DE102020208810A1 - Gear pair for a transmission and method for dimensioning tooth thicknesses on gears of a gear pair - Google Patents

Abstract

The invention relates to a gear pair (10) for a transmission, having a first gear (12) and a second gear (14), the gears (12, 14) being set up and intended to mesh with one another, the gears (12 , 14) each have a toothing (16, 18) in which a tooth (20, 22) and a tooth space (24, 26) follow one another in alternation, wherein in the region of the tooth space (24, 26) there is a rounded tooth base (28, 30) is provided. It is proposed that the tooth (20, 22) has a contact point (32, 34) to a 30° tangent (36, 38) on both tooth flanks, the 30° tangent (36, 38) being at an angle of 30° to a tooth center axis (40 42) and touches the tooth root fillet (28, 30) at the contact point (32, 34), the length of a chord (44, 46) connecting the contact points (32, 34) to the tooth flanks of the tooth (20, 22) together, each defines a tooth thickness at the point of contact of the 30° tangent, the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear (12) to the second gear (14) being in the range from 2.3:1.7 to 1.7:2.3.

Description

State of the art

The invention relates to a gear pair for a transmission according to the preamble of claim 1. The invention also relates to a transmission and a drive unit having the features of the independent claims. The invention further relates to a method for dimensioning tooth thicknesses on gear wheels of a gear wheel pair according to the preamble of the further independent claim.

The requirements for low-noise gears and gears are constantly increasing, which means that meeting NVH targets (targets with regard to "noise, vibration, harshness", i.e. with regard to noise, vibration, roughness) represents a growing challenge in the design of gear gears. Gearing noise is a vibration phenomenon. The reduction of vibration excitation during gear meshing therefore plays a central role in noise optimization of gearing.

A main reason for the vibration excitation in the meshing is the elastic deformation of the meshing teeth. Due to the forces on the tooth flanks, the teeth deform elastically when they mesh. This leads to brief pitch errors (changes in the tooth spacing) on the meshing teeth.

A pitch error means that the pair of teeth just entering the mesh does not come into optimal contact, but comes into contact too early when the tooth spacing is reduced or too late when the tooth spacing is increased. Similarly, the pair of teeth just leaving the engagement leaves the engagement too early or too late.

In both cases, the toothing is subjected to an impact with each pair of teeth that is newly engaged or is about to be disengaged, which impedes a uniform rotational movement of the two gears. This creates a vibration that is superimposed on the rotational movement of the gears.

Depending on the frequency (speed) and amplitude (strength of the impact), this vibration is audible and thus represents a quality defect in modern toothing and transmissions, e.g. in vehicle transmissions.

DE 10 2004 037 540 B4 discloses a gear ring for a stress wave gear, it being disclosed that at least one undercut extending into the base body of the gear ring is provided in at least one tooth gap. As a result, deformations of the gear or the gear ring can be accommodated.

EP 2 813 733 B1 discloses a gear with an involute tooth flank with a special geometry.

Disclosure of Invention

The problem on which the invention is based is solved by a gear pair having the features of claim 1 . Advantageous developments of the invention are specified in the dependent claims.

According to the invention, a gear pair for a transmission is proposed, which has a first gear and a second gear, the gears being set up and intended to mesh with one another. The gear wheels each have a toothing in which (along the circumferential direction) alternately a tooth and a tooth space follow one another. A rounded tooth base is provided in the area of the interdental space. The tooth has a point of contact to a 30° tangent on both tooth flanks, the 30° tangent being oriented at an angle of 30° to a central tooth axis and touching the rounded tooth base at the point of contact. The length of a chord (tooth thickness chord) connecting the contact points on the tooth flanks of the tooth (one and the same tooth) (at the contact point of the 30° tangent) defines a tooth thickness at the contact point of the 30° tangent. The tooth thicknesses at the point of contact of the 30° tangent of the gears are coordinated in such a way that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear to the second gear is in the range of 2.3 : 1.7 (larger tooth thickness at the point of contact of the 30° tangent on the first gear) to 1.7: 2.3 (larger tooth thickness at the contact point of the 30° tangent on the second gear).

With such a configuration, the geometric optimum for reducing the vibration excitation can be achieved. This is achieved through an optimized tooth geometry on the first gear and second gear, which maximizes the meshing stiffness and leads to a coordinated deformation of the gear pairs. This can reduce the running noise of meshing gears to a considerable extent and therefore leads to a gain in comfort.

The first gear wheel and the second gear wheel can be a wheel and a pinion, respectively. It should be noted that the number of teeth on a gear and the tooth thickness are, at least to a certain extent, independent of one another. This means that, for example, a gear wheel with a smaller number of teeth (pinion) can have a larger or smaller tooth thickness than a gear wheel with a larger number of teeth than the pinion.

The first gear wheel and the second gear wheel are in particular designed in such a way that they each have a circumferential toothing on the front side. If the gears are arranged in relation to one another in such a way that the toothing engages with one another, the gears mesh with one another at the front.

The first gear and the second gear are each designed as a spur gear, in particular with involute gearing. The central axis of the tooth is in particular an axis of symmetry of a tooth. In particular, the tooth center axis is an axis to which the tooth profile of the relevant tooth is axisymmetric.

According to a further development, the tooth thicknesses at the point of contact of the 30° tangent of the gears can be matched to one another in such a way that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear to the second gear is in the range of 2.1 : 1.9 (larger tooth thickness at the contact point of the 30° tangent on the first gear) to 1.9: 2.1 (larger tooth thickness at the contact point of the 30° tangent on the second gear). This contributes to improved engagement rigidity, so that vibration excitation can be further reduced.

According to a development, the tooth thicknesses at the point of contact of the 30° tangent of the gears can be matched to one another in such a way that the first gear and the second gear have identical tooth thicknesses at the point of contact of the 30° tangent or an identical tooth thickness at the point of contact of the 30° tangent . In other words, the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear wheel to the second gear wheel can be 2:2 or 1:1. In this way, the optimum engagement stiffness can be achieved, which leads to a minimization of the vibration excitation.

The basic idea of the invention is explained in more detail below. When meshing gears meshing with each other, the teeth in contact load each other with a bending load. Each tooth can be thought of as a cantilever bending about its base. The rigidity of this base is therefore decisive for the flexural rigidity of a tooth.

It is known from the literature (ISO 6336) that in the case of involute gearing (which is used, for example, in the automotive sector) under load, the greatest flexural strain can occur at the 30° tangent in the area of the tooth root. As explained, the 30° tangent is a tangent to the fillet of the tooth root, which is at an angle of 30° to the central axis of the tooth. The 30° tangent can be drawn on either side of a tooth (both tooth flanks), giving a tangent point to the 30° tangent on either side of the tooth. The length of the chord (tooth thickness chord) between the two contact points of the 30° tangent describes the tooth thickness at the contact point of the 30° tangent.

Transferred to the bending beam model, the tooth thickness chord at the 30° tangent represents the above-mentioned basis on which the tooth (bending beam) rests. Consequently, the length of the tooth thickness chord at the 30° tangent is a measure of the bending stiffness of a tooth. Hereinafter, one gear is referred to as a "pinion" and the other gear as a "wheel" (wheel and pinion mesh with each other).

Mit den Biegesteifigkeiten der Zähne k_Ritzel bzw. k_Rad: $$k_{Ritzel}=E_{Ritzel}{I}_{Ritzel}und{k}_{Rad}=E_{Rad}{I}_{Rad}$$

Mit den werkstoffabhängigen E-Moduli E_Ritzel und E_Rad sowie den für die Biegung relevanten, axialen Flächenträgheitsmomenten I_Ritzel und I_Rad, die sich aus der Zahngeometrie ergeben.Two meshing teeth (each of the two teeth with its individual bending stiffness k _pinion or k _wheel ) represent a series connection of the two bending beams or bending stiffnesses. The meshing stiffness is therefore as follows: $$\frac{1}{k_{EinG\mathrm{right}iff}}=\frac{1}{k_{Rit\mathrm{e.g}el}}+\frac{1}{k_{Ra\mathrm{i.e}}}$$

With the bending stiffness of the teeth k _pinion or k _wheel : $$k_{Rit\mathrm{e.g}el}=E_{Rit\mathrm{e.g}el}{I}_{Rit\mathrm{e.g}el}\mathrm{and}n\mathrm{i.e}{k}_{Ra\mathrm{i.e}}=E_{Ra\mathrm{i.e}}{I}_{Ra\mathrm{i.e}}$$

With the material-dependent moduli of elasticity E _pinion and E _wheel as well as the axial area moments of inertia I _pinion and I _wheel that are relevant for bending and result from the tooth geometry.

mit den Radbreiten b_Ritzel und b_Rad sowie den Zahndickensehnen an der 30°-Tangente S_{nf, 30, Ritzel} und S_{nf, 30}, _Rad.In _{turn, I pinion} and I _wheel result from: $$I_{Rit\mathrm{e.g}el}=\frac{b_{Rit\mathrm{e.g}el}\cdot s_{nf\mathrm{,30,}Rit\mathrm{<figure-callout\; id="3"\; label="e.g\; e\; l"\; filenames="DE102020208810A1\_0007.png"\; state="\{\{state\}\}">e.g</figure-callout>}el}^3}{12}\mathrm{and}n\mathrm{i.e}{I}_{Ra\mathrm{i.e}}=\frac{b_{Ra\mathrm{i.e}}\cdot s_{nf\mathrm{,30,}Ra\mathrm{i.e}}^3}{12}$$

with the wheel widths b _pinion and b _wheel as well as the tooth thickness chords at the 30° tangent S _{nf, 30, pinion} and S _{nf, 30} , _wheel .

wobei die E-Moduli und die Radbreiten weder von der Geometrie des Zahnprofils beeinflusst werden, noch dieses selbst beeinflussen. Sie spielen also bei der Auslegung des Zahnprofils keine oder zumindest eine vernachlässigbare Rolle und können als Konstante zusammengefasst werden: $$k_{Eingriff}=\frac{1}{\frac{C_{Ritzel}}{s_{nf\mathrm{,30,}Ritzel}^3}+\frac{C_{Rad}}{s_{nf\mathrm{,30,}Rad}^3}}$$

So wird ersichtlich, dass die Eingriffssteifigkeit in dritter Potenz von den Längen der Zahndickensehne an den 30°-Tangenten der beiden Zahnräder abhängt. Ihr Maximum erreicht die Eingriffssteifigkeit dann, wenn die Längen der Sehnen an den 30°-Tangenten von Rad und Ritzel gleich groß sind. Dies ist in 2 veranschaulicht.The engagement stiffness can thus be formulated as: $$k_{EinG\mathrm{right}iff}=\frac{1}{\frac{12}{E_{Rit\mathrm{e.g}el}\cdot b_{Rit\mathrm{e.g}el}\cdot s_{nf\mathrm{,30,}Rit\mathrm{<figure-callout\; id="3"\; label="e.g\; e\; l"\; filenames="DE102020208810A1\_0007.png"\; state="\{\{state\}\}">e.g</figure-callout>}el}^3}+\frac{12}{E_{Ra\mathrm{i.e}}\cdot b_{Ra\mathrm{i.e}}\cdot s_{nf\mathrm{,30,}Ra\mathrm{i.e}}^3}}$$

The moduli of elasticity and the wheel widths are neither influenced by the geometry of the tooth profile, nor do they influence it itself. They therefore play no or at least a negligible role in the design of the tooth profile and can be summarized as a constant: $$k_{EinG\mathrm{right}iff}=\frac{1}{\frac{C_{Rit\mathrm{e.g}el}}{s_{nf\mathrm{,30,}Rit\mathrm{e.g}el}^3}+\frac{C_{Ra\mathrm{i.e}}}{s_{nf\mathrm{,30,}Ra\mathrm{i.e}}^3}}$$

It can be seen that the meshing stiffness depends on the third power of the lengths of the tooth thickness chord at the 30° tangents of the two gears. The engagement stiffness reaches its maximum when the lengths of the chords at the 30° tangents of the wheel and pinion are equal. This is in 2 illustrated.

The object mentioned at the outset is also achieved by a transmission having the features of the independent claim. The transmission has at least one gear pair as described above.

With regard to the advantages that can be achieved with the transmission, reference is made to the relevant statements on the gear pair. The measures described in connection with the pair of gears can serve to further refine the transmission.

The transmission can have a transmission housing on and/or in which the components of the transmission are arranged. The first gear wheel and the second gear wheel can each be rotatably mounted on or in the gear housing, for example by means of appropriate shafts. The transmission can have such a gear pair or several such gear pairs.

The object mentioned at the outset is also achieved by a drive unit for a vehicle having the features of the independent claim. The drive unit has an electric machine and a transmission coupled thereto, as described above.

With regard to the advantages that can be achieved with the drive unit, reference is made to the relevant statements on the pair of gears. The measures described in connection with the pair of gears and/or with the transmission can be used to further refine the drive unit.

In the case of the drive unit, it can be provided that the electrical machine drives the transmission (for example the output shaft of the electrical machine is coupled in a torque-proof manner to an input shaft of the transmission). The drive unit can, for example, be designed as an e-axle or form part of an e-axle.

The object mentioned at the outset is also achieved by a method for designing tooth thicknesses on gear wheels with the features of the independent method claim.

The method is used to design tooth thicknesses on gears of a gear pair, in particular a gear pair as described above. The gear pair includes a first gear and a second gear, the gears being configured and intended to mesh with one another. The gear wheels each have a toothing in which (along the circumferential direction) a tooth and a tooth space alternately follow one another, with a tooth base rounding being provided in the region of the tooth space. The tooth has a point of contact to a 30° tangent on both tooth flanks, the 30° tangent being oriented at an angle of 30° to a central tooth axis and touching the rounded tooth base at the point of contact. The length of a chord connecting the contact points on the tooth flanks of the tooth defines (at the contact point of the 30° tangent) a tooth thickness. The tooth thickness at the point of contact of the 30° tangent on the first gear and on the second gear is adjusted in such a way that the ratio of the tooth thickness at the point of contact of the 30° tangent of the first gear to the second gear is in the range of 2.3 : 1.7 ( larger tooth thickness on the first gear) to 1.7: 2.3 (larger tooth thickness on the second gear).

With regard to the advantages that can be achieved in this way, reference is made to the relevant statements on the pair of gears.

According to a further development, the tooth thicknesses at the point of contact of the 30° tangent of the gears can be matched to one another in such a way that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear to the second gear is in the range of 2.1 : 1.9 (larger tooth thickness on the first gear) to 1.9: 2.1 (larger tooth thickness on the second gear). This contributes to improved engagement rigidity, so that vibration excitation can be further reduced.

According to a further development, the tooth thicknesses at the point of contact of the 30° tangent of the gear wheels can be matched to one another in such a way that the first gear wheel and the second gear wheel have identical tooth thicknesses at the point of contact of the 30° tangent, ie an identical tooth thickness at the point of contact of the 30° tangent. exhibit. In other words, the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear wheel to the second gear wheel can be 2:2 or 1:1. In this way, the optimum engagement stiffness can be achieved, which leads to a minimization of the vibration excitation.

• 1 eine schematische Schnittansicht durch ein Zahnradpaar; und
• 2 ein schematisches Diagramm mit Darstellung der Eingriffssteifigkeit in Abhängigkeit des Verhältnisses der Zahndicken des ersten Zahnrads und des zweiten Zahnrads.

Possible embodiments of the invention are explained below with reference to the accompanying drawings. Show it:

• 1 a schematic sectional view through a gear pair; and
• 2 a schematic diagram showing the engagement stiffness as a function of the ratio of the tooth thicknesses of the first gear and the second gear.

The pair of gears for a gearbox carries in 1 overall reference numeral 10. The pair of gears 10 has a first gear 12 and a second gear 14 on. The first gear 12 can be a pinion and the second gear 14 can be a driven gear. The gears 12,14 are arranged and intended to mesh with each other. For example, the gears 12, 14 can be installed in a transmission and rotatably mounted on or in a transmission housing (not shown).

The gear wheels 12, 14 each have a toothing 16, 18 in which a tooth 20, 22 and a tooth gap 24, 26 alternately follow one another along the circumferential direction. In the area of the interdental spaces 24, 26, a rounded tooth base 28, 30 is provided.

The tooth 20, 22 has on both of its tooth flanks a point of contact 32, 34 to a 30° tangent 36, 38, the 30° tangent being oriented at an angle of 30° to a tooth center axis 40, 42 and the tooth root fillet 28, 30 at the point of contact 32, 34 is touched.

The length of a chord 44, 46 (tooth thickness chord 44, 46), which connects the contact points 32, 34 on the tooth flanks of the relevant (one and the same) tooth 20, 22, defines (at the contact point of the 30° tangent) a tooth thickness in each case . The ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear 12 to the second gear 14 can range from 2.3:1.7 (larger tooth thickness on the first gear) to 1.7:2.3 (larger tooth thickness on the second gear) lie (cf. 2 ).

The example shows the geometric optimum for reducing vibration excitation (cf. 1 ). The tooth thicknesses at the contact point of the 30° tangent of the gears 12, 14 are matched to one another in such a way that the first gear 12 and the second gear 14 have identical tooth thicknesses at the contact point of the 30° tangent, i.e. an identical tooth thickness (tooth thickness chord 44, 46 at the point of contact of the 30° tangent have the same length). In other words, the ratio of the tooth thickness at the point of contact of the 30° tangent of the first gear wheel 12 to the second gear wheel 14 is 2:2 or 1:1.

2 shows a schematic diagram showing the engagement stiffness as a function of the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear wheel 12 and the second gear wheel 14.

Are the tooth thicknesses at the point of contact of the 30° tangent of the gears 12, 14 matched to one another in such a way that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear 12 to the second gear 14 is in the range of 2.3:1.7 ( larger tooth thickness on the first gear 12) to 1.7: 2.3 (larger tooth thickness on the second gear 14), 80% and more of the maximum achievable engagement rigidity can be achieved (see line A).

Are the tooth thicknesses at the point of contact of the 30° tangent of the gears 12, 14 matched to one another in such a way that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear 12 to the second gear 14 is in the range of 2.1:1.9 ( greater tooth thickness on the first gear) to 1.9: 2.1 (greater tooth thickness on the second gear), more than 90% and more of the maximum achievable engagement stiffness can be achieved (see line B).

Are the tooth thicknesses at the point of contact of the 30° tangent of the gear wheels 12, 14 matched to one another in such a way that the first gear wheel 12 and the second gear wheel 14 have an identical tooth thickness at the point of contact of the 30° tangent, i.e. the ratio of the tooth thickness at the point of contact of the 30 ° tangent of the first gear 12 to the second gear 14 is 2:2 or 1:1, the maximum achievable engagement stiffness can be achieved (see point C).

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• DE 102004037540 B4 [0007]
• EP 2813733 B1 [0008]

Claims (8)

Gear pair (10) for a transmission, having a first gear (12) and a second gear (14), the gears (12, 14) being arranged and intended to mesh with one another, the gears (12, 14) respectively have a tooth system (16, 18) in which a tooth (20, 22) and an interdental space (24, 26) follow one another in alternation, with a rounded tooth base (28, 30) being provided in the region of the interdental space (24, 26). , characterized in that the tooth (20, 22) has a contact point (32, 34) to a 30° tangent (36, 38) on both tooth flanks, the 30° tangent (36, 38) at an angle of 30° to a tooth center axis (40 42) and touches the tooth base fillet (28, 30) at the contact point (32, 34), the length of a chord (44, 46) connecting the contact points (32, 34) to the Tooth flanks of the tooth (20, 22) connects to one another, each defining a tooth thickness at the point of contact of the 30° tangent, the ratio of the tooth thicknesses ken at the point of contact of the 30 ° tangent of the first gear (12) to the second gear (14) in the range of 2.3: 1.7 to 1.7: 2.3. Gear pair (10) after claim 1 , characterized in that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear (12) to the second gear (14) is in the range from 2.1: 1.9 to 1.9: 2.1. Gear pair (10) after claim 1 or 2 , characterized in that the first gear (12) and the second gear (14) have identical tooth thicknesses at the point of contact of the 30° tangent. Transmission with at least one gear wheel pair (10) according to one of the preceding claims. Drive unit for a vehicle, with an electric machine and a transmission coupled thereto claim 4 . Method for designing tooth thicknesses on gears (12, 14) of a gear pair (10), in particular a gear pair (10) according to one of Claims 1 to 10, having a first gear (12) and a second gear (14), the gears (12, 14) being set up and intended to mesh with one another, the gears (12, 14) each having a toothing (16, 18) in which a tooth (20, 22) and an interdental space (24, 26) follow one another in alternation, with a rounded tooth base (28, 30) being provided in the region of the interdental space (24, 26), characterized in that the tooth (20, 22) has a contact point (32, 34) to a 30° tangent (36, 38) on both tooth flanks, the 30° tangent (36, 38) being at an angle of 30° to a Tooth center axis (40, 42) is oriented and touches the tooth root fillet (28, 30) at the contact point (32, 34), the length of a chord (44, 46) which touches the contact points (32, 34) on the tooth flanks of the tooth ( 20, 22) connects to each other, each defines a tooth thickness at the point of contact of the 30° tangent, the tooth thicknesses on the first gear wheel (12) and on the second Gear (14) are each matched in such a way that the ratio of the tooth thicknesses at the point of contact of the 30 ° tangent of the first gear (12) to the second gear (14) in the range of 2.3: 1.7 to 1.7: 2, 3 lies. procedure after claim 6 , characterized in that the ratio of the tooth thicknesses at the point of contact of the 30° tangent of the first gear (12) to the second gear (14) is in the range from 2.1: 1.9 to 1.9: 2.1. procedure after claim 6 or 7 , characterized in that the first gear (12) and the second gear (14) have identical tooth thicknesses at the point of contact of the 30° tangent.

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