Rolling bearing outer ring contact stiffness calibration method and system based on three-point ultrasonic method

Abstract

The present invention belongs to the technical field of bearing stiffness calibration, and specifically discloses a method and system for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method. The method approximates the contact surface between the rolling element and the outer ring of the bearing, and the outer surface of the outer ring of the bearing as an ellipsoidal surface; sets a measurement track, and has three measuring points under the measurement track. The measuring points are measured to obtain the acoustic time difference, and the focal centers of the three measuring points of the measurement track on the outer surface of the outer ring of the bearing, and the intersection coordinates of the focal center and the contact surface along the ultrasonic direction are calculated. The intersection coordinates are brought into the corresponding function, and n groups of ellipsoidal surface functions of the outer surface of the outer ring of the bearing and the ellipsoidal surface functions of the contact surface are fitted to obtain the optimal ellipsoidal surface, and the spatial distribution of the contact surface deformation variable and the contact stiffness are calculated. By adopting this technical solution, the outer surface of the outer ring of the bearing and the inner contact surface of the outer ring of the bearing are approximated as an ellipsoidal surface, and a more reasonable and closer to the true value contact area deformation variable spatial distribution is obtained, and a more accurate stiffness calibration is completed.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing stiffness calibration, and relates to a rolling bearing outer ring contact stiffness calibration method and system based on a three-point ultrasonic method. Background Art

[0002] As a key supporting element in the transmission device, the working performance of the rolling bearing has an important impact on the working performance and reliability of the entire transmission device, and the bearing support stiffness plays an important role in predicting the static and dynamic response of high-speed transmission devices. The rolling bearing support stiffness mainly includes the bearing radial support stiffness and the bearing support axial stiffness. The radial stiffness of the bearing is determined by the contact stiffness between the rolling element in the load-bearing area and the inner and outer ring raceways of the bearing. Since the rolling element is located in a small raceway space and the deformation of the rolling element in contact with the raceway is usually very small, it is difficult to calibrate its stiffness through conventional measurement methods.

[0003] Ultrasonic testing, as a commonly used non-contact, non-destructive measurement method, is very suitable for the task of carrying out stiffness calibration for seals. The deformation of the outer ring of the bearing is obtained through ultrasonic testing, and the contact stiffness between the outer ring of the bearing and the rolling element can be obtained based on the force applied to the rolling element. However, the deformation of the outer ring of the bearing measured by the ultrasonic probe is actually the average of the deformation in the focus area of ​​the ultrasonic probe, and the focus area of ​​the ultrasonic probe is often larger than the effective area at the maximum deformation of the outer ring of the bearing. Therefore, it is necessary to improve the ultrasonic measurement method to obtain accurate deformation of the outer ring of the bearing, so as to complete accurate stiffness calibration. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method, so as to obtain a more reasonable spatial distribution of the deformation variable in the contact area that is closer to the true value, and to complete a more accurate stiffness calibration.

[0005] In order to achieve the above object, the basic scheme of the present invention is: a method for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method, comprising the following steps:

[0006] S1, the contact surface between the rolling element and the outer ring of the bearing and the outer surface of the outer ring of the bearing are approximated as ellipsoidal surfaces;

[0007] S2, setting at least three measurement tracks on the outer surface of the bearing outer ring, each measurement track having three measurement points, and using an ultrasonic probe to measure each measurement point to obtain the acoustic time difference;

[0008] S3, calculating the focal centers of the three measuring points corresponding to each measurement trajectory on the outer surface of the bearing outer ring, and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction, according to the acoustic time difference;

[0009] S4, bringing the intersection coordinates into the pre-set ellipsoidal surface function of the outer surface of the outer ring of the bearing and the ellipsoidal surface function of the contact surface, and fitting to obtain a set of ellipsoidal surface functions of the outer surface of the outer ring of the bearing and the ellipsoidal surface function of the contact surface;

[0010] S5, repeating steps S2-S4 n times to obtain n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring and ellipsoidal surface functions of the contact surface;

[0011] S6, determining the optimal bearing outer ring outer surface ellipsoidal surface and contact surface ellipsoidal surface according to n groups of bearing outer ring outer surface ellipsoidal surface functions and contact surface ellipsoidal surface functions;

[0012] S7, combining the bearing outer ring thickness T and the applied known force F, calculate the spatial distribution of the contact surface deformation and the contact stiffness.

[0013] The working principle and beneficial effect of this basic scheme are: obtain multiple sets of coordinate values ​​through multiple rounds of three-point ultrasonic measurement, and fit multiple sets of ellipsoidal functions of the outer surface of the outer ring of the bearing and the ellipsoidal functions of the contact area of ​​the outer ring of the bearing. Approximate the outer surface of the outer ring of the bearing and the inner contact surface of the outer ring of the bearing as ellipsoidal surfaces, calculate multiple sets of corresponding position coordinates through multiple rounds of three-point measurement and spatial geometric relationships, and fit multiple sets of ellipsoidal formulas to calculate the optimal ellipsoidal surface, so as to obtain a more reasonable and closer to the true value of the contact area deformation variable spatial distribution, and obtain more accurate stiffness.

[0014] Further, the method for setting the measurement track on the outer surface of the bearing outer ring is as follows:

[0015] An annular water bath is provided on the outer side of the bearing outer ring, and an ultrasonic probe is arranged in the annular water bath to obtain the coordinates of the measuring points;

[0016] Assume that the angle between the line between the measuring point and the ultrasonic probe and the vertical direction is α j The three measuring points corresponding to each measurement trajectory are the points obtained by rotating the ultrasonic probe 120 degrees with the vertical direction passing through its center point as the axis.

[0017] An annular water bath is set on the outer ring of the bearing to avoid contact between the water bath and the outer ring of the bearing, and to avoid interference with the outer ring of the bearing when it is deformed by force, which may introduce measurement errors. An ultrasonic probe is arranged in the water bath to use ultrasound to perform non-destructive measurement of the spatial displacement of the outer surface of the outer ring of the bearing and the contact area of ​​the outer ring of the bearing, which is simple to operate and easy to use.

[0018] Further, the method of measuring each measuring point to obtain the acoustic time difference is as follows:

[0019] In the jth measurement track, the ultrasonic probe sends a detection wave to the i-th measurement point, and the transmission wave I is obtained in the water bath. i1 , define the time when the sound wave is emitted as t0;

[0020] The ultrasonic wave passes through the interface between the water bath and the outer ring of the bearing, and the reflected wave R i1 , define the received reflected wave R i1 The time is t1, and the first sound time difference Δt1=t1-t0 is calculated;

[0021] The ultrasonic wave passes through the bearing outer ring and rolling element interface to obtain the reflected wave R i2 , define the received reflected wave R i2 The time is t2, and the second sound time difference Δt2=t2-t1 is calculated;

[0022] Determine whether i is greater than or equal to 3. If so, execute S3; if not, measure the i+1th measuring point.

[0023] The acoustic time difference under the measurement track is calculated sequentially, which is simple to operate and easy to use.

[0024] Furthermore, the method for calculating the focal centers of the three measuring points corresponding to the measurement trajectory on the outer surface of the bearing outer ring and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction is as follows:

[0025] The calculation of the focal center coordinates of the ultrasonic probe on the outer surface of the bearing outer ring is:

[0026]

[0027]

[0028]

[0029] The coordinates of the intersection of the focus center along the ultrasonic direction and the contact surface are calculated as follows:

[0030]

[0031]

[0032]

[0033] Where i represents the i-th measuring point, c1 represents the sound velocity of the water bath, and c2 represents the sound velocity of the bearing outer ring material; α j represents the angle between the ultrasonic probe and the vertical direction under the jth measurement track; Δt1 and Δt2 are the acoustic time differences; θ i Represents the angle between the Y axis and the projection of the i-th measuring point on the XOY plane and the line connecting the coordinate origin, θ1 = -120°, θ2 = 0°, θ3 = 120°;

[0034] Determine whether j is greater than a threshold. If j is greater than or equal to the threshold, it indicates that the measurement of three measuring points on all measuring tracks has been completed, and proceed to step S4. If j is less than 3, it indicates that the measurement of measuring points under all measuring tracks has not been completed, and proceed to the measurement of the measuring points under the j+1th measuring track.

[0035] According to the measurement results at the measuring points and the spatial geometric relationship, the focusing center of the ultrasonic probe on the outer surface of the bearing outer ring and the coordinates of the intersection of the focusing center and the contact surface along the ultrasonic direction are calculated to facilitate subsequent use.

[0036] Furthermore, the method for fitting the ellipsoidal surface function of the outer surface of the bearing outer ring and the ellipsoidal surface function of the contact surface is as follows:

[0037] Assume that the ellipsoidal function of the outer surface of the bearing outer ring is The contact surface ellipsoid function is: Among them, x, y, z represent coordinates; a o , b o , c o The three parameters to be solved represent the ellipsoidal function of the outer surface of the outer ring of the assumed bearing, a c , b c , c c The three parameters to be solved represent the hypothetical contact surface ellipsoidal surface function;

[0038] Substitute the calculated intersection coordinates of the focal center along the ultrasonic direction and the contact surface into the ellipsoidal surface function of the outer surface of the bearing outer ring and the ellipsoidal surface function of the contact surface, and obtain a set of ellipsoidal surface functions of the outer surface of the bearing outer ring and the contact area by fitting;

[0039] Repeat S2-S4 n times to obtain n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring and ellipsoidal surface functions of the contact surface.

[0040] The calculation is simple and easy to use.

[0041] Furthermore, in order to express the radial deformation of the outer surface of the bearing outer ring and the contact surface of the bearing outer ring, the spatial ellipsoid surface obtained each time is expressed as a function of z with respect to x and y, that is,

[0042] Use functions to represent the corresponding deformation variables and use them for subsequent calculations.

[0043] Furthermore, the method for determining the optimal bearing outer ring outer surface ellipsoid and contact surface ellipsoid is as follows:

[0044] According to the obtained n groups of bearing outer ring outer surface ellipsoidal functions and contact surface ellipsoidal functions, the optimal space ellipsoidal surface is determined by the least square method. The calculation formula is:

[0045]

[0046] Among them, L n It represents the sum of squared errors of the Z values ​​of the nth ellipsoid surface and the corresponding points on other ellipsoid surfaces. Z refers to the value of each point on each ellipsoid surface in the z-axis direction. The subscript Z represents the number of times the z value in the ellipsoid surface equation is measured. n -z {1,2,..,N}-n It refers to the difference between the nth measurement result and the nth measurement result; by finding the smallest L n , to determine the optimal ellipsoidal surface of the outer ring of the bearing Ellipsoidal surface in contact area with bearing outer ring

[0047] The optimal ellipsoid is calculated using the least square method, which is simple to calculate and easy to operate.

[0048] Furthermore, the method for calculating the spatial distribution of the contact surface deformation variable is as follows:

[0049] According to the optimal ellipsoidal space function of the outer surface of the bearing outer ring and the optimal ellipsoidal space function of the bearing outer ring contact area Combined with the bearing outer ring thickness T, the spatial distribution of the contact surface deformation is calculated:

[0050]

[0051] Define the domain of the contact surface as x 2 +y 2 ≤r 2 , x and y are the domains of the contact area in the projection of the xoy plane in the x-axis and y-axis directions respectively; r is the radius of the rolling body.

[0052] The optimal ellipsoid surface is used to obtain a more reasonable spatial distribution of the contact area deformation that is closer to the true value.

[0053] Further, the method for calculating the contact stiffness is as follows:

[0054] Spatial distribution of contact surface deformation Combined with the known applied force F, the contact stiffness is calculated as:

[0055]

[0056] Where, T is the thickness of the bearing outer ring; is the thickness distribution of the bearing outer ring after contact deformation, that is, the distance between the outer surface of the bearing outer ring and the bearing contact surface; is the deformation variable of the contact surface, which is a spatial function of the z-axis direction variable with respect to x and y, denoted as D(x,y), and max(D(x,y)) is the value of the maximum deformation variable.

[0057] By using the more reasonable spatial distribution of the contact area deformation that is closer to the true value, a more accurate contact stiffness can be calculated.

[0058] The present invention also provides a rolling bearing outer ring contact stiffness calibration system based on a three-point ultrasonic method, comprising an annular water bath arranged on the outside of the bearing outer ring, an ultrasonic probe placed in the annular water bath, and a processing module. The processing module executes the method of the present invention to calibrate the contact stiffness of the rolling bearing outer ring.

[0059] The system improves the ultrasonic measurement method to obtain more accurate bearing outer ring deformation and complete accurate stiffness calibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic flow chart of a method for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method according to the present invention;

[0061] Figure 2 It is a schematic diagram of the bearing outer ring structure of the rolling bearing outer ring contact stiffness calibration system based on the three-point ultrasonic method of the present invention;

[0062] Figure 3 It is a schematic structural diagram of the measuring points of the rolling bearing outer ring contact stiffness calibration method based on the three-point ultrasonic method of the present invention;

[0063] Figure 4 is the angle α between the measuring point and the ultrasonic probe of the rolling bearing outer ring contact stiffness calibration method based on the three-point ultrasonic method of the present invention. j Schematic diagram of the structure;

[0064] Figure 5 yes Figure 3 Schematic diagram of the top view structure of the measuring points.

[0065] The reference numerals in the drawings of the specification include: bearing inner ring 1, bearing outer ring 2, rolling element 3, annular water bath 4, reference plane 5, ultrasonic probe 6, known force F7. DETAILED DESCRIPTION

[0066] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0067] In the description of the present invention, it is necessary to understand that the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0068] In the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the internal connection between two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0069] In the prior art, since the contact area between the rolling element and the outer ring is an ellipsoidal surface, the maximum contact deformation occurs in the middle part of the contact area, and the deformation measured by the ultrasonic probe is actually the average deformation of its focal area, resulting in uncertainty.

[0070] The present invention discloses a method for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method. Figure 1-Figure 5 As shown, multiple groups of coordinate values ​​are obtained through multiple rounds of three-point ultrasonic measurement, and multiple groups of ellipsoidal functions of the outer surface of the outer ring 2 of the bearing and the ellipsoidal functions of the contact area of ​​the outer ring 2 of the bearing are fitted. This scheme takes into account the deformation of the outer surface of the outer ring 2 of the bearing and the deformation of the inner surface of the outer ring 2 of the bearing when the rolling element 3 contacts the outer ring 2 of the bearing. The outer surface of the outer ring 2 of the bearing and the inner contact surface of the outer ring 2 of the bearing are approximated as ellipsoidal surfaces. Through multiple rounds of three-point measurement and spatial geometric relationships, multiple groups of corresponding position coordinates are calculated, and multiple groups of ellipsoidal formulas are fitted. The optimal ellipsoid is calculated using the least squares method, so as to obtain a more reasonable spatial distribution of the contact area deformation variable that is closer to the true value.

[0071] like Figure 1 and Figure 2 As shown, this method includes the following steps:

[0072] S1, the contact surface between the rolling element 3 and the bearing outer ring 2, and the outer surface of the bearing outer ring 2 are approximated as ellipsoidal surfaces;

[0073] S2, setting at least three measurement tracks on the outer surface of the bearing outer ring 2, each measurement track having three measurement points, and using an ultrasonic probe 6 to measure each measurement point to obtain the acoustic time difference;

[0074] S3, calculating the focal centers of the three measuring points corresponding to each measurement trajectory on the outer surface of the bearing outer ring 2, and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction according to the acoustic time difference;

[0075] S4, bringing the intersection coordinates into the pre-set ellipsoidal surface function of the outer surface of the bearing outer ring 2 and the ellipsoidal surface function of the contact surface, and fitting to obtain a set of ellipsoidal surface functions of the outer surface of the bearing outer ring 2 and the ellipsoidal surface function of the contact surface;

[0076] S5, repeating steps S2-S4 n times, obtaining n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring 2 and ellipsoidal surface functions of the contact surface;

[0077] S6, determining the optimal ellipsoidal surface of the outer surface of the outer ring 2 of the bearing and the ellipsoidal surface of the contact surface according to n groups of ellipsoidal surface functions of the outer surface of the outer ring 2 of the bearing and the ellipsoidal surface functions of the contact surface;

[0078] S7, combining the thickness T of the bearing outer ring 2 and the applied known force F7, calculates the spatial distribution of the contact surface deformation and the contact stiffness.

[0079] In a preferred embodiment of the present invention, the method for setting a measurement track on the outer surface of the bearing outer ring 2 is as follows:

[0080] An annular water bath 4 is provided on the outside of the bearing outer ring 2 to prevent the water bath from contacting the bearing outer ring 2 and causing interference to the bearing outer ring 2 when it is deformed by force, thereby introducing measurement errors. An ultrasonic probe 6 is provided in the annular water bath 4 to obtain the coordinates of the measuring points, and the spatial displacement of the outer surface of the bearing outer ring 2 and the contact area of ​​the bearing outer ring 2 is measured non-destructively by ultrasound. Combined with the thickness of the bearing outer ring 2 when it is not stressed, the spatial distribution of the deformation of the contact area of ​​the bearing outer ring 2 is calculated.

[0081] like Figure 3 , Figure 4 and Figure 5 As shown, the angle between the line direction between the measuring point and the ultrasonic probe 6 and the vertical direction is α j The three measuring points corresponding to each measuring track are the points obtained by rotating the ultrasonic probe 6 120 degrees with the vertical direction passing through the center point of the ultrasonic probe 6 as the axis.

[0082] In a preferred embodiment of the present invention, the method for measuring each measuring point to obtain the acoustic time difference is as follows:

[0083] In the jth measurement track, the ultrasonic probe 6 sends a detection wave to the i-th measurement point, and a transmission wave I is obtained in the water bath. i1 , define the time when the sound wave is emitted as t0;

[0084] The ultrasonic wave passes through the interface between the water bath and the bearing outer ring 2, and the reflected wave R i1 , define the received reflected wave R i1The time is t1, and the first sound time difference Δt1=t1-t0 is calculated;

[0085] The ultrasonic wave passes through the interface between the water bath and the outer ring 2 of the bearing, and the transmitted wave I is obtained. i2 The ultrasonic wave passes through the interface between the bearing outer ring 2 and the rolling element 3 to obtain the reflected wave R i2 , define the received reflected wave R i2 The time is t2, and the second sound time difference Δt2=t2-t1 is calculated;

[0086] Determine whether i is greater than or equal to 3. If so, execute S3; if not, measure the i+1th measuring point.

[0087] In a preferred embodiment of the present invention, the method for calculating the focal center of the three measuring points corresponding to the measurement trajectory on the outer surface of the bearing outer ring 2 and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction is as follows:

[0088] According to the acoustic time difference and the spatial collection relationship, the focal center coordinates of the ultrasonic probe 6 on the outer surface of the bearing outer ring 2 are calculated as follows:

[0089]

[0090]

[0091]

[0092] The coordinates of the intersection of the focus center along the ultrasonic direction and the contact surface are calculated as follows:

[0093]

[0094]

[0095]

[0096] Where i represents the i-th measuring point, c1 represents the sound velocity of the water bath, and c2 represents the sound velocity of the bearing outer ring 2 material; α j represents the angle between the ultrasonic probe 6 and the vertical direction under the jth measurement track; Δt1 and Δt2 are the acoustic time differences; θ i Indicates the angle between the Y axis and the projection of the i-th measuring point on the XOY plane and the line connecting the coordinate origin, θ1 = -120°, θ2 = 0°, θ3 = 120°, to ensure that the measuring points are evenly distributed;

[0097] Determine whether j is greater than a threshold. If j is greater than or equal to the threshold, it indicates that the measurement of three measuring points on all measuring tracks has been completed, and proceed to step S4. If j is less than 3, it indicates that the measurement of measuring points under all measuring tracks has not been completed, and proceed to the measurement of the measuring points under the j+1th measuring track.

[0098] In a preferred embodiment of the present invention, the method for fitting the ellipsoidal surface function of the outer surface of the bearing outer ring 2 and the ellipsoidal surface function of the contact surface is as follows:

[0099] Assume that the ellipsoidal function of the outer surface of the bearing outer ring 2 is The contact surface ellipsoid function is: Among them, x, y, z represent coordinates; a o , b o , c o represents the three parameters to be solved of the ellipsoidal surface function of the outer surface of the outer ring of the assumed bearing. Since three sets of three-dimensional coordinates will be obtained by measuring three times, the three parameters to be solved can be substituted into the equation to solve them, and then the ellipsoidal surface equation at that location can be obtained; a c , b c , c c Represents the three parameters to be solved of the hypothetical contact surface ellipsoidal surface function. Three sets of three-dimensional coordinates will be obtained by measuring three times. Therefore, the three parameters to be solved can be substituted into the equation to solve them, and then the ellipsoidal surface equation at that location can be obtained;

[0100] Substitute the calculated intersection coordinates of the focal center along the ultrasonic direction and the contact surface into the ellipsoidal surface function of the outer surface of the bearing outer ring 2 and the ellipsoidal surface function of the contact surface, and obtain a set of ellipsoidal surface functions of the outer surface of the bearing outer ring 2 and the contact area;

[0101] Repeat S2-S4 n times to obtain n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring 2 and the ellipsoidal surface functions of the contact surface.

[0102] More preferably, in order to express the radial deformation of the outer surface of the bearing outer ring 2 and the contact surface of the bearing outer ring 2, the spatial ellipsoidal surface obtained each time is expressed as a function of z with respect to x, y, that is,

[0103] In a preferred embodiment of the present invention, the method for determining the optimal outer surface ellipsoidal surface of the bearing outer ring 2 and the contact surface ellipsoidal surface is as follows:

[0104] According to the obtained ellipsoidal surface function z of the outer ring 2 of the n group of bearings o and the contact surface ellipsoid function z c , the least square method is used to determine the optimal space ellipsoid, and the calculation formula is:

[0105]

[0106] Among them, L n It represents the sum of square errors of the Z values ​​of the corresponding points on the nth ellipsoid and other ellipsoids. After each measurement, a three-dimensional function of the ellipsoid is obtained. Z refers to the value of each point on the ellipsoid in the z-axis direction. The subscript Z represents the z value in the ellipsoid equation obtained by the nth measurement.n -z {1,2,..,N}-n It refers to the difference between the nth measurement result and the nth measurement result; by finding the smallest L n , to determine the optimal ellipsoidal surface of the outer surface of the bearing outer ring 2 Ellipsoidal surface in contact area with bearing outer ring 2

[0107] In a preferred embodiment of the present invention, the method for calculating the spatial distribution of the contact surface deformation variable is as follows:

[0108] According to the optimal ellipsoidal space function of the outer surface of the bearing outer ring 2 and the optimal ellipsoidal space function of the contact area of ​​the outer ring 2 of the bearing The subscript definition here is the same as z in the above n Different, z n The z in the equation refers to the z-axis coordinate of the ellipsoidal surface (which can be the outer surface of the bearing outer ring or the contact area of ​​the bearing outer ring). and It is the spatial function of the optimized outer surface of the bearing outer ring and the contact area of ​​the bearing outer ring. Its subscript definition is specifically proposed for the outer surface of the bearing outer ring and the contact area of ​​the bearing outer ring. Combined with the thickness T of the bearing outer ring 2 (the thickness of the bearing outer ring 2 when not under force is T, which is a known parameter), the spatial distribution of the contact surface deformation variable is calculated:

[0109]

[0110] Define the domain of the contact surface as x 2 +y 2 ≤r 2 , x and y are the domains of the contact area in the projection of the xoy plane in the x-axis and y-axis directions, that is, the range of variation of the values ​​in the x-axis and y-axis directions. When x and y need to be measured, they can be set manually based on experience; r is the radius of the rolling element 3.

[0111] The optimal ellipsoid surface is used to obtain a more reasonable spatial distribution of the contact area deformation that is closer to the true value.

[0112] In a preferred embodiment of the present invention, the method for calculating the contact stiffness is as follows:

[0113] Spatial distribution of contact surface deformation Combined with the known applied force (radial force) F7, the contact stiffness between the rolling element 3 and the bearing outer ring 2 is calculated as:

[0114]

[0115] Where, T is the thickness of the bearing outer ring; is the thickness distribution of the bearing outer ring after contact deformation, that is, the distance between the outer surface of the bearing outer ring and the bearing contact surface; is the deformation variable of the contact surface, which is a spatial function of the z-axis direction variable with respect to x and y, denoted as D(x,y), and max(D(x,y)) is the value of the maximum deformation variable.

[0116] By using the more reasonable spatial distribution of the contact area deformation that is closer to the true value, a more accurate contact stiffness can be calculated.

[0117] The present invention also provides a contact stiffness calibration system for the outer ring 2 of a rolling bearing based on a three-point ultrasonic method, such as Figure 2 As shown, it includes an annular water bath 4 arranged outside the bearing outer ring 2, an ultrasonic probe 6 placed in the annular water bath 4 and a processing module, with one side of the bearing outer ring 2 as a reference plane 5, and a bearing inner ring 1 is arranged inside the bearing outer ring 2 in the prior art, and a rolling body 3 is arranged between the bearing inner ring 1 and the bearing outer ring 2. The processing module executes the method of the present invention to calibrate the contact stiffness of the rolling bearing outer ring 2. The system improves the ultrasonic measurement method, obtains a more accurate deformation of the bearing outer ring 2, and completes accurate stiffness calibration.

[0118] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0119] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for calibrating the contact stiffness of the outer ring of a rolling bearing based on a three-point ultrasonic method, characterized in that: The steps include: S1, the contact surface between the rolling element and the outer ring of the bearing and the outer surface of the outer ring of the bearing are approximated as ellipsoidal surfaces; S2, setting at least three measurement tracks on the outer surface of the bearing outer ring, each measurement track having three measurement points, and using an ultrasonic probe to measure each measurement point to obtain the acoustic time difference; S3, calculating the focal centers of the three measuring points corresponding to each measurement trajectory on the outer surface of the bearing outer ring, and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction, according to the acoustic time difference; S4, bringing the intersection coordinates into the pre-set ellipsoidal surface function of the outer surface of the outer ring of the bearing and the ellipsoidal surface function of the contact surface, and fitting to obtain a set of ellipsoidal surface functions of the outer surface of the outer ring of the bearing and the ellipsoidal surface function of the contact surface; S5, repeating steps S2-S4 n times to obtain n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring and ellipsoidal surface functions of the contact surface; S6, determining the optimal bearing outer ring outer surface ellipsoidal surface and contact surface ellipsoidal surface according to n groups of bearing outer ring outer surface ellipsoidal surface functions and contact surface ellipsoidal surface functions; S7, combining the bearing outer ring thickness T and the applied known force F, calculate the spatial distribution of the contact surface deformation and the contact stiffness.

2. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 1, characterized in that: The method for setting the measurement track on the outer surface of the bearing outer ring is as follows: An annular water bath is provided on the outer side of the bearing outer ring, and an ultrasonic probe is arranged in the annular water bath to obtain the coordinates of the measuring points; Assume that the angle between the line between the measuring point and the ultrasonic probe and the vertical direction is α j The three measuring points corresponding to each measurement trajectory are the points obtained by rotating the ultrasonic probe 120 degrees with the vertical direction passing through its center point as the axis.

3. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 2, characterized in that: The method for measuring each measuring point to obtain the acoustic time difference is as follows: In the jth measurement track, the ultrasonic probe sends a detection wave to the i-th measurement point, and the transmission wave I is obtained in the water bath. i1 , define the time when the sound wave is emitted as t0; The ultrasonic wave passes through the interface between the water bath and the outer ring of the bearing, and the reflected wave R i1 , define the received reflected wave R i1 The time is t1, and the first sound time difference Δt1=t1-t0 is calculated; The ultrasonic wave passes through the bearing outer ring and rolling element interface to obtain the reflected wave R i2 , define the received reflected wave R i2 The time is t2, and the second sound time difference Δt2=t2-t1 is calculated; Determine whether i is greater than or equal to 3. If so, execute S3; if not, measure the i+1th measuring point.

4. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 3, characterized in that: The method for calculating the focal centers of the three measuring points corresponding to the measurement trajectory on the outer surface of the bearing outer ring and the coordinates of the intersection of the focal center and the contact surface along the ultrasonic direction is as follows: The calculation of the focal center coordinates of the ultrasonic probe on the outer surface of the bearing outer ring is: The coordinates of the intersection of the focus center along the ultrasonic direction and the contact surface are calculated as follows: Where i represents the i-th measuring point, c1 represents the sound velocity of the water bath, and c2 represents the sound velocity of the bearing outer ring material; α j represents the angle between the ultrasonic probe and the vertical direction under the jth measurement track; Δt1 and Δt2 are the acoustic time differences; θ i Represents the angle between the Y axis and the projection of the i-th measuring point on the XOY plane and the line connecting the coordinate origin, θ1 = -120°, θ2 = 0°, θ3 = 120°; Determine whether j is greater than a threshold. If j is greater than or equal to the threshold, it indicates that the measurement of three measuring points on all measuring tracks has been completed, and proceed to step S4. If j is less than 3, it indicates that the measurement of measuring points under all measuring tracks has not been completed, and proceed to the measurement of the measuring points under the j+1th measuring track.

5. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 1, characterized in that: The method for fitting the ellipsoidal surface function of the outer surface of the bearing outer ring and the ellipsoidal surface function of the contact surface is as follows: Assume that the ellipsoidal function of the outer surface of the bearing outer ring is The contact surface ellipsoid function is: Among them, x, y, z represent coordinates; a o , b o , c o The three parameters to be solved represent the ellipsoidal function of the outer surface of the outer ring of the assumed bearing, a c , b c , c c The three parameters to be solved represent the hypothetical contact surface ellipsoidal surface function; Substitute the calculated intersection coordinates of the focal center along the ultrasonic direction and the contact surface into the ellipsoidal surface function of the outer surface of the bearing outer ring and the ellipsoidal surface function of the contact surface, and obtain a set of ellipsoidal surface functions of the outer surface of the bearing outer ring and the contact area by fitting; Repeat S2-S4n times to obtain n groups of ellipsoidal surface functions of the outer surface of the bearing outer ring and ellipsoidal surface functions of the contact surface.

6. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 5, characterized in that: In order to express the radial deformation of the outer surface of the bearing outer ring and the contact surface of the bearing outer ring, the spatial ellipsoid surface obtained each time is expressed as a function of z with respect to x and y, that is, 7. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 1, characterized in that: The method for determining the optimal bearing outer ring outer surface ellipsoid and contact surface ellipsoid is as follows: According to the obtained n groups of bearing outer ring outer surface ellipsoidal functions and contact surface ellipsoidal functions, the optimal space ellipsoidal surface is determined by the least square method. The calculation formula is: Among them, L n It represents the sum of squared errors of the Z values ​​of the nth ellipsoid surface and the corresponding points on other ellipsoid surfaces. Z refers to the value of each point on each ellipsoid surface in the z-axis direction. The subscript Z represents the number of times the z value in the ellipsoid surface equation is measured. n -z {1,2,..,N}-n It refers to the difference between the nth measurement result and the nth measurement result; by finding the smallest L n , to determine the optimal ellipsoidal surface of the outer ring of the bearing Ellipsoidal surface in contact with the bearing outer ring 8. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 1, characterized in that: The method for calculating the spatial distribution of the contact surface deformation is as follows: According to the optimal ellipsoidal space function of the outer surface of the bearing outer ring and the optimal ellipsoidal space function of the bearing outer ring contact area Combined with the bearing outer ring thickness T, the spatial distribution of the contact surface deformation is calculated: Define the domain of the contact surface as x 2 +y 2 ≤r 2 , x and y are the domains of the contact area in the projection of the xoy plane in the x-axis and y-axis directions respectively; r is the radius of the rolling body.

9. The method for calibrating the contact stiffness of the outer ring of a rolling bearing based on the three-point ultrasonic method according to claim 1, characterized in that: The contact stiffness is calculated as follows: Spatial distribution of contact surface deformation Combined with the known applied force F, the contact stiffness is calculated as: Where, T is the thickness of the bearing outer ring; is the thickness distribution of the bearing outer ring after contact deformation, that is, the distance between the outer surface of the bearing outer ring and the bearing contact surface; is the deformation variable of the contact surface, which is a spatial function of the z-axis direction variable with respect to x and y, denoted as D(x,y), and max(D(x,y)) is the value of the maximum deformation variable.

10. A rolling bearing outer ring contact stiffness calibration system based on a three-point ultrasonic method, characterized in that: It comprises an annular water bath arranged outside the outer ring of the bearing, an ultrasonic probe placed in the annular water bath and a processing module, wherein the processing module executes the method according to any one of claims 1 to 9 to calibrate the contact stiffness of the outer ring of the rolling bearing.

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