing determined. If the tooth tips of the Master gear teeth are flattened compared to their generation curve, that is Envelope cutting process, however, carried out with the generation curve not flattened. If for example, if the generation curve is an ellipse, the envelope cuts determined by means of the ellipse arc. An interpolating spline function is preferred at least grade three, preferably grade three. The support points can in particular formed by contact points of the rolling tooth flanks of the gear wheels become. The spline functions in one corresponding to the pitch of the counter toothing The number are put together, if necessary adjusted at the transition points, that at least continuously differentiable transitions are obtained. To that extent Counter toothing as such represents a toothing according to the invention, since its tooth profile is formed by a function that is continuously differentiable at least twice in parts. The spline functions are preferred at or very close to the vertices in the Put the feet together where there is no rolling.

In a particularly preferred embodiment, only the tooth tip profile of the counter toothing is used formed by a spline function, whose support points are the envelope intersection points, while the tooth root profile of the counter-toothing is a polygon that consists of the Gearing law connects points of the tooth base profile obtained. From the Interlocking law can easily make the points of the tooth root profile so tight can be determined side by side that a simple polyline as a connecting line enough. For the counter toothing, this means that an alternating spline function for a tooth profile and a polygon for the tooth profile are put together and continuously differentiable, i.e. tangential, merge.

A gear of the moving set according to the invention, for example the gear with the Counter-toothing, preferably after the shaping with a so-called offset provided by the toothing in question normal to their formed according to the invention Tooth profile exit contour equidistant over the entire contour of a given piece is withdrawn far. In principle, both gears can also be equidistant be withdrawn compared to the initial contour generated according to the invention. On Backlash of the meshing teeth, i.e. a backlash in Circumferential direction, can in particular be achieved by an equidistant withdrawal from receive one or both tooth profile contours compared to the generation specification become. In such a preferred embodiment, the intermeshing Gears formed according to their respective generation regulations so that they are in Circumferential direction on "zero clearance" are generated. Because of the preferred generation of the Tooth curve of the counter toothing from envelope cuts of the tooth profile of the This also applies to master teeth for the required radial play of the teeth the point of least tooth mesh. To the required radial tooth play, i.e. the It can do that to maintain a tooth play in the area of the smallest tooth mesh Tooth profile of the counter-toothing in relation to one of the generation instructions from Envelope cuts formed tooth tip profile be flattened, so that the radial tooth play is not only formed by an equidistant withdrawal.

Preferred uses of a gear pump according to the invention are, for example that of a lubricating oil pump of an internal combustion engine or a lubricating oil pump of a Gearbox of a wind power generator.

Figur 1   eine Ansicht auf eine Zahnringpumpe, in der eine Zahnradkammer mit einem Zahnradlaufsatz erkennbar ist,

Figur 2   einen Ausschnitt der ineinander greifenden Zahnprofile des Zahnradlaufsatzes der Figur 1,

Figur 3   einen Ausschnitt von ineinander greifenden Zahnprofilen einer Ausführungsvariante,

Figur 4   einen Ausschnitt von ineinander greifenden Zahnprofilen einer weiteren Ausführungsvariante,

Figur 5   ein Zahnkopfprofil einer Masterverzahnung, das von einem Ellipsenbogen gebildet wird,

Figur 6   das elliptische Zahnkopfprofil der Figur 5 und ein daran anschließendes Zahnfußprofil, das von einem Kreisbogen gebildet wird,

Figur 7   das Profil der Figur 6 und ein Zahnkopfprofil einer Gegenverzahnung,

Figur 8   die Bildung des Zahnkopfprofils der Gegenverzahnung aus Hüllschnitten und

Figur 9   eine Modifikation des Zahnprofils der Figuren 5 und 6.

Exemplary embodiments of the invention are explained below with reference to figures. Features which become apparent from the exemplary embodiments advantageously form the subject matter of the claims individually and in each combination of features. Show it:

FIG. 1 shows a view of a gear ring pump in which a gear chamber with a gear wheel set can be seen,

FIG. 2 shows a section of the interlocking tooth profiles of the gear wheel set of FIG. 1,

FIG. 3 shows a section of interlocking tooth profiles of an embodiment variant,

FIG. 4 shows a section of interlocking tooth profiles of a further embodiment,

FIG. 5 shows a tooth tip profile of a master toothing which is formed by an elliptical arch,

FIG. 6 shows the elliptical tooth tip profile of FIG. 5 and an adjoining tooth root profile, which is formed by a circular arc,

FIG. 7 the profile of FIG. 6 and a tooth tip profile of a counter toothing,

8 shows the formation of the tooth tip profile of the counter-toothing from envelope cuts and

9 shows a modification of the tooth profile of FIGS. 5 and 6.

FIG. 1 shows a gerotor pump in a view perpendicular to a gear wheel set, which is rotatably received in a gear chamber of a pump housing 1. On Cover of the pump housing is omitted, so that the gear chamber with the Gear wheel set is recognizable.

The gerotor pump has an outer rotor 3 with an internal toothing 3i and one Inner rotor 4 with an external toothing 4a, which form the gear wheel set. The External toothing 4a has one tooth less than the internal toothing 3i. The number of teeth the internal toothing of such internal-axis pumps is at least four and preferably at most fifteen, preferably the number of teeth is between five and ten; in the exemplary embodiment, the internal toothing 3i has nine teeth.

An axis of rotation 5 of the outer rotor 3 runs parallel spaced, i.e. eccentric, too an axis of rotation 6 of the inner rotor 4. The eccentricity, i.e. the distance between the two axes of rotation 5 and 6, is designated by "e".

The inner rotor 4 and the outer rotor 3 form a fluid delivery space between them. This Fluid delivery chamber is divided into delivery cells 7 which are sealed off from one another in a pressure-tight manner. The individual conveyor cells 7 are each between two successive teeth of the inner rotor 4 and the internal toothing 3i of the outer rotor 3 formed by two successive teeth of the inner rotor 4 head or flank contact with two each have successive, opposite teeth of the internal toothing 3i. Between the tooth heads 4k and 3k there can be a slight tooth mesh at the point there is little play, with the fluid being pumped between each other opposite tooth heads 4k and 3k of the two toothings 4a and 3i one Sealing film forms.

From a place of deepest tooth meshing to the place of lowest tooth meshing Delivery cells 7 increasingly larger in the direction of rotation D in order to then move from the location slightest meshing. The growing conveyor cells 7 form in pump operation a low pressure side and the shrinking delivery cells 7 one High pressure side. The low pressure side is with a pump inlet and the High pressure side connected to a pump outlet. In the housing 1 are in the side Area of the feed cells 7 closely adjacent, kidney-shaped slot openings 8 and 9 except that are separated from one another by webs. The opening 8 covers Delivery cells 7 on the low pressure side and accordingly forms an inflow opening, in pump operation, a low pressure opening, and the other opening 9 forms accordingly a high pressure opening. In an engine operation with such a Gear machine is also possible, the situation would of course be reversed. in the Area of the deepest tooth mesh and in the area of the lowest tooth mesh the housing forms a sealing web between the adjacent inlet and Drain openings 8 and 9.

When one of the rotors 3 and 4 is driven in rotation by the expanding ones Delivery cells 7 on the low pressure side sucked fluid through the opening 8, over the place The slightest tooth mesh is transported and on the high pressure side under higher pressure again conveyed through the opening 9 to the pump outlet. In the embodiment the pump receives its rotary drive from a rotary drive member 2, which by a Drive shaft is formed. The inner rotor 4 is connected to the rotary drive member 2 non-rotatably connected. In a preferred use of the pump as a lubricating oil or engine oil pump for an internal combustion engine, in particular a reciprocating piston engine, is the drive shaft 2 usually directly to the crankshaft or the output shaft of a gearbox, the input shaft of which is the crankshaft of the engine. Likewise, it can 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 rotor 4, the outer rotor 3 could also be driven in rotation and at take the inner rotor 4 with it when it rotates.

Figure 2 shows the profile contours of the teeth 3i and 4a at the point of the deepest Tooth engagement. The tooth heads 3k of the internal toothing 3i are elliptical arcs and Tooth feet 3f of the internal toothing 3i are designed as circular arcs. The ellipse arches and the arcs meet directly on the pitch circle T3 of the internal toothing 3i to each other and are nestled there so that they are so direct to each of the formed seams have the same slope. At the transition points of the The left-hand and right-hand derivatives are therefore the same for both curves, i.e. the tooth profile contour of the internal toothing 3i is everywhere, even on the Transition points, continuously differentiable function. The laws of the axes of the ellipse forming the ellipse arcs are from the basic gear data module and Number of teeth of the outer rotor 3 derived.

In the exemplary embodiment, the internal toothing 3i of the outer rotor 3 is Output gear or master gear. The Zalm foot profile contour of the inner rotor 4 is kinematically based on the tooth profile profile contour of the internal toothing 3i Gear Act derived. The tooth tip profile contour of the inner rotor 4 is made Obtain envelope cuts of the tooth profile profile contour of the internal toothing 3i. The profile contour the external toothing 4a is in total by spline functions and polygon formed, which are placed along the pitch circle T4 of the external toothing 4a. The spline functions are obtained at support points. The gearing law provides the support points for the polygons of the tooth feet 4f, and the envelope cut method provides the support points for the spline function of the tooth tips 4k. From, for example, the The snapshot of FIG. 1 shows the support points 10-16 for the tooth heads 4k. The support points 10 to 16 are the current contact points of the rolling flanks of the two Gears 3i and 4a and in the snapshot of FIG. 1 form just that Sealing points between the individual fluid cells 7. Are the two gears 3 and 4 A further set of support points can be rotated further by a small angle be won. The greater the number of support points or the denser the support points lie next to each other, the more precise the tooth tips 4k of the external toothing 4a become approximated by the same interpolating spline function.

Instead of specifying the internal toothing 3i as the master toothing, it can just as well the external toothing 4a be the master toothing and in this case the Internal gearing 3i through spline functions and polygons or just through Spline functions, namely one for the tooth tips and another for the tooth feet, to be discribed. If the external toothing 4a is the master toothing, their Tooth tips 4k are formed as described above for the tooth tips 3k, and there are their tooth bases 4f are formed as described above for the tooth bases 3f.

The area of deepest tooth engagement is shown enlarged in FIG. Clear to see is a cavity H1, which is in the area of the vertices between the straight in deepest tooth engagement tooth head 4k of the inner rotor 4 and the receiving Tooth root 3f of the outer rotor 3 results. The aspect ratio between the long and the short axis of the ellipse, which forms the ellipse arches of the internal toothing 3i in embodiment 3: 2. Aspect ratios up to 6: 5 or even 10: 9 are however also still beneficial. The two toothings 4a and 3i combine the noise advantages of one Gerotors with the volumetric advantages of a gear wheel set like the one from EP 0 552 443 B1 is known.

Figure 3 shows the location of the deepest meshing for a gear set, the Inner rotor 3 has the same internal toothing 3i as the inner rotor 3 of the gear wheel set of Figures 1 and 2. The external toothing 4a is also the same Curved curves are formed like the external toothing 4a of the first exemplary embodiment, however, indentations are formed in the tooth bases 4f, which provide additional cavities Create H2 for the fluid. Apart from the indentations, the tooth bases 4f are the Variant of Figure 3, however, identical to the tooth feet 4f of the first Embodiment.

In the variant of FIG. 4, the internal toothing 3i has the same tooth heads 3k as the internal toothing 3i of the first embodiment. The tooth feet 3f however formed by elliptical arches. These elliptical arches are in the range of theirs Provide an indentation in the apex. If because of the elliptical arches formed tooth feet 3f at the location of the deepest tooth engagement a sufficient Squeeze chamber not just because of the difference in the number of teeth between the two Toothings 3i and 4a can be created by the indentations of the tooth feet 3f nevertheless, a cavity H3 of sufficient size can be created. Basically, however, it is assumed that the inventive predetermined toothing, in the exemplary embodiment the internal toothing 3i, and the Counter-toothing formed according to the invention already without indentations at the point of the deepest tooth mesh sufficient squeeze space is created.

For completeness, it should also be noted that indentations in each of the two gears 3i and 4a can be realized in a single gear set can.

A preferred, but only exemplary, example should be used with reference to FIGS. 5 to 8 Generation rule for the two gears 3i and 4a illustrated in more detail become.

FIG. 5 shows the profile contour of an individual tooth head 3k of the master toothing 3i. Figure 6 shows the same tooth head 3k and a tooth base 3f, which is on the pitch circle T3 the master toothing 3i runs tangentially into the tooth head 3k. At the intersection with Tangent common to pitch circle T3 is designated P1. With P2 is the radial of the Pitch circle T3 designated by the center of the circle that the profile contour of Tooth base 3f forms.

As shown in FIG. 5, the ellipse arc of the tooth head 3k is an ellipse with a large semiaxis a and a small semiaxis b taken. The small semi-axis b is a radial of the pitch circle T3. The large semiaxis a is a tangent to the pitch circle T3. The arc of the ellipse located within the pitch circle T3 forms the profile contour of the tooth head 3k. It ends on the pitch circle T3.

• Modul m₃
• Zähnezahl z₃
• Profilverschiebung x₃

The basic toothing data of the master toothing 3i are:

• Module m ₃
• Number of teeth z ₃
• Profile shift x ₃

The module and number of teeth determine the diameter of the pitch circle T3 d 3 = m 3 * z 3 ,

The profile shift determines the ratio of the tooth head to the tooth base and in particular the curvature of the ellipse arch forming the tooth heads 3k. The sum of the profile shift of external teeth and internal teeth is equal to 1: Σ (x 3 ; X 4 ) = 1

The generation rule for the ellipse is: a = m 3 + C1 b = (m 3 + C1) * x 3 + C2.

The tip circle of the master toothing 3i is calculated as follows: dk 3 = d 3 - 2 * ((m 3 + C1) * x 3 + C2).

The constants C1 and C2 can either be used to create the gap between the Master toothing 3i and the counter toothing 4a are used or for adjustment the curvature of the ellipse or for both purposes at the same time. If they are for generation of the gap is used, the semiaxes a and b are changed by the same Amount advantageous in order to be as uniform as possible along the ellipse arc Maintain gap spread.

If you take the radial P2 as the y-axis of a Cartesian coordinate system with the center of the pitch circle T3 as the coordinate origin, the root circle of the master toothing 3i is calculated as: df 3 = 2 * (x1 + y1), where xl and y1 are the coordinates of the intersection of the tangent P1 with the pitch circle T3 (Fig. 6).

FIG. 7 shows the profile contour of FIG. 6 together with the profile contour of a tooth head 4k of the counter toothing 4a in the area of the deepest tooth engagement, where for squeezing fluid Cavity H1 between the profile contours of the tooth base 3f and the tooth head 4k remains. The profile contour of the adjacent tooth base of the counter toothing 4a is not located. According to the gearing law, it is created from the ellipse of the Tooth head 3k derived from the master toothing 3i.

The envelope cut method for generating the profile contour of the tooth tips 4k Counter toothing 4a is illustrated in FIG. 8. The profile contour of the tooth tips 4k is in the plane of the pitch circle T4 the connecting line that the envelope intersection of the Tooth tip curves 3k, i.e. the elliptical arches, the master teeth 3i with each other combines. Each of the points is the intersection of one of the tooth tip curves 3k with one Straight line V, which is the center point M of the respective ellipse and the intersection point C of the Radials connects with the pitch circle T4. The relevant radial through the intersection C has the same on the pitch circle T4 to the tooth bases 4f adjacent on both sides Distance on. The intersection point of the ellipse axes a and b understood. By a sufficiently large number of those forming the tooth heads 3k Ellipse arcs can be rotated to the same intersection point C (pitch point) Envelope intersections, i.e. Touch points are obtained in sufficient numbers that serve as support points for the profile contour of the tooth tips 4k to be generated.

The envelope intersection points are obtained by rotating tooth tip curves of the master toothing 3i about the pitch circle axis 6 of the counter toothing 4a, the tooth tip curves 3k of the master toothing 3i each being rotated onto the same tooth of the counter toothing 4a. For this, imagine the gear wheel set in the pitch circle plane. The master toothing 3i is known. The position of the pitch circle axis 6 of the counter toothing 4a relative to the master toothing 3i is also known. Furthermore, the number of teeth of the counter toothing 4a is known, so that one can position a star from radial starting from the pitch circle axis 6 of the counter toothing 4a to the apexes of the tooth heads 4k to be produced relative to the master toothing 3i. The tooth tip curves 3k of the toothing according to the invention are then rotated about the pitch circle axis 6 of the counter toothing 4a into one of the radial lines. In this way, for a specific position which the two toothings 3i and 4a hold relative to one another, a set of tooth tip curves of the master toothing 3i is obtained which envelop the tooth tip curve 4k to be generated, for example the tooth tip curves 3k ₁ to 3k ₅ of FIG. 8 Tooth curve 3k ₁ to 3k ₅ can be the tooth curve with the contact points 11 to 15 from the snapshot of Figure 1. This procedure is repeated for different relative positions of the two toothings 3i and 4a, the pitch circle axes 5 and 6 of course maintaining their positions. For each of the snapshots, the master toothing 3i is rotated about the pitch circle axis 6 of the counter toothing 4a in such a way that the respective radials of the counter toothing 4a are always overlapped with the same, once defined radial.

For the sake of completeness, the pitch circle diameter and the tip circle diameter of the counter toothing 4a are also given. The following applies to the diameter of the pitch circle T4: d 4 = m 4 * Z 4 . where the module m ₄ = m ₃ and the number of teeth z ₄ = Z ₃ - 1. The tip circle diameter results in: dk 4 = d 4 + 2 * ((m 4 - C1) * x 4 - C2).

Because the relationship: e + dk 4 / 2 <df 3 applies, the cavities H1 arise between the tooth bases 3f of the master toothing 3i and the tooth tips 4k of the counter toothing 4a. There is therefore already room for squeezing fluid from the generation regulation, which contributes to noise reduction.

FIG. 9 shows an example of how the cavity H1 is flattened by the tooth root curve 3f the master toothing can be reduced to reduce the dead volume. Therefor in the example, the profile contour of the tooth feet 3f compared to the Ellipse arc of the tooth heads 3k suitably chosen circular arc in the apex area flattened. The flattening is shown in dashed lines.

Claims (22)

Gear teeth made of tooth heads and tooth feet, which are second or from curves higher order are formed, the curves at their ends tangential point towards each other and at least the curves that form the tooth heads (3k), or at least the curves that form the tooth bases (3f) are not cycloids. Gear toothing according to claim 1, characterized in that neither the curves which form the tooth heads (3k) nor the curves which form the tooth bases (3f) are cycloids. Gear toothing according to one of the preceding claims, characterized in that a tooth profile contour formed by the curves is continuously differentiable, preferably continuously differentiable at least in part twice. Gear toothing according to one of the preceding claims, characterized in that the toothing in the tooth feet (3f) has indentations and the curves form at least up to the indentations a tooth profile contour which is continuously differentiable, preferably at least piecewise twice continuously differentiable. Gear teeth according to one of the preceding claims, characterized in that conical arches form at least the tooth heads (3k). Gear teeth according to one of the preceding claims, characterized in that conical arches form at least the tooth feet (3f). Gear teeth according to one of the preceding claims, characterized in that the tooth heads (3k) are each formed by a curve of a first shape and the tooth bases (3f) are each formed by a curve of a different, second shape. Gear teeth according to one of the preceding claims, characterized in that the tooth heads (3k) are formed by arcs of ellipses or ellipse-like curves. Gear teeth according to one of the preceding claims, characterized in that the tooth heads (3k) are formed by first conical arches and the tooth bases (3f) by second conical arches of a different type than the first conical arches. Gear teeth according to one of the preceding claims, characterized in that the tooth feet (3f) are formed by circular arcs. Gear teeth according to one of claims 1 to 9, characterized in that the tooth feet are formed by arcs of ellipses or ellipse-like curves. Gear toothing from tooth heads (3k) and tooth feet (3f) by curves second or higher order are formed, with the curves at their ends tangent to each other and the curves that flank the tooth tips (3k) form, arcs of an ellipse or Cassini curve in their ellipse-like shape are. Gear teeth according to the preceding claim, characterized in that the curves which form the tooth feet (3f) are not cycloids. Gear teeth according to one of the preceding claims, characterized in that the curves which form the flanks of the tooth feet (3f) are circular arcs. Gear wheel set for a gear machine (pump or motor), the gear wheel set comprising: a) a first gear (3) with a first toothing (3i) according to any one of the preceding claims b) and at least one second gearwheel (4) with a second toothing (4a) which meshes with the first toothing (3i) or can be brought into a meshing toothing, c) wherein at least one of the toothings (3i, 4a) has tooth bases (3f; 4f) which are shaped such that they each have a cavity in the deepest tooth engagement of one tooth tip (3k; 4k) of the other of the toothings (3i, 4a) (H1; H2; H3) form. Gear wheel set according to the preceding claim, characterized in that the second toothing (4a) for rolling the toothing (3i, 4a) has tooth bases (4f) which are formed by kinematic derivation of the first toothing (3i) according to the toothing law. Gear wheel set according to one of the preceding claims, characterized in that the profile contour of the tooth heads (4k) of the second toothing (4a) is obtained from envelope cuts of the profile contour of the tooth heads (3k) of the first toothing (3i). Gear wheel set according to one of the preceding claims, characterized in that the profile contour of the tooth heads (4k) and / or the tooth feet (4f) of the second toothing (4a) is formed by spline functions of at least grade three, preferably exactly grade three. Gear wheel set according to one of the preceding claims, characterized in that the second toothing (4a) each has an indentation in its tooth feet (4f) to form the cavity (H2). Gear wheel set according to one of the preceding claims, characterized in that the tooth heads (3k) of the first toothing (3i) are formed by conical arches and the tooth feet (3f) of the first toothing (3i) are shaped such that they are in the deepest tooth engagement of a tooth head (3k) of the second toothing (4a) each form the cavity (H1; H3). Gear set according to one of the preceding claims, characterized in that the first gear (3) an outer rotor or stator, the first toothing (3i) an internal toothing, the second gear (4) an inner rotor and the second toothing (4a) an external toothing of the are in-axis gear set. Gear ring machine (pump or motor), comprising: a) a housing (1) which contains a gear chamber which has at least one inflow opening (10) and at least one outflow opening (11) for a working fluid, b) an outer rotor or stator (3) accommodated in the gear chamber, which has a pitch circle axis (5) and an internal toothing (3i) about the pitch circle axis (5), c) an inner rotor (4) accommodated in the gear chamber, which is rotatably mounted about an axis of rotation (6) eccentric to the pitch circle axis (5) of the outer rotor or stator (3) and has an external toothing (4a) which is in line with the internal toothing ( 3i) is in a meshing tooth mesh, d) wherein the inner toothing (3i) has at least one tooth more than the outer toothing (4a) and the inner toothing (3i) and the outer toothing (4a) during a rotational movement which the inner rotor (4) relative to the outer rotor or stator (3 ), form expanding and compressing delivery cells (7) which lead a fluid from the at least one inflow opening (10) to the at least one outflow opening (11),
characterized in that e) the outer rotor or stator (3) and the inner rotor (4) form a gear wheel set according to one of the preceding claims.

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