DE102014206982B4 - Method for manufacturing a component and a roller bearing - Google Patents

Abstract

Method for producing a component (3), comprising a ring body (4) which can be supported with respect to an axis and a plurality N of essentially identical components (W) which are arranged on the ring body (4) in the circumferential direction, characterized in that the components (W ) be arranged such that the angular distance Δφ of the kth component (W) arranged in the circumferential direction to the k + 1th component (W) is given, whereby x is a modulation factor of the amount less than one, which is given at the angular distance Δφ, whereby the maximum of the discrete Sinus function with N equidistant abscissa, and where η is a parameter greater than or equal to one.

Description

Field of the Invention

The invention relates to a method for producing a component, comprising a ring body which can be supported with respect to an axis and a plurality of components of substantially identical construction which are arranged on the ring body in the circumferential direction. The invention further relates to a method for producing a rolling bearing.

Background of the Invention

In a rolling bearing, the rolling elements are usually arranged at a uniform distance between the inner ring and the outer ring of the rolling bearing. This means that even at comparatively low operating speeds, individual points on the treads of the inner ring and outer ring are periodically overrun in rapid succession, the rollover frequency being given by the number of rolling elements multiplied by the cage rotation frequency, which is approximately equal to half the speed of the rolling bearing. When rolling over unevenness of the running surfaces that is unavoidable in terms of production technology, the rolling bearing is excited to make noise during operation. Uncontrolled noise in the form of noise is often undesirable.

The DE 79 05 040 U1 describes a rolling bearing with two rings, which are supported against each other by rolling elements, and with a cage with guide pockets for the rolling elements, the distances between these guide pockets being different.

Also the DE 10 2009 009 529 A1 describes a roller bearing, with outer and inner ring and roller bodies arranged between them, which are arranged in receptacles distributed unevenly over the circumference of a cage.

The DE 10 2010 018 653 A1 describes a rolling bearing in which the rolling elements are arranged asymmetrically at different angular distances. When rotating according to the operating conditions, the induced vibrations are separated from each other by the individual rolling elements. The periodicity when rolling over unevenness in the running surfaces thus only corresponds to the cage rotation frequency, a collective vibration excitation of the bearing components by the rolling elements is suppressed. This should lead to a measurably reduced noise development.

Belt tensioning or deflection rollers with a roller bearing and so-called running disks are used in traction mechanism drives of motor vehicles and in industry. As a rule, the roller bearings are single or double row ball bearings due to the high operating speeds. The running disks are made of plastic, steel or light metal alloys. When in contact with a belt, the running disks have smooth or textured surfaces that correspond to the structure of the belts or bands. The running disks partially wrapped in the belt sit on the outer ring of these bearings. The inner rings sit on a bolt on a pivotable lever or on a housing. Belt tensioning and deflection rollers with a roller bearing are in DE 10 2008 059 577A1 described.

Vibration-damping elastic bearings of rotating shafts, such as the mounting of articulated drive shafts in motor vehicles, are formed from an elastic suspension or an elastic buffer and a roller bearing. The elastic suspension or the buffer surround the outer ring and are suspended on the vehicle. Such storage is in DE 43 20 642 C1 described.

US 6,170,993 B1 relates to a rolling bearing in which the arrangement of the rolling elements is based on the so-called random "chordal distance" principle. A random principle is therefore used in order to avoid the vibration excitation when the rolling elements roll over unevenness in the manufacturing process of the running surfaces.

Another random principle is explained below by dividing a full angle of 360 °. The sum of all pitch angles results in a full angle of 360 ° through which a circle is described. The number N of the pitch angles corresponds to the number of rolling elements. Each of the dividing angles is enclosed between two dividing lines. The dividing lines radiate from a point on the axis of rotation of the rolling bearing. At least two, preferably several, the pitch angle differ with regard to their size. The pitch angles are with regard to their respective numerical value and the The order in which they are arranged circumferentially depends on random numbers. The random numbers were generated from a predetermined amount with predetermined limits. The amount and the limits are freely selectable.

Alternatively, according to one embodiment, the limits are calculated from a difference between a basic pitch angle and a minimum pitch angle. The basic pitch angle is a quotient of the full angle 360 ° and the number of rolling elements in the rolling bearing. The minimum pitch angle results between the dividing lines of two rolling elements when these adjacent rolling elements are in direct contact with one another on the circumference.

According to a further embodiment, the limits are calculated for the case in which the directly adjacent rolling elements are accommodated in pockets of the cage, depending on the dimensions on the pitch circle of the at least one web between two rolling elements and taking into account a possible pocket play. In this case, the limits are calculated from a difference in the basic pitch angle and a so-called real minimum pitch angle, in which the dimensions of the web and the pocket play are taken into account.

In contrast to the prior art, the pockets for accommodating the rolling elements are irregularly distributed over the circumference. The size of the distances and the order of the different distances depend on random numbers, of which as many are determined as there are rolling elements in the rolling bearing. The pockets have the same pocket dimensions on the inside. If the rolling bodies are rollers, the pockets are preferably window-shaped and if the rolling bodies are balls, the pockets are preferably partially spherical or window-shaped as circular pockets. The pockets can all have identical inner shapes or differ from one another in terms of their inner shapes, for example in terms of their circumferential dimensions. The latter then makes e.g. It makes sense if more than one of the rolling elements is accommodated in one of the pockets. If identical pocket shapes are used, they are distributed around the circumference with divisions that differ from one another. The divisions correspond to the different distances between the ball centers. Accordingly, one embodiment provides that at least two, preferably more, of the distances between the centers from one another and thus also of the dividing lines and that of the rolling bodies differ from one another. The size of the distances and thus the pitch angle and also the distribution of the differently spaced rolling elements on the circumference depend on the random numbers determined.

Each pocket has in both circumferential directions with an adjacent pocket at least one common web and formed from a material of the cage. Bridges are holding elements and / or spacers. They lie between two rolling elements and prevent their direct contact. Alternatively, the webs encompass the rolling elements at locations where the rolling elements cannot touch. The respective web is formed in the circumferential direction between two adjacent rolling elements. Alternatively, each pocket is delimited on each side by a web, so that two of the webs are directly adjacent to one another in the circumferential direction between two rolling bodies. This is preferably the case in particular with so-called ball snap cages, on which two webs designed as snap cheeks per ball hold the ball in the cage. The webs are either made of the same material as the remaining part of the cage or of a different material than the other parts of the cage. Preferred materials are, for example, plastics, light metals or steels and their alloys.

The rolling elements are arranged in the respective pocket with a pocket play, which on the one hand ensures manufacturing tolerances and on the other hand ensures the necessary freedom of movement of the rolling elements when the roller bearing is in operation. The roller body is movable within this pocket game in the circumferential direction between the first web and the second web in both circumferential directions against the first web and second web. This also applies to ball snap cages, in the pockets of which the balls are snapped securely during assembly, but are not constrained during operation. The webs are the so-called brackets and are also called snap brackets.

One embodiment provides that all pocket games of the cage of the rolling bearing are of the same size. Alternatively, it is also conceivable that the pocket games differ from one another. If the pocket play is the same, but the rolling elements are arranged with different pitches, differences between the pockets result depending on the differences from the basic pitch. The term pitch means the pitch angles or the distances in the radians of the centers from each other on the pitch circle. The differences in the spacing between the pockets can be increased by of the material of the webs or by clearances between two adjacent webs and those arranged between two pockets.

In a rotating roller bearing according to the known state of the art, the rolling bodies on the raceways usually roll with a certain regularity. As a result, this regularity of the rollover processes is disturbed and self-exciting bearing vibrations are suppressed. Bearing rings that are kept free or only slightly clamped can, under certain circumstances, vibrate independently. The outer ring and / or inner ring or their add-on components vibrate relative to one another and cause noise. Natural vibrations of the cages or other bearing components are also conceivable. The excitation mechanism is therefore interrupted or weakened in a rolling bearing. The noises described above can be avoided by such an arrangement.

The number of random numbers corresponds to the number of divisions, the number of division lines and thus the number of rolling elements. Divisions are to be understood as the intervals into which the pitch circle is divided by dividing lines or dividing angles that follow one another on the circumference. The random numbers can be negative or positive and also the numerical value 0 correspond. The size, ie the numerical value of the pitch angle, is influenced by the random numbers. The number of rolling elements determines the number of random numbers in the set. At least two of the random numbers of a set can have the same numerical value with the same sign and thus at least two of the pitch angles. The pitch angles that are the same in numerical value can be directly adjacent to one another and / or in the vicinity of pitch angles of a different size. The order of the pitch angles with which they are arranged on the circumference, whether neighboring ones are the same or different, and also the arrangement of the pitch angles according to their size depends on the random numbers.

• 1a zeigt einen Querschnitt eines Wälzlagers 1a,
• 2a einen Längsschnitt entlang der Rotationsachse 6a des Wälzlagers 1a und
• 3a ein Ausführungsbeispiel eines Käfigs 4a des Wälzlagers 1a.

Below are further parameters and boundary conditions, some with the support of 1a , 2a , 3a , listed.

• 1a shows a cross section of a rolling bearing 1a ,
• 2a a longitudinal section along the axis of rotation 6a of the rolling bearing 1a and
• 3a an embodiment of a cage 4a of the rolling bearing 1a .

The roller bearing 1a has two bearing rings, an inner ring 6a and an outer ring 7a on. Each of the bearing rings has a roller raceway 2a or 3a Mistake. A number N = 11 of rolling elements RB1 , RB2 ,..., to RB11 is between the roller raceways 2a and 3a arranged and in a cage 4a guided. The rolling elements are balls on a pitch circle 16a circumferentially adjacent to each other between the inner roller raceway 2a and the outer roller raceway 3a are arranged. The inner roller raceway 2a is on the outer ring 6a and the outer roller raceway 3a is on the inner ring 7a educated. The roller bearing 1a is placed on a shaft or bolt of a component of a motor vehicle, not shown. The outer ring 6a sits in a rubber element or plastic element or aluminum housing, which can be assigned, for example, a bearing point of a drive shaft in a drive train of a motor vehicle, in vehicle transmissions, a belt wheel of a belt drive or a bearing point of an electric motor, for example an electric or hybrid vehicle.

Each of the rolling elements is in a pocket 5a of the cage 4a added. The cage 4a is a so-called ball snap cage and is a single part in 3a shown. The cage 4a points 11 Piece of bags 5a on. Between each of the pockets 5a is a footbridge 11a educated. The diameter DW the rolling body RB1 , RB2 ,... to RB11 are the same. Each of the rolling elements RB1 , RB2 ,... to RB11 is in one of the pockets 5a arranged. Between each two dividing lines P1, P2, to P11 of two of the rolling elements that are directly adjacent on the circumference RB1 , RB2 ,... to RB11 is a pitch angle α1 , α2 , ... α11 locked in. Several of the pitch angles α1 , α2 , ... to α11 differ from each other in size.

ergibt.An example of a bag 5a of the cage 4a is not to scale and is enlarged in 3a shown. A rolling body RB is outlined in dashed lines. 3a shows a longitudinal section through a cage 4a along its axis of symmetry. Each pocket points in both circumferential directions with an adjacent pocket at least one common web formed from the material of the cage 11a on. The respective web 11a is in the circumferential direction between two adjacent pockets 5a educated. Each of the piers 11a is at the end of each pocket 5a with a snap cheek 13a Mistake. The rolling elements are RBN in the respective bag 5a arranged with a pocket game X ( 1a) , which is reflected in the representation 1a out $\mathrm{2nd}x\frac{X}{\mathrm{2nd}}$

results.

The following general conditions or configurations apply, the description of which follows from the illustrations 4a is at least partially supported.

1. a. (nicht in 4a dargestellt): Es ist eine Anzahl N an Rollkörpern RB1, RB2, ... bis RBN am Umfang einer inneren und/oder äußeren Laufbahn verteilt angeordnet. Die Rollkörper weisen jeweils alle den gleichen Durchmesser DW auf und sind in Taschen des Käfigs an einem Teilkreis angeordnet. Die Rollkörper sind wahlweise Rollen oder vorzugsweise Kugeln. Käfige sind Abstandshalter für die Rollkörper, mit denen im Rahmen von zulässigen Taschenspielen die zueinander benachbarten Rollkörper umfangsseitig auf Abstand zueinander gehalten sind.
2. b. 4a - Die in einer senkrecht zur Rotationsachse verlaufenden Querschnittsebene des Wälzlagers betrachteten Zentren C1, C2,... bis CN der Rollkörper RB1, RB2,... bis RBN liegen auf dem Teilkreis. Die Zentren sind entweder die Kugelzentren der als Kugeln ausgebildeten Rollkörper oder die Zentren C1, C2,... bis CN, die durch die Wälzachsen der Rollen bestimmt und in der Querschnittsebene jeweils als Punkt abgebildet sind. Wobei die Wälzachsen die im Wesentlichen zur Rotationsachse des Wälzlagers ausgerichteten Symmetrieachsen der rotationssymmetrisch ausgebildeten Rollen sind. Dementsprechend schneidet der Teilkreis bei Rollen die Wälzachsen.
3. c. 4a - Der Teilkreis T ist durch einen von der Rotationsachse des Wälzlagers abgehenden Radius R beschrieben und überstreicht als Vollkreis einen Vollwinkel von 360°.
4. d. 4a - Das jeweilige Zentrum C1, C2,.. oder CN eines jeden Rollkörpers RB1, RB2,... oder RBN ist umfangsseitig in jede Richtung zu einem weiteren Zentrum C1, C2,.. oder CN eines weiteren Rollkörpers RB1, RB2,... oder RBN benachbart. Jeder Abstand zwischen den jeweiligen unmittelbar zueinander benachbarten Zentren ist auf dem Teilkreis jeweils durch ein Bogenmaß b1, b2,..oder bN eines durch den Radius R beschriebenen Bogenmaßes bestimmt, für das gilt: $$b=\alpha \times R$$
   
   wobei α als Teilungswinkel bezeichnet ist. Der jeweilige Teilungswinkel α1, α2, ..., oder aN ist jeweils zwischen zwei Teilungslinien P1, P2, ... oder PN von jeweils zwei am Umfang unmittelbar benachbarten der Rollkörper eingeschlossen.
5. e. 4a - Pro Rollkörper RB1, RB2,... und RBN geht eine der Teilungslinien P1, P2, ...oder PN gleichgerichtet mit dem Radius R ab und verläuft durch das Zentrum C1, C2, ... oder CN des jeweiligen Rollkörpers.
6. f. 4a - Es unterscheiden sich mindestens zwei der Teilungswinkel α1, α2, ... oder αN in den Größen ihrer Zahlenwerte voneinander. Wobei sich mindestens zwei benachbarte Teilungswinkel α1, α2, ... αN in ihrer Größe unterscheiden. Dadurch ergeben sich mindestens zwei Abstände b1, b2, ...,bN unterschiedlicher Größe auf dem Teilkreis zwischen jeweils zwei Zentren C1, C2, ..., CN. Die Abstände b1, b2, ...,bN verlaufen auf dem Teilkreis T jeweils zwischen den Schnittpunkten von zwei jeweils einen Teilungswinkel begrenzenden Teilungslinien P1, P2, ...PN mit dem Teilkreis T. Jeder der Schnittpunkte liegt in einem der Zentren. Die Abstände sind z.B. Bogenmaße, der sich zwischen den jeweiligen Zentren C1, C2, ..., CN erstreckenden Teilkreisbögen.
7. g. Die Summe aller Teilungswinkel α1, α2, ... αN ergibt den Vollwinkel 360°.
8. h. Zur Berechnung jedes einzelnen der in Umfangsrichtung des Teilkreises zueinander benachbarten Teilungswinkel α1, α2, ... αN wird jeweils eine Zufallszahl hinzugezogen, die in den Wert des Winkels mit eingeht, so dass jeder Teilungswinkel α1, α2, ... αN hinsichtlich der Größe seines Zahlenwertes von einer Zufallszahl Z1, Z2, ... ,ZN abhängig ist. Die Zufallszahlen der Anzahl N aus einer Menge Zufallszahlen mit vorher frei wählbaren, alternativ in Abhängigkeit von geometrischen Größen des Wälzlagers, alternativ in Abhängigkeit von geometrischen Größen des Wälzlagers und des Käfigs festgelegten Grenzen.
9. i. Außerdem sind die Teilungswinkel α1, α2, ... αN hinsichtlich der Größe dieses Zahlenwertes in einer von Zufallszahlen Z1, Z2, ... ,ZN vorgegebenen Reihenfolge aufeinander folgend am Umfang verteilt.
10. j. Die Anzahl der Zufallszahlen Z1, Z2, ... ,ZN entspricht der Anzahl N der Rollkörper RB1, RB2,...,RBN.

In the embodiment according to 4a the pitch geometry of rolling bearings is shown schematically.

1. a. (not in 4a shown): It is a number N of rolling elements RB1 , RB2 , ... to RBN distributed around the circumference of an inner and / or outer raceway. The rolling elements all have the same diameter DW on and are arranged in pockets of the cage on a pitch circle. The rolling elements are optionally rollers or preferably balls. Cages are spacers for the rolling elements, with which the mutually adjacent rolling elements are kept at a distance from one another on the circumference within the scope of permissible pocket play.
2. b. 4a - The centers considered in a cross-sectional plane of the rolling bearing perpendicular to the axis of rotation C1 , C2 ,... to CN the rolling body RB1 , RB2 ,... to RBN lie on the pitch circle. The centers are either the ball centers of the rolling bodies designed as balls or the centers C1 , C2 ,... to CN , which are determined by the rolling axes of the rollers and are each represented as a point in the cross-sectional plane. The roller axes are the axes of symmetry of the rotationally symmetrical rollers, which are essentially aligned with the axis of rotation of the roller bearing. Accordingly, the pitch circle intersects the rolling axes on rollers.
3. c. 4a - The pitch circle T is described by a radius R extending from the axis of rotation of the rolling bearing and sweeps over a full angle of 360 ° as a full circle.
4. d. 4a - The respective center C1 , C2 , .. or CN of each rolling body RB1 , RB2 , ... or RBN is circumferentially in every direction to another center C1 , C2 , .. or CN another rolling element RB1 , RB2 , ... or RBN adjacent. Each distance between the respective centers directly adjacent to each other is on the pitch circle by an arc measure b1 , b2 ,..or bN of a radian measure described by the radius R, for which the following applies: $$b=\alpha \times R$$
   
   in which α is referred to as the pitch angle. The respective pitch angle α1 , α2 , ..., or aN is enclosed between two dividing lines P1, P2, ... or PN of two rolling elements that are immediately adjacent on the circumference.
5. e. 4a - Per rolling element RB1 , RB2 ,... and RBN one of the dividing lines P1, P2, ... or PN goes in the same direction with the radius R and runs through the center C1 , C2 , ... or CN of the respective rolling element.
6. f. 4a - At least two of the pitch angles differ α1 , α2 , ... or αN in the sizes of their numerical values from each other. With at least two adjacent pitch angles α1 , α2 , ... αN differ in size. This results in at least two distances b1 , b2 , ..., bN different sizes on the pitch circle between two centers C1 , C2 , ..., CN . The distances b1 , b2 , ..., bN run on the pitch circle T between the intersection of two dividing lines P1, P2,... PN each delimiting a pitch angle with the pitch circle T . Each of the intersections lies in one of the centers. The distances are, for example, radians between the respective centers C1 , C2 , ..., CN extending arcs.
7. G. The sum of all pitch angles α1 , α2 , ... αN gives the full angle 360 °.
8. H. To calculate each of the pitch angles adjacent to each other in the circumferential direction of the pitch circle α1 , α2 , ... αN a random number is included, which is included in the value of the angle, so that each pitch angle α1 , α2 , ... αN is dependent on a random number Z1, Z2, ..., ZN with regard to the size of its numerical value. The random numbers of the number N from a set of random numbers with previously freely selectable limits, alternatively depending on the geometric sizes of the rolling bearing, alternatively depending on the geometric sizes of the rolling bearing and the cage.
9. i. In addition, the pitch angle α1 , α2 , ... αN with respect to the size of this numerical value in a sequence of random numbers Z1, Z2, ..., ZN successively distributed over the circumference.
10. j. The number of random numbers Z1, Z2, ..., ZN corresponds to the number N of rolling elements RB1 , RB2 , ..., RBN.

durch den die Rollkörper der Wälzlager des Standes der Technik mit gleicher Grundteilung zueinander am Umfang einer der Laufbahnen verteilt sind. Der Grundteilungswinkel αG ist ein Quotient aus dem Vollwinkel 360° und der Anzahl N der Rollkörper. 6a shows the pitch geometry of an otherwise not shown rolling bearing 8a According to the state of the art. In known roller bearings as in the example 6a are the rolling elements RB1 , RB2 , ... to RB15 distributed evenly over the circumference. In this case, N = 15, with only the rolling center of the rolling elements C1 , C2 , ... to C15 are shown. The uniform pitch angle included between the dividing lines P1, P2, ..., P15 is calculated accordingly α for a uniform radian b as the basic pitch angle already mentioned above αG out: $$\alpha G=\frac{360°}{N},$$

through which the rolling elements of the roller bearings of the prior art are distributed with the same basic pitch to one another on the circumference of one of the raceways. The basic pitch angle αG is a quotient of the full angle 360 ° and the number N of rolling elements.

ergibt sich ein Grundteilungswinkel αG=24°.The roller bearings of the prior art are about an axis of rotation 9a placed pitch circle 10a and through the centers C1 , C2 , C3 , C4 , C5 , C6 , C7 , C8 , C9 , C10 , C11 , C12 , C13 , C14 , C15 of N = 15 otherwise not shown rolling body dividing lines P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14 and P15. Out $$\alpha G=\frac{360°}{15}$$

the basic pitch angle αG = 24 °.

The random numbers Z1, Z2,... To ZN generated to determine the pitch angle of the roller bearing are from a predetermined number of numbers, for example random numbers generated by a random number generator, which corresponds to the number of rolling elements. The random numbers can be fractions, whole numbers as well as positive and negative numbers. One embodiment provides for the limits [- Δα; Δα] of the set N of the random numbers Z1, Z2, ... and ZN before that these result from a difference in the basic pitch angle αG and calculate amine from the smallest pitch angle: $$\pm \Delta \alpha =\alpha G-\alpha \text{min}\text{,}$$

The smallest possible pitch angle is the angle between the dividing lines of two roller heads lying on the circumference RB1 , RB2 , ..., RBN is included: $$\alpha \text{min}=360°\times \frac{DW}{\mathrm{2nd}\pi R}.$$

also [-12,54°; 12,54°] ermittelt.Example 1: A rolling bearing has a number of rolling elements with the number N = 15. The diameter DW the rolling body designed as a ball RB1 , RB2 , RB3 , RB4 , RB5 , RB6 , RB7 , RB8 , RB9 , RB10 , RB11 , RB13 , RB14 and RB15 is 8mm. The pitch circle has a radius of 40mm starting from the axis of rotation of the rolling bearing. Accordingly, the random numbers from a set with N = 15 random numbers Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14 and Z15 with the limits $$\pm \Delta \alpha =\alpha G-\alpha \text{min}=\frac{360°}{15}-360°\times \frac{\mathrm{8th}}{\mathrm{<figure-callout\; id="40"\; label="2nd\; \pi "\; filenames="DE102014206982B4\_0048.png"\; state="\{\{state\}\}">2nd\; </figure-callout>}\pi 40}=12.54°,$$

thus [-12.54 °; 12.54 °] determined.

The table in 5a shows embodiments of calculation methods of the pitch angle.

An example of such an arrangement is in the table below 5a shown. The first column I stands for the number N = 15 of the random numbers Z1 to Z15 which are listed in column II.

wobei αG der schon beschriebene Grundteilungswinkel $\alpha G=\frac{360°}{N}$

ist und für den kleinsten mögliche realen Teilungswinkel α' min gilt: $$\alpha \text{'}\text{min}=\frac{\left(DW+A\right)}{2\pi R}$$

Another embodiment provides that for the limits [-Δα; Δα] of the set N of the random numbers Z1, Z2, ..., ZN applies: $$\pm \Delta \alpha \text{'}=\alpha G-\alpha \text{'}\text{min}\text{,}$$

in which αG the basic pitch angle already described $\alpha G=\frac{360°}{N}$

and for the smallest possible real pitch angle α ' min applies: $$\alpha \text{'}\text{min}=\frac{\left(DW+A\right)}{\mathrm{2nd}\pi R}$$

The distance A results from the dependencies of the basic pitch angle aG on the radius R and on the rolling element diameter DW and is a minimal distance. The distance A, which can be specified as a radian measure, is required, for example, for manufacturing reasons as a minimum dimension for the realization of a web of the cage. A pocket play is also taken into account at distance A. The distance A = 0 for rolling bodies lying directly next to one another on the circumference.

innerhalb der Grenzen [-6,81°; 6,81°] eine
Menge von N=15 ermittelter Zufallszahlen Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14 bis Z15.Example 2: Based on the specifications for the rolling bearing geometry, for example 1, taking into account a minimum distance A = 4mm for another rolling bearing results $\pm \Delta \alpha =\alpha G-\alpha \text{'}\text{min}=\frac{360°}{15}-360°\times \frac{\left(\mathrm{8th}+\mathrm{4th}\right)}{\mathrm{<figure-callout\; id="40"\; label="2nd\; \pi "\; filenames="DE102014206982B4\_0048.png"\; state="\{\{state\}\}">2nd\; </figure-callout>}\pi 40}=6.81°$

within the limits [-6.81 °; 6.81 °] a
Set of N = 15 random numbers Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14 to Z15.

The distance A is accordingly for the limits A = 0 given in Example 1.

ergibt sich, wie oben schon erwähnt, $\alpha \text{min}=360°\times \frac{DW}{2\pi R}$

zwischen den Teilungslinien von zwei umfangsseitig aneinander liegenden Rollkörpern.Starting from
$\frac{DW}{\mathrm{2nd}\pi R}=\frac{\alpha \text{min}}{360°}$

as already mentioned above, $\alpha \text{min}=360°\times \frac{DW}{\mathrm{2nd}\pi R}$

between the dividing lines of two rolling elements lying on the circumference.

Provided that for a given roll body diameter DW and pitch circle radius R are distributed as much as possible on the circumference of the rolling elements and these are in contact with each other, results $$\alpha G\text{min}=360°\times \frac{DW}{\mathrm{2nd}\pi R}.$$

A possible end circle endgame is neglected. The pitch circle end game is to be understood as a circumferential gap between the last two rolling elements of a chain on the partial circle of rolling elements arranged in mutual contact, which can no longer be filled by an entire rolling element because this gap is too narrow.

so dass sich entsprechend der Anzahl N der Rollkörper die gleiche Anzahl N an skalierten Werten α seal ergibt, wobei jeder Wert das Produkt aus der jeweiligen Zufallszahl und α min ist: $$\alpha 1scal,\alpha 2scal,\dots oder\alpha Nscal=Z\mathrm{1,}Z\mathrm{2,}\dots oderZN\times \alpha \text{min}$$

With a view to the previously mentioned boundary conditions, it follows $$\alpha scal=\mathrm{Z.}\times \Delta \alpha ,$$

so that according to the number N of rolling elements, the same number N of scaled values α seal gives, where each value is the product of the respective random number and α min is: $$\alpha 1scal,\alpha \mathrm{2nd}scal,...Oder\alpha Nscal=\mathrm{Z.}\mathrm{1,}\mathrm{Z.}\mathrm{2,}...Oder\mathrm{Z.}N\times \alpha \text{min}$$

Examples of numerical values for a rolling bearing according to Example 1, i.e. with A = 0, are in 5a indicated in column III.

As further developments, two methods for calculating the pockets and rolling elements arranged with different division result from this, whereby according to the method 1 ( M1 ) applies that a sum S of the individual sums from the respective scaled value α1scal, α2scal, or αNscal and the basic pitch angle αG is not equal to the full angle 360 °: $$S=\left[\left(\alpha 1scal+\alpha G\right)+\left(\alpha \mathrm{2nd}scal+\alpha G\right),...+\left(\alpha Nscal+\alpha G\right)\right]\ne 360°$$

An example of this is in the table below 5a shown with column IV.

abgeglichen, indem diese Einzelsummen jeweils mit W multipliziert werden um die Teilungswinkel α1, α2, ... oder αN zu erhalten: $$\begin{array}{l}\alpha \mathrm{1,}\alpha \mathrm{2,}\dots \text{sowie }\alpha N=\\ \left(\left(\alpha 1scal+\alpha G\right)\times W\right),\left(\left(\alpha 2scal+\alpha G\right)\times W\right),\dots sowie\left(\left(\alpha 1scal+\alpha G\right)\times W\right)\end{array}$$

Therefore, each of the individual sums (α1scal + αG), (α2scal + αG) ... and (αNscal + αG) each have a value $W=\frac{360°}{S}$

adjusted by multiplying these individual sums by W by the pitch angle α1 , α2 , ... or αN to obtain: $$\begin{array}{l}\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="DE102014206982B4\_0048.png,DE102014206982B4\_0050.png"\; state="\{\{state\}\}">\alpha </figure-callout>}\mathrm{1,}\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="DE102014206982B4\_0048.png,DE102014206982B4\_0052.png"\; state="\{\{state\}\}">\alpha </figure-callout>}\mathrm{2,}...\text{such as}\alpha N=\\ \left(\left(\alpha 1scal+\alpha G\right)\times W\right),\left(\left(\alpha \mathrm{2nd}scal+\alpha G\right)\times W\right),...sOwie\left(\left(\alpha 1scal+\alpha G\right)\times W\right)\end{array}$$

The values determined in this way are shown in column V of the table 5a refer to.

und in Spalte VII die Zeile für Zeile aufsummierten Werte der nach der Methode M1 ermittelten Teilungswinkel, so dass schließlich in Zeile 15 die Summe aller Einzelwerte ${\displaystyle \sum _{N=1}^{15}\alpha }=360°$

steht.Column VI of the table 5a shows row by row the values of the basic pitch angles of the previous rows added up and accordingly in row 15 the sum of all individual values in this column ${\displaystyle \sum _{N=1}^{15}\alpha G}$

and in column VII the line-by-line total of the values of the method M1 determined pitch angle, so that finally in line 15 the sum of all individual values ${\displaystyle \sum _{N=1}^{15}\alpha }=360°$

stands.

auch einen Wert ≠ 360° bilden können. Die Berechnung nach Methode 2 ist solange erneut durchzuführen bis die Differenz aufeinander folgender Winkel (siehe kleinere Differenz der Werte in den Zeilen 11 und 12 in Spalte IX) den Wert von amin' nicht unterschreitet.According to the method 2nd In column IX, row by row, the totals of the individual values in columns III and VI are as a total ${\displaystyle \sum _{N=1}^{15}A+B}$

can also form a value ≠ 360 °. The calculation by method 2nd must be carried out again until the difference between successive angles (see smaller difference between the values in the lines 11 and 12th in column IX) does not fall below the value of amine.

The differences in the results of the methods 1 and 2nd are compared in columns VIII and X. The choice of method depends on the vibration behavior and, for example, the load distribution in the rolling bearing.

Description of the invention

It is desirable that in the case of a rolling bearing, both the noise generation is reduced and the rolling bearing, if necessary, emits a characteristic, distinguishable sound spectrum during operation, so that deviations from normal operation, such as wear, insufficient lubrication or minimal tilting, can be recognized early on using changes in the sound spectrum before damage to the rolling bearing occurs. The monitoring of the sound spectrum can be made particularly efficient by automated monitoring of characteristic frequencies. A completely chaotic or random distribution of the rolling elements, however, only allows a phenomenological description of the noises generated, which must be redetermined individually for each rolling bearing by means of test series. This applies both to the desired reduction in noise development and to an effective control of the correct operation of the rolling bearing by monitoring the sound spectrum.

The invention is based on the object, based on the prior art, of specifying a method for producing an annular component with components arranged in the circumferential direction, so that when rotating about its axis, the lowest possible noise development and controllable Has sound spectrum. Furthermore, a method for producing a corresponding roller bearing with the stated property is to be specified.

gilt, wobei N die Mehrzahl der in Umfangsrichtung angeordneten Komponenten bezeichnet, und wobei x ein Modulationsfaktor vom Betrag kleiner eins ist. Dies bedeutet, dass die Winkelabstandsfunktion für die Komponenten eine von einem Sinus überlagerte Gleichverteilung ist. Im Wesentlichen baugleiche Komponenten sind dabei so zu verstehen, dass unvermeidbare Abweichungen durch Fertigungstoleranzen sowie Änderungen, welche nicht die grundsätzliche Wirkweise der einzelnen Komponenten betreffen, von der Erfindung umfasst sind. Insbesondere sollen hierbei die radialen Abstände der Komponenten bis auf Fertigungstoleranzen als gleich angenommen werden.The first-mentioned object for the production of a component, comprising a ring body which can be supported with respect to an axis and a plurality of substantially identical components which are arranged on the ring body in the circumferential direction, is achieved according to the invention in that the angular distance Δφ _{k of} the kth component arranged in the circumferential direction for the k + 1 th component is chosen such that $$\Delta {\phi }_k=\frac{\mathrm{2nd}\pi }{N}\left[1+x\cdot \text{sin}\left(\frac{\mathrm{2nd}\pi k}{N}\right)\right],$$

applies, where N denotes the majority of the components arranged in the circumferential direction, and where x is a modulation factor of the magnitude less than one. This means that the angular distance function for the components is a uniform distribution superimposed by a sine. Components which are essentially identical in construction are to be understood in such a way that unavoidable deviations due to manufacturing tolerances and changes which do not affect the basic mode of operation of the individual components are encompassed by the invention. In particular, the radial distances between the components should be assumed to be the same except for manufacturing tolerances.

When the component rotates about an axis, the components arranged in the circumferential direction can excite other adjacent components or a medium to vibrate due to their periodic movement. In a first step, the invention is based on the fact that, with uniform angular distances between the components on the ring body, the excitations by the individual components are superimposed and amplified, whereas, by arranging the components with different angular distances, the periods of excitations by the individual components are at least partially apart be decoupled. In this way, overlaps of the suggestions can be at least partially prevented.

In a second step, the invention surprisingly recognizes that a sinusoidal modulation of the uniform distribution of the components effects a frequency modulation of the excitations. This is based on the following consideration: In the case of equal angular distances for the N components - that is, an angular distance of 2π / N between two components - when the component rotates with a given frequency f, a fixed point in the radial area of the components with the frequency N · f of these happens. This frequency therefore corresponds to the frequency with which other adjacent components or a medium are excited to vibrate by the components. If the components are now arranged in the circumferential direction on the ring body as described above, when the component rotates at frequency f per unit of time, the components pass a fixed point at time intervals, which results in a sinusoidal frequency modulation of the original excitation frequency N · f, which is then to be regarded as a carrier frequency, so that the excitations from the components also result in a sinusoidal frequency-modulated spectrum.

In a third step, the invention recognizes that during frequency modulation of a carrier wave, portions of the amplitude are transmitted in sidebands and the amplitude of the carrier wave is thereby reduced. The amplitude ratios of the individual sidebands and the carrier wave depend on the frequency swing, which denotes the maximum frequency deviation from the carrier frequency, and on a maximum frequency to be modulated, which is given for the component by its own rotation frequency f. The quotient of the frequency deviation and the maximum frequency to be modulated, which is referred to as the modulation index η, determines the ratios of the amplitudes of the carrier wave and sidebands in a non-linear form. A specific amplitude ratio can thus be achieved by specifically setting a specific modulation index η. Since the frequency deviation for the component is linearly dependent on the rotation frequency f, the modulation index η is independent of the rotation frequency f. The modulation factor x in the angular spacing can thus be selected so that when the component rotates, a certain modulation index η is achieved regardless of the rotation frequency f. Thus, with a variable rotation frequency, the amplitude ratio of the carrier wave and the sidebands remains constant, which leads to a characteristic noise development of the component when rotating about an axis and thus allows automated control of the correct operation via the sound spectrum. In particular, a value of η ≈ 1,435 for the modulation index allows the amplitudes of the carrier wave and the first sideband to be the same, except for relative deviations in the alcohol range.

wobei $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)$

das Maximum der diskreten Sinusfunktion mit N äquidistanten Abszissen bezeichnet, und wobei der Modulationsindex η bevorzugt größer oder gleich eins zu wählen ist. Für durch 4 teilbare Werte von N ist hierbei $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)=\mathrm{1,}$

für gerade, jedoch nicht durch 4 teilbare Werte von N ergibt sich $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)=\text{cos}\left(\pi /N\right).$

Für ungerade Werte von N erhält man $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)=\text{cos}\left[\pi /\left(2N\right)\right].$

According to the invention, the modulation factor x is given by the angular distance Δφ _k $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{N^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}}+1}-\frac{N}{\mathrm{2nd}\eta }\right],$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissa, and the modulation index η should preferably be chosen to be greater than or equal to one. For values of N divisible by 4 is here $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)=\mathrm{1,}$

for even, but not divisible by 4 values of N results in $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)=\text{cos}\left(\pi /N\right).$

For odd values of N one gets $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)=\text{cos}\left[\pi /\left(\mathrm{2nd}N\right)\right].$

In particular, the component can be designed as a turbomachine, for example as a turbine or propeller, the components arranged in the circumferential direction being designed as blades or blades and the annular body as a hub of the turbomachine. The component can preferably also be designed as a wheel, the components arranged in the circumferential direction forming the spokes, and the ring body being designed as a wheel hub. This allows a noise-reduced rotation of the component through the above-described frequency modulation of the vibration excitation of the surrounding air by the components.

wobei $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)$

das Maximum der diskreten Sinusfunktion mit N äquidistanten Abszissen bezeichnet. Der Modulationsindex η ist bevorzugt größer oder gleich eins zu wählen. Hierbei bezeichnet ord_IR die Anzahl der Wälzkörperüberrollungen eines festen Punktes im Innenring je vollständiger Umdrehung des Wälzlagers, gegeben durch $$or{d}_{IR}=\frac{N}{2}\left(1+\text{cos}\alpha \frac{dw}{d_T}\right),$$

und ord_C die die Anzahl der Umdrehungen des Wälzkörperkäfigs je vollständiger Umdrehung des Wälzlagers, gegeben durch $$or{d}_C=\frac{1}{2}\left(1\mp \text{cos}\alpha \frac{dw}{d_T}\right).$$

In ord_IR und ord_C ist α der Druckwinkel des Wälzlagers, d_w der mittlere Wälzkörperdurchmesser und d_T der Durchmesser Teilkreises, also des Kreises, auf dem die Mittelpunkte der Wälzkörper liegen. In ord_C steht das Minuszeichen für ein Wälzlager mit einem fest stehenden Außenring und einem rotierenden Innenring und das Pluszeichen für ein Wälzlager mit einem fest stehenden Innenring und einem rotierenden Außenring.In a further embodiment of the method according to the invention, the ring body is designed as a rolling body cage of a rolling bearing, comprising an inner ring and an outer ring, the components arranged in the circumferential direction on the ring body being designed as rolling bodies, and with the angular spacing Δφ _{k of} the kth rolling body k + 1-th rolling element the modulation factor x is given by $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{Or{d}_{\mathrm{I.}R}^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}Or{d}_{\mathrm{C.}}^{\mathrm{2nd}}}+1}-\frac{Or{d}_{\mathrm{I.}R}}{\mathrm{2nd}\eta Or{d}_{\mathrm{C.}}}\right],$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissa. The modulation index η should preferably be chosen to be greater than or equal to one. Ord _IR denotes the number of rolling element rollovers of a fixed point in the inner ring per complete revolution of the rolling bearing, given by $$Or{d}_{\mathrm{I.}R}=\frac{N}{\mathrm{2nd}}\left(1+\text{cos}\alpha \frac{dw}{d_T}\right),$$

and ord _C is the number of revolutions of the rolling element cage per complete revolution of the rolling bearing, given by $$Or{d}_{\mathrm{C.}}=\frac{1}{\mathrm{2nd}}\left(1\mp \text{cos}\alpha \frac{dw}{d_T}\right).$$

In ord _IR and ord _C. α the contact angle of the rolling bearing, d _w the mean rolling element diameter and d _T the diameter of the pitch circle, that is to say the circle on which the center points of the rolling elements lie. In ord _C the minus sign stands for a rolling bearing with a fixed outer ring and a rotating inner ring and the plus sign for a rolling bearing with a fixed inner ring and a rotating outer ring.

When the rolling bearing rotates at a frequency f, a fixed point on the inner ring of the bearing is thus overrun by the rolling elements at a frequency for _IR , which in turn is modulated with the frequency for _C , the modulation index being given by η . Vibration excitations of the roller bearing, which arise when the rolling elements roll over unavoidable production-related unevenness in the running surface of the inner ring, thus form their amplitudes in accordance with the modulation index in the sidebands, which noticeably reduces the development of noise.

wobei $\underset{k}{\text{max }}\text{sin}\left(2\pi k/N\right)$

das Maximum der diskreten Sinusfunktion mit N äquidistanten Abszissen bezeichnet. Der Modulationsindex η ist bevorzugt größer oder gleich eins zu wählen. Hierbei bezeichnet ord_AR die Anzahl der Wälzkörperüberrollungen eines festen Punktes im Außenringring je vollständiger Umdrehung des Wälzlagers, gegeben durch $$or{d}_{AR}=\frac{N}{2}\left(1-\text{cos}\alpha \frac{dw}{d_T}\right),$$

und ord_C die die Anzahl der Umdrehungen des Wälzkörperkäfigs je vollständiger Umdrehung des Wälzlagers. In an alternative advantageous embodiment of the method according to the invention, the ring body is designed as a rolling body cage of a rolling bearing, comprising an inner ring and an outer ring, the components arranged in the circumferential direction on the ring body being designed as rolling bodies, and with the angular spacing Δφ _{k of} the kth rolling body for the k + 1-th rolling element the modulation factor x is given by $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{Or{d}_{AR}^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}Or{d}_{\mathrm{C.}}^{\mathrm{2nd}}}+1}-\frac{Or{d}_{AR}}{\mathrm{2nd}\eta Or{d}_{\mathrm{C.}}}\right],$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissa. The modulation index η should preferably be chosen to be greater than or equal to one. Here, ord _AR denotes the number of rolling element rollovers of a fixed point in the outer ring ring per complete revolution of the rolling bearing, given by $$Or{d}_{AR}=\frac{N}{\mathrm{2nd}}\left(1-\text{cos}\alpha \frac{dw}{d_T}\right),$$

and ord _C the number of revolutions of the rolling element cage per complete revolution of the rolling bearing.

The rolling elements can in principle be arranged in such a way that frequency modulation of the vibration excitation of the rolling bearing with the desired modulation index is set either when rolling over in the inner ring or when rolling over in the outer ring. Due to the different signs for the depending on the geometry of the rolling bearing parameters cos α · d _w / d _T in ord _IR and ord _AR of the rolling bodies resulting from the fixed arrangement of two different modulation indices. If the rolling bearing is now designed for rotation with an operating frequency f and there is a critical resonance of the rolling bearing in the vicinity of the rollover frequency for _{IR of} the inner ring or the rollover frequency for _{AR of} the outer ring, the angular spacings can preferably be selected such that that exactly that rollover frequency is modulated with a desired modulation index, which is in the vicinity of a critical resonance of the rolling bearing, so that the amplitude for exciting this critical resonance is reduced as described. The rollover frequency with respect to the other ring is also modulated by the given arrangement of the rolling elements; a modulation index is set which also depends on the geometry of the rolling bearing.

The further object is achieved according to the invention by a method for producing a roller bearing, comprising an outer ring, an inner ring and a roller body cage, in which roller bodies are arranged in accordance with the type described above. The advantages specified for the rolling element cage and its further developments can be analogously transferred to the rolling bearing.

The rolling elements of the rolling bearing are preferably designed as balls. In the case of ball bearings, which can be designed for very high frequencies, a modulation of rollover frequencies has proven to be advantageous.

The roller bearing is expediently designed as an angular contact ball bearing. A reduction in the vibration excitation of the rolling bearing by modulating rollover frequencies is then particularly advantageous with regard to reduced axial components of the excitation, which enables the bearing to run more smoothly.

In a further advantageous embodiment, the rolling elements of the rolling bearing are designed as rollers. In particular, when rolling over essentially punctiform, production-related bumps in a running surface of the roller bearing, such a roller bearing can tend to increased vibration excitation due to the linear contact of the rollers. An axial vibration component can also be excited by a possible asymmetrical distribution of such bumps. A reduction in the vibration excitation of the rolling bearing by modulating rollover frequencies has proven particularly effective here.

• 1 schematisch ein Wälzlager mit Wälzlagerkäfig und darin eingebrachten Wälzkörpern, deren Winkelabstand sinusförmig moduliert ist, in der Draufsicht, und
• 2 für das Wälzlager nach 1 in einem Graphen den Winkelabstand jedes Wälzkörpers zum in Umlaufrichtung nächsten Wälzkörper und den absoluten Winkel jedes Wälzkörpers bezüglich eines frei gewählten Wälzkörpers.

An embodiment of the invention is explained in more detail with reference to a drawing. Show:

• 1 schematically shows a rolling bearing with a rolling bearing cage and rolling elements inserted therein, the angular distance of which is modulated sinusoidally, in plan view, and
• 2nd for the rolling bearing 1 in a graph the angular distance of each rolling element to the next rolling element in the direction of rotation and the absolute angle of each rolling element with respect to a freely selected rolling element.

wobei im Ausführungsbeispiel der Faktor x als x ≈ 0.356 gewählt ist. Die Abstandswinkel ergeben sich somit zu Δφ₁ = Δφ₄ = 43.5°, Δφ₂ = Δφ₃ = 48.2°, Δφ₅ = Δφ₁₀ = 36.0°, Δφ₆ = Δφ₉ = 28.5° und Δφ₇ = Δφ₈ = 23.8°.In 1 is a rolling bearing schematically 2nd with a cage unit 3rd shown which a rolling element cage 4th and comprises a number N of rolling elements W _k , where k is a running index for numbering the individual rolling elements W _k . The rolling bearing also includes 2nd an inner ring 6 and an outer ring 8th . In the exemplary embodiment, the number N of rolling elements W _k is 10. For k less than 10, Δφ _k denotes the angular distance from the kth rolling element to the k + 1th rolling element, and the angular distance from the tenth to the first rolling element is denoted by Δφ ₁₀ . The angular distance Δφ _k is given in the exemplary embodiment by $$\Delta {\phi }_k=\frac{\mathrm{2nd}\pi }{N}\left[1+x\cdot \text{sin}\left(\frac{\mathrm{2nd}\pi k}{N}\right)\right]=36°\cdot \left[1+x\cdot \text{sin}\left(\frac{\pi k}{5}\right)\right],$$

where in the exemplary embodiment the factor x is chosen as x ≈ 0.356. The distance angles thus result in Δφ ₁ = Δφ ₄ = 43.5 °, Δφ ₂ = Δφ ₃ = 48.2 °, Δφ ₅ = Δφ ₁₀ = 36.0 °, Δφ ₆ = Δφ ₉ = 28.5 ° and Δφ ₇ = Δφ ₈ = 23.8 ° .

ein Modulationsindex von η ≈ 3.83. Bei Schwingungsanregungen des Wälzlagers 2 durch Überrollen von Unebenheiten in der Lauffläche des Innenrings 6 findet eine Frequenzmodulation der Anregung statt, wobei die Überrollfrequenz f·ord_IR am Innenring die Trägerfrequenz der Modulation ist und das zu modulierende Signal ein Sinus der Frequenz f·ord_C ist. Die Amplitude der Anregung der Trägerfrequenz ist gemäß einer Frequenzmodulation mit Modulationsindex η ≈ 3.83 im Wesentlichen betragsgleich zur Amplitude des zweiten Seitenbandes, wohingegen die Anregung im ersten Seitenband im Wesentlichen unterdrückt wird. Soll der ordnungsgemäße Betrieb des Wälzlagers über das emittierte Schallspektrum kontrolliert werden, kann diese Information über die Amplituden der Anregungen in die Analyse einfließen.For the specified embodiment are in the rolling bearing 2nd the inner ring 6 as fixed and the outer ring 8th assumed to be rotating. The rollovers ord _IR on the inner ring 6 through the rolling elements W _k per revolution of the rolling bearing 2nd and the number of revolutions ord _{C of} the rolling element cage 4th per revolution of the rolling bearing 2nd then have a ratio of ord _IR / ord _C = 10. This means that each complete revolution of the rolling element cage 4th a reference point 10th on the inner ring 6 is rolled over exactly ten times by rolling elements W _k . Due to the sinusoidal superposition in the angular distances Δφ _{k of} the rolling elements W _k , the reference point becomes 10th with normal rotation of the rolling bearing 2nd with a frequency f not rolled over at uniform time intervals 1 / (for _IR ), but at sinusoidally varying time intervals according to the angular distances Δφ _k . The rollover frequency for _IR at the reference point 10th on the inner ring 6 a frequency for _C is thus superimposed. The geometry of the bearing and the resulting rollover ratios ord _IR / ord _C = 10 thus result in x ≈ 0.356 $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/\mathrm{10th}\right)}\left[\sqrt{\frac{Or{d}_{\mathrm{I.}R}^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}Or{d}_{\mathrm{C.}}^{\mathrm{2nd}}}+1}-\frac{Or{d}_{\mathrm{I.}R}}{\mathrm{2nd}\eta Or{d}_{\mathrm{C.}}}\right],$$

a modulation index of η ≈ 3.83. With vibration excitation of the rolling bearing 2nd by rolling over unevenness in the tread of the inner ring 6 the excitation is frequency modulated, the rollover frequency for _IR on the inner ring being the carrier frequency of the modulation and the signal to be modulated being a sine of the frequency for _C. According to a frequency modulation with modulation index η ≈ 3.83, the amplitude of the excitation of the carrier frequency is essentially the same as the amplitude of the second sideband, whereas the excitation in the first sideband is essentially suppressed. If the correct operation of the rolling bearing is to be checked via the emitted sound spectrum, this information about the amplitudes of the excitations can flow into the analysis.

In 2nd are for illustration for the rolling bearing 2nd out 1 two data series are shown in a diagram. The data series drawn in circles indicates for each rolling element W _k the angular distance Δφ _k to the next rolling element W _{k + 1} in the positive direction of rotation. For an overview, the individual data points are connected with a dashed line. What can be seen here is the sinusoidal superposition of the angular distances by an equal distribution, which is 360 ° / 10 = 36 ° = Δφ ₅ = Δφ ₁₀ . The data series represented by squares indicates for each rolling element W _k its absolute angular position Δφ _k with respect to a freely selectable first rolling element W ₁ . The individual data points are connected with a solid line for a better overview. Here you can see a sinusoidal superposition of a diagonal.

Claims (7)

Method for producing a component (3), comprising a ring body (4) which can be supported with respect to an axis and a plurality N of essentially identical components (W _k ) which are arranged on the ring body (4) in the circumferential direction, characterized in that the components ( W _k ) in this way be arranged such that the angular distance Δφ _{k of} the kth component (W _k ) arranged in the circumferential direction to the k + 1th component (W _{k + 1} ) is given by $$\Delta {\phi }_k=\frac{\mathrm{2nd}\pi }{N}\left[1+x\cdot \text{sin}\left(\frac{\mathrm{2nd}\pi k}{N}\right)\right],$$

where x is a modulation factor of the amount less than one, which is given by the angular distance Δφ _k $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{N^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}}+1}-\frac{N}{\mathrm{2nd}\eta }\right],$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissa, and where η is a parameter greater than or equal to one. Method for producing a component (3), comprising a rolling element cage (4) of a rolling bearing (2) which can be supported with respect to an axis, comprising an inner ring (6) and an outer ring (8), and a plurality N of substantially identical rolling elements (k W) , which are arranged in the circumferential direction on the roller bearing cage (4), characterized in that the roller bodies (W _k ) are arranged in such a way that the angular distance Δφ _{k of} the kth roller body (W _k ) to the k + 1th roller body (W _{k +1} ) the modulation factor x is given by $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{Or{d}_{\mathrm{I.}R}^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}Or{d}_{\mathrm{C.}}^{\mathrm{2nd}}}+1}-\frac{Or{d}_{\mathrm{I.}R}}{\mathrm{2nd}\eta Or{d}_{\mathrm{C.}}}\right]$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissa, and that ord _{IR is} the number of rolling element rollovers of a fixed point (10) in the inner ring (6) per complete revolution of the rolling bearing (2), and where ord _{C is} the number of revolutions of the rolling element cage (4) per complete revolution of the rolling bearing (2), and where η is a parameter greater than or equal to one. Method for producing a component (3), comprising a rolling element cage (4) of a rolling bearing (2) which can be supported with respect to an axis, comprising an inner ring (6) and an outer ring (8), and a plurality N of substantially identical rolling elements (k W) , which are arranged in the circumferential direction on the rolling bearing cage (4), characterized in that the rolling elements (W _k ) are arranged such that the angular distance Δφ _{k of} the kth rolling element (W _k ) to the k + 1th rolling element (W _{k + 1} ) the modulation factor x is given by $$x=\frac{1}{\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)}\left[\sqrt{\frac{Or{d}_{AR}^{\mathrm{2nd}}}{\mathrm{4th}{\eta }^{\mathrm{2nd}}Or{d}_{\mathrm{C.}}^{\mathrm{2nd}}}+1}-\frac{Or{d}_{AR}}{\mathrm{2nd}\eta Or{d}_{\mathrm{C.}}}\right],$$

in which $\underset{k}{\text{Max}}\text{sin}\left(\mathrm{2nd}\pi k/N\right)$

denotes the maximum of the discrete sine function with N equidistant abscissas, and where ord _{AR is} the number of rolling element rollovers of a fixed point in the outer ring (8) per complete revolution of the rolling bearing (2), and where ord _{C is} the number of revolutions of the rolling element cage (4) each complete revolution of the rolling bearing (2), and where η is a parameter greater than or equal to one. Method for producing a rolling bearing (2), comprising an outer ring (8), an inner ring (6) and a component (3), comprising the steps of the method according to Claim 1 , with the ring body as a Rolling body cage (4) and the components arranged in the circumferential direction are designed as rolling bodies (W _k ). Method of manufacturing a rolling bearing (2) according to Claim 4 , characterized in that the rolling elements (W _k ) are designed as balls. Method of manufacturing a rolling bearing (2) according to Claim 5 , characterized in that the rolling bearing (2) is designed as an angular contact ball bearing. Method of manufacturing a rolling bearing (2) according to Claim 4 , characterized in that the rolling elements (W _k ) are designed as rollers.

Images