WO2025082714A1

WO2025082714A1 - Device and method for estimating a contact angle in a rolling bearing

Info

Publication number: WO2025082714A1
Application number: PCT/EP2024/076995
Authority: WO
Inventors: Sven Börje Håkan BÅSTEDT
Original assignee: SKF AB
Current assignee: SKF AB
Priority date: 2023-10-18
Filing date: 2024-09-26
Publication date: 2025-04-24
Anticipated expiration: 2026-04-18
Also published as: DE102023210187A1

Abstract

Disclosed is a device (10) for estimating a contact angle in a rolling bearing (1), wherein the rolling bearing comprises at least one first bearing element (2) having at least one first raceway (24), at least one second bearing element (4) having at least one second raceway (26), a plurality of rolling elements (30) arranged between the at least first bearing element and the at least one second bearing element and configured to roll on the at least one first raceway and the at least one second raceway, wherein the device comprises at least one sensor element (6) configured to measure a rolling element pass frequency, wherein the device comprises an electronic control unit (14) configured to estimate the contact angle based on the measured rolling element pass frequency.

Description

D e s c r i p t i o n

Device and method for estimating a contact angle in a rolling bearing

Technical field of the invention

The present invention relates to a device for estimating a contact angle in a rolling bearing, and a method for estimating a contact angle in a rolling bearing.

Background of the invention

A rolling bearing usually comprises an inner ring having an inner raceway and an outer ring having an outer raceway, wherein a set of rolling elements is arranged between the inner and outer ring and configured to roll on the inner and outer raceway. A contact angle is measured from the normal vector in the contact between one of the raceways and the rolling element and can be different for the inner ring contact and the outer ring contact. A determination of this angle provides an extremely good check on the general geometrical accuracy of the various components in the bearing. It has also been established in certain applications that if a bearing is to function correctly for a predetermined operational life, then the contact angle must be within closely defined limits.

One way of determining the contact angle is to calculate the contact angle by solving the following set of equations that are derived by considering force equilibrium, forcedeformation relations plus typically a condition that the bearing ring does not move radially.

F_o sin a₀ — F_t sin cq = 0

F_o sin c_o F_axiai 0

F_o cos a₀ — F_t cos oq — F_c = 0 Y_tot - (Yt + y₀) = 0 in which F_o is proportional to a contact deformation (ORa)^{3 2} between the outer raceway, and the rolling element, and Fi is proportional to a contact deformation (IRa)^{3 2} between the inner raceway and the rolling element, and a₀ and ou are the contact angle at the outer ring and inner ring, respectively. The contact deformation is the deformation of two solids that touch each other at one point which, in this context, is measured normal to the contacting surfaces. F_axiaiis the axial force acting on the rolling bearing and F_c is the centrifugal force, which is proportional to the square of a rotational frequency of the rolling element, a mass of the rolling element, and an effective pitch diameter. Ytot is the radial distance between contacts in an unloaded condition. In the loaded condition, Yi is the radial distance of the inner ring from the ball center and is given by the following equation:

Yi = (Ki - R_b + lR_d) * cos(cq); wherein Ki is the inner ring raceway radius, Rb is the rolling element radius, and IRa is the contact inner ring deformation. Y_o is the radial distance of the outer ring from the ball center and is given by the following equation:

Y_o = (K_o - R_b + 0R_d) * cos(a₀) wherein K_o is the outer ring raceway radius, and ORa is the contact outer ring deformation.

These four equations allow to solve the set of equations for contact forces and contact angles. The solve is usually done numerically by minimizing. For this purpose the above four equations are rewritten in the following manner:

F_o sin a₀ — F_t sin oq = R

F_o sin c_o F_axiai R₃

And minimized by minimizing the residual term Res=Ri²+R2²+R3²+R4². However, this approach has the drawback that during the operation of the bearing, the condition that the bearing ring does not move radially may no longer be fulfilled, due to several reasons for example the bearing may heat up, especially in case of high-speed bearings, or the diametric dimensions of the bearing may change, for example due to an interaction with a housing. It is therefore object of the present invention to provide an improved method for estimating a contact angle in a running bearing.

Summary of the invention

This object is solved by a device for estimating a contact angle in a rolling bearing according to claim 1 and a method for estimating a contact angle in a rolling bearing according to claim 9.

In the following a device for estimating a contact angle in a rolling bearing is provided. The rolling bearing comprises at least one first bearing element having at least one first raceway, at least one second bearing element having at least one second raceway, and a plurality of rolling elements arranged between the at least first bearing element and the at least one second bearing element and configured to roll on the at least one first raceway and the at least one second raceway. The at least one first bearing element may be an inner ring of the bearing, a shaft, an axle, or the like. The at least one first raceway may be formed directly on the at least one first bearing element. Alternatively, the at least one first raceway may be formed on a separate element such as a bushing which is then couple with the at least one first bearing element. The at least one first bearing element may be rotating or stationary. Furthermore, the at least one second bearing element may be an outer ring of the bearing, a housing, a hub arrangement, or the like. The at least one second raceway may be formed directly on the at least one second bearing element. Alternatively, the at least one second raceway may be formed on a separate element such as a bushing which is then couple with the at least one second bearing element. The at least one second bearing element may be rotating or stationary.

The at least one plurality of rolling elements may be balls, tapered rollers, cylindrical rollers, spherical rollers, needle rollers, or any other type of rolling element. Additionally, the bearing may also include a cage configured to retain the rolling elements.

The device also comprises at least one sensor element configured to measure a rolling element pass frequency. The term “rolling element pass frequency” refers to the frequency with which any rolling element passes the at least one sensor element. Furthermore, it is assumed that the rolling element pass frequency is essentially constant for the duration of the estimation of the contact angle, wherein “essentially constant rolling element pass frequency” means that a rolling element speed deviation is less than 5%. The at least one sensor element may be configured to measure a displacement and/or strain of a component. Furthermore, the at least one sensor element may be an optical, electrical, magnetic and/or inductive sensor.

In order to provide an improved estimation of the contact angle in a bearing, particularly in a running bearing, the device comprises an electronic control unit configured to estimate the contact angle based on the measured rolling element pass frequency. This allows to omit the condition that the bearing elements do not move radially when estimating the contact angle in a running bearing. As this condition is usually not fulfilled in a running bearing due an expansion or shrinkage which may be caused by heating, cooling, compression by interaction from a housing, applied loads or the like, estimating the contact angle based on the measured rolling element pass frequency may also be performed on a running bearing. This may have the advantage that it is possible to judge, for example whether a four- point angular contact ball bearing is in the two-point or three-point contact regime. This information is important on how close the bearing is to a switching point is useful to avoid excessive sliding and/or wear.

Moreover, the at least one sensor element may be arranged at at least one of the at least first bearing element, the at least one second bearing element, at least one of the rolling elements and/or a cage configured to retain the rolling elements. Preferably, the device comprises a plurality of sensors elements, wherein the sensor elements are arranged at different locations on the rolling bearing. This allows to improve the determination of the rolling element pass frequency. More particularly, the plurality of sensor elements may be all of the same type of sensor element. Alternatively, the plurality of sensor elements may comprise at least one sensor element that is of a different type than the other sensor elements.

Preferably, at least one sensor element is a wireless sensor element that is configured to wirelessly transmit a signal to a receiving unit, and wherein the device further comprises the receiving unit configured to receive and transmit the sensor signal provided by the at least one sensor element. For example, the wireless sensor element may be located in and/or at a rolling element. Providing a wireless sensor element may have the advantage that a bearing can be monitored even if it is not directly accessible from the outside.

According to a further embodiment, the electronic control unit is further configured to estimate a geometric change of the at least one first raceway, the at least one second raceway, the at least one first bearing element and/or the at least one second bearing element based on the estimated contact angle. For example, the geometric change may be caused by heat expansion, wear, and/or loads acting on the bearing.

Furthermore, for a non-expanding bearing element, such as a bearing ring, there is a relation between a contact deformation, which is the deformation of two solids that touch each other at one point which, in this context, is measured normal to the contacting surfaces, a bearing geometry, such as a pitch radius, rolling element radius, raceway radius, etc., and the contact angle. Although the relation between the contact deformation, the bearing geometry and the contact angle may change in a running bearing depending on the bearing type and/or the rotational speed, there is a relation that links the rolling element pass frequency of a rolling element to the contact deformation, the bearing geometry, and the contact angles, wherein the device for estimating a contact angle allows to use measured data instead of fixed and/or theoretical values in this relation. These relations may be used to estimate a geometric change of a bearing component based on the estimated contact angles.

Furthermore, the electronic control unit may be further configured to determine a temperature of at least a part of the rolling bearing based estimated contact angle. Since the rolling bearing may expand due to heat which can lead to a change in contact angle, the electronic control unit can estimate an expansion amount and together with a knowledge of the shape, dimension and/material of the rolling bearing part, a temperature of the rolling bearing part

Also, the electronic control unit may be further configured to determine a status parameter of the rolling bearing. The status parameter may be a lubrication condition, a switching point between rolling and sliding of the rolling elements, and the like. Furthermore, the electronic control unit may be configured to generate a control signal for controlling a part of a system in which the monitored rolling bearing is used based on the estimated contact angle. For example, the electronic control unit may generate a control signal for controlling a rotation speed with which one of the bearing elements is rotated. Furthermore, a method for estimating a contact angle in a rolling bearing is provided, wherein the rolling bearing comprises at least one first bearing element, at least one second bearing element, a plurality of rolling elements arranged between the at least one first bearing element and the at least one at least one second bearing element. The rolling bearing may comprise at least one sensor element configured to estimate a rolling element pass frequency. The method comprises the following steps: receiving a signal from at least one sensor element configured to measure a rolling element pass frequency, determining a rolling element pass frequency from the received signal waveform, and estimating the contact angle based on the determined rolling element pass frequency.

Furthermore, the method may include solving the following equations:

F_o sin a₀ — F_t sin cq = 0 (eq. 1)

F_o sin a₀ - F_axial = 0 (eq. 2)

F_o cos a₀ — F_t cos cq = F_c (eq. 3) in which F_o is proportional to a contact deformation (ORa)^{3 2} between the second raceway, and the rolling element, and Fi is proportional to a contact deformation (IRa)^{3 2} between the first raceway and the rolling element, and a₀ and ou are the contact angle at the first and second bearing element, respectively. F_axiaiis the axial force acting on the rolling bearing and the centrifugal force F_c which is given by:

wherein mb is a mass of the ball, R_m is a pitch circle radius, and co_c is given by:

2irf_c

°c = M ; NRE wherein f_c is the rolling element pass frequency, and NRE is the number of rolling elements.

As mentioned above, there are relations between the contact deformation, the bearing geometry, and the contact angle. For example, the angular frequency co_c, which is used above to determine the centrifugal force in the rolling bearing, and which is also directly linked to the measured rolling element pass frequency, is also linked by the following equation,

to an effective rolling radius Rbe of the rolling element, which can be described as virtual disc that lies between a contact point of the rolling element at the first bearing element and a contact point of the rolling element at the second bearing element as well as a radius of the radial movement of the rolling elements or effective mean pitch radius R_me„ the contact angles a₀ and ou, and the angular frequency co_shaft of a shaft driving one of the first and second bearing element such that the above noted relation may be used to estimate a geometric change of a bearing component based on the estimated contact angles.

The equations eq. 1, eq. 2, eq. 3 eq4. allow to solve the set of equations for contact forces and contact angles. The solve may be performed numerically by minimizing. For this purpose the four equations are rewritten in the following manner:

F_o sin a₀ — F_t sin oq = R ( eq. 1) ’

F_o sin a_o F_axiai R2 ( q- )

F_o cos a₀ — F_t cos eq — F_c = R₃ (eq. 3)'

Preferably, the method includes a numerical minimizing of the residual term Res=Ri²+R2²+R3² +R4² in order to estimate the contact angle. Alternatively, any other relation that links the bearing geometry, the contact deformation, and the rolling element pass frequency may be used together with equation eq. 1, eq. 2, eq. 3 to estimate the contact angles.

Preferably, the method also comprises estimating a geometric change of the at least one first bearing element and/or the at least one second bearing element based on the estimated contact angle, and/or determine a temperature of at least one rolling bearing component based estimated contact angle, and/or determine a status parameter of the rolling bearing based on the estimated contact angle.

An even further aspect of the present invention relates to a computer program product comprising a computer program code which is adapted to prompt a control unit, e.g. a computer, and/or a computer of the above discussed device to perform the above discussed method steps.

The computer program product may be a provided as memory device, such as a memory card, USB stick, CD-ROM, DVD and/or may be a file which may be downloaded from a server, particularly a remote server, in a network. The network may be a wireless communication network for transferring the file with the computer program product.

Further preferred embodiments are defined in the dependent claims as well as in the description and the figures. Thereby, elements described or shown in combination with other elements may be present alone or in combination with other elements without departing from the scope of protection.

Brief description of the drawings

In the following, preferred embodiments of the invention are described in relation to the drawings, wherein the drawings are exemplarily only, and are not intended to limit the scope of protection. The scope of protection is defined by the accompanied claims, only.

The figures show:

Fig. 1 : a schematic view of a device for estimating a contact angle in a rolling bearing, and Fig. 2: a flow diagram for a method for estimating a contact angle in the rolling bearing.

Detailed description of the invention

In the following same or similar functioning elements are indicated with the same reference numerals.

Fig. 1 shows a schematic view of a device 10 for estimating a contact angle in a rolling bearing 1. The bearing 1 comprises at least one first bearing element 2, such as an inner ring, a shaft, an axle, or the like, having at least one first raceway 24, at least one second bearing element 4, such as an outer ring, a housing, a hub arrangement, or the like, having at least one second raceway 26, and at least one set of rolling elements 30 disposed between the first and second bearing element 2, 4. In Fig. 1, the rolling elements 30 are shown as be balls. However, the rolling elements, tapered rollers, cylindrical rollers, spherical rollers, needle rollers, or any other type of rolling element. In addition, the bearing 1 comprises a cage 8 configured to retain the rolling elements 30. The bearing 1 may be provided with a lubricant configured to lubricate the rolling elements 30. For example, the lubricant may be grease and/or oil. However, other suitable types of lubricant can also be used.

The rolling bearing 1 is equipped with a sensor element 6 configured to measure a rolling element pass frequency. The sensor element 6 is configured to measure a displacement and/or strain of a component it is attached to. In addition or alternatively, the sensor element 6 may be an optical, electrical, magnetic and/or inductive sensor. In Fig. 1, the sensor element 6 is arranged at the second bearing element 4. However, it is also possible to arrange the sensor element 6 at the first bearing element 2, at or in at least one of the rolling elements 30 and/or the cage 8.

Although in Fig. 1 only one sensor element 6 is depicted in Fig. 1, more than one sensor element 6 can be arranged at different locations on the rolling bearing 1. For example, the rolling element 1 may be provided with an additional sensor element 6 at the first bearing element 2 and/or the cage 8 and/or in one of the rolling elements 30. More particularly, the plurality of sensor elements may be all of the same type of sensor element 6. Alternatively, the plurality of sensor elements may comprise at least one sensor element 30 that is of a different type than the other sensor elements 6.

The sensor element 6 is connected to the device 10 via a cable 12 and/or a wireless connection 12 as indicated in Fig. 1 with the dashed line. For example, the sensor element 6 may be a wireless sensor element that is configured to wirelessly transmit a signal to a receiving unit 16 configured to receive and transmit signals to and/or from the sensor element 30. For example, the wireless sensor element may be located in and/or at a rolling element. Providing a wireless sensor element may have the advantage that a bearing can be monitored even if it is not directly accessible from the outside.

The rolling element pass frequency may be directly measured by the sensor element 6 and/or the signal of the sensor element 6 may be transmitted via the connection 12 to the device 1 which is then configured to determine the rolling element pass frequency based on the transmitted signal.

The device 10 comprises an electronic control unit 14 configured to estimate the contact angle based on the measured rolling element pass frequency. More particularly, the device is configured to solve the following equations, which have been described above in detail:

F_o sin a₀ — F_t sin cq = 0 (eq. 1)

These four equations eq. 1, eq. 2, eq. 3, eq. 4 allow to solve the set of equations for the contact forces F_o and Fi and contact angles a₀ and ou.

As mentioned above, eq. 4 links the angular frequency co_c to geometric metric properties of the rolling bearing 1, such as the effective rolling radius Rb_e of the rolling element 30, which can be described as virtual disc that lies between a contact point of the rolling element 30 at the first bearing element 2 and a contact point of the rolling element 30 at the second bearing element 4. In case the rolling bearing l is a ball bearing, the effective rolling radius Rbe of the rolling element can be calculated using the following equation:

wherein Rb is the rolling element radius.

Furthermore, eq. 4 also includes the contact angles a₀ and ou, the angular frequency co_shaft of a shaft driving one of the first and second bearing elements 2, 4, and the radius of the radial movement of the rolling elements 30 or effective mean pitch radius R_me. In case the rolling bearing l is a ball bearing, the effective mean pitch radius R_me can be calculated using the following equation:

Rme = Rma + R_b S (^) sin (^), wherein R_ma is the distance between a center of the first raceway 24 to the actual center of rolling element 30, which can be calculated using the following equation:

wherein Ki is a radius of the first raceway 24, and R_wi is a distance between a nominal center of the rolling element 30 and the center of the first raceway 24, which can be calculated with the following equation:

wherein R_m is the pitch radius, and a_nOm is a nominal contact angle of the second bearing element 4.

The parameters R_m, Ki, Rb, and a_nOm relate to geometric properties of each rolling bearing to be measured, which may be determined in advance and in the electronic control unit 14 of the device 1. Alternative, these parameters R_m, Ki, Rb, and a_nOm may be stored in an external storage device and transmitted to receiving unit 16 of the device. It should be noted that depending on the type of rolling bearing, the equations noted above may need to be adapted accordingly.

The device 10 may be configured to solve the above noted equations numerically, for example by minimizing. For this purpose, the above noted four equations are rewritten in the following manner:

F_o sin a₀ — F_t sin oq = R ( eq. 1) ’

F_o sin a_o F_axiai R2 (cq. 2 )

F_o cos a₀ — F_t cos eq — F_c = R₃ (eq. 3)'

and the residual term Res=Ri²+R2²+R3²+R4² is then minimized to estimate the contact angles a₀ and cii.

Furthermore, the electronic control unit 10 is further configured to estimate a geometric change of the first raceway 24, the second raceway 26, the first bearing element 2 and/or the second bearing element 4 based on the estimated contact angle.

Since the rolling bearing 1 may expand due to heat which can lead to a change in contact angle and/or contact forces, the electronic control unit 1 can estimate an expansion amount of one of the bearing components such as the first and/or second bearing element 2, 4 and together with a knowledge of the shape, dimension and/material of the rolling bearing component, a temperature of the rolling bearing component may be determined based estimated contact angle.

In addition or alternatively, the electronic control unit 10 is also configured to determine a status parameter of the rolling bearing 1. The status parameter may be a lubrication condition, a switching point between rolling and sliding of the rolling elements 30, and the like. Furthermore, the electronic control unit 10 may be configured to generate a control signal for controlling a part of a system in which the monitored rolling bearing 1 is used based on the estimated contact angle. For example, the electronic control unit 10 may generate a control signal for controlling a rotation speed with which one of the bearing elements is rotated.

Fig. 2 shows a flow diagram for a method for estimating a contact angle in the rolling bearing 1. In an initial step SO, parameters relating to the geometry of the rolling bearing such as the pitch circle radius R_m, the radius Ki of the inner raceway 24, the rolling element radius Rb, the mass of the rolling element mb and/ or the nominal contact angle a_nOm, and/or parameters relating to the method for estimating the contact angle such as the acting axial Force F_axiai, are collected. These parameters may be previously measured and/determined and stored in the electronic control unit 14 and/or retrieved from an external storage device.

The method comprises in a first step SI receiving a signal from the sensor element 6. In a second step S2, a rolling element pass frequency is determined from the received signal waveform. The method further comprises a step S3, in which the equations eq. 1’, 2’, 3’, 4’ are solved by minimizing the term Res=Ri²+R2²+R3²+R4², and a step S4 in which the contact angles a₀ and ou are estimated.

In summary, by estimating the contact angles and/or contact forces based on the measured rolling element pass frequency, it is possible to omit the condition that the bearing elements do not move radially. As this condition is usually not fulfilled in a running bearing due to several reasons such as expansion which may be caused by heating or change of diametric dimensions caused by an interaction with a housing, the above-described device and method may advantageously be performed on a running bearing. This has the advantage that it is possible to judge, for example whether a four-point angular contact ball bearing is in the two-point or three-point contact regime on a running bearing. This information is important on how close the bearing is to a switching point is useful to avoid excessive sliding and/or wear.

Reference numerals

1 bearing

2 first bearing element

4 second bearing element

6 sensor element

8 cage

10 device

12 connection

14 electronic control unit

16 receiving unit

24 first raceway

26 second raceway

S1-S4 method steps

Claims

C l a i m s Device and method for estimating a contact angle in a rolling bearing

1. Device (10) for estimating a contact angle in a rolling bearing (1), wherein the rolling bearing (1) comprises at least one first bearing element (2) having at least one first raceway (24), at least one second bearing element (4) having at least one second raceway (26), a plurality of rolling elements (30) arranged between the at least first bearing element (2) and the at least one second bearing element (4) and configured to roll on the at least one first raceway (24) and the at least one second raceway (26), wherein the device (10) comprises: at least one sensor element (6) configured to measure a rolling element pass frequency, characterized in that the device (10) comprises an electronic control unit (14) configured to estimate the contact angle based on the measured rolling element pass frequency.

2. Device (10) according to claim 1, wherein the at least one sensor element (6) is arranged at at least one of the at least first bearing element (2), the at least one second bearing element (4), at least one of the rolling elements (30) and/or a cage (8) configured to retain the rolling elements (30).

3. Device (10) according to claim 1 or 2, wherein the device (10) comprises a plurality of sensors elements (6), wherein the sensor elements (6) are arranged at different locations on the rolling bearing (1).

4. Device (10) according to any one of the previous claims, wherein at least one sensor element (6) is a wireless sensor element that is configured to wirelessly transmit a signal to a receiving unit (16), and wherein the device further comprises the receiving unit (16) configured to receive and transmit the sensor signal provided by the at least one sensor element (6).

5. Device (10) according to any one of the previous claims, wherein at least one sensor element (6) is configured to measure a displacement and/or strain of a component to which it is attached.

6. Device (10) according to any one of the previous claims, wherein the electronic control unit (14) is further configured to estimate a geometric change of the at least one first raceway (24), the at least one second raceway (26), the at least one first bearing element (2) and/or the at least one second bearing element (4) based on the estimated contact angle.

7. Device (10) according to any one of the previous claims, wherein the electronic control unit (14) is further configured to determine a temperature of at least a component of the rolling bearing (1) based estimated contact angle.

8. Device (10) according to any one of the previous claims, wherein the electronic control unit (14) is further configured to determine a status parameter of the rolling bearing (1).

9. Method for estimating a contact angle in a rolling bearing (1), wherein the rolling bearing (1) comprises at least one first bearing element (2), at least one second bearing element (4), a plurality of rolling elements (30) arranged between the at least one first bearing element (2) and the at least one at least one second bearing element (4), the method comprises the following steps: receiving (SI) a signal from at least one sensor element (6) configured to measure a rolling element pass frequency, determining (S2) a rolling element pass frequency from the received signal, and estimating (S4) the contact angle based on the determined rolling element pass frequency.