DE102006029153A1 - Inclined-toothed front wheel and straight-toothed front wheel constructing device, has construction model including computer-regulated description of tooth flank with analytical description of evolvent, which determines geometry of flank - Google Patents

Abstract

The device has an input device inputting a value for a parameter of a primary-construction model. The model is changed depending on a preset parameter value to produce a three-dimensional construction model of a tooth connection. The connection is designed such that a tooth flank of tooth of one of inclined-toothed and straight-toothed front wheels (10, 11) has a form of an evolvent. The primary model has a computer-regulated description of the flank of the tooth. The flank description has a computer-interpretable analytical description of the evolvent, which determines geometry of the flank.

Description

The The invention relates to an electronic device for constructing a two-part tooth connection. Every ingredient this tooth connection includes a gear or a gear segment.

An electronic construction device having the features of the preamble of claim 1 is made US 6,587,741 B1 known. This design device has read access to a respective computer-available design model of each component of the tooth connection. These design models are parametric, that is, depend on parameters that describe the geometry of the constituent design model and whose values a user can specify and manipulate.

The The geometry of a tooth flank is determined by means of a curve between interpolation points described. Between each two support points is the curve for the tooth flank approximately described by a polynomial. The accuracy of the design model depends on it from the number and positions of the interpolation points.

In US 4,868,761 describes a programmable CAD / CAM system that can produce three-dimensional freeform surfaces. The surface to be produced is described mathematically. How this is done in detail is not explained.

Of the Invention is based on the object, a construction device to provide with the features of the preamble of claim 1, when the accuracy of the design model does not depend on the number and the positions of interpolation points depends.

The Task is by a construction device with the features of claim 1. advantageous Embodiments are specified in the subclaims.

The Construction device is for generating a computer-accessible three-dimensional Construction model of the tooth connection by changing a Designed initial design model. This initial design model comprises at least one parameter.

The Tooth connection is made so that each tooth flank of each tooth each component has the shape of an involute. According to the invention, the initial design model comprises each one computer-accessible Description of each tooth flank of each tooth of each component. The Tooth flank description includes a computer-analyzable analytical description of an involute, which determines the geometry of the tooth flank.

The Construction device has input device for inputting one each Value for every parameter. The initial design model becomes dependent changed from the entered value of the at least one parameter. This Parameter is a parameter of the description of the edge by means of the involute.

The Construction device according to the invention comprises an initial design model that describes the components of the tooth connection describe analytically. This analytical description is much more accurate as an approximate Description by interpolation curves or splines between interpolation points. about that In addition, the use of an approximate solution with nodes has the disadvantage that the accuracy of the design model strongly and unpredictably depends on the number and positions of the support points. at few support points the model is too inaccurate. Many interpolation points require processing of the design model high computing power, resulting in a long term leads. Both are disadvantageous.

each Tooth flank of the tooth connection is described as involute. Become the tooth flanks from a blank by a rolling process (Hüllschnittverfahren) made, so performed a round tool a rolling motion. This rolling movement causes that the The geometry of the tooth flank describes a curve that is an involute is. If a taut thread is unwound from a cylinder, so each point on the tightened part of the thread describes one Involute.

A tooth connection with tooth flanks, which have the shape of involute, has desired technical characteristics: two corresponding gears are constantly engaged with each other, and the verbin is insensitive to changes in the distance between the axes of rotation of the tooth connection. The tooth flanks roll off each other and do not slide past each other or even against each other. Therefore, the tooth flanks are also preferably made in the form of involutes, if not a rolling process is used as a manufacturing process.

• – Durch Auswertung des Konstruktionsmodells wird die Zahnverbindung untersucht, ohne daß bereits eine reale Zahn verbindung vorzuliegen braucht. Dadurch sind Untersuchungen frühzeitig im Produktentstehungsprozeß möglich. Beispielsweise wird das Gewicht der Zahnverbindung vorhergesagt. Oder eine Toleranzuntersuchung wird mittels des Konstruktionsmodells durchgeführt. Hierbei werden die Abmessungen der Bestandteile innerhalb vorgegebener Toleranzen variiert. Mit Hilfe der Bestandteil-Konstruktionsmodelle werden Simulationen durchgeführt. In den Simulationen wird z. B. das resultierende Spiel der Zahnverbindung ermittelt und mit einer vorgegebenen Schranke verglichen.
• – Das Konstruktionsmodell der Zahnverbindung wird vernetzt. Gemäß der Methode der Finiten Elemente wird eine Untersuchung der Zahnverbindung z. B. auf Betriebsfestigkeit, auf Schwingungen, auf Verschleiß und/oder auf die Lebensdauer durchgeführt.
• – Auf Basis des Konstruktionsmodells werden Zeichnungen der Zahnverbindung erzeugt und ausgedruckt. Diese Zeichnungen zeigen die Zahnverbindung aus verschiedenen Blickrichtungen und sind bemaßt. Diese Zeichnungen werden verwendet, um die Zahnverbindung zu fertigen.
• – Eine reale Zahnverbindung wird gefertigt. Die gefertigte reale Zahnverbindung umfaßt beispielsweise mehrere Zahnräder oder eine Welle und eine Nabe. Um diesen Prototyp herzustellen, wird ein Werkstück durch Fräsen in eine Form gebracht, die durch das Konstruktionsmodell der Zahnverbindung vorgegeben ist. Das Konstruktionsmodell steuert somit den Fertigungsvorgang.
• – Durch Analyse des Konstruktionsmodells werden Referenz-Meßpunkte definiert. Das Konstruktionsmodell liefert die exakten Positionen dieser Meßpunkte in einem vorgegebenen Referenz-Koordinatensystem. Eine reale Zahnverbindung wird so wie durch das Konstruktionsmodell vorgegeben gefertigt. Die reale Zahnverbindung wird in einem Koordinatensystem positioniert und orientiert. Dieses Koordinatensystem wird mit dem Referenz-Koordinatensystem in eine Beziehung ge bracht. Die reale Zahnverbindung wird vermessen, und zwar an Meßpunkten im Koordinatensystem, die den Referenz-Meßpunkten im Referenz-Koordinatensystem entsprechen. Ermittelt wird der jeweilige Abstand zwischen dem Referenz-Meßpunkt und dem gemessenen Meßpunkt. Bei einer nahezu exakten Fertigung sind alle Abstände gleich Null. In der Realität wird verlangt, daß die Abstände eine zuvor festgelegte Toleranz einhalten. In der Praxis treten hingegen oft Abweichungen auf, die die Toleranz übersteigen. Dadurch wird die reale Zahnverbindung mit dem Konstruktionsmodell verglichen.

The design device creates a computer-available three-dimensional design model of a tooth connection. This design model includes computer-available design models of the components of the tooth connection. The design model of the tooth connection can be used, for example, for the following technical applications:

• - By evaluation of the design model, the tooth connection is examined without the need for a real tooth connection already exists. As a result, investigations are possible early in the product development process. For example, the weight of the tooth connection is predicted. Or a tolerance examination is carried out by means of the design model. Here, the dimensions of the components are varied within predetermined tolerances. Simulations are performed using the constituent design models. In the simulations z. B. determines the resulting game of the tooth connection and compared with a predetermined barrier.
• - The design model of the tooth connection is networked. According to the method of the finite elements, an examination of the tooth connection z. As to durability, to vibrations, wear and / or carried out on the life.
• - Drawings of the tooth connection are generated and printed on the basis of the design model. These drawings show the tooth connection from different directions and are dimensioned. These drawings are used to make the tooth connection.
• - A real tooth connection is made. The fabricated real tooth connection includes, for example, a plurality of gears or a shaft and a hub. To make this prototype, a workpiece is machined into a shape dictated by the design model of the tooth connection. The design model thus controls the manufacturing process.
• - By analyzing the design model, reference measurement points are defined. The design model provides the exact positions of these measurement points in a given reference coordinate system. A real tooth connection is made as dictated by the design model. The real tooth connection is positioned and oriented in a coordinate system. This coordinate system is related to the reference coordinate system. The real tooth connection is measured, namely at measuring points in the coordinate system, which correspond to the reference measuring points in the reference coordinate system. The respective distance between the reference measuring point and the measured measuring point is determined. With a nearly exact production all distances are equal to zero. In reality, it is required that the distances comply with a predetermined tolerance. In practice, however, deviations often occur that exceed the tolerance. This compares the real tooth connection with the design model.

Preferably comprises the construction model in addition a computer-accessible Curve that describes the respective tooth root. This curve lays especially the foot rounding firmly. The tooth flank is preferably as by means of the involute and the curve of the tooth base described.

in the The following is an embodiment the invention described in more detail with reference to the accompanying drawings. Showing:

1 , two spur gears in accordance with DIN 3960;

2 , four shaft-hub connections DIN 5480;

3 , a ring gear and a pinion engaged;

4 , Coupling flange, rear axle and bevel gear;

5 , an illustration of continuous milling;

6 , the milling of a tooth gap with a profile disc cutter;

7 , Quantities that determine a spur gear of a tooth connection;

8th , Sizes at an involute;

9 , other sizes on an involute;

10 , the pitch height and the pitch angle of a helical gear;

11 , an overall model of a tooth connection;

12 , a geometric and analytical description of a curve piece;

13 , the dependence of a point of the involute of further sizes;

14 , the calculation of the angle of rotation and the tooth gap width;

15 , the calculation of the involute angle of rotation for internal gears;

16 , various reference profiles of the involute toothing;

17 , a tool reference profile;

18 , the creation of a foot rounding;

19 , the relationships in creating a footing curve;

20 , the geometric description of a point on the footing curve;

21 , the trigonometry of the head rounding;

22 , the rolling of the tool when manufacturing a gear;

23 , a section of the reference profile;

24 , how to make a curve available to the design tool;

25 , an illustration of the rolling factor G;

26 , the blending of shortened involute and footing curve;

27 , the generation of a gullet profile by means of the curve of 26 and circular section pieces;

28 , schematically the two central curves for straight and helical gearing;

29 , a toothed shaft connection with involute flanks;

30 , the geometries of the tooth gaps of shaft and hub;

31 , the positive geometry of a hub toothing;

32 , two variants of shaft outlets;

33 , two variants of a hub toothing.

• – einer Stirnradverzahnung gemäß DIN 3960,
• – einer Welle-Nabe-Verbindung gemäß DIN 5480 und
• – einem Tellerrad und einem Ritzel, das in das Tellerrad eingreift.

In the exemplary embodiment, the construction device is used to construct the following tooth connections:

• - a spur gear toothing according to DIN 3960,
• - A shaft-hub connection according to DIN 5480 and
• - A ring gear and a pinion, which engages in the ring gear.

1 shows above a helical spur gear 10 and below a straight toothed spur gear 11 with undercut, both according to DIN 3960.

According to DIN 5480, splined shaft connections are used to detach shafts and hubs slidable or firmly connected. The toothed shaft connections have the properties required for torque transmission and centering. The essential distinguishing feature of these gear systems is the pressure angle, which is 30 °, 37.5 ° or 45 °. Connections with 30 ° pressure angle have reached the widest range of application

• – eine Nabe 12 gemäß DIN 5480 ohne Auslauf,
• – eine Welle 13 gemäß DIN 5480 ohne Auslauf,
• – eine Welle 14 gemäß DIN 5480 mit Auslaufradius und
• – eine Welle 15 gemäß DIN 5480 mit Auslaufradius und Gerade.

2 shows components of a shaft-hub connections DIN 5480. This shows 2 from top to bottom:

• - a hub 12 according to DIN 5480 without outlet,
• - a wave 13 according to DIN 5480 without outlet,
• - a wave 14 according to DIN 5480 with outlet radius and
• - a wave 15 according to DIN 5480 with discharge radius and straight line.

3 shows a ring gear 16 and a pinion 17 , The pinion 17 grips the ring gear 16 one.

4 shows a coupling flange 18 , a rear axle 19 and a bevel gear 20 a Hinterachsgetriebes of a motor vehicle. In this example, too, a tooth connection occurs.

• – ein Konstruktionsmodell, das die Rohteile der Bestandteile der Zahnverbindung beschreibt, und
• – ein Konstruktionsmodell, das quasi als Negativ die Geometrie der Zahnlücken beschreibt.

When manufacturing the tooth connection, a blank of each component of the tooth connection is first generated in each case. From these blanks, the tooth spaces are then milled or otherwise removed so that the teeth remain. Preferably, the construction device therefore produces two design models:

• A design model describing the blanks of the components of the tooth connection, and
• - A design model that describes the geometry of the tooth gaps as a negative.

The Construction model of the tooth connection is then the difference from blank design model and gullet design model.

Around on the one hand to achieve a high gear accuracy, on the other hand preferably To manufacture economically, a tooth connection is often used in made in two steps: the first step is with large feeds and meshed with a high cutting speed. At the second step a fine machining is carried out. For Vorverzahnen be mainly hobbing, the Wälzstoßen and Planing for large gearings used. The finishing is mainly by Wälz- or Mold grinding performed. Various Methods for producing tooth connections are also described in G. Niemann & H. Winter: Machine Elements Volume 2: Gears in General, Gears - Basics, Helical gear, 2nd edition, Springer-Verlag, 1989, described.

at Application of a rolling process (Hüllschnittverfahrens) The tooth profile is caused by a rolling movement between the tool and the gear to be produced. Instead of the tool can also be a planer toothing, which is embodied by the tool, be used. There are the same kinematic conditions like the wheels in the transmission. This cutting shaping in the rolling process can be achieved by planing, milling, Bump, Cockroaches and grinding done.

At the Rolling becomes the tooth flank of a tool with a straight reference profile, with simultaneous movement of the workpiece, generated. This is the tooth flank is created as an involute. In every situation tangent the cutting edges of the profile, so that the tooth flank of a Sequence of Hüllschnitten arises.

In a continuous rolling process, chip is continuously removed until completion of all teeth of a component of the tooth connection to be manufactured. Tool and workpiece rotate like two meshing gears (cutting, scraping or rolling) or like worm (milling, scraper or grinding worm) and worm wheel. 5 illustrates continuous milling.

At the Part-generating method becomes the tooth gap as well from the straight edge of the tool as Hüllschnitt generated, however, is the rolling motion the tool no longer running, but back and forth. After the rolling process the tool will be out of action Intervention brought and after switching the gear to one or more teeth (Sub-operation) the next Operation executed in the same way.

At the Profile process is the gear to be produced without rolling motion generated. Here the tool has the profile of the tooth gaps and is moved in the direction of the tooth flanks. This method is touching Tool and gear in the whole profile.

In the part profile process, the profiled tool (disc or end mill, impact or punching tool, broach or grinding wheel) grinds or cuts one tooth gap and the next after the parting process. In the complete profile process, the entire gearwheel is toothed with a punching, drawing or broaching tool in a cutting or drawing process. 6 illustrates how a tooth gap is milled with a profile disc cutter.

at the production in the spatial Molding process is a "mold" that forms a complete spatial matrix represents the gear. The gears are here as a whole (with teeth, possibly forehead cams, claws, etc.) poured, sintered, pressed or injected.

The Tooth flank represents the most important part of the gear. It ensures that two Cogs constantly in the Intervention and opposite center distance insensitive. Furthermore, the tooth flank must procure this way be that the gears do not slide on each other, but roll off. So the wear is very low. This property is achieved by the so-called circle involute.

If a taut thread is unwound from a cylinder, each point on the tightened part of the thread describes a circle involute. That is, all points of a tangent (the generator) that circulates on a circle describe circle involutes. For gears, this circle is called the base circle. With the base circle radius r _b , therefore, the involute is uniquely determined. The base point T of the generatrix on the base circle is the center of curvature of the involute in the corresponding point Y. The flank normal thus always affects the base circle.

From W. Matek et al .: Machine Element Standardization, Calculation and Design, Vieweg-Verlag, 2001, various sizes are known which describe a spur gear of a tooth connection. 7 illustrates these sizes. 8th and 9 illustrate the sizes of an involute.

The number of teeth on the wheel circumference is denoted by z. According to DIN 3960, the modulus m of the reference profile is the normal modulus m _n modulus in the normal section of the spur toothing. It is

Here, β is the helix angle and m _{t is} the forehead module. A module is a measure that z. B. measured in [mm].

berechnen.The partial cylinder is according to DIN 3960 the reference surface for the spur toothing. Its axis coincides with the guide axis of the wheel (wheel axle). Accordingly, in a rack, the part plane functions as the rack reference plane. The pitch circle is the section of the part cylinder with a front section plane. The pitch diameter d can be according to the calculation rule

to calculate.

Of the Base cylinder is in accordance with DIN 3960 the one to the cylinder part coaxial cylinder, for the production the involute area (Involute helical) is determinative. Sizes on the base cylinder are indicated by the index b.

berechnen. Hierbei ist α_t der Stirneingriffswinkel.The following definitions also come from DIN 3960. The base circle is the section of the base cylinder with a frontal plane; The involutes of the base circle contain the usable parts of the tooth profiles. The base circle diameter d _b can be in accordance with the calculation rule

to calculate. Here, α _{t is} the prewarning angle.

berechnen.The involute (always in a frontal section) is inclined according to DIN 3960 in the arbitrary point Y to the _front profile angle α _yt against the radius (center _beam ) by Y. The face profile angle can be according to the calculation rule

to calculate.

The prism engagement angle α _t is the acute angle between the tangent to the involute in its intersection with the pitch circle and the radius (midpoint beam) through that intersection. The following applies:

In the normal section through an involute screw surface, the tangent to the radius (center beam) placed at this point on any surface Y is inclined by Y about the normal profile angle α _yn . The corresponding inclination angle at the sub-cylinder is the normal engagement angle α _n ; it is equal to the profile angle α _{P of} the reference profile. The following applies: tanα n = tanα t · cosβ tanα yn = tanα yt · cosβ y

For a straight-toothed spur gear, β = 0 and α _n = α _t = α and α _yn = α _yt = α _y .

The centering angle determined by the involute origin point U and the point of contact T of the tangent from the point Y to the base circle is the rolling angle ξ _{y of} the involute. The base circle arc UT is equal to the tangent section YT. Therefore: ξ y = tanα yt

The tangent section YT is the radius of curvature ρ _{y of} the involute at the point Y and at the same time the pitch Y belonging to the pitch Ly, ie the unwound from the origin U of the involute from the base arc. In the triangle OTY, it is the countercathet of the _face profile angle α _yt lying at the circle center O.

The angular difference ξ - α _t is called involute function of the angle α _t and inv α _t (read: involut α _t ). The following applies: invα yt = ξ y - α yt = tanα yt - α yt

The pitch height p _{z of} an involute screw surface and thus a tooth flank is the portion of a surface line of a cylinder concentric with the wheel axis between two successive turns of an involute screw surface (a tooth flank). The pitch height is independent of the cylinder diameter. The following applies:

10 illustrates the pitch height p _z , the helix angle β and the helix angle γ of a helical gear. Shown are the plane 30 the reference profile as a profile reference line and the generatrix 31 of the part cylinder, which acts as a wheel axle.

The normal pitch p _n is the length of the helical arc between two consecutive right or left flanks on the sub-cylinder in the normal section of the toothing. The following applies: p n = p t · cosβ

The pitch angle γ is the acute angle at which the profile reference line intersects with the wheel axle. It is also the acute angle between a tangent to a partial cylinder flank line and the plane perpendicular to the wheel axis through the Tangentenberührpunkt. The helix angle β is the acute angle between a tangent to a partial cylinder flank line and the partial cylinder surface line through the tangent contact point. The following applies: | Β | = 90 ° - | γ |

For spur gears γ = 90 ° and β = 0 °. The pitch angle γ and the helix angle β have the same sign. The helix angle β _{R of} the right flanks may be different from the helix angle β _{L of} the left flanks.

The profile displacement of an involute toothing is the distance of the profile reference line from the part cylinder. The size of the profile shift is specified with the profile shift factor x as a multiple of the normal module. Therefore: Profile shift = x · m n

at spur gears applies: profile shift = x · m.

If necessary, a distinction must be made between the profile shift factor x, which is decisive for the nominal dimensions of the toothing, and the generation profile shift factor x _E which is to be used in the production of a dimensionally stable toothing. For the profile shift x · m _n = 0, the nominal dimensions of the tooth thickness and the gap width on the pitch circle are equal to half the pitch.

A Profile shift is positive if the profile reference line from the pitch circle moved towards the head circle. Here is the tooth thickness in the pitch circle greater than at the profile shift zero. A profile shift is negative, when the profile reference line is shifted from the pitch circle towards the root circle is; The tooth thickness is smaller in the pitch circle than in the profile shift Zero.

The head cylinder is the cylindrical surface on the teeth of a toothing teeth; a frontal section gives the top circle. The following applies: d a = d + 2 · h a = d + 2 · x · m n + h aP + 2 · k

Here h _{a is} the head height, h _{aP is} the head height of the reference profile and k is the head reduction.

The foot cylinder is the cylindrical surface at the bottom of the tooth gaps of a toothing. An endcut results in the root circle. The following applies: d f = d - 2 · h f = d + 2 · x · m n - 2 · h fP

Here _f d denote the diameter of the root circle and the dedendum h _f.

The tooth head height h _a and the tooth root height h _{f of} a spur gear are specified from the pitch circle. The denominations are calculated as follows: H a = h aP + x · m n + k H f = h fP - x · m n

The tooth height h _{P of} the reference profile is subdivided by the profile reference line into the head height h _aP and the foot height h _fP .

The head play c _P is the difference between the foot height h _{fP of} the reference profile and the head height h _{aP of} the counter reference profile. The following applies: H P = h * P · m n = 2 · m n + c P H aP = h * aP · m n = 1 · m n H fP = h * fP · m n = 1 · m n + c P

The front tooth thickness s _t is the length of the partial arc between the two flanks of a tooth. For a spur gear, the spur tooth thickness s _{t is} the tooth thickness s.

The gap width e _t is the length of the circular arc with the diameter d between the tooth flanks, which enclose a tooth gap. For a spur gear, the gap width e _{t is} equal to the gap width e. Tooth thickness s _t and gap width e _t together form the pitch circle pitch p _t .

The Construction device comprises an electronic library, in the predefined initial design models are stored by tooth connections. Each of these initial design models includes a computer-accessible analytical description of the respective tooth connection. Commercially available Construction tools, a data processing system and a Comprising a software system for computer aided design, enable such an analytical modeling.

The Tooth flank includes a tread in the form of an involute, as well as a tooth root, which by a Fußrundungskurve is described. The analytical models therefore include the description the shape (as curves) of the tread as involute and the foot rounding (Fußrundungskurve) in later End position. End position means that the Curves are already twisted in space so that building on the tooth gap modeled becomes.

11 shows an overall model of a tooth connection, from which the individual geometric representations of the involute and the Fußrundungskurve be derived. These individual geometric representations are used to derive parameter equations. The involutes are shown 32 and the foot rounding curve 33 ,

With reference to 8th and 9 now the parameter equations of the involute are derived. 12 shows a geometric and analytical description of the elbow b _E.

The tangent is extended by the left elbow ρ _y as a function of the angle of rotation ξ _y . The unrolled part of the circle can thus be described by the following formula: ρ _y = r _b · ξ ⁀ _y

Here, ξ ⁀ _{y is} the angle in radians.

For the later description the tooth must be Involute by an angle ΨE0 to be twisted. This twist angle ΨE0 of the involute for external gears will be out of the measure of gap et deduced and already taken into account in the parameter equations. Below is described his derivation.

ζE = ξy – αyt + ψE0 If one considers an arbitrary point Y (xE; yE) of the involute, geometrical relationships result 13 be illustrated. The following applies:

ζ e = ξ y - α yt + ψ E0

The _face profile angle α _yt is calculated as follows: α ⁀ yt = arctanξ ⁀ y

How out 13 As can be seen, the following relationships apply to the involute calculation angle ζ _E :

If the above equation is used, the result is: x e = r y * Cos (ξ y - α yt + ψ E0 ) and y e = r y * Sin (ξ y - α yt + ψ E0 )

From this one obtains the parameter equations of the coordinates of the points of the involute:

As already mentioned, the involute must be rotated for the later representation of the running surface of the tooth gap in the given three-dimensional coordinate system. The formula for the tooth gap width e _t serves this purpose. However, since the tooth gap width is measured in accordance with DIN 3960 in the pitch circle diameter, but the involute begins in the base circle, which results from 14 Procedure for calculating the involute angle ψ _{E0 of} the involute for external gears.

As stated above: invα yt = ξ y - α yt = tanα yt - α yt

If the arbitrary angles ( _face profile angle α _yt , rolling angle ξ _y ) of the involute function are replaced by the face engagement angle or face rolling angle, the following results: invα t = tanα t - α t

In interlocking tables, the details of the angles are always given in degrees. The correct expression is: invα t = tan α - α ⁀ t

Here, α ⁀ _{t is} the Stirneingriffswinkel radians.

The tooth gap width e _t results from the difference between the frontal division p _t and the tooth thickness s _t : p t = m t · Π and s t = m t · ( π 2 + 2 · x · tanα n ) and e t = p t - s t

For the tooth gap width e _t , therefore: e t = m t · Π - m t ( π 2 + 2 · x · tanα n ) = m t · ( π 2 - 2 · x · tanα n )

Join the in 14 illustrated geometry with the calculation rules set out above, the following calculation rules for the twist angle ψ _E0 arise:

By inserting results:

The α-angles become, as usual in gearing tables, used in the degree.

15 illustrates the calculation of the involute angle ψ _{E02 of} the involute for internal _gears . The angle of rotation of the involute for external gears ψ _E0 is calculated from the gap width in the front section e _t and the involute function in the front section invα _t . This derivation considers the later modeling of the tooth gap as a positive. The tooth gap of the hub teeth should also be modeled as positive (line 34 in 15 ). For this purpose, the twist angle is adjusted. 15 shows the geometric relationships.

With the same pitch diameters of the hub and shaft, the tooth gap of a hub toothing e ₂ and the tooth thickness of the associated shaft toothing s _{1 are the} same. Consequently, cf. 15 : s 1 = e 2 = 2 · r 2 · (Ψ ⁀ E0i - inva n ) as already stated, the following applies: invα yt = ξ y - α yt = tanα yt - α yt

The involute function in normal section is calculated from this as follows:

From the calculation _rules mentioned above, a calculation _rule for the angle of _rotation ψ _{E0I of} the involute for internal toothing in radians arises:

in the following is also the foot rounding exactly described. The description is based - just like the description the tooth flank - on the manufacturing process. By the exact description of the kinematics of the tool will also described this curve exactly.

For each Tool for the production of gears with involute toothing serves a reference profile. In the cutting gear manufacturing is usually used a gear tool with straight-edge reference profile. The reference profile is used to limit the tools to spur characteristics (a tool for both gears) to enable and to exchange the tools with almost identical wheel characteristics to ensure. For the most use cases receives By doing so, suitable and balanced gearing.

16 shows various reference profiles of the involute toothing. In 16 On the left, a reference rack according to DIN 867 is shown. Shown is the profile reference line 35 , the counter-reference profile 36 , the head line 37 , the foot line 38 and the foot rounding 39 ,

In 16 Center a protuberance tool is displayed. The tool profile will be shown 40 and the protuberance height prP0. The creation of a protuberance profile allows the free cutting of the tooth root to avoid notches during gear grinding. The reference profile is preferably for Derivation of the undercut curve used as it reflects the dimensions of the tool.

In 16 on the right side the tooth flank is shown, which with the tool profile, which is in 16 Center is shown was generated.

In 17 a tool reference profile is shown. This corresponds to the counter reference profile 16 Center, ie the head height of the tool reference profile corresponds to the foot height h _{fP of} the spur gear reference _profile (h _aP0 ≙ h _fP ) and the head rounding of the tool reference profile corresponds to the root radius of the spur reference profile (ρ _fP ≙ ρ _aP0 ).

18 shows the generation of a foot rounding, which is also described in G. Niemann & H. Winter, supra. The kinematics are described by the following processes:
Rolls the pitch circle on the Wälzlinie TT from, the envelope of the tool describes the shape of the tooth gap, as in 18c shown. During this bumping, milling, and grinding movement, the head of the tool cuts the root of the gear, the straight edge of the tool cuts the tooth flank, and the tool head radius ρ _fP forms the root of the gear. When making the teeth, the rolling line TT from the profile centerline PP of the tool by the amount x · m are shifted outwards or inwards, whereby during rolling a positive or a negative profile shift arises (+ x · m or -x · m). The base circle radii r _b = r · cos α remain unchanged, since the pitch circle continues to roll on the rolling line.

When rolling the rolling line on the pitch circle, the tool dips below the rolling line TT in the gear to be generated. During this movement, the center of the tool head radius below a profile displacement of a module describes a loop-like course. In the literature, this course is also referred to as loop involute. Above one module, the foot fillet corresponds to the tool head radius, as in 18a can be seen.

To generate the parametric equations of the foot fillet curves, the gear to be produced is considered static and the tool rolls on it. This approach allows a similar approach as in the derivation of the parameter equations of the involute. If one describes a point of the Wälzlinie, this has during the rolling process the course of an involute (with r corresponds to r _b ). However, this consideration is not enough. In addition, the part of the tool below the pitch line must be included in the calculation model, which dips later and generates the loop shape (<x · m = 1). Furthermore, the tool head radius plays a role, because this part generates the foot rounding curve.

19 shows schematically the relationships in the generation of a Fußrundungskurve. Shown are a rolled sheet 44 the rolling line and the foot rounding curve 45 ,

• – Bezugsprofil enthält die Maße des Werkzeugs
• – Wälzlinie TT rollt auf Teilkreis ab
• – Wälzlinie TT kann von Profilmittellinie PP um x·m verschoben werden
• – Kopfradius des Werkzeugs erzeugt Fußausrundung

This overall model contains all the information that is summarized here:

• - Reference profile contains the dimensions of the tool
• - rolling line TT rolls on pitch circle
• - rolling line TT can of profile centreline PP to be moved to x · m
• - Head radius of the tool creates foot rounding

20 shows a geometric description of a point on the footing curve 45 , 21 illustrates the trigonometry of the head rounding. An arbitrary point P _U (x _U ; y _U ) of the foot rounding curve 45 is described by the following relationships, which 20 and 21 to be illustrated.

The point P (x, y) in 21 is the center of the circle of tool rounding. Therefore, X _fP = ρ _fP · sinε and y _fP = ρ _fP · cosε.

The partial length of the tool below the rolling line, reduced by the tool head radius ρ _fP , is: c = h fP - x · m n - ρ fP

The center distance of the head rounding is calculated from the equation

The unrolled elbow of the rolling line is calculated as follows: ρ U = r · α ⁀ uy

The angle of the center distance results from the angular relationship ζ U = ξ uy - α uy + ψ U0

Of the Total angle of the foot rounding becomes like this certainly

0 and 21 show that the following trigonometric relationships apply:

The combination of the individual values leads to the calculation of the coordinates of the point of contact between tool and workpiece:

The parameter form for describing the point coordinates of the touch point thus has the following form:

The following describes how the twist angle of the foot rounding curve is described. The foot rounding of the gear wheel is generated by the head of the tool. For the derivation of the angle of rotation of the Fußrundungskurve two special situations of relative movement between the workpiece (gear) and tool are considered. These two situations are going through 22 illustrated.

The first situation will be in 22 shown on the left. The tool begins to undercut the tooth, ie to create the foot rounding. At this point, the center of the circle describing the tool head rounding is exactly perpendicular (in this illustration) above the center of the gear.

The second situation will be in 22 shown on the right. Gear and tooth have turned in the manufacturing process so that tooth and gear form a common axis of symmetry.

The angle that the gear has swept from the first to the second situation gives the Ver angle of rotation Ψ _{U0 of} the foot rounding curve.

23 shows a section of the reference profile. The frontal division p _t results from the product of the front module and the circle constant:

From the geometric contexts of in 23 shown partial section of the reference profile is calculated half the distance to the foot machining:

xu2 = tanαt·(hfP – ρfP)

The following two intermediate sizes, combined with half the distance for foot machining, result in the angle of rotation of the foot rounding curve ψ ⁀ _U0 :

x u2 = tanα t ·(H fP - ρ fP )

The Construction device comprises an electronic library with multiple initial design models of tooth connections. Each design model describes at the same time the tool with which the tooth connection is made, so far as required. The initial design model includes several Parameters whose values can be freely specified. The construction device comprises Input Devices, with which a user values for can specify these parameters.

Wird jedem dieser Parameter jeweils ein Wert zugeordnet, so ist das Konstruktionsmodell eindeutig festgelegt und beschreibt die Zahnverbindung vollständig.The following input parameters completely determine a gear:

If each of these parameters is assigned a value, the design model is clearly defined and describes the tooth connection completely.

The gear making tool is determined by the following input parameters:

Profile displacement x · m, tool head radius ρ _fP and head height h _aP and foot height h _fP are used as variable parameters. If fixed values were to stand here, geometries could overlap in the design model, which contradicts reality.

db = d·cosαt The design model has additional parameters that depend on the input parameters. In order to structure the design model clearly, parameters are introduced which are stored with the computer-evaluable calculation rules for the calculation of the equations mentioned above. Each subsequent calculation rule can thus refer to one of these parameters and does not again contain the entire formula. The following parameters are inserted and stored with the corresponding equations:
Pitch diameter d, frontal engagement angle α _t and base circle diameter d _b are determined by the following stored calculation instructions:

d b = d · cosα t

The tip diameter d _a and the root diameter are calculated as follows: da = d + 2 · (h * aP · m n + x · m n + k) and df = d + 2 · m n · (X - h * fP )

pt = mt·π ρfP = ρfP·mn hfP = h*fP ·mn Forehead module m _t , face pitch p _t , tool head radius ρ _fP and foot height h _fp are calculated using the following calculation rules:

p t = m t · π ρ fP = ρ fP · m n H fP = h * fP · m n

The partial length c of the tool is calculated as follows: c = h fP - x · m n - ρ fP

The calculation rules for the angle of torsion Ψ _{E0 of} the involute for external toothing and for the angle of rotation Ψ _{U0 of} the foot rounding curve are prepared in advance.

The Calculation rules for Parameters are stored in a form in which the construction device she can evaluate. Preferably, the software system of the construction device comprises a functionality Calculation rules in the form of rules or dependency rules To store ("constraints") and evaluate. These rules are within explicit equations Variables and constants for the software system "recognizable" defined.

25 illustrates how to make a curve available to the design tool. Such a rule is z. For example, you can use the parallel curve functionality to process computer-available curves in a plane based on a reference line 50 in 25 and a plane 51 tangent to this line. Starting from a length of the line 50 the resulting first curve changes 52 in length. The amplitude remains constant.

In the same way, a second resulting curve 53 generated. The same reference line is used as a basis 50 and a second plane perpendicular to the plane described above 51 stands.

In the next step, both curves are superimposed on each other. This will create a three-dimensional curve 54 generated. By projection of this three-dimensional curve 54 the third level in space becomes a curve 55 generated on the basis of the derived calculation rules.

This method is used in the same way to describe the involute and the foot rounding curve. In 25a ) the description of the involute is shown in 25b ) that of the foot rounding curve. In 25c ) both resulting curves are shown.

angewendet.The variable of this rule is preferably calculated between the values zero and one in a sequence of steps predetermined by the software system. the last calculated value of the variable ξ ⁀ _y corresponds to the value one. Here are the calculation rules

applied.

The rolling angle ξ _{y of} the involute can be freely selected in the value and is connected to the _face profile angle α _yt :

Preferably becomes a rolling factor G calculated. This rolling factor G causes the Curve starts at the base circle diameter and at the tip circle diameter ends. This makes the involute in the design model on the required size limited. Furthermore becomes G-values that are always less than 1, accuracy the results by the constant number of calculation steps elevated.

25 illustrates the rolling factor G. Shown is the shortened involute 46 , The rolling factor G is calculated as follows:

If the rolling factor G is used, the following calculation rules are used:

in the Design model becomes the involute, which by means of the rolling factor G shortened became, with the Fußrundungskurve blended. Since the angle of rotation is considered from the outset were already both curves are in the later end position.

26 illustrates the blending of the shortened involute 46 and the foot rounding curve 33 , The starting position is shown on the left, a curve on the right 47 that by blending of 46 and 33 arises.

Subsequently, each intersecting curve 47 mirrored and connected with additional inserted head and Fußkreisteilstücken. 27 shows the generation of a gullet profile by means of the curve of 26 and circular section pieces. In 27 is a curve on the left 47 and one by mirroring the curve 47 resulting curve 47a shown. Right is shown as the curves 47 and 47a through a head section 48 and a Fußkreisteilstück 49 supplemented and assembled to a tooth space profile of a flat toothing.

Preferably For example, the software system of the design device has the functionality "rib." A rib needed a central curve, a flat profile and optionally a reference element or a separation direction. The three-dimensional computer-accessible geometry arises as an extrusion of the profile along the central curve. The extension direction is used to align the profile to influence.

For a straight or helical gearing, the construction device initially generates two central curves. 28 schematically shows the two central curves. The first central curve 56 is a "line" normal to the flat gullet profile, the length of which corresponds to the tooth width, thus giving the plane profile a height, as the second central curve 57 serves a "helix" (helix).

berechnet. Die Zahnbreite b ist gleich der Höhe der Helix.In order to define the second central curve as a helix, a starting point, a slope P, a central axis and a height are specified and left or right slope is determined. To specify slope, a rise height according to the calculation rule

calculated. The tooth width b is equal to the height of the helix.

By the definition of the helix alone can not achieve spur toothing be there for this the slope P would be infinitely large. Therefore an additional "rule" is stored Rule automatically selects between the previously defined ones Central curves. Before editing this rule will be a third Curve inserted. This curve, here called mean curve, serves as a dummy. Becomes a helix angle greater than 0 used, so the mean curve is equal to the helix. At a helix angle equals 0, the mean curve is the o.g. Line.

Then the rib is finished. For this, the plane tooth profile, the mean curve and the reference line of the involute and the undercut curve are used for complete definition. Finally, the rib is circularly arranged with a "circle pattern." The number with the parameter "number of teeth" and the setting option "Parameter" is set to "Complete garland".

in the embodiment becomes the parametric design model of a tooth connection stored in an electronic library, preferably as a user-defined feature.

• – Der Eingriffswinkel α_n beträgt wahlweise 30° oder 37,5° oder 45°.
• – Die Kopfhöhe h_aP des Bezugsprofils beträgt vorzugsweise 0,45.
• – Die Fußhöhe h_fP des Bezugsprofils beträgt vorzugsweise 0,55 bei Fertigung durch Räumen, 0,60 bei Wälzfräsen und 0,65 bei Wälzstoßen.

29 shows a toothed shaft connection with involute flanks, which connects a shaft and a hub with each other. Shown are the profile 60 of wheel 1 (shaft) and the profile 61 of wheel 2 (hub). A spline is a form of spur gear teeth. Therefore, calculation rules for a spur gear toothing are also valid for a shaft toothing. The parameters preferably have the following alternative values:

• - The pressure angle α _n is either 30 ° or 37.5 ° or 45 °.
• The head height h _{aP of} the reference profile is preferably 0.45.
• - The foot height h _{fP of} the reference profile is preferably 0.55 when manufactured by broaching, 0.60 for hobbing and 0.65 at Wälzstoßen.

These Sizes apply equally for the Nabeverzahnung. However, the hub toothing is an internal toothing and must be modeled independently become. This will be the initial design model adapted to the spur gear toothing, by replacing some geometries and parameters. Hereinafter is explained how to proceed. Here are all the symbols of the wave teeth additionally marked with the index 1 and the hub teeth with the index 2.

The number of teeth z of an internally toothed spur gear (ring gear) is to be used as a negative size. This corresponds to the idea that the transition from the outer wheel to a ring gear, the wheel diameter is increased until at d = + ∞ initially the rack is achieved with z = + ∞. In the further course of the transition, the wheel diameter jumps to -∞ and then assumes finite negative sizes. This results in the following relationships:

This information results in all diameters of the hub teeth with negative signs. In practical application, the absolute values are to be used. This results in the following calculation rules for the diameters of the hub toothing:
for the pitch circle diameter: d ₂ = | -z · m _n |
for the base diameter d _{b 2} = | z _n · m · cos _n |
for the tip circle diameter: d a2 = | -Z · m n + 2 · m n · (X 2 + h * aP ) |
for the root diameter: d f2 = | -Z · m n + 2 · m n · (X 2 - H * fP ) |

The values of the pitch circle diameter and the base circle diameter of the hub toothing are identical to the same diameters of the shaft toothing. Tip diameter and root diameter differ, because with internal gears, the tip circle is inside and the root circle outside. This will be in 29 illustrated. For this purpose, the rolling factor G is calculated individually:

The angle of rotation ψ ⁀ _{E0I of} the involute for internal _gears in radians is calculated according to the following calculation rule:

Above, two arithmetic rules were given to obtain the coordinates of a point on the shortened involute 46 to calculate. In the following, the corresponding calculation rules for an internal toothing are given. The involute angle Ψ _{EI of} the involute for internal gears is used with negative prefix.

The last two specified calculation instructions are stored in the design device in computer evaluable form. The shortened involute 46 is mirrored. The shortened involute 46 is connected to the mirrored shortened involute by head and foot sections. Since the angles of rotation are taken into account from the outset, both curves already exist in the later end position. The foot rounding curve can not be used in this context. Instead, radii are applied.

In 30 The geometries of the tooth gaps of shaft and hub are shown. Shown are the tooth gap 62 a wave and the tooth gap 63 a hub. The gap twist angle η ensures that no changes must be made in the application. It is defined as follows: η = 180 ° z

The tooth of the hub is then extruded with a block from the flat tooth space profile and arranged in a circular pattern with a "circle pattern." The number is calculated using the parameter "number of teeth". 31 shows the completed positive geometry of the initial design model of the hub toothing from two different viewing directions. Also, this initial design model is preferably stored as a custom design element in the electronic library. To apply the initial design model, the positive geometry of the tooth gap is then subtracted from a previously modeled geometry.

A computer-accessible Description of the shaft toothing is also generated by that they are in later Application of other geometries subtracted with Boolean operations becomes. These shaft gears are manufactured with shaft outlets, i.e. the tool moves from the workpiece out. These are two common Wellenausläufe additionally modeled.

32 shows two variants of wave outlets. The variant shown on the left has a rounding and then runs straight. At the in 32 shown on the right is the shaft outlet a rounding.

33 shows the two resulting hub teeth. These arise from the design models of 31 Using the two variants of wave outlets, which in 32 to be shown. List of used reference signs and symbols

Claims (4)

An electronic device for constructing a two-part tooth connection, wherein - each component of the tooth connection comprises a gear or a gear segment, - the design device has read access to a data memory, - in which a computer-available three-dimensional initial construction model of the tooth connection is stored, - Initial design model comprises at least one parameter, and the design device - an input device for inputting a value for each parameter and - designed to generate a computer-accessible three-dimensional design model of the tooth connection by modifying the initial design model in dependence on the input parameter values, characterized that - the tooth connection is made so that each tooth flank of each tooth of each component has the shape of an involute, - the initial construction model jewei ls comprises a computer-accessible description of each tooth flank of each tooth of each component, - the tooth flank description comprises a computer evaluable analytical description of an involute defining the geometry of the tooth flank, and - the at least one parameter is a parameter of the involute description. A construction device according to claim 1, characterized in that the initial design model of at least one component has at least one of the following parameters as the variable parameter: - the helix angle (β) as the angle between the crest line of each tooth and the axis of rotation of the component, - the tooth width ( b), - the normal engagement angle (an), - the preassembly angle (α _t ), - the normal modulus (m _n ) as the module in the normal section, - the profile shift factor (x) as the quotient of the profile shift and normal modulus (m _n ), - the number (z) of the teeth. Construction device according to claim 1 or claim 2 characterized in that each Initial Design Model A computer-accessible description of the tooth gap between two teeth and the tooth gap description a computer-evaluable description of a foot rounding curve, in which the footer curve description the shape of the tooth gap describes and of the parameter and of at least one other parameter depends. Construction device according to claim 3, characterized in that the at least one further parameter - the head height factor (H * aP ) - the foot height factor (H * fP ) - the factor of the footing radius (ρ * fP ) or - the head reduction (k) is.